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5.1 12cm Diameter Quartz Reactor Model Setup
Researchers have been developing a combustion model of the quartz flow reactor as
shown in Figure 5.1 (Strebinger, et al., 2018). The model has a domain height of 12cm, which is
the inner diameter of the quartz flow reactor, and length of 1.5m. In order to accurately model
methane-air deflagration physics, researchers are using the following settings in ANSYS Fluent
(v17.2):
• 2D planar assumption for all 2D models
• Pressure-Based Solver
• Energy Equation
• Viscous Standard k-ω Turbulence Model
o Low Re Corrections
o Shear Flow Corrections
• Species Transport
o Volumetric Reactions
o Stiff Chemistry Solver
o Finite Rate Chemistry
▪ Density solved using ideal gas theory
▪ Diffusion solved using kinetic theory
▪ Metghalchi and Keck laminar flame speed theory
• Spark Ignition Model
• PISO pressure-velocity coupling
• CEI: 2 levels of mesh adaption on the gradient of temperature every 2-10 time steps
• 2D Model: Residuals set to 10-6, dropping at least 3 orders or magnitude
• 3D Model: Continuity and species residuals were set to 10-3, still dropping 3 orders of
magnitude. All other residuals are set to 10-6
• Second order in time and space
• Time step = 0.1ms for open-end ignition, 0.01ms for closed-end ignition
• Boundary Conditions:
o Closed End Wall – aluminum, no slip, adiabatic
o Tube Walls – quartz, no slip, adiabatic
o Outlets – 0 gauge pressure outlets
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o Obstacles– no slip, adiabatic, assuming no heat transfer into the material
Figure 5.1 CFD geometry of 12cm inner diameter quartz flow reactor and seeded lines at
different vertical, y, positions used to find the flame front. Model height = 12cm, length = 1.5m.
The compressible flow model is being used to capture the large density changes during
combustion and the compression of the unburned and burned gas mixture upstream and
downstream, respectively. The viscous-standard k-ω model is used because compared to other
turbulence models, the k-ω model better predicts lower Reynolds number flows and flow
separation, which often occurs when a flame passes over an obstacle; this assumption will be
revisited in later sections of this manuscript. The transient time solver is a second order implicit
time solver and the governing equations are solved using the PISO pressure-velocity coupling
solver. The species transport model is used instead of the premixed combustion models because
it allows for more control over mixture stoichiometry as well as the number of chemical
reactions. The inlet and outlet boundary conditions are modeled as zero gauge pressure outlets to
simulate ambient conditions in the laboratory and all solid boundaries are modeled as walls
assuming no slip and adiabatic conditions. The obstacles are also modeled with a no slip
boundary condition and adiabatic. Adiabatic conditions are assumed for the walls and obstacles
because the flame is in contact with the walls of the tube for a very short time such that there is
minimum heat transfer by conduction and convection. Radiation may play a role in flame
enhancement and may need to be investigated in the future, however, Fig performed a
preliminary investigation of including a radiation model, but found the error associated with the
models is larger than not including radiation (Fig, 2019). Finally, the finite rate chemistry model
is used in lieu of the turbulent chemistry interaction models, however, as will be shown in this
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research, this will need to be revisited for highly turbulent flow interaction with obstacles as well
as the inclusion of more detailed chemistry.
Although previous research has shown that using a methane-air 2-step mechanism is not
as accurate as solving the chemistry fully (Fig, 2019), it allows for faster simulation times which
is important since these models typically run for a week or more. The first reaction of the 2-step
mechanism is the reaction of methane and oxygen to form H 0 and intermediate species, CO:
2
(5.1)
The second reaction is forwards and backwards and is the reaction of CO and oxygen to form
CO :
2
(5.2)
Table 5.1 Table showing the ANSYS Fluent 2-step methane-air chemical mechanism settings.
Reaction 1 and 2 from (Dryer & Glassman, 1973). R stands for reactant and P stands for product.
Pre- Activation
Reaction Stoichiometric Temperature
Molecule Path Exponential Energy
Number Coefficient Exponent (K)
Factor (J/kg-mol)
1 CH 1 R 5.012x1011 2x108 0
4
1 O 1.5 R
2
1 CO 1 P
1 H 0 2 P
2
2 CO 1 R 2.239x1012 1.7x108 0
2 O 0.5 R
2
2 CO 1 P
2
2 H 0 0 P
2
3 CO 1 R 5x108 1.7x108 0
2
3 CO 1 P
3 O 0.5 P
2
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This research has explored two major ways of modeling the spark, referred to as the
electrode model (EM) (Fig, Bogin, Brune, & Grubb, 2016; Fig, Bogin, Brune, & Grubb, 2017;
Fig M. , 2019) and the spark model (SM) (Strebinger, Bogin, & Brune, 2019). The EM model
uses an aluminum circle with a diameter of 1mm to represent the electrodes from the spark
system. At time, t=0s, the aluminum wall has a heat flux boundary that produces 2.5x106 W/m2
of energy to the surroundings. After 25ms of simulation time, the heat flux boundary is set to 0
W/m2, assuming adiabatic. This produces approximately 5mJ of energy which is enough to ignite
methane-air mixtures at the lean and rich limits.
The SM model using the ANSYS Spark Model (v17.2) and the following settings shown
in Table 5.2. Although, Table 5.2 shows the total ignition energy as 60mJ which is different than
the 5mJ used in the EM, this difference will be explored in Section 5.1.2.
Table 5.2 Table showing the ANSYS Fluent spark model (SM) settings.
Start Time (s) 0
Duration (s) 0.001
Initial Spark Radius (m) 0.005
Ignition Energy (J) 0.06
Kernel Expansion Model Laminar
5.1.1 2D Mesh Independence Study
Using these model settings, the first step of the modeling process is to determine mesh
independence for an open-end ignition event. The spark was located at 11cm from the open end
of the reactor. The ANSYS meshing client was used to develop the mesh for this model. The
fluid body was meshed using quadrilaterals as shown in Figure 5.5. To compare the results of
each body mesh size, researchers sampled five horizontal lines along the y-axis spanning the
reactor as shown in Figure 5.1. Data was extracted from each line at different time steps and
compared to one another to confirm the actual flame front; additionally, manually, researchers
confirmed this was the actual flame front by comparing axial values to temperature and methane
concentration contours. To determine the best method of finding the flame front, researchers
compared defining the flame front as the maximum kinetic rate of reaction 1, the maximum total
temperature at the gradient of the main flame brush, and different values of mass fraction of
methane. All methods used were comparable and the difference error in determining the flame
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front amongst methods was less than 1%. This was also compared to finding the maximum total
temperature and the error between these methods is less than 1%. Thus, due to ease and
comparability with Matt Fig’s work, researchers are determining the flame front by values of
temperature along the gradient of the flame front (Fig, 2019).
Results from the mesh independence study (Figure 5.2) show that a mesh size of 1mm is
sufficient grid resolution to resolve the flame front. The error between the 1mm and 0.5mm mesh
was 1% as shown in Figure 5.2. Results also show that a mesh size of 1mm takes 9.5days to run
versus a 0.5mm mesh which takes over 20 days to complete as shown in Figure 5.3; note that the
first 3-4 days is spent on flame development in the first 25cm from kernel initiation. Thus, all 2D
models use a base mesh sizing of at least 1mm unless otherwise noted in this manuscript.
Figure 5.2 Mesh independence study for the 2D, 12cm diameter quartz flow reactor. Mesh
independence was achieved with a mesh size of 1mm and the average percent relative error of
flame front location based on maximum temperature of 1%. Error bars represent the standard
deviation of the relative error between mesh sizes.
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Figure 5.3 Mesh size versus simulated time for the 2D, 12cm diameter quartz reactor model.
Mesh independence is reached with a body mesh size of 1mm, taking approximately 9.5days to
complete on an 8 core compute, 3.06GHz, 24GB RAM.
After determining the mesh size, researchers investigated the effects of including wall
inflation or wall edge sizing since resolving the boundary layer is important for modeling
methane flame deflagrations in cylindrical reactors. Results from Table 5.3 show that adding
edge sizing or wall inflation greatly affects the simulation. A uniform 1mm body mesh without
any edge sizing or wall inflation does not accurately resolve the boundary layers as shown in
Figure 5.4. Because of this the flame for the base case, 1mm body mesh, does not flip over until
after 1s simulation time. However, in experiments it is observed that the flame turns over in the
first 50ms before traveling halfway down the quartz reactor. Thus, from this study it was
determined that resolving the boundary layer is of utmost importance and a 0.25mm edge sizing
was used. Both edge sizing and inflation layer methods were tested and results are shown in
Table 5.3 and Figure 5.4. As can be seen in these results, the edge sizing method and inflation
layer methods help to better resolve the impact of the boundary layer in the turn-over of the
flame. However, looking ahead to future modeling of obstacles inside the reactor, using an edge
sizing can more easily be applied to meshing around irregular-shaped obstacles. Thus, the edge
sizing was used over the inflation layers due to ease of meshing when obstacles are present in the
reactor.
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Table 5.3 Average percent error in flame front location between the 1mm body mesh with no
wall sizing compared to adding edge sizing or wall inflation layers for the 2D, 12cm diameter
quartz reactor model.
0.25mm Edge 40 layers, Single 80 layers, Single
Sizing layer height = layer height =
0.5mm 0.5mm
Average Error (%) 17 24 25
Figure 5.4 Temperature contours of 2D, 12cm diameter quartz reactor model comparing the
impact of number of wall inflation layers on methane flame propagation. Simulation time=1.0s.
Time step = 0.1ms. Ignition location is 11cm from the open end (left). Mesh cell size = 1mm,
0.5mm inflation cells, varying number of inflation layers. CH =9.5%. Temperature = 293K,
4
Pressure = 82kPa. One relief hole.
An image of the 1mm body mesh with 0.25mm edge sizing is shown in Figure 5.5. As
can be seen in this mesh, the mesh is unstructured and consists of both quadrilaterals and
triangles. Mesh statistics are summarized in Table 5.4 and show a total cell count of
approximately 250,000 cells. The orthogonality quality is close to 1 and skewness is close to 0
which means that flow quantities are transferred from one cell to the next well from one cell face
to another. Also the aspect ratio is close to 1 which means the cells are not too stretched.
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Altogether, these mesh statistics show a good quality mesh has been obtained. The same mesh
was used for open-end ignition and closed-end ignition.
Figure 5.5 Image of the 2D, 12cm diameter reactor mesh with a quadrilateral dominant 1mm
body mesh and 0.25mm edge sizing on the tube walls.
Table 5.4 2D, 12cm diameter reactor mesh statistics: number of elements, number of nodes,
average orthogonality quality, average skewness, and average aspect ratio. Body mesh = 1mm.
Edge sizing = 0.25mm.
Average
Number of Number of Average Average Aspect
Orthogonality
Elements Nodes Skewness Ratio
Quality
254,148 258,367 0.99 ± 0.03 0.08 ± 0.1 1.2 ± 0.2
5.1.2 3D Mesh Independence Study
Finally, a mesh independence study was undertaken for the 3D model of the 12cm
diameter quartz reactor for a closed-end ignition using a base mesh of 8mm, 4mm, and 2mm
with no edge sizing. An example of the mesh is shown in Figure 5.6 and mesh statistics for all
meshes are summarized in
Table 5.5. As can be seen, the mesh is a structured mesh and mesh statistics show low
skewness and high aspect ratios. The high aspect ratios are mainly due to the cells at the tube
walls, which is to be expected when using a structured mesh on a cylindrical body. Edge sizing
may be used to help resolve the high aspect ratios, however, no edge sizing was used in order to
improve the quality of the cells inside the 3D domain. Instead of specifying an edge sizing, mesh
adaption was used. Previous work by M.K. Fig, 2019 investigated the best variable to adapt on to
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better resolve the flame front (Fig M. , 2019). Results of Fig’s study showed that adapting on the
temperature gradient helped to best resolve the flame front, using at least 2-3 levels of adaption.
