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ssalentin/plip | plip/modules/preparation.py | Ligand.find_charged | def find_charged(self, all_atoms):
"""Identify all positively charged groups in a ligand. This search is not exhaustive, as the cases can be quite
diverse. The typical cases seem to be protonated amines, quaternary ammoinium and sulfonium
as mentioned in 'Cation-pi interactions in ligand recognition and catalysis' (Zacharias et al., 2002)).
Identify negatively charged groups in the ligand.
"""
data = namedtuple('lcharge', 'atoms orig_atoms atoms_orig_idx type center fgroup')
a_set = []
for a in all_atoms:
a_orig_idx = self.Mapper.mapid(a.idx, mtype=self.mtype, bsid=self.bsid)
a_orig = self.Mapper.id_to_atom(a_orig_idx)
if self.is_functional_group(a, 'quartamine'):
a_set.append(data(atoms=[a, ], orig_atoms=[a_orig, ], atoms_orig_idx=[a_orig_idx, ], type='positive',
center=list(a.coords), fgroup='quartamine'))
elif self.is_functional_group(a, 'tertamine'):
a_set.append(data(atoms=[a, ], orig_atoms=[a_orig, ], atoms_orig_idx=[a_orig_idx, ], type='positive', center=list(a.coords),
fgroup='tertamine'))
if self.is_functional_group(a, 'sulfonium'):
a_set.append(data(atoms=[a, ], orig_atoms=[a_orig, ], atoms_orig_idx=[a_orig_idx, ], type='positive', center=list(a.coords),
fgroup='sulfonium'))
if self.is_functional_group(a, 'phosphate'):
a_contributing = [a, ]
a_contributing_orig_idx = [a_orig_idx, ]
[a_contributing.append(pybel.Atom(neighbor)) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom)]
[a_contributing_orig_idx.append(self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid))
for neighbor in a_contributing]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='negative',
center=a.coords, fgroup='phosphate'))
if self.is_functional_group(a, 'sulfonicacid'):
a_contributing = [a, ]
a_contributing_orig_idx = [a_orig_idx, ]
[a_contributing.append(pybel.Atom(neighbor)) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom) if
neighbor.GetAtomicNum() == 8]
[a_contributing_orig_idx.append(self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid))
for neighbor in a_contributing]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='negative',
center=a.coords, fgroup='sulfonicacid'))
elif self.is_functional_group(a, 'sulfate'):
a_contributing = [a, ]
a_contributing_orig_idx = [a_orig_idx, ]
[a_contributing_orig_idx.append(self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid))
for neighbor in a_contributing]
[a_contributing.append(pybel.Atom(neighbor)) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom)]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='negative',
center=a.coords, fgroup='sulfate'))
if self.is_functional_group(a, 'carboxylate'):
a_contributing = [pybel.Atom(neighbor) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom)
if neighbor.GetAtomicNum() == 8]
a_contributing_orig_idx = [self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid)
for neighbor in a_contributing]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='negative',
center=centroid([a.coords for a in a_contributing]), fgroup='carboxylate'))
elif self.is_functional_group(a, 'guanidine'):
a_contributing = [pybel.Atom(neighbor) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom)
if neighbor.GetAtomicNum() == 7]
a_contributing_orig_idx = [self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid)
for neighbor in a_contributing]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='positive',
center=a.coords, fgroup='guanidine'))
return a_set | python | def find_charged(self, all_atoms):
"""Identify all positively charged groups in a ligand. This search is not exhaustive, as the cases can be quite
diverse. The typical cases seem to be protonated amines, quaternary ammoinium and sulfonium
as mentioned in 'Cation-pi interactions in ligand recognition and catalysis' (Zacharias et al., 2002)).
Identify negatively charged groups in the ligand.
"""
data = namedtuple('lcharge', 'atoms orig_atoms atoms_orig_idx type center fgroup')
a_set = []
for a in all_atoms:
a_orig_idx = self.Mapper.mapid(a.idx, mtype=self.mtype, bsid=self.bsid)
a_orig = self.Mapper.id_to_atom(a_orig_idx)
if self.is_functional_group(a, 'quartamine'):
a_set.append(data(atoms=[a, ], orig_atoms=[a_orig, ], atoms_orig_idx=[a_orig_idx, ], type='positive',
center=list(a.coords), fgroup='quartamine'))
elif self.is_functional_group(a, 'tertamine'):
a_set.append(data(atoms=[a, ], orig_atoms=[a_orig, ], atoms_orig_idx=[a_orig_idx, ], type='positive', center=list(a.coords),
fgroup='tertamine'))
if self.is_functional_group(a, 'sulfonium'):
a_set.append(data(atoms=[a, ], orig_atoms=[a_orig, ], atoms_orig_idx=[a_orig_idx, ], type='positive', center=list(a.coords),
fgroup='sulfonium'))
if self.is_functional_group(a, 'phosphate'):
a_contributing = [a, ]
a_contributing_orig_idx = [a_orig_idx, ]
[a_contributing.append(pybel.Atom(neighbor)) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom)]
[a_contributing_orig_idx.append(self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid))
for neighbor in a_contributing]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='negative',
center=a.coords, fgroup='phosphate'))
if self.is_functional_group(a, 'sulfonicacid'):
a_contributing = [a, ]
a_contributing_orig_idx = [a_orig_idx, ]
[a_contributing.append(pybel.Atom(neighbor)) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom) if
neighbor.GetAtomicNum() == 8]
[a_contributing_orig_idx.append(self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid))
for neighbor in a_contributing]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='negative',
center=a.coords, fgroup='sulfonicacid'))
elif self.is_functional_group(a, 'sulfate'):
a_contributing = [a, ]
a_contributing_orig_idx = [a_orig_idx, ]
[a_contributing_orig_idx.append(self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid))
for neighbor in a_contributing]
[a_contributing.append(pybel.Atom(neighbor)) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom)]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='negative',
center=a.coords, fgroup='sulfate'))
if self.is_functional_group(a, 'carboxylate'):
a_contributing = [pybel.Atom(neighbor) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom)
if neighbor.GetAtomicNum() == 8]
a_contributing_orig_idx = [self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid)
for neighbor in a_contributing]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='negative',
center=centroid([a.coords for a in a_contributing]), fgroup='carboxylate'))
elif self.is_functional_group(a, 'guanidine'):
a_contributing = [pybel.Atom(neighbor) for neighbor in pybel.ob.OBAtomAtomIter(a.OBAtom)
if neighbor.GetAtomicNum() == 7]
a_contributing_orig_idx = [self.Mapper.mapid(neighbor.idx, mtype=self.mtype, bsid=self.bsid)
for neighbor in a_contributing]
orig_contributing = [self.Mapper.id_to_atom(idx) for idx in a_contributing_orig_idx]
a_set.append(data(atoms=a_contributing, orig_atoms=orig_contributing, atoms_orig_idx=a_contributing_orig_idx, type='positive',
center=a.coords, fgroup='guanidine'))
return a_set | Identify all positively charged groups in a ligand. This search is not exhaustive, as the cases can be quite
diverse. The typical cases seem to be protonated amines, quaternary ammoinium and sulfonium
as mentioned in 'Cation-pi interactions in ligand recognition and catalysis' (Zacharias et al., 2002)).
Identify negatively charged groups in the ligand. | https://github.com/ssalentin/plip/blob/906c8d36463689779b403f6c2c9ed06174acaf9a/plip/modules/preparation.py#L1131-L1195 |
ssalentin/plip | plip/modules/preparation.py | Ligand.find_metal_binding | def find_metal_binding(self, lig_atoms, water_oxygens):
"""Looks for atoms that could possibly be involved in binding a metal ion.
This can be any water oxygen, as well as oxygen from carboxylate, phophoryl, phenolate, alcohol;
nitrogen from imidazole; sulfur from thiolate.
"""
a_set = []
data = namedtuple('metal_binding', 'atom orig_atom atom_orig_idx type fgroup restype resnr reschain location')
for oxygen in water_oxygens:
a_set.append(data(atom=oxygen.oxy, atom_orig_idx=oxygen.oxy_orig_idx, type='O', fgroup='water',
restype=whichrestype(oxygen.oxy), resnr=whichresnumber(oxygen.oxy),
reschain=whichchain(oxygen.oxy), location='water', orig_atom=self.Mapper.id_to_atom(oxygen.oxy_orig_idx)))
# #@todo Refactor code
for a in lig_atoms:
a_orig_idx = self.Mapper.mapid(a.idx, mtype='ligand', bsid=self.bsid)
n_atoms = pybel.ob.OBAtomAtomIter(a.OBAtom) # Neighboring atoms
# All atomic numbers of neighboring atoms
n_atoms_atomicnum = [n.GetAtomicNum() for n in pybel.ob.OBAtomAtomIter(a.OBAtom)]
if a.atomicnum == 8: # Oxygen
if n_atoms_atomicnum.count('1') == 1 and len(n_atoms_atomicnum) == 2: # Oxygen in alcohol (R-[O]-H)
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='O', fgroup='alcohol',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if True in [n.IsAromatic() for n in n_atoms] and not a.OBAtom.IsAromatic(): # Phenolate oxygen
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='O', fgroup='phenolate',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if a.atomicnum == 6: # It's a carbon atom
if n_atoms_atomicnum.count(8) == 2 and n_atoms_atomicnum.count(6) == 1: # It's a carboxylate group
for neighbor in [n for n in n_atoms if n.GetAtomicNum() == 8]:
neighbor_orig_idx = self.Mapper.mapid(neighbor.GetIdx(), mtype='ligand', bsid=self.bsid)
a_set.append(data(atom=pybel.Atom(neighbor), atom_orig_idx=neighbor_orig_idx, type='O',
fgroup='carboxylate',
restype=self.hetid,
resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if a.atomicnum == 15: # It's a phosphor atom
if n_atoms_atomicnum.count(8) >= 3: # It's a phosphoryl
for neighbor in [n for n in n_atoms if n.GetAtomicNum() == 8]:
neighbor_orig_idx = self.Mapper.mapid(neighbor.GetIdx(), mtype='ligand', bsid=self.bsid)
a_set.append(data(atom=pybel.Atom(neighbor), atom_orig_idx=neighbor_orig_idx, type='O',
fgroup='phosphoryl',
restype=self.hetid,
resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if n_atoms_atomicnum.count(8) == 2: # It's another phosphor-containing group #@todo (correct name?)
for neighbor in [n for n in n_atoms if n.GetAtomicNum() == 8]:
neighbor_orig_idx = self.Mapper.mapid(neighbor.GetIdx(), mtype='ligand', bsid=self.bsid)
a_set.append(data(atom=pybel.Atom(neighbor), atom_orig_idx=neighbor_orig_idx, type='O',
fgroup='phosphor.other', restype=self.hetid,
resnr=self.position,
reschain=self.chain, location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if a.atomicnum == 7: # It's a nitrogen atom
if n_atoms_atomicnum.count(6) == 2: # It's imidazole/pyrrole or similar
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='N', fgroup='imidazole/pyrrole',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if a.atomicnum == 16: # It's a sulfur atom
if True in [n.IsAromatic() for n in n_atoms] and not a.OBAtom.IsAromatic(): # Thiolate
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='S', fgroup='thiolate',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if set(n_atoms_atomicnum) == {26}: # Sulfur in Iron sulfur cluster
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='S', fgroup='iron-sulfur.cluster',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
return a_set | python | def find_metal_binding(self, lig_atoms, water_oxygens):
"""Looks for atoms that could possibly be involved in binding a metal ion.
This can be any water oxygen, as well as oxygen from carboxylate, phophoryl, phenolate, alcohol;
nitrogen from imidazole; sulfur from thiolate.
"""
a_set = []
data = namedtuple('metal_binding', 'atom orig_atom atom_orig_idx type fgroup restype resnr reschain location')
for oxygen in water_oxygens:
a_set.append(data(atom=oxygen.oxy, atom_orig_idx=oxygen.oxy_orig_idx, type='O', fgroup='water',
restype=whichrestype(oxygen.oxy), resnr=whichresnumber(oxygen.oxy),
reschain=whichchain(oxygen.oxy), location='water', orig_atom=self.Mapper.id_to_atom(oxygen.oxy_orig_idx)))
# #@todo Refactor code
for a in lig_atoms:
a_orig_idx = self.Mapper.mapid(a.idx, mtype='ligand', bsid=self.bsid)
n_atoms = pybel.ob.OBAtomAtomIter(a.OBAtom) # Neighboring atoms
# All atomic numbers of neighboring atoms
n_atoms_atomicnum = [n.GetAtomicNum() for n in pybel.ob.OBAtomAtomIter(a.OBAtom)]
if a.atomicnum == 8: # Oxygen
if n_atoms_atomicnum.count('1') == 1 and len(n_atoms_atomicnum) == 2: # Oxygen in alcohol (R-[O]-H)
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='O', fgroup='alcohol',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if True in [n.IsAromatic() for n in n_atoms] and not a.OBAtom.IsAromatic(): # Phenolate oxygen
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='O', fgroup='phenolate',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if a.atomicnum == 6: # It's a carbon atom
if n_atoms_atomicnum.count(8) == 2 and n_atoms_atomicnum.count(6) == 1: # It's a carboxylate group
for neighbor in [n for n in n_atoms if n.GetAtomicNum() == 8]:
neighbor_orig_idx = self.Mapper.mapid(neighbor.GetIdx(), mtype='ligand', bsid=self.bsid)
a_set.append(data(atom=pybel.Atom(neighbor), atom_orig_idx=neighbor_orig_idx, type='O',
fgroup='carboxylate',
restype=self.hetid,
resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if a.atomicnum == 15: # It's a phosphor atom
if n_atoms_atomicnum.count(8) >= 3: # It's a phosphoryl
for neighbor in [n for n in n_atoms if n.GetAtomicNum() == 8]:
neighbor_orig_idx = self.Mapper.mapid(neighbor.GetIdx(), mtype='ligand', bsid=self.bsid)
a_set.append(data(atom=pybel.Atom(neighbor), atom_orig_idx=neighbor_orig_idx, type='O',
fgroup='phosphoryl',
restype=self.hetid,
resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if n_atoms_atomicnum.count(8) == 2: # It's another phosphor-containing group #@todo (correct name?)
for neighbor in [n for n in n_atoms if n.GetAtomicNum() == 8]:
neighbor_orig_idx = self.Mapper.mapid(neighbor.GetIdx(), mtype='ligand', bsid=self.bsid)
a_set.append(data(atom=pybel.Atom(neighbor), atom_orig_idx=neighbor_orig_idx, type='O',
fgroup='phosphor.other', restype=self.hetid,
resnr=self.position,
reschain=self.chain, location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if a.atomicnum == 7: # It's a nitrogen atom
if n_atoms_atomicnum.count(6) == 2: # It's imidazole/pyrrole or similar
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='N', fgroup='imidazole/pyrrole',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if a.atomicnum == 16: # It's a sulfur atom
if True in [n.IsAromatic() for n in n_atoms] and not a.OBAtom.IsAromatic(): # Thiolate
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='S', fgroup='thiolate',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
if set(n_atoms_atomicnum) == {26}: # Sulfur in Iron sulfur cluster
a_set.append(data(atom=a, atom_orig_idx=a_orig_idx, type='S', fgroup='iron-sulfur.cluster',
restype=self.hetid, resnr=self.position, reschain=self.chain,
location='ligand', orig_atom=self.Mapper.id_to_atom(a_orig_idx)))
return a_set | Looks for atoms that could possibly be involved in binding a metal ion.
This can be any water oxygen, as well as oxygen from carboxylate, phophoryl, phenolate, alcohol;
nitrogen from imidazole; sulfur from thiolate. | https://github.com/ssalentin/plip/blob/906c8d36463689779b403f6c2c9ed06174acaf9a/plip/modules/preparation.py#L1197-L1263 |
ssalentin/plip | plip/modules/preparation.py | PDBComplex.load_pdb | def load_pdb(self, pdbpath, as_string=False):
"""Loads a pdb file with protein AND ligand(s), separates and prepares them.
If specified 'as_string', the input is a PDB string instead of a path."""
if as_string:
self.sourcefiles['pdbcomplex.original'] = None
self.sourcefiles['pdbcomplex'] = None
self.sourcefiles['pdbstring'] = pdbpath
else:
self.sourcefiles['pdbcomplex.original'] = pdbpath
self.sourcefiles['pdbcomplex'] = pdbpath
self.information['pdbfixes'] = False
pdbparser = PDBParser(pdbpath, as_string=as_string) # Parse PDB file to find errors and get additonal data
# #@todo Refactor and rename here
self.Mapper.proteinmap = pdbparser.proteinmap
self.Mapper.reversed_proteinmap = {v: k for k, v in self.Mapper.proteinmap.items()}
self.modres = pdbparser.modres
self.covalent = pdbparser.covalent
self.altconf = pdbparser.altconformations
self.corrected_pdb = pdbparser.corrected_pdb
if not config.PLUGIN_MODE:
if pdbparser.num_fixed_lines > 0:
write_message('%i lines automatically fixed in PDB input file.\n' % pdbparser.num_fixed_lines)
# Save modified PDB file
if not as_string:
basename = os.path.basename(pdbpath).split('.')[0]
else:
basename = "from_stdin"
pdbpath_fixed = tmpfile(prefix='plipfixed.' + basename + '_', direc=self.output_path)
create_folder_if_not_exists(self.output_path)
self.sourcefiles['pdbcomplex'] = pdbpath_fixed
self.corrected_pdb = re.sub(r'[^\x00-\x7F]+', ' ', self.corrected_pdb) # Strip non-unicode chars
if not config.NOFIXFILE: # Only write to file if this option is not activated
with open(pdbpath_fixed, 'w') as f:
f.write(self.corrected_pdb)
self.information['pdbfixes'] = True
if not as_string:
self.sourcefiles['filename'] = os.path.basename(self.sourcefiles['pdbcomplex'])
self.protcomplex, self.filetype = read_pdb(self.corrected_pdb, as_string=True)
# Update the model in the Mapper class instance
self.Mapper.original_structure = self.protcomplex.OBMol
write_message('PDB structure successfully read.\n')
# Determine (temporary) PyMOL Name from Filename
self.pymol_name = pdbpath.split('/')[-1].split('.')[0] + '-Protein'
# Replace characters causing problems in PyMOL
self.pymol_name = self.pymol_name.replace(' ', '').replace('(', '').replace(')', '').replace('-', '_')
# But if possible, name it after PDBID in Header
if 'HEADER' in self.protcomplex.data: # If the PDB file has a proper header
potential_name = self.protcomplex.data['HEADER'][56:60].lower()
if extract_pdbid(potential_name) != 'UnknownProtein':
self.pymol_name = potential_name
write_message("Pymol Name set as: '%s'\n" % self.pymol_name, mtype='debug')
# Extract and prepare ligands
ligandfinder = LigandFinder(self.protcomplex, self.altconf, self.modres, self.covalent, self.Mapper)
self.ligands = ligandfinder.ligands
self.excluded = ligandfinder.excluded
# Add polar hydrogens
self.protcomplex.OBMol.AddPolarHydrogens()
for atm in self.protcomplex:
self.atoms[atm.idx] = atm
write_message("Assigned polar hydrogens\n", mtype='debug')
if len(self.excluded) != 0:
write_message("Excluded molecules as ligands: %s\n" % ','.join([lig for lig in self.excluded]))
if config.DNARECEPTOR:
self.resis = [obres for obres in pybel.ob.OBResidueIter(
self.protcomplex.OBMol) if obres.GetName() in config.DNA+config.RNA]
else:
self.resis = [obres for obres in pybel.ob.OBResidueIter(
self.protcomplex.OBMol) if obres.GetResidueProperty(0)]
num_ligs = len(self.ligands)
if num_ligs == 1:
write_message("Analyzing one ligand...\n")
elif num_ligs > 1:
write_message("Analyzing %i ligands...\n" % num_ligs)
else:
write_message("Structure contains no ligands.\n\n") | python | def load_pdb(self, pdbpath, as_string=False):
"""Loads a pdb file with protein AND ligand(s), separates and prepares them.
If specified 'as_string', the input is a PDB string instead of a path."""
if as_string:
self.sourcefiles['pdbcomplex.original'] = None
self.sourcefiles['pdbcomplex'] = None
self.sourcefiles['pdbstring'] = pdbpath
else:
self.sourcefiles['pdbcomplex.original'] = pdbpath
self.sourcefiles['pdbcomplex'] = pdbpath
self.information['pdbfixes'] = False
pdbparser = PDBParser(pdbpath, as_string=as_string) # Parse PDB file to find errors and get additonal data
# #@todo Refactor and rename here
self.Mapper.proteinmap = pdbparser.proteinmap
self.Mapper.reversed_proteinmap = {v: k for k, v in self.Mapper.proteinmap.items()}
self.modres = pdbparser.modres
self.covalent = pdbparser.covalent
self.altconf = pdbparser.altconformations
self.corrected_pdb = pdbparser.corrected_pdb
if not config.PLUGIN_MODE:
if pdbparser.num_fixed_lines > 0:
write_message('%i lines automatically fixed in PDB input file.\n' % pdbparser.num_fixed_lines)
# Save modified PDB file
if not as_string:
basename = os.path.basename(pdbpath).split('.')[0]
else:
basename = "from_stdin"
pdbpath_fixed = tmpfile(prefix='plipfixed.' + basename + '_', direc=self.output_path)
create_folder_if_not_exists(self.output_path)
self.sourcefiles['pdbcomplex'] = pdbpath_fixed
self.corrected_pdb = re.sub(r'[^\x00-\x7F]+', ' ', self.corrected_pdb) # Strip non-unicode chars
if not config.NOFIXFILE: # Only write to file if this option is not activated
with open(pdbpath_fixed, 'w') as f:
f.write(self.corrected_pdb)
self.information['pdbfixes'] = True
if not as_string:
self.sourcefiles['filename'] = os.path.basename(self.sourcefiles['pdbcomplex'])
self.protcomplex, self.filetype = read_pdb(self.corrected_pdb, as_string=True)
# Update the model in the Mapper class instance
self.Mapper.original_structure = self.protcomplex.OBMol
write_message('PDB structure successfully read.\n')
# Determine (temporary) PyMOL Name from Filename
self.pymol_name = pdbpath.split('/')[-1].split('.')[0] + '-Protein'
# Replace characters causing problems in PyMOL
self.pymol_name = self.pymol_name.replace(' ', '').replace('(', '').replace(')', '').replace('-', '_')
# But if possible, name it after PDBID in Header
if 'HEADER' in self.protcomplex.data: # If the PDB file has a proper header
potential_name = self.protcomplex.data['HEADER'][56:60].lower()
if extract_pdbid(potential_name) != 'UnknownProtein':
self.pymol_name = potential_name
write_message("Pymol Name set as: '%s'\n" % self.pymol_name, mtype='debug')
# Extract and prepare ligands
ligandfinder = LigandFinder(self.protcomplex, self.altconf, self.modres, self.covalent, self.Mapper)
self.ligands = ligandfinder.ligands
self.excluded = ligandfinder.excluded
# Add polar hydrogens
self.protcomplex.OBMol.AddPolarHydrogens()
for atm in self.protcomplex:
self.atoms[atm.idx] = atm
write_message("Assigned polar hydrogens\n", mtype='debug')
if len(self.excluded) != 0:
write_message("Excluded molecules as ligands: %s\n" % ','.join([lig for lig in self.excluded]))
if config.DNARECEPTOR:
self.resis = [obres for obres in pybel.ob.OBResidueIter(
self.protcomplex.OBMol) if obres.GetName() in config.DNA+config.RNA]
else:
self.resis = [obres for obres in pybel.ob.OBResidueIter(
self.protcomplex.OBMol) if obres.GetResidueProperty(0)]
num_ligs = len(self.ligands)
if num_ligs == 1:
write_message("Analyzing one ligand...\n")
elif num_ligs > 1:
write_message("Analyzing %i ligands...\n" % num_ligs)
else:
write_message("Structure contains no ligands.\n\n") | Loads a pdb file with protein AND ligand(s), separates and prepares them.
If specified 'as_string', the input is a PDB string instead of a path. | https://github.com/ssalentin/plip/blob/906c8d36463689779b403f6c2c9ed06174acaf9a/plip/modules/preparation.py#L1294-L1377 |
ssalentin/plip | plip/modules/preparation.py | PDBComplex.characterize_complex | def characterize_complex(self, ligand):
"""Handles all basic functions for characterizing the interactions for one ligand"""
single_sites = []
for member in ligand.members:
single_sites.append(':'.join([str(x) for x in member]))
site = ' + '.join(single_sites)
site = site if not len(site) > 20 else site[:20] + '...'
longname = ligand.longname if not len(ligand.longname) > 20 else ligand.longname[:20] + '...'
ligtype = 'Unspecified type' if ligand.type == 'UNSPECIFIED' else ligand.type
ligtext = "\n%s [%s] -- %s" % (longname, ligtype, site)
if ligtype == 'PEPTIDE':
ligtext = '\n Chain %s [PEPTIDE / INTER-CHAIN]' % ligand.chain
if ligtype == 'INTRA':
ligtext = "\n Chain %s [INTRA-CHAIN]" % ligand.chain
any_in_biolip = len(set([x[0] for x in ligand.members]).intersection(config.biolip_list)) != 0
write_message(ligtext)
write_message('\n' + '-' * len(ligtext) + '\n')
if ligtype not in ['POLYMER', 'DNA', 'ION', 'DNA+ION', 'RNA+ION', 'SMALLMOLECULE+ION'] and any_in_biolip:
write_message('may be biologically irrelevant\n', mtype='info', indent=True)
lig_obj = Ligand(self, ligand)
cutoff = lig_obj.max_dist_to_center + config.BS_DIST
bs_res = self.extract_bs(cutoff, lig_obj.centroid, self.resis)
# Get a list of all atoms belonging to the binding site, search by idx
bs_atoms = [self.atoms[idx] for idx in [i for i in self.atoms.keys()
if self.atoms[i].OBAtom.GetResidue().GetIdx() in bs_res]
if idx in self.Mapper.proteinmap and self.Mapper.mapid(idx, mtype='protein') not in self.altconf]
if ligand.type == 'PEPTIDE':
# If peptide, don't consider the peptide chain as part of the protein binding site
bs_atoms = [a for a in bs_atoms if a.OBAtom.GetResidue().GetChain() != lig_obj.chain]
if ligand.type == 'INTRA':
# Interactions within the chain
bs_atoms = [a for a in bs_atoms if a.OBAtom.GetResidue().GetChain() == lig_obj.chain]
bs_atoms_refined = []
# Create hash with BSRES -> (MINDIST_TO_LIG, AA_TYPE)
# and refine binding site atom selection with exact threshold
min_dist = {}
for r in bs_atoms:
bs_res_id = ''.join([str(whichresnumber(r)), whichchain(r)])
for l in ligand.mol.atoms:
distance = euclidean3d(r.coords, l.coords)
if bs_res_id not in min_dist:
min_dist[bs_res_id] = (distance, whichrestype(r))
elif min_dist[bs_res_id][0] > distance:
min_dist[bs_res_id] = (distance, whichrestype(r))
if distance <= config.BS_DIST and r not in bs_atoms_refined:
bs_atoms_refined.append(r)
num_bs_atoms = len(bs_atoms_refined)
write_message('Binding site atoms in vicinity (%.1f A max. dist: %i).\n' % (config.BS_DIST, num_bs_atoms),
indent=True)
bs_obj = BindingSite(bs_atoms_refined, self.protcomplex, self, self.altconf, min_dist, self.Mapper)
pli_obj = PLInteraction(lig_obj, bs_obj, self)
self.interaction_sets[ligand.mol.title] = pli_obj | python | def characterize_complex(self, ligand):
"""Handles all basic functions for characterizing the interactions for one ligand"""
single_sites = []
for member in ligand.members:
single_sites.append(':'.join([str(x) for x in member]))
site = ' + '.join(single_sites)
site = site if not len(site) > 20 else site[:20] + '...'
longname = ligand.longname if not len(ligand.longname) > 20 else ligand.longname[:20] + '...'
ligtype = 'Unspecified type' if ligand.type == 'UNSPECIFIED' else ligand.type
ligtext = "\n%s [%s] -- %s" % (longname, ligtype, site)
if ligtype == 'PEPTIDE':
ligtext = '\n Chain %s [PEPTIDE / INTER-CHAIN]' % ligand.chain
if ligtype == 'INTRA':
ligtext = "\n Chain %s [INTRA-CHAIN]" % ligand.chain
any_in_biolip = len(set([x[0] for x in ligand.members]).intersection(config.biolip_list)) != 0
write_message(ligtext)
write_message('\n' + '-' * len(ligtext) + '\n')
if ligtype not in ['POLYMER', 'DNA', 'ION', 'DNA+ION', 'RNA+ION', 'SMALLMOLECULE+ION'] and any_in_biolip:
write_message('may be biologically irrelevant\n', mtype='info', indent=True)
lig_obj = Ligand(self, ligand)
cutoff = lig_obj.max_dist_to_center + config.BS_DIST
bs_res = self.extract_bs(cutoff, lig_obj.centroid, self.resis)
# Get a list of all atoms belonging to the binding site, search by idx
bs_atoms = [self.atoms[idx] for idx in [i for i in self.atoms.keys()
if self.atoms[i].OBAtom.GetResidue().GetIdx() in bs_res]
if idx in self.Mapper.proteinmap and self.Mapper.mapid(idx, mtype='protein') not in self.altconf]
if ligand.type == 'PEPTIDE':
# If peptide, don't consider the peptide chain as part of the protein binding site
bs_atoms = [a for a in bs_atoms if a.OBAtom.GetResidue().GetChain() != lig_obj.chain]
if ligand.type == 'INTRA':
# Interactions within the chain
bs_atoms = [a for a in bs_atoms if a.OBAtom.GetResidue().GetChain() == lig_obj.chain]
bs_atoms_refined = []
# Create hash with BSRES -> (MINDIST_TO_LIG, AA_TYPE)
# and refine binding site atom selection with exact threshold
min_dist = {}
for r in bs_atoms:
bs_res_id = ''.join([str(whichresnumber(r)), whichchain(r)])
for l in ligand.mol.atoms:
distance = euclidean3d(r.coords, l.coords)
if bs_res_id not in min_dist:
min_dist[bs_res_id] = (distance, whichrestype(r))
elif min_dist[bs_res_id][0] > distance:
min_dist[bs_res_id] = (distance, whichrestype(r))
if distance <= config.BS_DIST and r not in bs_atoms_refined:
bs_atoms_refined.append(r)
num_bs_atoms = len(bs_atoms_refined)
write_message('Binding site atoms in vicinity (%.1f A max. dist: %i).\n' % (config.BS_DIST, num_bs_atoms),
indent=True)
bs_obj = BindingSite(bs_atoms_refined, self.protcomplex, self, self.altconf, min_dist, self.Mapper)
pli_obj = PLInteraction(lig_obj, bs_obj, self)
self.interaction_sets[ligand.mol.title] = pli_obj | Handles all basic functions for characterizing the interactions for one ligand | https://github.com/ssalentin/plip/blob/906c8d36463689779b403f6c2c9ed06174acaf9a/plip/modules/preparation.py#L1384-L1440 |
ssalentin/plip | plip/modules/preparation.py | PDBComplex.extract_bs | def extract_bs(self, cutoff, ligcentroid, resis):
"""Return list of ids from residues belonging to the binding site"""
return [obres.GetIdx() for obres in resis if self.res_belongs_to_bs(obres, cutoff, ligcentroid)] | python | def extract_bs(self, cutoff, ligcentroid, resis):
"""Return list of ids from residues belonging to the binding site"""
return [obres.GetIdx() for obres in resis if self.res_belongs_to_bs(obres, cutoff, ligcentroid)] | Return list of ids from residues belonging to the binding site | https://github.com/ssalentin/plip/blob/906c8d36463689779b403f6c2c9ed06174acaf9a/plip/modules/preparation.py#L1442-L1444 |
ssalentin/plip | plip/modules/preparation.py | PDBComplex.res_belongs_to_bs | def res_belongs_to_bs(self, res, cutoff, ligcentroid):
"""Check for each residue if its centroid is within a certain distance to the ligand centroid.
Additionally checks if a residue belongs to a chain restricted by the user (e.g. by defining a peptide chain)"""
rescentroid = centroid([(atm.x(), atm.y(), atm.z()) for atm in pybel.ob.OBResidueAtomIter(res)])
# Check geometry
near_enough = True if euclidean3d(rescentroid, ligcentroid) < cutoff else False
# Check chain membership
restricted_chain = True if res.GetChain() in config.PEPTIDES else False
return (near_enough and not restricted_chain) | python | def res_belongs_to_bs(self, res, cutoff, ligcentroid):
"""Check for each residue if its centroid is within a certain distance to the ligand centroid.
Additionally checks if a residue belongs to a chain restricted by the user (e.g. by defining a peptide chain)"""
rescentroid = centroid([(atm.x(), atm.y(), atm.z()) for atm in pybel.ob.OBResidueAtomIter(res)])
# Check geometry
near_enough = True if euclidean3d(rescentroid, ligcentroid) < cutoff else False
# Check chain membership
restricted_chain = True if res.GetChain() in config.PEPTIDES else False
return (near_enough and not restricted_chain) | Check for each residue if its centroid is within a certain distance to the ligand centroid.
Additionally checks if a residue belongs to a chain restricted by the user (e.g. by defining a peptide chain) | https://github.com/ssalentin/plip/blob/906c8d36463689779b403f6c2c9ed06174acaf9a/plip/modules/preparation.py#L1446-L1454 |
ella/ella | ella/core/context_processors.py | url_info | def url_info(request):
"""
Make MEDIA_URL and current HttpRequest object
available in template code.
"""
return {
'MEDIA_URL' : core_settings.MEDIA_URL,
'STATIC_URL': core_settings.STATIC_URL,
'VERSION' : core_settings.VERSION,
'SERVER_INFO' : core_settings.SERVER_INFO,
'SITE_NAME' : current_site_name,
'CURRENT_SITE': current_site,
} | python | def url_info(request):
"""
Make MEDIA_URL and current HttpRequest object
available in template code.
"""
return {
'MEDIA_URL' : core_settings.MEDIA_URL,
'STATIC_URL': core_settings.STATIC_URL,
'VERSION' : core_settings.VERSION,
'SERVER_INFO' : core_settings.SERVER_INFO,
'SITE_NAME' : current_site_name,
'CURRENT_SITE': current_site,
} | Make MEDIA_URL and current HttpRequest object
available in template code. | https://github.com/ella/ella/blob/4a1414991f649dc21c4b777dc6b41a922a13faa7/ella/core/context_processors.py#L9-L22 |
ella/ella | ella/core/middleware.py | UpdateCacheMiddleware.process_response | def process_response(self, request, response):
"""Sets the cache, if needed."""
# never cache headers + ETag
add_never_cache_headers(response)
if not hasattr(request, '_cache_update_cache') or not request._cache_update_cache:
# We don't need to update the cache, just return.
return response
if request.method != 'GET':
# This is a stronger requirement than above. It is needed
# because of interactions between this middleware and the
# HTTPMiddleware, which throws the body of a HEAD-request
# away before this middleware gets a chance to cache it.
return response
if not response.status_code == 200:
return response
# use the precomputed cache_key
if request._cache_middleware_key:
cache_key = request._cache_middleware_key
else:
cache_key = learn_cache_key(request, response, self.cache_timeout, self.key_prefix)
# include the orig_time information within the cache
cache.set(cache_key, (time.time(), response), self.cache_timeout)
return response | python | def process_response(self, request, response):
"""Sets the cache, if needed."""
# never cache headers + ETag
add_never_cache_headers(response)
if not hasattr(request, '_cache_update_cache') or not request._cache_update_cache:
# We don't need to update the cache, just return.
return response
if request.method != 'GET':
# This is a stronger requirement than above. It is needed
# because of interactions between this middleware and the
# HTTPMiddleware, which throws the body of a HEAD-request
# away before this middleware gets a chance to cache it.
return response
if not response.status_code == 200:
return response
# use the precomputed cache_key
if request._cache_middleware_key:
cache_key = request._cache_middleware_key
else:
cache_key = learn_cache_key(request, response, self.cache_timeout, self.key_prefix)
# include the orig_time information within the cache
cache.set(cache_key, (time.time(), response), self.cache_timeout)
return response | Sets the cache, if needed. | https://github.com/ella/ella/blob/4a1414991f649dc21c4b777dc6b41a922a13faa7/ella/core/middleware.py#L85-L111 |
ella/ella | ella/core/middleware.py | FetchFromCacheMiddleware.process_request | def process_request(self, request):
"""
Checks whether the page is already cached and returns the cached
version if available.
"""
if self.cache_anonymous_only:
assert hasattr(request, 'user'), "The Django cache middleware with CACHE_MIDDLEWARE_ANONYMOUS_ONLY=True requires authentication middleware to be installed. Edit your MIDDLEWARE_CLASSES setting to insert 'django.contrib.auth.middleware.AuthenticationMiddleware' before the CacheMiddleware."
if not request.method in ('GET', 'HEAD') or request.GET:
request._cache_update_cache = False
return None # Don't bother checking the cache.
if self.cache_anonymous_only and request.user.is_authenticated():
request._cache_update_cache = False
return None # Don't cache requests from authenticated users.
cache_key = get_cache_key(request, self.key_prefix)
request._cache_middleware_key = cache_key
if cache_key is None:
request._cache_update_cache = True
return None # No cache information available, need to rebuild.
response = cache.get(cache_key, None)
if response is None:
request._cache_update_cache = True
return None # No cache information available, need to rebuild.
orig_time, response = response
# time to refresh the cache
if orig_time and ((time.time() - orig_time) > self.cache_refresh_timeout):
request._cache_update_cache = True
# keep the response in the cache for just self.timeout seconds and mark it for update
# other requests will continue werving this response from cache while I alone work on refreshing it
cache.set(cache_key, (None, response), self.timeout)
return None
request._cache_update_cache = False
return response | python | def process_request(self, request):
"""
Checks whether the page is already cached and returns the cached
version if available.
"""
if self.cache_anonymous_only:
assert hasattr(request, 'user'), "The Django cache middleware with CACHE_MIDDLEWARE_ANONYMOUS_ONLY=True requires authentication middleware to be installed. Edit your MIDDLEWARE_CLASSES setting to insert 'django.contrib.auth.middleware.AuthenticationMiddleware' before the CacheMiddleware."
if not request.method in ('GET', 'HEAD') or request.GET:
request._cache_update_cache = False
return None # Don't bother checking the cache.
if self.cache_anonymous_only and request.user.is_authenticated():
request._cache_update_cache = False
return None # Don't cache requests from authenticated users.
cache_key = get_cache_key(request, self.key_prefix)
request._cache_middleware_key = cache_key
if cache_key is None:
request._cache_update_cache = True
return None # No cache information available, need to rebuild.
response = cache.get(cache_key, None)
if response is None:
request._cache_update_cache = True
return None # No cache information available, need to rebuild.
orig_time, response = response
# time to refresh the cache
if orig_time and ((time.time() - orig_time) > self.cache_refresh_timeout):
request._cache_update_cache = True
# keep the response in the cache for just self.timeout seconds and mark it for update
# other requests will continue werving this response from cache while I alone work on refreshing it
cache.set(cache_key, (None, response), self.timeout)
return None
request._cache_update_cache = False
return response | Checks whether the page is already cached and returns the cached
version if available. | https://github.com/ella/ella/blob/4a1414991f649dc21c4b777dc6b41a922a13faa7/ella/core/middleware.py#L128-L166 |
ella/ella | ella/core/managers.py | RelatedManager.collect_related | def collect_related(self, finder_funcs, obj, count, *args, **kwargs):
"""
Collects objects related to ``obj`` using a list of ``finder_funcs``.
Stops when required count is collected or the function list is
exhausted.
"""
collected = []
for func in finder_funcs:
gathered = func(obj, count, collected, *args, **kwargs)
if gathered:
collected += gathered
if len(collected) >= count:
return collected[:count]
return collected | python | def collect_related(self, finder_funcs, obj, count, *args, **kwargs):
"""
Collects objects related to ``obj`` using a list of ``finder_funcs``.
Stops when required count is collected or the function list is
exhausted.
"""
collected = []
for func in finder_funcs:
gathered = func(obj, count, collected, *args, **kwargs)
if gathered:
collected += gathered
if len(collected) >= count:
return collected[:count]
return collected | Collects objects related to ``obj`` using a list of ``finder_funcs``.
Stops when required count is collected or the function list is
exhausted. | https://github.com/ella/ella/blob/4a1414991f649dc21c4b777dc6b41a922a13faa7/ella/core/managers.py#L83-L97 |
ella/ella | ella/core/managers.py | RelatedManager.get_related_for_object | def get_related_for_object(self, obj, count, finder=None, mods=[], only_from_same_site=True):
"""
Returns at most ``count`` publishable objects related to ``obj`` using
named related finder ``finder``.
If only specific type of publishable is prefered, use ``mods`` attribute
to list required classes.
Finally, use ``only_from_same_site`` if you don't want cross-site
content.
``finder`` atribute uses ``RELATED_FINDERS`` settings to find out
what finder function to use. If none is specified, ``default``
is used to perform the query.
"""
return self.collect_related(self._get_finders(finder), obj, count, mods, only_from_same_site) | python | def get_related_for_object(self, obj, count, finder=None, mods=[], only_from_same_site=True):
"""
Returns at most ``count`` publishable objects related to ``obj`` using
named related finder ``finder``.
If only specific type of publishable is prefered, use ``mods`` attribute
to list required classes.
Finally, use ``only_from_same_site`` if you don't want cross-site
content.
``finder`` atribute uses ``RELATED_FINDERS`` settings to find out
what finder function to use. If none is specified, ``default``
is used to perform the query.
"""
return self.collect_related(self._get_finders(finder), obj, count, mods, only_from_same_site) | Returns at most ``count`` publishable objects related to ``obj`` using
named related finder ``finder``.
If only specific type of publishable is prefered, use ``mods`` attribute
to list required classes.
Finally, use ``only_from_same_site`` if you don't want cross-site
content.
``finder`` atribute uses ``RELATED_FINDERS`` settings to find out
what finder function to use. If none is specified, ``default``
is used to perform the query. | https://github.com/ella/ella/blob/4a1414991f649dc21c4b777dc6b41a922a13faa7/ella/core/managers.py#L123-L138 |
ella/ella | ella/core/managers.py | ListingManager.get_listing | def get_listing(self, category=None, children=ListingHandler.NONE, count=10, offset=0, content_types=[], date_range=(), exclude=None, **kwargs):
"""
Get top objects for given category and potentionally also its child categories.
Params:
category - Category object to list objects for. None if any category will do
count - number of objects to output, defaults to 10
offset - starting with object number... 1-based
content_types - list of ContentTypes to list, if empty, object from all models are included
date_range - range for listing's publish_from field
**kwargs - rest of the parameter are passed to the queryset unchanged
"""
assert offset >= 0, "Offset must be a positive integer"
assert count >= 0, "Count must be a positive integer"
if not count:
return []
limit = offset + count
qset = self.get_listing_queryset(category, children, content_types, date_range, exclude, **kwargs)
# direct listings, we don't need to check for duplicates
if children == ListingHandler.NONE:
return qset[offset:limit]
seen = set()
out = []
while len(out) < count:
skip = 0
# 2 i a reasonable value for padding, wouldn't you say dear Watson?
for l in qset[offset:limit + 2]:
if l.publishable_id not in seen:
seen.add(l.publishable_id)
out.append(l)
if len(out) == count:
break
else:
skip += 1
# no enough skipped, or not enough listings to work with, no need for another try
if skip <= 2 or (len(out) + skip) < (count + 2):
break
# get another page to fill in the gaps
offset += count
limit += count
return out | python | def get_listing(self, category=None, children=ListingHandler.NONE, count=10, offset=0, content_types=[], date_range=(), exclude=None, **kwargs):
"""
Get top objects for given category and potentionally also its child categories.
Params:
category - Category object to list objects for. None if any category will do
count - number of objects to output, defaults to 10
offset - starting with object number... 1-based
content_types - list of ContentTypes to list, if empty, object from all models are included
date_range - range for listing's publish_from field
**kwargs - rest of the parameter are passed to the queryset unchanged
"""
assert offset >= 0, "Offset must be a positive integer"
assert count >= 0, "Count must be a positive integer"
if not count:
return []
limit = offset + count
qset = self.get_listing_queryset(category, children, content_types, date_range, exclude, **kwargs)
# direct listings, we don't need to check for duplicates
if children == ListingHandler.NONE:
return qset[offset:limit]
seen = set()
out = []
while len(out) < count:
skip = 0
# 2 i a reasonable value for padding, wouldn't you say dear Watson?
for l in qset[offset:limit + 2]:
if l.publishable_id not in seen:
seen.add(l.publishable_id)
out.append(l)
if len(out) == count:
break
else:
skip += 1
# no enough skipped, or not enough listings to work with, no need for another try
if skip <= 2 or (len(out) + skip) < (count + 2):
break
# get another page to fill in the gaps
offset += count
limit += count
return out | Get top objects for given category and potentionally also its child categories.
Params:
category - Category object to list objects for. None if any category will do
count - number of objects to output, defaults to 10
offset - starting with object number... 1-based
content_types - list of ContentTypes to list, if empty, object from all models are included
date_range - range for listing's publish_from field
**kwargs - rest of the parameter are passed to the queryset unchanged | https://github.com/ella/ella/blob/4a1414991f649dc21c4b777dc6b41a922a13faa7/ella/core/managers.py#L258-L306 |
ella/ella | ella/core/templatetags/pagination.py | paginator | def paginator(context, adjacent_pages=2, template_name=None):
"""
Renders a ``inclusion_tags/paginator.html`` or ``inc/paginator.html``
template with additional pagination context. To be used in conjunction
with the ``object_list`` generic
view.
If ``TEMPLATE_NAME`` parameter is given,
``inclusion_tags/paginator_TEMPLATE_NAME.html`` or
``inc/paginator_TEMPLATE_NAME.html`` will be used instead.
Adds pagination context variables for use in displaying first, adjacent pages and
last page links in addition to those created by the ``object_list`` generic
view.
Taken from http://www.djangosnippets.org/snippets/73/
Syntax::
{% paginator [NUMBER_OF_ADJACENT_PAGES] [TEMPLATE_NAME] %}
Examples::
{% paginator %}
{% paginator 5 %}
{% paginator 5 "special" %}
# with Django 1.4 and above you can also do:
{% paginator template_name="special" %}
"""
tname, context = _do_paginator(context, adjacent_pages, template_name)
return render_to_string(tname, context) | python | def paginator(context, adjacent_pages=2, template_name=None):
"""
Renders a ``inclusion_tags/paginator.html`` or ``inc/paginator.html``
template with additional pagination context. To be used in conjunction
with the ``object_list`` generic
view.
If ``TEMPLATE_NAME`` parameter is given,
``inclusion_tags/paginator_TEMPLATE_NAME.html`` or
``inc/paginator_TEMPLATE_NAME.html`` will be used instead.
Adds pagination context variables for use in displaying first, adjacent pages and
last page links in addition to those created by the ``object_list`` generic
view.
Taken from http://www.djangosnippets.org/snippets/73/
Syntax::
{% paginator [NUMBER_OF_ADJACENT_PAGES] [TEMPLATE_NAME] %}
Examples::
{% paginator %}
{% paginator 5 %}
{% paginator 5 "special" %}
# with Django 1.4 and above you can also do:
{% paginator template_name="special" %}
"""
tname, context = _do_paginator(context, adjacent_pages, template_name)
return render_to_string(tname, context) | Renders a ``inclusion_tags/paginator.html`` or ``inc/paginator.html``
template with additional pagination context. To be used in conjunction
with the ``object_list`` generic
view.
If ``TEMPLATE_NAME`` parameter is given,
``inclusion_tags/paginator_TEMPLATE_NAME.html`` or
``inc/paginator_TEMPLATE_NAME.html`` will be used instead.
Adds pagination context variables for use in displaying first, adjacent pages and
last page links in addition to those created by the ``object_list`` generic
view.
Taken from http://www.djangosnippets.org/snippets/73/
Syntax::
{% paginator [NUMBER_OF_ADJACENT_PAGES] [TEMPLATE_NAME] %}
Examples::
{% paginator %}
{% paginator 5 %}
{% paginator 5 "special" %}
# with Django 1.4 and above you can also do:
{% paginator template_name="special" %} | https://github.com/ella/ella/blob/4a1414991f649dc21c4b777dc6b41a922a13faa7/ella/core/templatetags/pagination.py#L45-L75 |
ella/ella | ella/core/templatetags/authors.py | do_author_listing | def do_author_listing(parser, token):
"""
Get N listing objects that were published by given author recently and optionally
omit a publishable object in results.
**Usage**::
{% author_listing <author> <limit> as <result> [omit <obj>] %}
**Parameters**::
================================== ================================================
Option Description
================================== ================================================
``author`` Author to load objects for.
``limit`` Maximum number of objects to store,
``result`` Store the resulting list in context under given
name.
================================== ================================================
**Examples**::
{% author_listing object.authors.all.0 10 as article_listing %}
"""
contents = token.split_contents()
if len(contents) not in [5, 7]:
raise template.TemplateSyntaxError('%r tag requires 4 or 6 arguments.' % contents[0])
elif len(contents) == 5:
tag, obj_var, count, fill, var_name = contents
return AuthorListingNode(obj_var, count, var_name)
else:
tag, obj_var, count, fill, var_name, filll, omit_var = contents
return AuthorListingNode(obj_var, count, var_name, omit_var) | python | def do_author_listing(parser, token):
"""
Get N listing objects that were published by given author recently and optionally
omit a publishable object in results.
**Usage**::
{% author_listing <author> <limit> as <result> [omit <obj>] %}
**Parameters**::
================================== ================================================
Option Description
================================== ================================================
``author`` Author to load objects for.
``limit`` Maximum number of objects to store,
``result`` Store the resulting list in context under given
name.
================================== ================================================
**Examples**::
{% author_listing object.authors.all.0 10 as article_listing %}
"""
contents = token.split_contents()
if len(contents) not in [5, 7]:
raise template.TemplateSyntaxError('%r tag requires 4 or 6 arguments.' % contents[0])
elif len(contents) == 5:
tag, obj_var, count, fill, var_name = contents
return AuthorListingNode(obj_var, count, var_name)
else:
tag, obj_var, count, fill, var_name, filll, omit_var = contents
return AuthorListingNode(obj_var, count, var_name, omit_var) | Get N listing objects that were published by given author recently and optionally
omit a publishable object in results.
**Usage**::
{% author_listing <author> <limit> as <result> [omit <obj>] %}
**Parameters**::
================================== ================================================
Option Description
================================== ================================================
``author`` Author to load objects for.
``limit`` Maximum number of objects to store,
``result`` Store the resulting list in context under given
name.
================================== ================================================
**Examples**::
{% author_listing object.authors.all.0 10 as article_listing %} | https://github.com/ella/ella/blob/4a1414991f649dc21c4b777dc6b41a922a13faa7/ella/core/templatetags/authors.py#L40-L72 |
jjgomera/iapws | iapws/iapws08.py | _Tb | def _Tb(P, S):
"""Procedure to calculate the boiling temperature of seawater
Parameters
----------
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
Tb : float
Boiling temperature, [K]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 7
"""
def f(T):
pw = _Region1(T, P)
gw = pw["h"]-T*pw["s"]
pv = _Region2(T, P)
gv = pv["h"]-T*pv["s"]
ps = SeaWater._saline(T, P, S)
return -ps["g"]+S*ps["gs"]-gw+gv
Tb = fsolve(f, 300)[0]
return Tb | python | def _Tb(P, S):
"""Procedure to calculate the boiling temperature of seawater
Parameters
----------
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
Tb : float
Boiling temperature, [K]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 7
"""
def f(T):
pw = _Region1(T, P)
gw = pw["h"]-T*pw["s"]
pv = _Region2(T, P)
gv = pv["h"]-T*pv["s"]
ps = SeaWater._saline(T, P, S)
return -ps["g"]+S*ps["gs"]-gw+gv
Tb = fsolve(f, 300)[0]
return Tb | Procedure to calculate the boiling temperature of seawater
Parameters
----------
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
Tb : float
Boiling temperature, [K]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 7 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L408-L439 |
jjgomera/iapws | iapws/iapws08.py | _Tf | def _Tf(P, S):
"""Procedure to calculate the freezing temperature of seawater
Parameters
----------
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
Tf : float
Freezing temperature, [K]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 12
"""
def f(T):
T = float(T)
pw = _Region1(T, P)
gw = pw["h"]-T*pw["s"]
gih = _Ice(T, P)["g"]
ps = SeaWater._saline(T, P, S)
return -ps["g"]+S*ps["gs"]-gw+gih
Tf = fsolve(f, 300)[0]
return Tf | python | def _Tf(P, S):
"""Procedure to calculate the freezing temperature of seawater
Parameters
----------
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
Tf : float
Freezing temperature, [K]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 12
"""
def f(T):
T = float(T)
pw = _Region1(T, P)
gw = pw["h"]-T*pw["s"]
gih = _Ice(T, P)["g"]
ps = SeaWater._saline(T, P, S)
return -ps["g"]+S*ps["gs"]-gw+gih
Tf = fsolve(f, 300)[0]
return Tf | Procedure to calculate the freezing temperature of seawater
Parameters
----------
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
Tf : float
Freezing temperature, [K]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 12 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L442-L473 |
jjgomera/iapws | iapws/iapws08.py | _Triple | def _Triple(S):
"""Procedure to calculate the triple point pressure and temperature for
seawater
Parameters
----------
S : float
Salinity, [kg/kg]
Returns
-------
prop : dict
Dictionary with the triple point properties:
* Tt: Triple point temperature, [K]
* Pt: Triple point pressure, [MPa]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 7
"""
def f(parr):
T, P = parr
pw = _Region1(T, P)
gw = pw["h"]-T*pw["s"]
pv = _Region2(T, P)
gv = pv["h"]-T*pv["s"]
gih = _Ice(T, P)["g"]
ps = SeaWater._saline(T, P, S)
return -ps["g"]+S*ps["gs"]-gw+gih, -ps["g"]+S*ps["gs"]-gw+gv
Tt, Pt = fsolve(f, [273, 6e-4])
prop = {}
prop["Tt"] = Tt
prop["Pt"] = Pt
return prop | python | def _Triple(S):
"""Procedure to calculate the triple point pressure and temperature for
seawater
Parameters
----------
S : float
Salinity, [kg/kg]
Returns
-------
prop : dict
Dictionary with the triple point properties:
* Tt: Triple point temperature, [K]
* Pt: Triple point pressure, [MPa]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 7
"""
def f(parr):
T, P = parr
pw = _Region1(T, P)
gw = pw["h"]-T*pw["s"]
pv = _Region2(T, P)
gv = pv["h"]-T*pv["s"]
gih = _Ice(T, P)["g"]
ps = SeaWater._saline(T, P, S)
return -ps["g"]+S*ps["gs"]-gw+gih, -ps["g"]+S*ps["gs"]-gw+gv
Tt, Pt = fsolve(f, [273, 6e-4])
prop = {}
prop["Tt"] = Tt
prop["Pt"] = Pt
return prop | Procedure to calculate the triple point pressure and temperature for
seawater
Parameters
----------
S : float
Salinity, [kg/kg]
Returns
-------
prop : dict
Dictionary with the triple point properties:
* Tt: Triple point temperature, [K]
* Pt: Triple point pressure, [MPa]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 7 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L476-L516 |
jjgomera/iapws | iapws/iapws08.py | _OsmoticPressure | def _OsmoticPressure(T, P, S):
"""Procedure to calculate the osmotic pressure of seawater
Parameters
----------
T : float
Tmperature, [K]
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
Posm : float
Osmotic pressure, [MPa]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 15
"""
pw = _Region1(T, P)
gw = pw["h"]-T*pw["s"]
def f(Posm):
pw2 = _Region1(T, P+Posm)
gw2 = pw2["h"]-T*pw2["s"]
ps = SeaWater._saline(T, P+Posm, S)
return -ps["g"]+S*ps["gs"]-gw+gw2
Posm = fsolve(f, 0)[0]
return Posm | python | def _OsmoticPressure(T, P, S):
"""Procedure to calculate the osmotic pressure of seawater
Parameters
----------
T : float
Tmperature, [K]
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
Posm : float
Osmotic pressure, [MPa]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 15
"""
pw = _Region1(T, P)
gw = pw["h"]-T*pw["s"]
def f(Posm):
pw2 = _Region1(T, P+Posm)
gw2 = pw2["h"]-T*pw2["s"]
ps = SeaWater._saline(T, P+Posm, S)
return -ps["g"]+S*ps["gs"]-gw+gw2
Posm = fsolve(f, 0)[0]
return Posm | Procedure to calculate the osmotic pressure of seawater
Parameters
----------
T : float
Tmperature, [K]
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
Posm : float
Osmotic pressure, [MPa]
References
----------
IAPWS, Advisory Note No. 5: Industrial Calculation of the Thermodynamic
Properties of Seawater, http://www.iapws.org/relguide/Advise5.html, Eq 15 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L519-L551 |
jjgomera/iapws | iapws/iapws08.py | _ThCond_SeaWater | def _ThCond_SeaWater(T, P, S):
"""Equation for the thermal conductivity of seawater
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
k : float
Thermal conductivity excess relative to that of the pure water, [W/mK]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 273.15 ≤ T ≤ 523.15
* 0 ≤ P ≤ 140
* 0 ≤ S ≤ 0.17
Examples
--------
>>> _ThCond_Seawater(293.15, 0.1, 0.035)
-0.00418604
References
----------
IAPWS, Guideline on the Thermal Conductivity of Seawater,
http://www.iapws.org/relguide/Seawater-ThCond.html
"""
# Check input parameters
if T < 273.15 or T > 523.15 or P < 0 or P > 140 or S < 0 or S > 0.17:
raise NotImplementedError("Incoming out of bound")
# Eq 4
a1 = -7.180891e-5+1.831971e-7*P
a2 = 1.048077e-3-4.494722e-6*P
# Eq 5
b1 = 1.463375e-1+9.208586e-4*P
b2 = -3.086908e-3+1.798489e-5*P
a = a1*exp(a2*(T-273.15)) # Eq 2
b = b1*exp(b2*(T-273.15)) # Eq 3
# Eq 1
DL = a*(1000*S)**(1+b)
return DL | python | def _ThCond_SeaWater(T, P, S):
"""Equation for the thermal conductivity of seawater
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
k : float
Thermal conductivity excess relative to that of the pure water, [W/mK]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 273.15 ≤ T ≤ 523.15
* 0 ≤ P ≤ 140
* 0 ≤ S ≤ 0.17
Examples
--------
>>> _ThCond_Seawater(293.15, 0.1, 0.035)
-0.00418604
References
----------
IAPWS, Guideline on the Thermal Conductivity of Seawater,
http://www.iapws.org/relguide/Seawater-ThCond.html
"""
# Check input parameters
if T < 273.15 or T > 523.15 or P < 0 or P > 140 or S < 0 or S > 0.17:
raise NotImplementedError("Incoming out of bound")
# Eq 4
a1 = -7.180891e-5+1.831971e-7*P
a2 = 1.048077e-3-4.494722e-6*P
# Eq 5
b1 = 1.463375e-1+9.208586e-4*P
b2 = -3.086908e-3+1.798489e-5*P
a = a1*exp(a2*(T-273.15)) # Eq 2
b = b1*exp(b2*(T-273.15)) # Eq 3
# Eq 1
DL = a*(1000*S)**(1+b)
return DL | Equation for the thermal conductivity of seawater
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
S : float
Salinity, [kg/kg]
Returns
-------
k : float
Thermal conductivity excess relative to that of the pure water, [W/mK]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 273.15 ≤ T ≤ 523.15
* 0 ≤ P ≤ 140
* 0 ≤ S ≤ 0.17
Examples
--------
>>> _ThCond_Seawater(293.15, 0.1, 0.035)
-0.00418604
References
----------
IAPWS, Guideline on the Thermal Conductivity of Seawater,
http://www.iapws.org/relguide/Seawater-ThCond.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L554-L606 |
jjgomera/iapws | iapws/iapws08.py | _solNa2SO4 | def _solNa2SO4(T, mH2SO4, mNaCl):
"""Equation for the solubility of sodium sulfate in aqueous mixtures of
sodium chloride and sulfuric acid
Parameters
----------
T : float
Temperature, [K]
mH2SO4 : float
Molality of sufuric acid, [mol/kg(water)]
mNaCl : float
Molality of sodium chloride, [mol/kg(water)]
Returns
-------
S : float
Molal solutility of sodium sulfate, [mol/kg(water)]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 523.15 ≤ T ≤ 623.15
* 0 ≤ mH2SO4 ≤ 0.75
* 0 ≤ mNaCl ≤ 2.25
Examples
--------
>>> _solNa2SO4(523.15, 0.25, 0.75)
2.68
References
----------
IAPWS, Solubility of Sodium Sulfate in Aqueous Mixtures of Sodium Chloride
and Sulfuric Acid from Water to Concentrated Solutions,
http://www.iapws.org/relguide/na2so4.pdf
"""
# Check input parameters
if T < 523.15 or T > 623.15 or mH2SO4 < 0 or mH2SO4 > 0.75 or \
mNaCl < 0 or mNaCl > 2.25:
raise NotImplementedError("Incoming out of bound")
A00 = -0.8085987*T+81.4613752+0.10537803*T*log(T)
A10 = 3.4636364*T-281.63322-0.46779874*T*log(T)
A20 = -6.0029634*T+480.60108+0.81382854*T*log(T)
A30 = 4.4540258*T-359.36872-0.60306734*T*log(T)
A01 = 0.4909061*T-46.556271-0.064612393*T*log(T)
A02 = -0.002781314*T+1.722695+0.0000013319698*T*log(T)
A03 = -0.014074108*T+0.99020227+0.0019397832*T*log(T)
A11 = -0.87146573*T+71.808756+0.11749585*T*log(T)
S = A00 + A10*mH2SO4 + A20*mH2SO4**2 + A30*mH2SO4**3 + A01*mNaCl + \
A02*mNaCl**2 + A03*mNaCl**3 + A11*mH2SO4*mNaCl
return S | python | def _solNa2SO4(T, mH2SO4, mNaCl):
"""Equation for the solubility of sodium sulfate in aqueous mixtures of
sodium chloride and sulfuric acid
Parameters
----------
T : float
Temperature, [K]
mH2SO4 : float
Molality of sufuric acid, [mol/kg(water)]
mNaCl : float
Molality of sodium chloride, [mol/kg(water)]
Returns
-------
S : float
Molal solutility of sodium sulfate, [mol/kg(water)]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 523.15 ≤ T ≤ 623.15
* 0 ≤ mH2SO4 ≤ 0.75
* 0 ≤ mNaCl ≤ 2.25
Examples
--------
>>> _solNa2SO4(523.15, 0.25, 0.75)
2.68
References
----------
IAPWS, Solubility of Sodium Sulfate in Aqueous Mixtures of Sodium Chloride
and Sulfuric Acid from Water to Concentrated Solutions,
http://www.iapws.org/relguide/na2so4.pdf
"""
# Check input parameters
if T < 523.15 or T > 623.15 or mH2SO4 < 0 or mH2SO4 > 0.75 or \
mNaCl < 0 or mNaCl > 2.25:
raise NotImplementedError("Incoming out of bound")
A00 = -0.8085987*T+81.4613752+0.10537803*T*log(T)
A10 = 3.4636364*T-281.63322-0.46779874*T*log(T)
A20 = -6.0029634*T+480.60108+0.81382854*T*log(T)
A30 = 4.4540258*T-359.36872-0.60306734*T*log(T)
A01 = 0.4909061*T-46.556271-0.064612393*T*log(T)
A02 = -0.002781314*T+1.722695+0.0000013319698*T*log(T)
A03 = -0.014074108*T+0.99020227+0.0019397832*T*log(T)
A11 = -0.87146573*T+71.808756+0.11749585*T*log(T)
S = A00 + A10*mH2SO4 + A20*mH2SO4**2 + A30*mH2SO4**3 + A01*mNaCl + \
A02*mNaCl**2 + A03*mNaCl**3 + A11*mH2SO4*mNaCl
return S | Equation for the solubility of sodium sulfate in aqueous mixtures of
sodium chloride and sulfuric acid
Parameters
----------
T : float
Temperature, [K]
mH2SO4 : float
Molality of sufuric acid, [mol/kg(water)]
mNaCl : float
Molality of sodium chloride, [mol/kg(water)]
Returns
-------
S : float
Molal solutility of sodium sulfate, [mol/kg(water)]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 523.15 ≤ T ≤ 623.15
* 0 ≤ mH2SO4 ≤ 0.75
* 0 ≤ mNaCl ≤ 2.25
Examples
--------
>>> _solNa2SO4(523.15, 0.25, 0.75)
2.68
References
----------
IAPWS, Solubility of Sodium Sulfate in Aqueous Mixtures of Sodium Chloride
and Sulfuric Acid from Water to Concentrated Solutions,
http://www.iapws.org/relguide/na2so4.pdf | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L609-L663 |
jjgomera/iapws | iapws/iapws08.py | _critNaCl | def _critNaCl(x):
"""Equation for the critical locus of aqueous solutions of sodium chloride
Parameters
----------
x : float
Mole fraction of NaCl, [-]
Returns
-------
prop : dict
A dictionary withe the properties:
* Tc: critical temperature, [K]
* Pc: critical pressure, [MPa]
* rhoc: critical density, [kg/m³]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0 ≤ x ≤ 0.12
Examples
--------
>>> _critNaCl(0.1)
975.571016
References
----------
IAPWS, Revised Guideline on the Critical Locus of Aqueous Solutions of
Sodium Chloride, http://www.iapws.org/relguide/critnacl.html
"""
# Check input parameters
if x < 0 or x > 0.12:
raise NotImplementedError("Incoming out of bound")
T1 = Tc*(1 + 2.3e1*x - 3.3e2*x**1.5 - 1.8e3*x**2)
T2 = Tc*(1 + 1.757e1*x - 3.026e2*x**1.5 + 2.838e3*x**2 - 1.349e4*x**2.5 +
3.278e4*x**3 - 3.674e4*x**3.5 + 1.437e4*x**4)
f1 = (abs(10000*x-10-1)-abs(10000*x-10+1))/4+0.5
f2 = (abs(10000*x-10+1)-abs(10000*x-10-1))/4+0.5
# Eq 1
tc = f1*T1+f2*T2
# Eq 7
rc = rhoc*(1 + 1.7607e2*x - 2.9693e3*x**1.5 + 2.4886e4*x**2 -
1.1377e5*x**2.5 + 2.8847e5*x**3 - 3.8195e5*x**3.5 +
2.0633e5*x**4)
# Eq 8
DT = tc-Tc
pc = Pc*(1+9.1443e-3*DT+5.1636e-5*DT**2-2.5360e-7*DT**3+3.6494e-10*DT**4)
prop = {}
prop["Tc"] = tc
prop["rhoc"] = rc
prop["Pc"] = pc
return prop | python | def _critNaCl(x):
"""Equation for the critical locus of aqueous solutions of sodium chloride
Parameters
----------
x : float
Mole fraction of NaCl, [-]
Returns
-------
prop : dict
A dictionary withe the properties:
* Tc: critical temperature, [K]
* Pc: critical pressure, [MPa]
* rhoc: critical density, [kg/m³]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0 ≤ x ≤ 0.12
Examples
--------
>>> _critNaCl(0.1)
975.571016
References
----------
IAPWS, Revised Guideline on the Critical Locus of Aqueous Solutions of
Sodium Chloride, http://www.iapws.org/relguide/critnacl.html
"""
# Check input parameters
if x < 0 or x > 0.12:
raise NotImplementedError("Incoming out of bound")
T1 = Tc*(1 + 2.3e1*x - 3.3e2*x**1.5 - 1.8e3*x**2)
T2 = Tc*(1 + 1.757e1*x - 3.026e2*x**1.5 + 2.838e3*x**2 - 1.349e4*x**2.5 +
3.278e4*x**3 - 3.674e4*x**3.5 + 1.437e4*x**4)
f1 = (abs(10000*x-10-1)-abs(10000*x-10+1))/4+0.5
f2 = (abs(10000*x-10+1)-abs(10000*x-10-1))/4+0.5
# Eq 1
tc = f1*T1+f2*T2
# Eq 7
rc = rhoc*(1 + 1.7607e2*x - 2.9693e3*x**1.5 + 2.4886e4*x**2 -
1.1377e5*x**2.5 + 2.8847e5*x**3 - 3.8195e5*x**3.5 +
2.0633e5*x**4)
# Eq 8
DT = tc-Tc
pc = Pc*(1+9.1443e-3*DT+5.1636e-5*DT**2-2.5360e-7*DT**3+3.6494e-10*DT**4)
prop = {}
prop["Tc"] = tc
prop["rhoc"] = rc
prop["Pc"] = pc
return prop | Equation for the critical locus of aqueous solutions of sodium chloride
Parameters
----------
x : float
Mole fraction of NaCl, [-]
Returns
-------
prop : dict
A dictionary withe the properties:
* Tc: critical temperature, [K]
* Pc: critical pressure, [MPa]
* rhoc: critical density, [kg/m³]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0 ≤ x ≤ 0.12
Examples
--------
>>> _critNaCl(0.1)
975.571016
References
----------
IAPWS, Revised Guideline on the Critical Locus of Aqueous Solutions of
Sodium Chloride, http://www.iapws.org/relguide/critnacl.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L666-L725 |
jjgomera/iapws | iapws/iapws08.py | SeaWater.calculo | def calculo(self):
"""Calculate procedure"""
T = self.kwargs["T"]
P = self.kwargs["P"]
S = self.kwargs["S"]
self.m = S/(1-S)/Ms
if self.kwargs["fast"] and T <= 313.15:
pw = self._waterSupp(T, P)
elif self.kwargs["IF97"]:
pw = self._waterIF97(T, P)
else:
pw = self._water(T, P)
ps = self._saline(T, P, S)
prop = {}
for key in ps:
prop[key] = pw[key]+ps[key]
self.__setattr__(key, prop[key])
self.T = T
self.P = P
self.rho = 1./prop["gp"]
self.v = prop["gp"]
self.s = -prop["gt"]
self.cp = -T*prop["gtt"]
self.cv = T*(prop["gtp"]**2/prop["gpp"]-prop["gtt"])
self.h = prop["g"]-T*prop["gt"]
self.u = prop["g"]-T*prop["gt"]-P*1000*prop["gp"]
self.a = prop["g"]-P*1000*prop["gp"]
self.alfav = prop["gtp"]/prop["gp"]
self.betas = -prop["gtp"]/prop["gtt"]
self.xkappa = -prop["gpp"]/prop["gp"]
self.ks = (prop["gtp"]**2-prop["gtt"]*prop["gpp"])/prop["gp"] / \
prop["gtt"]
self.w = prop["gp"]*(prop["gtt"]*1000/(prop["gtp"]**2 -
prop["gtt"]*1000*prop["gpp"]*1e-6))**0.5
if "thcond" in pw:
kw = pw["thcond"]
else:
kw = _ThCond(1/pw["gp"], T)
try:
self.k = _ThCond_SeaWater(T, P, S)+kw
except NotImplementedError:
self.k = None
if S:
self.mu = prop["gs"]
self.muw = prop["g"]-S*prop["gs"]
self.mus = prop["g"]+(1-S)*prop["gs"]
self.osm = -(ps["g"]-S*prop["gs"])/self.m/Rm/T
self.haline = -prop["gsp"]/prop["gp"]
else:
self.mu = None
self.muw = None
self.mus = None
self.osm = None
self.haline = None | python | def calculo(self):
"""Calculate procedure"""
T = self.kwargs["T"]
P = self.kwargs["P"]
S = self.kwargs["S"]
self.m = S/(1-S)/Ms
if self.kwargs["fast"] and T <= 313.15:
pw = self._waterSupp(T, P)
elif self.kwargs["IF97"]:
pw = self._waterIF97(T, P)
else:
pw = self._water(T, P)
ps = self._saline(T, P, S)
prop = {}
for key in ps:
prop[key] = pw[key]+ps[key]
self.__setattr__(key, prop[key])
self.T = T
self.P = P
self.rho = 1./prop["gp"]
self.v = prop["gp"]
self.s = -prop["gt"]
self.cp = -T*prop["gtt"]
self.cv = T*(prop["gtp"]**2/prop["gpp"]-prop["gtt"])
self.h = prop["g"]-T*prop["gt"]
self.u = prop["g"]-T*prop["gt"]-P*1000*prop["gp"]
self.a = prop["g"]-P*1000*prop["gp"]
self.alfav = prop["gtp"]/prop["gp"]
self.betas = -prop["gtp"]/prop["gtt"]
self.xkappa = -prop["gpp"]/prop["gp"]
self.ks = (prop["gtp"]**2-prop["gtt"]*prop["gpp"])/prop["gp"] / \
prop["gtt"]
self.w = prop["gp"]*(prop["gtt"]*1000/(prop["gtp"]**2 -
prop["gtt"]*1000*prop["gpp"]*1e-6))**0.5
if "thcond" in pw:
kw = pw["thcond"]
else:
kw = _ThCond(1/pw["gp"], T)
try:
self.k = _ThCond_SeaWater(T, P, S)+kw
except NotImplementedError:
self.k = None
if S:
self.mu = prop["gs"]
self.muw = prop["g"]-S*prop["gs"]
self.mus = prop["g"]+(1-S)*prop["gs"]
self.osm = -(ps["g"]-S*prop["gs"])/self.m/Rm/T
self.haline = -prop["gsp"]/prop["gp"]
else:
self.mu = None
self.muw = None
self.mus = None
self.osm = None
self.haline = None | Calculate procedure | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L178-L236 |
jjgomera/iapws | iapws/iapws08.py | SeaWater._water | def _water(cls, T, P):
"""Get properties of pure water, Table4 pag 8"""
water = IAPWS95(P=P, T=T)
prop = {}
prop["g"] = water.h-T*water.s
prop["gt"] = -water.s
prop["gp"] = 1./water.rho
prop["gtt"] = -water.cp/T
prop["gtp"] = water.betas*water.cp/T
prop["gpp"] = -1e6/(water.rho*water.w)**2-water.betas**2*1e3*water.cp/T
prop["gs"] = 0
prop["gsp"] = 0
prop["thcond"] = water.k
return prop | python | def _water(cls, T, P):
"""Get properties of pure water, Table4 pag 8"""
water = IAPWS95(P=P, T=T)
prop = {}
prop["g"] = water.h-T*water.s
prop["gt"] = -water.s
prop["gp"] = 1./water.rho
prop["gtt"] = -water.cp/T
prop["gtp"] = water.betas*water.cp/T
prop["gpp"] = -1e6/(water.rho*water.w)**2-water.betas**2*1e3*water.cp/T
prop["gs"] = 0
prop["gsp"] = 0
prop["thcond"] = water.k
return prop | Get properties of pure water, Table4 pag 8 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L244-L257 |
jjgomera/iapws | iapws/iapws08.py | SeaWater._waterSupp | def _waterSupp(cls, T, P):
"""Get properties of pure water using the supplementary release SR7-09,
Table4 pag 6"""
tau = (T-273.15)/40
pi = (P-0.101325)/100
J = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3,
3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7]
K = [0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2,
3, 4, 5, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 0, 1]
G = [0.101342743139674e3, 0.100015695367145e6, -0.254457654203630e4,
0.284517778446287e3, -0.333146754253611e2, 0.420263108803084e1,
-0.546428511471039, 0.590578347909402e1, -0.270983805184062e3,
0.776153611613101e3, -0.196512550881220e3, 0.289796526294175e2,
-0.213290083518327e1, -0.123577859330390e5, 0.145503645404680e4,
-0.756558385769359e3, 0.273479662323528e3, -0.555604063817218e2,
0.434420671917197e1, 0.736741204151612e3, -0.672507783145070e3,
0.499360390819152e3, -0.239545330654412e3, 0.488012518593872e2,
-0.166307106208905e1, -0.148185936433658e3, 0.397968445406972e3,
-0.301815380621876e3, 0.152196371733841e3, -0.263748377232802e2,
0.580259125842571e2, -0.194618310617595e3, 0.120520654902025e3,
-0.552723052340152e2, 0.648190668077221e1, -0.189843846514172e2,
0.635113936641785e2, -0.222897317140459e2, 0.817060541818112e1,
0.305081646487967e1, -0.963108119393062e1]
g, gt, gp, gtt, gtp, gpp = 0, 0, 0, 0, 0, 0
for j, k, gi in zip(J, K, G):
g += gi*tau**j*pi**k
if j >= 1:
gt += gi*j*tau**(j-1)*pi**k
if k >= 1:
gp += k*gi*tau**j*pi**(k-1)
if j >= 2:
gtt += j*(j-1)*gi*tau**(j-2)*pi**k
if j >= 1 and k >= 1:
gtp += j*k*gi*tau**(j-1)*pi**(k-1)
if k >= 2:
gpp += k*(k-1)*gi*tau**j*pi**(k-2)
prop = {}
prop["g"] = g*1e-3
prop["gt"] = gt/40*1e-3
prop["gp"] = gp/100*1e-6
prop["gtt"] = gtt/40**2*1e-3
prop["gtp"] = gtp/40/100*1e-6
prop["gpp"] = gpp/100**2*1e-6
prop["gs"] = 0
prop["gsp"] = 0
return prop | python | def _waterSupp(cls, T, P):
"""Get properties of pure water using the supplementary release SR7-09,
Table4 pag 6"""
tau = (T-273.15)/40
pi = (P-0.101325)/100
J = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3,
3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7]
K = [0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2,
3, 4, 5, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 0, 1]
G = [0.101342743139674e3, 0.100015695367145e6, -0.254457654203630e4,
0.284517778446287e3, -0.333146754253611e2, 0.420263108803084e1,
-0.546428511471039, 0.590578347909402e1, -0.270983805184062e3,
0.776153611613101e3, -0.196512550881220e3, 0.289796526294175e2,
-0.213290083518327e1, -0.123577859330390e5, 0.145503645404680e4,
-0.756558385769359e3, 0.273479662323528e3, -0.555604063817218e2,
0.434420671917197e1, 0.736741204151612e3, -0.672507783145070e3,
0.499360390819152e3, -0.239545330654412e3, 0.488012518593872e2,
-0.166307106208905e1, -0.148185936433658e3, 0.397968445406972e3,
-0.301815380621876e3, 0.152196371733841e3, -0.263748377232802e2,
0.580259125842571e2, -0.194618310617595e3, 0.120520654902025e3,
-0.552723052340152e2, 0.648190668077221e1, -0.189843846514172e2,
0.635113936641785e2, -0.222897317140459e2, 0.817060541818112e1,
0.305081646487967e1, -0.963108119393062e1]
g, gt, gp, gtt, gtp, gpp = 0, 0, 0, 0, 0, 0
for j, k, gi in zip(J, K, G):
g += gi*tau**j*pi**k
if j >= 1:
gt += gi*j*tau**(j-1)*pi**k
if k >= 1:
gp += k*gi*tau**j*pi**(k-1)
if j >= 2:
gtt += j*(j-1)*gi*tau**(j-2)*pi**k
if j >= 1 and k >= 1:
gtp += j*k*gi*tau**(j-1)*pi**(k-1)
if k >= 2:
gpp += k*(k-1)*gi*tau**j*pi**(k-2)
prop = {}
prop["g"] = g*1e-3
prop["gt"] = gt/40*1e-3
prop["gp"] = gp/100*1e-6
prop["gtt"] = gtt/40**2*1e-3
prop["gtp"] = gtp/40/100*1e-6
prop["gpp"] = gpp/100**2*1e-6
prop["gs"] = 0
prop["gsp"] = 0
return prop | Get properties of pure water using the supplementary release SR7-09,
Table4 pag 6 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L275-L323 |
jjgomera/iapws | iapws/iapws08.py | SeaWater._saline | def _saline(cls, T, P, S):
"""Eq 4"""
# Check input in range of validity
if T <= 261 or T > 353 or P <= 0 or P > 100 or S < 0 or S > 0.12:
warnings.warn("Incoming out of bound")
S_ = 0.03516504*40/35
X = (S/S_)**0.5
tau = (T-273.15)/40
pi = (P-0.101325)/100
I = [1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 2, 3, 4, 2, 3, 4, 2, 3, 4,
2, 4, 2, 2, 3, 4, 5, 2, 3, 4, 2, 3, 2, 3, 2, 3, 2, 3, 4, 2, 3, 2,
3, 2, 2, 2, 3, 4, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2]
J = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4,
5, 5, 6, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 0, 0, 0, 1, 1, 2,
2, 3, 4, 0, 0, 0, 1, 1, 2, 2, 3, 4, 0, 0, 1, 2, 3, 0, 1, 2]
K = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2,
2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5]
G = [0.581281456626732e4, 0.141627648484197e4, -0.243214662381794e4,
0.202580115603697e4, -0.109166841042967e4, 0.374601237877840e3,
-0.485891069025409e2, 0.851226734946706e3, 0.168072408311545e3,
-0.493407510141682e3, 0.543835333000098e3, -0.196028306689776e3,
0.367571622995805e2, 0.880031352997204e3, -0.430664675978042e2,
-0.685572509204491e2, -0.225267649263401e3, -0.100227370861875e2,
0.493667694856254e2, 0.914260447751259e2, 0.875600661808945,
-0.171397577419788e2, -0.216603240875311e2, 0.249697009569508e1,
0.213016970847183e1, -0.331049154044839e4, 0.199459603073901e3,
-0.547919133532887e2, 0.360284195611086e2, 0.729116529735046e3,
-0.175292041186547e3, -0.226683558512829e2, -0.860764303783977e3,
0.383058066002476e3, 0.694244814133268e3, -0.460319931801257e3,
-0.297728741987187e3, 0.234565187611355e3, 0.384794152978599e3,
-0.522940909281335e2, -0.408193978912261e1, -0.343956902961561e3,
0.831923927801819e2, 0.337409530269367e3, -0.541917262517112e2,
-0.204889641964903e3, 0.747261411387560e2, -0.965324320107458e2,
0.680444942726459e2, -0.301755111971161e2, 0.124687671116248e3,
-0.294830643494290e2, -0.178314556207638e3, 0.256398487389914e2,
0.113561697840594e3, -0.364872919001588e2, 0.158408172766824e2,
-0.341251932441282e1, -0.316569643860730e2, 0.442040358308000e2,
-0.111282734326413e2, -0.262480156590992e1, 0.704658803315449e1,
-0.792001547211682e1]
g, gt, gp, gtt, gtp, gpp, gs, gsp = 0, 0, 0, 0, 0, 0, 0, 0
# Calculate only for some salinity
if S != 0:
for i, j, k, gi in zip(I, J, K, G):
if i == 1:
g += gi*X**2*log(X)*tau**j*pi**k
gs += gi*(2*log(X)+1)*tau**j*pi**k
else:
g += gi*X**i*tau**j*pi**k
gs += i*gi*X**(i-2)*tau**j*pi**k
if j >= 1:
if i == 1:
gt += gi*X**2*log(X)*j*tau**(j-1)*pi**k
else:
gt += gi*X**i*j*tau**(j-1)*pi**k
if k >= 1:
gp += k*gi*X**i*tau**j*pi**(k-1)
gsp += i*k*gi*X**(i-2)*tau**j*pi**(k-1)
if j >= 2:
gtt += j*(j-1)*gi*X**i*tau**(j-2)*pi**k
if j >= 1 and k >= 1:
gtp += j*k*gi*X**i*tau**(j-1)*pi**(k-1)
if k >= 2:
gpp += k*(k-1)*gi*X**i*tau**j*pi**(k-2)
prop = {}
prop["g"] = g*1e-3
prop["gt"] = gt/40*1e-3
prop["gp"] = gp/100*1e-6
prop["gtt"] = gtt/40**2*1e-3
prop["gtp"] = gtp/40/100*1e-6
prop["gpp"] = gpp/100**2*1e-6
prop["gs"] = gs/S_/2*1e-3
prop["gsp"] = gsp/S_/2/100*1e-6
return prop | python | def _saline(cls, T, P, S):
"""Eq 4"""
# Check input in range of validity
if T <= 261 or T > 353 or P <= 0 or P > 100 or S < 0 or S > 0.12:
warnings.warn("Incoming out of bound")
S_ = 0.03516504*40/35
X = (S/S_)**0.5
tau = (T-273.15)/40
pi = (P-0.101325)/100
I = [1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 2, 3, 4, 2, 3, 4, 2, 3, 4,
2, 4, 2, 2, 3, 4, 5, 2, 3, 4, 2, 3, 2, 3, 2, 3, 2, 3, 4, 2, 3, 2,
3, 2, 2, 2, 3, 4, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2]
J = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4,
5, 5, 6, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 0, 0, 0, 1, 1, 2,
2, 3, 4, 0, 0, 0, 1, 1, 2, 2, 3, 4, 0, 0, 1, 2, 3, 0, 1, 2]
K = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2,
2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5]
G = [0.581281456626732e4, 0.141627648484197e4, -0.243214662381794e4,
0.202580115603697e4, -0.109166841042967e4, 0.374601237877840e3,
-0.485891069025409e2, 0.851226734946706e3, 0.168072408311545e3,
-0.493407510141682e3, 0.543835333000098e3, -0.196028306689776e3,
0.367571622995805e2, 0.880031352997204e3, -0.430664675978042e2,
-0.685572509204491e2, -0.225267649263401e3, -0.100227370861875e2,
0.493667694856254e2, 0.914260447751259e2, 0.875600661808945,
-0.171397577419788e2, -0.216603240875311e2, 0.249697009569508e1,
0.213016970847183e1, -0.331049154044839e4, 0.199459603073901e3,
-0.547919133532887e2, 0.360284195611086e2, 0.729116529735046e3,
-0.175292041186547e3, -0.226683558512829e2, -0.860764303783977e3,
0.383058066002476e3, 0.694244814133268e3, -0.460319931801257e3,
-0.297728741987187e3, 0.234565187611355e3, 0.384794152978599e3,
-0.522940909281335e2, -0.408193978912261e1, -0.343956902961561e3,
0.831923927801819e2, 0.337409530269367e3, -0.541917262517112e2,
-0.204889641964903e3, 0.747261411387560e2, -0.965324320107458e2,
0.680444942726459e2, -0.301755111971161e2, 0.124687671116248e3,
-0.294830643494290e2, -0.178314556207638e3, 0.256398487389914e2,
0.113561697840594e3, -0.364872919001588e2, 0.158408172766824e2,
-0.341251932441282e1, -0.316569643860730e2, 0.442040358308000e2,
-0.111282734326413e2, -0.262480156590992e1, 0.704658803315449e1,
-0.792001547211682e1]
g, gt, gp, gtt, gtp, gpp, gs, gsp = 0, 0, 0, 0, 0, 0, 0, 0
# Calculate only for some salinity
if S != 0:
for i, j, k, gi in zip(I, J, K, G):
if i == 1:
g += gi*X**2*log(X)*tau**j*pi**k
gs += gi*(2*log(X)+1)*tau**j*pi**k
else:
g += gi*X**i*tau**j*pi**k
gs += i*gi*X**(i-2)*tau**j*pi**k
if j >= 1:
if i == 1:
gt += gi*X**2*log(X)*j*tau**(j-1)*pi**k
else:
gt += gi*X**i*j*tau**(j-1)*pi**k
if k >= 1:
gp += k*gi*X**i*tau**j*pi**(k-1)
gsp += i*k*gi*X**(i-2)*tau**j*pi**(k-1)
if j >= 2:
gtt += j*(j-1)*gi*X**i*tau**(j-2)*pi**k
if j >= 1 and k >= 1:
gtp += j*k*gi*X**i*tau**(j-1)*pi**(k-1)
if k >= 2:
gpp += k*(k-1)*gi*X**i*tau**j*pi**(k-2)
prop = {}
prop["g"] = g*1e-3
prop["gt"] = gt/40*1e-3
prop["gp"] = gp/100*1e-6
prop["gtt"] = gtt/40**2*1e-3
prop["gtp"] = gtp/40/100*1e-6
prop["gpp"] = gpp/100**2*1e-6
prop["gs"] = gs/S_/2*1e-3
prop["gsp"] = gsp/S_/2/100*1e-6
return prop | Eq 4 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws08.py#L326-L405 |
jjgomera/iapws | iapws/iapws95.py | _phir | def _phir(tau, delta, coef):
"""Residual contribution to the adimensional free Helmholtz energy
Parameters
----------
tau : float
Inverse reduced temperature Tc/T, [-]
delta : float
Reduced density rho/rhoc, [-]
coef : dict
Dictionary with equation of state parameters
Returns
-------
fir : float
Adimensional free Helmholtz energy
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 5
http://www.iapws.org/relguide/IAPWS-95.html
"""
fir = 0
# Polinomial terms
nr1 = coef.get("nr1", [])
d1 = coef.get("d1", [])
t1 = coef.get("t1", [])
for n, d, t in zip(nr1, d1, t1):
fir += n*delta**d*tau**t
# Exponential terms
nr2 = coef.get("nr2", [])
d2 = coef.get("d2", [])
g2 = coef.get("gamma2", [])
t2 = coef.get("t2", [])
c2 = coef.get("c2", [])
for n, d, g, t, c in zip(nr2, d2, g2, t2, c2):
fir += n*delta**d*tau**t*exp(-g*delta**c)
# Gaussian terms
nr3 = coef.get("nr3", [])
d3 = coef.get("d3", [])
t3 = coef.get("t3", [])
a3 = coef.get("alfa3", [])
e3 = coef.get("epsilon3", [])
b3 = coef.get("beta3", [])
g3 = coef.get("gamma3", [])
for n, d, t, a, e, b, g in zip(nr3, d3, t3, a3, e3, b3, g3):
fir += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)
# Non analitic terms
nr4 = coef.get("nr4", [])
a4 = coef.get("a4", [])
b4 = coef.get("b4", [])
Ai = coef.get("A", [])
Bi = coef.get("B", [])
Ci = coef.get("C", [])
Di = coef.get("D", [])
bt4 = coef.get("beta4", [])
for n, a, b, A, B, C, D, bt in zip(nr4, a4, b4, Ai, Bi, Ci, Di, bt4):
Tita = (1-tau)+A*((delta-1)**2)**(0.5/bt)
F = exp(-C*(delta-1)**2-D*(tau-1)**2)
Delta = Tita**2+B*((delta-1)**2)**a
fir += n*Delta**b*delta*F
return fir | python | def _phir(tau, delta, coef):
"""Residual contribution to the adimensional free Helmholtz energy
Parameters
----------
tau : float
Inverse reduced temperature Tc/T, [-]
delta : float
Reduced density rho/rhoc, [-]
coef : dict
Dictionary with equation of state parameters
Returns
-------
fir : float
Adimensional free Helmholtz energy
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 5
http://www.iapws.org/relguide/IAPWS-95.html
"""
fir = 0
# Polinomial terms
nr1 = coef.get("nr1", [])
d1 = coef.get("d1", [])
t1 = coef.get("t1", [])
for n, d, t in zip(nr1, d1, t1):
fir += n*delta**d*tau**t
# Exponential terms
nr2 = coef.get("nr2", [])
d2 = coef.get("d2", [])
g2 = coef.get("gamma2", [])
t2 = coef.get("t2", [])
c2 = coef.get("c2", [])
for n, d, g, t, c in zip(nr2, d2, g2, t2, c2):
fir += n*delta**d*tau**t*exp(-g*delta**c)
# Gaussian terms
nr3 = coef.get("nr3", [])
d3 = coef.get("d3", [])
t3 = coef.get("t3", [])
a3 = coef.get("alfa3", [])
e3 = coef.get("epsilon3", [])
b3 = coef.get("beta3", [])
g3 = coef.get("gamma3", [])
for n, d, t, a, e, b, g in zip(nr3, d3, t3, a3, e3, b3, g3):
fir += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)
# Non analitic terms
nr4 = coef.get("nr4", [])
a4 = coef.get("a4", [])
b4 = coef.get("b4", [])
Ai = coef.get("A", [])
Bi = coef.get("B", [])
Ci = coef.get("C", [])
Di = coef.get("D", [])
bt4 = coef.get("beta4", [])
for n, a, b, A, B, C, D, bt in zip(nr4, a4, b4, Ai, Bi, Ci, Di, bt4):
Tita = (1-tau)+A*((delta-1)**2)**(0.5/bt)
F = exp(-C*(delta-1)**2-D*(tau-1)**2)
Delta = Tita**2+B*((delta-1)**2)**a
fir += n*Delta**b*delta*F
return fir | Residual contribution to the adimensional free Helmholtz energy
Parameters
----------
tau : float
Inverse reduced temperature Tc/T, [-]
delta : float
Reduced density rho/rhoc, [-]
coef : dict
Dictionary with equation of state parameters
Returns
-------
fir : float
Adimensional free Helmholtz energy
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 5
http://www.iapws.org/relguide/IAPWS-95.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L28-L96 |
jjgomera/iapws | iapws/iapws95.py | mainClassDoc | def mainClassDoc():
"""Function decorator used to automatic adiction of base class MEoS in
subclass __doc__"""
def decorator(f):
# __doc__ is only writable in python3.
# The doc build must be done with python3 so this snnippet do the work
py_version = platform.python_version()
if py_version[0] == "3":
doc = f.__doc__.split(os.linesep)
try:
ind = doc.index("")
except ValueError:
ind = 1
doc1 = os.linesep.join(doc[:ind])
doc3 = os.linesep.join(doc[ind:])
doc2 = os.linesep.join(MEoS.__doc__.split(os.linesep)[3:])
f.__doc__ = doc1 + os.linesep + os.linesep + \
doc2 + os.linesep + os.linesep + doc3
return f
return decorator | python | def mainClassDoc():
"""Function decorator used to automatic adiction of base class MEoS in
subclass __doc__"""
def decorator(f):
# __doc__ is only writable in python3.
# The doc build must be done with python3 so this snnippet do the work
py_version = platform.python_version()
if py_version[0] == "3":
doc = f.__doc__.split(os.linesep)
try:
ind = doc.index("")
except ValueError:
ind = 1
doc1 = os.linesep.join(doc[:ind])
doc3 = os.linesep.join(doc[ind:])
doc2 = os.linesep.join(MEoS.__doc__.split(os.linesep)[3:])
f.__doc__ = doc1 + os.linesep + os.linesep + \
doc2 + os.linesep + os.linesep + doc3
return f
return decorator | Function decorator used to automatic adiction of base class MEoS in
subclass __doc__ | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L2195-L2217 |
jjgomera/iapws | iapws/iapws95.py | MEoS.calculable | def calculable(self):
"""Check if inputs are enough to define state"""
self._mode = ""
if self.kwargs["T"] and self.kwargs["P"]:
self._mode = "TP"
elif self.kwargs["T"] and self.kwargs["rho"]:
self._mode = "Trho"
elif self.kwargs["T"] and self.kwargs["h"] is not None:
self._mode = "Th"
elif self.kwargs["T"] and self.kwargs["s"] is not None:
self._mode = "Ts"
elif self.kwargs["T"] and self.kwargs["u"] is not None:
self._mode = "Tu"
elif self.kwargs["P"] and self.kwargs["rho"]:
self._mode = "Prho"
elif self.kwargs["P"] and self.kwargs["h"] is not None:
self._mode = "Ph"
elif self.kwargs["P"] and self.kwargs["s"] is not None:
self._mode = "Ps"
elif self.kwargs["P"] and self.kwargs["u"] is not None:
self._mode = "Pu"
elif self.kwargs["rho"] and self.kwargs["h"] is not None:
self._mode = "rhoh"
elif self.kwargs["rho"] and self.kwargs["s"] is not None:
self._mode = "rhos"
elif self.kwargs["rho"] and self.kwargs["u"] is not None:
self._mode = "rhou"
elif self.kwargs["h"] is not None and self.kwargs["s"] is not None:
self._mode = "hs"
elif self.kwargs["h"] is not None and self.kwargs["u"] is not None:
self._mode = "hu"
elif self.kwargs["s"] is not None and self.kwargs["u"] is not None:
self._mode = "su"
elif self.kwargs["T"] and self.kwargs["x"] is not None:
self._mode = "Tx"
elif self.kwargs["P"] and self.kwargs["x"] is not None:
self._mode = "Px"
return bool(self._mode) | python | def calculable(self):
"""Check if inputs are enough to define state"""
self._mode = ""
if self.kwargs["T"] and self.kwargs["P"]:
self._mode = "TP"
elif self.kwargs["T"] and self.kwargs["rho"]:
self._mode = "Trho"
elif self.kwargs["T"] and self.kwargs["h"] is not None:
self._mode = "Th"
elif self.kwargs["T"] and self.kwargs["s"] is not None:
self._mode = "Ts"
elif self.kwargs["T"] and self.kwargs["u"] is not None:
self._mode = "Tu"
elif self.kwargs["P"] and self.kwargs["rho"]:
self._mode = "Prho"
elif self.kwargs["P"] and self.kwargs["h"] is not None:
self._mode = "Ph"
elif self.kwargs["P"] and self.kwargs["s"] is not None:
self._mode = "Ps"
elif self.kwargs["P"] and self.kwargs["u"] is not None:
self._mode = "Pu"
elif self.kwargs["rho"] and self.kwargs["h"] is not None:
self._mode = "rhoh"
elif self.kwargs["rho"] and self.kwargs["s"] is not None:
self._mode = "rhos"
elif self.kwargs["rho"] and self.kwargs["u"] is not None:
self._mode = "rhou"
elif self.kwargs["h"] is not None and self.kwargs["s"] is not None:
self._mode = "hs"
elif self.kwargs["h"] is not None and self.kwargs["u"] is not None:
self._mode = "hu"
elif self.kwargs["s"] is not None and self.kwargs["u"] is not None:
self._mode = "su"
elif self.kwargs["T"] and self.kwargs["x"] is not None:
self._mode = "Tx"
elif self.kwargs["P"] and self.kwargs["x"] is not None:
self._mode = "Px"
return bool(self._mode) | Check if inputs are enough to define state | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L434-L471 |
jjgomera/iapws | iapws/iapws95.py | MEoS.calculo | def calculo(self):
"""Calculate procedure"""
T = self.kwargs["T"]
rho = self.kwargs["rho"]
P = self.kwargs["P"]
s = self.kwargs["s"]
h = self.kwargs["h"]
u = self.kwargs["u"]
x = self.kwargs["x"]
# Initial values
T0 = self.kwargs["T0"]
rho0 = self.kwargs["rho0"]
if T0 or rho0:
To = T0
rhoo = rho0
elif self.name == "air":
To = 300
rhoo = 1e-3
else:
try:
st0 = IAPWS97(**self.kwargs)
except NotImplementedError:
To = 300
rhoo = 900
else:
if st0.status:
To = st0.T
rhoo = st0.rho
else:
To = 300
rhoo = 900
self.R = self._constants["R"]/self._constants.get("M", self.M)
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
propiedades = None
if self._mode not in ("Tx", "Px"):
# Method with iteration necessary to get x
if self._mode == "TP":
try:
if self.name == "air":
raise ValueError
st0 = IAPWS97(**self.kwargs)
rhoo = st0.rho
except NotImplementedError:
if rho0:
rhoo = rho0
elif T < self.Tc and P < self.Pc and \
self._Vapor_Pressure(T) < P:
rhoo = self._Liquid_Density(T)
elif T < self.Tc and P < self.Pc:
rhoo = self._Vapor_Density(T)
else:
rhoo = self.rhoc*3
except ValueError:
rhoo = 1e-3
def f(rho):
delta = rho/rhoc
tau = Tc/T
fird = _phird(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
return Po-P*1000
rho = fsolve(f, rhoo)[0]
# Calculate quality
if T > self.Tc:
x = 1
else:
Ps = self._Vapor_Pressure(T)
if Ps*0.95 < P < Ps*1.05:
rhol, rhov, Ps = self._saturation(T)
Ps *= 1e-3
if Ps > P:
x = 1
else:
x = 0
elif self._mode == "Th":
tau = Tc/T
ideal = self._phi0(tau, 1)
fiot = ideal["fiot"]
def f(rho):
delta = rho/rhoc
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-h
if T >= self.Tc:
rhoo = self.rhoc
rho = fsolve(f, rhoo)[0]
else:
x0 = self.kwargs["x0"]
rhov = self._Vapor_Density(T)
rhol = self._Liquid_Density(T)
deltaL = rhol/rhoc
deltaG = rhov/rhoc
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hl = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
hv = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
if x0 not in (0, 1) and hl <= h <= hv:
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
hv = vapor["h"]
hl = liquido["h"]
x = (h-hl)/(hv-hl)
rho = 1/(x/rhov+(1-x)/rhol)
P = Ps/1000
else:
if h > hv:
rhoo = rhov
else:
rhoo = rhol
rho = fsolve(f, rhoo)[0]
elif self._mode == "Ts":
tau = Tc/T
def f(rho):
if rho < 0:
rho = 1e-20
delta = rho/rhoc
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
so = self.R*(tau*(fiot+firt)-fio-fir)
return so-s
if T >= self.Tc:
rhoo = self.rhoc
rho = fsolve(f, rhoo)[0]
else:
rhov = self._Vapor_Density(T)
rhol = self._Liquid_Density(T)
deltaL = rhol/rhoc
deltaG = rhov/rhoc
idealL = self._phi0(tau, deltaL)
idealG = self._phi0(tau, deltaG)
fioL = idealL["fio"]
fioG = idealG["fio"]
fiot = idealL["fiot"]
firL = _phir(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
sl = self.R*(tau*(fiot+firtL)-fioL-firL)
firG = _phir(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
sv = self.R*(tau*(fiot+firtG)-fioG-firG)
if sl <= s <= sv:
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
sv = vapor["s"]
sl = liquido["s"]
x = (s-sl)/(sv-sl)
rho = 1/(x/rhov+(1-x)/rhol)
P = Ps/1000
else:
if s > sv:
rhoo = rhov
else:
rhoo = rhol
rho = fsolve(f, rhoo)[0]
elif self._mode == "Tu":
tau = Tc/T
ideal = self._phi0(tau, 1)
fiot = ideal["fiot"]
def f(rho):
delta = rho/rhoc
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-Po/rho-u
if T >= self.Tc:
rhoo = self.rhoc
rho = fsolve(f, rhoo)[0]
else:
rhov = self._Vapor_Density(T)
rhol = self._Liquid_Density(T)
deltaL = rhol/rhoc
deltaG = rhov/rhoc
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
PoL = (1+deltaL*firdL)*self.R*T*rhol
PoG = (1+deltaG*firdG)*self.R*T*rhov
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
uv = hoG-PoG/rhov
ul = hoL-PoL/rhol
if ul <= u <= uv:
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
uv = vapor["h"]-vapor["P"]/rhov
ul = liquido["h"]-liquido["P"]/rhol
x = (u-ul)/(uv-ul)
rho = 1/(x/rhov-(1-x)/rhol)
P = Ps/1000
else:
if u > uv:
rhoo = rhov
else:
rhoo = rhol
rho = fsolve(f, rhoo)[0]
elif self._mode == "Prho":
delta = rho/rhoc
def f(T):
tau = Tc/T
fird = _phird(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
return Po-P*1000
T = fsolve(f, To)[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == To or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
Ps - P*1000)
for to in [To, 300, 400, 500, 600]:
rhoLo = self._Liquid_Density(to)
rhoGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rhoLo, rhoGo], full_output=True)
T, rhoL, rhoG = sol[0]
x = (1./rho-1/rhoL)/(1/rhoG-1/rhoL)
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "Ph":
def funcion(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return Po-P*1000, ho-h
rho, T = fsolve(funcion, [rhoo, To])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rho == rhoo or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
hoL*(1-x)+hoG*x - h,
Ps - P*1000)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "Ps":
try:
x0 = st0.x
except NameError:
x0 = None
if x0 is None or x0 == 0 or x0 == 1:
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
so = self.R*(tau*(fiot+firt)-fio-fir)
return Po-P*1000, so-s
rho, T = fsolve(f, [rhoo, To])
else:
def funcion(parr):
rho, T = parr
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return Ps-P*1000, vapor["s"]*x+liquido["s"]*(1-x)-s
rho, T = fsolve(funcion, [2., 500.])