Therefore, this research also uses grid adaption on the gradient of temperature using 3 levels,
every 2 time steps. This helped to resolve the flame front and flame propagation, but as will be
discussed, there was some error at the tube wall boundaries.
Figure 5.6 Image of a 3D, 12cm diameter reactor mesh with a quadrilateral dominant 4mm, cut
cell body mesh.
Table 5.5: 3D, 12cm diameter reactor mesh statistics for an 8mm, 4mm, and 2mm body mesh:
number of elements, number of nodes, minimum orthogonality quality, maximum skewness, and
maximum aspect ratio. No edge sizing.
Minimum
Number of Number of Maximum Maximum
Orthogonality
Elements Nodes Skewness Aspect Ratio
Quality
8mm body mesh 26,240 28,497 0.4 0.4 7.1
4mm body mesh 194,560 201,909 0.5 0.2 5.1
2mm body mesh 1,520,640 1,554,425 0.4 0.4 6.4
Results of the mesh independence study are tabulated in Table 5.6 and shown in Figure
5.7 and Figure 5.8. Results show that a base mesh of 8mm is inadequate in capturing the flame
front location compared to the 4mm or 2mm mesh. The average percent error between the 8mm
and 4mm mesh was 25%, reducing to below 5% for the 4mm and 2mm mesh. To investigate this
further, researchers made an estimation of the size of the boundary layer using turbulent fluid
flow estimates. The mixture was approximated as air at standard temperature and pressure,
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101kPa and 300K; the density was 1.2kg/m3, dynamic viscosity of 1.72x10-5 Pa-s, and a velocity
range of 25-60m/s was used. The results of calculating the Reynold’s number based on the axial
location indicate a turbulent regime (Re = 440,000 to 6,800,000). The boundary layer thickness
x
was calculated based on turbulent boundary layer theory and approximated using the following
equation:
(5.3)
From this equation a range of boundary layer thicknesses, δ, dependent on the x location were
calculated to be 7-24mm. Based on the results shown, it makes sense that the 8mm body mesh
performed poorly at earlier times compared to the 4mm and 2mm since the 8mm cell can be
larger than the boundary at certain locations. Therefore, based on flame front location and
boundary layer thickness, the 4mm and 2mm body meshes are more accurate than the 8mm.
Table 5.6 Table showing the percent error of the 3D, 12cm diameter quartz reactor model for
different mesh sizes (8mm and 4mm, 4mm and 2mm). Time step = 0.01ms. Ignition location is
1.39m from the open end. CH =9.5%. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ.
4 ign
No relief hole.
Time (s) Percent Error Percent Error
8mm : 4mm (%) 4mm : 2mm (%)
0.004 52 4.3
0.006 47 3.9
0.008 38 4.3
0.010 17 1.9
0.012 4.2 2.6
0.014 7.6 4.1
0.015 - 5.1
Average = 25±10% 4±0.4%
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As discussed, evaluating the mesh based on the flame front location shows that a 4mm
and 2mm body mesh sizing are adequate to resolve the boundary layers and the calculated error
between the flame front locations are within 5%. However, the relative error of the flame front
location was based on the axial movement of the flame and not all the flow quantities. Therefore,
a study was performed investigating the percent difference in total temperature and flow velocity
comparing the 4mm and 2mm body meshes for the 3D, 12cm diameter reactor model. To do this,
five (5) XY planes were made 0.25m apart at z = 0.25, 0.5, 0.75, 1.0, 1.25m with a seeded line
extending in the x direction as shown in Figure 5.9. Results of the flames propagating are shown
in Figure 5.10, Figure 5.11, Figure 5.12, and Figure 5.13. As shown in these figures, there is little
difference in the shape and propagation of the flame. However, extracting data from the seeded
lines shows that there are differences in the total temperature and the fluid velocity magnitude as
shown in Figure 5.14 through Figure 5.21. As can be seen, the difference in the total
temperatures between the 4mm mesh and 2mm mesh are small. Although this is for a single time
step, other time steps have been evaluated and the average percent difference across time steps is
less than 5% and is mainly accumulated at the flow boundaries. This is not of surprise since the
2mm mesh has more cells in the boundary than the 4mm mesh, which allows the 2mm mesh to
more accurately solve boundary effects. Evaluation of the flow velocities shows a much larger
difference in predicted velocities between the 4mm mesh and 2mm mesh and the average percent
difference across time steps is less than 13%. Note that in all these simulations mesh adaption on
the gradient of temperature is employed every 2 time steps, 3 levels. Since the grid adaption is on
the gradient of temperature, the percent difference of total temperature values between the 4mm
and 2mm meshes are within 5%. However, because the adaption is on the gradient of
temperature the flow velocities are not fully resolved using the 4mm mesh. Therefore researchers
suggest using the 2mm mesh for more accurate predictions of flow velocities and turbulent
quantities. If simulation time is of the utmost importance, a 4mm mesh can be used, but will
provide less accurate predictions of the local flow and turbulence.
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5.1.3 Modeling the Spark
As previously discussed, two main methods of initiating combustion in the combustion
models have been investigated: the EM uses a constant heat flux from a small disc and the SM
uses the improved ANSYS Fluent Spark Model (v17.2). In order to compare these two methods
of initiating combustion, a 2D model of the 12cm diameter reactor was setup and all parameters,
meshes, were the exact same; researchers only changed the method of initiating combustion, EM
versus SM. As shown in Figure 5.22 and Figure 5.23, both the EM and SM were able to capture
the eventual flip over of the open-end ignition flame. However, both models predicted this flame
turn over much later in the combustion process; this discrepancy is likely due to the fact that
accurately modeling buoyancy is a difficult problem. This difference is also captured in the
prediction of flame front propagation velocity as a function of distance. Figure 5.23 shows that
the SM predicts a slightly faster flame than the EM, but both models predict the turnover too
slowly resulting in a decreasing flame front propagation velocity instead of increasing as shown
by the experimental results.
Figure 5.22 Temperature contours of 2D, 12cm diameter quartz reactor model comparing the
impact of methods modeling the spark electrodes. Simulation time=0.9s. Time step = 0.1ms.
Ignition location is 11cm from the open end (left). Mesh cell size = 1mm, 0.25mm edge sizing.
CH =9.5%. Temperature = 293K, Pressure = 82kPa. One relief hole H=1.2cm.
4
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Figure 5.23 Comparison of flame front propagation velocity results from experiments to the 2D,
12cm diameter quartz reactor model using the spark model and electrode model. Time step =
0.1ms. Ignition location is 11cm from the open end (left). Mesh cell size = 1mm, 0.25mm edge
sizing. CH =9.5%. Temperature = 293K, Pressure = 82kPa. One relief hole H=1.2cm.
4
Another important factor to consider in both of these methods is the amount of total
simulation time as indicated on Figure 5.22. The SM takes 4 days to reach t = 0.9s versus the EM
which takes 6 days to reach t = 0.9s. Further exploration into this difference has shown that the
initial kernel expansion in the EM takes 3 days to simulate. This is important because for a
confined ignition the time scales are much shorter, requiring a time step of 0.01ms to solve in a
reasonable amount of time. For example, Figure 5.24 and Figure 5.25 show results of a confined,
closed-end ignition (ignition 11cm from the closed end of the reactor). The geometry shown in
these figures was cut in half to 0.75m instead of the full 1.5m. The base mesh was 1mm and the
edge sizing on the walls was 0.25mm. Combustion was initiated using the EM and to simulate
36ms of flame propagation took over 21 days on an 8 core compute, 3.06GHz, 24GB RAM,
compared to the SM which takes only 2-3 days to model the full 12cm diameter, 1.5m long
reactor with the same mesh. Although the flame front propagation velocity results match the
experiments within 5%, the large simulation times required of using the EM are infeasible for
this modeling combustion in the large and full-scale models. In comparison, the SM matches the
maximum flame front propagation velocity within 12% and matches the flame acceleration as
will be discussed in Chapter 6.
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Figure 5.24 Temperature contours of 2D, 12cm diameter quartz reactor model for a closed-end
ignition using the electrode model. Domain length = 0.75m. Simulation time=36ms. Time step =
0.01ms. Ignition location is 11cm from the closed end (left). Mesh cell size = 1mm, 0.25mm
edge sizing. CH =9.5%. Temperature = 293K, Pressure = 82kPa. One relief hole.
4
Figure 5.25 Comparison of flame front propagation velocity results from experiments to the 2D,
12cm diameter quartz reactor model using the electrode model. Domain length = 0.75m. Time
step = 0.01ms. Ignition location is 11cm from the closed end. Mesh cell size = 1mm, 0.25mm
edge sizing. CH =9.5%. Temperature = 293K, Pressure = 82kPa. EM E = 5mJ. One relief hole.
4 ign
Therefore, due to the large simulations times required by using the EM that would be
required for full-scale longwall model explosion modeling it was decided to investigate using the
t using the ANSYS Fluent Spark Model (SM). A sensitivity analysis was performed to determine
which parameters of the ANSYS Fluent Spark Model is the flame most sensitive to: duration,
initial kernel diameter, spark energy, or flame speed model. It was found that the model was
sensitive to the initial kernel diameter and the amount of spark energy.
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Ignition energies were tested between 5mJ and 1J and modeling results with the
improved SM show no significant differences (<2%) between these energies as shown in Figure
5.26 , Figure 5.27, and Table 5.7. In 2014, Zipf, et al. (2013) performed experiments in a large
1.05m diameter, 73m long flame reactor investigating the detonability of natural gas-air mixtures
and found transition to detonation and detonations for some experiments. In their experimental
setup, the ignition source was an electric match that produced multiple sparks with a total energy
of 2kJ. Therefore, researchers investigated the possibility of 1kJ of energy transfer to determine
whether or not this large amount of energy impacts methane flame acceleration – results are
shown in Figure 5.28 and Table 5.7. As can be seen, the 1kJ of energy shows differences in
predicted methane flame speeds and flame shapes compared to 1J (6.8% difference); whether
this amount of energy is realistic in a methane gas explosion accident is under investigation. This
amount of energy could be the result of a possible lightning strike or an explosive, but in most
methane gas explosion cases the ignition source is a result of machine friction, hot streaks, or
rock friction, which all have lower energies than 1kJ.
Figure 5.26 Temperature contours of 2D, 12cm diameter quartz reactor model comparing the
impact of ignition energy of the SM on flame propagation. Simulation time=10ms. Time step =
0.01ms. Ignition location is 1.39cm from the open end. Mesh cell size = 1mm, 0.25mm edge
sizing. CH =9.5%. Temperature = 293K, Pressure = 82kPa. E = 5mJ,120mJ,480mJ, and
4 ign
1000mJ. One relief hole.