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
sv = vapor["s"]
sl = liquido["s"]
x = (s-sl)/(sv-sl)
elif self._mode == "Pu":
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-Po/rho-u, Po-P*1000
sol = fsolve(f, [rhoo, To], full_output=True)
rho, T = sol[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rho == rhoo or sol[2] != 1:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
vu = hoG-Ps/rhog
lu = hoL-Ps/rhol
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
lu*(1-x)+vu*x - u,
Ps - P*1000)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "rhoh":
delta = rho/rhoc
def f(T):
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-h
T = fsolve(f, To)[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == To or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
x = (1./rho-1/rhol)/(1/rhog-1/rhol)
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
hoL*(1-x)+hoG*x - h)
for to in [To, 300, 400, 500, 600]:
rhoLo = self._Liquid_Density(to)
rhoGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rhoLo, rhoGo], full_output=True)
T, rhoL, rhoG = sol[0]
x = (1./rho-1/rhoL)/(1/rhoG-1/rhoL)
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "rhos":
delta = rho/rhoc
def f(T):
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
so = self.R*(tau*(fiot+firt)-fio-fir)
return so-s
T = fsolve(f, To)[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == To or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
idealL = self._phi0(tau, deltaL)
fioL = idealL["fio"]
fiot = idealL["fiot"]
idealG = self._phi0(tau, deltaG)
fioG = idealG["fio"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
soL = self.R*(tau*(fiot+firtL)-fioL-firL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
soG = self.R*(tau*(fiot+firtG)-fioG-firG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
x = (1./rho-1/rhol)/(1/rhog-1/rhol)
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
soL*(1-x)+soG*x - s)
for to in [To, 300, 400, 500, 600]:
rhoLo = self._Liquid_Density(to)
rhoGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rhoLo, rhoGo], full_output=True)
T, rhoL, rhoG = sol[0]
x = (1./rho-1/rhoL)/(1/rhoG-1/rhoL)
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "rhou":
delta = rho/rhoc
def f(T):
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-Po/rho-u
T = fsolve(f, To)[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == To or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
x = (1./rho-1/rhol)/(1/rhog-1/rhol)
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
vu = hoG-Ps/rhog
lu = hoL-Ps/rhol
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
lu*(1-x)+vu*x - u)
for to in [To, 300, 400, 500, 600]:
rhoLo = self._Liquid_Density(to)
rhoGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rhoLo, rhoGo], full_output=True)
T, rhoL, rhoG = sol[0]
x = (1./rho-1/rhoL)/(1/rhoG-1/rhoL)
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "hs":
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
so = self.R*(tau*(fiot+firt)-fio-fir)
return ho-h, so-s
rho, T = fsolve(f, [rhoo, To])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
idealL = self._phi0(tau, deltaL)
fiot = idealL["fiot"]
fioL = idealL["fio"]
idealG = self._phi0(tau, deltaG)
fioG = idealG["fio"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
soL = self.R*(tau*(fiot+firtL)-fioL-firL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
soG = self.R*(tau*(fiot+firtG)-fioG-firG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
hoL*(1-x)+hoG*x - h,
soL*(1-x)+soG*x - s)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "hu":
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-Po/rho-u, ho-h
sol = fsolve(f, [rhoo, To], full_output=True)
rho, T = sol[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if sol[2] != 1 or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
vu = hoG-Ps/rhog
lu = hoL-Ps/rhol
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
hoL*(1-x)+hoG*x - h,
lu*(1-x)+vu*x - u)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "su":
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
so = self.R*(tau*(fiot+firt)-fio-fir)
Po = (1+delta*fird)*self.R*T*rho
return ho-Po/rho-u, so-s
sol = fsolve(f, [rhoo, To], full_output=True)
rho, T = sol[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if sol[2] != 1 or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
idealL = self._phi0(tau, deltaL)
fiot = idealL["fiot"]
fioL = idealL["fio"]
idealG = self._phi0(tau, deltaG)
fioG = idealG["fio"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
soL = self.R*(tau*(fiot+firtL)-fioL-firL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
soG = self.R*(tau*(fiot+firtG)-fioG-firG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
vu = hoG-Ps/rhog
lu = hoL-Ps/rhol
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
soL*(1-x)+soG*x - s,
lu*(1-x)+vu*x - u)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "Trho":
if T < self.Tc:
rhov = self._Vapor_Density(T)
rhol = self._Liquid_Density(T)
if rhol > rho > rhov:
rhol, rhov, Ps = self._saturation(T)
if rhol > rho > rhov:
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
x = (1/rho-1/rhol)/(1/rhov-1/rhol)
P = Ps/1000
rho = float(rho)
T = float(T)
propiedades = self._Helmholtz(rho, T)
if T > self.Tc:
x = 1
elif x is None:
x = 0
if not P:
P = propiedades["P"]/1000.
elif self._mode == "Tx":
# Check input T in saturation range
if self.Tt > T or self.Tc < T or x > 1 or x < 0:
raise NotImplementedError("Incoming out of bound")
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
if x == 0:
propiedades = liquido
elif x == 1:
propiedades = vapor
P = Ps/1000.
elif self._mode == "Px":
# Check input P in saturation range
if self.Pc < P or x > 1 or x < 0:
raise NotImplementedError("Incoming out of bound")
# Iterate over saturation routine to get T
def f(T):
rhol = self._Liquid_Density(T)
rhog = self._Vapor_Density(T)
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
tau = Tc/T
firL = _phir(tau, deltaL, self._constants)
firG = _phir(tau, deltaG, self._constants)
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(
firL-firG+log(deltaL/deltaG))
return Ps/1000-P
if T0:
To = T0
elif self.name == "water":
To = _TSat_P(P)
else:
To = (self.Tc+self.Tt)/2
T = fsolve(f, To)[0]
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
if x == 0:
propiedades = liquido
elif x == 1:
propiedades = vapor
self.T = T
self.Tr = T/self.Tc
self.P = P
self.Pr = self.P/self.Pc
self.x = x
if self._mode in ["Tx", "Px"] or 0 < x < 1:
region = 4
else:
region = 0
self.phase = getphase(self.Tc, self.Pc, self.T, self.P, self.x, region)
self.Liquid = _fase()
self.Gas = _fase()
if x == 0:
# liquid phase
self.fill(self.Liquid, propiedades)
self.fill(self, propiedades)
elif x == 1:
# vapor phase
self.fill(self.Gas, propiedades)
self.fill(self, propiedades)
else:
self.fill(self.Liquid, liquido)
self.fill(self.Gas, vapor)
self.v = x*self.Gas.v+(1-x)*self.Liquid.v
self.rho = 1./self.v
self.h = x*self.Gas.h+(1-x)*self.Liquid.h
self.s = x*self.Gas.s+(1-x)*self.Liquid.s
self.u = x*self.Gas.u+(1-x)*self.Liquid.u
self.a = x*self.Gas.a+(1-x)*self.Liquid.a
self.g = x*self.Gas.g+(1-x)*self.Liquid.g
self.Z = x*self.Gas.Z+(1-x)*self.Liquid.Z
self.f = x*self.Gas.f+(1-x)*self.Liquid.f
self.Z_rho = x*self.Gas.Z_rho+(1-x)*self.Liquid.Z_rho
self.IntP = x*self.Gas.IntP+(1-x)*self.Liquid.IntP
# Calculate special properties useful only for one phase
if self._mode in ("Px", "Tx") or (x < 1 and self.Tt <= T <= self.Tc):
self.sigma = self._surface(T)
else:
self.sigma = None
vir = self._virial(T)
self.virialB = vir["B"]/self.rhoc
self.virialC = vir["C"]/self.rhoc**2
if 0 < x < 1:
self.Hvap = vapor["h"]-liquido["h"]
self.Svap = vapor["s"]-liquido["s"]
else:
self.Hvap = None
self.Svap = None
self.invT = -1/self.T
# Ideal properties
cp0 = self._prop0(self.rho, self.T)
self.v0 = self.R*self.T/self.P/1000
self.rho0 = 1./self.v0
self.h0 = cp0.h
self.u0 = self.h0-self.P*self.v0
self.s0 = cp0.s
self.a0 = self.u0-self.T*self.s0
self.g0 = self.h0-self.T*self.s0
self.cp0 = cp0.cp
self.cv0 = cp0.cv
self.cp0_cv = self.cp0/self.cv0
cp0.v = self.v0
self.gamma0 = -self.v0/self.P/1000*self.derivative("P", "v", "s", cp0) | python | def calculo(self):
"""Calculate procedure"""
T = self.kwargs["T"]
rho = self.kwargs["rho"]
P = self.kwargs["P"]
s = self.kwargs["s"]
h = self.kwargs["h"]
u = self.kwargs["u"]
x = self.kwargs["x"]
# Initial values
T0 = self.kwargs["T0"]
rho0 = self.kwargs["rho0"]
if T0 or rho0:
To = T0
rhoo = rho0
elif self.name == "air":
To = 300
rhoo = 1e-3
else:
try:
st0 = IAPWS97(**self.kwargs)
except NotImplementedError:
To = 300
rhoo = 900
else:
if st0.status:
To = st0.T
rhoo = st0.rho
else:
To = 300
rhoo = 900
self.R = self._constants["R"]/self._constants.get("M", self.M)
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
propiedades = None
if self._mode not in ("Tx", "Px"):
# Method with iteration necessary to get x
if self._mode == "TP":
try:
if self.name == "air":
raise ValueError
st0 = IAPWS97(**self.kwargs)
rhoo = st0.rho
except NotImplementedError:
if rho0:
rhoo = rho0
elif T < self.Tc and P < self.Pc and \
self._Vapor_Pressure(T) < P:
rhoo = self._Liquid_Density(T)
elif T < self.Tc and P < self.Pc:
rhoo = self._Vapor_Density(T)
else:
rhoo = self.rhoc*3
except ValueError:
rhoo = 1e-3
def f(rho):
delta = rho/rhoc
tau = Tc/T
fird = _phird(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
return Po-P*1000
rho = fsolve(f, rhoo)[0]
# Calculate quality
if T > self.Tc:
x = 1
else:
Ps = self._Vapor_Pressure(T)
if Ps*0.95 < P < Ps*1.05:
rhol, rhov, Ps = self._saturation(T)
Ps *= 1e-3
if Ps > P:
x = 1
else:
x = 0
elif self._mode == "Th":
tau = Tc/T
ideal = self._phi0(tau, 1)
fiot = ideal["fiot"]
def f(rho):
delta = rho/rhoc
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-h
if T >= self.Tc:
rhoo = self.rhoc
rho = fsolve(f, rhoo)[0]
else:
x0 = self.kwargs["x0"]
rhov = self._Vapor_Density(T)
rhol = self._Liquid_Density(T)
deltaL = rhol/rhoc
deltaG = rhov/rhoc
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hl = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
hv = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
if x0 not in (0, 1) and hl <= h <= hv:
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
hv = vapor["h"]
hl = liquido["h"]
x = (h-hl)/(hv-hl)
rho = 1/(x/rhov+(1-x)/rhol)
P = Ps/1000
else:
if h > hv:
rhoo = rhov
else:
rhoo = rhol
rho = fsolve(f, rhoo)[0]
elif self._mode == "Ts":
tau = Tc/T
def f(rho):
if rho < 0:
rho = 1e-20
delta = rho/rhoc
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
so = self.R*(tau*(fiot+firt)-fio-fir)
return so-s
if T >= self.Tc:
rhoo = self.rhoc
rho = fsolve(f, rhoo)[0]
else:
rhov = self._Vapor_Density(T)
rhol = self._Liquid_Density(T)
deltaL = rhol/rhoc
deltaG = rhov/rhoc
idealL = self._phi0(tau, deltaL)
idealG = self._phi0(tau, deltaG)
fioL = idealL["fio"]
fioG = idealG["fio"]
fiot = idealL["fiot"]
firL = _phir(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
sl = self.R*(tau*(fiot+firtL)-fioL-firL)
firG = _phir(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
sv = self.R*(tau*(fiot+firtG)-fioG-firG)
if sl <= s <= sv:
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
sv = vapor["s"]
sl = liquido["s"]
x = (s-sl)/(sv-sl)
rho = 1/(x/rhov+(1-x)/rhol)
P = Ps/1000
else:
if s > sv:
rhoo = rhov
else:
rhoo = rhol
rho = fsolve(f, rhoo)[0]
elif self._mode == "Tu":
tau = Tc/T
ideal = self._phi0(tau, 1)
fiot = ideal["fiot"]
def f(rho):
delta = rho/rhoc
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-Po/rho-u
if T >= self.Tc:
rhoo = self.rhoc
rho = fsolve(f, rhoo)[0]
else:
rhov = self._Vapor_Density(T)
rhol = self._Liquid_Density(T)
deltaL = rhol/rhoc
deltaG = rhov/rhoc
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
PoL = (1+deltaL*firdL)*self.R*T*rhol
PoG = (1+deltaG*firdG)*self.R*T*rhov
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
uv = hoG-PoG/rhov
ul = hoL-PoL/rhol
if ul <= u <= uv:
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
uv = vapor["h"]-vapor["P"]/rhov
ul = liquido["h"]-liquido["P"]/rhol
x = (u-ul)/(uv-ul)
rho = 1/(x/rhov-(1-x)/rhol)
P = Ps/1000
else:
if u > uv:
rhoo = rhov
else:
rhoo = rhol
rho = fsolve(f, rhoo)[0]
elif self._mode == "Prho":
delta = rho/rhoc
def f(T):
tau = Tc/T
fird = _phird(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
return Po-P*1000
T = fsolve(f, To)[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == To or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
Ps - P*1000)
for to in [To, 300, 400, 500, 600]:
rhoLo = self._Liquid_Density(to)
rhoGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rhoLo, rhoGo], full_output=True)
T, rhoL, rhoG = sol[0]
x = (1./rho-1/rhoL)/(1/rhoG-1/rhoL)
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "Ph":
def funcion(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return Po-P*1000, ho-h
rho, T = fsolve(funcion, [rhoo, To])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rho == rhoo or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
hoL*(1-x)+hoG*x - h,
Ps - P*1000)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "Ps":
try:
x0 = st0.x
except NameError:
x0 = None
if x0 is None or x0 == 0 or x0 == 1:
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
so = self.R*(tau*(fiot+firt)-fio-fir)
return Po-P*1000, so-s
rho, T = fsolve(f, [rhoo, To])
else:
def funcion(parr):
rho, T = parr
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
x = (1./rho-1/rhol)/(1/rhov-1/rhol)
return Ps-P*1000, vapor["s"]*x+liquido["s"]*(1-x)-s
rho, T = fsolve(funcion, [2., 500.])
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
sv = vapor["s"]
sl = liquido["s"]
x = (s-sl)/(sv-sl)
elif self._mode == "Pu":
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-Po/rho-u, Po-P*1000
sol = fsolve(f, [rhoo, To], full_output=True)
rho, T = sol[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rho == rhoo or sol[2] != 1:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
vu = hoG-Ps/rhog
lu = hoL-Ps/rhol
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
lu*(1-x)+vu*x - u,
Ps - P*1000)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "rhoh":
delta = rho/rhoc
def f(T):
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-h
T = fsolve(f, To)[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == To or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
x = (1./rho-1/rhol)/(1/rhog-1/rhol)
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
hoL*(1-x)+hoG*x - h)
for to in [To, 300, 400, 500, 600]:
rhoLo = self._Liquid_Density(to)
rhoGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rhoLo, rhoGo], full_output=True)
T, rhoL, rhoG = sol[0]
x = (1./rho-1/rhoL)/(1/rhoG-1/rhoL)
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "rhos":
delta = rho/rhoc
def f(T):
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
so = self.R*(tau*(fiot+firt)-fio-fir)
return so-s
T = fsolve(f, To)[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == To or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
idealL = self._phi0(tau, deltaL)
fioL = idealL["fio"]
fiot = idealL["fiot"]
idealG = self._phi0(tau, deltaG)
fioG = idealG["fio"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
soL = self.R*(tau*(fiot+firtL)-fioL-firL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
soG = self.R*(tau*(fiot+firtG)-fioG-firG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
x = (1./rho-1/rhol)/(1/rhog-1/rhol)
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
soL*(1-x)+soG*x - s)
for to in [To, 300, 400, 500, 600]:
rhoLo = self._Liquid_Density(to)
rhoGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rhoLo, rhoGo], full_output=True)
T, rhoL, rhoG = sol[0]
x = (1./rho-1/rhoL)/(1/rhoG-1/rhoL)
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "rhou":
delta = rho/rhoc
def f(T):
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-Po/rho-u
T = fsolve(f, To)[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if T == To or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
x = (1./rho-1/rhol)/(1/rhog-1/rhol)
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
vu = hoG-Ps/rhog
lu = hoL-Ps/rhol
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
lu*(1-x)+vu*x - u)
for to in [To, 300, 400, 500, 600]:
rhoLo = self._Liquid_Density(to)
rhoGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rhoLo, rhoGo], full_output=True)
T, rhoL, rhoG = sol[0]
x = (1./rho-1/rhoL)/(1/rhoG-1/rhoL)
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "hs":
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
so = self.R*(tau*(fiot+firt)-fio-fir)
return ho-h, so-s
rho, T = fsolve(f, [rhoo, To])
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
idealL = self._phi0(tau, deltaL)
fiot = idealL["fiot"]
fioL = idealL["fio"]
idealG = self._phi0(tau, deltaG)
fioG = idealG["fio"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
soL = self.R*(tau*(fiot+firtL)-fioL-firL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
soG = self.R*(tau*(fiot+firtG)-fioG-firG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
hoL*(1-x)+hoG*x - h,
soL*(1-x)+soG*x - s)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "hu":
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
Po = (1+delta*fird)*self.R*T*rho
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
return ho-Po/rho-u, ho-h
sol = fsolve(f, [rhoo, To], full_output=True)
rho, T = sol[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if sol[2] != 1 or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
ideal = self._phi0(tau, deltaL)
fiot = ideal["fiot"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
vu = hoG-Ps/rhog
lu = hoL-Ps/rhol
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
hoL*(1-x)+hoG*x - h,
lu*(1-x)+vu*x - u)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "su":
def f(parr):
rho, T = parr
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fird = _phird(tau, delta, self._constants)
fir = _phir(tau, delta, self._constants)
firt = _phirt(tau, delta, self._constants)
ho = self.R*T*(1+tau*(fiot+firt)+delta*fird)
so = self.R*(tau*(fiot+firt)-fio-fir)
Po = (1+delta*fird)*self.R*T*rho
return ho-Po/rho-u, so-s
sol = fsolve(f, [rhoo, To], full_output=True)
rho, T = sol[0]
rhol = self._Liquid_Density(T)
rhov = self._Vapor_Density(T)
if sol[2] != 1 or rhov <= rho <= rhol:
def f(parr):
T, rhol, rhog, x = parr
tau = Tc/T
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
idealL = self._phi0(tau, deltaL)
fiot = idealL["fiot"]
fioL = idealL["fio"]
idealG = self._phi0(tau, deltaG)
fioG = idealG["fio"]
firL = _phir(tau, deltaL, self._constants)
firdL = _phird(tau, deltaL, self._constants)
firtL = _phirt(tau, deltaL, self._constants)
hoL = self.R*T*(1+tau*(fiot+firtL)+deltaL*firdL)
soL = self.R*(tau*(fiot+firtL)-fioL-firL)
firG = _phir(tau, deltaG, self._constants)
firdG = _phird(tau, deltaG, self._constants)
firtG = _phirt(tau, deltaG, self._constants)
hoG = self.R*T*(1+tau*(fiot+firtG)+deltaG*firdG)
soG = self.R*(tau*(fiot+firtG)-fioG-firG)
Jl = rhol*(1+deltaL*firdL)
Jv = rhog*(1+deltaG*firdG)
K = firL-firG
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(K+log(rhol/rhog))
vu = hoG-Ps/rhog
lu = hoL-Ps/rhol
return (Jl-Jv,
Jl*(1/rhog-1/rhol)-log(rhol/rhog)-K,
soL*(1-x)+soG*x - s,
lu*(1-x)+vu*x - u)
for to in [To, 300, 400, 500, 600]:
rLo = self._Liquid_Density(to)
rGo = self._Vapor_Density(to)
sol = fsolve(f, [to, rLo, rGo, 0.5], full_output=True)
T, rhoL, rhoG, x = sol[0]
if sol[2] == 1 and 0 <= x <= 1 and \
sum(abs(sol[1]["fvec"])) < 1e-5:
break
if sum(abs(sol[1]["fvec"])) > 1e-5:
raise(RuntimeError(sol[3]))
liquido = self._Helmholtz(rhoL, T)
vapor = self._Helmholtz(rhoG, T)
P = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(
liquido["fir"]-vapor["fir"]+log(rhoL/rhoG))/1000
elif self._mode == "Trho":
if T < self.Tc:
rhov = self._Vapor_Density(T)
rhol = self._Liquid_Density(T)
if rhol > rho > rhov:
rhol, rhov, Ps = self._saturation(T)
if rhol > rho > rhov:
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
x = (1/rho-1/rhol)/(1/rhov-1/rhol)
P = Ps/1000
rho = float(rho)
T = float(T)
propiedades = self._Helmholtz(rho, T)
if T > self.Tc:
x = 1
elif x is None:
x = 0
if not P:
P = propiedades["P"]/1000.
elif self._mode == "Tx":
# Check input T in saturation range
if self.Tt > T or self.Tc < T or x > 1 or x < 0:
raise NotImplementedError("Incoming out of bound")
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
if x == 0:
propiedades = liquido
elif x == 1:
propiedades = vapor
P = Ps/1000.
elif self._mode == "Px":
# Check input P in saturation range
if self.Pc < P or x > 1 or x < 0:
raise NotImplementedError("Incoming out of bound")
# Iterate over saturation routine to get T
def f(T):
rhol = self._Liquid_Density(T)
rhog = self._Vapor_Density(T)
deltaL = rhol/self.rhoc
deltaG = rhog/self.rhoc
tau = Tc/T
firL = _phir(tau, deltaL, self._constants)
firG = _phir(tau, deltaG, self._constants)
Ps = self.R*T*rhol*rhog/(rhol-rhog)*(
firL-firG+log(deltaL/deltaG))
return Ps/1000-P
if T0:
To = T0
elif self.name == "water":
To = _TSat_P(P)
else:
To = (self.Tc+self.Tt)/2
T = fsolve(f, To)[0]
rhol, rhov, Ps = self._saturation(T)
vapor = self._Helmholtz(rhov, T)
liquido = self._Helmholtz(rhol, T)
if x == 0:
propiedades = liquido
elif x == 1:
propiedades = vapor
self.T = T
self.Tr = T/self.Tc
self.P = P
self.Pr = self.P/self.Pc
self.x = x
if self._mode in ["Tx", "Px"] or 0 < x < 1:
region = 4
else:
region = 0
self.phase = getphase(self.Tc, self.Pc, self.T, self.P, self.x, region)
self.Liquid = _fase()
self.Gas = _fase()
if x == 0:
# liquid phase
self.fill(self.Liquid, propiedades)
self.fill(self, propiedades)
elif x == 1:
# vapor phase
self.fill(self.Gas, propiedades)
self.fill(self, propiedades)
else:
self.fill(self.Liquid, liquido)
self.fill(self.Gas, vapor)
self.v = x*self.Gas.v+(1-x)*self.Liquid.v
self.rho = 1./self.v
self.h = x*self.Gas.h+(1-x)*self.Liquid.h
self.s = x*self.Gas.s+(1-x)*self.Liquid.s
self.u = x*self.Gas.u+(1-x)*self.Liquid.u
self.a = x*self.Gas.a+(1-x)*self.Liquid.a
self.g = x*self.Gas.g+(1-x)*self.Liquid.g
self.Z = x*self.Gas.Z+(1-x)*self.Liquid.Z
self.f = x*self.Gas.f+(1-x)*self.Liquid.f
self.Z_rho = x*self.Gas.Z_rho+(1-x)*self.Liquid.Z_rho
self.IntP = x*self.Gas.IntP+(1-x)*self.Liquid.IntP
# Calculate special properties useful only for one phase
if self._mode in ("Px", "Tx") or (x < 1 and self.Tt <= T <= self.Tc):
self.sigma = self._surface(T)
else:
self.sigma = None
vir = self._virial(T)
self.virialB = vir["B"]/self.rhoc
self.virialC = vir["C"]/self.rhoc**2
if 0 < x < 1:
self.Hvap = vapor["h"]-liquido["h"]
self.Svap = vapor["s"]-liquido["s"]
else:
self.Hvap = None
self.Svap = None
self.invT = -1/self.T
# Ideal properties
cp0 = self._prop0(self.rho, self.T)
self.v0 = self.R*self.T/self.P/1000
self.rho0 = 1./self.v0
self.h0 = cp0.h
self.u0 = self.h0-self.P*self.v0
self.s0 = cp0.s
self.a0 = self.u0-self.T*self.s0
self.g0 = self.h0-self.T*self.s0
self.cp0 = cp0.cp
self.cv0 = cp0.cv
self.cp0_cv = self.cp0/self.cv0
cp0.v = self.v0
self.gamma0 = -self.v0/self.P/1000*self.derivative("P", "v", "s", cp0) | Calculate procedure | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L473-L1477 |
jjgomera/iapws | iapws/iapws95.py | MEoS.fill | def fill(self, fase, estado):
"""Fill phase properties"""
fase.rho = estado["rho"]
fase.v = 1/fase.rho
fase.h = estado["h"]
fase.s = estado["s"]
fase.u = fase.h-self.P*1000*fase.v
fase.a = fase.u-self.T*fase.s
fase.g = fase.h-self.T*fase.s
fase.Z = self.P*fase.v/self.T/self.R*1e3
fase.fi = exp(estado["fir"]+estado["delta"]*estado["fird"] -
log(1+estado["delta"]*estado["fird"]))
fase.f = fase.fi*self.P
fase.cv = estado["cv"]
fase.rhoM = fase.rho/self.M
fase.hM = fase.h*self.M
fase.sM = fase.s*self.M
fase.uM = fase.u*self.M
fase.aM = fase.a*self.M
fase.gM = fase.g*self.M
fase.alfap = estado["alfap"]
fase.betap = estado["betap"]
fase.cp = self.derivative("h", "T", "P", fase)
fase.cp_cv = fase.cp/fase.cv
fase.w = (self.derivative("P", "rho", "s", fase)*1000)**0.5
fase.cvM = fase.cv*self.M
fase.cpM = fase.cp*self.M
fase.joule = self.derivative("T", "P", "h", fase)*1e3
fase.Gruneisen = fase.v/fase.cv*self.derivative("P", "T", "v", fase)
fase.alfav = self.derivative("v", "T", "P", fase)/fase.v
fase.kappa = -self.derivative("v", "P", "T", fase)/fase.v*1e3
fase.betas = self.derivative("T", "P", "s", fase)
fase.gamma = -fase.v/self.P*self.derivative("P", "v", "s", fase)*1e-3
fase.kt = -fase.v/self.P*self.derivative("P", "v", "T", fase)*1e-3
fase.ks = -self.derivative("v", "P", "s", fase)/fase.v*1e3
fase.Kt = -fase.v*self.derivative("P", "v", "s", fase)*1e-3
fase.Ks = -fase.v*self.derivative("P", "v", "T", fase)*1e-3
fase.dhdT_rho = self.derivative("h", "T", "rho", fase)
fase.dhdT_P = self.derivative("h", "T", "P", fase)
fase.dhdP_T = self.derivative("h", "P", "T", fase)*1e3
fase.dhdP_rho = self.derivative("h", "P", "rho", fase)*1e3
fase.dhdrho_T = self.derivative("h", "rho", "T", fase)
fase.dhdrho_P = self.derivative("h", "rho", "P", fase)
fase.dpdT_rho = self.derivative("P", "T", "rho", fase)*1e-3
fase.dpdrho_T = self.derivative("P", "rho", "T", fase)*1e-3
fase.drhodP_T = self.derivative("rho", "P", "T", fase)*1e3
fase.drhodT_P = self.derivative("rho", "T", "P", fase)
fase.Z_rho = (fase.Z-1)/fase.rho
fase.IntP = self.T*self.derivative("P", "T", "rho", fase)*1e-3-self.P
fase.hInput = fase.v*self.derivative("h", "v", "P", fase)
fase.mu = self._visco(fase.rho, self.T, fase)
fase.k = self._thermo(fase.rho, self.T, fase)
fase.nu = fase.mu/fase.rho
fase.alfa = fase.k/1000/fase.rho/fase.cp
fase.Prandt = fase.mu*fase.cp*1000/fase.k
if self.name == "water":
try:
fase.epsilon = _Dielectric(fase.rho, self.T)
except NotImplementedError:
fase.epsilon = None
try:
fase.n = _Refractive(fase.rho, self.T, self.kwargs["l"])
except NotImplementedError:
fase.n = None
else:
fase.epsilon = None
fase.n = None | python | def fill(self, fase, estado):
"""Fill phase properties"""
fase.rho = estado["rho"]
fase.v = 1/fase.rho
fase.h = estado["h"]
fase.s = estado["s"]
fase.u = fase.h-self.P*1000*fase.v
fase.a = fase.u-self.T*fase.s
fase.g = fase.h-self.T*fase.s
fase.Z = self.P*fase.v/self.T/self.R*1e3
fase.fi = exp(estado["fir"]+estado["delta"]*estado["fird"] -
log(1+estado["delta"]*estado["fird"]))
fase.f = fase.fi*self.P
fase.cv = estado["cv"]
fase.rhoM = fase.rho/self.M
fase.hM = fase.h*self.M
fase.sM = fase.s*self.M
fase.uM = fase.u*self.M
fase.aM = fase.a*self.M
fase.gM = fase.g*self.M
fase.alfap = estado["alfap"]
fase.betap = estado["betap"]
fase.cp = self.derivative("h", "T", "P", fase)
fase.cp_cv = fase.cp/fase.cv
fase.w = (self.derivative("P", "rho", "s", fase)*1000)**0.5
fase.cvM = fase.cv*self.M
fase.cpM = fase.cp*self.M
fase.joule = self.derivative("T", "P", "h", fase)*1e3
fase.Gruneisen = fase.v/fase.cv*self.derivative("P", "T", "v", fase)
fase.alfav = self.derivative("v", "T", "P", fase)/fase.v
fase.kappa = -self.derivative("v", "P", "T", fase)/fase.v*1e3
fase.betas = self.derivative("T", "P", "s", fase)
fase.gamma = -fase.v/self.P*self.derivative("P", "v", "s", fase)*1e-3
fase.kt = -fase.v/self.P*self.derivative("P", "v", "T", fase)*1e-3
fase.ks = -self.derivative("v", "P", "s", fase)/fase.v*1e3
fase.Kt = -fase.v*self.derivative("P", "v", "s", fase)*1e-3
fase.Ks = -fase.v*self.derivative("P", "v", "T", fase)*1e-3
fase.dhdT_rho = self.derivative("h", "T", "rho", fase)
fase.dhdT_P = self.derivative("h", "T", "P", fase)
fase.dhdP_T = self.derivative("h", "P", "T", fase)*1e3
fase.dhdP_rho = self.derivative("h", "P", "rho", fase)*1e3
fase.dhdrho_T = self.derivative("h", "rho", "T", fase)
fase.dhdrho_P = self.derivative("h", "rho", "P", fase)
fase.dpdT_rho = self.derivative("P", "T", "rho", fase)*1e-3
fase.dpdrho_T = self.derivative("P", "rho", "T", fase)*1e-3
fase.drhodP_T = self.derivative("rho", "P", "T", fase)*1e3
fase.drhodT_P = self.derivative("rho", "T", "P", fase)
fase.Z_rho = (fase.Z-1)/fase.rho
fase.IntP = self.T*self.derivative("P", "T", "rho", fase)*1e-3-self.P
fase.hInput = fase.v*self.derivative("h", "v", "P", fase)
fase.mu = self._visco(fase.rho, self.T, fase)
fase.k = self._thermo(fase.rho, self.T, fase)
fase.nu = fase.mu/fase.rho
fase.alfa = fase.k/1000/fase.rho/fase.cp
fase.Prandt = fase.mu*fase.cp*1000/fase.k
if self.name == "water":
try:
fase.epsilon = _Dielectric(fase.rho, self.T)
except NotImplementedError:
fase.epsilon = None
try:
fase.n = _Refractive(fase.rho, self.T, self.kwargs["l"])
except NotImplementedError:
fase.n = None
else:
fase.epsilon = None
fase.n = None | Fill phase properties | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L1479-L1555 |
jjgomera/iapws | iapws/iapws95.py | MEoS.derivative | def derivative(self, z, x, y, fase):
"""Wrapper derivative for custom derived properties
where x, y, z can be: P, T, v, rho, u, h, s, g, a"""
return deriv_H(self, z, x, y, fase) | python | def derivative(self, z, x, y, fase):
"""Wrapper derivative for custom derived properties
where x, y, z can be: P, T, v, rho, u, h, s, g, a"""
return deriv_H(self, z, x, y, fase) | Wrapper derivative for custom derived properties
where x, y, z can be: P, T, v, rho, u, h, s, g, a | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L1557-L1560 |
jjgomera/iapws | iapws/iapws95.py | MEoS._saturation | def _saturation(self, T):
"""Saturation calculation for two phase search"""
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
if T > Tc:
T = Tc
tau = Tc/T
rhoLo = self._Liquid_Density(T)
rhoGo = self._Vapor_Density(T)
def f(parr):
rhol, rhog = parr
deltaL = rhol/rhoc
deltaG = rhog/rhoc
phirL = _phir(tau, deltaL, self._constants)
phirG = _phir(tau, deltaG, self._constants)
phirdL = _phird(tau, deltaL, self._constants)
phirdG = _phird(tau, deltaG, self._constants)
Jl = deltaL*(1+deltaL*phirdL)
Jv = deltaG*(1+deltaG*phirdG)
Kl = deltaL*phirdL+phirL+log(deltaL)
Kv = deltaG*phirdG+phirG+log(deltaG)
return Kv-Kl, Jv-Jl
rhoL, rhoG = fsolve(f, [rhoLo, rhoGo])
if rhoL == rhoG:
Ps = self.Pc
else:
deltaL = rhoL/self.rhoc
deltaG = rhoG/self.rhoc
firL = _phir(tau, deltaL, self._constants)
firG = _phir(tau, deltaG, self._constants)
Ps = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(firL-firG+log(deltaL/deltaG))
return rhoL, rhoG, Ps | python | def _saturation(self, T):
"""Saturation calculation for two phase search"""
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
if T > Tc:
T = Tc
tau = Tc/T
rhoLo = self._Liquid_Density(T)
rhoGo = self._Vapor_Density(T)
def f(parr):
rhol, rhog = parr
deltaL = rhol/rhoc
deltaG = rhog/rhoc
phirL = _phir(tau, deltaL, self._constants)
phirG = _phir(tau, deltaG, self._constants)
phirdL = _phird(tau, deltaL, self._constants)
phirdG = _phird(tau, deltaG, self._constants)
Jl = deltaL*(1+deltaL*phirdL)
Jv = deltaG*(1+deltaG*phirdG)
Kl = deltaL*phirdL+phirL+log(deltaL)
Kv = deltaG*phirdG+phirG+log(deltaG)
return Kv-Kl, Jv-Jl
rhoL, rhoG = fsolve(f, [rhoLo, rhoGo])
if rhoL == rhoG:
Ps = self.Pc
else:
deltaL = rhoL/self.rhoc
deltaG = rhoG/self.rhoc
firL = _phir(tau, deltaL, self._constants)
firG = _phir(tau, deltaG, self._constants)
Ps = self.R*T*rhoL*rhoG/(rhoL-rhoG)*(firL-firG+log(deltaL/deltaG))
return rhoL, rhoG, Ps | Saturation calculation for two phase search | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L1562-L1598 |
jjgomera/iapws | iapws/iapws95.py | MEoS._Helmholtz | def _Helmholtz(self, rho, T):
"""Calculated properties from helmholtz free energy and derivatives
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dictionary with calculated properties:
* fir: [-]
* fird: ∂fir/∂δ|τ
* firdd: ∂²fir/∂δ²|τ
* delta: Reducen density rho/rhoc, [-]
* P: Pressure, [kPa]
* h: Enthalpy, [kJ/kg]
* s: Entropy, [kJ/kgK]
* cv: Isochoric specific heat, [kJ/kgK]
* alfav: Thermal expansion coefficient, [1/K]
* betap: Isothermal compressibility, [1/kPa]
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 3
http://www.iapws.org/relguide/IAPWS-95.html
"""
if isinstance(rho, ndarray):
rho = rho[0]
if isinstance(T, ndarray):
T = T[0]
if rho < 0:
rho = 1e-20
if T < 50:
T = 50
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fiott = ideal["fiott"]
res = self._phir(tau, delta)
fir = res["fir"]
firt = res["firt"]
firtt = res["firtt"]
fird = res["fird"]
firdd = res["firdd"]
firdt = res["firdt"]
propiedades = {}
propiedades["fir"] = fir
propiedades["fird"] = fird
propiedades["firdd"] = firdd
propiedades["delta"] = delta
propiedades["rho"] = rho
propiedades["P"] = (1+delta*fird)*self.R*T*rho
propiedades["h"] = self.R*T*(1+tau*(fiot+firt)+delta*fird)
propiedades["s"] = self.R*(tau*(fiot+firt)-fio-fir)
propiedades["cv"] = -self.R*tau**2*(fiott+firtt)
propiedades["alfap"] = (1-delta*tau*firdt/(1+delta*fird))/T
propiedades["betap"] = rho*(
1+(delta*fird+delta**2*firdd)/(1+delta*fird))
return propiedades | python | def _Helmholtz(self, rho, T):
"""Calculated properties from helmholtz free energy and derivatives
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dictionary with calculated properties:
* fir: [-]
* fird: ∂fir/∂δ|τ
* firdd: ∂²fir/∂δ²|τ
* delta: Reducen density rho/rhoc, [-]
* P: Pressure, [kPa]
* h: Enthalpy, [kJ/kg]
* s: Entropy, [kJ/kgK]
* cv: Isochoric specific heat, [kJ/kgK]
* alfav: Thermal expansion coefficient, [1/K]
* betap: Isothermal compressibility, [1/kPa]
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 3
http://www.iapws.org/relguide/IAPWS-95.html
"""
if isinstance(rho, ndarray):
rho = rho[0]
if isinstance(T, ndarray):
T = T[0]
if rho < 0:
rho = 1e-20
if T < 50:
T = 50
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fiott = ideal["fiott"]
res = self._phir(tau, delta)
fir = res["fir"]
firt = res["firt"]
firtt = res["firtt"]
fird = res["fird"]
firdd = res["firdd"]
firdt = res["firdt"]
propiedades = {}
propiedades["fir"] = fir
propiedades["fird"] = fird
propiedades["firdd"] = firdd
propiedades["delta"] = delta
propiedades["rho"] = rho
propiedades["P"] = (1+delta*fird)*self.R*T*rho
propiedades["h"] = self.R*T*(1+tau*(fiot+firt)+delta*fird)
propiedades["s"] = self.R*(tau*(fiot+firt)-fio-fir)
propiedades["cv"] = -self.R*tau**2*(fiott+firtt)
propiedades["alfap"] = (1-delta*tau*firdt/(1+delta*fird))/T
propiedades["betap"] = rho*(
1+(delta*fird+delta**2*firdd)/(1+delta*fird))
return propiedades | Calculated properties from helmholtz free energy and derivatives
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dictionary with calculated properties:
* fir: [-]
* fird: ∂fir/∂δ|τ
* firdd: ∂²fir/∂δ²|τ
* delta: Reducen density rho/rhoc, [-]
* P: Pressure, [kPa]
* h: Enthalpy, [kJ/kg]
* s: Entropy, [kJ/kgK]
* cv: Isochoric specific heat, [kJ/kgK]
* alfav: Thermal expansion coefficient, [1/K]
* betap: Isothermal compressibility, [1/kPa]
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 3
http://www.iapws.org/relguide/IAPWS-95.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L1600-L1671 |
jjgomera/iapws | iapws/iapws95.py | MEoS._prop0 | def _prop0(self, rho, T):
"""Ideal gas properties"""
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fiott = ideal["fiott"]
propiedades = _fase()
propiedades.h = self.R*T*(1+tau*fiot)
propiedades.s = self.R*(tau*fiot-fio)
propiedades.cv = -self.R*tau**2*fiott
propiedades.cp = self.R*(-tau**2*fiott+1)
propiedades.alfap = 1/T
propiedades.betap = rho
return propiedades | python | def _prop0(self, rho, T):
"""Ideal gas properties"""
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fiott = ideal["fiott"]
propiedades = _fase()
propiedades.h = self.R*T*(1+tau*fiot)
propiedades.s = self.R*(tau*fiot-fio)
propiedades.cv = -self.R*tau**2*fiott
propiedades.cp = self.R*(-tau**2*fiott+1)
propiedades.alfap = 1/T
propiedades.betap = rho
return propiedades | Ideal gas properties | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L1673-L1691 |
jjgomera/iapws | iapws/iapws95.py | MEoS._phi0 | def _phi0(self, tau, delta):
"""Ideal gas Helmholtz free energy and derivatives
Parameters
----------
tau : float
Inverse reduced temperature Tc/T, [-]
delta : float
Reduced density rho/rhoc, [-]
Returns
-------
prop : dictionary with ideal adimensional helmholtz energy and deriv
fio, [-]
fiot: ∂fio/∂τ|δ
fiod: ∂fio/∂δ|τ
fiott: ∂²fio/∂τ²|δ
fiodt: ∂²fio/∂τ∂δ
fiodd: ∂²fio/∂δ²|τ
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 4
http://www.iapws.org/relguide/IAPWS-95.html
"""
Fi0 = self.Fi0
fio = Fi0["ao_log"][0]*log(delta)+Fi0["ao_log"][1]*log(tau)
fiot = +Fi0["ao_log"][1]/tau
fiott = -Fi0["ao_log"][1]/tau**2
fiod = 1/delta
fiodd = -1/delta**2
fiodt = 0
for n, t in zip(Fi0["ao_pow"], Fi0["pow"]):
fio += n*tau**t
if t != 0:
fiot += t*n*tau**(t-1)
if t not in [0, 1]:
fiott += n*t*(t-1)*tau**(t-2)
for n, t in zip(Fi0["ao_exp"], Fi0["titao"]):
fio += n*log(1-exp(-tau*t))
fiot += n*t*((1-exp(-t*tau))**-1-1)
fiott -= n*t**2*exp(-t*tau)*(1-exp(-t*tau))**-2
# Extension to especial terms of air
if "ao_exp2" in Fi0:
for n, g, C in zip(Fi0["ao_exp2"], Fi0["titao2"], Fi0["sum2"]):
fio += n*log(C+exp(g*tau))
fiot += n*g/(C*exp(-g*tau)+1)
fiott += C*n*g**2*exp(-g*tau)/(C*exp(-g*tau)+1)**2
prop = {}
prop["fio"] = fio
prop["fiot"] = fiot
prop["fiott"] = fiott
prop["fiod"] = fiod
prop["fiodd"] = fiodd
prop["fiodt"] = fiodt
return prop | python | def _phi0(self, tau, delta):
"""Ideal gas Helmholtz free energy and derivatives
Parameters
----------
tau : float
Inverse reduced temperature Tc/T, [-]
delta : float
Reduced density rho/rhoc, [-]
Returns
-------
prop : dictionary with ideal adimensional helmholtz energy and deriv
fio, [-]
fiot: ∂fio/∂τ|δ
fiod: ∂fio/∂δ|τ
fiott: ∂²fio/∂τ²|δ
fiodt: ∂²fio/∂τ∂δ
fiodd: ∂²fio/∂δ²|τ
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 4
http://www.iapws.org/relguide/IAPWS-95.html
"""
Fi0 = self.Fi0
fio = Fi0["ao_log"][0]*log(delta)+Fi0["ao_log"][1]*log(tau)
fiot = +Fi0["ao_log"][1]/tau
fiott = -Fi0["ao_log"][1]/tau**2
fiod = 1/delta
fiodd = -1/delta**2
fiodt = 0
for n, t in zip(Fi0["ao_pow"], Fi0["pow"]):
fio += n*tau**t
if t != 0:
fiot += t*n*tau**(t-1)
if t not in [0, 1]:
fiott += n*t*(t-1)*tau**(t-2)
for n, t in zip(Fi0["ao_exp"], Fi0["titao"]):
fio += n*log(1-exp(-tau*t))
fiot += n*t*((1-exp(-t*tau))**-1-1)
fiott -= n*t**2*exp(-t*tau)*(1-exp(-t*tau))**-2
# Extension to especial terms of air
if "ao_exp2" in Fi0:
for n, g, C in zip(Fi0["ao_exp2"], Fi0["titao2"], Fi0["sum2"]):
fio += n*log(C+exp(g*tau))
fiot += n*g/(C*exp(-g*tau)+1)
fiott += C*n*g**2*exp(-g*tau)/(C*exp(-g*tau)+1)**2
prop = {}
prop["fio"] = fio
prop["fiot"] = fiot
prop["fiott"] = fiott
prop["fiod"] = fiod
prop["fiodd"] = fiodd
prop["fiodt"] = fiodt
return prop | Ideal gas Helmholtz free energy and derivatives
Parameters
----------
tau : float
Inverse reduced temperature Tc/T, [-]
delta : float
Reduced density rho/rhoc, [-]
Returns
-------
prop : dictionary with ideal adimensional helmholtz energy and deriv
fio, [-]
fiot: ∂fio/∂τ|δ
fiod: ∂fio/∂δ|τ
fiott: ∂²fio/∂τ²|δ
fiodt: ∂²fio/∂τ∂δ
fiodd: ∂²fio/∂δ²|τ
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 4
http://www.iapws.org/relguide/IAPWS-95.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L1693-L1756 |
jjgomera/iapws | iapws/iapws95.py | MEoS._phir | def _phir(self, tau, delta):
"""Residual contribution to the free Helmholtz energy
Parameters
----------
tau : float
Inverse reduced temperature Tc/T, [-]
delta : float
Reduced density rho/rhoc, [-]
Returns
-------
prop : dict
Dictionary with residual adimensional helmholtz energy and deriv:
* fir
* firt: ∂fir/∂τ|δ,x
* fird: ∂fir/∂δ|τ,x
* firtt: ∂²fir/∂τ²|δ,x
* firdt: ∂²fir/∂τ∂δ|x
* firdd: ∂²fir/∂δ²|τ,x
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 5
http://www.iapws.org/relguide/IAPWS-95.html
"""
fir = fird = firdd = firt = firtt = firdt = 0
# Polinomial terms
nr1 = self._constants.get("nr1", [])
d1 = self._constants.get("d1", [])
t1 = self._constants.get("t1", [])
for n, d, t in zip(nr1, d1, t1):
fir += n*delta**d*tau**t
fird += n*d*delta**(d-1)*tau**t
firdd += n*d*(d-1)*delta**(d-2)*tau**t
firt += n*t*delta**d*tau**(t-1)
firtt += n*t*(t-1)*delta**d*tau**(t-2)
firdt += n*t*d*delta**(d-1)*tau**(t-1)
# Exponential terms
nr2 = self._constants.get("nr2", [])
d2 = self._constants.get("d2", [])
g2 = self._constants.get("gamma2", [])
t2 = self._constants.get("t2", [])
c2 = self._constants.get("c2", [])
for n, d, g, t, c in zip(nr2, d2, g2, t2, c2):
fir += n*delta**d*tau**t*exp(-g*delta**c)
fird += n*exp(-g*delta**c)*delta**(d-1)*tau**t*(d-g*c*delta**c)
firdd += n*exp(-g*delta**c)*delta**(d-2)*tau**t * \
((d-g*c*delta**c)*(d-1-g*c*delta**c)-g**2*c**2*delta**c)
firt += n*t*delta**d*tau**(t-1)*exp(-g*delta**c)
firtt += n*t*(t-1)*delta**d*tau**(t-2)*exp(-g*delta**c)
firdt += n*t*delta**(d-1)*tau**(t-1)*(d-g*c*delta**c)*exp(
-g*delta**c)
# Gaussian terms
nr3 = self._constants.get("nr3", [])
d3 = self._constants.get("d3", [])
t3 = self._constants.get("t3", [])
a3 = self._constants.get("alfa3", [])
e3 = self._constants.get("epsilon3", [])
b3 = self._constants.get("beta3", [])
g3 = self._constants.get("gamma3", [])
for n, d, t, a, e, b, g in zip(nr3, d3, t3, a3, e3, b3, g3):
fir += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)
fird += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
d/delta-2*a*(delta-e))
firdd += n*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
-2*a*delta**d + 4*a**2*delta**d*(delta-e)**2 -
4*d*a*delta**(d-1)*(delta-e) + d*(d-1)*delta**(d-2))
firt += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
t/tau-2*b*(tau-g))
firtt += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
(t/tau-2*b*(tau-g))**2-t/tau**2-2*b)
firdt += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
t/tau-2*b*(tau-g))*(d/delta-2*a*(delta-e))
# Non analitic terms
nr4 = self._constants.get("nr4", [])
a4 = self._constants.get("a4", [])
b4 = self._constants.get("b4", [])
Ai = self._constants.get("A", [])
Bi = self._constants.get("B", [])
Ci = self._constants.get("C", [])
Di = self._constants.get("D", [])
bt4 = self._constants.get("beta4", [])
for n, a, b, A, B, C, D, bt in zip(nr4, a4, b4, Ai, Bi, Ci, Di, bt4):
Tita = (1-tau)+A*((delta-1)**2)**(0.5/bt)
F = exp(-C*(delta-1)**2-D*(tau-1)**2)
Fd = -2*C*F*(delta-1)
Fdd = 2*C*F*(2*C*(delta-1)**2-1)
Ft = -2*D*F*(tau-1)
Ftt = 2*D*F*(2*D*(tau-1)**2-1)
Fdt = 4*C*D*F*(delta-1)*(tau-1)
Delta = Tita**2+B*((delta-1)**2)**a
Deltad = (delta-1)*(A*Tita*2/bt*((delta-1)**2)**(0.5/bt-1) +
2*B*a*((delta-1)**2)**(a-1))
if delta == 1:
Deltadd = 0
else:
Deltadd = Deltad/(delta-1)+(delta-1)**2*(
4*B*a*(a-1)*((delta-1)**2)**(a-2) +
2*A**2/bt**2*(((delta-1)**2)**(0.5/bt-1))**2 +
A*Tita*4/bt*(0.5/bt-1)*((delta-1)**2)**(0.5/bt-2))
DeltaBd = b*Delta**(b-1)*Deltad
DeltaBdd = b*(Delta**(b-1)*Deltadd+(b-1)*Delta**(b-2)*Deltad**2)
DeltaBt = -2*Tita*b*Delta**(b-1)
DeltaBtt = 2*b*Delta**(b-1)+4*Tita**2*b*(b-1)*Delta**(b-2)
DeltaBdt = -A*b*2/bt*Delta**(b-1)*(delta-1)*((delta-1)**2)**(
0.5/bt-1)-2*Tita*b*(b-1)*Delta**(b-2)*Deltad
fir += n*Delta**b*delta*F
fird += n*(Delta**b*(F+delta*Fd)+DeltaBd*delta*F)
firdd += n*(Delta**b*(2*Fd+delta*Fdd) + 2*DeltaBd*(F+delta*Fd) +
DeltaBdd*delta*F)
firt += n*delta*(DeltaBt*F+Delta**b*Ft)
firtt += n*delta*(DeltaBtt*F+2*DeltaBt*Ft+Delta**b*Ftt)
firdt += n*(Delta**b*(Ft+delta*Fdt)+delta*DeltaBd*Ft +
DeltaBt*(F+delta*Fd)+DeltaBdt*delta*F)
prop = {}
prop["fir"] = fir
prop["firt"] = firt
prop["firtt"] = firtt
prop["fird"] = fird
prop["firdd"] = firdd
prop["firdt"] = firdt
return prop | python | def _phir(self, tau, delta):
"""Residual contribution to the free Helmholtz energy
Parameters
----------
tau : float
Inverse reduced temperature Tc/T, [-]
delta : float
Reduced density rho/rhoc, [-]
Returns
-------
prop : dict
Dictionary with residual adimensional helmholtz energy and deriv:
* fir
* firt: ∂fir/∂τ|δ,x
* fird: ∂fir/∂δ|τ,x
* firtt: ∂²fir/∂τ²|δ,x
* firdt: ∂²fir/∂τ∂δ|x
* firdd: ∂²fir/∂δ²|τ,x
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 5
http://www.iapws.org/relguide/IAPWS-95.html
"""
fir = fird = firdd = firt = firtt = firdt = 0
# Polinomial terms
nr1 = self._constants.get("nr1", [])
d1 = self._constants.get("d1", [])
t1 = self._constants.get("t1", [])
for n, d, t in zip(nr1, d1, t1):
fir += n*delta**d*tau**t
fird += n*d*delta**(d-1)*tau**t
firdd += n*d*(d-1)*delta**(d-2)*tau**t
firt += n*t*delta**d*tau**(t-1)
firtt += n*t*(t-1)*delta**d*tau**(t-2)
firdt += n*t*d*delta**(d-1)*tau**(t-1)
# Exponential terms
nr2 = self._constants.get("nr2", [])
d2 = self._constants.get("d2", [])
g2 = self._constants.get("gamma2", [])
t2 = self._constants.get("t2", [])
c2 = self._constants.get("c2", [])
for n, d, g, t, c in zip(nr2, d2, g2, t2, c2):
fir += n*delta**d*tau**t*exp(-g*delta**c)
fird += n*exp(-g*delta**c)*delta**(d-1)*tau**t*(d-g*c*delta**c)
firdd += n*exp(-g*delta**c)*delta**(d-2)*tau**t * \
((d-g*c*delta**c)*(d-1-g*c*delta**c)-g**2*c**2*delta**c)
firt += n*t*delta**d*tau**(t-1)*exp(-g*delta**c)
firtt += n*t*(t-1)*delta**d*tau**(t-2)*exp(-g*delta**c)
firdt += n*t*delta**(d-1)*tau**(t-1)*(d-g*c*delta**c)*exp(
-g*delta**c)
# Gaussian terms
nr3 = self._constants.get("nr3", [])
d3 = self._constants.get("d3", [])
t3 = self._constants.get("t3", [])
a3 = self._constants.get("alfa3", [])
e3 = self._constants.get("epsilon3", [])
b3 = self._constants.get("beta3", [])
g3 = self._constants.get("gamma3", [])
for n, d, t, a, e, b, g in zip(nr3, d3, t3, a3, e3, b3, g3):
fir += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)
fird += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
d/delta-2*a*(delta-e))
firdd += n*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
-2*a*delta**d + 4*a**2*delta**d*(delta-e)**2 -
4*d*a*delta**(d-1)*(delta-e) + d*(d-1)*delta**(d-2))
firt += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
t/tau-2*b*(tau-g))
firtt += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
(t/tau-2*b*(tau-g))**2-t/tau**2-2*b)
firdt += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
t/tau-2*b*(tau-g))*(d/delta-2*a*(delta-e))
# Non analitic terms
nr4 = self._constants.get("nr4", [])
a4 = self._constants.get("a4", [])
b4 = self._constants.get("b4", [])
Ai = self._constants.get("A", [])
Bi = self._constants.get("B", [])
Ci = self._constants.get("C", [])
Di = self._constants.get("D", [])
bt4 = self._constants.get("beta4", [])
for n, a, b, A, B, C, D, bt in zip(nr4, a4, b4, Ai, Bi, Ci, Di, bt4):
Tita = (1-tau)+A*((delta-1)**2)**(0.5/bt)
F = exp(-C*(delta-1)**2-D*(tau-1)**2)
Fd = -2*C*F*(delta-1)
Fdd = 2*C*F*(2*C*(delta-1)**2-1)
Ft = -2*D*F*(tau-1)
Ftt = 2*D*F*(2*D*(tau-1)**2-1)
Fdt = 4*C*D*F*(delta-1)*(tau-1)
Delta = Tita**2+B*((delta-1)**2)**a
Deltad = (delta-1)*(A*Tita*2/bt*((delta-1)**2)**(0.5/bt-1) +
2*B*a*((delta-1)**2)**(a-1))
if delta == 1:
Deltadd = 0
else:
Deltadd = Deltad/(delta-1)+(delta-1)**2*(
4*B*a*(a-1)*((delta-1)**2)**(a-2) +
2*A**2/bt**2*(((delta-1)**2)**(0.5/bt-1))**2 +
A*Tita*4/bt*(0.5/bt-1)*((delta-1)**2)**(0.5/bt-2))
DeltaBd = b*Delta**(b-1)*Deltad
DeltaBdd = b*(Delta**(b-1)*Deltadd+(b-1)*Delta**(b-2)*Deltad**2)
DeltaBt = -2*Tita*b*Delta**(b-1)
DeltaBtt = 2*b*Delta**(b-1)+4*Tita**2*b*(b-1)*Delta**(b-2)
DeltaBdt = -A*b*2/bt*Delta**(b-1)*(delta-1)*((delta-1)**2)**(
0.5/bt-1)-2*Tita*b*(b-1)*Delta**(b-2)*Deltad
fir += n*Delta**b*delta*F
fird += n*(Delta**b*(F+delta*Fd)+DeltaBd*delta*F)
firdd += n*(Delta**b*(2*Fd+delta*Fdd) + 2*DeltaBd*(F+delta*Fd) +
DeltaBdd*delta*F)
firt += n*delta*(DeltaBt*F+Delta**b*Ft)
firtt += n*delta*(DeltaBtt*F+2*DeltaBt*Ft+Delta**b*Ftt)
firdt += n*(Delta**b*(Ft+delta*Fdt)+delta*DeltaBd*Ft +
DeltaBt*(F+delta*Fd)+DeltaBdt*delta*F)
prop = {}
prop["fir"] = fir
prop["firt"] = firt
prop["firtt"] = firtt
prop["fird"] = fird
prop["firdd"] = firdd
prop["firdt"] = firdt
return prop | Residual contribution to the free Helmholtz energy
Parameters
----------
tau : float
Inverse reduced temperature Tc/T, [-]
delta : float
Reduced density rho/rhoc, [-]
Returns
-------
prop : dict
Dictionary with residual adimensional helmholtz energy and deriv:
* fir
* firt: ∂fir/∂τ|δ,x
* fird: ∂fir/∂δ|τ,x
* firtt: ∂²fir/∂τ²|δ,x
* firdt: ∂²fir/∂τ∂δ|x
* firdd: ∂²fir/∂δ²|τ,x
References
----------
IAPWS, Revised Release on the IAPWS Formulation 1995 for the
Thermodynamic Properties of Ordinary Water Substance for General and
Scientific Use, September 2016, Table 5
http://www.iapws.org/relguide/IAPWS-95.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L1758-L1890 |
jjgomera/iapws | iapws/iapws95.py | MEoS._virial | def _virial(self, T):
"""Virial coefficient
Parameters
----------
T : float
Temperature [K]
Returns
-------
prop : dict
Dictionary with residual adimensional helmholtz energy:
* B: ∂fir/∂δ|δ->0
* C: ∂²fir/∂δ²|δ->0
"""
Tc = self._constants.get("Tref", self.Tc)
tau = Tc/T
B = C = 0
delta = 1e-200
# Polinomial terms
nr1 = self._constants.get("nr1", [])
d1 = self._constants.get("d1", [])
t1 = self._constants.get("t1", [])
for n, d, t in zip(nr1, d1, t1):
B += n*d*delta**(d-1)*tau**t
C += n*d*(d-1)*delta**(d-2)*tau**t
# Exponential terms
nr2 = self._constants.get("nr2", [])
d2 = self._constants.get("d2", [])
g2 = self._constants.get("gamma2", [])
t2 = self._constants.get("t2", [])
c2 = self._constants.get("c2", [])
for n, d, g, t, c in zip(nr2, d2, g2, t2, c2):
B += n*exp(-g*delta**c)*delta**(d-1)*tau**t*(d-g*c*delta**c)
C += n*exp(-g*delta**c)*(delta**(d-2)*tau**t*(
(d-g*c*delta**c)*(d-1-g*c*delta**c)-g**2*c**2*delta**c))
# Gaussian terms
nr3 = self._constants.get("nr3", [])
d3 = self._constants.get("d3", [])
t3 = self._constants.get("t3", [])
a3 = self._constants.get("alfa3", [])
e3 = self._constants.get("epsilon3", [])
b3 = self._constants.get("beta3", [])
g3 = self._constants.get("gamma3", [])
for n, d, t, a, e, b, g in zip(nr3, d3, t3, a3, e3, b3, g3):
B += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
d/delta-2*a*(delta-e))
C += n*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
-2*a*delta**d+4*a**2*delta**d*(
delta-e)**2-4*d*a*delta**2*(
delta-e)+d*2*delta)
# Non analitic terms
nr4 = self._constants.get("nr4", [])
a4 = self._constants.get("a4", [])
b4 = self._constants.get("b4", [])
Ai = self._constants.get("A", [])
Bi = self._constants.get("B", [])
Ci = self._constants.get("C", [])
Di = self._constants.get("D", [])
bt4 = self._constants.get("beta4", [])
for n, a, b, A, B, C, D, bt in zip(nr4, a4, b4, Ai, Bi, Ci, Di, bt4):
Tita = (1-tau)+A*((delta-1)**2)**(0.5/bt)
Delta = Tita**2+B*((delta-1)**2)**a
Deltad = (delta-1)*(A*Tita*2/bt*((delta-1)**2)**(
0.5/bt-1)+2*B*a*((delta-1)**2)**(a-1))
Deltadd = Deltad/(delta-1) + (delta-1)**2*(
4*B*a*(a-1)*((delta-1)**2)**(a-2) +
2*A**2/bt**2*(((delta-1)**2)**(0.5/bt-1))**2 +
A*Tita*4/bt*(0.5/bt-1)*((delta-1)**2)**(0.5/bt-2))
DeltaBd = b*Delta**(b-1)*Deltad
DeltaBdd = b*(Delta**(b-1)*Deltadd+(b-1)*Delta**(b-2)*Deltad**2)
F = exp(-C*(delta-1)**2-D*(tau-1)**2)
Fd = -2*C*F*(delta-1)
Fdd = 2*C*F*(2*C*(delta-1)**2-1)
B += n*(Delta**b*(F+delta*Fd)+DeltaBd*delta*F)
C += n*(Delta**b*(2*Fd+delta*Fdd)+2*DeltaBd*(F+delta*Fd) +
DeltaBdd*delta*F)
prop = {}
prop["B"] = B
prop["C"] = C
return prop | python | def _virial(self, T):
"""Virial coefficient
Parameters
----------
T : float
Temperature [K]
Returns
-------
prop : dict
Dictionary with residual adimensional helmholtz energy:
* B: ∂fir/∂δ|δ->0
* C: ∂²fir/∂δ²|δ->0
"""
Tc = self._constants.get("Tref", self.Tc)
tau = Tc/T
B = C = 0
delta = 1e-200
# Polinomial terms
nr1 = self._constants.get("nr1", [])
d1 = self._constants.get("d1", [])
t1 = self._constants.get("t1", [])
for n, d, t in zip(nr1, d1, t1):
B += n*d*delta**(d-1)*tau**t
C += n*d*(d-1)*delta**(d-2)*tau**t
# Exponential terms
nr2 = self._constants.get("nr2", [])
d2 = self._constants.get("d2", [])
g2 = self._constants.get("gamma2", [])
t2 = self._constants.get("t2", [])
c2 = self._constants.get("c2", [])
for n, d, g, t, c in zip(nr2, d2, g2, t2, c2):
B += n*exp(-g*delta**c)*delta**(d-1)*tau**t*(d-g*c*delta**c)
C += n*exp(-g*delta**c)*(delta**(d-2)*tau**t*(
(d-g*c*delta**c)*(d-1-g*c*delta**c)-g**2*c**2*delta**c))
# Gaussian terms
nr3 = self._constants.get("nr3", [])
d3 = self._constants.get("d3", [])
t3 = self._constants.get("t3", [])
a3 = self._constants.get("alfa3", [])
e3 = self._constants.get("epsilon3", [])
b3 = self._constants.get("beta3", [])
g3 = self._constants.get("gamma3", [])
for n, d, t, a, e, b, g in zip(nr3, d3, t3, a3, e3, b3, g3):
B += n*delta**d*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
d/delta-2*a*(delta-e))
C += n*tau**t*exp(-a*(delta-e)**2-b*(tau-g)**2)*(
-2*a*delta**d+4*a**2*delta**d*(
delta-e)**2-4*d*a*delta**2*(
delta-e)+d*2*delta)
# Non analitic terms
nr4 = self._constants.get("nr4", [])
a4 = self._constants.get("a4", [])
b4 = self._constants.get("b4", [])
Ai = self._constants.get("A", [])
Bi = self._constants.get("B", [])
Ci = self._constants.get("C", [])
Di = self._constants.get("D", [])
bt4 = self._constants.get("beta4", [])
for n, a, b, A, B, C, D, bt in zip(nr4, a4, b4, Ai, Bi, Ci, Di, bt4):
Tita = (1-tau)+A*((delta-1)**2)**(0.5/bt)
Delta = Tita**2+B*((delta-1)**2)**a
Deltad = (delta-1)*(A*Tita*2/bt*((delta-1)**2)**(
0.5/bt-1)+2*B*a*((delta-1)**2)**(a-1))
Deltadd = Deltad/(delta-1) + (delta-1)**2*(
4*B*a*(a-1)*((delta-1)**2)**(a-2) +
2*A**2/bt**2*(((delta-1)**2)**(0.5/bt-1))**2 +
A*Tita*4/bt*(0.5/bt-1)*((delta-1)**2)**(0.5/bt-2))
DeltaBd = b*Delta**(b-1)*Deltad
DeltaBdd = b*(Delta**(b-1)*Deltadd+(b-1)*Delta**(b-2)*Deltad**2)
F = exp(-C*(delta-1)**2-D*(tau-1)**2)
Fd = -2*C*F*(delta-1)
Fdd = 2*C*F*(2*C*(delta-1)**2-1)
B += n*(Delta**b*(F+delta*Fd)+DeltaBd*delta*F)
C += n*(Delta**b*(2*Fd+delta*Fdd)+2*DeltaBd*(F+delta*Fd) +
DeltaBdd*delta*F)
prop = {}
prop["B"] = B
prop["C"] = C
return prop | Virial coefficient
Parameters
----------
T : float
Temperature [K]
Returns
-------
prop : dict
Dictionary with residual adimensional helmholtz energy:
* B: ∂fir/∂δ|δ->0
* C: ∂²fir/∂δ²|δ->0 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L1892-L1978 |
jjgomera/iapws | iapws/iapws95.py | MEoS._derivDimensional | def _derivDimensional(self, rho, T):
"""Calcule the dimensional form or Helmholtz free energy derivatives
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dictionary with residual helmholtz energy and derivatives:
* fir, [kJ/kg]
* firt: ∂fir/∂T|ρ, [kJ/kgK]
* fird: ∂fir/∂ρ|T, [kJ/m³kg²]
* firtt: ∂²fir/∂T²|ρ, [kJ/kgK²]
* firdt: ∂²fir/∂T∂ρ, [kJ/m³kg²K]
* firdd: ∂²fir/∂ρ²|T, [kJ/m⁶kg]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 7,
http://www.iapws.org/relguide/SeaAir.html
"""
if not rho:
prop = {}
prop["fir"] = 0
prop["firt"] = 0
prop["fird"] = 0
prop["firtt"] = 0
prop["firdt"] = 0
prop["firdd"] = 0
return prop
R = self._constants.get("R")/self._constants.get("M", self.M)
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fiott = ideal["fiott"]
fiod = ideal["fiod"]
fiodd = ideal["fiodd"]
res = self._phir(tau, delta)
fir = res["fir"]
firt = res["firt"]
firtt = res["firtt"]
fird = res["fird"]
firdd = res["firdd"]
firdt = res["firdt"]
prop = {}
prop["fir"] = R*T*(fio+fir)
prop["firt"] = R*(fio+fir-(fiot+firt)*tau)
prop["fird"] = R*T/rhoc*(fiod+fird)
prop["firtt"] = R*tau**2/T*(fiott+firtt)
prop["firdt"] = R/rhoc*(fiod+fird-firdt*tau)
prop["firdd"] = R*T/rhoc**2*(fiodd+firdd)
return prop | python | def _derivDimensional(self, rho, T):
"""Calcule the dimensional form or Helmholtz free energy derivatives
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dictionary with residual helmholtz energy and derivatives:
* fir, [kJ/kg]
* firt: ∂fir/∂T|ρ, [kJ/kgK]
* fird: ∂fir/∂ρ|T, [kJ/m³kg²]
* firtt: ∂²fir/∂T²|ρ, [kJ/kgK²]
* firdt: ∂²fir/∂T∂ρ, [kJ/m³kg²K]
* firdd: ∂²fir/∂ρ²|T, [kJ/m⁶kg]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 7,
http://www.iapws.org/relguide/SeaAir.html
"""
if not rho:
prop = {}
prop["fir"] = 0
prop["firt"] = 0
prop["fird"] = 0
prop["firtt"] = 0
prop["firdt"] = 0
prop["firdd"] = 0
return prop
R = self._constants.get("R")/self._constants.get("M", self.M)
rhoc = self._constants.get("rhoref", self.rhoc)
Tc = self._constants.get("Tref", self.Tc)
delta = rho/rhoc
tau = Tc/T
ideal = self._phi0(tau, delta)
fio = ideal["fio"]
fiot = ideal["fiot"]
fiott = ideal["fiott"]
fiod = ideal["fiod"]
fiodd = ideal["fiodd"]
res = self._phir(tau, delta)
fir = res["fir"]
firt = res["firt"]
firtt = res["firtt"]
fird = res["fird"]
firdd = res["firdd"]
firdt = res["firdt"]
prop = {}
prop["fir"] = R*T*(fio+fir)
prop["firt"] = R*(fio+fir-(fiot+firt)*tau)
prop["fird"] = R*T/rhoc*(fiod+fird)
prop["firtt"] = R*tau**2/T*(fiott+firtt)
prop["firdt"] = R/rhoc*(fiod+fird-firdt*tau)
prop["firdd"] = R*T/rhoc**2*(fiodd+firdd)
return prop | Calcule the dimensional form or Helmholtz free energy derivatives
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dictionary with residual helmholtz energy and derivatives:
* fir, [kJ/kg]
* firt: ∂fir/∂T|ρ, [kJ/kgK]
* fird: ∂fir/∂ρ|T, [kJ/m³kg²]
* firtt: ∂²fir/∂T²|ρ, [kJ/kgK²]
* firdt: ∂²fir/∂T∂ρ, [kJ/m³kg²K]
* firdd: ∂²fir/∂ρ²|T, [kJ/m⁶kg]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 7,
http://www.iapws.org/relguide/SeaAir.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L1980-L2047 |
jjgomera/iapws | iapws/iapws95.py | MEoS._surface | def _surface(self, T):
"""Generic equation for the surface tension
Parameters
----------
T : float
Temperature, [K]
Returns
-------
σ : float
Surface tension, [N/m]
Notes
-----
Need a _surf dict in the derived class with the parameters keys:
sigma: coefficient
exp: exponent
"""
tau = 1-T/self.Tc
sigma = 0
for n, t in zip(self._surf["sigma"], self._surf["exp"]):
sigma += n*tau**t
return sigma | python | def _surface(self, T):
"""Generic equation for the surface tension
Parameters
----------
T : float
Temperature, [K]
Returns
-------
σ : float
Surface tension, [N/m]
Notes
-----
Need a _surf dict in the derived class with the parameters keys:
sigma: coefficient
exp: exponent
"""
tau = 1-T/self.Tc
sigma = 0
for n, t in zip(self._surf["sigma"], self._surf["exp"]):
sigma += n*tau**t
return sigma | Generic equation for the surface tension
Parameters
----------
T : float
Temperature, [K]
Returns
-------
σ : float
Surface tension, [N/m]
Notes
-----
Need a _surf dict in the derived class with the parameters keys:
sigma: coefficient
exp: exponent | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L2049-L2072 |
jjgomera/iapws | iapws/iapws95.py | MEoS._Vapor_Pressure | def _Vapor_Pressure(cls, T):
"""Auxiliary equation for the vapour pressure
Parameters
----------
T : float
Temperature, [K]
Returns
-------
Pv : float
Vapour pressure, [Pa]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, Eq.1
"""
Tita = 1-T/cls.Tc
suma = 0
for n, x in zip(cls._Pv["ao"], cls._Pv["exp"]):
suma += n*Tita**x
Pr = exp(cls.Tc/T*suma)
Pv = Pr*cls.Pc
return Pv | python | def _Vapor_Pressure(cls, T):
"""Auxiliary equation for the vapour pressure
Parameters
----------
T : float
Temperature, [K]
Returns
-------
Pv : float
Vapour pressure, [Pa]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, Eq.1
"""
Tita = 1-T/cls.Tc
suma = 0
for n, x in zip(cls._Pv["ao"], cls._Pv["exp"]):
suma += n*Tita**x
Pr = exp(cls.Tc/T*suma)
Pv = Pr*cls.Pc
return Pv | Auxiliary equation for the vapour pressure
Parameters
----------
T : float
Temperature, [K]
Returns
-------
Pv : float
Vapour pressure, [Pa]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, Eq.1 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L2075-L2100 |
jjgomera/iapws | iapws/iapws95.py | MEoS._Liquid_Density | def _Liquid_Density(cls, T):
"""Auxiliary equation for the density of saturated liquid
Parameters
----------
T : float
Temperature, [K]
Returns
-------
rho : float
Saturated liquid density, [kg/m³]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, Eq.2
"""
eq = cls._rhoL["eq"]
Tita = 1-T/cls.Tc
if eq == 2:
Tita = Tita**(1./3)
suma = 0
for n, x in zip(cls._rhoL["ao"], cls._rhoL["exp"]):
suma += n*Tita**x
Pr = suma+1
rho = Pr*cls.rhoc
return rho | python | def _Liquid_Density(cls, T):
"""Auxiliary equation for the density of saturated liquid
Parameters
----------
T : float
Temperature, [K]
Returns
-------
rho : float
Saturated liquid density, [kg/m³]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, Eq.2
"""
eq = cls._rhoL["eq"]
Tita = 1-T/cls.Tc
if eq == 2:
Tita = Tita**(1./3)
suma = 0
for n, x in zip(cls._rhoL["ao"], cls._rhoL["exp"]):
suma += n*Tita**x
Pr = suma+1
rho = Pr*cls.rhoc
return rho | Auxiliary equation for the density of saturated liquid
Parameters
----------
T : float
Temperature, [K]
Returns
-------
rho : float
Saturated liquid density, [kg/m³]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, Eq.2 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L2103-L2131 |
jjgomera/iapws | iapws/iapws95.py | MEoS._Vapor_Density | def _Vapor_Density(cls, T):
"""Auxiliary equation for the density of saturated vapor
Parameters
----------
T : float
Temperature, [K]
Returns
-------
rho : float
Saturated vapor density, [kg/m³]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, Eq.3
"""
eq = cls._rhoG["eq"]
Tita = 1-T/cls.Tc
if eq == 4:
Tita = Tita**(1./3)
suma = 0
for n, x in zip(cls._rhoG["ao"], cls._rhoG["exp"]):
suma += n*Tita**x
Pr = exp(suma)
rho = Pr*cls.rhoc
return rho | python | def _Vapor_Density(cls, T):
"""Auxiliary equation for the density of saturated vapor
Parameters
----------
T : float
Temperature, [K]
Returns
-------
rho : float
Saturated vapor density, [kg/m³]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, Eq.3
"""
eq = cls._rhoG["eq"]
Tita = 1-T/cls.Tc
if eq == 4:
Tita = Tita**(1./3)
suma = 0
for n, x in zip(cls._rhoG["ao"], cls._rhoG["exp"]):
suma += n*Tita**x
Pr = exp(suma)
rho = Pr*cls.rhoc
return rho | Auxiliary equation for the density of saturated vapor
Parameters
----------
T : float
Temperature, [K]
Returns
-------
rho : float
Saturated vapor density, [kg/m³]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, Eq.3 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L2134-L2162 |
jjgomera/iapws | iapws/iapws95.py | MEoS._dPdT_sat | def _dPdT_sat(cls, T):
"""Auxiliary equation for the dP/dT along saturation line
Parameters
----------
T : float
Temperature, [K]
Returns
-------
dPdT : float
dPdT, [MPa/K]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, derived from Eq.1
"""
Tita = 1-T/cls.Tc
suma1 = 0
suma2 = 0
for n, x in zip(cls._Pv["ao"], cls._Pv["exp"]):
suma1 -= n*x*Tita**(x-1)/cls.Tc
suma2 += n*Tita**x
Pr = (cls.Tc*suma1/T-cls.Tc/T**2*suma2)*exp(cls.Tc/T*suma2)
dPdT = Pr*cls.Pc
return dPdT | python | def _dPdT_sat(cls, T):
"""Auxiliary equation for the dP/dT along saturation line
Parameters
----------
T : float
Temperature, [K]
Returns
-------
dPdT : float
dPdT, [MPa/K]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, derived from Eq.1
"""
Tita = 1-T/cls.Tc
suma1 = 0
suma2 = 0
for n, x in zip(cls._Pv["ao"], cls._Pv["exp"]):
suma1 -= n*x*Tita**(x-1)/cls.Tc
suma2 += n*Tita**x
Pr = (cls.Tc*suma1/T-cls.Tc/T**2*suma2)*exp(cls.Tc/T*suma2)
dPdT = Pr*cls.Pc
return dPdT | Auxiliary equation for the dP/dT along saturation line
Parameters
----------
T : float
Temperature, [K]
Returns
-------
dPdT : float
dPdT, [MPa/K]
References
----------
IAPWS, Revised Supplementary Release on Saturation Properties of
Ordinary Water Substance September 1992,
http://www.iapws.org/relguide/Supp-sat.html, derived from Eq.1 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws95.py#L2165-L2192 |
jjgomera/iapws | iapws/humidAir.py | _virial | def _virial(T):
"""Virial equations for humid air
Parameters
----------
T : float
Temperature [K]
Returns
-------
prop : dict
Dictionary with critical coefficient:
* Baa: Second virial coefficient of dry air, [m³/mol]
* Baw: Second air-water cross virial coefficient, [m³/mol]
* Bww: Second virial coefficient of water, [m³/mol]
* Caaa: Third virial coefficient of dry air, [m⁶/mol]
* Caaw: Third air-water cross virial coefficient, [m⁶/mol]
* Caww: Third air-water cross virial coefficient, [m⁶/mol]
* Cwww: Third virial coefficient of dry air, [m⁶/mol]
* Bawt: dBaw/dT, [m³/molK]
* Bawtt: d²Baw/dT², [m³/molK²]
* Caawt: dCaaw/dT, [m⁶/molK]
* Caawtt: d²Caaw/dT², [m⁶/molK²]
* Cawwt: dCaww/dT, [m⁶/molK]
* Cawwtt: d²Caww/dT², [m⁶/molK²]
Notes
------
Raise :class:`Warning` if T isn't in range of validity:
* Baa: 60 ≤ T ≤ 2000
* Baw: 130 ≤ T ≤ 2000
* Bww: 130 ≤ T ≤ 1273
* Caaa: 60 ≤ T ≤ 2000
* Caaw: 193 ≤ T ≤ 493
* Caww: 173 ≤ T ≤ 473
* Cwww: 130 ≤ T ≤ 1273
Examples
--------
>>> _virial(200)["Baa"]
-3.92722567e-5
References
----------
IAPWS, Guideline on a Virial Equation for the Fugacity of H2O in Humid Air,
http://www.iapws.org/relguide/VirialFugacity.html
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 10,
http://www.iapws.org/relguide/SeaAir.html
"""
# Check input parameters
if T < 60 or T > 2000:
warnings.warn("Baa out of validity range")
if T < 130 or T > 2000:
warnings.warn("Baw out of validity range")
if T < 130 or T > 1273:
warnings.warn("Bww out of validity range")
if T < 60 or T > 2000:
warnings.warn("Caaa out of validity range")
if T < 193 or T > 493:
warnings.warn("Caaw out of validity range")
if T < 173 or T > 473:
warnings.warn("Caww out of validity range")
if T < 130 or T > 1273:
warnings.warn("Cwww out of validity range")
T_ = T/100
tau = IAPWS95.Tc/T
# Table 1
# Reorganizated to easy use in equations
tb = [-0.5, 0.875, 1, 4, 6, 12, 7]
nb = [0.12533547935523e-1, 0.78957634722828e1, -0.87803203303561e1,
-0.66856572307965, 0.20433810950965, -0.66212605039687e-4,
-0.10793600908932]
bc = [0.5, 0.75, 1, 5, 1, 9, 10]
nc = [0.31802509345418, -0.26145533859358, -0.19232721156002,
-0.25709043003438, 0.17611491008752e-1, 0.22132295167546,
-0.40247669763528]
bc2 = [4, 6, 12]
nc2 = [-0.66856572307965, 0.20433810950965, -0.66212605039687e-4]
# Table 2
ai = [3.5, 3.5]
bi = [0.85, 0.95]
Bi = [0.2, 0.2]
ni = [-0.14874640856724, 0.31806110878444]
Ci = [28, 32]
Di = [700, 800]
Ai = [0.32, 0.32]
betai = [0.3, 0.3]
# Eq 5
sum1 = sum([n*tau**t for n, t in zip(nb, tb)])
sum2 = 0
for n, b, B, A, C, D in zip(ni, bi, Bi, Ai, Ci, Di):
sum2 += n*((A+1-tau)**2+B)**b*exp(-C-D*(tau-1)**2)
Bww = Mw/IAPWS95.rhoc*(sum1+sum2)
# Eq 6
sum1 = sum([n*tau**t for n, t in zip(nc, bc)])
sum2 = sum([n*tau**t for n, t in zip(nc2, bc2)])
sum3 = 0
for a, b, B, n, C, D, A, beta in zip(ai, bi, Bi, ni, Ci, Di, Ai, betai):
Tita = A+1-tau
sum3 += n*(C*(Tita**2+B)-b*(A*Tita/beta+B*a))*(Tita**2+B)**(b-1) * \
exp(-C-D*(tau-1)**2)
Cwww = 2*(Mw/IAPWS95.rhoc)**2*(sum1-sum2+2*sum3)
# Table 3
ai = [0.482737e-3, 0.105678e-2, -0.656394e-2, 0.294442e-1, -0.319317e-1]
bi = [-10.728876, 34.7802, -38.3383, 33.406]
ci = [66.5687, -238.834, -176.755]
di = [-0.237, -1.048, -3.183]
Baw = 1e-6*sum([c*T_**d for c, d in zip(ci, di)]) # Eq 7
Caaw = 1e-6*sum([a/T_**i for i, a in enumerate(ai)]) # Eq 8
Caww = -1e-6*exp(sum([b/T_**i for i, b in enumerate(bi)])) # Eq 9
# Eq T56
Bawt = 1e-6*T_/T*sum([c*d*T_**(d-1) for c, d in zip(ci, di)])
# Eq T57
Bawtt = 1e-6*T_**2/T**2*sum(
[c*d*(d-1)*T_**(d-2) for c, d in zip(ci, di)])
# Eq T59
Caawt = -1e-6*T_/T*sum([i*a*T_**(-i-1) for i, a in enumerate(ai)])
# Eq T60
Caawtt = 1e-6*T_**2/T**2*sum(
[i*(i+1)*a*T_**(-i-2) for i, a in enumerate(ai)])
# Eq T62
Cawwt = 1e-6*T_/T*sum([i*b*T_**(-i-1) for i, b in enumerate(bi)]) * \
exp(sum([b/T_**i for i, b in enumerate(bi)]))
# Eq T63
Cawwtt = -1e-6*T_**2/T**2*((
sum([i*(i+1)*b*T_**(-i-2) for i, b in enumerate(bi)]) +
sum([i*b*T_**(-i-1) for i, b in enumerate(bi)])**2) *
exp(sum([b/T_**i for i, b in enumerate(bi)])))
# Table 4
# Reorganizated to easy use in equations
ji = [0, 0.33, 1.01, 1.6, 3.6, 3.5]
ni = [0.118160747229, 0.713116392079, -0.161824192067e1, -0.101365037912,
-0.146629609713, 0.148287891978e-1]
tau = 132.6312/T
Baa = 1/10.4477*sum([n*tau**j for j, n in zip(ji, ni)]) # Eq 10
Caaa = 2/10.4477**2*(0.714140178971e-1+0.101365037912*tau**1.6) # Eq 11
prop = {}
prop["Baa"] = Baa/1000
prop["Baw"] = Baw
prop["Bww"] = Bww/1000
prop["Caaa"] = Caaa/1e6
prop["Caaw"] = Caaw
prop["Caww"] = Caww
prop["Cwww"] = Cwww/1e6
prop["Bawt"] = Bawt
prop["Bawtt"] = Bawtt
prop["Caawt"] = Caawt
prop["Caawtt"] = Caawtt
prop["Cawwt"] = Cawwt
prop["Cawwtt"] = Cawwtt
return prop | python | def _virial(T):
"""Virial equations for humid air
Parameters
----------
T : float
Temperature [K]
Returns
-------
prop : dict
Dictionary with critical coefficient:
* Baa: Second virial coefficient of dry air, [m³/mol]
* Baw: Second air-water cross virial coefficient, [m³/mol]
* Bww: Second virial coefficient of water, [m³/mol]
* Caaa: Third virial coefficient of dry air, [m⁶/mol]
* Caaw: Third air-water cross virial coefficient, [m⁶/mol]
* Caww: Third air-water cross virial coefficient, [m⁶/mol]
* Cwww: Third virial coefficient of dry air, [m⁶/mol]
* Bawt: dBaw/dT, [m³/molK]
* Bawtt: d²Baw/dT², [m³/molK²]
* Caawt: dCaaw/dT, [m⁶/molK]
* Caawtt: d²Caaw/dT², [m⁶/molK²]
* Cawwt: dCaww/dT, [m⁶/molK]
* Cawwtt: d²Caww/dT², [m⁶/molK²]
Notes
------
Raise :class:`Warning` if T isn't in range of validity:
* Baa: 60 ≤ T ≤ 2000
* Baw: 130 ≤ T ≤ 2000
* Bww: 130 ≤ T ≤ 1273
* Caaa: 60 ≤ T ≤ 2000
* Caaw: 193 ≤ T ≤ 493
* Caww: 173 ≤ T ≤ 473
* Cwww: 130 ≤ T ≤ 1273
Examples
--------
>>> _virial(200)["Baa"]
-3.92722567e-5
References
----------
IAPWS, Guideline on a Virial Equation for the Fugacity of H2O in Humid Air,
http://www.iapws.org/relguide/VirialFugacity.html
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 10,
http://www.iapws.org/relguide/SeaAir.html
"""
# Check input parameters
if T < 60 or T > 2000:
warnings.warn("Baa out of validity range")
if T < 130 or T > 2000:
warnings.warn("Baw out of validity range")
if T < 130 or T > 1273:
warnings.warn("Bww out of validity range")
if T < 60 or T > 2000:
warnings.warn("Caaa out of validity range")
if T < 193 or T > 493:
warnings.warn("Caaw out of validity range")
if T < 173 or T > 473:
warnings.warn("Caww out of validity range")
if T < 130 or T > 1273:
warnings.warn("Cwww out of validity range")
T_ = T/100
tau = IAPWS95.Tc/T
# Table 1
# Reorganizated to easy use in equations
tb = [-0.5, 0.875, 1, 4, 6, 12, 7]
nb = [0.12533547935523e-1, 0.78957634722828e1, -0.87803203303561e1,
-0.66856572307965, 0.20433810950965, -0.66212605039687e-4,
-0.10793600908932]
bc = [0.5, 0.75, 1, 5, 1, 9, 10]
nc = [0.31802509345418, -0.26145533859358, -0.19232721156002,
-0.25709043003438, 0.17611491008752e-1, 0.22132295167546,
-0.40247669763528]
bc2 = [4, 6, 12]
nc2 = [-0.66856572307965, 0.20433810950965, -0.66212605039687e-4]
# Table 2
ai = [3.5, 3.5]
bi = [0.85, 0.95]
Bi = [0.2, 0.2]
ni = [-0.14874640856724, 0.31806110878444]
Ci = [28, 32]
Di = [700, 800]
Ai = [0.32, 0.32]
betai = [0.3, 0.3]
# Eq 5
sum1 = sum([n*tau**t for n, t in zip(nb, tb)])
sum2 = 0
for n, b, B, A, C, D in zip(ni, bi, Bi, Ai, Ci, Di):
sum2 += n*((A+1-tau)**2+B)**b*exp(-C-D*(tau-1)**2)
Bww = Mw/IAPWS95.rhoc*(sum1+sum2)
# Eq 6
sum1 = sum([n*tau**t for n, t in zip(nc, bc)])
sum2 = sum([n*tau**t for n, t in zip(nc2, bc2)])
sum3 = 0
for a, b, B, n, C, D, A, beta in zip(ai, bi, Bi, ni, Ci, Di, Ai, betai):
Tita = A+1-tau
sum3 += n*(C*(Tita**2+B)-b*(A*Tita/beta+B*a))*(Tita**2+B)**(b-1) * \
exp(-C-D*(tau-1)**2)
Cwww = 2*(Mw/IAPWS95.rhoc)**2*(sum1-sum2+2*sum3)
# Table 3
ai = [0.482737e-3, 0.105678e-2, -0.656394e-2, 0.294442e-1, -0.319317e-1]
bi = [-10.728876, 34.7802, -38.3383, 33.406]
ci = [66.5687, -238.834, -176.755]
di = [-0.237, -1.048, -3.183]
Baw = 1e-6*sum([c*T_**d for c, d in zip(ci, di)]) # Eq 7
Caaw = 1e-6*sum([a/T_**i for i, a in enumerate(ai)]) # Eq 8
Caww = -1e-6*exp(sum([b/T_**i for i, b in enumerate(bi)])) # Eq 9
# Eq T56
Bawt = 1e-6*T_/T*sum([c*d*T_**(d-1) for c, d in zip(ci, di)])
# Eq T57
Bawtt = 1e-6*T_**2/T**2*sum(
[c*d*(d-1)*T_**(d-2) for c, d in zip(ci, di)])
# Eq T59
Caawt = -1e-6*T_/T*sum([i*a*T_**(-i-1) for i, a in enumerate(ai)])
# Eq T60
Caawtt = 1e-6*T_**2/T**2*sum(
[i*(i+1)*a*T_**(-i-2) for i, a in enumerate(ai)])
# Eq T62
Cawwt = 1e-6*T_/T*sum([i*b*T_**(-i-1) for i, b in enumerate(bi)]) * \
exp(sum([b/T_**i for i, b in enumerate(bi)]))
# Eq T63
Cawwtt = -1e-6*T_**2/T**2*((
sum([i*(i+1)*b*T_**(-i-2) for i, b in enumerate(bi)]) +
sum([i*b*T_**(-i-1) for i, b in enumerate(bi)])**2) *
exp(sum([b/T_**i for i, b in enumerate(bi)])))
# Table 4
# Reorganizated to easy use in equations
ji = [0, 0.33, 1.01, 1.6, 3.6, 3.5]
ni = [0.118160747229, 0.713116392079, -0.161824192067e1, -0.101365037912,
-0.146629609713, 0.148287891978e-1]
tau = 132.6312/T
Baa = 1/10.4477*sum([n*tau**j for j, n in zip(ji, ni)]) # Eq 10
Caaa = 2/10.4477**2*(0.714140178971e-1+0.101365037912*tau**1.6) # Eq 11
prop = {}
prop["Baa"] = Baa/1000
prop["Baw"] = Baw
prop["Bww"] = Bww/1000
prop["Caaa"] = Caaa/1e6
prop["Caaw"] = Caaw
prop["Caww"] = Caww
prop["Cwww"] = Cwww/1e6
prop["Bawt"] = Bawt
prop["Bawtt"] = Bawtt
prop["Caawt"] = Caawt
prop["Caawtt"] = Caawtt
prop["Cawwt"] = Cawwt
prop["Cawwtt"] = Cawwtt
return prop | Virial equations for humid air
Parameters
----------
T : float
Temperature [K]
Returns
-------
prop : dict
Dictionary with critical coefficient:
* Baa: Second virial coefficient of dry air, [m³/mol]
* Baw: Second air-water cross virial coefficient, [m³/mol]
* Bww: Second virial coefficient of water, [m³/mol]
* Caaa: Third virial coefficient of dry air, [m⁶/mol]
* Caaw: Third air-water cross virial coefficient, [m⁶/mol]
* Caww: Third air-water cross virial coefficient, [m⁶/mol]
* Cwww: Third virial coefficient of dry air, [m⁶/mol]
* Bawt: dBaw/dT, [m³/molK]
* Bawtt: d²Baw/dT², [m³/molK²]
* Caawt: dCaaw/dT, [m⁶/molK]
* Caawtt: d²Caaw/dT², [m⁶/molK²]
* Cawwt: dCaww/dT, [m⁶/molK]
* Cawwtt: d²Caww/dT², [m⁶/molK²]
Notes
------
Raise :class:`Warning` if T isn't in range of validity:
* Baa: 60 ≤ T ≤ 2000
* Baw: 130 ≤ T ≤ 2000
* Bww: 130 ≤ T ≤ 1273
* Caaa: 60 ≤ T ≤ 2000
* Caaw: 193 ≤ T ≤ 493
* Caww: 173 ≤ T ≤ 473
* Cwww: 130 ≤ T ≤ 1273
Examples
--------
>>> _virial(200)["Baa"]
-3.92722567e-5
References
----------
IAPWS, Guideline on a Virial Equation for the Fugacity of H2O in Humid Air,
http://www.iapws.org/relguide/VirialFugacity.html
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 10,
http://www.iapws.org/relguide/SeaAir.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L32-L198 |
jjgomera/iapws | iapws/humidAir.py | _fugacity | def _fugacity(T, P, x):
"""Fugacity equation for humid air
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
x : float
Mole fraction of water-vapor, [-]
Returns
-------
fv : float
fugacity coefficient, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in range of validity:
* 193 ≤ T ≤ 473
* 0 ≤ P ≤ 5
* 0 ≤ x ≤ 1
Really the xmax is the xsaturation but isn't implemented
Examples
--------
>>> _fugacity(300, 1, 0.1)
0.0884061686
References
----------
IAPWS, Guideline on a Virial Equation for the Fugacity of H2O in Humid Air,
http://www.iapws.org/relguide/VirialFugacity.html
"""
# Check input parameters
if T < 193 or T > 473 or P < 0 or P > 5 or x < 0 or x > 1:
raise(NotImplementedError("Input not in range of validity"))
R = 8.314462 # J/molK
# Virial coefficients
vir = _virial(T)
# Eq 3
beta = x*(2-x)*vir["Bww"]+(1-x)**2*(2*vir["Baw"]-vir["Baa"])
# Eq 4
gamma = x**2*(3-2*x)*vir["Cwww"] + \
(1-x)**2*(6*x*vir["Caww"]+3*(1-2*x)*vir["Caaw"]-2*(1-x)*vir["Caaa"]) +\
(x**2*vir["Bww"]+2*x*(1-x)*vir["Baw"]+(1-x)**2*vir["Baa"]) * \
(x*(3*x-4)*vir["Bww"]+2*(1-x)*(3*x-2)*vir["Baw"]+3*(1-x)**2*vir["Baa"])
# Eq 2
fv = x*P*exp(beta*P*1e6/R/T+0.5*gamma*(P*1e6/R/T)**2)
return fv | python | def _fugacity(T, P, x):
"""Fugacity equation for humid air
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
x : float
Mole fraction of water-vapor, [-]
Returns
-------
fv : float
fugacity coefficient, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in range of validity:
* 193 ≤ T ≤ 473
* 0 ≤ P ≤ 5
* 0 ≤ x ≤ 1
Really the xmax is the xsaturation but isn't implemented
Examples
--------
>>> _fugacity(300, 1, 0.1)
0.0884061686
References
----------
IAPWS, Guideline on a Virial Equation for the Fugacity of H2O in Humid Air,
http://www.iapws.org/relguide/VirialFugacity.html
"""
# Check input parameters
if T < 193 or T > 473 or P < 0 or P > 5 or x < 0 or x > 1:
raise(NotImplementedError("Input not in range of validity"))
R = 8.314462 # J/molK
# Virial coefficients
vir = _virial(T)
# Eq 3
beta = x*(2-x)*vir["Bww"]+(1-x)**2*(2*vir["Baw"]-vir["Baa"])
# Eq 4
gamma = x**2*(3-2*x)*vir["Cwww"] + \
(1-x)**2*(6*x*vir["Caww"]+3*(1-2*x)*vir["Caaw"]-2*(1-x)*vir["Caaa"]) +\
(x**2*vir["Bww"]+2*x*(1-x)*vir["Baw"]+(1-x)**2*vir["Baa"]) * \
(x*(3*x-4)*vir["Bww"]+2*(1-x)*(3*x-2)*vir["Baw"]+3*(1-x)**2*vir["Baa"])
# Eq 2
fv = x*P*exp(beta*P*1e6/R/T+0.5*gamma*(P*1e6/R/T)**2)
return fv | Fugacity equation for humid air
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
x : float
Mole fraction of water-vapor, [-]
Returns
-------
fv : float
fugacity coefficient, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in range of validity:
* 193 ≤ T ≤ 473
* 0 ≤ P ≤ 5
* 0 ≤ x ≤ 1
Really the xmax is the xsaturation but isn't implemented
Examples
--------
>>> _fugacity(300, 1, 0.1)
0.0884061686
References
----------
IAPWS, Guideline on a Virial Equation for the Fugacity of H2O in Humid Air,
http://www.iapws.org/relguide/VirialFugacity.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L201-L258 |
jjgomera/iapws | iapws/humidAir.py | MEoSBlend._bubbleP | def _bubbleP(cls, T):
"""Using ancillary equation return the pressure of bubble point"""
c = cls._blend["bubble"]
Tj = cls._blend["Tj"]
Pj = cls._blend["Pj"]
Tita = 1-T/Tj
suma = 0
for i, n in zip(c["i"], c["n"]):
suma += n*Tita**(i/2.)
P = Pj*exp(Tj/T*suma)
return P | python | def _bubbleP(cls, T):
"""Using ancillary equation return the pressure of bubble point"""
c = cls._blend["bubble"]
Tj = cls._blend["Tj"]
Pj = cls._blend["Pj"]
Tita = 1-T/Tj
suma = 0
for i, n in zip(c["i"], c["n"]):
suma += n*Tita**(i/2.)
P = Pj*exp(Tj/T*suma)
return P | Using ancillary equation return the pressure of bubble point | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L279-L290 |
jjgomera/iapws | iapws/humidAir.py | HumidAir.calculable | def calculable(self):
"""Check if inputs are enough to define state"""
self._mode = ""
if self.kwargs["T"] and self.kwargs["P"]:
self._mode = "TP"
elif self.kwargs["T"] and self.kwargs["rho"]:
self._mode = "Trho"
elif self.kwargs["P"] and self.kwargs["rho"]:
self._mode = "Prho"
# Composition definition
self._composition = ""
if self.kwargs["A"] is not None:
self._composition = "A"
elif self.kwargs["xa"] is not None:
self._composition = "xa"
return bool(self._mode) and bool(self._composition) | python | def calculable(self):
"""Check if inputs are enough to define state"""
self._mode = ""
if self.kwargs["T"] and self.kwargs["P"]:
self._mode = "TP"
elif self.kwargs["T"] and self.kwargs["rho"]:
self._mode = "Trho"
elif self.kwargs["P"] and self.kwargs["rho"]:
self._mode = "Prho"
# Composition definition
self._composition = ""
if self.kwargs["A"] is not None:
self._composition = "A"
elif self.kwargs["xa"] is not None:
self._composition = "xa"
return bool(self._mode) and bool(self._composition) | Check if inputs are enough to define state | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L643-L660 |
jjgomera/iapws | iapws/humidAir.py | HumidAir.calculo | def calculo(self):
"""Calculate procedure"""
T = self.kwargs["T"]
rho = self.kwargs["rho"]
P = self.kwargs["P"]
# Composition alternate definition
if self._composition == "A":
A = self.kwargs["A"]
elif self._composition == "xa":
xa = self.kwargs["xa"]
A = xa/(1-(1-xa)*(1-Mw/Ma))
# Thermodynamic definition
if self._mode == "TP":
def f(rho):
fav = self._fav(T, rho, A)
return rho**2*fav["fird"]/1000-P
rho = fsolve(f, 1)[0]
elif self._mode == "Prho":
def f(T):
fav = self._fav(T, rho, A)
return rho**2*fav["fird"]/1000-P
T = fsolve(f, 300)[0]
# General calculation procedure
fav = self._fav(T, rho, A)
# Common thermodynamic properties
prop = self._prop(T, rho, fav)
self.T = T
self.rho = rho
self.v = 1/rho
self.P = prop["P"]
self.s = prop["s"]
self.cp = prop["cp"]
self.h = prop["h"]
self.g = prop["g"]
self.u = self.h-self.P*1000*self.v
self.alfav = prop["alfav"]
self.betas = prop["betas"]
self.xkappa = prop["xkappa"]
self.ks = prop["ks"]
self.w = prop["w"]
# Coligative properties
coligative = self._coligative(rho, A, fav)
self.A = A
self.W = 1-A
self.mu = coligative["mu"]
self.muw = coligative["muw"]
self.M = coligative["M"]
self.HR = coligative["HR"]
self.xa = coligative["xa"]
self.xw = coligative["xw"]
self.Pv = (1-self.xa)*self.P
# Saturation related properties
A_sat = self._eq(self.T, self.P)
self.xa_sat = A_sat*Mw/Ma/(1-A_sat*(1-Mw/Ma))
self.RH = (1-self.xa)/(1-self.xa_sat) | python | def calculo(self):
"""Calculate procedure"""
T = self.kwargs["T"]
rho = self.kwargs["rho"]
P = self.kwargs["P"]
# Composition alternate definition
if self._composition == "A":
A = self.kwargs["A"]
elif self._composition == "xa":
xa = self.kwargs["xa"]
A = xa/(1-(1-xa)*(1-Mw/Ma))
# Thermodynamic definition
if self._mode == "TP":
def f(rho):
fav = self._fav(T, rho, A)
return rho**2*fav["fird"]/1000-P
rho = fsolve(f, 1)[0]
elif self._mode == "Prho":
def f(T):
fav = self._fav(T, rho, A)
return rho**2*fav["fird"]/1000-P
T = fsolve(f, 300)[0]
# General calculation procedure
fav = self._fav(T, rho, A)
# Common thermodynamic properties
prop = self._prop(T, rho, fav)
self.T = T
self.rho = rho
self.v = 1/rho
self.P = prop["P"]
self.s = prop["s"]
self.cp = prop["cp"]
self.h = prop["h"]
self.g = prop["g"]
self.u = self.h-self.P*1000*self.v
self.alfav = prop["alfav"]
self.betas = prop["betas"]
self.xkappa = prop["xkappa"]
self.ks = prop["ks"]
self.w = prop["w"]
# Coligative properties
coligative = self._coligative(rho, A, fav)
self.A = A
self.W = 1-A
self.mu = coligative["mu"]
self.muw = coligative["muw"]
self.M = coligative["M"]
self.HR = coligative["HR"]
self.xa = coligative["xa"]
self.xw = coligative["xw"]
self.Pv = (1-self.xa)*self.P
# Saturation related properties
A_sat = self._eq(self.T, self.P)
self.xa_sat = A_sat*Mw/Ma/(1-A_sat*(1-Mw/Ma))
self.RH = (1-self.xa)/(1-self.xa_sat) | Calculate procedure | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L662-L722 |
jjgomera/iapws | iapws/humidAir.py | HumidAir._eq | def _eq(self, T, P):
"""Procedure for calculate the composition in saturation state
Parameters
----------
T : float
Temperature [K]
P : float
Pressure [MPa]
Returns
-------
Asat : float
Saturation mass fraction of dry air in humid air [kg/kg]
"""
if T <= 273.16:
ice = _Ice(T, P)
gw = ice["g"]
else:
water = IAPWS95(T=T, P=P)
gw = water.g
def f(parr):
rho, a = parr
if a > 1:
a = 1
fa = self._fav(T, rho, a)
muw = fa["fir"]+rho*fa["fird"]-a*fa["fira"]
return gw-muw, rho**2*fa["fird"]/1000-P
rinput = fsolve(f, [1, 0.95], full_output=True)
Asat = rinput[0][1]
return Asat | python | def _eq(self, T, P):
"""Procedure for calculate the composition in saturation state
Parameters
----------
T : float
Temperature [K]
P : float
Pressure [MPa]
Returns
-------
Asat : float
Saturation mass fraction of dry air in humid air [kg/kg]
"""
if T <= 273.16:
ice = _Ice(T, P)
gw = ice["g"]
else:
water = IAPWS95(T=T, P=P)
gw = water.g
def f(parr):
rho, a = parr
if a > 1:
a = 1
fa = self._fav(T, rho, a)
muw = fa["fir"]+rho*fa["fird"]-a*fa["fira"]
return gw-muw, rho**2*fa["fird"]/1000-P
rinput = fsolve(f, [1, 0.95], full_output=True)
Asat = rinput[0][1]
return Asat | Procedure for calculate the composition in saturation state
Parameters
----------
T : float
Temperature [K]
P : float
Pressure [MPa]
Returns
-------
Asat : float
Saturation mass fraction of dry air in humid air [kg/kg] | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L729-L761 |
jjgomera/iapws | iapws/humidAir.py | HumidAir._prop | def _prop(self, T, rho, fav):
"""Thermodynamic properties of humid air
Parameters
----------
T : float
Temperature, [K]
rho : float
Density, [kg/m³]
fav : dict
dictionary with helmholtz energy and derivatives
Returns
-------
prop : dict
Dictionary with thermodynamic properties of humid air:
* P: Pressure, [MPa]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* h: Specific enthalpy, [kJ/kg]
* g: Specific gibbs energy, [kJ/kg]
* alfav: Thermal expansion coefficient, [1/K]
* betas: Isentropic T-P coefficient, [K/MPa]
* xkappa: Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* w: Speed of sound, [m/s]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 5,
http://www.iapws.org/relguide/SeaAir.html
"""
prop = {}
prop["P"] = rho**2*fav["fird"]/1000 # Eq T1
prop["s"] = -fav["firt"] # Eq T2
prop["cp"] = -T*fav["firtt"]+T*rho*fav["firdt"]**2/( # Eq T3
2*fav["fird"]+rho*fav["firdd"])
prop["h"] = fav["fir"]-T*fav["firt"]+rho*fav["fird"] # Eq T4
prop["g"] = fav["fir"]+rho*fav["fird"] # Eq T5
prop["alfav"] = fav["firdt"]/(2*fav["fird"]+rho*fav["firdd"]) # Eq T6
prop["betas"] = 1000*fav["firdt"]/rho/( # Eq T7
rho*fav["firdt"]**2-fav["firtt"]*(2*fav["fird"]+rho*fav["firdd"]))
prop["xkappa"] = 1e3/(rho**2*(2*fav["fird"]+rho*fav["firdd"])) # Eq T8
prop["ks"] = 1000*fav["firtt"]/rho**2/( # Eq T9
fav["firtt"]*(2*fav["fird"]+rho*fav["firdd"])-rho*fav["firdt"]**2)
prop["w"] = (rho**2*1000*(fav["firtt"]*fav["firdd"]-fav["firdt"]**2) /
fav["firtt"]+2*rho*fav["fird"]*1000)**0.5 # Eq T10
return prop | python | def _prop(self, T, rho, fav):
"""Thermodynamic properties of humid air
Parameters
----------
T : float
Temperature, [K]
rho : float
Density, [kg/m³]
fav : dict
dictionary with helmholtz energy and derivatives
Returns
-------
prop : dict
Dictionary with thermodynamic properties of humid air:
* P: Pressure, [MPa]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* h: Specific enthalpy, [kJ/kg]
* g: Specific gibbs energy, [kJ/kg]
* alfav: Thermal expansion coefficient, [1/K]
* betas: Isentropic T-P coefficient, [K/MPa]
* xkappa: Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* w: Speed of sound, [m/s]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 5,
http://www.iapws.org/relguide/SeaAir.html
"""
prop = {}
prop["P"] = rho**2*fav["fird"]/1000 # Eq T1
prop["s"] = -fav["firt"] # Eq T2
prop["cp"] = -T*fav["firtt"]+T*rho*fav["firdt"]**2/( # Eq T3
2*fav["fird"]+rho*fav["firdd"])
prop["h"] = fav["fir"]-T*fav["firt"]+rho*fav["fird"] # Eq T4
prop["g"] = fav["fir"]+rho*fav["fird"] # Eq T5
prop["alfav"] = fav["firdt"]/(2*fav["fird"]+rho*fav["firdd"]) # Eq T6
prop["betas"] = 1000*fav["firdt"]/rho/( # Eq T7
rho*fav["firdt"]**2-fav["firtt"]*(2*fav["fird"]+rho*fav["firdd"]))
prop["xkappa"] = 1e3/(rho**2*(2*fav["fird"]+rho*fav["firdd"])) # Eq T8
prop["ks"] = 1000*fav["firtt"]/rho**2/( # Eq T9
fav["firtt"]*(2*fav["fird"]+rho*fav["firdd"])-rho*fav["firdt"]**2)
prop["w"] = (rho**2*1000*(fav["firtt"]*fav["firdd"]-fav["firdt"]**2) /
fav["firtt"]+2*rho*fav["fird"]*1000)**0.5 # Eq T10
return prop | Thermodynamic properties of humid air
Parameters
----------
T : float
Temperature, [K]
rho : float
Density, [kg/m³]
fav : dict
dictionary with helmholtz energy and derivatives
Returns
-------
prop : dict
Dictionary with thermodynamic properties of humid air:
* P: Pressure, [MPa]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* h: Specific enthalpy, [kJ/kg]
* g: Specific gibbs energy, [kJ/kg]
* alfav: Thermal expansion coefficient, [1/K]
* betas: Isentropic T-P coefficient, [K/MPa]
* xkappa: Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* w: Speed of sound, [m/s]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 5,
http://www.iapws.org/relguide/SeaAir.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L763-L813 |
jjgomera/iapws | iapws/humidAir.py | HumidAir._coligative | def _coligative(self, rho, A, fav):
"""Miscelaneous properties of humid air
Parameters
----------
rho : float
Density, [kg/m³]
A : float
Mass fraction of dry air in humid air, [kg/kg]
fav : dict
dictionary with helmholtz energy and derivatives
Returns
-------
prop : dict
Dictionary with calculated properties:
* mu: Relative chemical potential, [kJ/kg]
* muw: Chemical potential of water, [kJ/kg]
* M: Molar mass of humid air, [g/mol]
* HR: Humidity ratio, [-]
* xa: Mole fraction of dry air, [-]
* xw: Mole fraction of water, [-]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 12,
http://www.iapws.org/relguide/SeaAir.html
"""
prop = {}
prop["mu"] = fav["fira"]
prop["muw"] = fav["fir"]+rho*fav["fird"]-A*fav["fira"]
prop["M"] = 1/((1-A)/Mw+A/Ma)
prop["HR"] = 1/A-1
prop["xa"] = A*Mw/Ma/(1-A*(1-Mw/Ma))
prop["xw"] = 1-prop["xa"]
return prop | python | def _coligative(self, rho, A, fav):
"""Miscelaneous properties of humid air
Parameters
----------
rho : float
Density, [kg/m³]
A : float
Mass fraction of dry air in humid air, [kg/kg]
fav : dict
dictionary with helmholtz energy and derivatives
Returns
-------
prop : dict
Dictionary with calculated properties:
* mu: Relative chemical potential, [kJ/kg]
* muw: Chemical potential of water, [kJ/kg]