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Table 5.7 Table showing the average percent difference and standard deviation between different
ignition energies in the 2D, 12cm diameter quartz reactor model for a closed-end ignition. Time
step = 0.01ms. Ignition location is 1.39m from the open end. CH =9.5%. Temperature = 293K,
4
Pressure = 82kPa. SM E = 60mJ. One relief hole.
ign
Percent Difference (%)
60mJ : 120mJ :
5mJ : 60mJ 480mJ : 1J 1J : 1kJ
120mJ 480mJ
Average 0.06% 0.06% 0.17% 0.78% 6.8%
Standard
0.12% 0.12% 0.19% 0.45% 3.9%
Deviation
Maximum 0.48% 0.48% 0.64% 1.8% 11%
In the experiments, the distance between the spark electrodes was measured to be
between 5-10mm, which corresponds to the 5mm and 2.5mm spark radius settings. Initial spark
radii of 5mm, 2.5mm, and 1.5mm were tested using the SM for a confined, closed-end ignition
as shown in Figure 5.29 and Figure 5.30. Results show that the model is highly sensitive to the
initial spark kernel radius and the difference in flame front results continue to grow as a function
of time. Comparing the pressure results from Figure 5.30 to Figure 4.11 shows that the model
captures a rise in the overpressure, but the model predicted overpressure is almost 3 times greater
than the experiments (3.25kPa).
Figure 5.29 Comparison of flame front propagation velocity results from experiments to the 2D,
12cm diameter quartz reactor model using the spark model for different initial kernel radii. R =
ini
5, 2.5, 1.5mm. Time step = 0.01ms. Ignition location is 1.39m from the open end. Mesh cell size
= 1mm, 0.25mm edge sizing. CH =9.5%. Temperature = 293K, Pressure = 82kPa. SM E =
4 ign
60mJ. No relief hole.
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initial spark kernel of 5mm, 2.5mm, and 1.5mm. Results are similar to the 2D model and the
relative percent error between these cases ranges from 5-17%, the average being approximately
12%. Based on the 2D and 3D cases, this research determined using an initial spark kernel radius
of 5mm because it better captures the continual acceleration of the flame shown in Figure 5.29
without significant differences in predicted overpressure and flame trends. To note, these were
performed with no relief hole on the closed end; when the relief is included, the flame does slow
down near the end, similar to the experiments which will be discussed in subsequent sections.
Table 5.8 Table showing the percent error of the 3D, 12cm diameter quartz reactor model
comparing the initial spark kernel radius for the 4mm body mesh (R = 5mm and 2.5mm). Time
ini
step = 0.01ms. Ignition location is 1.39m from the open end. CH =9.5%. Temperature = 293K,
4
Pressure = 82kPa. SM E = 60mJ. No relief hole.
ign
Percent Error (4mm body)
Time (s)
R =5mm : R =2.5mm (%)
ini ini
0.004 5.1
0.006 7.1
0.008 11.1
0.010 13.3
0.012 13.3
0.014 16.4
0.015 16.9
Average = 12%
5.1.4 Turbulence Model and Parameter Study
As discussed in Section 2.8, there are many different turbulence models which can be
employed to model methane flame propagation. Previous research concluded for the 2D models
of the small-scale 5cm diameter, 9.5cm diameter, and 71cm diameter reactors that the standard
k-ε turbulence model best matched experiments (Fig, 2019). However, as discussed, that model
uses a different method of initiating combustion which can significantly change the turbulence
parameter settings of the model. This section aims at describing how this current research
determined the appropriate turbulence parameters and turbulence model for initiating combustion
via a spark model. This section also discusses the difference in assuming a 2D planar geometry
versus axisymmetric.
In ANSYS Fluent, using the Reynold’s Averaged Navier-Stokes equations with
difference closure models requires model initialization of turbulence parameters such as
turbulent kinetic energy (k), turbulent dissipation rate (ε), and specific dissipation rate (ω). To
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calculate these quantities requires certain information about the flow including fluid properties
and upstream flow properties. The first quantity which must be calculated is the Reynold’s
number which depends on the mean flow velocity, kinematic viscosity, and hydraulic diameter
shown in Equation (5.4). In this case, the hydraulic diameter of the cylindrical reactors is the
reactor diameter, but for the experimental box, the hydraulic diameter is much more difficult to
estimate and is estimated using a square duct equation.
(5.4)
Next, the turbulent length scale, l, as smaller than the hydraulic diameter of the reactor. A
factor of 0.07 is recommended if there are obstacles in the flow, the length scale or hydraulic
diameter may be more appropriately based on the obstacle size (ANSYS© Fluent, 2009).
However, in order to directly compare the impact of obstacles on the flow, the current model
uses the same initialization parameters for open reactors and those with obstacles.
(5.5)
After determining the flow regime and length scale, an estimation of the turbulent
intensity can be made using Equation (5.6). The turbulent intensity (I) is the ratio of the RMS
velocity fluctuations and the mean flow inside the reactor, but for a cylindrical reactor can be
estimated from the following empirical correlation (ANSYS© Fluent, 2009):
(5.6)
Next, estimations for the turbulent kinetic energy (k), turbulent dissipation rate (ε), and
specific dissipation rate (ω) are made using Equations (5.7), (5.8), and (5.9), where Cμ is an
empirical constant usually 0.09 (ANSYS© Fluent, 2009).
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(5.7)
(5.8)
(5.9)
Unfortunately, the upstream conditions of the confined ignition are not well known,
which requires a sensitivity analysis of initial turbulence parameters on flame front propagation.
To do this, various mean flow velocities were estimated based on a range of velocities between 0
and the maximum flame front propagation velocities. From these, turbulent quantities were
calculated for a closed-end ignition in the 12cm diameter reactor as shown in Table 5.9. In future
work, the upstream turbulence conditions may be estimated using flow sensors and schlieren
photography to gain a stronger understanding of local fluid fluctuations and the average size of
the eddies in the flow.
Table 5.9 Table showing calculated turbulent initialization parameters based off different flame
front propagation velocities of a closed-end ignition in the 12cm diameter quartz reactor.
u (m/s) 1 5 10 20 30 60
avg
k (m2/s2) 0.004 0.07 0.24 0.8 1.6 5.5
ε (m2/s3) 0.005 0.37 2.3 14 40 250
ω (1/s) 14 58 106 195 278 509
As shown in the table, depending on how the mean flow velocity is defined, the
turbulence parameters have quite a large range. Therefore, simulations were set up initializing
with different turbulent parameters based on mean flow velocities of 1, 5, 10, 20, 30, and 60m/s.
In the future, these flow velocities can be estimated based on the kernel expansion rate, but this
will require additional imaging with a faster rate of frames per second than what was used in this
research (above 240fps).
Qualitative results of the simulations are shown in Figure 5.32, Figure 5.33, and Figure
5.34. Compared to experimental images in Figure 4.8, estimating the initial turbulence
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parameters using 5m/s and 10m/s results in flame shapes which are different than those observed
in experiments. Estimating the initial turbulence parameters based off mean flow velocities of
20m/s and 30m/s result in flame shapes which are more closely related to those observed in
experiments. One interesting flame shape observed in experiments and the model is shown in
Figure 5.35 at the open end of the reactor during a closed-end ignition. This shape was not
observed in approximately 50% of the closed-end ignition experiments and in all of the 2D,
12cm diameter models of closed-end ignition. Investigation of this shape was performed and it
was determined this is due to the boundary condition on the open end; the density differences
between the ambient air and combustion products resulted in flame instabilities leading to a
slight flame inversion.
Figure 5.32 Temperature contours of the 2D, 12cm diameter quartz reactor model investigating
the impact of different turbulence initialization parameters on flame propagation for a closed-end
ignition. Simulation time=10ms. Time step = 0.01ms. Ignition location is 1.39cm from the open
end. CH =9.5%. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. Relief hole height =
4 ign
1.2cm.
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Figure 5.35 Comparison of methane flame inversion at the open end of the reactor from a closed-
end ignition in the 12cm diameter quartz reactor. Top – Temperature contour from Figure 5.35
initialization parameters, k = 1.5m2/s2 and ω = 250 1/s. Bottom – Experimental image showing
flame inversion. Simulation time = 28ms. CH =9.5%. Temperature = 293K, Pressure = 82kPa.
4
SM E = 60mJ. Relief hole height = 1.2cm.
ign
After comparing the turbulent sensitivity results qualitatively, results were compared
quantitatively as shown in Figure 5.36 and Figure 5.37. These figures compare the results of
estimating turbulent properties based of 5, 10, 20, 30m/s as well as a case which rounds the
turbulent values calculated based off 30m/s to k = 1.5m2/s2 and ω = 250 1/s. As can be seen in
these figures, there is no one value which absolutely matches experiments perfectly. All of the
modeling results predict flame arrival at the open end much faster than experiments.
To investigate this, using the case of k = 1.5m2/s2 and ω = 250 1/s, the kernel diameter at
time t = 2ms was calculated as dk=0.06m. Complimentary high-speed imaging at 480 fps, 720
pixels, found that the average kernel diameter of three experiments at time t = 2ms was an order
of magnitude less, dk=0.008m. At time t = 12.5ms, the measured average flame kernel diameter
of experiments was dk=0.06m. From these results, it was concluded that the ANSYS Fluent
Spark Model (v17.2) overpredicts the initial kernel expansion of the flame in 2D. Despite this
difference, when the results of Figure 5.36 are normalized as shown in Figure 5.37, the rate of
increase of flame front propagation velocity in experiments match the 2D model when the
turbulent initialization parameters are estimated based off a mean flow velocity of 30m/s, or
simplified to k = 1.5m2/s2 and ω = 250 1/s (model – red circles compared to experiments – black
diamonds).
Additionally, when comparing the 2D model results to experiments, Figure 5.38, the
model does a good job at predicting the flame propagation trends towards the open end of the
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reactor. Although the model predicts more flame slow-down near the open end, this is difficult to
conclude from the experiments because there were no additional ion sensors between x = 0-25cm
from the open end. The flame slow down will be discussed in regards to modeling the relief hole
in Section 5.1.6. Despite this difference, the flame shape of the model near the open end matches
experiments. Therefore, it was concluded that initializing the model based off a mean flow
velocity that is approximately 50% of the maximum measured flame front propagation velocity
qualitatively and quantitatively matches the flame shape and flame acceleration down the
reactor. Thus, 12cm diameter reactor models modeling closed-end ignition uses the following
initial turbulent quantities: k = 1.5m2/s2 and ω = 250 1/s. This study was repeated for an open-
end ignition in the 12cm diameter reactor and it determined the following quantities most
accurately capture flame propagation: k = 0.004m2/s2 and ω = 0.1 1/s. This study was repeated
for the other experimental reactors and will be discussed in subsequent sections.
Figure 5.36 Flame front propagation velocity (FFPV) results of the 2D, 12cm diameter quartz
reactor model investigating the impact of different turbulence initialization parameters on flame
propagation for a closed-end ignition. Time step = 0.01ms. Ignition location is 1.39cm from the
open end. CH =9.5%. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. Relief hole
4 ign
height = 1.2cm.
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Figure 5.37 Normalized flame front propagation velocity (FFPV) results of the 2D, 12cm
diameter quartz reactor model versus experiments for a closed-end ignition. Time step = 0.01ms.
Ignition location is 1.39cm from the open end. CH =9.5%. Temperature = 293K, Pressure =
4
82kPa. SM E = 60mJ. Relief hole height = 1.2cm.
ign
Figure 5.38 2D, 12cm diameter quartz reactor model results compared to experiments for a
closed-end ignition. Time step = 0.01ms. Ignition location is 1.39cm from the open end.