* M: Molar mass of humid air, [g/mol]
* HR: Humidity ratio, [-]
* xa: Mole fraction of dry air, [-]
* xw: Mole fraction of water, [-]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 12,
http://www.iapws.org/relguide/SeaAir.html
"""
prop = {}
prop["mu"] = fav["fira"]
prop["muw"] = fav["fir"]+rho*fav["fird"]-A*fav["fira"]
prop["M"] = 1/((1-A)/Mw+A/Ma)
prop["HR"] = 1/A-1
prop["xa"] = A*Mw/Ma/(1-A*(1-Mw/Ma))
prop["xw"] = 1-prop["xa"]
return prop | Miscelaneous properties of humid air
Parameters
----------
rho : float
Density, [kg/m³]
A : float
Mass fraction of dry air in humid air, [kg/kg]
fav : dict
dictionary with helmholtz energy and derivatives
Returns
-------
prop : dict
Dictionary with calculated properties:
* mu: Relative chemical potential, [kJ/kg]
* muw: Chemical potential of water, [kJ/kg]
* M: Molar mass of humid air, [g/mol]
* HR: Humidity ratio, [-]
* xa: Mole fraction of dry air, [-]
* xw: Mole fraction of water, [-]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 12,
http://www.iapws.org/relguide/SeaAir.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L815-L853 |
jjgomera/iapws | iapws/humidAir.py | HumidAir._fav | def _fav(self, T, rho, A):
r"""Specific Helmholtz energy of humid air and derivatives
Parameters
----------
T : float
Temperature, [K]
rho : float
Density, [kg/m³]
A : float
Mass fraction of dry air in humid air, [kg/kg]
Returns
-------
prop : dict
Dictionary with helmholtz energy and derivatives:
* fir, [kJ/kg]
* fira: :math:`\left.\frac{\partial f_{av}}{\partial A}\right|_{T,\rho}`, [kJ/kg]
* firt: :math:`\left.\frac{\partial f_{av}}{\partial T}\right|_{A,\rho}`, [kJ/kgK]
* fird: :math:`\left.\frac{\partial f_{av}}{\partial \rho}\right|_{A,T}`, [kJ/m³kg²]
* firaa: :math:`\left.\frac{\partial^2 f_{av}}{\partial A^2}\right|_{T, \rho}`, [kJ/kg]
* firat: :math:`\left.\frac{\partial^2 f_{av}}{\partial A \partial T}\right|_{\rho}`, [kJ/kgK]
* firad: :math:`\left.\frac{\partial^2 f_{av}}{\partial A \partial \rho}\right|_T`, [kJ/m³kg²]
* firtt: :math:`\left.\frac{\partial^2 f_{av}}{\partial T^2}\right|_{A, \rho}`, [kJ/kgK²]
* firdt: :math:`\left.\frac{\partial^2 f_{av}}{\partial \rho \partial T}\right|_A`, [kJ/m³kg²K]
* firdd: :math:`\left.\frac{\partial^2 f_{av}}{\partial \rho^2}\right|_{A, T}`, [kJ/m⁶kg³]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 6,
http://www.iapws.org/relguide/SeaAir.html
"""
water = IAPWS95()
rhov = (1-A)*rho
fv = water._derivDimensional(rhov, T)
air = Air()
rhoa = A*rho
fa = air._derivDimensional(rhoa, T)
fmix = self._fmix(T, rho, A)
prop = {}
# Eq T11
prop["fir"] = (1-A)*fv["fir"] + A*fa["fir"] + fmix["fir"]
# Eq T12
prop["fira"] = -fv["fir"]-rhov*fv["fird"]+fa["fir"] + \
rhoa*fa["fird"]+fmix["fira"]
# Eq T13
prop["firt"] = (1-A)*fv["firt"]+A*fa["firt"]+fmix["firt"]
# Eq T14
prop["fird"] = (1-A)**2*fv["fird"]+A**2*fa["fird"]+fmix["fird"]
# Eq T15
prop["firaa"] = rho*(2*fv["fird"]+rhov*fv["firdd"] +
2*fa["fird"]+rhoa*fa["firdd"])+fmix["firaa"]
# Eq T16
prop["firat"] = -fv["firt"]-rhov*fv["firdt"]+fa["firt"] + \
rhoa*fa["firdt"]+fmix["firat"]
# Eq T17
prop["firad"] = -(1-A)*(2*fv["fird"]+rhov*fv["firdd"]) + \
A*(2*fa["fird"]+rhoa*fa["firdd"])+fmix["firad"]
# Eq T18
prop["firtt"] = (1-A)*fv["firtt"]+A*fa["firtt"]+fmix["firtt"]
# Eq T19
prop["firdt"] = (1-A)**2*fv["firdt"]+A**2*fa["firdt"]+fmix["firdt"]
# Eq T20
prop["firdd"] = (1-A)**3*fv["firdd"]+A**3*fa["firdd"]+fmix["firdd"]
return prop | python | def _fav(self, T, rho, A):
r"""Specific Helmholtz energy of humid air and derivatives
Parameters
----------
T : float
Temperature, [K]
rho : float
Density, [kg/m³]
A : float
Mass fraction of dry air in humid air, [kg/kg]
Returns
-------
prop : dict
Dictionary with helmholtz energy and derivatives:
* fir, [kJ/kg]
* fira: :math:`\left.\frac{\partial f_{av}}{\partial A}\right|_{T,\rho}`, [kJ/kg]
* firt: :math:`\left.\frac{\partial f_{av}}{\partial T}\right|_{A,\rho}`, [kJ/kgK]
* fird: :math:`\left.\frac{\partial f_{av}}{\partial \rho}\right|_{A,T}`, [kJ/m³kg²]
* firaa: :math:`\left.\frac{\partial^2 f_{av}}{\partial A^2}\right|_{T, \rho}`, [kJ/kg]
* firat: :math:`\left.\frac{\partial^2 f_{av}}{\partial A \partial T}\right|_{\rho}`, [kJ/kgK]
* firad: :math:`\left.\frac{\partial^2 f_{av}}{\partial A \partial \rho}\right|_T`, [kJ/m³kg²]
* firtt: :math:`\left.\frac{\partial^2 f_{av}}{\partial T^2}\right|_{A, \rho}`, [kJ/kgK²]
* firdt: :math:`\left.\frac{\partial^2 f_{av}}{\partial \rho \partial T}\right|_A`, [kJ/m³kg²K]
* firdd: :math:`\left.\frac{\partial^2 f_{av}}{\partial \rho^2}\right|_{A, T}`, [kJ/m⁶kg³]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 6,
http://www.iapws.org/relguide/SeaAir.html
"""
water = IAPWS95()
rhov = (1-A)*rho
fv = water._derivDimensional(rhov, T)
air = Air()
rhoa = A*rho
fa = air._derivDimensional(rhoa, T)
fmix = self._fmix(T, rho, A)
prop = {}
# Eq T11
prop["fir"] = (1-A)*fv["fir"] + A*fa["fir"] + fmix["fir"]
# Eq T12
prop["fira"] = -fv["fir"]-rhov*fv["fird"]+fa["fir"] + \
rhoa*fa["fird"]+fmix["fira"]
# Eq T13
prop["firt"] = (1-A)*fv["firt"]+A*fa["firt"]+fmix["firt"]
# Eq T14
prop["fird"] = (1-A)**2*fv["fird"]+A**2*fa["fird"]+fmix["fird"]
# Eq T15
prop["firaa"] = rho*(2*fv["fird"]+rhov*fv["firdd"] +
2*fa["fird"]+rhoa*fa["firdd"])+fmix["firaa"]
# Eq T16
prop["firat"] = -fv["firt"]-rhov*fv["firdt"]+fa["firt"] + \
rhoa*fa["firdt"]+fmix["firat"]
# Eq T17
prop["firad"] = -(1-A)*(2*fv["fird"]+rhov*fv["firdd"]) + \
A*(2*fa["fird"]+rhoa*fa["firdd"])+fmix["firad"]
# Eq T18
prop["firtt"] = (1-A)*fv["firtt"]+A*fa["firtt"]+fmix["firtt"]
# Eq T19
prop["firdt"] = (1-A)**2*fv["firdt"]+A**2*fa["firdt"]+fmix["firdt"]
# Eq T20
prop["firdd"] = (1-A)**3*fv["firdd"]+A**3*fa["firdd"]+fmix["firdd"]
return prop | r"""Specific Helmholtz energy of humid air and derivatives
Parameters
----------
T : float
Temperature, [K]
rho : float
Density, [kg/m³]
A : float
Mass fraction of dry air in humid air, [kg/kg]
Returns
-------
prop : dict
Dictionary with helmholtz energy and derivatives:
* fir, [kJ/kg]
* fira: :math:`\left.\frac{\partial f_{av}}{\partial A}\right|_{T,\rho}`, [kJ/kg]
* firt: :math:`\left.\frac{\partial f_{av}}{\partial T}\right|_{A,\rho}`, [kJ/kgK]
* fird: :math:`\left.\frac{\partial f_{av}}{\partial \rho}\right|_{A,T}`, [kJ/m³kg²]
* firaa: :math:`\left.\frac{\partial^2 f_{av}}{\partial A^2}\right|_{T, \rho}`, [kJ/kg]
* firat: :math:`\left.\frac{\partial^2 f_{av}}{\partial A \partial T}\right|_{\rho}`, [kJ/kgK]
* firad: :math:`\left.\frac{\partial^2 f_{av}}{\partial A \partial \rho}\right|_T`, [kJ/m³kg²]
* firtt: :math:`\left.\frac{\partial^2 f_{av}}{\partial T^2}\right|_{A, \rho}`, [kJ/kgK²]
* firdt: :math:`\left.\frac{\partial^2 f_{av}}{\partial \rho \partial T}\right|_A`, [kJ/m³kg²K]
* firdd: :math:`\left.\frac{\partial^2 f_{av}}{\partial \rho^2}\right|_{A, T}`, [kJ/m⁶kg³]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 6,
http://www.iapws.org/relguide/SeaAir.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L855-L925 |
jjgomera/iapws | iapws/humidAir.py | HumidAir._fmix | def _fmix(self, T, rho, A):
r"""Specific Helmholtz energy of air-water interaction
Parameters
----------
T : float
Temperature, [K]
rho : float
Density, [kg/m³]
A : float
Mass fraction of dry air in humid air, [kg/kg]
Returns
-------
prop : dict
Dictionary with helmholtz energy and derivatives:
* fir, [kJ/kg]
* fira: :math:`\left.\frac{\partial f_{mix}}{\partial A}\right|_{T,\rho}`, [kJ/kg]
* firt: :math:`\left.\frac{\partial f_{mix}}{\partial T}\right|_{A,\rho}`, [kJ/kgK]
* fird: :math:`\left.\frac{\partial f_{mix}}{\partial \rho}\right|_{A,T}`, [kJ/m³kg²]
* firaa: :math:`\left.\frac{\partial^2 f_{mix}}{\partial A^2}\right|_{T, \rho}`, [kJ/kg]
* firat: :math:`\left.\frac{\partial^2 f_{mix}}{\partial A \partial T}\right|_{\rho}`, [kJ/kgK]
* firad: :math:`\left.\frac{\partial^2 f_{mix}}{\partial A \partial \rho}\right|_T`, [kJ/m³kg²]
* firtt: :math:`\left.\frac{\partial^2 f_{mix}}{\partial T^2}\right|_{A, \rho}`, [kJ/kgK²]
* firdt: :math:`\left.\frac{\partial^2 f_{mix}}{\partial \rho \partial T}\right|_A`, [kJ/m³kg²K]
* firdd: :math:`\left.\frac{\partial^2 f_{mix}}{\partial \rho^2}\right|_{A, T}`, [kJ/m⁶kg³]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 10,
http://www.iapws.org/relguide/SeaAir.html
"""
Ma = Air.M/1000
Mw = IAPWS95.M/1000
vir = _virial(T)
Baw = vir["Baw"]
Bawt = vir["Bawt"]
Bawtt = vir["Bawtt"]
Caaw = vir["Caaw"]
Caawt = vir["Caawt"]
Caawtt = vir["Caawtt"]
Caww = vir["Caww"]
Cawwt = vir["Cawwt"]
Cawwtt = vir["Cawwtt"]
# Eq T45
f = 2*A*(1-A)*rho*R*T/Ma/Mw*(Baw+3*rho/4*(A/Ma*Caaw+(1-A)/Mw*Caww))
# Eq T46
fa = 2*rho*R*T/Ma/Mw*((1-2*A)*Baw+3*rho/4*(
A*(2-3*A)/Ma*Caaw+(1-A)*(1-3*A)/Mw*Caww))
# Eq T47
ft = 2*A*(1-A)*rho*R/Ma/Mw*(
Baw+T*Bawt+3*rho/4*(A/Ma*(Caaw+T*Caawt)+(1-A)/Mw*(Caww+T*Cawwt)))
# Eq T48
fd = A*(1-A)*R*T/Ma/Mw*(2*Baw+3*rho*(A/Ma*Caaw+(1-A)/Mw*Caww))
# Eq T49
faa = rho*R*T/Ma/Mw*(-4*Baw+3*rho*((1-3*A)/Ma*Caaw-(2-3*A)/Mw*Caww))
# Eq T50
fat = 2*rho*R/Ma/Mw*(1-2*A)*(Baw+T*Bawt)+3*rho**2*R/2/Ma/Mw*(
A*(2-3*A)/Ma*(Caaw+T*Caawt)+(1-A)*(1-3*A)/Mw*(Caww+T*Cawwt))
# Eq T51
fad = 2*R*T/Ma/Mw*((1-2*A)*Baw+3/2*rho*(
A*(2-3*A)/Ma*Caaw+(1-A)*(1-3*A)/Mw*Caww))
# Eq T52
ftt = 2*A*(1-A)*rho*R/Ma/Mw*(2*Bawt+T*Bawtt+3*rho/4*(
A/Ma*(2*Caawt+T*Caawtt)+(1-A)/Mw*(2*Cawwt+T*Cawwtt)))
# Eq T53
ftd = 2*A*(1-A)*R/Ma/Mw*(Baw+T*Bawt+3*rho/2*(
A/Ma*(Caaw+T*Caawt)+(1-A)/Mw*(Caww+T*Cawwt)))
# Eq T54
fdd = 3*A*(1-A)*R*T/Ma/Mw*(A/Ma*Caaw+(1-A)/Mw*Caww)
prop = {}
prop["fir"] = f/1000
prop["fira"] = fa/1000
prop["firt"] = ft/1000
prop["fird"] = fd/1000
prop["firaa"] = faa/1000
prop["firat"] = fat/1000
prop["firad"] = fad/1000
prop["firtt"] = ftt/1000
prop["firdt"] = ftd/1000
prop["firdd"] = fdd/1000
return prop | python | def _fmix(self, T, rho, A):
r"""Specific Helmholtz energy of air-water interaction
Parameters
----------
T : float
Temperature, [K]
rho : float
Density, [kg/m³]
A : float
Mass fraction of dry air in humid air, [kg/kg]
Returns
-------
prop : dict
Dictionary with helmholtz energy and derivatives:
* fir, [kJ/kg]
* fira: :math:`\left.\frac{\partial f_{mix}}{\partial A}\right|_{T,\rho}`, [kJ/kg]
* firt: :math:`\left.\frac{\partial f_{mix}}{\partial T}\right|_{A,\rho}`, [kJ/kgK]
* fird: :math:`\left.\frac{\partial f_{mix}}{\partial \rho}\right|_{A,T}`, [kJ/m³kg²]
* firaa: :math:`\left.\frac{\partial^2 f_{mix}}{\partial A^2}\right|_{T, \rho}`, [kJ/kg]
* firat: :math:`\left.\frac{\partial^2 f_{mix}}{\partial A \partial T}\right|_{\rho}`, [kJ/kgK]
* firad: :math:`\left.\frac{\partial^2 f_{mix}}{\partial A \partial \rho}\right|_T`, [kJ/m³kg²]
* firtt: :math:`\left.\frac{\partial^2 f_{mix}}{\partial T^2}\right|_{A, \rho}`, [kJ/kgK²]
* firdt: :math:`\left.\frac{\partial^2 f_{mix}}{\partial \rho \partial T}\right|_A`, [kJ/m³kg²K]
* firdd: :math:`\left.\frac{\partial^2 f_{mix}}{\partial \rho^2}\right|_{A, T}`, [kJ/m⁶kg³]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 10,
http://www.iapws.org/relguide/SeaAir.html
"""
Ma = Air.M/1000
Mw = IAPWS95.M/1000
vir = _virial(T)
Baw = vir["Baw"]
Bawt = vir["Bawt"]
Bawtt = vir["Bawtt"]
Caaw = vir["Caaw"]
Caawt = vir["Caawt"]
Caawtt = vir["Caawtt"]
Caww = vir["Caww"]
Cawwt = vir["Cawwt"]
Cawwtt = vir["Cawwtt"]
# Eq T45
f = 2*A*(1-A)*rho*R*T/Ma/Mw*(Baw+3*rho/4*(A/Ma*Caaw+(1-A)/Mw*Caww))
# Eq T46
fa = 2*rho*R*T/Ma/Mw*((1-2*A)*Baw+3*rho/4*(
A*(2-3*A)/Ma*Caaw+(1-A)*(1-3*A)/Mw*Caww))
# Eq T47
ft = 2*A*(1-A)*rho*R/Ma/Mw*(
Baw+T*Bawt+3*rho/4*(A/Ma*(Caaw+T*Caawt)+(1-A)/Mw*(Caww+T*Cawwt)))
# Eq T48
fd = A*(1-A)*R*T/Ma/Mw*(2*Baw+3*rho*(A/Ma*Caaw+(1-A)/Mw*Caww))
# Eq T49
faa = rho*R*T/Ma/Mw*(-4*Baw+3*rho*((1-3*A)/Ma*Caaw-(2-3*A)/Mw*Caww))
# Eq T50
fat = 2*rho*R/Ma/Mw*(1-2*A)*(Baw+T*Bawt)+3*rho**2*R/2/Ma/Mw*(
A*(2-3*A)/Ma*(Caaw+T*Caawt)+(1-A)*(1-3*A)/Mw*(Caww+T*Cawwt))
# Eq T51
fad = 2*R*T/Ma/Mw*((1-2*A)*Baw+3/2*rho*(
A*(2-3*A)/Ma*Caaw+(1-A)*(1-3*A)/Mw*Caww))
# Eq T52
ftt = 2*A*(1-A)*rho*R/Ma/Mw*(2*Bawt+T*Bawtt+3*rho/4*(
A/Ma*(2*Caawt+T*Caawtt)+(1-A)/Mw*(2*Cawwt+T*Cawwtt)))
# Eq T53
ftd = 2*A*(1-A)*R/Ma/Mw*(Baw+T*Bawt+3*rho/2*(
A/Ma*(Caaw+T*Caawt)+(1-A)/Mw*(Caww+T*Cawwt)))
# Eq T54
fdd = 3*A*(1-A)*R*T/Ma/Mw*(A/Ma*Caaw+(1-A)/Mw*Caww)
prop = {}
prop["fir"] = f/1000
prop["fira"] = fa/1000
prop["firt"] = ft/1000
prop["fird"] = fd/1000
prop["firaa"] = faa/1000
prop["firat"] = fat/1000
prop["firad"] = fad/1000
prop["firtt"] = ftt/1000
prop["firdt"] = ftd/1000
prop["firdd"] = fdd/1000
return prop | r"""Specific Helmholtz energy of air-water interaction
Parameters
----------
T : float
Temperature, [K]
rho : float
Density, [kg/m³]
A : float
Mass fraction of dry air in humid air, [kg/kg]
Returns
-------
prop : dict
Dictionary with helmholtz energy and derivatives:
* fir, [kJ/kg]
* fira: :math:`\left.\frac{\partial f_{mix}}{\partial A}\right|_{T,\rho}`, [kJ/kg]
* firt: :math:`\left.\frac{\partial f_{mix}}{\partial T}\right|_{A,\rho}`, [kJ/kgK]
* fird: :math:`\left.\frac{\partial f_{mix}}{\partial \rho}\right|_{A,T}`, [kJ/m³kg²]
* firaa: :math:`\left.\frac{\partial^2 f_{mix}}{\partial A^2}\right|_{T, \rho}`, [kJ/kg]
* firat: :math:`\left.\frac{\partial^2 f_{mix}}{\partial A \partial T}\right|_{\rho}`, [kJ/kgK]
* firad: :math:`\left.\frac{\partial^2 f_{mix}}{\partial A \partial \rho}\right|_T`, [kJ/m³kg²]
* firtt: :math:`\left.\frac{\partial^2 f_{mix}}{\partial T^2}\right|_{A, \rho}`, [kJ/kgK²]
* firdt: :math:`\left.\frac{\partial^2 f_{mix}}{\partial \rho \partial T}\right|_A`, [kJ/m³kg²K]
* firdd: :math:`\left.\frac{\partial^2 f_{mix}}{\partial \rho^2}\right|_{A, T}`, [kJ/m⁶kg³]
References
----------
IAPWS, Guideline on an Equation of State for Humid Air in Contact with
Seawater and Ice, Consistent with the IAPWS Formulation 2008 for the
Thermodynamic Properties of Seawater, Table 10,
http://www.iapws.org/relguide/SeaAir.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/humidAir.py#L927-L1013 |
jjgomera/iapws | iapws/_iapws.py | _Ice | def _Ice(T, P):
"""Basic state equation for Ice Ih
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties of ice. The available properties are:
* rho: Density, [kg/m³]
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* alfav: Cubic expansion coefficient, [1/K]
* beta: Pressure coefficient, [MPa/K]
* xkappa: Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* gt: [∂g/∂T]P
* gtt: [∂²g/∂T²]P
* gp: [∂g/∂P]T
* gpp: [∂²g/∂P²]T
* gtp: [∂²g/∂T∂P]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* T ≤ 273.16
* P ≤ 208.566
* State below the melting and sublimation lines
Examples
--------
>>> st1 = _Ice(100, 100)
>>> st1["rho"], st1["h"], st1["s"]
941.678203297 -483.491635676 -2.61195122589
>>> st2 = _Ice(273.152519,0.101325)
>>> st2["a"], st2["u"], st2["cp"]
-0.00918701567 -333.465403393 2.09671391024
>>> st3 = _Ice(273.16,611.657e-6)
>>> st3["alfav"], st3["beta"], st3["xkappa"], st3["ks"]
0.000159863102566 1.35714764659 1.17793449348e-04 1.14161597779e-04
References
----------
IAPWS, Revised Release on the Equation of State 2006 for H2O Ice Ih
September 2009, http://iapws.org/relguide/Ice-2009.html
"""
# Check input in range of validity
if T > 273.16:
# No Ice Ih stable
warnings.warn("Metastable ice")
elif P > 208.566:
# Ice Ih limit upper pressure
raise NotImplementedError("Incoming out of bound")
elif P < Pt:
Psub = _Sublimation_Pressure(T)
if Psub > P:
# Zone Gas
warnings.warn("Metastable ice in vapor region")
elif 251.165 < T:
Pmel = _Melting_Pressure(T)
if Pmel < P:
# Zone Liquid
warnings.warn("Metastable ice in liquid region")
Tr = T/Tt
Pr = P/Pt
P0 = 101325e-6/Pt
s0 = -0.332733756492168e4*1e-3 # Express in kJ/kgK
gok = [-0.632020233335886e6, 0.655022213658955, -0.189369929326131e-7,
0.339746123271053e-14, -0.556464869058991e-21]
r2k = [complex(-0.725974574329220e2, -0.781008427112870e2)*1e-3,
complex(-0.557107698030123e-4, 0.464578634580806e-4)*1e-3,
complex(0.234801409215913e-10, -0.285651142904972e-10)*1e-3]
t1 = complex(0.368017112855051e-1, 0.510878114959572e-1)
t2 = complex(0.337315741065416, 0.335449415919309)
r1 = complex(0.447050716285388e2, 0.656876847463481e2)*1e-3
go = gop = gopp = 0
for k in range(5):
go += gok[k]*1e-3*(Pr-P0)**k
for k in range(1, 5):
gop += gok[k]*1e-3*k/Pt*(Pr-P0)**(k-1)
for k in range(2, 5):
gopp += gok[k]*1e-3*k*(k-1)/Pt**2*(Pr-P0)**(k-2)
r2 = r2p = 0
for k in range(3):
r2 += r2k[k]*(Pr-P0)**k
for k in range(1, 3):
r2p += r2k[k]*k/Pt*(Pr-P0)**(k-1)
r2pp = r2k[2]*2/Pt**2
c = r1*((t1-Tr)*log_c(t1-Tr)+(t1+Tr)*log_c(t1+Tr)-2*t1*log_c(
t1)-Tr**2/t1)+r2*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ct = r1*(-log_c(t1-Tr)+log_c(t1+Tr)-2*Tr/t1)+r2*(
-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
ctt = r1*(1/(t1-Tr)+1/(t1+Tr)-2/t1) + r2*(1/(t2-Tr)+1/(t2+Tr)-2/t2)
cp = r2p*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ctp = r2p*(-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
cpp = r2pp*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
g = go-s0*Tt*Tr+Tt*c.real
gt = -s0+ct.real
gp = gop+Tt*cp.real
gtt = ctt.real/Tt
gtp = ctp.real
gpp = gopp+Tt*cpp.real
propiedades = {}
propiedades["gt"] = gt
propiedades["gp"] = gp
propiedades["gtt"] = gtt
propiedades["gpp"] = gpp
propiedades["gtp"] = gtp
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = gp/1000
propiedades["rho"] = 1000./gp
propiedades["h"] = g-T*gt
propiedades["s"] = -gt
propiedades["cp"] = -T*gtt
propiedades["u"] = g-T*gt-P*gp
propiedades["g"] = g
propiedades["a"] = g-P*gp
propiedades["alfav"] = gtp/gp
propiedades["beta"] = -gtp/gpp
propiedades["xkappa"] = -gpp/gp
propiedades["ks"] = (gtp**2-gtt*gpp)/gp/gtt
return propiedades | python | def _Ice(T, P):
"""Basic state equation for Ice Ih
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties of ice. The available properties are:
* rho: Density, [kg/m³]
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* alfav: Cubic expansion coefficient, [1/K]
* beta: Pressure coefficient, [MPa/K]
* xkappa: Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* gt: [∂g/∂T]P
* gtt: [∂²g/∂T²]P
* gp: [∂g/∂P]T
* gpp: [∂²g/∂P²]T
* gtp: [∂²g/∂T∂P]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* T ≤ 273.16
* P ≤ 208.566
* State below the melting and sublimation lines
Examples
--------
>>> st1 = _Ice(100, 100)
>>> st1["rho"], st1["h"], st1["s"]
941.678203297 -483.491635676 -2.61195122589
>>> st2 = _Ice(273.152519,0.101325)
>>> st2["a"], st2["u"], st2["cp"]
-0.00918701567 -333.465403393 2.09671391024
>>> st3 = _Ice(273.16,611.657e-6)
>>> st3["alfav"], st3["beta"], st3["xkappa"], st3["ks"]
0.000159863102566 1.35714764659 1.17793449348e-04 1.14161597779e-04
References
----------
IAPWS, Revised Release on the Equation of State 2006 for H2O Ice Ih
September 2009, http://iapws.org/relguide/Ice-2009.html
"""
# Check input in range of validity
if T > 273.16:
# No Ice Ih stable
warnings.warn("Metastable ice")
elif P > 208.566:
# Ice Ih limit upper pressure
raise NotImplementedError("Incoming out of bound")
elif P < Pt:
Psub = _Sublimation_Pressure(T)
if Psub > P:
# Zone Gas
warnings.warn("Metastable ice in vapor region")
elif 251.165 < T:
Pmel = _Melting_Pressure(T)
if Pmel < P:
# Zone Liquid
warnings.warn("Metastable ice in liquid region")
Tr = T/Tt
Pr = P/Pt
P0 = 101325e-6/Pt
s0 = -0.332733756492168e4*1e-3 # Express in kJ/kgK
gok = [-0.632020233335886e6, 0.655022213658955, -0.189369929326131e-7,
0.339746123271053e-14, -0.556464869058991e-21]
r2k = [complex(-0.725974574329220e2, -0.781008427112870e2)*1e-3,
complex(-0.557107698030123e-4, 0.464578634580806e-4)*1e-3,
complex(0.234801409215913e-10, -0.285651142904972e-10)*1e-3]
t1 = complex(0.368017112855051e-1, 0.510878114959572e-1)
t2 = complex(0.337315741065416, 0.335449415919309)
r1 = complex(0.447050716285388e2, 0.656876847463481e2)*1e-3
go = gop = gopp = 0
for k in range(5):
go += gok[k]*1e-3*(Pr-P0)**k
for k in range(1, 5):
gop += gok[k]*1e-3*k/Pt*(Pr-P0)**(k-1)
for k in range(2, 5):
gopp += gok[k]*1e-3*k*(k-1)/Pt**2*(Pr-P0)**(k-2)
r2 = r2p = 0
for k in range(3):
r2 += r2k[k]*(Pr-P0)**k
for k in range(1, 3):
r2p += r2k[k]*k/Pt*(Pr-P0)**(k-1)
r2pp = r2k[2]*2/Pt**2
c = r1*((t1-Tr)*log_c(t1-Tr)+(t1+Tr)*log_c(t1+Tr)-2*t1*log_c(
t1)-Tr**2/t1)+r2*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ct = r1*(-log_c(t1-Tr)+log_c(t1+Tr)-2*Tr/t1)+r2*(
-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
ctt = r1*(1/(t1-Tr)+1/(t1+Tr)-2/t1) + r2*(1/(t2-Tr)+1/(t2+Tr)-2/t2)
cp = r2p*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
ctp = r2p*(-log_c(t2-Tr)+log_c(t2+Tr)-2*Tr/t2)
cpp = r2pp*((t2-Tr)*log_c(t2-Tr)+(t2+Tr)*log_c(
t2+Tr)-2*t2*log_c(t2)-Tr**2/t2)
g = go-s0*Tt*Tr+Tt*c.real
gt = -s0+ct.real
gp = gop+Tt*cp.real
gtt = ctt.real/Tt
gtp = ctp.real
gpp = gopp+Tt*cpp.real
propiedades = {}
propiedades["gt"] = gt
propiedades["gp"] = gp
propiedades["gtt"] = gtt
propiedades["gpp"] = gpp
propiedades["gtp"] = gtp
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = gp/1000
propiedades["rho"] = 1000./gp
propiedades["h"] = g-T*gt
propiedades["s"] = -gt
propiedades["cp"] = -T*gtt
propiedades["u"] = g-T*gt-P*gp
propiedades["g"] = g
propiedades["a"] = g-P*gp
propiedades["alfav"] = gtp/gp
propiedades["beta"] = -gtp/gpp
propiedades["xkappa"] = -gpp/gp
propiedades["ks"] = (gtp**2-gtt*gpp)/gp/gtt
return propiedades | Basic state equation for Ice Ih
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties of ice. The available properties are:
* rho: Density, [kg/m³]
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* alfav: Cubic expansion coefficient, [1/K]
* beta: Pressure coefficient, [MPa/K]
* xkappa: Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* gt: [∂g/∂T]P
* gtt: [∂²g/∂T²]P
* gp: [∂g/∂P]T
* gpp: [∂²g/∂P²]T
* gtp: [∂²g/∂T∂P]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* T ≤ 273.16
* P ≤ 208.566
* State below the melting and sublimation lines
Examples
--------
>>> st1 = _Ice(100, 100)
>>> st1["rho"], st1["h"], st1["s"]
941.678203297 -483.491635676 -2.61195122589
>>> st2 = _Ice(273.152519,0.101325)
>>> st2["a"], st2["u"], st2["cp"]
-0.00918701567 -333.465403393 2.09671391024
>>> st3 = _Ice(273.16,611.657e-6)
>>> st3["alfav"], st3["beta"], st3["xkappa"], st3["ks"]
0.000159863102566 1.35714764659 1.17793449348e-04 1.14161597779e-04
References
----------
IAPWS, Revised Release on the Equation of State 2006 for H2O Ice Ih
September 2009, http://iapws.org/relguide/Ice-2009.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L62-L206 |
jjgomera/iapws | iapws/_iapws.py | _Liquid | def _Liquid(T, P=0.1):
"""Supplementary release on properties of liquid water at 0.1 MPa
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Although this relation is for P=0.1MPa, can be extrapoled at pressure
0.3 MPa
Returns
-------
prop : dict
Dict with calculated properties of water. The available properties are:
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isochoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s²]
* rho: Density, [kg/m³]
* v: Specific volume, [m³/kg]
* vt: [∂v/∂T]P, [m³/kgK]
* vtt: [∂²v/∂T²]P, [m³/kgK²]
* vp: [∂v/∂P]T, [m³/kg/MPa]
* vtp: [∂²v/∂T∂P], [m³/kg/MPa]
* alfav: Cubic expansion coefficient, [1/K]
* xkappa : Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* mu: Viscosity, [mPas]
* k: Thermal conductivity, [W/mK]
* epsilon: Dielectric constant, [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 253.15 ≤ T ≤ 383.15
* 0.1 ≤ P ≤ 0.3
Examples
--------
>>> st1 = _Liquid(260)
>>> st1["rho"], st1["h"], st1["s"]
997.0683602710492 -55.86223174460868 -0.20998554842619535
References
----------
IAPWS, Revised Supplementary Release on Properties of Liquid Water at 0.1
MPa, http://www.iapws.org/relguide/LiquidWater.html
"""
# Check input in range of validity
if T <= 253.15 or T >= 383.15 or P < 0.1 or P > 0.3:
raise NotImplementedError("Incoming out of bound")
elif P != 0.1:
# Raise a warning if the P value is extrapolated
warnings.warn("Using extrapolated values")
R = 0.46151805 # kJ/kgK
Po = 0.1
Tr = 10
tau = T/Tr
alfa = Tr/(593-T)
beta = Tr/(T-232)
a = [None, -1.661470539e5, 2.708781640e6, -1.557191544e8, None,
1.93763157e-2, 6.74458446e3, -2.22521604e5, 1.00231247e8,
-1.63552118e9, 8.32299658e9, -7.5245878e-6, -1.3767418e-2,
1.0627293e1, -2.0457795e2, 1.2037414e3]
b = [None, -8.237426256e-1, 1.908956353, -2.017597384, 8.546361348e-1,
5.78545292e-3, -1.53195665E-2, 3.11337859e-2, -4.23546241e-2,
3.38713507e-2, -1.19946761e-2, -3.1091470e-6, 2.8964919e-5,
-1.3112763e-4, 3.0410453e-4, -3.9034594e-4, 2.3403117e-4,
-4.8510101e-5]
c = [None, -2.452093414e2, 3.869269598e1, -8.983025854]
n = [None, 4, 5, 7, None, None, 4, 5, 7, 8, 9, 1, 3, 5, 6, 7]
m = [None, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 3, 4, 5, 6, 7, 9]
suma1 = sum([a[i]*alfa**n[i] for i in range(1, 4)])
suma2 = sum([b[i]*beta**m[i] for i in range(1, 5)])
go = R*Tr*(c[1]+c[2]*tau+c[3]*tau*log(tau)+suma1+suma2)
suma1 = sum([a[i]*alfa**n[i] for i in range(6, 11)])
suma2 = sum([b[i]*beta**m[i] for i in range(5, 11)])
vo = R*Tr/Po/1000*(a[5]+suma1+suma2)
suma1 = sum([a[i]*alfa**n[i] for i in range(11, 16)])
suma2 = sum([b[i]*beta**m[i] for i in range(11, 18)])
vpo = R*Tr/Po**2/1000*(suma1+suma2)
suma1 = sum([n[i]*a[i]*alfa**(n[i]+1) for i in range(1, 4)])
suma2 = sum([m[i]*b[i]*beta**(m[i]+1) for i in range(1, 5)])
so = -R*(c[2]+c[3]*(1+log(tau))+suma1-suma2)
suma1 = sum([n[i]*(n[i]+1)*a[i]*alfa**(n[i]+2) for i in range(1, 4)])
suma2 = sum([m[i]*(m[i]+1)*b[i]*beta**(m[i]+2) for i in range(1, 5)])
cpo = -R*(c[3]+tau*suma1+tau*suma2)
suma1 = sum([n[i]*a[i]*alfa**(n[i]+1) for i in range(6, 11)])
suma2 = sum([m[i]*b[i]*beta**(m[i]+1) for i in range(5, 11)])
vto = R/Po/1000*(suma1-suma2)
# This properties are only neccessary for computing thermodynamic
# properties at pressures different from 0.1 MPa
suma1 = sum([n[i]*(n[i]+1)*a[i]*alfa**(n[i]+2) for i in range(6, 11)])
suma2 = sum([m[i]*(m[i]+1)*b[i]*beta**(m[i]+2) for i in range(5, 11)])
vtto = R/Tr/Po/1000*(suma1+suma2)
suma1 = sum([n[i]*a[i]*alfa**(n[i]+1) for i in range(11, 16)])
suma2 = sum([m[i]*b[i]*beta**(m[i]+1) for i in range(11, 18)])
vpto = R/Po**2/1000*(suma1-suma2)
if P != 0.1:
go += vo*(P-0.1)
so -= vto*(P-0.1)
cpo -= T*vtto*(P-0.1)
vo -= vpo*(P-0.1)
vto += vpto*(P-0.1)
vppo = 3.24e-10*R*Tr/0.1**3
vpo += vppo*(P-0.1)
h = go+T*so
u = h-P*vo
a = go-P*vo
cv = cpo+T*vto**2/vpo
xkappa = -vpo/vo
alfa = vto/vo
ks = -(T*vto**2/cpo+vpo)/vo
w = (-vo**2*1e9/(vpo*1e3+T*vto**2*1e6/cpo))**0.5
propiedades = {}
propiedades["g"] = go
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = vo
propiedades["vt"] = vto
propiedades["vp"] = vpo
propiedades["vpt"] = vpto
propiedades["vtt"] = vtto
propiedades["rho"] = 1/vo
propiedades["h"] = h
propiedades["s"] = so
propiedades["cp"] = cpo
propiedades["cv"] = cv
propiedades["u"] = u
propiedades["a"] = a
propiedades["xkappa"] = xkappa
propiedades["alfav"] = vto/vo
propiedades["ks"] = ks
propiedades["w"] = w
# Viscosity correlation, Eq 7
a = [None, 280.68, 511.45, 61.131, 0.45903]
b = [None, -1.9, -7.7, -19.6, -40]
T_ = T/300
mu = sum([a[i]*T_**b[i] for i in range(1, 5)])/1e6
propiedades["mu"] = mu
# Thermal conductivity correlation, Eq 8
c = [None, 1.6630, -1.7781, 1.1567, -0.432115]
d = [None, -1.15, -3.4, -6.0, -7.6]
k = sum([c[i]*T_**d[i] for i in range(1, 5)])
propiedades["k"] = k
# Dielectric constant correlation, Eq 9
e = [None, -43.7527, 299.504, -399.364, 221.327]
f = [None, -0.05, -1.47, -2.11, -2.31]
epsilon = sum([e[i]*T_**f[i] for i in range(1, 5)])
propiedades["epsilon"] = epsilon
return propiedades | python | def _Liquid(T, P=0.1):
"""Supplementary release on properties of liquid water at 0.1 MPa
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Although this relation is for P=0.1MPa, can be extrapoled at pressure
0.3 MPa
Returns
-------
prop : dict
Dict with calculated properties of water. The available properties are:
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isochoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s²]
* rho: Density, [kg/m³]
* v: Specific volume, [m³/kg]
* vt: [∂v/∂T]P, [m³/kgK]
* vtt: [∂²v/∂T²]P, [m³/kgK²]
* vp: [∂v/∂P]T, [m³/kg/MPa]
* vtp: [∂²v/∂T∂P], [m³/kg/MPa]
* alfav: Cubic expansion coefficient, [1/K]
* xkappa : Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* mu: Viscosity, [mPas]
* k: Thermal conductivity, [W/mK]
* epsilon: Dielectric constant, [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 253.15 ≤ T ≤ 383.15
* 0.1 ≤ P ≤ 0.3
Examples
--------
>>> st1 = _Liquid(260)
>>> st1["rho"], st1["h"], st1["s"]
997.0683602710492 -55.86223174460868 -0.20998554842619535
References
----------
IAPWS, Revised Supplementary Release on Properties of Liquid Water at 0.1
MPa, http://www.iapws.org/relguide/LiquidWater.html
"""
# Check input in range of validity
if T <= 253.15 or T >= 383.15 or P < 0.1 or P > 0.3:
raise NotImplementedError("Incoming out of bound")
elif P != 0.1:
# Raise a warning if the P value is extrapolated
warnings.warn("Using extrapolated values")
R = 0.46151805 # kJ/kgK
Po = 0.1
Tr = 10
tau = T/Tr
alfa = Tr/(593-T)
beta = Tr/(T-232)
a = [None, -1.661470539e5, 2.708781640e6, -1.557191544e8, None,
1.93763157e-2, 6.74458446e3, -2.22521604e5, 1.00231247e8,
-1.63552118e9, 8.32299658e9, -7.5245878e-6, -1.3767418e-2,
1.0627293e1, -2.0457795e2, 1.2037414e3]
b = [None, -8.237426256e-1, 1.908956353, -2.017597384, 8.546361348e-1,
5.78545292e-3, -1.53195665E-2, 3.11337859e-2, -4.23546241e-2,
3.38713507e-2, -1.19946761e-2, -3.1091470e-6, 2.8964919e-5,
-1.3112763e-4, 3.0410453e-4, -3.9034594e-4, 2.3403117e-4,
-4.8510101e-5]
c = [None, -2.452093414e2, 3.869269598e1, -8.983025854]
n = [None, 4, 5, 7, None, None, 4, 5, 7, 8, 9, 1, 3, 5, 6, 7]
m = [None, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 3, 4, 5, 6, 7, 9]
suma1 = sum([a[i]*alfa**n[i] for i in range(1, 4)])
suma2 = sum([b[i]*beta**m[i] for i in range(1, 5)])
go = R*Tr*(c[1]+c[2]*tau+c[3]*tau*log(tau)+suma1+suma2)
suma1 = sum([a[i]*alfa**n[i] for i in range(6, 11)])
suma2 = sum([b[i]*beta**m[i] for i in range(5, 11)])
vo = R*Tr/Po/1000*(a[5]+suma1+suma2)
suma1 = sum([a[i]*alfa**n[i] for i in range(11, 16)])
suma2 = sum([b[i]*beta**m[i] for i in range(11, 18)])
vpo = R*Tr/Po**2/1000*(suma1+suma2)
suma1 = sum([n[i]*a[i]*alfa**(n[i]+1) for i in range(1, 4)])
suma2 = sum([m[i]*b[i]*beta**(m[i]+1) for i in range(1, 5)])
so = -R*(c[2]+c[3]*(1+log(tau))+suma1-suma2)
suma1 = sum([n[i]*(n[i]+1)*a[i]*alfa**(n[i]+2) for i in range(1, 4)])
suma2 = sum([m[i]*(m[i]+1)*b[i]*beta**(m[i]+2) for i in range(1, 5)])
cpo = -R*(c[3]+tau*suma1+tau*suma2)
suma1 = sum([n[i]*a[i]*alfa**(n[i]+1) for i in range(6, 11)])
suma2 = sum([m[i]*b[i]*beta**(m[i]+1) for i in range(5, 11)])
vto = R/Po/1000*(suma1-suma2)
# This properties are only neccessary for computing thermodynamic
# properties at pressures different from 0.1 MPa
suma1 = sum([n[i]*(n[i]+1)*a[i]*alfa**(n[i]+2) for i in range(6, 11)])
suma2 = sum([m[i]*(m[i]+1)*b[i]*beta**(m[i]+2) for i in range(5, 11)])
vtto = R/Tr/Po/1000*(suma1+suma2)
suma1 = sum([n[i]*a[i]*alfa**(n[i]+1) for i in range(11, 16)])
suma2 = sum([m[i]*b[i]*beta**(m[i]+1) for i in range(11, 18)])
vpto = R/Po**2/1000*(suma1-suma2)
if P != 0.1:
go += vo*(P-0.1)
so -= vto*(P-0.1)
cpo -= T*vtto*(P-0.1)
vo -= vpo*(P-0.1)
vto += vpto*(P-0.1)
vppo = 3.24e-10*R*Tr/0.1**3
vpo += vppo*(P-0.1)
h = go+T*so
u = h-P*vo
a = go-P*vo
cv = cpo+T*vto**2/vpo
xkappa = -vpo/vo
alfa = vto/vo
ks = -(T*vto**2/cpo+vpo)/vo
w = (-vo**2*1e9/(vpo*1e3+T*vto**2*1e6/cpo))**0.5
propiedades = {}
propiedades["g"] = go
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = vo
propiedades["vt"] = vto
propiedades["vp"] = vpo
propiedades["vpt"] = vpto
propiedades["vtt"] = vtto
propiedades["rho"] = 1/vo
propiedades["h"] = h
propiedades["s"] = so
propiedades["cp"] = cpo
propiedades["cv"] = cv
propiedades["u"] = u
propiedades["a"] = a
propiedades["xkappa"] = xkappa
propiedades["alfav"] = vto/vo
propiedades["ks"] = ks
propiedades["w"] = w
# Viscosity correlation, Eq 7
a = [None, 280.68, 511.45, 61.131, 0.45903]
b = [None, -1.9, -7.7, -19.6, -40]
T_ = T/300
mu = sum([a[i]*T_**b[i] for i in range(1, 5)])/1e6
propiedades["mu"] = mu
# Thermal conductivity correlation, Eq 8
c = [None, 1.6630, -1.7781, 1.1567, -0.432115]
d = [None, -1.15, -3.4, -6.0, -7.6]
k = sum([c[i]*T_**d[i] for i in range(1, 5)])
propiedades["k"] = k
# Dielectric constant correlation, Eq 9
e = [None, -43.7527, 299.504, -399.364, 221.327]
f = [None, -0.05, -1.47, -2.11, -2.31]
epsilon = sum([e[i]*T_**f[i] for i in range(1, 5)])
propiedades["epsilon"] = epsilon
return propiedades | Supplementary release on properties of liquid water at 0.1 MPa
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Although this relation is for P=0.1MPa, can be extrapoled at pressure
0.3 MPa
Returns
-------
prop : dict
Dict with calculated properties of water. The available properties are:
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isochoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s²]
* rho: Density, [kg/m³]
* v: Specific volume, [m³/kg]
* vt: [∂v/∂T]P, [m³/kgK]
* vtt: [∂²v/∂T²]P, [m³/kgK²]
* vp: [∂v/∂P]T, [m³/kg/MPa]
* vtp: [∂²v/∂T∂P], [m³/kg/MPa]
* alfav: Cubic expansion coefficient, [1/K]
* xkappa : Isothermal compressibility, [1/MPa]
* ks: Isentropic compressibility, [1/MPa]
* mu: Viscosity, [mPas]
* k: Thermal conductivity, [W/mK]
* epsilon: Dielectric constant, [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 253.15 ≤ T ≤ 383.15
* 0.1 ≤ P ≤ 0.3
Examples
--------
>>> st1 = _Liquid(260)
>>> st1["rho"], st1["h"], st1["s"]
997.0683602710492 -55.86223174460868 -0.20998554842619535
References
----------
IAPWS, Revised Supplementary Release on Properties of Liquid Water at 0.1
MPa, http://www.iapws.org/relguide/LiquidWater.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L210-L385 |
jjgomera/iapws | iapws/_iapws.py | _Supercooled | def _Supercooled(T, P):
"""Guideline on thermodynamic properties of supercooled water
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties of water. The available properties are:
* L: Ordering field, [-]
* x: Mole fraction of low-density structure, [-]
* rho: Density, [kg/m³]
* s: Specific entropy, [kJ/kgK]
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* alfap: Thermal expansion coefficient, [1/K]
* xkappa : Isothermal compressibility, [1/MPa]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isochoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s²]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* Tm ≤ T ≤ 300
* 0 < P ≤ 1000
The minimum temperature in range of validity is the melting temperature, it
depend of pressure
Examples
--------
>>> liq = _Supercooled(235.15, 0.101325)
>>> liq["rho"], liq["cp"], liq["w"]
968.09999 5.997563 1134.5855
References
----------
IAPWS, Guideline on Thermodynamic Properties of Supercooled Water,
http://iapws.org/relguide/Supercooled.html
"""
# Check input in range of validity
if P < 198.9:
Tita = T/235.15
Ph = 0.1+228.27*(1-Tita**6.243)+15.724*(1-Tita**79.81)
if P < Ph or T > 300:
raise NotImplementedError("Incoming out of bound")
else:
Th = 172.82+0.03718*P+3.403e-5*P**2-1.573e-8*P**3
if T < Th or T > 300 or P > 1000:
raise NotImplementedError("Incoming out of bound")
# Parameters, Table 1
Tll = 228.2
rho0 = 1081.6482
R = 0.461523087
pi0 = 300e3/rho0/R/Tll
omega0 = 0.5212269
L0 = 0.76317954
k0 = 0.072158686
k1 = -0.31569232
k2 = 5.2992608
# Reducing parameters, Eq 2
tau = T/Tll-1
p = P*1000/rho0/R/Tll
tau_ = tau+1
p_ = p+pi0
# Eq 3
ci = [-8.1570681381655, 1.2875032, 7.0901673598012, -3.2779161e-2,
7.3703949e-1, -2.1628622e-1, -5.1782479, 4.2293517e-4, 2.3592109e-2,
4.3773754, -2.9967770e-3, -9.6558018e-1, 3.7595286, 1.2632441,
2.8542697e-1, -8.5994947e-1, -3.2916153e-1, 9.0019616e-2,
8.1149726e-2, -3.2788213]
ai = [0, 0, 1, -0.2555, 1.5762, 1.6400, 3.6385, -0.3828, 1.6219, 4.3287,
3.4763, 5.1556, -0.3593, 5.0361, 2.9786, 6.2373, 4.0460, 5.3558,
9.0157, 1.2194]
bi = [0, 1, 0, 2.1051, 1.1422, 0.9510, 0, 3.6402, 2.0760, -0.0016, 2.2769,
0.0008, 0.3706, -0.3975, 2.9730, -0.3180, 2.9805, 2.9265, 0.4456,
0.1298]
di = [0, 0, 0, -0.0016, 0.6894, 0.0130, 0.0002, 0.0435, 0.0500, 0.0004,
0.0528, 0.0147, 0.8584, 0.9924, 1.0041, 1.0961, 1.0228, 1.0303,
1.6180, 0.5213]
phir = phirt = phirp = phirtt = phirtp = phirpp = 0
for c, a, b, d in zip(ci, ai, bi, di):
phir += c*tau_**a*p_**b*exp(-d*p_)
phirt += c*a*tau_**(a-1)*p_**b*exp(-d*p_)
phirp += c*tau_**a*p_**(b-1)*(b-d*p_)*exp(-d*p_)
phirtt += c*a*(a-1)*tau_**(a-2)*p_**b*exp(-d*p_)
phirtp += c*a*tau_**(a-1)*p_**(b-1)*(b-d*p_)*exp(-d*p_)
phirpp += c*tau_**a*p_**(b-2)*((d*p_-b)**2-b)*exp(-d*p_)
# Eq 5
K1 = ((1+k0*k2+k1*(p-k2*tau))**2-4*k0*k1*k2*(p-k2*tau))**0.5
K2 = (1+k2**2)**0.5
# Eq 6
omega = 2+omega0*p
# Eq 4
L = L0*K2/2/k1/k2*(1+k0*k2+k1*(p+k2*tau)-K1)
# Define interval of solution, Table 4
if omega < 10/9*(log(19)-L):
xmin = 0.049
xmax = 0.5
elif 10/9*(log(19)-L) <= omega < 50/49*(log(99)-L):
xmin = 0.0099
xmax = 0.051
else:
xmin = 0.99*exp(-50/49*L-omega)
xmax = min(1.1*exp(-L-omega), 0.0101)
def f(x):
return abs(L+log(x/(1-x))+omega*(1-2*x))
x = minimize(f, ((xmin+xmax)/2,), bounds=((xmin, xmax),))["x"][0]
# Eq 12
fi = 2*x-1
Xi = 1/(2/(1-fi**2)-omega)
# Derivatives, Table 3
Lt = L0*K2/2*(1+(1-k0*k2+k1*(p-k2*tau))/K1)
Lp = L0*K2*(K1+k0*k2-k1*p+k1*k2*tau-1)/2/k2/K1
Ltt = -2*L0*K2*k0*k1*k2**2/K1**3
Ltp = 2*L0*K2*k0*k1*k2/K1**3
Lpp = -2*L0*K2*k0*k1/K1**3
prop = {}
prop["L"] = L
prop["x"] = x
# Eq 13
prop["rho"] = rho0/((tau+1)/2*(omega0/2*(1-fi**2)+Lp*(fi+1))+phirp)
# Eq 1
prop["g"] = phir+(tau+1)*(x*L+x*log(x)+(1-x)*log(1-x)+omega*x*(1-x))
# Eq 14
prop["s"] = -R*((tau+1)/2*Lt*(fi+1) +
(x*L+x*log(x)+(1-x)*log(1-x)+omega*x*(1-x))+phirt)
# Basic derived state properties
prop["h"] = prop["g"]+T*prop["s"]
prop["u"] = prop["h"]+P/prop["rho"]
prop["a"] = prop["u"]-T*prop["s"]
# Eq 15
prop["xkappa"] = prop["rho"]/rho0**2/R*1000/Tll*(
(tau+1)/2*(Xi*(Lp-omega0*fi)**2-(fi+1)*Lpp)-phirpp)
prop["alfap"] = prop["rho"]/rho0/Tll*(
Ltp/2*(tau+1)*(fi+1) + (omega0*(1-fi**2)/2+Lp*(fi+1))/2 -
(tau+1)*Lt/2*Xi*(Lp-omega0*fi) + phirtp)
prop["cp"] = -R*(tau+1)*(Lt*(fi+1)+(tau+1)/2*(Ltt*(fi+1)-Lt**2*Xi)+phirtt)
# Eq 16
prop["cv"] = prop["cp"]-T*prop["alfap"]**2/prop["rho"]/prop["xkappa"]*1e3
# Eq 17
prop["w"] = (prop["rho"]*prop["xkappa"]*1e-6*prop["cv"]/prop["cp"])**-0.5
return prop | python | def _Supercooled(T, P):
"""Guideline on thermodynamic properties of supercooled water
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties of water. The available properties are:
* L: Ordering field, [-]
* x: Mole fraction of low-density structure, [-]
* rho: Density, [kg/m³]
* s: Specific entropy, [kJ/kgK]
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* alfap: Thermal expansion coefficient, [1/K]
* xkappa : Isothermal compressibility, [1/MPa]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isochoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s²]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* Tm ≤ T ≤ 300
* 0 < P ≤ 1000
The minimum temperature in range of validity is the melting temperature, it
depend of pressure
Examples
--------
>>> liq = _Supercooled(235.15, 0.101325)
>>> liq["rho"], liq["cp"], liq["w"]
968.09999 5.997563 1134.5855
References
----------
IAPWS, Guideline on Thermodynamic Properties of Supercooled Water,
http://iapws.org/relguide/Supercooled.html
"""
# Check input in range of validity
if P < 198.9:
Tita = T/235.15
Ph = 0.1+228.27*(1-Tita**6.243)+15.724*(1-Tita**79.81)
if P < Ph or T > 300:
raise NotImplementedError("Incoming out of bound")
else:
Th = 172.82+0.03718*P+3.403e-5*P**2-1.573e-8*P**3
if T < Th or T > 300 or P > 1000:
raise NotImplementedError("Incoming out of bound")
# Parameters, Table 1
Tll = 228.2
rho0 = 1081.6482
R = 0.461523087
pi0 = 300e3/rho0/R/Tll
omega0 = 0.5212269
L0 = 0.76317954
k0 = 0.072158686
k1 = -0.31569232
k2 = 5.2992608
# Reducing parameters, Eq 2
tau = T/Tll-1
p = P*1000/rho0/R/Tll
tau_ = tau+1
p_ = p+pi0
# Eq 3
ci = [-8.1570681381655, 1.2875032, 7.0901673598012, -3.2779161e-2,
7.3703949e-1, -2.1628622e-1, -5.1782479, 4.2293517e-4, 2.3592109e-2,
4.3773754, -2.9967770e-3, -9.6558018e-1, 3.7595286, 1.2632441,
2.8542697e-1, -8.5994947e-1, -3.2916153e-1, 9.0019616e-2,
8.1149726e-2, -3.2788213]
ai = [0, 0, 1, -0.2555, 1.5762, 1.6400, 3.6385, -0.3828, 1.6219, 4.3287,
3.4763, 5.1556, -0.3593, 5.0361, 2.9786, 6.2373, 4.0460, 5.3558,
9.0157, 1.2194]
bi = [0, 1, 0, 2.1051, 1.1422, 0.9510, 0, 3.6402, 2.0760, -0.0016, 2.2769,
0.0008, 0.3706, -0.3975, 2.9730, -0.3180, 2.9805, 2.9265, 0.4456,
0.1298]
di = [0, 0, 0, -0.0016, 0.6894, 0.0130, 0.0002, 0.0435, 0.0500, 0.0004,
0.0528, 0.0147, 0.8584, 0.9924, 1.0041, 1.0961, 1.0228, 1.0303,
1.6180, 0.5213]
phir = phirt = phirp = phirtt = phirtp = phirpp = 0
for c, a, b, d in zip(ci, ai, bi, di):
phir += c*tau_**a*p_**b*exp(-d*p_)
phirt += c*a*tau_**(a-1)*p_**b*exp(-d*p_)
phirp += c*tau_**a*p_**(b-1)*(b-d*p_)*exp(-d*p_)
phirtt += c*a*(a-1)*tau_**(a-2)*p_**b*exp(-d*p_)
phirtp += c*a*tau_**(a-1)*p_**(b-1)*(b-d*p_)*exp(-d*p_)
phirpp += c*tau_**a*p_**(b-2)*((d*p_-b)**2-b)*exp(-d*p_)
# Eq 5
K1 = ((1+k0*k2+k1*(p-k2*tau))**2-4*k0*k1*k2*(p-k2*tau))**0.5
K2 = (1+k2**2)**0.5
# Eq 6
omega = 2+omega0*p
# Eq 4
L = L0*K2/2/k1/k2*(1+k0*k2+k1*(p+k2*tau)-K1)
# Define interval of solution, Table 4
if omega < 10/9*(log(19)-L):
xmin = 0.049
xmax = 0.5
elif 10/9*(log(19)-L) <= omega < 50/49*(log(99)-L):
xmin = 0.0099
xmax = 0.051
else:
xmin = 0.99*exp(-50/49*L-omega)
xmax = min(1.1*exp(-L-omega), 0.0101)
def f(x):
return abs(L+log(x/(1-x))+omega*(1-2*x))
x = minimize(f, ((xmin+xmax)/2,), bounds=((xmin, xmax),))["x"][0]
# Eq 12
fi = 2*x-1
Xi = 1/(2/(1-fi**2)-omega)
# Derivatives, Table 3
Lt = L0*K2/2*(1+(1-k0*k2+k1*(p-k2*tau))/K1)
Lp = L0*K2*(K1+k0*k2-k1*p+k1*k2*tau-1)/2/k2/K1
Ltt = -2*L0*K2*k0*k1*k2**2/K1**3
Ltp = 2*L0*K2*k0*k1*k2/K1**3
Lpp = -2*L0*K2*k0*k1/K1**3
prop = {}
prop["L"] = L
prop["x"] = x
# Eq 13
prop["rho"] = rho0/((tau+1)/2*(omega0/2*(1-fi**2)+Lp*(fi+1))+phirp)
# Eq 1
prop["g"] = phir+(tau+1)*(x*L+x*log(x)+(1-x)*log(1-x)+omega*x*(1-x))
# Eq 14
prop["s"] = -R*((tau+1)/2*Lt*(fi+1) +
(x*L+x*log(x)+(1-x)*log(1-x)+omega*x*(1-x))+phirt)
# Basic derived state properties
prop["h"] = prop["g"]+T*prop["s"]
prop["u"] = prop["h"]+P/prop["rho"]
prop["a"] = prop["u"]-T*prop["s"]
# Eq 15
prop["xkappa"] = prop["rho"]/rho0**2/R*1000/Tll*(
(tau+1)/2*(Xi*(Lp-omega0*fi)**2-(fi+1)*Lpp)-phirpp)
prop["alfap"] = prop["rho"]/rho0/Tll*(
Ltp/2*(tau+1)*(fi+1) + (omega0*(1-fi**2)/2+Lp*(fi+1))/2 -
(tau+1)*Lt/2*Xi*(Lp-omega0*fi) + phirtp)
prop["cp"] = -R*(tau+1)*(Lt*(fi+1)+(tau+1)/2*(Ltt*(fi+1)-Lt**2*Xi)+phirtt)
# Eq 16
prop["cv"] = prop["cp"]-T*prop["alfap"]**2/prop["rho"]/prop["xkappa"]*1e3
# Eq 17
prop["w"] = (prop["rho"]*prop["xkappa"]*1e-6*prop["cv"]/prop["cp"])**-0.5
return prop | Guideline on thermodynamic properties of supercooled water
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties of water. The available properties are:
* L: Ordering field, [-]
* x: Mole fraction of low-density structure, [-]
* rho: Density, [kg/m³]
* s: Specific entropy, [kJ/kgK]
* h: Specific enthalpy, [kJ/kg]
* u: Specific internal energy, [kJ/kg]
* a: Specific Helmholtz energy, [kJ/kg]
* g: Specific Gibbs energy, [kJ/kg]
* alfap: Thermal expansion coefficient, [1/K]
* xkappa : Isothermal compressibility, [1/MPa]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isochoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s²]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* Tm ≤ T ≤ 300
* 0 < P ≤ 1000
The minimum temperature in range of validity is the melting temperature, it
depend of pressure
Examples
--------
>>> liq = _Supercooled(235.15, 0.101325)
>>> liq["rho"], liq["cp"], liq["w"]
968.09999 5.997563 1134.5855
References
----------
IAPWS, Guideline on Thermodynamic Properties of Supercooled Water,
http://iapws.org/relguide/Supercooled.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L389-L561 |
jjgomera/iapws | iapws/_iapws.py | _Sublimation_Pressure | def _Sublimation_Pressure(T):
"""Sublimation Pressure correlation
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure at sublimation line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 50 ≤ T ≤ 273.16
Examples
--------
>>> _Sublimation_Pressure(230)
8.947352740189152e-06
References
----------
IAPWS, Revised Release on the Pressure along the Melting and Sublimation
Curves of Ordinary Water Substance, http://iapws.org/relguide/MeltSub.html.