CH =9.5%. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. Relief hole height =
4 ign
1.2cm.
After determining the most appropriate turbulent initialization parameters, a study was
performed investigating the 2D planar assumption by modeling the reactor as axisymmetric. To
do this requires modeling the 2D, planar 12cm diameter reactor without a relief hole since the
axisymmetric case cannot assume this. Also explored was a comparison of using the k-ω
turbulent model to the k-ε turbulence model using initial turbulence parameters based off the
same mean flow velocity, 30m/s. Results of these studies are shown in Figure 5.39, Figure 5.40,
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and Figure 5.41. Results show that not modeling the relief hole on the closed end of the reactor
results in faster flame propagation than modeling the relief hole; this shall be discussed further in
the subsequent section, however, it is introduced here in order to make a direct comparison
between the 2D planar assumption and axisymmetric assumption. As shown in the figures,
assuming axisymmetric using the same model setup results in much faster flame speeds than the
2D planar assumption. Additionally, using the k-ε model results in even faster flame speeds
compared to the k-ω turbulence model, which agrees with previous findings (Fig M. , 2019). The
difference between these turbulence models is due to the fact that the k-ε turbulence model uses
approximations in the boundary layer and is more often used for flows with high turbulence in
the bulk of the flow. Therefore, researchers recommend future work performing a sensitivity
study of the k- ε model investigating different initial turbulence parameters. In contrast, the k-ω
turbulence model is more well-suited for shear flows, which as it has been shown, has quite an
impact on the flame shape observed in experiments. Therefore, this manuscript will continue
using the k-ω turbulence model, but shall revisit this assumption as models continue to increase
in scale.
Figure 5.39 Temperature contours of the 2D, 12cm diameter quartz reactor model investigating
the impact of mesh size, relief on the closed end, planar versus axisymmetric assumptions, and
turbulence model on flame propagation for a closed-end ignition. Simulation time=8ms. Time
step = 0.01ms. Ignition location is 1.39cm from the open end (left). CH =9.5%. Temperature =
4
293K, Pressure = 82kPa. SM E = 60mJ. Relief hole height = 1.2cm.
ign
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5.1.5 Impact of Modeling Ion Sensors
As described in Chapter 3, the 12cm diameter quartz flow reactor uses ion sensors to
measure the flame front propagation velocity. The ion sensors are shown in Figure 3.5 on page
53, where the electrodes are enclosed in ceramic tubes that are 0.5cm in diameter. For open-end
ignition experiments, the ion sensors were located flush with the top of the reactor, but as shown
in Figure 3.8 on page 54, the flame resulting from a closed-end ignition requires the sensors to be
located at least 2cm down into the reactor to more accurately measure the flame front
propagation velocity. However, from the experiments, given the cross-sectional area of the ion
probes relative to the cross-sectional area of the reactor it is expected that changing the depth of
the ion sensors from 1-2cm will have very little impact on the flame characteristics and flame
propagation velocities. To confirm this hypothesis, a study was performed using the 2D and 3D
CFD models of the 12cm diameter reactor which included the ion sensors 0.5cm in diameter and
2cm long.
Results of modeling the ion sensors in 2D are shown in Figure 5.42 and indicate that the
ion sensors can impact methane flame propagation; increasing the overall speed of the flame as
well as the turbulence induced downstream of the obstacles. However, modeling this scenario in
2D does not fully resolve turbulence in the third dimension. Results of modeling the ion sensors
in 3D are shown in Figure 5.43 and show that the ion sensors do not impact methane flame
propagation. Additionally, in 3D the turbulence induced by the ion sensors is much less than that
induced by the ion sensors in 2D. This main difference is to the fact that in 2D, the turbulence is
not fully being resolved, and thus is overestimated. Coupled with the fact that the ion sensors, in
reality, do not take up the entire cross section of the reactor, the 2D model overpredicts the
impact of the ion sensors. These results are important because 1) they show that the ion sensors
do not have a significant impact on the experimental results and 2) they show that to model
turbulence, especially turbulent flame propagation, requires solving the third dimension.
Unfortunately, as the models continue to get larger and larger, they require more computational
time and solving all scenarios in 3D require the use of parallelization over multiple compute
nodes. Thus, it is important when interpreting 2D modeling results to have a strong knowledge of
model sensitivity as shown in these studies.
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Figure 5.43 Temperature and turbulent intensity contours of the 3D, 12cm diameter quartz
reactor model investigating the impact the ion sensors on flame propagation for a closed-end
ignition. Simulation time=12ms. Time step = 0.01ms. Ignition location is 1.39cm from the open
end. CH =9.5%. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. No relief hole. 3D
4 ign
Body mesh size = 2mm.
5.1.6 Impact of Modeling Relief Holes
As discussed in the experimental setup, the relief holes size on the closed end of the
reactor is 1±0.2cm. In most of the experiments, a single relief hole was opened in order to help
stabilize the flame front which agrees with findings of other researchers (Andrews & Bradley,
1972; Rallis & Garforth, 1980). However, determining an adequate representation of the hole in
the 2D model was done by modeling the relief hole height as a fraction of the total diameter of
the reactor. This fraction was determined by the total area of the relief hole divided by the total
area of the closed end also shown in the following equation:
(5.10)
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As can be seen in Equation (5.10), the ratio of the area of the hole, ‘h’, to the area of the reactor,
‘r’, is 10%. For the model this was done by taking an edge split of 10% on the closed end of the
reactor, which means the height of the relief hole modeled in 2D is 1.2cm.
Results of modeling the relief hole with H=1.2cm versus not modeling the relief hole for
an open-end ignition is shown in Figure 5.44 and Figure 5.45 and results are tabulated in Table
6.1. As can be seen in the following two figures, modeling the relief hole allows for improved
flame stability and faster flame turn over. However, modeling the relief hole also allows for less
pressure built up on the closed end of the reactor leading to slower overall flame speeds. When
comparing the flame speeds, modeling the relief hole better estimates the maximum speed of the
stoichiometric flame, but overestimates the rich flame speed and underestimates the lean flame
speed. Not modeling the relief hole better estimates the lean flame speed and overestimates all
other cases. Also, temperature magnitudes from the model agree with fundamental flame theory
that a stoichiometric mixture (9.5% methane by volume) is the highest, then rich, and finally the
lean case. Taking all of this into account, this research shows that modeling the relief hole in 2D
must be taken with caution because the flame stability and propagation velocities are sensitive to
the relief hole sized used. For the open-end ignition case without an obstacle, this shall be
discussed further in subsequent sections.
Figure 5.46 shows results of an open-end ignition with an obstacle wall located 37cm
from the open end. This figure compares modeling flame propagation across the obstacle with
and without a relief hole of H=1.2cm. Comparing Figure 5.46 to images of flames passing over
the obstacle wall in Figure 6.18 shows that not modeling the relief hole results in more realistic
flame shapes passing over the wall. Results of modeling the relief hole shows that the flame
expands farther axially than radially, whereas images of the flame show that the flame tends to
move both axially and radially. Based on these results, it was concluded that modeling an open-
end ignition with an obstacle in 2D does not require modeling the current size of the relief hole
because it may be artificially allowing faster flame propagation past the obstacle. In the future, a
better representation of the relief hole may be obtained by measuring the rate of gas expansion
out of the hole and setting the size of the hole for the model based on gas expansion.
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Figure 5.44 Temperature contours of the 2D, 12cm diameter quartz reactor model without
modeling the relief hole for an open-end ignition. Simulation time=1.4s. Time step = 0.1ms.
Ignition location is 11cm from the open end (left). CH =9.5%. Temperature = 293K, Pressure =
4
82kPa. SM E = 60mJ. No relief hole.
ign
Finally, closed-end ignition results modeling the relief hole versus not modeling the relief
hole are shown in Figure 5.47. As shown in this figure, not modeling the relief hole results in
flame front propagation velocities over 115% greater than modeling the closed-end ignition with
a relief hole. Closed-end ignition experiments predict a maximum flame front propagation
velocity of 65m/s and the 2D model with a relief hole predicts a maximum flame speed of 72m/s,
which is only 11% greater than experiments (Table 6.2, page 185). Additionally, the rate of
flame front propagation increase (or acceleration) of the flame is greater without modeling the
relief hole versus modeling the relief hole which was previously shown to match experiments
well in Figure 5.37. Finally, as shown in Figure 5.34 and Figure 5.35, the 2D model predicts the
flame stretching and flame shape well compared to experiments (Figure 4.8, page 67). Therefore,
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Figure 5.47 Flame front propagation velocity location results of the 2D and 3D, 12cm diameter
quartz reactor model investigating the impact of modeling the relief hole on the closed end of the
reactor. Time step = 0.01ms. Ignition location is 1.39cm from the open end. CH =9.5%.
4
Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. Relief hole H = 1.2cm.
ign
5.1.7 Impact of Extending the Domain
One of the major concerns with evaluating the flame shapes observed in Figure 5.35 was
that the inversion was due to the zero gauge boundary condition on the open end of the reactor.
To explore the impact of the open end boundary condition on a closed-end ignition, a study was
performed extending the domain another 1m and initializing it to stagnant, air at 293K and
82kPa. In this scenario, the methane-air mixture was stoichiometric, 9.5% methane by volume,
and the mixture was ignited from the closed end of the reactor. Results are presented in Figure
5.48-Figure 5.53 and show that extending the domain can change the exact location of the
inversion, but results in similar flame propagation trends. Figure 5.48 compares the flame front
propagation velocity versus time when adding the extension slows the flame front propagation
velocity because as the volume expands, the flame slows in order to maintain mass flow.
Although the flame front propagation velocities are slightly slow, the extended domain values
are within 10% of the case not modeling an extension. In general, however, the simulation results
are fairly similar and the time cost of running a longer model does not outweigh the results.
Finally, another interesting finding was that, unlike the open-end ignition flame which consumes
almost all the methane in the reactor domain, the closed-end flame generates enough pressure to
push out a significant amount of methane. Unfortunately in the experimental setup, probes were
not set up to measure the flow of methane out of the reactor, but other researchers have also
noted that these types of flames could push out a significant amount of gas mixture (Bradley &
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5.2 Box Reactor Model Setup
To understand the impact of reactor shape on methane flame propagation and interaction
with obstacles, CFD combustion models of the box experiments were setup as shown in 2D in
Figure 5.54. The model settings of the experimental box reactor are the same as the 12cm
diameter quartz reactor, including the spark model settings in Table 5.2 (ANSYS Fluent v17.2):
• 2D planar assumption for all 2D models
• Pressure-Based Solver
• Energy Equation
• Viscous Standard k-ω Turbulence Model
o Low Re Corrections
o Shear Flow Corrections
• Species Transport
o Volumetric Reactions
o Stiff Chemistry Solver
o Finite Rate Chemistry
▪ Density solved using ideal gas theory
▪ Diffusion solved using kinetic theory
▪ Metghalchi and Keck laminar flame speed theory
• Spark Ignition Model
• PISO pressure-velocity coupling
• 2 levels of mesh adaption on the gradient of temperature every 2-10 time steps
• 2D Model: Residuals set to 10-6, dropping at least 3 orders or magnitude
• 3D Model: Continuity/velocity residuals set to 10-4, Energy/turbulent 10-6
• Second order in time and space
• Time step = 0.1ms for open-end ignition, 0.01ms for closed-end & center ignition
• Boundary Conditions:
o Walls – no slip, adiabatic
o Relief opening – 0 gauge pressure outlets
o Obstacles– no slip, adiabatic, assuming no heat transfer into the material
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Figure 5.54 Schematic of 2-D combustion model setup of the box experiments.
In this model, ignition was located near the open end, closed end, and the center of the
gob in order to understand how the flame might propagate if it were ignited from within the gob
and might travel towards the longwall face. Although it is not well known if an ignition can
travel from deep within the gob to the working face, a center ignition is most indicative if there is
an ignition in the fallen roof gob near the tailgate entry, where explosive gas zones are known to
exist.
As discussed previously, determining the size of the relief opening in 2D is difficult and
this research recognizes that this can be considered a tuning parameter in this model. For the
experiment box, if one were to determine the size of the relief opening based on the ratio of areas
then the opening would be 5.6cm. However, if the relief opening was determined based off the
hydraulic diameter of the relief, then it would be 8.8cm. Averaging these two methods leads to a
relief opening size of 7.2cm, which is approximately the height of the opening, 7cm. Since this
average value is similar to the height of the opening, researchers are using a relief size of 7cm for
the 2D model. Noted that for the 12cm diameter reactor the height of the relief was also used in
the 2D model. However, to reiterate, the relief opening can be seen as a tuning parameter of the
model.
Additionally, estimating the turbulence parameters, as previous shown with the 2D 12cm
diameter reactor model, is difficult and requires a sensitivity analysis to be performed.
Unfortunately Equation (5.4) and Equation (5.5) are derived for pipe flow, thus, researchers
determined the appropriate turbulence initialization parameters by comparing CFD flame
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propagation results to the flame kernel growth and propagation recorded from experimental high-
speed imaging. To begin, values from the 2D, 12cm diameter model were used: open-end
ignition k = 0.004m2/s2 and ω = 0.1 1/s, closed-end ignition k = 1.5m2/s2 and ω = 250 1/s. The
turbulent kinetic energies and specific dissipations were changed orders of magnitude away from
these values. Based on flame shape and flame speed, it was determined the following turbulence
values best represented what was observed from experiments: open-end ignition k = 0.001m2/s2
and ω = 0.1 1/s (corresponding to flow velocities less than 1m/s), closed-end ignition k =
1.5m2/s2 and ω = 25 1/s. Result comparisons are shown in subsequent sections of this
manuscript.
5.2.1 2D Mesh Independence Study
To begin modeling the experimental box as described in Section 3.1.2, a 2D model was
created and a variety of meshes were compared: 2mm, 1mm, and 0.5mm. All of the meshes were
quadrilateral dominant as shown in Figure 5.55 and mesh statistics are summarized in Table
5.10. As can be seen the mesh is primarily structured, but some of the cells are skewed and have
aspect ratios larger than 1. However, despite these drawbacks, the meshes have fairly good
quality. Additionally, for all models which include obstacles, the obstacles have a constant edge
sizing of 0.5mm as shown in Figure 5.56. Edge sizing was used on the obstacles to help resolve
the boundary layers as the flame interacts with the obstacles. Additionally, all models presented
employ mesh adaption on the gradient of temperature, 2 levels every 2-10 time steps depending
on whether the flame is highly turbulent or mainly wrinkled laminar.
Figure 5.55 Image of the 2D, box reactor mesh with a quadrilateral dominant 0.5mm body mesh.
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Table 5.10 2D, box reactor mesh statistics for a 2mm, 1mm, and 0.5mm body mesh: number of
elements, number of nodes, minimum orthogonality quality, maximum skewness, and maximum
aspect ratio. No edge sizing.
Minimum
Number of Number of Maximum Maximum
Orthogonality
Elements Nodes Skewness Aspect Ratio
Quality
2mm body mesh 42,591 43,010 0.7 0.3 3.2
1mm body mesh 169,763 170,594 0.8 0.2 2.7
0.5mm body mesh 688,999 690,640 0.6 0.3 4.1
Figure 5.56 Image of the 2D, box reactor mesh with a quadrilateral dominant 1mm body mesh
and 0.5mm edge sizing on obstacle boundaries.
A mesh independence study for the 2D box model was performed alongside determining
the appropriate turbulence initialization settings. Mesh independence results were determined by
taking a seeded diagonal line as shown in Figure 5.57 and results are tabulated in Table 5.11. As
shown, a mesh size of 1mm results in flame front locations less than 1% different than the
0.5mm case. Additionally, the standard deviation and maximum errors are less than 1% for the
1mm mesh. Therefore, all 2D models use a 1mm quadrilateral base mesh with a 0.5mm edge
sizing on all obstacles to resolve the boundary layers.
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Table 5.11 Average percent error, standard deviation, and maximum error in the flame front
location between different body meshes for the 2D, box model.
Percent Error (%)
2mm : 1mm 1mm : 0.5mm
Average 1.9 0.0
Standard Deviation 2.5 0.6
Maximum Error 10 0.5
Figure 5.57 Schematic of the 2-D combustion model setup of the box experiments with a yellow
line indicates seeded line used to compared flame front propagation towards the relief opening
for different mesh sizes for a confined ignition.
5.2.2 3D Mesh Independence Study
A 3D mesh was created for the experimental box using a cut cell, quadrilateral dominant,
method as shown in Figure 5.58. Two different meshes were compared for the 3D, box model, a
5mm mesh and a 2.5mm mesh. Mesh statistics are presented in Table 5.12 and show that the
orthogonality quality is very close to one with maximum skewness below 0.2. Also, the
maximum aspect ratios are close to 2 which means the dimensions of the cells are mostly
proportional. Altogether, these statistics show a very good quality mesh. As a note, the 2.5mm
cut cell mesh resulted in over 1.5 million cells. A mesh of 1-1.25mm was attempted, but resulted
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in a large amount of cells which was not feasible to run on an 8 core compute. In the future,
running across nodes should be investigated so that finer meshes can be used. To help overcome
some of the error of a 2.5mm mesh, aggressive mesh adaption was used: 3 levels every 2 time
steps. As will be shown, this helped resolved the flame front propagation well, but resulted in
some error associated with other flow quantities.
Figure 5.58 Image of the 3D, box reactor mesh with a quadrilateral dominant 2.5mm body mesh.
Table 5.12 3D, box reactor mesh statistics for a 5mm and 2.5mm body mesh: number of
elements, number of nodes, minimum orthogonality quality, maximum skewness, and maximum
aspect ratio. No edge sizing.
Minimum
Number of Number of Maximum Maximum
Orthogonality
Elements Nodes Skewness Aspect Ratio
Quality
5mm body mesh 216,039 228,480 1 0 1.8
2.5mm body mesh 1,704,543 1,757,663 0.8 0.2 2.2
To begin, a mesh independence study was also undertaken for the 3D box model using
the same initialization settings as the 2D model for a confined ignition (k = 1.5m2/s2 and ω = 25
1/s). A seeded line extending from the confined ignition towards the relief opening was used to
determine flame front location and compare meshes. This research recognizes that in 3D the
flame can propagate in all directions, but this analysis was performed to directly compare flame
location to the average velocities observed in experiments., The 3D mesh independence study
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shows that using mesh adaption on the temperature gradient, 3 levels every 2 time steps (0.01ms
time step), with a coarse 5mm mesh is within 1±1% of the flame front location compared to a
2.5mm mesh, with a maximum relative error below 2%.
Figure 5.59 Schematic of 3-D combustion model setup of the box experiments. XY plane is
located in the middle of the reactor, at z = 0.075m. Yellow line indicates seeded line used to
compared flame front propagation towards the relief opening for different mesh sizes for a
confined ignition.
Table 5.13 Average relative error and standard deviation in the flame front location between
different body meshes of the 3D box model for a confined ignition. Adaption on the temperature
gradient, 3 levels every 2 times steps.
Time (s) Relative Error (%)
5mm : 2.5mm
0.02 0.4
0.045 0.0
0.06 -0.8
0.08 -1.6
0.105 -1.6
0.12 -0.5
Average -0.7
Standard Deviation 0.8
As discussed with the 3D model of the 12cm diameter reactor, evaluating mesh
independence in 3D is quite complex and requires investigation of flow properties in 3D space.
Thus far for the 3D, box reactor model, the flame front location as a function of time has been
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evaluated and the relative error between a 5mm and 2.5mm mesh is less than 2%. The next step
of the mesh independence process is to plot and compare flow quantities. To do this, three (3)
XZ planes were compared with two (2) seeded lines at different locations as shown in Figure
5.60. Temperature contours are shown as a function of time in Figure 5.61, Figure 5.62, and
Figure 5.63; as shown in these figures, the temperature contours are similar, but the 5mm mesh
shows a much coarser resolution. Results of probing the seeded lines (999 points were taken and
averaged) are tabulated in Table 5.14 and Table 5.15. Although these results are only tabulated
for time t=11ms, they have been reviewed over several time steps. In general, results show that
evaluating the 5mm and 2.5mm mesh based on the total temperature results in average percent
differences less than 5%, though the standard deviations range from 7-11%. Note that grid
adaption is used in these models and resolves the flame front by employing 3 levels of mesh
adaption on the gradient of temperature every 2 time steps. Since the grid adaption resolves the
temperature with higher accuracy compared to the flow velocities, the large average percent
differences calculated based off the fluid velocity magnitude is of no surprise, 15-40%
differences. This was also observed with the 3D model of the 12cm diameter reactor. Based on
these results, this research has concluded that for the 3D box model, a base mesh of 5mm with
aggressive mesh adaption is adequate to resolve the flame front, but a base mesh of 2.5mm is
highly recommended to better resolve local flow velocities and temperature gradients.
Figure 5.60 Schematic of 3-D combustion model setup of the box experiments showing three XZ
planes with two seeded lines per plane used to extract data for further mesh independence
investigation.
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Figure 5.63 Temperature contours of the 3D, box reactor model investigating the impact of mesh
size on flame propagation. Temperature and velocity data was extracted from the seeded lines on
XZ planes. Simulation time = 11ms. Time step = 0.01ms. Confined ignition located opposite the
relief. CH = 9.5%. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. Body mesh size =
4 ign
5mm and 2.5mm.
Table 5.14 Average percent difference and standard deviation in the total temperature between
different body meshes of the 3D box model for a confined ignition at time, t = 11ms. Body mesh
sizes compared are 5mm and 2.5mm. Lines are seeded with 999 points.
XZ Plane at XZ Plane at XZ Plane at
y = 0.125m y = 0.25m y = 0.375m
Top Bottom Top Bottom Top Bottom
Line Line Line Line Line Line
Average Difference (%) 0 1 3 3 4 4
Standard Deviation (%) 8 7 9 9 11 11
Table 5.15 Average percent difference and standard deviation in the fluid velocity magnitude
between different body meshes of the 3D box model for a confined ignition at time, t = 11ms.
Body mesh sizes compared are 5mm and 2.5mm. Lines are seeded with 999 points.