"""
if 50 <= T <= 273.16:
Tita = T/Tt
suma = 0
a = [-0.212144006e2, 0.273203819e2, -0.61059813e1]
expo = [0.333333333e-2, 1.20666667, 1.70333333]
for ai, expi in zip(a, expo):
suma += ai*Tita**expi
return exp(suma/Tita)*Pt
else:
raise NotImplementedError("Incoming out of bound") | python | def _Sublimation_Pressure(T):
"""Sublimation Pressure correlation
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure at sublimation line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 50 ≤ T ≤ 273.16
Examples
--------
>>> _Sublimation_Pressure(230)
8.947352740189152e-06
References
----------
IAPWS, Revised Release on the Pressure along the Melting and Sublimation
Curves of Ordinary Water Substance, http://iapws.org/relguide/MeltSub.html.
"""
if 50 <= T <= 273.16:
Tita = T/Tt
suma = 0
a = [-0.212144006e2, 0.273203819e2, -0.61059813e1]
expo = [0.333333333e-2, 1.20666667, 1.70333333]
for ai, expi in zip(a, expo):
suma += ai*Tita**expi
return exp(suma/Tita)*Pt
else:
raise NotImplementedError("Incoming out of bound") | Sublimation Pressure correlation
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure at sublimation line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 50 ≤ T ≤ 273.16
Examples
--------
>>> _Sublimation_Pressure(230)
8.947352740189152e-06
References
----------
IAPWS, Revised Release on the Pressure along the Melting and Sublimation
Curves of Ordinary Water Substance, http://iapws.org/relguide/MeltSub.html. | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L564-L602 |
jjgomera/iapws | iapws/_iapws.py | _Melting_Pressure | def _Melting_Pressure(T, ice="Ih"):
"""Melting Pressure correlation
Parameters
----------
T : float
Temperature, [K]
ice: string
Type of ice: Ih, III, V, VI, VII.
Below 273.15 is a mandatory input, the ice Ih is the default value.
Above 273.15, the ice type is unnecesary.
Returns
-------
P : float
Pressure at sublimation line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 251.165 ≤ T ≤ 715
Examples
--------
>>> _Melting_Pressure(260)
8.947352740189152e-06
>>> _Melting_Pressure(254, "III")
268.6846466336108
References
----------
IAPWS, Revised Release on the Pressure along the Melting and Sublimation
Curves of Ordinary Water Substance, http://iapws.org/relguide/MeltSub.html.
"""
if ice == "Ih" and 251.165 <= T <= 273.16:
# Ice Ih
Tref = Tt
Pref = Pt
Tita = T/Tref
a = [0.119539337e7, 0.808183159e5, 0.33382686e4]
expo = [3., 0.2575e2, 0.10375e3]
suma = 1
for ai, expi in zip(a, expo):
suma += ai*(1-Tita**expi)
P = suma*Pref
elif ice == "III" and 251.165 < T <= 256.164:
# Ice III
Tref = 251.165
Pref = 208.566
Tita = T/Tref
P = Pref*(1-0.299948*(1-Tita**60.))
elif (ice == "V" and 256.164 < T <= 273.15) or 273.15 < T <= 273.31:
# Ice V
Tref = 256.164
Pref = 350.100
Tita = T/Tref
P = Pref*(1-1.18721*(1-Tita**8.))
elif 273.31 < T <= 355:
# Ice VI
Tref = 273.31
Pref = 632.400
Tita = T/Tref
P = Pref*(1-1.07476*(1-Tita**4.6))
elif 355. < T <= 715:
# Ice VII
Tref = 355
Pref = 2216.000
Tita = T/Tref
P = Pref*exp(1.73683*(1-1./Tita)-0.544606e-1*(1-Tita**5) +
0.806106e-7*(1-Tita**22))
else:
raise NotImplementedError("Incoming out of bound")
return P | python | def _Melting_Pressure(T, ice="Ih"):
"""Melting Pressure correlation
Parameters
----------
T : float
Temperature, [K]
ice: string
Type of ice: Ih, III, V, VI, VII.
Below 273.15 is a mandatory input, the ice Ih is the default value.
Above 273.15, the ice type is unnecesary.
Returns
-------
P : float
Pressure at sublimation line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 251.165 ≤ T ≤ 715
Examples
--------
>>> _Melting_Pressure(260)
8.947352740189152e-06
>>> _Melting_Pressure(254, "III")
268.6846466336108
References
----------
IAPWS, Revised Release on the Pressure along the Melting and Sublimation
Curves of Ordinary Water Substance, http://iapws.org/relguide/MeltSub.html.
"""
if ice == "Ih" and 251.165 <= T <= 273.16:
# Ice Ih
Tref = Tt
Pref = Pt
Tita = T/Tref
a = [0.119539337e7, 0.808183159e5, 0.33382686e4]
expo = [3., 0.2575e2, 0.10375e3]
suma = 1
for ai, expi in zip(a, expo):
suma += ai*(1-Tita**expi)
P = suma*Pref
elif ice == "III" and 251.165 < T <= 256.164:
# Ice III
Tref = 251.165
Pref = 208.566
Tita = T/Tref
P = Pref*(1-0.299948*(1-Tita**60.))
elif (ice == "V" and 256.164 < T <= 273.15) or 273.15 < T <= 273.31:
# Ice V
Tref = 256.164
Pref = 350.100
Tita = T/Tref
P = Pref*(1-1.18721*(1-Tita**8.))
elif 273.31 < T <= 355:
# Ice VI
Tref = 273.31
Pref = 632.400
Tita = T/Tref
P = Pref*(1-1.07476*(1-Tita**4.6))
elif 355. < T <= 715:
# Ice VII
Tref = 355
Pref = 2216.000
Tita = T/Tref
P = Pref*exp(1.73683*(1-1./Tita)-0.544606e-1*(1-Tita**5) +
0.806106e-7*(1-Tita**22))
else:
raise NotImplementedError("Incoming out of bound")
return P | Melting Pressure correlation
Parameters
----------
T : float
Temperature, [K]
ice: string
Type of ice: Ih, III, V, VI, VII.
Below 273.15 is a mandatory input, the ice Ih is the default value.
Above 273.15, the ice type is unnecesary.
Returns
-------
P : float
Pressure at sublimation line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 251.165 ≤ T ≤ 715
Examples
--------
>>> _Melting_Pressure(260)
8.947352740189152e-06
>>> _Melting_Pressure(254, "III")
268.6846466336108
References
----------
IAPWS, Revised Release on the Pressure along the Melting and Sublimation
Curves of Ordinary Water Substance, http://iapws.org/relguide/MeltSub.html. | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L605-L678 |
jjgomera/iapws | iapws/_iapws.py | _Viscosity | def _Viscosity(rho, T, fase=None, drho=None):
"""Equation for the Viscosity
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
fase: dict, optional for calculate critical enhancement
phase properties
drho: float, optional for calculate critical enhancement
[∂ρ/∂P]T at reference state,
Returns
-------
μ : float
Viscosity, [Pa·s]
Examples
--------
>>> _Viscosity(998, 298.15)
0.0008897351001498108
>>> _Viscosity(600, 873.15)
7.743019522728247e-05
References
----------
IAPWS, Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary
Water Substance, http://www.iapws.org/relguide/viscosity.html
"""
Tr = T/Tc
Dr = rho/rhoc
# Eq 11
H = [1.67752, 2.20462, 0.6366564, -0.241605]
mu0 = 100*Tr**0.5/sum([Hi/Tr**i for i, Hi in enumerate(H)])
# Eq 12
I = [0, 1, 2, 3, 0, 1, 2, 3, 5, 0, 1, 2, 3, 4, 0, 1, 0, 3, 4, 3, 5]
J = [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6]
Hij = [0.520094, 0.850895e-1, -0.108374e1, -0.289555, 0.222531, 0.999115,
0.188797e1, 0.126613e1, 0.120573, -0.281378, -0.906851, -0.772479,
-0.489837, -0.257040, 0.161913, 0.257399, -0.325372e-1, 0.698452e-1,
0.872102e-2, -0.435673e-2, -0.593264e-3]
mu1 = exp(Dr*sum([(1/Tr-1)**i*h*(Dr-1)**j for i, j, h in zip(I, J, Hij)]))
# Critical enhancement
if fase and drho:
qc = 1/1.9
qd = 1/1.1
# Eq 21
DeltaX = Pc*Dr**2*(fase.drhodP_T/rho-drho/rho*1.5/Tr)
if DeltaX < 0:
DeltaX = 0
# Eq 20
X = 0.13*(DeltaX/0.06)**(0.63/1.239)
if X <= 0.3817016416:
# Eq 15
Y = qc/5*X*(qd*X)**5*(1-qc*X+(qc*X)**2-765./504*(qd*X)**2)
else:
Fid = acos((1+qd**2*X**2)**-0.5) # Eq 17
w = abs((qc*X-1)/(qc*X+1))**0.5*tan(Fid/2) # Eq 19
# Eq 18
if qc*X > 1:
Lw = log((1+w)/(1-w))
else:
Lw = 2*atan(abs(w))
# Eq 16
Y = sin(3*Fid)/12-sin(2*Fid)/4/qc/X+(1-5/4*(qc*X)**2)/(
qc*X)**2*sin(Fid)-((1-3/2*(qc*X)**2)*Fid-abs((
qc*X)**2-1)**1.5*Lw)/(qc*X)**3
# Eq 14
mu2 = exp(0.068*Y)
else:
mu2 = 1
# Eq 10
mu = mu0*mu1*mu2
return mu*1e-6 | python | def _Viscosity(rho, T, fase=None, drho=None):
"""Equation for the Viscosity
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
fase: dict, optional for calculate critical enhancement
phase properties
drho: float, optional for calculate critical enhancement
[∂ρ/∂P]T at reference state,
Returns
-------
μ : float
Viscosity, [Pa·s]
Examples
--------
>>> _Viscosity(998, 298.15)
0.0008897351001498108
>>> _Viscosity(600, 873.15)
7.743019522728247e-05
References
----------
IAPWS, Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary
Water Substance, http://www.iapws.org/relguide/viscosity.html
"""
Tr = T/Tc
Dr = rho/rhoc
# Eq 11
H = [1.67752, 2.20462, 0.6366564, -0.241605]
mu0 = 100*Tr**0.5/sum([Hi/Tr**i for i, Hi in enumerate(H)])
# Eq 12
I = [0, 1, 2, 3, 0, 1, 2, 3, 5, 0, 1, 2, 3, 4, 0, 1, 0, 3, 4, 3, 5]
J = [0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 5, 6, 6]
Hij = [0.520094, 0.850895e-1, -0.108374e1, -0.289555, 0.222531, 0.999115,
0.188797e1, 0.126613e1, 0.120573, -0.281378, -0.906851, -0.772479,
-0.489837, -0.257040, 0.161913, 0.257399, -0.325372e-1, 0.698452e-1,
0.872102e-2, -0.435673e-2, -0.593264e-3]
mu1 = exp(Dr*sum([(1/Tr-1)**i*h*(Dr-1)**j for i, j, h in zip(I, J, Hij)]))
# Critical enhancement
if fase and drho:
qc = 1/1.9
qd = 1/1.1
# Eq 21
DeltaX = Pc*Dr**2*(fase.drhodP_T/rho-drho/rho*1.5/Tr)
if DeltaX < 0:
DeltaX = 0
# Eq 20
X = 0.13*(DeltaX/0.06)**(0.63/1.239)
if X <= 0.3817016416:
# Eq 15
Y = qc/5*X*(qd*X)**5*(1-qc*X+(qc*X)**2-765./504*(qd*X)**2)
else:
Fid = acos((1+qd**2*X**2)**-0.5) # Eq 17
w = abs((qc*X-1)/(qc*X+1))**0.5*tan(Fid/2) # Eq 19
# Eq 18
if qc*X > 1:
Lw = log((1+w)/(1-w))
else:
Lw = 2*atan(abs(w))
# Eq 16
Y = sin(3*Fid)/12-sin(2*Fid)/4/qc/X+(1-5/4*(qc*X)**2)/(
qc*X)**2*sin(Fid)-((1-3/2*(qc*X)**2)*Fid-abs((
qc*X)**2-1)**1.5*Lw)/(qc*X)**3
# Eq 14
mu2 = exp(0.068*Y)
else:
mu2 = 1
# Eq 10
mu = mu0*mu1*mu2
return mu*1e-6 | Equation for the Viscosity
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
fase: dict, optional for calculate critical enhancement
phase properties
drho: float, optional for calculate critical enhancement
[∂ρ/∂P]T at reference state,
Returns
-------
μ : float
Viscosity, [Pa·s]
Examples
--------
>>> _Viscosity(998, 298.15)
0.0008897351001498108
>>> _Viscosity(600, 873.15)
7.743019522728247e-05
References
----------
IAPWS, Release on the IAPWS Formulation 2008 for the Viscosity of Ordinary
Water Substance, http://www.iapws.org/relguide/viscosity.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L682-L768 |
jjgomera/iapws | iapws/_iapws.py | _ThCond | def _ThCond(rho, T, fase=None, drho=None):
"""Equation for the thermal conductivity
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
fase: dict, optional for calculate critical enhancement
phase properties
drho: float, optional for calculate critical enhancement
[∂ρ/∂P]T at reference state,
Returns
-------
k : float
Thermal conductivity, [W/mK]
Examples
--------
>>> _ThCond(998, 298.15)
0.6077128675880629
>>> _ThCond(0, 873.15)
0.07910346589648833
References
----------
IAPWS, Release on the IAPWS Formulation 2011 for the Thermal Conductivity
of Ordinary Water Substance, http://www.iapws.org/relguide/ThCond.html
"""
d = rho/rhoc
Tr = T/Tc
# Eq 16
no = [2.443221e-3, 1.323095e-2, 6.770357e-3, -3.454586e-3, 4.096266e-4]
k0 = Tr**0.5/sum([n/Tr**i for i, n in enumerate(no)])
# Eq 17
I = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4,
4, 4, 4, 4, 4]
J = [0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0,
1, 2, 3, 4, 5]
nij = [1.60397357, -0.646013523, 0.111443906, 0.102997357, -0.0504123634,
0.00609859258, 2.33771842, -2.78843778, 1.53616167, -0.463045512,
0.0832827019, -0.00719201245, 2.19650529, -4.54580785, 3.55777244,
-1.40944978, 0.275418278, -0.0205938816, -1.21051378, 1.60812989,
-0.621178141, 0.0716373224, -2.7203370, 4.57586331, -3.18369245,
1.1168348, -0.19268305, 0.012913842]
k1 = exp(d*sum([(1/Tr-1)**i*n*(d-1)**j for i, j, n in zip(I, J, nij)]))
# Critical enhancement
if fase:
R = 0.46151805
if not drho:
# Industrial formulation
# Eq 25
if d <= 0.310559006:
ai = [6.53786807199516, -5.61149954923348, 3.39624167361325,
-2.27492629730878, 10.2631854662709, 1.97815050331519]
elif d <= 0.776397516:
ai = [6.52717759281799, -6.30816983387575, 8.08379285492595,
-9.82240510197603, 12.1358413791395, -5.54349664571295]
elif d <= 1.242236025:
ai = [5.35500529896124, -3.96415689925446, 8.91990208918795,
-12.0338729505790, 9.19494865194302, -2.16866274479712]
elif d <= 1.863354037:
ai = [1.55225959906681, 0.464621290821181, 8.93237374861479,
-11.0321960061126, 6.16780999933360, -0.965458722086812]
else:
ai = [1.11999926419994, 0.595748562571649, 9.88952565078920,
-10.3255051147040, 4.66861294457414, -0.503243546373828]
drho = 1/sum([a*d**i for i, a in enumerate(ai)])*rhoc/Pc
DeltaX = d*(Pc/rhoc*fase.drhodP_T-Pc/rhoc*drho*1.5/Tr)
if DeltaX < 0:
DeltaX = 0
X = 0.13*(DeltaX/0.06)**(0.63/1.239) # Eq 22
y = X/0.4 # Eq 20
# Eq 19
if y < 1.2e-7:
Z = 0
else:
Z = 2/pi/y*(((1-1/fase.cp_cv)*atan(y)+y/fase.cp_cv)-(
1-exp(-1/(1/y+y**2/3/d**2))))
# Eq 18
k2 = 177.8514*d*fase.cp/R*Tr/fase.mu*1e-6*Z
else:
# No critical enhancement
k2 = 0
# Eq 10
k = k0*k1+k2
return 1e-3*k | python | def _ThCond(rho, T, fase=None, drho=None):
"""Equation for the thermal conductivity
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
fase: dict, optional for calculate critical enhancement
phase properties
drho: float, optional for calculate critical enhancement
[∂ρ/∂P]T at reference state,
Returns
-------
k : float
Thermal conductivity, [W/mK]
Examples
--------
>>> _ThCond(998, 298.15)
0.6077128675880629
>>> _ThCond(0, 873.15)
0.07910346589648833
References
----------
IAPWS, Release on the IAPWS Formulation 2011 for the Thermal Conductivity
of Ordinary Water Substance, http://www.iapws.org/relguide/ThCond.html
"""
d = rho/rhoc
Tr = T/Tc
# Eq 16
no = [2.443221e-3, 1.323095e-2, 6.770357e-3, -3.454586e-3, 4.096266e-4]
k0 = Tr**0.5/sum([n/Tr**i for i, n in enumerate(no)])
# Eq 17
I = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4,
4, 4, 4, 4, 4]
J = [0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0,
1, 2, 3, 4, 5]
nij = [1.60397357, -0.646013523, 0.111443906, 0.102997357, -0.0504123634,
0.00609859258, 2.33771842, -2.78843778, 1.53616167, -0.463045512,
0.0832827019, -0.00719201245, 2.19650529, -4.54580785, 3.55777244,
-1.40944978, 0.275418278, -0.0205938816, -1.21051378, 1.60812989,
-0.621178141, 0.0716373224, -2.7203370, 4.57586331, -3.18369245,
1.1168348, -0.19268305, 0.012913842]
k1 = exp(d*sum([(1/Tr-1)**i*n*(d-1)**j for i, j, n in zip(I, J, nij)]))
# Critical enhancement
if fase:
R = 0.46151805
if not drho:
# Industrial formulation
# Eq 25
if d <= 0.310559006:
ai = [6.53786807199516, -5.61149954923348, 3.39624167361325,
-2.27492629730878, 10.2631854662709, 1.97815050331519]
elif d <= 0.776397516:
ai = [6.52717759281799, -6.30816983387575, 8.08379285492595,
-9.82240510197603, 12.1358413791395, -5.54349664571295]
elif d <= 1.242236025:
ai = [5.35500529896124, -3.96415689925446, 8.91990208918795,
-12.0338729505790, 9.19494865194302, -2.16866274479712]
elif d <= 1.863354037:
ai = [1.55225959906681, 0.464621290821181, 8.93237374861479,
-11.0321960061126, 6.16780999933360, -0.965458722086812]
else:
ai = [1.11999926419994, 0.595748562571649, 9.88952565078920,
-10.3255051147040, 4.66861294457414, -0.503243546373828]
drho = 1/sum([a*d**i for i, a in enumerate(ai)])*rhoc/Pc
DeltaX = d*(Pc/rhoc*fase.drhodP_T-Pc/rhoc*drho*1.5/Tr)
if DeltaX < 0:
DeltaX = 0
X = 0.13*(DeltaX/0.06)**(0.63/1.239) # Eq 22
y = X/0.4 # Eq 20
# Eq 19
if y < 1.2e-7:
Z = 0
else:
Z = 2/pi/y*(((1-1/fase.cp_cv)*atan(y)+y/fase.cp_cv)-(
1-exp(-1/(1/y+y**2/3/d**2))))
# Eq 18
k2 = 177.8514*d*fase.cp/R*Tr/fase.mu*1e-6*Z
else:
# No critical enhancement
k2 = 0
# Eq 10
k = k0*k1+k2
return 1e-3*k | Equation for the thermal conductivity
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
fase: dict, optional for calculate critical enhancement
phase properties
drho: float, optional for calculate critical enhancement
[∂ρ/∂P]T at reference state,
Returns
-------
k : float
Thermal conductivity, [W/mK]
Examples
--------
>>> _ThCond(998, 298.15)
0.6077128675880629
>>> _ThCond(0, 873.15)
0.07910346589648833
References
----------
IAPWS, Release on the IAPWS Formulation 2011 for the Thermal Conductivity
of Ordinary Water Substance, http://www.iapws.org/relguide/ThCond.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L771-L869 |
jjgomera/iapws | iapws/_iapws.py | _Tension | def _Tension(T):
"""Equation for the surface tension
Parameters
----------
T : float
Temperature, [K]
Returns
-------
σ : float
Surface tension, [N/m]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 248.15 ≤ T ≤ 647
* Estrapolate to -25ºC in supercooled liquid metastable state
Examples
--------
>>> _Tension(300)
0.0716859625
>>> _Tension(450)
0.0428914992
References
----------
IAPWS, Revised Release on Surface Tension of Ordinary Water Substance
June 2014, http://www.iapws.org/relguide/Surf-H2O.html
"""
if 248.15 <= T <= Tc:
Tr = T/Tc
return 1e-3*(235.8*(1-Tr)**1.256*(1-0.625*(1-Tr)))
else:
raise NotImplementedError("Incoming out of bound") | python | def _Tension(T):
"""Equation for the surface tension
Parameters
----------
T : float
Temperature, [K]
Returns
-------
σ : float
Surface tension, [N/m]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 248.15 ≤ T ≤ 647
* Estrapolate to -25ºC in supercooled liquid metastable state
Examples
--------
>>> _Tension(300)
0.0716859625
>>> _Tension(450)
0.0428914992
References
----------
IAPWS, Revised Release on Surface Tension of Ordinary Water Substance
June 2014, http://www.iapws.org/relguide/Surf-H2O.html
"""
if 248.15 <= T <= Tc:
Tr = T/Tc
return 1e-3*(235.8*(1-Tr)**1.256*(1-0.625*(1-Tr)))
else:
raise NotImplementedError("Incoming out of bound") | Equation for the surface tension
Parameters
----------
T : float
Temperature, [K]
Returns
-------
σ : float
Surface tension, [N/m]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 248.15 ≤ T ≤ 647
* Estrapolate to -25ºC in supercooled liquid metastable state
Examples
--------
>>> _Tension(300)
0.0716859625
>>> _Tension(450)
0.0428914992
References
----------
IAPWS, Revised Release on Surface Tension of Ordinary Water Substance
June 2014, http://www.iapws.org/relguide/Surf-H2O.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L872-L908 |
jjgomera/iapws | iapws/_iapws.py | _Dielectric | def _Dielectric(rho, T):
"""Equation for the Dielectric constant
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
epsilon : float
Dielectric constant, [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 238 ≤ T ≤ 1200
Examples
--------
>>> _Dielectric(999.242866, 298.15)
78.5907250
>>> _Dielectric(26.0569558, 873.15)
1.12620970
References
----------
IAPWS, Release on the Static Dielectric Constant of Ordinary Water
Substance for Temperatures from 238 K to 873 K and Pressures up to 1000
MPa, http://www.iapws.org/relguide/Dielec.html
"""
# Check input parameters
if T < 238 or T > 1200:
raise NotImplementedError("Incoming out of bound")
k = 1.380658e-23
Na = 6.0221367e23
alfa = 1.636e-40
epsilon0 = 8.854187817e-12
mu = 6.138e-30
d = rho/rhoc
Tr = Tc/T
I = [1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 10, None]
J = [0.25, 1, 2.5, 1.5, 1.5, 2.5, 2, 2, 5, 0.5, 10, None]
n = [0.978224486826, -0.957771379375, 0.237511794148, 0.714692244396,
-0.298217036956, -0.108863472196, .949327488264e-1, -.980469816509e-2,
.165167634970e-4, .937359795772e-4, -.12317921872e-9,
.196096504426e-2]
g = 1+n[11]*d/(Tc/228/Tr-1)**1.2
for i in range(11):
g += n[i]*d**I[i]*Tr**J[i]
A = Na*mu**2*rho*g/M*1000/epsilon0/k/T
B = Na*alfa*rho/3/M*1000/epsilon0
e = (1+A+5*B+(9+2*A+18*B+A**2+10*A*B+9*B**2)**0.5)/4/(1-B)
return e | python | def _Dielectric(rho, T):
"""Equation for the Dielectric constant
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
epsilon : float
Dielectric constant, [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 238 ≤ T ≤ 1200
Examples
--------
>>> _Dielectric(999.242866, 298.15)
78.5907250
>>> _Dielectric(26.0569558, 873.15)
1.12620970
References
----------
IAPWS, Release on the Static Dielectric Constant of Ordinary Water
Substance for Temperatures from 238 K to 873 K and Pressures up to 1000
MPa, http://www.iapws.org/relguide/Dielec.html
"""
# Check input parameters
if T < 238 or T > 1200:
raise NotImplementedError("Incoming out of bound")
k = 1.380658e-23
Na = 6.0221367e23
alfa = 1.636e-40
epsilon0 = 8.854187817e-12
mu = 6.138e-30
d = rho/rhoc
Tr = Tc/T
I = [1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 10, None]
J = [0.25, 1, 2.5, 1.5, 1.5, 2.5, 2, 2, 5, 0.5, 10, None]
n = [0.978224486826, -0.957771379375, 0.237511794148, 0.714692244396,
-0.298217036956, -0.108863472196, .949327488264e-1, -.980469816509e-2,
.165167634970e-4, .937359795772e-4, -.12317921872e-9,
.196096504426e-2]
g = 1+n[11]*d/(Tc/228/Tr-1)**1.2
for i in range(11):
g += n[i]*d**I[i]*Tr**J[i]
A = Na*mu**2*rho*g/M*1000/epsilon0/k/T
B = Na*alfa*rho/3/M*1000/epsilon0
e = (1+A+5*B+(9+2*A+18*B+A**2+10*A*B+9*B**2)**0.5)/4/(1-B)
return e | Equation for the Dielectric constant
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
epsilon : float
Dielectric constant, [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 238 ≤ T ≤ 1200
Examples
--------
>>> _Dielectric(999.242866, 298.15)
78.5907250
>>> _Dielectric(26.0569558, 873.15)
1.12620970
References
----------
IAPWS, Release on the Static Dielectric Constant of Ordinary Water
Substance for Temperatures from 238 K to 873 K and Pressures up to 1000
MPa, http://www.iapws.org/relguide/Dielec.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L911-L970 |
jjgomera/iapws | iapws/_iapws.py | _Refractive | def _Refractive(rho, T, l=0.5893):
"""Equation for the refractive index
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
l : float, optional
Light Wavelength, [μm]
Returns
-------
n : float
Refractive index, [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0 ≤ ρ ≤ 1060
* 261.15 ≤ T ≤ 773.15
* 0.2 ≤ λ ≤ 1.1
Examples
--------
>>> _Refractive(997.047435, 298.15, 0.2265)
1.39277824
>>> _Refractive(30.4758534, 773.15, 0.5893)
1.00949307
References
----------
IAPWS, Release on the Refractive Index of Ordinary Water Substance as a
Function of Wavelength, Temperature and Pressure,
http://www.iapws.org/relguide/rindex.pdf
"""
# Check input parameters
if rho < 0 or rho > 1060 or T < 261.15 or T > 773.15 or l < 0.2 or l > 1.1:
raise NotImplementedError("Incoming out of bound")
Lir = 5.432937
Luv = 0.229202
d = rho/1000.
Tr = T/273.15
L = l/0.589
a = [0.244257733, 0.974634476e-2, -0.373234996e-2, 0.268678472e-3,
0.158920570e-2, 0.245934259e-2, 0.900704920, -0.166626219e-1]
A = d*(a[0]+a[1]*d+a[2]*Tr+a[3]*L**2*Tr+a[4]/L**2+a[5]/(L**2-Luv**2)+a[6]/(
L**2-Lir**2)+a[7]*d**2)
return ((2*A+1)/(1-A))**0.5 | python | def _Refractive(rho, T, l=0.5893):
"""Equation for the refractive index
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
l : float, optional
Light Wavelength, [μm]
Returns
-------
n : float
Refractive index, [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0 ≤ ρ ≤ 1060
* 261.15 ≤ T ≤ 773.15
* 0.2 ≤ λ ≤ 1.1
Examples
--------
>>> _Refractive(997.047435, 298.15, 0.2265)
1.39277824
>>> _Refractive(30.4758534, 773.15, 0.5893)
1.00949307
References
----------
IAPWS, Release on the Refractive Index of Ordinary Water Substance as a
Function of Wavelength, Temperature and Pressure,
http://www.iapws.org/relguide/rindex.pdf
"""
# Check input parameters
if rho < 0 or rho > 1060 or T < 261.15 or T > 773.15 or l < 0.2 or l > 1.1:
raise NotImplementedError("Incoming out of bound")
Lir = 5.432937
Luv = 0.229202
d = rho/1000.
Tr = T/273.15
L = l/0.589
a = [0.244257733, 0.974634476e-2, -0.373234996e-2, 0.268678472e-3,
0.158920570e-2, 0.245934259e-2, 0.900704920, -0.166626219e-1]
A = d*(a[0]+a[1]*d+a[2]*Tr+a[3]*L**2*Tr+a[4]/L**2+a[5]/(L**2-Luv**2)+a[6]/(
L**2-Lir**2)+a[7]*d**2)
return ((2*A+1)/(1-A))**0.5 | Equation for the refractive index
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
l : float, optional
Light Wavelength, [μm]
Returns
-------
n : float
Refractive index, [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0 ≤ ρ ≤ 1060
* 261.15 ≤ T ≤ 773.15
* 0.2 ≤ λ ≤ 1.1
Examples
--------
>>> _Refractive(997.047435, 298.15, 0.2265)
1.39277824
>>> _Refractive(30.4758534, 773.15, 0.5893)
1.00949307
References
----------
IAPWS, Release on the Refractive Index of Ordinary Water Substance as a
Function of Wavelength, Temperature and Pressure,
http://www.iapws.org/relguide/rindex.pdf | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L973-L1024 |
jjgomera/iapws | iapws/_iapws.py | _Kw | def _Kw(rho, T):
"""Equation for the ionization constant of ordinary water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
pKw : float
Ionization constant in -log10(kw), [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0 ≤ ρ ≤ 1250
* 273.15 ≤ T ≤ 1073.15
Examples
--------
>>> _Kw(1000, 300)
13.906565
References
----------
IAPWS, Release on the Ionization Constant of H2O,
http://www.iapws.org/relguide/Ionization.pdf
"""
# Check input parameters
if rho < 0 or rho > 1250 or T < 273.15 or T > 1073.15:
raise NotImplementedError("Incoming out of bound")
# The internal method of calculation use rho in g/cm³
d = rho/1000.
# Water molecular weight different
Mw = 18.015268
gamma = [6.1415e-1, 4.825133e4, -6.770793e4, 1.01021e7]
pKg = 0
for i, g in enumerate(gamma):
pKg += g/T**i
Q = d*exp(-0.864671+8659.19/T-22786.2/T**2*d**(2./3))
pKw = -12*(log10(1+Q)-Q/(Q+1)*d*(0.642044-56.8534/T-0.375754*d)) + \
pKg+2*log10(Mw/1000)
return pKw | python | def _Kw(rho, T):
"""Equation for the ionization constant of ordinary water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
pKw : float
Ionization constant in -log10(kw), [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0 ≤ ρ ≤ 1250
* 273.15 ≤ T ≤ 1073.15
Examples
--------
>>> _Kw(1000, 300)
13.906565
References
----------
IAPWS, Release on the Ionization Constant of H2O,
http://www.iapws.org/relguide/Ionization.pdf
"""
# Check input parameters
if rho < 0 or rho > 1250 or T < 273.15 or T > 1073.15:
raise NotImplementedError("Incoming out of bound")
# The internal method of calculation use rho in g/cm³
d = rho/1000.
# Water molecular weight different
Mw = 18.015268
gamma = [6.1415e-1, 4.825133e4, -6.770793e4, 1.01021e7]
pKg = 0
for i, g in enumerate(gamma):
pKg += g/T**i
Q = d*exp(-0.864671+8659.19/T-22786.2/T**2*d**(2./3))
pKw = -12*(log10(1+Q)-Q/(Q+1)*d*(0.642044-56.8534/T-0.375754*d)) + \
pKg+2*log10(Mw/1000)
return pKw | Equation for the ionization constant of ordinary water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
pKw : float
Ionization constant in -log10(kw), [-]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0 ≤ ρ ≤ 1250
* 273.15 ≤ T ≤ 1073.15
Examples
--------
>>> _Kw(1000, 300)
13.906565
References
----------
IAPWS, Release on the Ionization Constant of H2O,
http://www.iapws.org/relguide/Ionization.pdf | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L1027-L1077 |
jjgomera/iapws | iapws/_iapws.py | _Conductivity | def _Conductivity(rho, T):
"""Equation for the electrolytic conductivity of liquid and dense
supercrítical water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
K : float
Electrolytic conductivity, [S/m]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 600 ≤ ρ ≤ 1200
* 273.15 ≤ T ≤ 1073.15
Examples
--------
>>> _Conductivity(1000, 373.15)
1.13
References
----------
IAPWS, Electrolytic Conductivity (Specific Conductance) of Liquid and Dense
Supercritical Water from 0°C to 800°C and Pressures up to 1000 MPa,
http://www.iapws.org/relguide/conduct.pdf
"""
# FIXME: Dont work
rho_ = rho/1000
kw = 10**-_Kw(rho, T)
A = [1850., 1410., 2.16417e-6, 1.81609e-7, -1.75297e-9, 7.20708e-12]
B = [16., 11.6, 3.26e-4, -2.3e-6, 1.1e-8]
t = T-273.15
Loo = A[0]-1/(1/A[1]+sum([A[i+2]*t**(i+1) for i in range(4)])) # Eq 5
rho_h = B[0]-1/(1/B[1]+sum([B[i+2]*t**(i+1) for i in range(3)])) # Eq 6
# Eq 4
L_o = (rho_h-rho_)*Loo/rho_h
# Eq 1
k = 100*1e-3*L_o*kw**0.5*rho_
return k | python | def _Conductivity(rho, T):
"""Equation for the electrolytic conductivity of liquid and dense
supercrítical water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
K : float
Electrolytic conductivity, [S/m]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 600 ≤ ρ ≤ 1200
* 273.15 ≤ T ≤ 1073.15
Examples
--------
>>> _Conductivity(1000, 373.15)
1.13
References
----------
IAPWS, Electrolytic Conductivity (Specific Conductance) of Liquid and Dense
Supercritical Water from 0°C to 800°C and Pressures up to 1000 MPa,
http://www.iapws.org/relguide/conduct.pdf
"""
# FIXME: Dont work
rho_ = rho/1000
kw = 10**-_Kw(rho, T)
A = [1850., 1410., 2.16417e-6, 1.81609e-7, -1.75297e-9, 7.20708e-12]
B = [16., 11.6, 3.26e-4, -2.3e-6, 1.1e-8]
t = T-273.15
Loo = A[0]-1/(1/A[1]+sum([A[i+2]*t**(i+1) for i in range(4)])) # Eq 5
rho_h = B[0]-1/(1/B[1]+sum([B[i+2]*t**(i+1) for i in range(3)])) # Eq 6
# Eq 4
L_o = (rho_h-rho_)*Loo/rho_h
# Eq 1
k = 100*1e-3*L_o*kw**0.5*rho_
return k | Equation for the electrolytic conductivity of liquid and dense
supercrítical water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
K : float
Electrolytic conductivity, [S/m]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 600 ≤ ρ ≤ 1200
* 273.15 ≤ T ≤ 1073.15
Examples
--------
>>> _Conductivity(1000, 373.15)
1.13
References
----------
IAPWS, Electrolytic Conductivity (Specific Conductance) of Liquid and Dense
Supercritical Water from 0°C to 800°C and Pressures up to 1000 MPa,
http://www.iapws.org/relguide/conduct.pdf | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L1080-L1130 |
jjgomera/iapws | iapws/_iapws.py | _D2O_Viscosity | def _D2O_Viscosity(rho, T):
"""Equation for the Viscosity of heavy water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
μ : float
Viscosity, [Pa·s]
Examples
--------
>>> _D2O_Viscosity(998, 298.15)
0.0008897351001498108
>>> _D2O_Viscosity(600, 873.15)
7.743019522728247e-05
References
----------
IAPWS, Revised Release on Viscosity and Thermal Conductivity of Heavy
Water Substance, http://www.iapws.org/relguide/TransD2O-2007.pdf
"""
Tr = T/643.847
rhor = rho/358.0
no = [1.0, 0.940695, 0.578377, -0.202044]
fi0 = Tr**0.5/sum([n/Tr**i for i, n in enumerate(no)])
Li = [0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 2, 5, 0, 1, 2, 3, 0, 1, 3,
5, 0, 1, 5, 3]
Lj = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4,
4, 5, 5, 5, 6]
Lij = [0.4864192, -0.2448372, -0.8702035, 0.8716056, -1.051126,
0.3458395, 0.3509007, 1.315436, 1.297752, 1.353448, -0.2847572,
-1.037026, -1.287846, -0.02148229, 0.07013759, 0.4660127,
0.2292075, -0.4857462, 0.01641220, -0.02884911, 0.1607171,
-.009603846, -.01163815, -.008239587, 0.004559914, -0.003886659]
arr = [lij*(1./Tr-1)**i*(rhor-1)**j for i, j, lij in zip(Li, Lj, Lij)]
fi1 = exp(rhor*sum(arr))
return 55.2651e-6*fi0*fi1 | python | def _D2O_Viscosity(rho, T):
"""Equation for the Viscosity of heavy water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
μ : float
Viscosity, [Pa·s]
Examples
--------
>>> _D2O_Viscosity(998, 298.15)
0.0008897351001498108
>>> _D2O_Viscosity(600, 873.15)
7.743019522728247e-05
References
----------
IAPWS, Revised Release on Viscosity and Thermal Conductivity of Heavy
Water Substance, http://www.iapws.org/relguide/TransD2O-2007.pdf
"""
Tr = T/643.847
rhor = rho/358.0
no = [1.0, 0.940695, 0.578377, -0.202044]
fi0 = Tr**0.5/sum([n/Tr**i for i, n in enumerate(no)])
Li = [0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 0, 1, 2, 5, 0, 1, 2, 3, 0, 1, 3,
5, 0, 1, 5, 3]
Lj = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4,
4, 5, 5, 5, 6]
Lij = [0.4864192, -0.2448372, -0.8702035, 0.8716056, -1.051126,
0.3458395, 0.3509007, 1.315436, 1.297752, 1.353448, -0.2847572,
-1.037026, -1.287846, -0.02148229, 0.07013759, 0.4660127,
0.2292075, -0.4857462, 0.01641220, -0.02884911, 0.1607171,
-.009603846, -.01163815, -.008239587, 0.004559914, -0.003886659]
arr = [lij*(1./Tr-1)**i*(rhor-1)**j for i, j, lij in zip(Li, Lj, Lij)]
fi1 = exp(rhor*sum(arr))
return 55.2651e-6*fi0*fi1 | Equation for the Viscosity of heavy water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
μ : float
Viscosity, [Pa·s]
Examples
--------
>>> _D2O_Viscosity(998, 298.15)
0.0008897351001498108
>>> _D2O_Viscosity(600, 873.15)
7.743019522728247e-05
References
----------
IAPWS, Revised Release on Viscosity and Thermal Conductivity of Heavy
Water Substance, http://www.iapws.org/relguide/TransD2O-2007.pdf | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L1134-L1180 |
jjgomera/iapws | iapws/_iapws.py | _D2O_ThCond | def _D2O_ThCond(rho, T):
"""Equation for the thermal conductivity of heavy water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
k : float
Thermal conductivity, [W/mK]
Examples
--------
>>> _D2O_ThCond(998, 298.15)
0.6077128675880629
>>> _D2O_ThCond(0, 873.15)
0.07910346589648833
References
----------
IAPWS, Revised Release on Viscosity and Thermal Conductivity of Heavy
Water Substance, http://www.iapws.org/relguide/TransD2O-2007.pdf
"""
rhor = rho/358
Tr = T/643.847
tau = Tr/(abs(Tr-1.1)+1.1)
no = [1.0, 37.3223, 22.5485, 13.0465, 0.0, -2.60735]
Lo = sum([Li*Tr**i for i, Li in enumerate(no)])
nr = [483.656, -191.039, 73.0358, -7.57467]
Lr = -167.31*(1-exp(-2.506*rhor))+sum(
[Li*rhor**(i+1) for i, Li in enumerate(nr)])
f1 = exp(0.144847*Tr-5.64493*Tr**2)
f2 = exp(-2.8*(rhor-1)**2)-0.080738543*exp(-17.943*(rhor-0.125698)**2)
f3 = 1+exp(60*(tau-1)+20)
f4 = 1+exp(100*(tau-1)+15)
Lc = 35429.6*f1*f2*(1+f2**2*(5e9*f1**4/f3+3.5*f2/f4))
Ll = -741.112*f1**1.2*(1-exp(-(rhor/2.5)**10))
return 0.742128e-3*(Lo+Lr+Lc+Ll) | python | def _D2O_ThCond(rho, T):
"""Equation for the thermal conductivity of heavy water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
k : float
Thermal conductivity, [W/mK]
Examples
--------
>>> _D2O_ThCond(998, 298.15)
0.6077128675880629
>>> _D2O_ThCond(0, 873.15)
0.07910346589648833
References
----------
IAPWS, Revised Release on Viscosity and Thermal Conductivity of Heavy
Water Substance, http://www.iapws.org/relguide/TransD2O-2007.pdf
"""
rhor = rho/358
Tr = T/643.847
tau = Tr/(abs(Tr-1.1)+1.1)
no = [1.0, 37.3223, 22.5485, 13.0465, 0.0, -2.60735]
Lo = sum([Li*Tr**i for i, Li in enumerate(no)])
nr = [483.656, -191.039, 73.0358, -7.57467]
Lr = -167.31*(1-exp(-2.506*rhor))+sum(
[Li*rhor**(i+1) for i, Li in enumerate(nr)])
f1 = exp(0.144847*Tr-5.64493*Tr**2)
f2 = exp(-2.8*(rhor-1)**2)-0.080738543*exp(-17.943*(rhor-0.125698)**2)
f3 = 1+exp(60*(tau-1)+20)
f4 = 1+exp(100*(tau-1)+15)
Lc = 35429.6*f1*f2*(1+f2**2*(5e9*f1**4/f3+3.5*f2/f4))
Ll = -741.112*f1**1.2*(1-exp(-(rhor/2.5)**10))
return 0.742128e-3*(Lo+Lr+Lc+Ll) | Equation for the thermal conductivity of heavy water
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
k : float
Thermal conductivity, [W/mK]
Examples
--------
>>> _D2O_ThCond(998, 298.15)
0.6077128675880629
>>> _D2O_ThCond(0, 873.15)
0.07910346589648833
References
----------
IAPWS, Revised Release on Viscosity and Thermal Conductivity of Heavy
Water Substance, http://www.iapws.org/relguide/TransD2O-2007.pdf | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L1183-L1229 |
jjgomera/iapws | iapws/_iapws.py | _D2O_Sublimation_Pressure | def _D2O_Sublimation_Pressure(T):
"""Sublimation Pressure correlation for heavy water
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure at sublimation line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 210 ≤ T ≤ 276.969
Examples
--------
>>> _Sublimation_Pressure(245)
3.27390934e-5
References
----------
IAPWS, Revised Release on the IAPWS Formulation 2017 for the Thermodynamic
Properties of Heavy Water, http://www.iapws.org/relguide/Heavy.html.
"""
if 210 <= T <= 276.969:
Tita = T/276.969
suma = 0
ai = [-0.1314226e2, 0.3212969e2]
ti = [-1.73, -1.42]
for a, t in zip(ai, ti):
suma += a*(1-Tita**t)
return exp(suma)*0.00066159
else:
raise NotImplementedError("Incoming out of bound") | python | def _D2O_Sublimation_Pressure(T):
"""Sublimation Pressure correlation for heavy water
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure at sublimation line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 210 ≤ T ≤ 276.969
Examples
--------
>>> _Sublimation_Pressure(245)
3.27390934e-5
References
----------
IAPWS, Revised Release on the IAPWS Formulation 2017 for the Thermodynamic
Properties of Heavy Water, http://www.iapws.org/relguide/Heavy.html.
"""
if 210 <= T <= 276.969:
Tita = T/276.969
suma = 0
ai = [-0.1314226e2, 0.3212969e2]
ti = [-1.73, -1.42]
for a, t in zip(ai, ti):
suma += a*(1-Tita**t)
return exp(suma)*0.00066159
else:
raise NotImplementedError("Incoming out of bound") | Sublimation Pressure correlation for heavy water
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure at sublimation line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 210 ≤ T ≤ 276.969
Examples
--------
>>> _Sublimation_Pressure(245)
3.27390934e-5
References
----------
IAPWS, Revised Release on the IAPWS Formulation 2017 for the Thermodynamic
Properties of Heavy Water, http://www.iapws.org/relguide/Heavy.html. | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L1270-L1308 |
jjgomera/iapws | iapws/_iapws.py | _D2O_Melting_Pressure | def _D2O_Melting_Pressure(T, ice="Ih"):
"""Melting Pressure correlation for heavy water
Parameters
----------
T : float
Temperature, [K]
ice: string
Type of ice: Ih, III, V, VI, VII.
Below 276.969 is a mandatory input, the ice Ih is the default value.
Above 276.969, the ice type is unnecesary.
Returns
-------
P : float
Pressure at melting line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 254.415 ≤ T ≤ 315
Examples
--------
>>> _D2O__Melting_Pressure(260)
8.947352740189152e-06
>>> _D2O__Melting_Pressure(254, "III")
268.6846466336108
References
----------
IAPWS, Revised Release on the Pressure along the Melting and Sublimation
Curves of Ordinary Water Substance, http://iapws.org/relguide/MeltSub.html.
"""
if ice == "Ih" and 254.415 <= T <= 276.969:
# Ice Ih, Eq 9
Tita = T/276.969
ai = [-0.30153e5, 0.692503e6]
ti = [5.5, 8.2]
suma = 1
for a, t in zip(ai, ti):
suma += a*(1-Tita**t)
P = suma*0.00066159
elif ice == "III" and 254.415 < T <= 258.661:
# Ice III, Eq 10
Tita = T/254.415
P = 222.41*(1-0.802871*(1-Tita**33))
elif ice == "V" and 258.661 < T <= 275.748:
# Ice V, Eq 11
Tita = T/258.661
P = 352.19*(1-1.280388*(1-Tita**7.6))
elif (ice == "VI" and 275.748 < T <= 276.969) or 276.969 < T <= 315:
# Ice VI
Tita = T/275.748
P = 634.53*(1-1.276026*(1-Tita**4))
else:
raise NotImplementedError("Incoming out of bound")
return P | python | def _D2O_Melting_Pressure(T, ice="Ih"):
"""Melting Pressure correlation for heavy water
Parameters
----------
T : float
Temperature, [K]
ice: string
Type of ice: Ih, III, V, VI, VII.
Below 276.969 is a mandatory input, the ice Ih is the default value.
Above 276.969, the ice type is unnecesary.
Returns
-------
P : float
Pressure at melting line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 254.415 ≤ T ≤ 315
Examples
--------
>>> _D2O__Melting_Pressure(260)
8.947352740189152e-06
>>> _D2O__Melting_Pressure(254, "III")
268.6846466336108
References
----------
IAPWS, Revised Release on the Pressure along the Melting and Sublimation
Curves of Ordinary Water Substance, http://iapws.org/relguide/MeltSub.html.
"""
if ice == "Ih" and 254.415 <= T <= 276.969:
# Ice Ih, Eq 9
Tita = T/276.969
ai = [-0.30153e5, 0.692503e6]
ti = [5.5, 8.2]
suma = 1
for a, t in zip(ai, ti):
suma += a*(1-Tita**t)
P = suma*0.00066159
elif ice == "III" and 254.415 < T <= 258.661:
# Ice III, Eq 10
Tita = T/254.415
P = 222.41*(1-0.802871*(1-Tita**33))
elif ice == "V" and 258.661 < T <= 275.748:
# Ice V, Eq 11
Tita = T/258.661
P = 352.19*(1-1.280388*(1-Tita**7.6))
elif (ice == "VI" and 275.748 < T <= 276.969) or 276.969 < T <= 315:
# Ice VI
Tita = T/275.748
P = 634.53*(1-1.276026*(1-Tita**4))
else:
raise NotImplementedError("Incoming out of bound")
return P | Melting Pressure correlation for heavy water
Parameters
----------
T : float
Temperature, [K]
ice: string
Type of ice: Ih, III, V, VI, VII.
Below 276.969 is a mandatory input, the ice Ih is the default value.
Above 276.969, the ice type is unnecesary.