XZ Plane at XZ Plane at XZ Plane at
y = 0.125m y = 0.25m y = 0.375m
Top Bottom Top Bottom Top Bottom
Line Line Line Line Line Line
Average Difference (%) 40 32 23 15 23 22
Standard Deviation (%) 43 32 18 13 16 16
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5.2.3 Mesh Adaption Study
As shown in the previous section, for the 3D model of the experimental box a coarse
mesh size of 5mm is adequate to resolve the flame front within 2% of a 2.5mm mesh using mesh
adaption on the temperature gradient. A further study was performed to determine the best
settings to use for the mesh adaption by comparing the frequency at which the model is adapting
and the levels of adaption. Results of this study are shown in Table 5.16 and Figure 5.70. As can
be seen, using 2 levels of adaption results in shorter simulations times than using 3 levels of
adaption and the less frequent the mesh adaption the less total simulation time. Based on the total
temperature on the diagonal line (shown in Figure 5.59 on page 162), for this coarse grid using 3
levels of adaption every 2 time steps results in flames that are almost 5% faster than using 2
levels of adaption. However, the simulation time of modeling the box with 3 levels every 2 times
steps is twice the amount of simulation time when using 2 levels of adaption. Therefore, it is
recommended that for flame front accuracy, 3 levels every 2 times steps is used, but 2 levels
every 2 time steps may be appropriate when simulation time is of concern. This is important as
models continue to increase in size and simulation time becomes more important to balance.
Figure 5.70 Total temperature versus location results of the 3D, box reactor model investigating
the impact of mesh adaption settings. Simulation time = 5ms. Time step = 0.01ms. Confined
ignition. CH = 9.5%. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ.
4 ign
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Table 5.16 Comparison of mesh adaption settings and simulation times of the 3D box model for
a confined ignition. Adaption on the temperature gradient with varying levels and frequency.
Models run on an 8 core compute, 3.06GHz, 24GB RAM.
Levels 2 2 2 3 3
Frequency 1 2 5 1 2
Simulation Time 14hr, 42min 12hr, 33min 11hr, 27min 48hr 30hr
5.3 2D 71cm Diameter Reactor Model Setup
A 2D combustion model of the 71cm diameter, 6.1m long reactor was developed as
shown in Figure 5.71.
Figure 5.71 Schematic of 2D combustion model geometry setup of the 71cm diameter steel
reactor located at Edgar Experimental Mine in Idaho Springs, CO.
The model settings of the 71cm diameter reactor are the same as the 12cm diameter quartz
reactor and box model, including the spark model settings in Table 5.2 (ANSYS Fluent v17.2):
• 2D planar assumption for all 2D models
• Pressure-Based Solver
• Energy Equation
• Viscous Standard k-ω Turbulence Model
o Low Re Corrections
o Shear Flow Corrections
• Species Transport
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o Volumetric Reactions
o Stiff Chemistry Solver
o Finite Rate Chemistry
▪ Density solved using ideal gas theory
▪ Diffusion solved using kinetic theory
▪ Metaghalchi and Keck laminar flame speed theory
• Spark Ignition Model
• PISO pressure-velocity coupling
• Continuity/energy residuals set to 10-5, Velocity/species residuals set to 10-3
• Second order in time and space
• Time step = 0.01ms
• Boundary Conditions:
o Walls – steel, 5mm roughness height, adiabatic
o Obstacles– no slip, adiabatic, assuming no heat transfer into the material
5.3.1 2D Turbulence Model Settings & Mesh Independence Study
To begin modeling the 71cm diameter reactor presented in Section 3.2, a 2D quadrilateral
dominant mesh was created as demonstrated in Figure 5.72. As can be seen in this image, the
mesh is primarily structured, but based on the mesh statistics shown in Table 5.17 some of the
cells are slightly skewed and can have large aspect ratios. Two main base meshes were
compared, a 4mm and 2mm mesh, however a third mesh was created with slightly larger cells:
5mm base mesh with 1mm edge sizing on the walls as shown in Figure 5.73. The 5mm base
mesh with 1mm edge sizing results in a similar number of cells as the 4mm mesh, but the
maximum skewness increases due to the unstructured mesh. This 5mm mesh with 1mm edge
sizing was primarily used when considering flame propagation across obstacles; unfortunately,
Fluent’s meshing client had difficulties meshing at 4mm and 2mm when considering obstacles in
the flow, thus a slightly coarser mesh was used with edge sizing on the obstacles to help resolve
boundary layers. Additionally, mesh adaption was employed to help resolve the flame front in
the bulk flow.
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Table 5.17 2D, 71cm diameter reactor mesh statistics for a 2mm body mesh, a 4mm body mesh,
and a 5mm body mesh with 1mm edge sizing: number of elements, number of nodes, minimum
orthogonality quality, maximum skewness, and maximum aspect ratio.
Minimum
Number of Number of Maximum Maximum
Orthogonality
Elements Nodes Skewness Aspect Ratio
Quality
2mm body mesh 979,191 982,147 0.4 0.4 6.1
4mm body mesh 250,358 251,866 0.4 0.4 5.3
5mm body mesh,
254,386 258,813 0.5 0.7 3.2
1mm edge sizing
Determining the turbulence parameters, as previous shown with the 12cm diameter
reactor model and box model, can be difficult, but researchers used their knowledge of flame
front propagation velocities and flame shape to help determine the most appropriate parameters.
For example, for the 12cm diameter reactor the most appropriate turbulent quantities were based
off an average flow velocity of 30m/s, which was slightly less than half the maximum flame
front propagation velocity. Thus, to begin this for the 2D, 71cm diameter reactor model,
researchers began with estimating the flow quantities based off an average flow velocity of
40m/s, corresponding to k = 1m2/s2 and ω = 45 1/s (maximum flame front propagation velocity
was approximately 125m/s). After this, a parametric study was performed changing the kinetic
energy and the dissipation rate orders of magnitude. Results of this study are shown in Figure
5.74 and show that estimating the turbulence parameters as k = 0.1m2/s2 and ω = 45 1/s gives the
closest agreement between the 2D CFD model and experiments.
After determining the best turbulence parameters, a 2D mesh independence study was
performed and results are shown in Table 5.18. Results show that the flame front calculated
using a 4mm body mesh is within 15% the flame front for a 2mm body mesh. Although an error
of 15% seems large, Figure 5.75 and Figure 5.76 show there is a very close agreement between
the 4mm and 2mm body meshes. Unfortunately comparing these meshes to a 1mm body mesh
was infeasible with the current computational power. Additionally, the total simulation time for
the 4mm body mesh was 5 days and the total simulation time for the 2mm body mesh was 15
days. Extrapolating this to a 1mm body mesh would mean an estimating simulation time of 45
days. Taking all of this into account, researchers recommend a 4mm body mesh due to ease of
meshing, reduced simulation times, and reasonable flame front propagation velocity estimates.
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Figure 5.74 Flame front propagation velocity versus distance for the 2D 71cm diameter reactor
model for a closed-end ignition with varying turbulence initialization parameters. Ignition
location is 28.5cm from the closed end. Time step = 0.01ms. CH = 9.5%. Body mesh size = 4-
4
5mm. Temperature = 295K, Pressure = 76kPa. SM E = 60mJ.
ign
Table 5.18 Average percent error, standard deviation, and maximum error in the flame front
location between different body meshes for the 2D, 71cm diameter reactor model. k = 0.1m2/s2
and ω = 45 1/s. 4mm mesh uses grid adaption on the temperature gradient, 2 levels every 2 time
steps.
4mm : 2mm
Average Error (%) 15
Standard Deviation (%) 7
Maximum Error (%) 25
Figure 5.75 Flame front propagation velocity versus time for the 2D 71cm diameter reactor
model for a closed-end ignition with varying body mesh sizes. k = 0.1m2/s2 and ω = 45 1/s.
Ignition location is 28.5cm from the closed end. Time step = 0.01ms. CH = 9.5%. Body mesh
4
size = 4mm and 2mm. Temperature = 295K, Pressure = 76kPa. SM E = 60mJ.
ign
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Figure 5.78 Temperature contours of the axisymmetric 2D, 71cm diameter quartz reactor model
using k = 1.5m2/s2 and ω = 45 1/s. Simulation time=14ms. Time step = 0.01ms. Ignition location
is 28.5cm from the closed end. Time step = 0.01ms. CH = 9.5%. Body mesh size = 4-5mm.
4
Temperature = 295K, Pressure = 79kPa. SM E = 60mJ.
ign
Researchers also investigating possibly using an asymmetric model instead of a 2D
planar model. Results of the investigating are presented in Figure 5.77 and Figure 5.78. As can
be seen in these figures, the axisymmetric case predicts faster flame front propagation velocities
than the 2D planar case agreeing with previous observations modeling the 12cm diameter quartz
reactor. Although the axisymmetric case predicts faster flames than assuming a 2D planar
geometry, the predict flame shape shown in Figure 5.78 shows flame inversion at the line of
symmetry. However, if the shape of the flame is assumed to look more like a closed-end ignition
flame (Figure 2.7) then the axisymmetric case does not predict this well. Unfortunately there is
no photographic evidence of the shape of this flame to help determine whether the axisymmetric
assumption is valid. Also, one of the reasons the axisymmetric case is predicting faster flames
than the 2D planar case is because the same turbulence parameters were used. This is important
because in the planar case the turbulence parameters compensate for some of the turbulence in
the radial direction, whereas the axisymmetric case already takes this swirl into account.
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CHAPTER 6
CFD MODELING OF PREMIXED METHANE-AIR DEFLAGRATIONS IN
EXPERIMENTAL REACTORS
The previous chapter, Chapter 5, discusses the model setups for the 12cm diameter
reactor, experimental box, and 71cm diameter reactor. Additionally, Chapter 5 discusses the
combustion model settings such as the turbulence model, turbulence initialization parameters,
and spark initiation methods and how these settings impact model predicted methane gas
deflagrations. This chapter summarizes the major modeling results of the 12cm diameter reactor,
experimental box, and 71cm diameter reactor in 2D and 3D and compares these results to flame
front propagation velocities, flame trends, and flame shapes observed from experiments
presented in Chapter 4.
6.1 2D 12cm Diameter Quartz Reactor Modeling Results
Experiments in the 12cm diameter reactor are presented in Section 4.1-4.5 and the CFD
model settings are presented in Section 5.1. This section shall present complimentary 2D and 3D
modeling results and discuss the model performance compared to experiments and other
researchers.
6.1.1 Empty Reactor: Impact of Mixture Stoichiometry
It is well known that EGZs exist underground in longwall coal mines and although there
has been significant research modeling these EGZs (Juganda, Brune, Bogin, Grubb, & Lolon,
2017; Ren & Edwards, 2000; Tanguturi, Balusu, & Bongani, 2017), still not a lot is known about
the location, movement, and actual composition since a mine environment is inherently transient.
Therefore, it is important to capture the impact of stoichiometry on methane flame propagation
in the CFD models in order to build a comprehensive model capable of modeling methane gas
explosions in underground coal mines.
Previous open-end ignition experiments investigating the impact of methane-air mixture
stoichiometry on flame propagation in the 12cm diameter quartz flow reactor found that the
stoichiometric flame (9.5% methane by volume) was fastest, followed by the lean (7.5%) and
rich flame (11.5%) (Figure 4.3 and Figure 4.4 in Section 4.1). However, according to laminar
flame theory, a rich 11.5% laminar flame at standard temperature and pressure is faster than a
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stoichiometric or 7.5% lean flame as shown in Figure 2.4. The reason for this difference is that in
the experiments, a diffusion flame was observed on the open end of the reactor during the rich
flame propagation. This diffusion flame acted similar to a counter balance, slowing down the
main rich flame front, reducing the overall speed of the flame.
Figure 6.1: 2D 12cm diameter reactor results of investigating the impact of mixture
stoichiometry on methane flame front location versus time for an open-end ignition. Ignition
location is 11cm from the open end. Time step = 0.1ms. CH = 7.5, 9.5, 11.5%. Body mesh size
4
= 1mm, 0.25mm edge sizing. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. No relief
ign
hole.
Table 6.1 Table comparing experimental data to the 2D 12cm reactor model predictions of
maximum flame front propagation velocity (FFPV) and standard deviation of the mean for an
open-end ignition with different mixture stoichiometries. Temperature = 293K, Pressure =
82kPa. SM E = 60mJ.
ign
2D Model with Relief
2D Model without Relief Experiments
H=1.2cm
Mixture
7.5% 9.5% 11.5% 7.5% 9.5% 11.5% 7.5% 9.5% 11.5%
Stoichiometry
Max FFPV
1.05 1.65 1.65 0.85 1.39 1.46 1.05 1.32 0.95
(m/s)
Standard
Deviation - - - - - - 0.04 0.04 0.14
(m/s)
These experiments were modeled using the 2D 12cm diameter reactor model (without a
relief hole) and results are presented in Figure 6.1 and Table 6.1. Results show that the rich and
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stoichiometric flames propagate at similar speeds, but near the end of the reactor the rich flame
propagates faster than the stoichiometric flame. The lean flame propagates slowest, as expected,
and the maximum flame front propagation velocity calculated from the lean flame matches the
experiments well. The 2D model without a relief hole predicts a 25% increase in the maximum
flame front propagation velocity of the stoichiometric flame measured in experiments. This is
mainly due to the simplified 2-step methane-air mechanism summarized in Table 5.1: the first
reaction of methane of oxygen was experimentally determined at high temperatures (>1000C)
and an equivalence ratio range of 0.05-0.5 and the second reaction of CO and oxygen is validated
over an equivalence ratio range of 0.04-0.5 (Dryer & Glassman, 1973). Since these mechanisms
have been validated under the lean conditions, it makes sense that the model results would more
accurately predict the lean flame propagation. In summary, the increased speeds predicted by the
2D model for the stoichiometric and rich case can be attributed to the reduced 2-step methane-air
mechanism employed coupled with the simplicity of the 2D model. Since the chemistry is
reduced to a 2-step mechanism, the heat release by the reaction of methane and oxygen is
overpredicted leading to faster flame speeds for the stoichiometric and rich flame.
As discussed, one of the main advantages of the 12cm diameter quartz reactor is the
optical access to the flame, allowing validation of the models based on flame speeds as well as
flame shape and trends. Thus, in addition to capturing the overall flame trends and approximately
flame front propagation velocities, the 2D 12cm diameter reactor model (without a relief) also
captures the general flame shape as shown in Figure 6.2, Figure 6.3, and Figure 6.4. As can be
seen in these transient images, the flame propagates and eventually turns over due to hot,
buoyant product gases rising to the top of the reactor and pushing over the flame front agreeing
with observations by other researchers (Guenoche & Jouy, 1953). Compared to experimental
images in Figure 4.5, Section 4.1, the model captures this turn over well, but later in the flame
development than observed in experiments. This is due to the fact that buoyancy is a slow
process and it is difficult to accurately capture this phenomenon, which is a 3D process.
Additionally, the 2D model without a relief shows that the stoichiometric flame does not fully
turn over into the classic angled flame. This is because the model does not include the relief hole
on the closed end of the reactor which increases the pressure build up such that it is more
difficult for the flame to turn over. These results also help demonstrate the need to accurately
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model the experiment and the sensitivity of the model to the pressure relief hole, and if ignored,
will provide results which overpredict the maximum flame front propagation velocities.
To investigate this flame turnover discrepancy, additional 2D models were run with the
relief hole, H=1.2cm; flame shapes are presented in Figure 6.5 and maximum flame front
propagation velocities are shown in Table 6.1. As shown, modeling the relief allows for some
additional flame stability and slightly less pressure build up which allows the buoyant gases time
to rise and push over the top of the flame, decreasing the overall speed of the flame. Thus, the
resulting maximum flame front propagation velocity of the modeled stoichiometric flame is
within 5% of the measured flame speed.
These results are important because they show that the model accurately captures the
flame propagation shape and trends and predicts the maximum flame front propagation velocity
well in 2D. These model results also capture the flame temperature trends well: the highest being
stoichiometric, then rich, followed by the lean case, which agrees with fundamental flame theory
(Turns, 2012). Additionally, the results show how small changes to the 2D model can result in
large changes to the predicted flame shapes and speeds. Most of these differences can be
attributed to the model being 2D and assuming a 2-step methane-air chemistry mechanism, but
these differences should be noted and taken into account as the model is transformed to 3D.
Experiments showed that a confined ignition at the closed end of the reactor resulted in
flame front propagation velocities approximately 50 times greater than an unconfined, open-end
ignition. Additionally, the closed-end flame had a very different shape than the open-end flame
as shown in Figure 4.5 and Figure 4.8 in Section 4.1. Since the confined, closed-end flame was
significantly faster than the open-end flame, buoyancy was essentially negligible, and the flame
looks more parabolic which agrees with observations made by other researchers (Clanet &
Searby, 1996; Ellis & Wheeler, 1928; Guenoche & Jouy, 1953).
As discussed in Chapter 5, modeling a closed-end ignition in the 12cm diameter reactor
in 2D is most accurate by modeling the relief hole on the closed end of the reactor. Results of
modeling a closed-end ignition with varying stoichiometry is shown in Figure 6.6-Figure 6.10
and Table 6.2 on pages 184-188. Comparing modeling results in Figure 6.6 to experimental
results shown in Figure 4.6 and Figure 4.7 of Section 4.1, the trends of flame acceleration match
experiments, but the rich flame travels faster than observed in experiments. This is due to the 2-
step methane air mechanism predicting faster conversion of methane to CO and CO instead of
2
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intermediate species such as OH and other radicals, leading to faster rich flames. Despite this
simplification, the maximum flame front propagation velocities predicted by the 2D model are
within 12% of the experiments. Additionally, the flame shapes predicted by the 2D model match
well with experimental images; the flame is the traditional “finger shape” and due to flame
stretching, the flame tears apart. Overall, the 2D model predicts the lean and stoichiometric
flame well, but overpredicts the speed of the rich flame. The model does a good job of predicting
flame acceleration and flame shape, but shows a significant flame slow-down near the open end
of the reactor. This slow down occurs in the last 25-35cm of the reactor, where there is only one
sensor so it is difficult to determine whether the slow down occurs experimentally. Also, using
high-speed imaging at 240fps only shows 1 or 2 frames near the open end which is not sufficient
to adequately resolve the change in propagation velocity during the last 25cm of the reactor.
Figure 6.2 Temperature contours of methane flame propagation for an open-end ignition with
varying stoichiometry at time, t=0.2s. Ignition location is 11cm from the open end. Simulation
time=0.2s. Time step = 0.1ms.CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing.
4
Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. No relief hole.
ign
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Figure 6.10 Temperature contours of methane flame propagation for a closed-end ignition with
varying stoichiometry at time, t = 25ms. Ignition location is 1.39cm from the open end.
Simulation time = 25ms. Time step = 0.01ms.CH = 9.5%. Body mesh size = 1mm, 0.25mm
4
edge sizing. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. Relief hole, H=1.2cm.
ign
6.1.2 Modeling an Obstacle Wall
As described in Section 2.6 and Section 2.3, obstacles can greatly accelerate flames and
in some cases, can transition a flame from a deflagration to a detonation. Therefore, it is
important to capture the effects of obstacles on methane gas deflagrations since methane gas
explosions in longwall coal mines can occur in working areas where equipment, miners, etc. are
located.
Experiments have shown flame acceleration across an obstacle wall made of 6.35mm
diameter spheres as shown in Chapter 4, Section 4.3. In the experiments, 6.35mm diameter solid
glass spheres were arranged in a wall geometry such that the flame could only pass through the
void space above the obstacle wall. The height of the walls is 7.62cm and the axial width of the
walls are 6.35mm. The obstacle walls were modeled in two difference ways as shown in Figure
6.11: a wall of spheres (which is best representative of experiments) and a smooth, solid,
rectangular wall. The sphere wall was made of 6.35mm diameter spheres and solid connections
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were made between the spheres to not allow for any flame propagation between the spheres and
also reduces meshing complexities. If the spheres were left with one point of contact this would
create a pinch point, which is difficult to mesh and would require many small triangle cells. To
compare to the sphere wall, a solid wall of H=7.62cm and W=6.25mm was created and both
walls were meshed with an edge sizing of 0.25mm to help resolve boundary layers forming on
the obstacles.
Results of comparing the sphere wall to the solid wall are shown in Figure 6.11, Figure
6.12, and Figure 6.13. As can be seen, as the flame approaches the wall there is a very slight
difference in flame shape and the turbulent intensity contours are different as well. In general,
the sharp edges of the solid wall tend to increase the local turbulence near the top of the wall due
to vortex shedding. However, because these geometries are small and thin, the flame front
location is unaffected by the slight changes in local turbulence across the obstacle (<1%
difference). Due to ease of meshing, researchers will continue using the solid wall geometry to
investigate the impact of the obstacle walls on methane flame propagation.
Figure 6.11 Temperature contours of the 2D 12cm diameter reactor model showing flame
propagation across an obstacle wall modeled as solid, connected spheres versus a straight, solid
rectangular wall. Obstacle: 6.35mm spheres arranged in a wall geometry and a solid, smooth
wall, H = 7.62cm, L = 6.25mm. Ignition location is 11cm from the open end (left). Simulation
Time = 0.1s. Time step = 0.1ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing.
4
Temperature = 294K, Pressure = 82kPa. E = 60mJ. No relief hole.
ign
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Figure 6.12 Turbulent intensity contours of the 2D 12cm diameter reactor model showing flame
propagation across an obstacle wall modeled as solid, connected spheres versus a straight, solid
rectangular wall. Obstacle: 6.35mm spheres arranged in a wall geometry and a solid, smooth
wall, H = 7.62cm, L = 6.25mm. Ignition location is 11cm from the open end (left). Simulation
Time = 0.1s. Time step = 0.1ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing.
4
Temperature = 294K, Pressure = 82kPa. E = 60mJ. No relief hole.
ign
Figure 6.13 2D 12cm diameter reactor results of investigating the impact of modeling the
obstacle wall on methane flame front location versus time for an open-end ignition. Obstacle:
6.35mm spheres arranged in a wall geometry and a solid, smooth wall, H = 7.62cm, L =
6.35mm. Ignition location is 11cm from the open end. Time step = 0.1ms. CH = 9.5% Body
4
mesh size = 1mm, 0.25mm edge sizing. Temperature = 293K, Pressure = 82kPa. SM E =
ign
60mJ. No relief hole.