Returns
-------
P : float
Pressure at melting line, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 254.415 ≤ T ≤ 315
Examples
--------
>>> _D2O__Melting_Pressure(260)
8.947352740189152e-06
>>> _D2O__Melting_Pressure(254, "III")
268.6846466336108
References
----------
IAPWS, Revised Release on the Pressure along the Melting and Sublimation
Curves of Ordinary Water Substance, http://iapws.org/relguide/MeltSub.html. | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L1311-L1369 |
jjgomera/iapws | iapws/_iapws.py | _Henry | def _Henry(T, gas, liquid="H2O"):
"""Equation for the calculation of Henry's constant
Parameters
----------
T : float
Temperature, [K]
gas : string
Name of gas to calculate solubility
liquid : string
Name of liquid solvent, can be H20 (default) or D2O
Returns
-------
kw : float
Henry's constant, [MPa]
Notes
-----
The gas availables for H2O solvent are He, Ne, Ar, Kr, Xe, H2, N2, O2, CO,
CO2, H2S, CH4, C2H6, SF6
For D2O as solvent He, Ne, Ar, Kr, Xe, D2, CH4
Raise :class:`NotImplementedError` if input gas or liquid are unsupported
Examples
--------
>>> _Henry(500, "He")
1.1973
>>> _Henry(300, "D2", "D2O")
1.6594
References
----------
IAPWS, Guideline on the Henry's Constant and Vapor-Liquid Distribution
Constant for Gases in H2O and D2O at High Temperatures,
http://www.iapws.org/relguide/HenGuide.html
"""
if liquid == "D2O":
gas += "(D2O)"
limit = {
"He": (273.21, 553.18),
"Ne": (273.20, 543.36),
"Ar": (273.19, 568.36),
"Kr": (273.19, 525.56),
"Xe": (273.22, 574.85),
"H2": (273.15, 636.09),
"N2": (278.12, 636.46),
"O2": (274.15, 616.52),
"CO": (278.15, 588.67),
"CO2": (274.19, 642.66),
"H2S": (273.15, 533.09),
"CH4": (275.46, 633.11),
"C2H6": (275.44, 473.46),
"SF6": (283.14, 505.55),
"He(D2O)": (288.15, 553.18),
"Ne(D2O)": (288.18, 549.96),
"Ar(D2O)": (288.30, 583.76),
"Kr(D2O)": (288.19, 523.06),
"Xe(D2O)": (295.39, 574.85),
"D2(D2O)": (288.17, 581.00),
"CH4(D2O)": (288.16, 517.46)}
# Check input parameters
if liquid != "D2O" and liquid != "H2O":
raise NotImplementedError("Solvent liquid unsupported")
if gas not in limit:
raise NotImplementedError("Gas unsupported")
Tmin, Tmax = limit[gas]
if T < Tmin or T > Tmax:
warnings.warn("Temperature out of data of correlation")
if liquid == "D2O":
Tc = 643.847
Pc = 21.671
else:
Tc = 647.096
Pc = 22.064
Tr = T/Tc
tau = 1-Tr
# Eq 4
if liquid == "H2O":
ai = [-7.85951783, 1.84408259, -11.7866497, 22.6807411, -15.9618719,
1.80122502]
bi = [1, 1.5, 3, 3.5, 4, 7.5]
else:
ai = [-7.896657, 24.73308, -27.81128, 9.355913, -9.220083]
bi = [1, 1.89, 2, 3, 3.6]
ps = Pc*exp(1/Tr*sum([a*tau**b for a, b in zip(ai, bi)]))
# Select values from Table 2
par = {
"He": (-3.52839, 7.12983, 4.47770),
"Ne": (-3.18301, 5.31448, 5.43774),
"Ar": (-8.40954, 4.29587, 10.52779),
"Kr": (-8.97358, 3.61508, 11.29963),
"Xe": (-14.21635, 4.00041, 15.60999),
"H2": (-4.73284, 6.08954, 6.06066),
"N2": (-9.67578, 4.72162, 11.70585),
"O2": (-9.44833, 4.43822, 11.42005),
"CO": (-10.52862, 5.13259, 12.01421),
"CO2": (-8.55445, 4.01195, 9.52345),
"H2S": (-4.51499, 5.23538, 4.42126),
"CH4": (-10.44708, 4.66491, 12.12986),
"C2H6": (-19.67563, 4.51222, 20.62567),
"SF6": (-16.56118, 2.15289, 20.35440),
"He(D2O)": (-0.72643, 7.02134, 2.04433),
"Ne(D2O)": (-0.91999, 5.65327, 3.17247),
"Ar(D2O)": (-7.17725, 4.48177, 9.31509),
"Kr(D2O)": (-8.47059, 3.91580, 10.69433),
"Xe(D2O)": (-14.46485, 4.42330, 15.60919),
"D2(D2O)": (-5.33843, 6.15723, 6.53046),
"CH4(D2O)": (-10.01915, 4.73368, 11.75711)}
A, B, C = par[gas]
# Eq 3
kh = ps*exp(A/Tr+B*tau**0.355/Tr+C*Tr**-0.41*exp(tau))
return kh | python | def _Henry(T, gas, liquid="H2O"):
"""Equation for the calculation of Henry's constant
Parameters
----------
T : float
Temperature, [K]
gas : string
Name of gas to calculate solubility
liquid : string
Name of liquid solvent, can be H20 (default) or D2O
Returns
-------
kw : float
Henry's constant, [MPa]
Notes
-----
The gas availables for H2O solvent are He, Ne, Ar, Kr, Xe, H2, N2, O2, CO,
CO2, H2S, CH4, C2H6, SF6
For D2O as solvent He, Ne, Ar, Kr, Xe, D2, CH4
Raise :class:`NotImplementedError` if input gas or liquid are unsupported
Examples
--------
>>> _Henry(500, "He")
1.1973
>>> _Henry(300, "D2", "D2O")
1.6594
References
----------
IAPWS, Guideline on the Henry's Constant and Vapor-Liquid Distribution
Constant for Gases in H2O and D2O at High Temperatures,
http://www.iapws.org/relguide/HenGuide.html
"""
if liquid == "D2O":
gas += "(D2O)"
limit = {
"He": (273.21, 553.18),
"Ne": (273.20, 543.36),
"Ar": (273.19, 568.36),
"Kr": (273.19, 525.56),
"Xe": (273.22, 574.85),
"H2": (273.15, 636.09),
"N2": (278.12, 636.46),
"O2": (274.15, 616.52),
"CO": (278.15, 588.67),
"CO2": (274.19, 642.66),
"H2S": (273.15, 533.09),
"CH4": (275.46, 633.11),
"C2H6": (275.44, 473.46),
"SF6": (283.14, 505.55),
"He(D2O)": (288.15, 553.18),
"Ne(D2O)": (288.18, 549.96),
"Ar(D2O)": (288.30, 583.76),
"Kr(D2O)": (288.19, 523.06),
"Xe(D2O)": (295.39, 574.85),
"D2(D2O)": (288.17, 581.00),
"CH4(D2O)": (288.16, 517.46)}
# Check input parameters
if liquid != "D2O" and liquid != "H2O":
raise NotImplementedError("Solvent liquid unsupported")
if gas not in limit:
raise NotImplementedError("Gas unsupported")
Tmin, Tmax = limit[gas]
if T < Tmin or T > Tmax:
warnings.warn("Temperature out of data of correlation")
if liquid == "D2O":
Tc = 643.847
Pc = 21.671
else:
Tc = 647.096
Pc = 22.064
Tr = T/Tc
tau = 1-Tr
# Eq 4
if liquid == "H2O":
ai = [-7.85951783, 1.84408259, -11.7866497, 22.6807411, -15.9618719,
1.80122502]
bi = [1, 1.5, 3, 3.5, 4, 7.5]
else:
ai = [-7.896657, 24.73308, -27.81128, 9.355913, -9.220083]
bi = [1, 1.89, 2, 3, 3.6]
ps = Pc*exp(1/Tr*sum([a*tau**b for a, b in zip(ai, bi)]))
# Select values from Table 2
par = {
"He": (-3.52839, 7.12983, 4.47770),
"Ne": (-3.18301, 5.31448, 5.43774),
"Ar": (-8.40954, 4.29587, 10.52779),
"Kr": (-8.97358, 3.61508, 11.29963),
"Xe": (-14.21635, 4.00041, 15.60999),
"H2": (-4.73284, 6.08954, 6.06066),
"N2": (-9.67578, 4.72162, 11.70585),
"O2": (-9.44833, 4.43822, 11.42005),
"CO": (-10.52862, 5.13259, 12.01421),
"CO2": (-8.55445, 4.01195, 9.52345),
"H2S": (-4.51499, 5.23538, 4.42126),
"CH4": (-10.44708, 4.66491, 12.12986),
"C2H6": (-19.67563, 4.51222, 20.62567),
"SF6": (-16.56118, 2.15289, 20.35440),
"He(D2O)": (-0.72643, 7.02134, 2.04433),
"Ne(D2O)": (-0.91999, 5.65327, 3.17247),
"Ar(D2O)": (-7.17725, 4.48177, 9.31509),
"Kr(D2O)": (-8.47059, 3.91580, 10.69433),
"Xe(D2O)": (-14.46485, 4.42330, 15.60919),
"D2(D2O)": (-5.33843, 6.15723, 6.53046),
"CH4(D2O)": (-10.01915, 4.73368, 11.75711)}
A, B, C = par[gas]
# Eq 3
kh = ps*exp(A/Tr+B*tau**0.355/Tr+C*Tr**-0.41*exp(tau))
return kh | Equation for the calculation of Henry's constant
Parameters
----------
T : float
Temperature, [K]
gas : string
Name of gas to calculate solubility
liquid : string
Name of liquid solvent, can be H20 (default) or D2O
Returns
-------
kw : float
Henry's constant, [MPa]
Notes
-----
The gas availables for H2O solvent are He, Ne, Ar, Kr, Xe, H2, N2, O2, CO,
CO2, H2S, CH4, C2H6, SF6
For D2O as solvent He, Ne, Ar, Kr, Xe, D2, CH4
Raise :class:`NotImplementedError` if input gas or liquid are unsupported
Examples
--------
>>> _Henry(500, "He")
1.1973
>>> _Henry(300, "D2", "D2O")
1.6594
References
----------
IAPWS, Guideline on the Henry's Constant and Vapor-Liquid Distribution
Constant for Gases in H2O and D2O at High Temperatures,
http://www.iapws.org/relguide/HenGuide.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L1372-L1493 |
jjgomera/iapws | iapws/_iapws.py | _Kvalue | def _Kvalue(T, gas, liquid="H2O"):
"""Equation for the vapor-liquid distribution constant
Parameters
----------
T : float
Temperature, [K]
gas : string
Name of gas to calculate solubility
liquid : string
Name of liquid solvent, can be H20 (default) or D2O
Returns
-------
kd : float
Vapor-liquid distribution constant, [-]
Notes
-----
The gas availables for H2O solvent are He, Ne, Ar, Kr, Xe, H2, N2, O2, CO,
CO2, H2S, CH4, C2H6, SF6
For D2O as solvent He, Ne, Ar, Kr, Xe, D2, CH4
Raise :class:`NotImplementedError` if input gas or liquid are unsupported
Examples
--------
>>> _Kvalue(600, "He")
3.8019
>>> _Kvalue(300, "D2", "D2O")
14.3520
References
----------
IAPWS, Guideline on the Henry's Constant and Vapor-Liquid Distribution
Constant for Gases in H2O and D2O at High Temperatures,
http://www.iapws.org/relguide/HenGuide.html
"""
if liquid == "D2O":
gas += "(D2O)"
limit = {
"He": (273.21, 553.18),
"Ne": (273.20, 543.36),
"Ar": (273.19, 568.36),
"Kr": (273.19, 525.56),
"Xe": (273.22, 574.85),
"H2": (273.15, 636.09),
"N2": (278.12, 636.46),
"O2": (274.15, 616.52),
"CO": (278.15, 588.67),
"CO2": (274.19, 642.66),
"H2S": (273.15, 533.09),
"CH4": (275.46, 633.11),
"C2H6": (275.44, 473.46),
"SF6": (283.14, 505.55),
"He(D2O)": (288.15, 553.18),
"Ne(D2O)": (288.18, 549.96),
"Ar(D2O)": (288.30, 583.76),
"Kr(D2O)": (288.19, 523.06),
"Xe(D2O)": (295.39, 574.85),
"D2(D2O)": (288.17, 581.00),
"CH4(D2O)": (288.16, 517.46)}
# Check input parameters
if liquid != "D2O" and liquid != "H2O":
raise NotImplementedError("Solvent liquid unsupported")
if gas not in limit:
raise NotImplementedError("Gas unsupported")
Tmin, Tmax = limit[gas]
if T < Tmin or T > Tmax:
warnings.warn("Temperature out of data of correlation")
if liquid == "D2O":
Tc = 643.847
else:
Tc = 647.096
Tr = T/Tc
tau = 1-Tr
# Eq 6
if liquid == "H2O":
ci = [1.99274064, 1.09965342, -0.510839303, -1.75493479, -45.5170352,
-6.7469445e5]
di = [1/3, 2/3, 5/3, 16/3, 43/3, 110/3]
q = -0.023767
else:
ci = [2.7072, 0.58662, -1.3069, -45.663]
di = [0.374, 1.45, 2.6, 12.3]
q = -0.024552
f = sum([c*tau**d for c, d in zip(ci, di)])
# Select values from Table 2
par = {"He": (2267.4082, -2.9616, -3.2604, 7.8819),
"Ne": (2507.3022, -38.6955, 110.3992, -71.9096),
"Ar": (2310.5463, -46.7034, 160.4066, -118.3043),
"Kr": (2276.9722, -61.1494, 214.0117, -159.0407),
"Xe": (2022.8375, 16.7913, -61.2401, 41.9236),
"H2": (2286.4159, 11.3397, -70.7279, 63.0631),
"N2": (2388.8777, -14.9593, 42.0179, -29.4396),
"O2": (2305.0674, -11.3240, 25.3224, -15.6449),
"CO": (2346.2291, -57.6317, 204.5324, -152.6377),
"CO2": (1672.9376, 28.1751, -112.4619, 85.3807),
"H2S": (1319.1205, 14.1571, -46.8361, 33.2266),
"CH4": (2215.6977, -0.1089, -6.6240, 4.6789),
"C2H6": (2143.8121, 6.8859, -12.6084, 0),
"SF6": (2871.7265, -66.7556, 229.7191, -172.7400),
"He(D2O)": (2293.2474, -54.7707, 194.2924, -142.1257),
"Ne(D2O)": (2439.6677, -93.4934, 330.7783, -243.0100),
"Ar(D2O)": (2269.2352, -53.6321, 191.8421, -143.7659),
"Kr(D2O)": (2250.3857, -42.0835, 140.7656, -102.7592),
"Xe(D2O)": (2038.3656, 68.1228, -271.3390, 207.7984),
"D2(D2O)": (2141.3214, -1.9696, 1.6136, 0),
"CH4(D2O)": (2216.0181, -40.7666, 152.5778, -117.7430)}
E, F, G, H = par[gas]
# Eq 5
kd = exp(q*F+E/T*f+(F+G*tau**(2./3)+H*tau)*exp((273.15-T)/100))
return kd | python | def _Kvalue(T, gas, liquid="H2O"):
"""Equation for the vapor-liquid distribution constant
Parameters
----------
T : float
Temperature, [K]
gas : string
Name of gas to calculate solubility
liquid : string
Name of liquid solvent, can be H20 (default) or D2O
Returns
-------
kd : float
Vapor-liquid distribution constant, [-]
Notes
-----
The gas availables for H2O solvent are He, Ne, Ar, Kr, Xe, H2, N2, O2, CO,
CO2, H2S, CH4, C2H6, SF6
For D2O as solvent He, Ne, Ar, Kr, Xe, D2, CH4
Raise :class:`NotImplementedError` if input gas or liquid are unsupported
Examples
--------
>>> _Kvalue(600, "He")
3.8019
>>> _Kvalue(300, "D2", "D2O")
14.3520
References
----------
IAPWS, Guideline on the Henry's Constant and Vapor-Liquid Distribution
Constant for Gases in H2O and D2O at High Temperatures,
http://www.iapws.org/relguide/HenGuide.html
"""
if liquid == "D2O":
gas += "(D2O)"
limit = {
"He": (273.21, 553.18),
"Ne": (273.20, 543.36),
"Ar": (273.19, 568.36),
"Kr": (273.19, 525.56),
"Xe": (273.22, 574.85),
"H2": (273.15, 636.09),
"N2": (278.12, 636.46),
"O2": (274.15, 616.52),
"CO": (278.15, 588.67),
"CO2": (274.19, 642.66),
"H2S": (273.15, 533.09),
"CH4": (275.46, 633.11),
"C2H6": (275.44, 473.46),
"SF6": (283.14, 505.55),
"He(D2O)": (288.15, 553.18),
"Ne(D2O)": (288.18, 549.96),
"Ar(D2O)": (288.30, 583.76),
"Kr(D2O)": (288.19, 523.06),
"Xe(D2O)": (295.39, 574.85),
"D2(D2O)": (288.17, 581.00),
"CH4(D2O)": (288.16, 517.46)}
# Check input parameters
if liquid != "D2O" and liquid != "H2O":
raise NotImplementedError("Solvent liquid unsupported")
if gas not in limit:
raise NotImplementedError("Gas unsupported")
Tmin, Tmax = limit[gas]
if T < Tmin or T > Tmax:
warnings.warn("Temperature out of data of correlation")
if liquid == "D2O":
Tc = 643.847
else:
Tc = 647.096
Tr = T/Tc
tau = 1-Tr
# Eq 6
if liquid == "H2O":
ci = [1.99274064, 1.09965342, -0.510839303, -1.75493479, -45.5170352,
-6.7469445e5]
di = [1/3, 2/3, 5/3, 16/3, 43/3, 110/3]
q = -0.023767
else:
ci = [2.7072, 0.58662, -1.3069, -45.663]
di = [0.374, 1.45, 2.6, 12.3]
q = -0.024552
f = sum([c*tau**d for c, d in zip(ci, di)])
# Select values from Table 2
par = {"He": (2267.4082, -2.9616, -3.2604, 7.8819),
"Ne": (2507.3022, -38.6955, 110.3992, -71.9096),
"Ar": (2310.5463, -46.7034, 160.4066, -118.3043),
"Kr": (2276.9722, -61.1494, 214.0117, -159.0407),
"Xe": (2022.8375, 16.7913, -61.2401, 41.9236),
"H2": (2286.4159, 11.3397, -70.7279, 63.0631),
"N2": (2388.8777, -14.9593, 42.0179, -29.4396),
"O2": (2305.0674, -11.3240, 25.3224, -15.6449),
"CO": (2346.2291, -57.6317, 204.5324, -152.6377),
"CO2": (1672.9376, 28.1751, -112.4619, 85.3807),
"H2S": (1319.1205, 14.1571, -46.8361, 33.2266),
"CH4": (2215.6977, -0.1089, -6.6240, 4.6789),
"C2H6": (2143.8121, 6.8859, -12.6084, 0),
"SF6": (2871.7265, -66.7556, 229.7191, -172.7400),
"He(D2O)": (2293.2474, -54.7707, 194.2924, -142.1257),
"Ne(D2O)": (2439.6677, -93.4934, 330.7783, -243.0100),
"Ar(D2O)": (2269.2352, -53.6321, 191.8421, -143.7659),
"Kr(D2O)": (2250.3857, -42.0835, 140.7656, -102.7592),
"Xe(D2O)": (2038.3656, 68.1228, -271.3390, 207.7984),
"D2(D2O)": (2141.3214, -1.9696, 1.6136, 0),
"CH4(D2O)": (2216.0181, -40.7666, 152.5778, -117.7430)}
E, F, G, H = par[gas]
# Eq 5
kd = exp(q*F+E/T*f+(F+G*tau**(2./3)+H*tau)*exp((273.15-T)/100))
return kd | Equation for the vapor-liquid distribution constant
Parameters
----------
T : float
Temperature, [K]
gas : string
Name of gas to calculate solubility
liquid : string
Name of liquid solvent, can be H20 (default) or D2O
Returns
-------
kd : float
Vapor-liquid distribution constant, [-]
Notes
-----
The gas availables for H2O solvent are He, Ne, Ar, Kr, Xe, H2, N2, O2, CO,
CO2, H2S, CH4, C2H6, SF6
For D2O as solvent He, Ne, Ar, Kr, Xe, D2, CH4
Raise :class:`NotImplementedError` if input gas or liquid are unsupported
Examples
--------
>>> _Kvalue(600, "He")
3.8019
>>> _Kvalue(300, "D2", "D2O")
14.3520
References
----------
IAPWS, Guideline on the Henry's Constant and Vapor-Liquid Distribution
Constant for Gases in H2O and D2O at High Temperatures,
http://www.iapws.org/relguide/HenGuide.html | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_iapws.py#L1496-L1617 |
jjgomera/iapws | iapws/_utils.py | getphase | def getphase(Tc, Pc, T, P, x, region):
"""Return fluid phase string name
Parameters
----------
Tc : float
Critical temperature, [K]
Pc : float
Critical pressure, [MPa]
T : float
Temperature, [K]
P : float
Pressure, [MPa]
x : float
Quality, [-]
region: int
Region number, used only for IAPWS97 region definition
Returns
-------
phase : str
Phase name
"""
# Avoid round problem
P = round(P, 8)
T = round(T, 8)
if P > Pc and T > Tc:
phase = "Supercritical fluid"
elif T > Tc:
phase = "Gas"
elif P > Pc:
phase = "Compressible liquid"
elif P == Pc and T == Tc:
phase = "Critical point"
elif region == 4 and x == 1:
phase = "Saturated vapor"
elif region == 4 and x == 0:
phase = "Saturated liquid"
elif region == 4:
phase = "Two phases"
elif x == 1:
phase = "Vapour"
elif x == 0:
phase = "Liquid"
return phase | python | def getphase(Tc, Pc, T, P, x, region):
"""Return fluid phase string name
Parameters
----------
Tc : float
Critical temperature, [K]
Pc : float
Critical pressure, [MPa]
T : float
Temperature, [K]
P : float
Pressure, [MPa]
x : float
Quality, [-]
region: int
Region number, used only for IAPWS97 region definition
Returns
-------
phase : str
Phase name
"""
# Avoid round problem
P = round(P, 8)
T = round(T, 8)
if P > Pc and T > Tc:
phase = "Supercritical fluid"
elif T > Tc:
phase = "Gas"
elif P > Pc:
phase = "Compressible liquid"
elif P == Pc and T == Tc:
phase = "Critical point"
elif region == 4 and x == 1:
phase = "Saturated vapor"
elif region == 4 and x == 0:
phase = "Saturated liquid"
elif region == 4:
phase = "Two phases"
elif x == 1:
phase = "Vapour"
elif x == 0:
phase = "Liquid"
return phase | Return fluid phase string name
Parameters
----------
Tc : float
Critical temperature, [K]
Pc : float
Critical pressure, [MPa]
T : float
Temperature, [K]
P : float
Pressure, [MPa]
x : float
Quality, [-]
region: int
Region number, used only for IAPWS97 region definition
Returns
-------
phase : str
Phase name | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_utils.py#L17-L61 |
jjgomera/iapws | iapws/_utils.py | deriv_H | def deriv_H(state, z, x, y, fase):
r"""Calculate generic partial derivative
:math:`\left.\frac{\partial z}{\partial x}\right|_{y}` from a fundamental
helmholtz free energy equation of state
Parameters
----------
state : any python object
Only need to define P and T properties, non phase specific properties
z : str
Name of variables in numerator term of derivatives
x : str
Name of variables in denominator term of derivatives
y : str
Name of constant variable in partial derivaritive
fase : any python object
Define phase specific properties (v, cv, alfap, s, betap)
Notes
-----
x, y and z can be the following values:
* P: Pressure
* T: Temperature
* v: Specific volume
* rho: Density
* u: Internal Energy
* h: Enthalpy
* s: Entropy
* g: Gibbs free energy
* a: Helmholtz free energy
Returns
-------
deriv : float
∂z/∂x|y
References
----------
IAPWS, Revised Advisory Note No. 3: Thermodynamic Derivatives from IAPWS
Formulations, http://www.iapws.org/relguide/Advise3.pdf
"""
# We use the relation between rho and v and his partial derivative
# ∂v/∂b|c = -1/ρ² ∂ρ/∂b|c
# ∂a/∂v|c = -ρ² ∂a/∂ρ|c
mul = 1
if z == "rho":
mul = -fase.rho**2
z = "v"
if x == "rho":
mul = -1/fase.rho**2
x = "v"
if y == "rho":
y = "v"
dT = {"P": state.P*1000*fase.alfap,
"T": 1,
"v": 0,
"u": fase.cv,
"h": fase.cv+state.P*1000*fase.v*fase.alfap,
"s": fase.cv/state.T,
"g": state.P*1000*fase.v*fase.alfap-fase.s,
"a": -fase.s}
dv = {"P": -state.P*1000*fase.betap,
"T": 0,
"v": 1,
"u": state.P*1000*(state.T*fase.alfap-1),
"h": state.P*1000*(state.T*fase.alfap-fase.v*fase.betap),
"s": state.P*1000*fase.alfap,
"g": -state.P*1000*fase.v*fase.betap,
"a": -state.P*1000}
deriv = (dv[z]*dT[y]-dT[z]*dv[y])/(dv[x]*dT[y]-dT[x]*dv[y])
return mul*deriv | python | def deriv_H(state, z, x, y, fase):
r"""Calculate generic partial derivative
:math:`\left.\frac{\partial z}{\partial x}\right|_{y}` from a fundamental
helmholtz free energy equation of state
Parameters
----------
state : any python object
Only need to define P and T properties, non phase specific properties
z : str
Name of variables in numerator term of derivatives
x : str
Name of variables in denominator term of derivatives
y : str
Name of constant variable in partial derivaritive
fase : any python object
Define phase specific properties (v, cv, alfap, s, betap)
Notes
-----
x, y and z can be the following values:
* P: Pressure
* T: Temperature
* v: Specific volume
* rho: Density
* u: Internal Energy
* h: Enthalpy
* s: Entropy
* g: Gibbs free energy
* a: Helmholtz free energy
Returns
-------
deriv : float
∂z/∂x|y
References
----------
IAPWS, Revised Advisory Note No. 3: Thermodynamic Derivatives from IAPWS
Formulations, http://www.iapws.org/relguide/Advise3.pdf
"""
# We use the relation between rho and v and his partial derivative
# ∂v/∂b|c = -1/ρ² ∂ρ/∂b|c
# ∂a/∂v|c = -ρ² ∂a/∂ρ|c
mul = 1
if z == "rho":
mul = -fase.rho**2
z = "v"
if x == "rho":
mul = -1/fase.rho**2
x = "v"
if y == "rho":
y = "v"
dT = {"P": state.P*1000*fase.alfap,
"T": 1,
"v": 0,
"u": fase.cv,
"h": fase.cv+state.P*1000*fase.v*fase.alfap,
"s": fase.cv/state.T,
"g": state.P*1000*fase.v*fase.alfap-fase.s,
"a": -fase.s}
dv = {"P": -state.P*1000*fase.betap,
"T": 0,
"v": 1,
"u": state.P*1000*(state.T*fase.alfap-1),
"h": state.P*1000*(state.T*fase.alfap-fase.v*fase.betap),
"s": state.P*1000*fase.alfap,
"g": -state.P*1000*fase.v*fase.betap,
"a": -state.P*1000}
deriv = (dv[z]*dT[y]-dT[z]*dv[y])/(dv[x]*dT[y]-dT[x]*dv[y])
return mul*deriv | r"""Calculate generic partial derivative
:math:`\left.\frac{\partial z}{\partial x}\right|_{y}` from a fundamental
helmholtz free energy equation of state
Parameters
----------
state : any python object
Only need to define P and T properties, non phase specific properties
z : str
Name of variables in numerator term of derivatives
x : str
Name of variables in denominator term of derivatives
y : str
Name of constant variable in partial derivaritive
fase : any python object
Define phase specific properties (v, cv, alfap, s, betap)
Notes
-----
x, y and z can be the following values:
* P: Pressure
* T: Temperature
* v: Specific volume
* rho: Density
* u: Internal Energy
* h: Enthalpy
* s: Entropy
* g: Gibbs free energy
* a: Helmholtz free energy
Returns
-------
deriv : float
∂z/∂x|y
References
----------
IAPWS, Revised Advisory Note No. 3: Thermodynamic Derivatives from IAPWS
Formulations, http://www.iapws.org/relguide/Advise3.pdf | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_utils.py#L119-L191 |
jjgomera/iapws | iapws/_utils.py | deriv_G | def deriv_G(state, z, x, y, fase):
r"""Calculate generic partial derivative
:math:`\left.\frac{\partial z}{\partial x}\right|_{y}` from a fundamental
Gibbs free energy equation of state
Parameters
----------
state : any python object
Only need to define P and T properties, non phase specific properties
z : str
Name of variables in numerator term of derivatives
x : str
Name of variables in denominator term of derivatives
y : str
Name of constant variable in partial derivaritive
fase : any python object
Define phase specific properties (v, cp, alfav, s, xkappa)
Notes
-----
x, y and z can be the following values:
* P: Pressure
* T: Temperature
* v: Specific volume
* rho: Density
* u: Internal Energy
* h: Enthalpy
* s: Entropy
* g: Gibbs free energy
* a: Helmholtz free energy
Returns
-------
deriv : float
∂z/∂x|y
References
----------
IAPWS, Revised Advisory Note No. 3: Thermodynamic Derivatives from IAPWS
Formulations, http://www.iapws.org/relguide/Advise3.pdf
"""
mul = 1
if z == "rho":
mul = -fase.rho**2
z = "v"
if x == "rho":
mul = -1/fase.rho**2
x = "v"
dT = {"P": 0,
"T": 1,
"v": fase.v*fase.alfav,
"u": fase.cp-state.P*1000*fase.v*fase.alfav,
"h": fase.cp,
"s": fase.cp/state.T,
"g": -fase.s,
"a": -state.P*1000*fase.v*fase.alfav-fase.s}
dP = {"P": 1,
"T": 0,
"v": -fase.v*fase.xkappa,
"u": fase.v*(state.P*1000*fase.xkappa-state.T*fase.alfav),
"h": fase.v*(1-state.T*fase.alfav),
"s": -fase.v*fase.alfav,
"g": fase.v,
"a": state.P*1000*fase.v*fase.xkappa}
deriv = (dP[z]*dT[y]-dT[z]*dP[y])/(dP[x]*dT[y]-dT[x]*dP[y])
return mul*deriv | python | def deriv_G(state, z, x, y, fase):
r"""Calculate generic partial derivative
:math:`\left.\frac{\partial z}{\partial x}\right|_{y}` from a fundamental
Gibbs free energy equation of state
Parameters
----------
state : any python object
Only need to define P and T properties, non phase specific properties
z : str
Name of variables in numerator term of derivatives
x : str
Name of variables in denominator term of derivatives
y : str
Name of constant variable in partial derivaritive
fase : any python object
Define phase specific properties (v, cp, alfav, s, xkappa)
Notes
-----
x, y and z can be the following values:
* P: Pressure
* T: Temperature
* v: Specific volume
* rho: Density
* u: Internal Energy
* h: Enthalpy
* s: Entropy
* g: Gibbs free energy
* a: Helmholtz free energy
Returns
-------
deriv : float
∂z/∂x|y
References
----------
IAPWS, Revised Advisory Note No. 3: Thermodynamic Derivatives from IAPWS
Formulations, http://www.iapws.org/relguide/Advise3.pdf
"""
mul = 1
if z == "rho":
mul = -fase.rho**2
z = "v"
if x == "rho":
mul = -1/fase.rho**2
x = "v"
dT = {"P": 0,
"T": 1,
"v": fase.v*fase.alfav,
"u": fase.cp-state.P*1000*fase.v*fase.alfav,
"h": fase.cp,
"s": fase.cp/state.T,
"g": -fase.s,
"a": -state.P*1000*fase.v*fase.alfav-fase.s}
dP = {"P": 1,
"T": 0,
"v": -fase.v*fase.xkappa,
"u": fase.v*(state.P*1000*fase.xkappa-state.T*fase.alfav),
"h": fase.v*(1-state.T*fase.alfav),
"s": -fase.v*fase.alfav,
"g": fase.v,
"a": state.P*1000*fase.v*fase.xkappa}
deriv = (dP[z]*dT[y]-dT[z]*dP[y])/(dP[x]*dT[y]-dT[x]*dP[y])
return mul*deriv | r"""Calculate generic partial derivative
:math:`\left.\frac{\partial z}{\partial x}\right|_{y}` from a fundamental
Gibbs free energy equation of state
Parameters
----------
state : any python object
Only need to define P and T properties, non phase specific properties
z : str
Name of variables in numerator term of derivatives
x : str
Name of variables in denominator term of derivatives
y : str
Name of constant variable in partial derivaritive
fase : any python object
Define phase specific properties (v, cp, alfav, s, xkappa)
Notes
-----
x, y and z can be the following values:
* P: Pressure
* T: Temperature
* v: Specific volume
* rho: Density
* u: Internal Energy
* h: Enthalpy
* s: Entropy
* g: Gibbs free energy
* a: Helmholtz free energy
Returns
-------
deriv : float
∂z/∂x|y
References
----------
IAPWS, Revised Advisory Note No. 3: Thermodynamic Derivatives from IAPWS
Formulations, http://www.iapws.org/relguide/Advise3.pdf | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/_utils.py#L194-L261 |
jjgomera/iapws | iapws/iapws97.py | _h13_s | def _h13_s(s):
"""Define the boundary between Region 1 and 3, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* s(100MPa,623.15K) ≤ s ≤ s'(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 7
Examples
--------
>>> _h13_s(3.7)
1632.525047
>>> _h13_s(3.5)
1566.104611
"""
# Check input parameters
if s < 3.397782955 or s > 3.77828134:
raise NotImplementedError("Incoming out of bound")
sigma = s/3.8
I = [0, 1, 1, 3, 5, 6]
J = [0, -2, 2, -12, -4, -3]
n = [0.913965547600543, -0.430944856041991e-4, 0.603235694765419e2,
0.117518273082168e-17, 0.220000904781292, -0.690815545851641e2]
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (sigma-0.884)**i * (sigma-0.864)**j
return 1700 * suma | python | def _h13_s(s):
"""Define the boundary between Region 1 and 3, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* s(100MPa,623.15K) ≤ s ≤ s'(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 7
Examples
--------
>>> _h13_s(3.7)
1632.525047
>>> _h13_s(3.5)
1566.104611
"""
# Check input parameters
if s < 3.397782955 or s > 3.77828134:
raise NotImplementedError("Incoming out of bound")
sigma = s/3.8
I = [0, 1, 1, 3, 5, 6]
J = [0, -2, 2, -12, -4, -3]
n = [0.913965547600543, -0.430944856041991e-4, 0.603235694765419e2,
0.117518273082168e-17, 0.220000904781292, -0.690815545851641e2]
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (sigma-0.884)**i * (sigma-0.864)**j
return 1700 * suma | Define the boundary between Region 1 and 3, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* s(100MPa,623.15K) ≤ s ≤ s'(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 7
Examples
--------
>>> _h13_s(3.7)
1632.525047
>>> _h13_s(3.5)
1566.104611 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L106-L153 |
jjgomera/iapws | iapws/iapws97.py | _PSat_T | def _PSat_T(T):
"""Define the saturated line, P=f(T)
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 273.15 ≤ T ≤ 647.096
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 30
Examples
--------
>>> _PSat_T(500)
2.63889776
"""
# Check input parameters
if T < 273.15 or T > Tc:
raise NotImplementedError("Incoming out of bound")
n = [0, 0.11670521452767E+04, -0.72421316703206E+06, -0.17073846940092E+02,
0.12020824702470E+05, -0.32325550322333E+07, 0.14915108613530E+02,
-0.48232657361591E+04, 0.40511340542057E+06, -0.23855557567849E+00,
0.65017534844798E+03]
tita = T+n[9]/(T-n[10])
A = tita**2+n[1]*tita+n[2]
B = n[3]*tita**2+n[4]*tita+n[5]
C = n[6]*tita**2+n[7]*tita+n[8]
return (2*C/(-B+(B**2-4*A*C)**0.5))**4 | python | def _PSat_T(T):
"""Define the saturated line, P=f(T)
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 273.15 ≤ T ≤ 647.096
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 30
Examples
--------
>>> _PSat_T(500)
2.63889776
"""
# Check input parameters
if T < 273.15 or T > Tc:
raise NotImplementedError("Incoming out of bound")
n = [0, 0.11670521452767E+04, -0.72421316703206E+06, -0.17073846940092E+02,
0.12020824702470E+05, -0.32325550322333E+07, 0.14915108613530E+02,
-0.48232657361591E+04, 0.40511340542057E+06, -0.23855557567849E+00,
0.65017534844798E+03]
tita = T+n[9]/(T-n[10])
A = tita**2+n[1]*tita+n[2]
B = n[3]*tita**2+n[4]*tita+n[5]
C = n[6]*tita**2+n[7]*tita+n[8]
return (2*C/(-B+(B**2-4*A*C)**0.5))**4 | Define the saturated line, P=f(T)
Parameters
----------
T : float
Temperature, [K]
Returns
-------
P : float
Pressure, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 273.15 ≤ T ≤ 647.096
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 30
Examples
--------
>>> _PSat_T(500)
2.63889776 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L278-L320 |
jjgomera/iapws | iapws/iapws97.py | _TSat_P | def _TSat_P(P):
"""Define the saturated line, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0.00061121 ≤ P ≤ 22.064
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 31
Examples
--------
>>> _TSat_P(10)
584.149488
"""
# Check input parameters
if P < 611.212677/1e6 or P > 22.064:
raise NotImplementedError("Incoming out of bound")
n = [0, 0.11670521452767E+04, -0.72421316703206E+06, -0.17073846940092E+02,
0.12020824702470E+05, -0.32325550322333E+07, 0.14915108613530E+02,
-0.48232657361591E+04, 0.40511340542057E+06, -0.23855557567849E+00,
0.65017534844798E+03]
beta = P**0.25
E = beta**2+n[3]*beta+n[6]
F = n[1]*beta**2+n[4]*beta+n[7]
G = n[2]*beta**2+n[5]*beta+n[8]
D = 2*G/(-F-(F**2-4*E*G)**0.5)
return (n[10]+D-((n[10]+D)**2-4*(n[9]+n[10]*D))**0.5)/2 | python | def _TSat_P(P):
"""Define the saturated line, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0.00061121 ≤ P ≤ 22.064
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 31
Examples
--------
>>> _TSat_P(10)
584.149488
"""
# Check input parameters
if P < 611.212677/1e6 or P > 22.064:
raise NotImplementedError("Incoming out of bound")
n = [0, 0.11670521452767E+04, -0.72421316703206E+06, -0.17073846940092E+02,
0.12020824702470E+05, -0.32325550322333E+07, 0.14915108613530E+02,
-0.48232657361591E+04, 0.40511340542057E+06, -0.23855557567849E+00,
0.65017534844798E+03]
beta = P**0.25
E = beta**2+n[3]*beta+n[6]
F = n[1]*beta**2+n[4]*beta+n[7]
G = n[2]*beta**2+n[5]*beta+n[8]
D = 2*G/(-F-(F**2-4*E*G)**0.5)
return (n[10]+D-((n[10]+D)**2-4*(n[9]+n[10]*D))**0.5)/2 | Define the saturated line, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 0.00061121 ≤ P ≤ 22.064
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 31
Examples
--------
>>> _TSat_P(10)
584.149488 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L323-L366 |
jjgomera/iapws | iapws/iapws97.py | _PSat_h | def _PSat_h(h):
"""Define the saturated line, P=f(h) for region 3
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
P : float
Pressure, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* h'(623.15K) ≤ h ≤ h''(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 10
Examples
--------
>>> _PSat_h(1700)
17.24175718
>>> _PSat_h(2400)
20.18090839
"""
# Check input parameters
hmin_Ps3 = _Region1(623.15, Ps_623)["h"]
hmax_Ps3 = _Region2(623.15, Ps_623)["h"]
if h < hmin_Ps3 or h > hmax_Ps3:
raise NotImplementedError("Incoming out of bound")
nu = h/2600
I = [0, 1, 1, 1, 1, 5, 7, 8, 14, 20, 22, 24, 28, 36]
J = [0, 1, 3, 4, 36, 3, 0, 24, 16, 16, 3, 18, 8, 24]
n = [0.600073641753024, -0.936203654849857e1, 0.246590798594147e2,
-0.107014222858224e3, -0.915821315805768e14, -0.862332011700662e4,
-0.235837344740032e2, 0.252304969384128e18, -0.389718771997719e19,
-0.333775713645296e23, 0.356499469636328e11, -0.148547544720641e27,
0.330611514838798e19, 0.813641294467829e38]
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (nu-1.02)**i * (nu-0.608)**j
return 22*suma | python | def _PSat_h(h):
"""Define the saturated line, P=f(h) for region 3
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
P : float
Pressure, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* h'(623.15K) ≤ h ≤ h''(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 10
Examples
--------
>>> _PSat_h(1700)
17.24175718
>>> _PSat_h(2400)
20.18090839
"""
# Check input parameters
hmin_Ps3 = _Region1(623.15, Ps_623)["h"]
hmax_Ps3 = _Region2(623.15, Ps_623)["h"]
if h < hmin_Ps3 or h > hmax_Ps3:
raise NotImplementedError("Incoming out of bound")
nu = h/2600
I = [0, 1, 1, 1, 1, 5, 7, 8, 14, 20, 22, 24, 28, 36]
J = [0, 1, 3, 4, 36, 3, 0, 24, 16, 16, 3, 18, 8, 24]
n = [0.600073641753024, -0.936203654849857e1, 0.246590798594147e2,
-0.107014222858224e3, -0.915821315805768e14, -0.862332011700662e4,
-0.235837344740032e2, 0.252304969384128e18, -0.389718771997719e19,
-0.333775713645296e23, 0.356499469636328e11, -0.148547544720641e27,
0.330611514838798e19, 0.813641294467829e38]
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (nu-1.02)**i * (nu-0.608)**j
return 22*suma | Define the saturated line, P=f(h) for region 3
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
P : float
Pressure, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* h'(623.15K) ≤ h ≤ h''(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 10
Examples
--------
>>> _PSat_h(1700)
17.24175718
>>> _PSat_h(2400)
20.18090839 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L369-L420 |
jjgomera/iapws | iapws/iapws97.py | _PSat_s | def _PSat_s(s):
"""Define the saturated line, P=f(s) for region 3
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* s'(623.15K) ≤ s ≤ s''(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 11
Examples
--------
>>> _PSat_s(3.8)
16.87755057
>>> _PSat_s(5.2)
16.68968482
"""
# Check input parameters
smin_Ps3 = _Region1(623.15, Ps_623)["s"]
smax_Ps3 = _Region2(623.15, Ps_623)["s"]
if s < smin_Ps3 or s > smax_Ps3:
raise NotImplementedError("Incoming out of bound")
sigma = s/5.2
I = [0, 1, 1, 4, 12, 12, 16, 24, 28, 32]
J = [0, 1, 32, 7, 4, 14, 36, 10, 0, 18]
n = [0.639767553612785, -0.129727445396014e2, -0.224595125848403e16,
0.177466741801846e7, 0.717079349571538e10, -0.378829107169011e18,
-0.955586736431328e35, 0.187269814676188e24, 0.119254746466473e12,
0.110649277244882e37]
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (sigma-1.03)**i * (sigma-0.699)**j
return 22*suma | python | def _PSat_s(s):
"""Define the saturated line, P=f(s) for region 3
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* s'(623.15K) ≤ s ≤ s''(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 11
Examples
--------
>>> _PSat_s(3.8)
16.87755057
>>> _PSat_s(5.2)
16.68968482
"""
# Check input parameters
smin_Ps3 = _Region1(623.15, Ps_623)["s"]
smax_Ps3 = _Region2(623.15, Ps_623)["s"]
if s < smin_Ps3 or s > smax_Ps3:
raise NotImplementedError("Incoming out of bound")
sigma = s/5.2
I = [0, 1, 1, 4, 12, 12, 16, 24, 28, 32]
J = [0, 1, 32, 7, 4, 14, 36, 10, 0, 18]
n = [0.639767553612785, -0.129727445396014e2, -0.224595125848403e16,
0.177466741801846e7, 0.717079349571538e10, -0.378829107169011e18,
-0.955586736431328e35, 0.187269814676188e24, 0.119254746466473e12,
0.110649277244882e37]
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (sigma-1.03)**i * (sigma-0.699)**j
return 22*suma | Define the saturated line, P=f(s) for region 3
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* s'(623.15K) ≤ s ≤ s''(623.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 11
Examples
--------
>>> _PSat_s(3.8)
16.87755057
>>> _PSat_s(5.2)
16.68968482 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L423-L473 |
jjgomera/iapws | iapws/iapws97.py | _h2ab_s | def _h2ab_s(s):
"""Define the saturated line boundary between Region 4 and 2a-2b, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 5.85 ≤ s ≤ s"(273.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 5
Examples
--------
>>> _h2ab_s(7)
2723.729985
>>> _h2ab_s(9)
2511.861477
"""
# Check input parameters
if s < 5.85 or s > 9.155759395:
raise NotImplementedError("Incoming out of bound")
sigma1 = s/5.21
sigma2 = s/9.2
I = [1, 1, 2, 2, 4, 4, 7, 8, 8, 10, 12, 12, 18, 20, 24, 28, 28, 28, 28, 28,
32, 32, 32, 32, 32, 36, 36, 36, 36, 36]
J = [8, 24, 4, 32, 1, 2, 7, 5, 12, 1, 0, 7, 10, 12, 32, 8, 12, 20, 22, 24,
2, 7, 12, 14, 24, 10, 12, 20, 22, 28]
n = [-0.524581170928788e3, -0.926947218142218e7, -0.237385107491666e3,
0.210770155812776e11, -0.239494562010986e2, 0.221802480294197e3,
-0.510472533393438e7, 0.124981396109147e7, 0.200008436996201e10,
-0.815158509791035e3, -0.157612685637523e3, -0.114200422332791e11,
0.662364680776872e16, -0.227622818296144e19, -0.171048081348406e32,
0.660788766938091e16, 0.166320055886021e23, -0.218003784381501e30,
-0.787276140295618e30, 0.151062329700346e32, 0.795732170300541e7,
0.131957647355347e16, -0.325097068299140e24, -0.418600611419248e26,
0.297478906557467e35, -0.953588761745473e20, 0.166957699620939e25,
-0.175407764869978e33, 0.347581490626396e35, -0.710971318427851e39]
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (1/sigma1-0.513)**i * (sigma2-0.524)**j
return 2800*exp(suma) | python | def _h2ab_s(s):
"""Define the saturated line boundary between Region 4 and 2a-2b, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 5.85 ≤ s ≤ s"(273.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 5
Examples
--------
>>> _h2ab_s(7)
2723.729985
>>> _h2ab_s(9)
2511.861477
"""
# Check input parameters
if s < 5.85 or s > 9.155759395:
raise NotImplementedError("Incoming out of bound")
sigma1 = s/5.21
sigma2 = s/9.2
I = [1, 1, 2, 2, 4, 4, 7, 8, 8, 10, 12, 12, 18, 20, 24, 28, 28, 28, 28, 28,
32, 32, 32, 32, 32, 36, 36, 36, 36, 36]
J = [8, 24, 4, 32, 1, 2, 7, 5, 12, 1, 0, 7, 10, 12, 32, 8, 12, 20, 22, 24,
2, 7, 12, 14, 24, 10, 12, 20, 22, 28]
n = [-0.524581170928788e3, -0.926947218142218e7, -0.237385107491666e3,
0.210770155812776e11, -0.239494562010986e2, 0.221802480294197e3,
-0.510472533393438e7, 0.124981396109147e7, 0.200008436996201e10,
-0.815158509791035e3, -0.157612685637523e3, -0.114200422332791e11,
0.662364680776872e16, -0.227622818296144e19, -0.171048081348406e32,
0.660788766938091e16, 0.166320055886021e23, -0.218003784381501e30,
-0.787276140295618e30, 0.151062329700346e32, 0.795732170300541e7,
0.131957647355347e16, -0.325097068299140e24, -0.418600611419248e26,
0.297478906557467e35, -0.953588761745473e20, 0.166957699620939e25,
-0.175407764869978e33, 0.347581490626396e35, -0.710971318427851e39]
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (1/sigma1-0.513)**i * (sigma2-0.524)**j
return 2800*exp(suma) | Define the saturated line boundary between Region 4 and 2a-2b, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
Notes
------
Raise :class:`NotImplementedError` if input isn't in limit:
* 5.85 ≤ s ≤ s"(273.15K)
References
----------
IAPWS, Revised Supplementary Release on Backward Equations p(h,s) for
Region 3, Equations as a Function of h and s for the Region Boundaries, and
an Equation Tsat(h,s) for Region 4 of the IAPWS Industrial Formulation 1997
for the Thermodynamic Properties of Water and Steam,
http://www.iapws.org/relguide/Supp-phs3-2014.pdf. Eq 5
Examples
--------
>>> _h2ab_s(7)
2723.729985
>>> _h2ab_s(9)
2511.861477 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L590-L648 |
jjgomera/iapws | iapws/iapws97.py | _Region1 | def _Region1(T, P):
"""Basic equation for region 1
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 7
Examples
--------
>>> _Region1(300,3)["v"]
0.00100215168
>>> _Region1(300,3)["h"]
115.331273
>>> _Region1(300,3)["h"]-3000*_Region1(300,3)["v"]
112.324818
>>> _Region1(300,80)["s"]
0.368563852
>>> _Region1(300,80)["cp"]
4.01008987
>>> _Region1(300,80)["cv"]
3.91736606
>>> _Region1(500,3)["w"]
1240.71337
>>> _Region1(500,3)["alfav"]
0.00164118128
>>> _Region1(500,3)["kt"]
0.00112892188
"""
if P < 0:
P = Pmin
I = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4,
4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32]
J = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0,
6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41]
n = [0.14632971213167, -0.84548187169114, -0.37563603672040e1,
0.33855169168385e1, -0.95791963387872, 0.15772038513228,
-0.16616417199501e-1, 0.81214629983568e-3, 0.28319080123804e-3,
-0.60706301565874e-3, -0.18990068218419e-1, -0.32529748770505e-1,
-0.21841717175414e-1, -0.52838357969930e-4, -0.47184321073267e-3,
-0.30001780793026e-3, 0.47661393906987e-4, -0.44141845330846e-5,
-0.72694996297594e-15, -0.31679644845054e-4, -0.28270797985312e-5,
-0.85205128120103e-9, -0.22425281908000e-5, -0.65171222895601e-6,
-0.14341729937924e-12, -0.40516996860117e-6, -0.12734301741641e-8,
-0.17424871230634e-9, -0.68762131295531e-18, 0.14478307828521e-19,
0.26335781662795e-22, -0.11947622640071e-22, 0.18228094581404e-23,
-0.93537087292458e-25]
Tr = 1386/T
Pr = P/16.53
g = gp = gpp = gt = gtt = gpt = 0
for i, j, ni in zip(I, J, n):
g += ni * (7.1-Pr)**i * (Tr-1.222)**j
gp -= ni*i * (7.1-Pr)**(i-1) * (Tr-1.222)**j
gpp += ni*i*(i-1) * (7.1-Pr)**(i-2) * (Tr-1.222)**j
gt += ni*j * (7.1-Pr)**i * (Tr-1.222)**(j-1)
gtt += ni*j*(j-1) * (7.1-Pr)**i * (Tr-1.222)**(j-2)
gpt -= ni*i*j * (7.1-Pr)**(i-1) * (Tr-1.222)**(j-1)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = Pr*gp*R*T/P/1000
propiedades["h"] = Tr*gt*R*T
propiedades["s"] = R*(Tr*gt-g)
propiedades["cp"] = -R*Tr**2*gtt
propiedades["cv"] = R*(-Tr**2*gtt+(gp-Tr*gpt)**2/gpp)
propiedades["w"] = sqrt(R*T*1000*gp**2/((gp-Tr*gpt)**2/(Tr**2*gtt)-gpp))
propiedades["alfav"] = (1-Tr*gpt/gp)/T
propiedades["kt"] = -Pr*gpp/gp/P
propiedades["region"] = 1
propiedades["x"] = 0
return propiedades | python | def _Region1(T, P):
"""Basic equation for region 1
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 7
Examples
--------
>>> _Region1(300,3)["v"]
0.00100215168
>>> _Region1(300,3)["h"]
115.331273
>>> _Region1(300,3)["h"]-3000*_Region1(300,3)["v"]
112.324818
>>> _Region1(300,80)["s"]
0.368563852
>>> _Region1(300,80)["cp"]
4.01008987
>>> _Region1(300,80)["cv"]
3.91736606
>>> _Region1(500,3)["w"]
1240.71337
>>> _Region1(500,3)["alfav"]
0.00164118128
>>> _Region1(500,3)["kt"]
0.00112892188
"""
if P < 0:
P = Pmin
I = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4,
4, 4, 5, 8, 8, 21, 23, 29, 30, 31, 32]
J = [-2, -1, 0, 1, 2, 3, 4, 5, -9, -7, -1, 0, 1, 3, -3, 0, 1, 3, 17, -4, 0,
6, -5, -2, 10, -8, -11, -6, -29, -31, -38, -39, -40, -41]
n = [0.14632971213167, -0.84548187169114, -0.37563603672040e1,
0.33855169168385e1, -0.95791963387872, 0.15772038513228,
-0.16616417199501e-1, 0.81214629983568e-3, 0.28319080123804e-3,
-0.60706301565874e-3, -0.18990068218419e-1, -0.32529748770505e-1,
-0.21841717175414e-1, -0.52838357969930e-4, -0.47184321073267e-3,
-0.30001780793026e-3, 0.47661393906987e-4, -0.44141845330846e-5,
-0.72694996297594e-15, -0.31679644845054e-4, -0.28270797985312e-5,
-0.85205128120103e-9, -0.22425281908000e-5, -0.65171222895601e-6,
-0.14341729937924e-12, -0.40516996860117e-6, -0.12734301741641e-8,
-0.17424871230634e-9, -0.68762131295531e-18, 0.14478307828521e-19,
0.26335781662795e-22, -0.11947622640071e-22, 0.18228094581404e-23,
-0.93537087292458e-25]
Tr = 1386/T
Pr = P/16.53
g = gp = gpp = gt = gtt = gpt = 0
for i, j, ni in zip(I, J, n):
g += ni * (7.1-Pr)**i * (Tr-1.222)**j
gp -= ni*i * (7.1-Pr)**(i-1) * (Tr-1.222)**j
gpp += ni*i*(i-1) * (7.1-Pr)**(i-2) * (Tr-1.222)**j
gt += ni*j * (7.1-Pr)**i * (Tr-1.222)**(j-1)
gtt += ni*j*(j-1) * (7.1-Pr)**i * (Tr-1.222)**(j-2)
gpt -= ni*i*j * (7.1-Pr)**(i-1) * (Tr-1.222)**(j-1)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = Pr*gp*R*T/P/1000
propiedades["h"] = Tr*gt*R*T
propiedades["s"] = R*(Tr*gt-g)
propiedades["cp"] = -R*Tr**2*gtt
propiedades["cv"] = R*(-Tr**2*gtt+(gp-Tr*gpt)**2/gpp)
propiedades["w"] = sqrt(R*T*1000*gp**2/((gp-Tr*gpt)**2/(Tr**2*gtt)-gpp))
propiedades["alfav"] = (1-Tr*gpt/gp)/T
propiedades["kt"] = -Pr*gpp/gp/P
propiedades["region"] = 1
propiedades["x"] = 0
return propiedades | Basic equation for region 1
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 7
Examples
--------
>>> _Region1(300,3)["v"]
0.00100215168
>>> _Region1(300,3)["h"]
115.331273
>>> _Region1(300,3)["h"]-3000*_Region1(300,3)["v"]
112.324818
>>> _Region1(300,80)["s"]
0.368563852
>>> _Region1(300,80)["cp"]
4.01008987
>>> _Region1(300,80)["cv"]
3.91736606
>>> _Region1(500,3)["w"]
1240.71337
>>> _Region1(500,3)["alfav"]
0.00164118128
>>> _Region1(500,3)["kt"]
0.00112892188 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L706-L800 |
jjgomera/iapws | iapws/iapws97.py | _Backward1_T_Ph | def _Backward1_T_Ph(P, h):
"""
Backward equation for region 1, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 11
Examples
--------
>>> _Backward1_T_Ph(3,500)
391.798509
>>> _Backward1_T_Ph(80,1500)
611.041229
"""
I = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6]
J = [0, 1, 2, 6, 22, 32, 0, 1, 2, 3, 4, 10, 32, 10, 32, 10, 32, 32, 32, 32]
n = [-0.23872489924521e3, 0.40421188637945e3, 0.11349746881718e3,
-0.58457616048039e1, -0.15285482413140e-3, -0.10866707695377e-5,
-0.13391744872602e2, 0.43211039183559e2, -0.54010067170506e2,
0.30535892203916e2, -0.65964749423638e1, 0.93965400878363e-2,
0.11573647505340e-6, -0.25858641282073e-4, -0.40644363084799e-8,
0.66456186191635e-7, 0.80670734103027e-10, -0.93477771213947e-12,
0.58265442020601e-14, -0.15020185953503e-16]
Pr = P/1
nu = h/2500
T = 0
for i, j, ni in zip(I, J, n):
T += ni * Pr**i * (nu+1)**j
return T | python | def _Backward1_T_Ph(P, h):
"""
Backward equation for region 1, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 11
Examples
--------
>>> _Backward1_T_Ph(3,500)
391.798509
>>> _Backward1_T_Ph(80,1500)
611.041229
"""
I = [0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6]
J = [0, 1, 2, 6, 22, 32, 0, 1, 2, 3, 4, 10, 32, 10, 32, 10, 32, 32, 32, 32]
n = [-0.23872489924521e3, 0.40421188637945e3, 0.11349746881718e3,
-0.58457616048039e1, -0.15285482413140e-3, -0.10866707695377e-5,
-0.13391744872602e2, 0.43211039183559e2, -0.54010067170506e2,
0.30535892203916e2, -0.65964749423638e1, 0.93965400878363e-2,
0.11573647505340e-6, -0.25858641282073e-4, -0.40644363084799e-8,
0.66456186191635e-7, 0.80670734103027e-10, -0.93477771213947e-12,
0.58265442020601e-14, -0.15020185953503e-16]
Pr = P/1
nu = h/2500
T = 0
for i, j, ni in zip(I, J, n):
T += ni * Pr**i * (nu+1)**j
return T | Backward equation for region 1, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 11
Examples
--------
>>> _Backward1_T_Ph(3,500)
391.798509
>>> _Backward1_T_Ph(80,1500)
611.041229 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L803-L847 |
jjgomera/iapws | iapws/iapws97.py | _Backward1_P_hs | def _Backward1_P_hs(h, s):
"""Backward equation for region 1, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 1
Examples
--------
>>> _Backward1_P_hs(0.001,0)
0.0009800980612
>>> _Backward1_P_hs(90,0)
91.92954727
>>> _Backward1_P_hs(1500,3.4)
58.68294423
"""
I = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5]
J = [0, 1, 2, 4, 5, 6, 8, 14, 0, 1, 4, 6, 0, 1, 10, 4, 1, 4, 0]
n = [-0.691997014660582, -0.183612548787560e2, -0.928332409297335e1,
0.659639569909906e2, -0.162060388912024e2, 0.450620017338667e3,
0.854680678224170e3, 0.607523214001162e4, 0.326487682621856e2,
-0.269408844582931e2, -0.319947848334300e3, -0.928354307043320e3,
0.303634537455249e2, -0.650540422444146e2, -0.430991316516130e4,
-0.747512324096068e3, 0.730000345529245e3, 0.114284032569021e4,
-0.436407041874559e3]
nu = h/3400
sigma = s/7.6
P = 0
for i, j, ni in zip(I, J, n):
P += ni * (nu+0.05)**i * (sigma+0.05)**j
return 100*P | python | def _Backward1_P_hs(h, s):
"""Backward equation for region 1, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 1
Examples
--------
>>> _Backward1_P_hs(0.001,0)
0.0009800980612
>>> _Backward1_P_hs(90,0)
91.92954727
>>> _Backward1_P_hs(1500,3.4)
58.68294423
"""
I = [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 5]
J = [0, 1, 2, 4, 5, 6, 8, 14, 0, 1, 4, 6, 0, 1, 10, 4, 1, 4, 0]
n = [-0.691997014660582, -0.183612548787560e2, -0.928332409297335e1,
0.659639569909906e2, -0.162060388912024e2, 0.450620017338667e3,
0.854680678224170e3, 0.607523214001162e4, 0.326487682621856e2,
-0.269408844582931e2, -0.319947848334300e3, -0.928354307043320e3,
0.303634537455249e2, -0.650540422444146e2, -0.430991316516130e4,
-0.747512324096068e3, 0.730000345529245e3, 0.114284032569021e4,
-0.436407041874559e3]
nu = h/3400
sigma = s/7.6
P = 0
for i, j, ni in zip(I, J, n):
P += ni * (nu+0.05)**i * (sigma+0.05)**j
return 100*P | Backward equation for region 1, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 1
Examples
--------
>>> _Backward1_P_hs(0.001,0)
0.0009800980612
>>> _Backward1_P_hs(90,0)
91.92954727
>>> _Backward1_P_hs(1500,3.4)
58.68294423 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L896-L942 |
jjgomera/iapws | iapws/iapws97.py | _Region2 | def _Region2(T, P):
"""Basic equation for region 2
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 15-17
Examples
--------
>>> _Region2(700,30)["v"]
0.00542946619
>>> _Region2(700,30)["h"]
2631.49474
>>> _Region2(700,30)["h"]-30000*_Region2(700,30)["v"]
2468.61076
>>> _Region2(700,0.0035)["s"]
10.1749996
>>> _Region2(700,0.0035)["cp"]
2.08141274
>>> _Region2(700,0.0035)["cv"]
1.61978333
>>> _Region2(300,0.0035)["w"]
427.920172
>>> _Region2(300,0.0035)["alfav"]
0.00337578289
>>> _Region2(300,0.0035)["kt"]
286.239651
"""
if P < 0:
P = Pmin
Tr = 540/T
Pr = P/1
go, gop, gopp, got, gott, gopt = Region2_cp0(Tr, Pr)
Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7,
7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24,
24, 24]
Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35,
0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39,
26, 40, 58]
nr = [-0.0017731742473212999, -0.017834862292357999, -0.045996013696365003,
-0.057581259083432, -0.050325278727930002, -3.3032641670203e-05,
-0.00018948987516315, -0.0039392777243355001, -0.043797295650572998,
-2.6674547914087001e-05, 2.0481737692308999e-08,
4.3870667284435001e-07, -3.2277677238570002e-05, -0.0015033924542148,
-0.040668253562648998, -7.8847309559367001e-10,
1.2790717852285001e-08, 4.8225372718507002e-07,
2.2922076337661001e-06, -1.6714766451061001e-11,
-0.0021171472321354998, -23.895741934103999, -5.9059564324270004e-18,
-1.2621808899101e-06, -0.038946842435739003, 1.1256211360459e-11,
-8.2311340897998004, 1.9809712802088e-08, 1.0406965210174e-19,
-1.0234747095929e-13, -1.0018179379511e-09, -8.0882908646984998e-11,
0.10693031879409, -0.33662250574170999, 8.9185845355420999e-25,
3.0629316876231997e-13, -4.2002467698208001e-06,
-5.9056029685639003e-26, 3.7826947613457002e-06,
-1.2768608934681e-15, 7.3087610595061e-29, 5.5414715350778001e-17,
-9.4369707241209998e-07]
gr = grp = grpp = grt = grtt = grpt = 0
for i, j, ni in zip(Ir, Jr, nr):
gr += ni * Pr**i * (Tr-0.5)**j
grp += ni*i * Pr**(i-1) * (Tr-0.5)**j
grpp += ni*i*(i-1) * Pr**(i-2) * (Tr-0.5)**j
grt += ni*j * Pr**i * (Tr-0.5)**(j-1)
grtt += ni*j*(j-1) * Pr**i * (Tr-0.5)**(j-2)
grpt += ni*i*j * Pr**(i-1) * (Tr-0.5)**(j-1)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = Pr*(gop+grp)*R*T/P/1000
propiedades["h"] = Tr*(got+grt)*R*T
propiedades["s"] = R*(Tr*(got+grt)-(go+gr))
propiedades["cp"] = -R*Tr**2*(gott+grtt)
propiedades["cv"] = R*(-Tr**2*(gott+grtt)-(1+Pr*grp-Tr*Pr*grpt)**2 /
(1-Pr**2*grpp))
propiedades["w"] = (R*T*1000*(1+2*Pr*grp+Pr**2*grp**2)/(1-Pr**2*grpp+(
1+Pr*grp-Tr*Pr*grpt)**2/Tr**2/(gott+grtt)))**0.5
propiedades["alfav"] = (1+Pr*grp-Tr*Pr*grpt)/(1+Pr*grp)/T
propiedades["kt"] = (1-Pr**2*grpp)/(1+Pr*grp)/P
propiedades["region"] = 2
propiedades["x"] = 1
return propiedades | python | def _Region2(T, P):
"""Basic equation for region 2
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 15-17
Examples
--------
>>> _Region2(700,30)["v"]
0.00542946619
>>> _Region2(700,30)["h"]
2631.49474
>>> _Region2(700,30)["h"]-30000*_Region2(700,30)["v"]
2468.61076
>>> _Region2(700,0.0035)["s"]
10.1749996
>>> _Region2(700,0.0035)["cp"]
2.08141274
>>> _Region2(700,0.0035)["cv"]
1.61978333
>>> _Region2(300,0.0035)["w"]
427.920172
>>> _Region2(300,0.0035)["alfav"]
0.00337578289
>>> _Region2(300,0.0035)["kt"]
286.239651
"""
if P < 0:
P = Pmin
Tr = 540/T
Pr = P/1
go, gop, gopp, got, gott, gopt = Region2_cp0(Tr, Pr)
Ir = [1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 5, 6, 6, 6, 7,
7, 7, 8, 8, 9, 10, 10, 10, 16, 16, 18, 20, 20, 20, 21, 22, 23, 24,
24, 24]
Jr = [0, 1, 2, 3, 6, 1, 2, 4, 7, 36, 0, 1, 3, 6, 35, 1, 2, 3, 7, 3, 16, 35,
0, 11, 25, 8, 36, 13, 4, 10, 14, 29, 50, 57, 20, 35, 48, 21, 53, 39,
26, 40, 58]
nr = [-0.0017731742473212999, -0.017834862292357999, -0.045996013696365003,
-0.057581259083432, -0.050325278727930002, -3.3032641670203e-05,
-0.00018948987516315, -0.0039392777243355001, -0.043797295650572998,
-2.6674547914087001e-05, 2.0481737692308999e-08,
4.3870667284435001e-07, -3.2277677238570002e-05, -0.0015033924542148,
-0.040668253562648998, -7.8847309559367001e-10,
1.2790717852285001e-08, 4.8225372718507002e-07,
2.2922076337661001e-06, -1.6714766451061001e-11,
-0.0021171472321354998, -23.895741934103999, -5.9059564324270004e-18,
-1.2621808899101e-06, -0.038946842435739003, 1.1256211360459e-11,
-8.2311340897998004, 1.9809712802088e-08, 1.0406965210174e-19,
-1.0234747095929e-13, -1.0018179379511e-09, -8.0882908646984998e-11,
0.10693031879409, -0.33662250574170999, 8.9185845355420999e-25,
3.0629316876231997e-13, -4.2002467698208001e-06,
-5.9056029685639003e-26, 3.7826947613457002e-06,
-1.2768608934681e-15, 7.3087610595061e-29, 5.5414715350778001e-17,
-9.4369707241209998e-07]
gr = grp = grpp = grt = grtt = grpt = 0
for i, j, ni in zip(Ir, Jr, nr):
gr += ni * Pr**i * (Tr-0.5)**j
grp += ni*i * Pr**(i-1) * (Tr-0.5)**j
grpp += ni*i*(i-1) * Pr**(i-2) * (Tr-0.5)**j
grt += ni*j * Pr**i * (Tr-0.5)**(j-1)
grtt += ni*j*(j-1) * Pr**i * (Tr-0.5)**(j-2)
grpt += ni*i*j * Pr**(i-1) * (Tr-0.5)**(j-1)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = P
propiedades["v"] = Pr*(gop+grp)*R*T/P/1000
propiedades["h"] = Tr*(got+grt)*R*T
propiedades["s"] = R*(Tr*(got+grt)-(go+gr))
propiedades["cp"] = -R*Tr**2*(gott+grtt)
propiedades["cv"] = R*(-Tr**2*(gott+grtt)-(1+Pr*grp-Tr*Pr*grpt)**2 /
(1-Pr**2*grpp))
propiedades["w"] = (R*T*1000*(1+2*Pr*grp+Pr**2*grp**2)/(1-Pr**2*grpp+(
1+Pr*grp-Tr*Pr*grpt)**2/Tr**2/(gott+grtt)))**0.5
propiedades["alfav"] = (1+Pr*grp-Tr*Pr*grpt)/(1+Pr*grp)/T
propiedades["kt"] = (1-Pr**2*grpp)/(1+Pr*grp)/P
propiedades["region"] = 2
propiedades["x"] = 1
return propiedades | Basic equation for region 2
Parameters
----------
T : float
Temperature, [K]
P : float
Pressure, [MPa]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 15-17
Examples
--------
>>> _Region2(700,30)["v"]
0.00542946619
>>> _Region2(700,30)["h"]
2631.49474
>>> _Region2(700,30)["h"]-30000*_Region2(700,30)["v"]
2468.61076
>>> _Region2(700,0.0035)["s"]
10.1749996
>>> _Region2(700,0.0035)["cp"]
2.08141274
>>> _Region2(700,0.0035)["cv"]
1.61978333
>>> _Region2(300,0.0035)["w"]
427.920172
>>> _Region2(300,0.0035)["alfav"]
0.00337578289
>>> _Region2(300,0.0035)["kt"]
286.239651 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L946-L1053 |
jjgomera/iapws | iapws/iapws97.py | Region2_cp0 | def Region2_cp0(Tr, Pr):
"""Ideal properties for Region 2
Parameters
----------
Tr : float
Reduced temperature, [-]
Pr : float
Reduced pressure, [-]
Returns
-------
prop : array
Array with ideal Gibbs energy partial derivatives:
* g: Ideal Specific Gibbs energy [kJ/kg]
* gp: ∂g/∂P|T
* gpp: ∂²g/∂P²|T
* gt: ∂g/∂T|P
* gtt: ∂²g/∂T²|P
* gpt: ∂²g/∂T∂P
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 16
"""
Jo = [0, 1, -5, -4, -3, -2, -1, 2, 3]
no = [-0.96927686500217E+01, 0.10086655968018E+02, -0.56087911283020E-02,
0.71452738081455E-01, -0.40710498223928E+00, 0.14240819171444E+01,
-0.43839511319450E+01, -0.28408632460772E+00, 0.21268463753307E-01]
go = log(Pr)
gop = Pr**-1
gopp = -Pr**-2
got = gott = gopt = 0
for j, ni in zip(Jo, no):
go += ni * Tr**j
got += ni*j * Tr**(j-1)
gott += ni*j*(j-1) * Tr**(j-2)
return go, gop, gopp, got, gott, gopt | python | def Region2_cp0(Tr, Pr):
"""Ideal properties for Region 2
Parameters
----------
Tr : float
Reduced temperature, [-]
Pr : float
Reduced pressure, [-]
Returns
-------
prop : array
Array with ideal Gibbs energy partial derivatives:
* g: Ideal Specific Gibbs energy [kJ/kg]
* gp: ∂g/∂P|T
* gpp: ∂²g/∂P²|T
* gt: ∂g/∂T|P
* gtt: ∂²g/∂T²|P
* gpt: ∂²g/∂T∂P
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 16
"""
Jo = [0, 1, -5, -4, -3, -2, -1, 2, 3]
no = [-0.96927686500217E+01, 0.10086655968018E+02, -0.56087911283020E-02,
0.71452738081455E-01, -0.40710498223928E+00, 0.14240819171444E+01,
-0.43839511319450E+01, -0.28408632460772E+00, 0.21268463753307E-01]
go = log(Pr)
gop = Pr**-1
gopp = -Pr**-2
got = gott = gopt = 0
for j, ni in zip(Jo, no):
go += ni * Tr**j
got += ni*j * Tr**(j-1)
gott += ni*j*(j-1) * Tr**(j-2)
return go, gop, gopp, got, gott, gopt | Ideal properties for Region 2
Parameters
----------
Tr : float
Reduced temperature, [-]
Pr : float
Reduced pressure, [-]
Returns
-------
prop : array
Array with ideal Gibbs energy partial derivatives:
* g: Ideal Specific Gibbs energy [kJ/kg]
* gp: ∂g/∂P|T
* gpp: ∂²g/∂P²|T
* gt: ∂g/∂T|P
* gtt: ∂²g/∂T²|P
* gpt: ∂²g/∂T∂P
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 16 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L1056-L1097 |
jjgomera/iapws | iapws/iapws97.py | _hab_s | def _hab_s(s):
"""Define the boundary between Region 2a and 2b, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 2
Examples
--------
>>> _hab_s(7)
3376.437884
"""
smin = _Region2(_TSat_P(4), 4)["s"]
smax = _Region2(1073.15, 4)["s"]
if s < smin:
h = 0
elif s > smax:
h = 5000
else:
h = -0.349898083432139e4 + 0.257560716905876e4*s - \
0.421073558227969e3*s**2+0.276349063799944e2*s**3
return h | python | def _hab_s(s):
"""Define the boundary between Region 2a and 2b, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 2
Examples
--------
>>> _hab_s(7)
3376.437884
"""
smin = _Region2(_TSat_P(4), 4)["s"]
smax = _Region2(1073.15, 4)["s"]
if s < smin:
h = 0
elif s > smax:
h = 5000
else:
h = -0.349898083432139e4 + 0.257560716905876e4*s - \
0.421073558227969e3*s**2+0.276349063799944e2*s**3
return h | Define the boundary between Region 2a and 2b, h=f(s)
Parameters
----------
s : float
Specific entropy, [kJ/kgK]
Returns
-------
h : float
Specific enthalpy, [kJ/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Pressure
as a Function of Enthalpy and Entropy p(h,s) for Regions 1 and 2 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of
Water and Steam, http://www.iapws.org/relguide/Supp-PHS12-2014.pdf, Eq 2
Examples
--------
>>> _hab_s(7)
3376.437884 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L1154-L1188 |
jjgomera/iapws | iapws/iapws97.py | _Backward2_T_Ph | def _Backward2_T_Ph(P, h):
"""Backward equation for region 2, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
"""
if P <= 4:
T = _Backward2a_T_Ph(P, h)
elif 4 < P <= 6.546699678:
T = _Backward2b_T_Ph(P, h)
else:
hf = _hbc_P(P)
if h >= hf:
T = _Backward2b_T_Ph(P, h)
else:
T = _Backward2c_T_Ph(P, h)
if P <= 22.064:
Tsat = _TSat_P(P)
T = max(Tsat, T)
return T | python | def _Backward2_T_Ph(P, h):
"""Backward equation for region 2, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
"""
if P <= 4:
T = _Backward2a_T_Ph(P, h)
elif 4 < P <= 6.546699678:
T = _Backward2b_T_Ph(P, h)
else:
hf = _hbc_P(P)
if h >= hf:
T = _Backward2b_T_Ph(P, h)
else:
T = _Backward2c_T_Ph(P, h)
if P <= 22.064:
Tsat = _TSat_P(P)
T = max(Tsat, T)
return T | Backward equation for region 2, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K] | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L1347-L1376 |
jjgomera/iapws | iapws/iapws97.py | _Backward2a_T_Ps | def _Backward2a_T_Ps(P, s):
"""Backward equation for region 2a, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 25
Examples
--------
>>> _Backward2a_T_Ps(0.1,7.5)
399.517097
>>> _Backward2a_T_Ps(2.5,8)
1039.84917
"""
I = [-1.5, -1.5, -1.5, -1.5, -1.5, -1.5, -1.25, -1.25, -1.25, -1.0, -1.0,
-1.0, -1.0, -1.0, -1.0, -0.75, -0.75, -0.5, -0.5, -0.5, -0.5, -0.25,
-0.25, -0.25, -0.25, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 0.75, 0.75, 0.75, 0.75, 1.0, 1.0, 1.25, 1.25, 1.5, 1.5]
J = [-24, -23, -19, -13, -11, -10, -19, -15, -6, -26, -21, -17, -16, -9,
-8, -15, -14, -26, -13, -9, -7, -27, -25, -11, -6, 1, 4, 8, 11, 0, 1,
5, 6, 10, 14, 16, 0, 4, 9, 17, 7, 18, 3, 15, 5, 18]
n = [-0.39235983861984e6, 0.51526573827270e6, 0.40482443161048e5,
-0.32193790923902e3, 0.96961424218694e2, -0.22867846371773e2,
-0.44942914124357e6, -0.50118336020166e4, 0.35684463560015,
0.44235335848190e5, -0.13673388811708e5, 0.42163260207864e6,
0.22516925837475e5, 0.47442144865646e3, -0.14931130797647e3,
-0.19781126320452e6, -0.23554399470760e5, -0.19070616302076e5,
0.55375669883164e5, 0.38293691437363e4, -0.60391860580567e3,
0.19363102620331e4, 0.42660643698610e4, -0.59780638872718e4,
-0.70401463926862e3, 0.33836784107553e3, 0.20862786635187e2,
0.33834172656196e-1, -0.43124428414893e-4, 0.16653791356412e3,
-0.13986292055898e3, -0.78849547999872, 0.72132411753872e-1,
-0.59754839398283e-2, -0.12141358953904e-4, 0.23227096733871e-6,
-0.10538463566194e2, 0.20718925496502e1, -0.72193155260427e-1,
0.20749887081120e-6, -0.18340657911379e-1, 0.29036272348696e-6,
0.21037527893619, 0.25681239729999e-3, -0.12799002933781e-1,
-0.82198102652018e-5]
Pr = P/1
sigma = s/2
T = 0
for i, j, ni in zip(I, J, n):
T += ni * Pr**i * (sigma-2)**j
return T | python | def _Backward2a_T_Ps(P, s):
"""Backward equation for region 2a, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 25
Examples
--------
>>> _Backward2a_T_Ps(0.1,7.5)
399.517097
>>> _Backward2a_T_Ps(2.5,8)
1039.84917
"""
I = [-1.5, -1.5, -1.5, -1.5, -1.5, -1.5, -1.25, -1.25, -1.25, -1.0, -1.0,
-1.0, -1.0, -1.0, -1.0, -0.75, -0.75, -0.5, -0.5, -0.5, -0.5, -0.25,
-0.25, -0.25, -0.25, 0.25, 0.25, 0.25, 0.25, 0.5, 0.5, 0.5, 0.5, 0.5,
0.5, 0.5, 0.75, 0.75, 0.75, 0.75, 1.0, 1.0, 1.25, 1.25, 1.5, 1.5]
J = [-24, -23, -19, -13, -11, -10, -19, -15, -6, -26, -21, -17, -16, -9,
-8, -15, -14, -26, -13, -9, -7, -27, -25, -11, -6, 1, 4, 8, 11, 0, 1,
5, 6, 10, 14, 16, 0, 4, 9, 17, 7, 18, 3, 15, 5, 18]
n = [-0.39235983861984e6, 0.51526573827270e6, 0.40482443161048e5,
-0.32193790923902e3, 0.96961424218694e2, -0.22867846371773e2,
-0.44942914124357e6, -0.50118336020166e4, 0.35684463560015,
0.44235335848190e5, -0.13673388811708e5, 0.42163260207864e6,
0.22516925837475e5, 0.47442144865646e3, -0.14931130797647e3,
-0.19781126320452e6, -0.23554399470760e5, -0.19070616302076e5,
0.55375669883164e5, 0.38293691437363e4, -0.60391860580567e3,
0.19363102620331e4, 0.42660643698610e4, -0.59780638872718e4,
-0.70401463926862e3, 0.33836784107553e3, 0.20862786635187e2,
0.33834172656196e-1, -0.43124428414893e-4, 0.16653791356412e3,
-0.13986292055898e3, -0.78849547999872, 0.72132411753872e-1,
-0.59754839398283e-2, -0.12141358953904e-4, 0.23227096733871e-6,
-0.10538463566194e2, 0.20718925496502e1, -0.72193155260427e-1,
0.20749887081120e-6, -0.18340657911379e-1, 0.29036272348696e-6,
0.21037527893619, 0.25681239729999e-3, -0.12799002933781e-1,
-0.82198102652018e-5]
Pr = P/1
sigma = s/2
T = 0
for i, j, ni in zip(I, J, n):
T += ni * Pr**i * (sigma-2)**j
return T | Backward equation for region 2a, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 25
Examples
--------
>>> _Backward2a_T_Ps(0.1,7.5)
399.517097
>>> _Backward2a_T_Ps(2.5,8)
1039.84917 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L1379-L1436 |
jjgomera/iapws | iapws/iapws97.py | _Backward2_T_Ps | def _Backward2_T_Ps(P, s):
"""Backward equation for region 2, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
"""
if P <= 4:
T = _Backward2a_T_Ps(P, s)
elif s >= 5.85:
T = _Backward2b_T_Ps(P, s)
else:
T = _Backward2c_T_Ps(P, s)
if P <= 22.064:
Tsat = _TSat_P(P)
T = max(Tsat, T)
return T | python | def _Backward2_T_Ps(P, s):
"""Backward equation for region 2, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
"""
if P <= 4:
T = _Backward2a_T_Ps(P, s)
elif s >= 5.85:
T = _Backward2b_T_Ps(P, s)
else:
T = _Backward2c_T_Ps(P, s)
if P <= 22.064:
Tsat = _TSat_P(P)
T = max(Tsat, T)
return T | Backward equation for region 2, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K] | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L1547-L1572 |
jjgomera/iapws | iapws/iapws97.py | _Backward2_P_hs | def _Backward2_P_hs(h, s):
"""Backward equation for region 2, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
"""
sfbc = 5.85
hamin = _hab_s(s)
if h <= hamin:
P = _Backward2a_P_hs(h, s)
elif s >= sfbc:
P = _Backward2b_P_hs(h, s)
else:
P = _Backward2c_P_hs(h, s)
return P | python | def _Backward2_P_hs(h, s):
"""Backward equation for region 2, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa]
"""
sfbc = 5.85
hamin = _hab_s(s)
if h <= hamin:
P = _Backward2a_P_hs(h, s)
elif s >= sfbc:
P = _Backward2b_P_hs(h, s)
else:
P = _Backward2c_P_hs(h, s)
return P | Backward equation for region 2, P=f(h,s)
Parameters
----------
h : float
Specific enthalpy, [kJ/kg]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
P : float
Pressure, [MPa] | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L1739-L1762 |
jjgomera/iapws | iapws/iapws97.py | _Region3 | def _Region3(rho, T):
"""Basic equation for region 3
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 28
Examples
--------
>>> _Region3(500,650)["P"]
25.5837018
>>> _Region3(500,650)["h"]
1863.43019
>>> p = _Region3(500, 650)
>>> p["h"]-p["P"]*1000*p["v"]
1812.26279
>>> _Region3(200,650)["s"]
4.85438792
>>> _Region3(200,650)["cp"]
44.6579342
>>> _Region3(200,650)["cv"]
4.04118076
>>> _Region3(200,650)["w"]
383.444594
>>> _Region3(500,750)["alfav"]
0.00441515098
>>> _Region3(500,750)["kt"]
0.00806710817
"""
I = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4,
4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11]
J = [0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16,
26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26]
n = [-0.15732845290239e2, 0.20944396974307e2, -0.76867707878716e1,
0.26185947787954e1, -0.28080781148620e1, 0.12053369696517e1,
-0.84566812812502e-2, -0.12654315477714e1, -0.11524407806681e1,
0.88521043984318, -0.64207765181607, 0.38493460186671,
-0.85214708824206, 0.48972281541877e1, -0.30502617256965e1,
0.39420536879154e-1, 0.12558408424308, -0.27999329698710,
0.13899799569460e1, -0.20189915023570e1, -0.82147637173963e-2,
-0.47596035734923, 0.43984074473500e-1, -0.44476435428739,
0.90572070719733, .70522450087967, .10770512626332, -0.32913623258954,
-0.50871062041158, -0.22175400873096e-1, 0.94260751665092e-1,
0.16436278447961, -0.13503372241348e-1, -0.14834345352472e-1,
0.57922953628084e-3, 0.32308904703711e-2, 0.80964802996215e-4,
-0.16557679795037e-3, -0.44923899061815e-4]
d = rho/rhoc
Tr = Tc/T
g = 1.0658070028513*log(d)
gd = 1.0658070028513/d
gdd = -1.0658070028513/d**2
gt = gtt = gdt = 0
for i, j, ni in zip(I, J, n):
g += ni * d**i * Tr**j
gd += ni*i * d**(i-1) * Tr**j
gdd += ni*i*(i-1) * d**(i-2) * Tr**j
gt += ni*j * d**i * Tr**(j-1)
gtt += ni*j*(j-1) * d**i * Tr**(j-2)
gdt += ni*i*j * d**(i-1) * Tr**(j-1)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = d*gd*R*T*rho/1000
propiedades["v"] = 1/rho
propiedades["h"] = R*T*(Tr*gt+d*gd)
propiedades["s"] = R*(Tr*gt-g)
propiedades["cp"] = R*(-Tr**2*gtt+(d*gd-d*Tr*gdt)**2/(2*d*gd+d**2*gdd))
propiedades["cv"] = -R*Tr**2*gtt
propiedades["w"] = sqrt(R*T*1000*(2*d*gd+d**2*gdd-(d*gd-d*Tr*gdt)**2 /
Tr**2/gtt))
propiedades["alfav"] = (gd-Tr*gdt)/(2*gd+d*gdd)/T
propiedades["kt"] = 1/(2*d*gd+d**2*gdd)/rho/R/T*1000
propiedades["region"] = 3
propiedades["x"] = 1
return propiedades | python | def _Region3(rho, T):
"""Basic equation for region 3
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 28
Examples
--------
>>> _Region3(500,650)["P"]
25.5837018
>>> _Region3(500,650)["h"]
1863.43019
>>> p = _Region3(500, 650)
>>> p["h"]-p["P"]*1000*p["v"]
1812.26279
>>> _Region3(200,650)["s"]
4.85438792
>>> _Region3(200,650)["cp"]
44.6579342
>>> _Region3(200,650)["cv"]
4.04118076
>>> _Region3(200,650)["w"]
383.444594
>>> _Region3(500,750)["alfav"]
0.00441515098
>>> _Region3(500,750)["kt"]
0.00806710817
"""
I = [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4,
4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11]
J = [0, 1, 2, 7, 10, 12, 23, 2, 6, 15, 17, 0, 2, 6, 7, 22, 26, 0, 2, 4, 16,
26, 0, 2, 4, 26, 1, 3, 26, 0, 2, 26, 2, 26, 2, 26, 0, 1, 26]
n = [-0.15732845290239e2, 0.20944396974307e2, -0.76867707878716e1,
0.26185947787954e1, -0.28080781148620e1, 0.12053369696517e1,
-0.84566812812502e-2, -0.12654315477714e1, -0.11524407806681e1,
0.88521043984318, -0.64207765181607, 0.38493460186671,
-0.85214708824206, 0.48972281541877e1, -0.30502617256965e1,
0.39420536879154e-1, 0.12558408424308, -0.27999329698710,
0.13899799569460e1, -0.20189915023570e1, -0.82147637173963e-2,
-0.47596035734923, 0.43984074473500e-1, -0.44476435428739,
0.90572070719733, .70522450087967, .10770512626332, -0.32913623258954,
-0.50871062041158, -0.22175400873096e-1, 0.94260751665092e-1,
0.16436278447961, -0.13503372241348e-1, -0.14834345352472e-1,
0.57922953628084e-3, 0.32308904703711e-2, 0.80964802996215e-4,
-0.16557679795037e-3, -0.44923899061815e-4]
d = rho/rhoc
Tr = Tc/T
g = 1.0658070028513*log(d)
gd = 1.0658070028513/d
gdd = -1.0658070028513/d**2
gt = gtt = gdt = 0
for i, j, ni in zip(I, J, n):
g += ni * d**i * Tr**j
gd += ni*i * d**(i-1) * Tr**j
gdd += ni*i*(i-1) * d**(i-2) * Tr**j
gt += ni*j * d**i * Tr**(j-1)
gtt += ni*j*(j-1) * d**i * Tr**(j-2)
gdt += ni*i*j * d**(i-1) * Tr**(j-1)
propiedades = {}
propiedades["T"] = T
propiedades["P"] = d*gd*R*T*rho/1000
propiedades["v"] = 1/rho
propiedades["h"] = R*T*(Tr*gt+d*gd)
propiedades["s"] = R*(Tr*gt-g)
propiedades["cp"] = R*(-Tr**2*gtt+(d*gd-d*Tr*gdt)**2/(2*d*gd+d**2*gdd))
propiedades["cv"] = -R*Tr**2*gtt
propiedades["w"] = sqrt(R*T*1000*(2*d*gd+d**2*gdd-(d*gd-d*Tr*gdt)**2 /
Tr**2/gtt))
propiedades["alfav"] = (gd-Tr*gdt)/(2*gd+d*gdd)/T
propiedades["kt"] = 1/(2*d*gd+d**2*gdd)/rho/R/T*1000
propiedades["region"] = 3
propiedades["x"] = 1
return propiedades | Basic equation for region 3
Parameters
----------
rho : float
Density, [kg/m³]
T : float
Temperature, [K]
Returns
-------
prop : dict
Dict with calculated properties. The available properties are:
* v: Specific volume, [m³/kg]
* h: Specific enthalpy, [kJ/kg]
* s: Specific entropy, [kJ/kgK]
* cp: Specific isobaric heat capacity, [kJ/kgK]
* cv: Specific isocoric heat capacity, [kJ/kgK]
* w: Speed of sound, [m/s]
* alfav: Cubic expansion coefficient, [1/K]
* kt: Isothermal compressibility, [1/MPa]
References
----------
IAPWS, Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam August 2007,
http://www.iapws.org/relguide/IF97-Rev.html, Eq 28
Examples
--------
>>> _Region3(500,650)["P"]
25.5837018
>>> _Region3(500,650)["h"]
1863.43019
>>> p = _Region3(500, 650)
>>> p["h"]-p["P"]*1000*p["v"]
1812.26279
>>> _Region3(200,650)["s"]
4.85438792
>>> _Region3(200,650)["cp"]
44.6579342
>>> _Region3(200,650)["cv"]
4.04118076
>>> _Region3(200,650)["w"]
383.444594
>>> _Region3(500,750)["alfav"]
0.00441515098
>>> _Region3(500,750)["kt"]
0.00806710817 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L1766-L1865 |
jjgomera/iapws | iapws/iapws97.py | _tab_P | def _tab_P(P):
"""Define the boundary between Region 3a-3b, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 2
Examples
--------
>>> _tab_P(40)
693.0341408
"""
I = [0, 1, 2, -1, -2]
n = [0.154793642129415e4, -0.187661219490113e3, 0.213144632222113e2,
-0.191887498864292e4, 0.918419702359447e3]
Pr = P/1
T = 0
for i, ni in zip(I, n):
T += ni * log(Pr)**i
return T | python | def _tab_P(P):
"""Define the boundary between Region 3a-3b, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 2
Examples
--------
>>> _tab_P(40)
693.0341408
"""
I = [0, 1, 2, -1, -2]
n = [0.154793642129415e4, -0.187661219490113e3, 0.213144632222113e2,
-0.191887498864292e4, 0.918419702359447e3]
Pr = P/1
T = 0
for i, ni in zip(I, n):
T += ni * log(Pr)**i
return T | Define the boundary between Region 3a-3b, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 2
Examples
--------
>>> _tab_P(40)
693.0341408 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L1890-L1923 |
jjgomera/iapws | iapws/iapws97.py | _txx_P | def _txx_P(P, xy):
"""Define the boundary between 3x-3y, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
xy: string
Subregions options: cd, gh, ij, jk, mn, qu, rx, uv
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 1
Examples
--------
>>> _txx_P(25,"cd")
649.3659208
>>> _txx_P(23,"gh")
649.8873759
>>> _txx_P(23,"ij")
651.5778091
>>> _txx_P(23,"jk")
655.8338344
>>> _txx_P(22.8,"mn")
649.6054133
>>> _txx_P(22,"qu")
645.6355027
>>> _txx_P(22,"rx")
648.2622754
>>> _txx_P(22.3,"uv")
647.7996121
"""
ng = {
"cd": [0.585276966696349e3, 0.278233532206915e1, -0.127283549295878e-1,
0.159090746562729e-3],
"gh": [-0.249284240900418e5, 0.428143584791546e4, -0.269029173140130e3,
0.751608051114157e1, -0.787105249910383e-1],
"ij": [0.584814781649163e3, -0.616179320924617, 0.260763050899562,
-0.587071076864459e-2, 0.515308185433082e-4],
"jk": [0.617229772068439e3, -0.770600270141675e1, 0.697072596851896,
-0.157391839848015e-1, 0.137897492684194e-3],
"mn": [0.535339483742384e3, 0.761978122720128e1, -0.158365725441648,
0.192871054508108e-2],
"qu": [0.565603648239126e3, 0.529062258221222e1, -0.102020639611016,
0.122240301070145e-2],
"rx": [0.584561202520006e3, -0.102961025163669e1, 0.243293362700452,
-0.294905044740799e-2],
"uv": [0.528199646263062e3, 0.890579602135307e1, -0.222814134903755,
0.286791682263697e-2]}
n = ng[xy]
Pr = P/1
T = 0
for i, ni in enumerate(n):
T += ni * Pr**i
return T | python | def _txx_P(P, xy):
"""Define the boundary between 3x-3y, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
xy: string
Subregions options: cd, gh, ij, jk, mn, qu, rx, uv
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 1
Examples
--------
>>> _txx_P(25,"cd")
649.3659208
>>> _txx_P(23,"gh")
649.8873759
>>> _txx_P(23,"ij")
651.5778091
>>> _txx_P(23,"jk")
655.8338344
>>> _txx_P(22.8,"mn")
649.6054133
>>> _txx_P(22,"qu")
645.6355027
>>> _txx_P(22,"rx")
648.2622754
>>> _txx_P(22.3,"uv")
647.7996121
"""
ng = {
"cd": [0.585276966696349e3, 0.278233532206915e1, -0.127283549295878e-1,
0.159090746562729e-3],
"gh": [-0.249284240900418e5, 0.428143584791546e4, -0.269029173140130e3,
0.751608051114157e1, -0.787105249910383e-1],
"ij": [0.584814781649163e3, -0.616179320924617, 0.260763050899562,
-0.587071076864459e-2, 0.515308185433082e-4],
"jk": [0.617229772068439e3, -0.770600270141675e1, 0.697072596851896,
-0.157391839848015e-1, 0.137897492684194e-3],
"mn": [0.535339483742384e3, 0.761978122720128e1, -0.158365725441648,
0.192871054508108e-2],
"qu": [0.565603648239126e3, 0.529062258221222e1, -0.102020639611016,
0.122240301070145e-2],
"rx": [0.584561202520006e3, -0.102961025163669e1, 0.243293362700452,
-0.294905044740799e-2],
"uv": [0.528199646263062e3, 0.890579602135307e1, -0.222814134903755,
0.286791682263697e-2]}
n = ng[xy]
Pr = P/1
T = 0
for i, ni in enumerate(n):
T += ni * Pr**i
return T | Define the boundary between 3x-3y, T=f(P)
Parameters
----------
P : float
Pressure, [MPa]
xy: string
Subregions options: cd, gh, ij, jk, mn, qu, rx, uv
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for Specific
Volume as a Function of Pressure and Temperature v(p,T) for Region 3 of the
IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water
and Steam, http://www.iapws.org/relguide/Supp-VPT3-2016.pdf, Eq. 1
Examples
--------
>>> _txx_P(25,"cd")
649.3659208
>>> _txx_P(23,"gh")
649.8873759
>>> _txx_P(23,"ij")
651.5778091
>>> _txx_P(23,"jk")
655.8338344
>>> _txx_P(22.8,"mn")
649.6054133
>>> _txx_P(22,"qu")
645.6355027
>>> _txx_P(22,"rx")
648.2622754
>>> _txx_P(22.3,"uv")
647.7996121 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L2026-L2090 |
jjgomera/iapws | iapws/iapws97.py | _Backward3a_v_Ph | def _Backward3a_v_Ph(P, h):
"""Backward equation for region 3a, v=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 4
Returns
-------
v : float
Specific volume, [m³/kg]
Examples
--------
>>> _Backward3a_v_Ph(20,1700)
0.001749903962
>>> _Backward3a_v_Ph(100,2100)
0.001676229776
"""
I = [-12, -12, -12, -12, -10, -10, -10, -8, -8, -6, -6, -6, -4, -4, -3, -2,
-2, -1, -1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, 8]
J = [6, 8, 12, 18, 4, 7, 10, 5, 12, 3, 4, 22, 2, 3, 7, 3, 16, 0, 1, 2, 3,
0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2]
n = [0.529944062966028e-2, -0.170099690234461, 0.111323814312927e2,
-0.217898123145125e4, -0.506061827980875e-3, 0.556495239685324,
-0.943672726094016e1, -0.297856807561527, 0.939353943717186e2,
0.192944939465981e-1, 0.421740664704763, -0.368914126282330e7,
-0.737566847600639e-2, -0.354753242424366, -0.199768169338727e1,
0.115456297059049e1, 0.568366875815960e4, 0.808169540124668e-2,
0.172416341519307, 0.104270175292927e1, -0.297691372792847,
0.560394465163593, 0.275234661176914, -0.148347894866012,
-0.651142513478515e-1, -0.292468715386302e1, 0.664876096952665e-1,
0.352335014263844e1, -0.146340792313332e-1, -0.224503486668184e1,
0.110533464706142e1, -0.408757344495612e-1]
Pr = P/100
nu = h/2100
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (Pr+0.128)**i * (nu-0.727)**j
return 0.0028*suma | python | def _Backward3a_v_Ph(P, h):
"""Backward equation for region 3a, v=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 4
Returns
-------
v : float
Specific volume, [m³/kg]
Examples
--------
>>> _Backward3a_v_Ph(20,1700)
0.001749903962
>>> _Backward3a_v_Ph(100,2100)
0.001676229776
"""
I = [-12, -12, -12, -12, -10, -10, -10, -8, -8, -6, -6, -6, -4, -4, -3, -2,
-2, -1, -1, -1, -1, 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, 8]
J = [6, 8, 12, 18, 4, 7, 10, 5, 12, 3, 4, 22, 2, 3, 7, 3, 16, 0, 1, 2, 3,
0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2]
n = [0.529944062966028e-2, -0.170099690234461, 0.111323814312927e2,
-0.217898123145125e4, -0.506061827980875e-3, 0.556495239685324,
-0.943672726094016e1, -0.297856807561527, 0.939353943717186e2,
0.192944939465981e-1, 0.421740664704763, -0.368914126282330e7,
-0.737566847600639e-2, -0.354753242424366, -0.199768169338727e1,
0.115456297059049e1, 0.568366875815960e4, 0.808169540124668e-2,
0.172416341519307, 0.104270175292927e1, -0.297691372792847,
0.560394465163593, 0.275234661176914, -0.148347894866012,
-0.651142513478515e-1, -0.292468715386302e1, 0.664876096952665e-1,
0.352335014263844e1, -0.146340792313332e-1, -0.224503486668184e1,
0.110533464706142e1, -0.408757344495612e-1]
Pr = P/100
nu = h/2100
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (Pr+0.128)**i * (nu-0.727)**j
return 0.0028*suma | Backward equation for region 3a, v=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 4
Returns
-------
v : float
Specific volume, [m³/kg]
Examples
--------
>>> _Backward3a_v_Ph(20,1700)
0.001749903962
>>> _Backward3a_v_Ph(100,2100)
0.001676229776 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L2093-L2143 |
jjgomera/iapws | iapws/iapws97.py | _Backward3_v_Ph | def _Backward3_v_Ph(P, h):
"""Backward equation for region 3, v=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
v : float
Specific volume, [m³/kg]
"""
hf = _h_3ab(P)
if h <= hf:
return _Backward3a_v_Ph(P, h)
else:
return _Backward3b_v_Ph(P, h) | python | def _Backward3_v_Ph(P, h):
"""Backward equation for region 3, v=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
v : float
Specific volume, [m³/kg]
"""
hf = _h_3ab(P)
if h <= hf:
return _Backward3a_v_Ph(P, h)
else:
return _Backward3b_v_Ph(P, h) | Backward equation for region 3, v=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
v : float
Specific volume, [m³/kg] | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L2198-L2217 |
jjgomera/iapws | iapws/iapws97.py | _Backward3a_T_Ph | def _Backward3a_T_Ph(P, h):
"""Backward equation for region 3a, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 2
Examples
--------
>>> _Backward3a_T_Ph(20,1700)
629.3083892
>>> _Backward3a_T_Ph(100,2100)
733.6163014
"""
I = [-12, -12, -12, -12, -12, -12, -12, -12, -10, -10, -10, -8, -8, -8, -8,
-5, -3, -2, -2, -2, -1, -1, 0, 0, 1, 3, 3, 4, 4, 10, 12]
J = [0, 1, 2, 6, 14, 16, 20, 22, 1, 5, 12, 0, 2, 4, 10, 2, 0, 1, 3, 4, 0,
2, 0, 1, 1, 0, 1, 0, 3, 4, 5]
n = [-0.133645667811215e-6, 0.455912656802978e-5, -0.146294640700979e-4,
0.639341312970080e-2, 0.372783927268847e3, -0.718654377460447e4,
0.573494752103400e6, -0.267569329111439e7, -0.334066283302614e-4,
-0.245479214069597e-1, 0.478087847764996e2, 0.764664131818904e-5,
0.128350627676972e-2, 0.171219081377331e-1, -0.851007304583213e1,
-0.136513461629781e-1, -0.384460997596657e-5, 0.337423807911655e-2,
-0.551624873066791, 0.729202277107470, -0.992522757376041e-2,
-.119308831407288, .793929190615421, .454270731799386,
.20999859125991, -0.642109823904738e-2, -0.235155868604540e-1,
0.252233108341612e-2, -0.764885133368119e-2, 0.136176427574291e-1,
-0.133027883575669e-1]
Pr = P/100.
nu = h/2300.
suma = 0
for i, j, n in zip(I, J, n):
suma += n*(Pr+0.240)**i*(nu-0.615)**j
return 760*suma | python | def _Backward3a_T_Ph(P, h):
"""Backward equation for region 3a, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 2
Examples
--------
>>> _Backward3a_T_Ph(20,1700)
629.3083892
>>> _Backward3a_T_Ph(100,2100)
733.6163014
"""
I = [-12, -12, -12, -12, -12, -12, -12, -12, -10, -10, -10, -8, -8, -8, -8,
-5, -3, -2, -2, -2, -1, -1, 0, 0, 1, 3, 3, 4, 4, 10, 12]
J = [0, 1, 2, 6, 14, 16, 20, 22, 1, 5, 12, 0, 2, 4, 10, 2, 0, 1, 3, 4, 0,
2, 0, 1, 1, 0, 1, 0, 3, 4, 5]
n = [-0.133645667811215e-6, 0.455912656802978e-5, -0.146294640700979e-4,
0.639341312970080e-2, 0.372783927268847e3, -0.718654377460447e4,
0.573494752103400e6, -0.267569329111439e7, -0.334066283302614e-4,
-0.245479214069597e-1, 0.478087847764996e2, 0.764664131818904e-5,
0.128350627676972e-2, 0.171219081377331e-1, -0.851007304583213e1,
-0.136513461629781e-1, -0.384460997596657e-5, 0.337423807911655e-2,
-0.551624873066791, 0.729202277107470, -0.992522757376041e-2,
-.119308831407288, .793929190615421, .454270731799386,
.20999859125991, -0.642109823904738e-2, -0.235155868604540e-1,
0.252233108341612e-2, -0.764885133368119e-2, 0.136176427574291e-1,
-0.133027883575669e-1]
Pr = P/100.
nu = h/2300.
suma = 0
for i, j, n in zip(I, J, n):
suma += n*(Pr+0.240)**i*(nu-0.615)**j
return 760*suma | Backward equation for region 3a, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 2
Examples
--------
>>> _Backward3a_T_Ph(20,1700)
629.3083892
>>> _Backward3a_T_Ph(100,2100)
733.6163014 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L2220-L2270 |
jjgomera/iapws | iapws/iapws97.py | _Backward3_T_Ph | def _Backward3_T_Ph(P, h):
"""Backward equation for region 3, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
"""
hf = _h_3ab(P)
if h <= hf:
T = _Backward3a_T_Ph(P, h)
else:
T = _Backward3b_T_Ph(P, h)
return T | python | def _Backward3_T_Ph(P, h):
"""Backward equation for region 3, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K]
"""
hf = _h_3ab(P)
if h <= hf:
T = _Backward3a_T_Ph(P, h)
else:
T = _Backward3b_T_Ph(P, h)
return T | Backward equation for region 3, T=f(P,h)
Parameters
----------
P : float
Pressure, [MPa]
h : float
Specific enthalpy, [kJ/kg]
Returns
-------
T : float
Temperature, [K] | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L2326-L2346 |
jjgomera/iapws | iapws/iapws97.py | _Backward3_v_Ps | def _Backward3_v_Ps(P, s):
"""Backward equation for region 3, v=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
v : float
Specific volume, [m³/kg]
"""
if s <= sc:
return _Backward3a_v_Ps(P, s)
else:
return _Backward3b_v_Ps(P, s) | python | def _Backward3_v_Ps(P, s):
"""Backward equation for region 3, v=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
v : float
Specific volume, [m³/kg]
"""
if s <= sc:
return _Backward3a_v_Ps(P, s)
else:
return _Backward3b_v_Ps(P, s) | Backward equation for region 3, v=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
v : float
Specific volume, [m³/kg] | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L2454-L2472 |
jjgomera/iapws | iapws/iapws97.py | _Backward3a_T_Ps | def _Backward3a_T_Ps(P, s):
"""Backward equation for region 3a, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 6
Examples
--------
>>> _Backward3a_T_Ps(20,3.8)
628.2959869
>>> _Backward3a_T_Ps(100,4)
705.6880237
"""
I = [-12, -12, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5,
-4, -4, -4, -2, -2, -1, -1, 0, 0, 0, 1, 2, 2, 3, 8, 8, 10]
J = [28, 32, 4, 10, 12, 14, 5, 7, 8, 28, 2, 6, 32, 0, 14, 32, 6, 10, 36, 1,
4, 1, 6, 0, 1, 4, 0, 0, 3, 2, 0, 1, 2]
n = [0.150042008263875e10, -0.159397258480424e12, 0.502181140217975e-3,
-0.672057767855466e2, 0.145058545404456e4, -0.823889534888890e4,
-0.154852214233853, 0.112305046746695e2, -0.297000213482822e2,
0.438565132635495e11, 0.137837838635464e-2, -0.297478527157462e1,
0.971777947349413e13, -0.571527767052398e-4, 0.288307949778420e5,
-0.744428289262703e14, 0.128017324848921e2, -0.368275545889071e3,
0.664768904779177e16, 0.449359251958880e-1, -0.422897836099655e1,
-0.240614376434179, -0.474341365254924e1, 0.724093999126110,
0.923874349695897, 0.399043655281015e1, 0.384066651868009e-1,
-0.359344365571848e-2, -0.735196448821653, 0.188367048396131,
0.141064266818704e-3, -0.257418501496337e-2, 0.123220024851555e-2]
Pr = P/100
sigma = s/4.4
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (Pr+0.240)**i * (sigma-0.703)**j
return 760*suma | python | def _Backward3a_T_Ps(P, s):
"""Backward equation for region 3a, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 6
Examples
--------
>>> _Backward3a_T_Ps(20,3.8)
628.2959869
>>> _Backward3a_T_Ps(100,4)
705.6880237
"""
I = [-12, -12, -10, -10, -10, -10, -8, -8, -8, -8, -6, -6, -6, -5, -5, -5,
-4, -4, -4, -2, -2, -1, -1, 0, 0, 0, 1, 2, 2, 3, 8, 8, 10]
J = [28, 32, 4, 10, 12, 14, 5, 7, 8, 28, 2, 6, 32, 0, 14, 32, 6, 10, 36, 1,
4, 1, 6, 0, 1, 4, 0, 0, 3, 2, 0, 1, 2]
n = [0.150042008263875e10, -0.159397258480424e12, 0.502181140217975e-3,
-0.672057767855466e2, 0.145058545404456e4, -0.823889534888890e4,
-0.154852214233853, 0.112305046746695e2, -0.297000213482822e2,
0.438565132635495e11, 0.137837838635464e-2, -0.297478527157462e1,
0.971777947349413e13, -0.571527767052398e-4, 0.288307949778420e5,
-0.744428289262703e14, 0.128017324848921e2, -0.368275545889071e3,
0.664768904779177e16, 0.449359251958880e-1, -0.422897836099655e1,
-0.240614376434179, -0.474341365254924e1, 0.724093999126110,
0.923874349695897, 0.399043655281015e1, 0.384066651868009e-1,
-0.359344365571848e-2, -0.735196448821653, 0.188367048396131,
0.141064266818704e-3, -0.257418501496337e-2, 0.123220024851555e-2]
Pr = P/100
sigma = s/4.4
suma = 0
for i, j, ni in zip(I, J, n):
suma += ni * (Pr+0.240)**i * (sigma-0.703)**j
return 760*suma | Backward equation for region 3a, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
References
----------
IAPWS, Revised Supplementary Release on Backward Equations for the
Functions T(p,h), v(p,h) and T(p,s), v(p,s) for Region 3 of the IAPWS
Industrial Formulation 1997 for the Thermodynamic Properties of Water and
Steam, http://www.iapws.org/relguide/Supp-Tv%28ph,ps%293-2014.pdf, Eq 6
Examples
--------
>>> _Backward3a_T_Ps(20,3.8)
628.2959869
>>> _Backward3a_T_Ps(100,4)
705.6880237 | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L2475-L2525 |
jjgomera/iapws | iapws/iapws97.py | _Backward3_T_Ps | def _Backward3_T_Ps(P, s):
"""Backward equation for region 3, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
"""
sc = 4.41202148223476
if s <= sc:
T = _Backward3a_T_Ps(P, s)
else:
T = _Backward3b_T_Ps(P, s)
return T | python | def _Backward3_T_Ps(P, s):
"""Backward equation for region 3, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K]
"""
sc = 4.41202148223476
if s <= sc:
T = _Backward3a_T_Ps(P, s)
else:
T = _Backward3b_T_Ps(P, s)
return T | Backward equation for region 3, T=f(P,s)
Parameters
----------
P : float
Pressure, [MPa]
s : float
Specific entropy, [kJ/kgK]
Returns
-------
T : float
Temperature, [K] | https://github.com/jjgomera/iapws/blob/1e5812aab38212fb8a63736f61cdcfa427d223b1/iapws/iapws97.py#L2580-L2600 |
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