Experimental results in Figure 4.24 and Figure 4.25 in Section 4.2.3 show that methane
flames accelerate across obstacle walls, but as the obstacle is moved further from ignition, the
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relative acceleration decreases. This trend was investigated using the 2D 12cm diameter
combustion model by modeling an obstacle wall, H = 7.62cm L = 6.35mm, at different locations
in the reactor, 37cm, 62cm, and 87cm from the open end. Results of modeling the obstacle wall
at difference locations is shown in Figure 6.14, Figure 6.15, and Figure 6.16. Results show that
an obstacle wall at 37cm results in the greatest acceleration across the obstacle, but the flame
arrives at the closed end slower compared to an obstacle wall at 62cm or 87cm. As can be seen,
as the obstacle wall is moved from 37cm from the open end to 62cm and 87cm, the relative
acceleration across the obstacle decreases. Additionally, Figure 6.16 shows how the modeled
flame passes over the obstacle; the flame tends to move in all directions, meaning both axially
and radially as it passes over the obstacle wall. These results show that the modeled flame shape
and trends across the obstacle match experiments, which is important to capture because the
mechanism for flame acceleration across an obstacle for an unconfined (open-end ignition) is
much different than a confined (closed-end ignition) which will be presented subsequently.
Figure 6.14 2D 12cm diameter reactor results of investigating the impact of obstacle wall
location on methane flame front location versus time for an open-end ignition. Obstacle: solid,
smooth wall, H = 7.62cm, L = 6.35mm. Ignition location is 11cm from the open end. Time step
= 0.1ms. CH = 9.5% Body mesh size = 1mm, 0.25mm edge sizing. Temperature = 293K,
4
Pressure = 82kPa. SM E = 60mJ. No relief hole.
ign
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Figure 6.15 2D 12cm diameter reactor results of investigating the impact of obstacle wall
location on methane flame front propagation velocity versus distance for an open-end ignition.
Obstacle: solid, smooth wall, H = 7.62cm, L = 6.35mm. Ignition location is 11cm from the open
end. Time step = 0.1ms. CH = 9.5% Body mesh size = 1mm, 0.25mm edge sizing. Temperature
4
= 293K, Pressure = 82kPa. SM E = 60mJ. No relief hole.
ign
Figure 6.16 Images of stoichiometric methane-air flame passing over a glass sphere wall,
H=7.62cm, L=12.35mm compared to 2D modeling results. Flame travels from left to right. CH
4
= 9.5%. Operating conditions 293K, 82kPa. E =60mJ. No relief hole modeled.
ign
Experiments of a closed-end ignition flame propagation over an obstacle wall was
presented in Figure 4.16 and Figure 4.17 in Section 4.2.1. Results showed that even a short
obstacle wall greatly accelerated the closed-end ignition flame across the obstacle wall.
Additionally, the method of flame acceleration past an obstacle wall for an open-end versus
closed-end ignition flame were different. As discussed, the open-end flame moves both radially
and axially across the obstacle wall. The closed-end flame passed over the wall, accelerating
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mainly in the axial direction, creating flow separation past the obstacle wall. This flow separation
is important because it forms eddies on the downstream side of the wall, trapping unburned gases
and increasing fluid motion, agreeing with observations made by other researchers (Chapman &
Wheeler, 1926) (Moen, Lee, Hjertager, Fuhre, & Eckhoff, 1982).
The experiments presented in Figure 4.16 were modeled and results are shown in Figure
6.17, Figure 6.18, and Figure 6.19. 2D modeling results show that as the flame approaches the
obstacle wall it is slowed down and then accelerated up to 88m/s across the wall. In the
experiments, the recorded flame front propagation velocity across the wall was 81m/s, which is
a 9% difference compared to the 2D model. Also the modeling results show that the shape of the
flame propagating across the wall matches the flow separation observed from experiments.
Turbulent intensity contours at 24ms show that there is more fluid motion downstream of the
wall as the flame passes over. Overall the 2D closed-end ignition model accurately captures the
flame acceleration across the wall both quantitatively and qualitatively.
Figure 6.17 2D 12cm diameter reactor results of investigating the impact of an obstacle wall on
methane flame front propagation velocity versus time for a closed-end ignition. Obstacle: wall H
= 3.81cm, L = 6.35mm located at 0.37m from the open end (1.13m from the closed end).
Ignition location is 1.39cm from the open end. Time step = 0.01ms. CH = 9.5% Body mesh size
4
= 1mm, 0.25mm edge sizing. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. Relief
ign
hole H = 1.2cm.
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Figure 6.18 Images of stoichiometric methane-air flame passing over a glass sphere wall, H =
3.81cm, L = 6.35mm compared to 2D modeling results. Flame travels from right to left. CH =
4
9.5%. Operating conditions 293K, 82kPa. E = 60mJ. Relief hole H = 1.2cm.
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Figure 6.19 Turbulent intensity contours of the 2D 12cm diameter reactor model showing flame
propagation across an obstacle wall for a closed-end ignition. Obstacle: wall H = 3.81cm, L =
6.35mm located at 37cm from the open end. Ignition location is 1.39cm from the open end.
Time step = 0.01ms. CH = 9.5% Body mesh size = 1mm, 0.25mm edge sizing. Temperature =
4
293K, Pressure = 82kPa. SM E = 60mJ. Relief hole H = 1.2cm.
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6.1.3 Modeling a Checkerboard Obstacle
After modeling the impact of an obstacle wall on methane flame enhancement,
researchers also modeled a checkerboard obstacle. The main purpose of the checkerboard
obstacle was to isolate and understand the impact of porosity on flame enhancement. This is
important because in a real mine explosion the flame can interact with piles of rock rubble that
have varying porosities. Similar to the obstacle wall, the checkerboard obstacles, as described in
Chapter 4, also resulted in flame acceleration across the obstacle, creating local fluid motion near
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the checkerboard obstacle. To model this in 2D, researchers modeled the obstacle as nine (9)
solid spheres with a diameter of 6.35mm in the vertical direction (this equates to the maximum
amount of spheres in the y-direction as used in the experiments experiments). The checkerboard
obstacle was modeled at three different locations, 37cm, 62cm, and 87cm from the open end.
Results are shown in Figure 6.20 through Figure 6.28 and the general trends observed in the
obstacle wall experiments were captured with the model: the flame passing over the
checkerboard obstacle located 37cm from the open end reached the closed end of the reactor
before those located at 62cm and 87cm. These flame propagation trends are similar to those
observed with moving the non-reacting metal cage and obstacle wall at different locations in the
reactor as shown in Figure 4.24, Section 4.2.3. As expected from the cage and checkerboard
obstacles, the obstacles induce movement in the nearby gases resulting in slight upstream
turbulence as shown in Figure 6.22. This is important to capture because it shows that discretely
modeling the objects can improve local turbulence prediction and thus, more accurate flame
propagation trends. This shall be explored further in the following section as well as modeling
the porous medium in the experimental box.
Figure 6.20 2D 12cm diameter reactor results of investigating the impact of checkerboard
obstacle location on methane flame front location versus time for an open-end ignition. Obstacle:
6.35mm spheres in a checkerboard pattern (9 total in the y direction) located at 37, 62, and 87cm
from the open end. Ignition location is 11cm from the open end. Time step = 0.1ms. CH = 9.5%
4
Body mesh size = 1mm, 0.25mm edge sizing. Temperature = 293K, Pressure = 82kPa. SM E =
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60mJ. No relief hole.
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Figure 6.28 Temperature contours of the 2D 12cm diameter reactor model showing flame
propagation across a checkerboard obstacle (77% porosity) for an open-end ignition. Obstacle:
6.35mm spheres in a checkerboard pattern (9 total in the y direction) located at 37, 62, and 87cm
from the open end. Ignition location is 11cm from the open end. Simulation Time = 1.5s. Time
step = 0.1ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing. Temperature = 294K,
4
Pressure = 82kPa. E = 60mJ. No relief hole.
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6.1.4 Modeling a Simulated Gob Bed
Previous experiments by Fig (2019) have shown flame acceleration across a pile of rock
rubble as described and shown in Figure 4.1 and Figure 4.2 on page 62 and page 63. However,
the main purpose of this research is to understand what property of the rock pile has the largest
impact on methane flame acceleration. As previously shown, the obstacle location, void spacing,
and porosity can all impact methane flame acceleration. Also, closed-end ignition experiments
with a simulated gob bed have been presented in Chapter 4 and results in Figure 4.28, Figure
4.29, and Table 4.1 (pages 82-84) show that the flame accelerates across the simulated gob bed
made of 1cm diameter spheres, creating a turbulent boundary layer above and slow burning
down into the gob. An example of the simulated gob bed used in experiments is reproduced in
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Figure 6.29. To replicate these experiments in the 2D model, a comparison was made modeling
the simulated gob bed as solid spheres versus a solid rectangle, H = 2cm, L = 30cm located 44cm
from the open end as shown in Figure 6.30. In the experiments, the spheres were aligned next to
each other, but in the model, the spheres were spaced 0.2cm apart to allow for at least 2 cells
between each sphere to help model the flame propagation down into the simulated gob bed.
Figure 6.29 Images of glass spheres and example of simulated gob bed.
2D modeling results are shown in Figure 6.30 through Figure 6.34. Modeling results
accurately capture the flame acceleration across the obstacle, but overestimates the maximum
flame front propagation velocity by 25%. Some of this overprediction is due to the fact that in
the experiments, the flame burns above the simulated gob bed as well as down into the gob bed.
Because the model is in 2D, the void spacing between the spheres (circles) is not truly indicative
of the void spaces in the experimental simulated gob and thus, the flame does not burn down into
the gob as quickly as the experiments. Modeling the simulated gob bed as a rectangle gob gives a
good approximation of the acceleration, but produces much higher turbulence in the turbulent
boundary layer above the obstacle than the modeled sphere gob (Figure 6.34). Overall, 2D
modeling of flame propagation past a simulated gob bed matches experimental trends, captures
the local fluid motion within and above the gob, and burning down into the modeled gob. It is
important that the model captures the movement of nearby gases and burning down into the gob
because the additional burning within the gob increases local temperatures and pressures, which
feeds back to the main flame brush, accelerating combustion rates. This flame acceleration
phenomena has been observed by other researchers who found that the properties of the “bead
layer” can impact the main flame brush (Babkin, Korzhavin, & Bunev, 1991) (Howell, Hall, &
Ellzey, 1996). These results also indicate that modeling a simulated gob will require discretely
modeling of the obstacles, which shall be revisited in later sections..
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Figure 6.30 2D 12cm diameter reactor results of investigating the impact of an obstacle on
methane flame front location versus time for a closed-end ignition. Obstacle: a solid rectangle
H=2cm L=30cm located 44cm from the open end, and a 1cm diameter sphere gob H = 2 spheres
L=30cm located 44cm from the open end. Ignition location is 1.39cm from the open end. Time
step = 0.01ms. CH = 9.5% Body mesh size = 1mm, 0.25mm edge sizing. Temperature = 293K,
4
Pressure = 82kPa. SM E = 60mJ. Relief hold H=1.2cm.
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Figure 6.31 Temperature contours of the 2D 12cm diameter reactor model showing flame
propagation across an obstacle for a closed-end ignition. Obstacle: a solid rectangle H=2cm
L=30cm located 44cm from the open end, and a 1cm diameter sphere gob H = 2 spheres L=30cm
located 44cm from the open end. Ignition location is 1.39cm from the open end. Simulation Time
= 10ms. Time step = 0.01ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing.
4
Temperature = 294K, Pressure = 82kPa. E = 60mJ. No relief hole.
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Figure 6.32 Temperature contours of the 2D 12cm diameter reactor model showing flame
propagation across an obstacle for a closed-end ignition. Obstacle: a solid rectangle H=2cm
L=30cm located 44cm from the open end, and a 1cm diameter sphere gob H = 2 spheres L=30cm
located 44cm from the open end. Ignition location is 1.39cm from the open end. Simulation Time
= 16ms. Time step = 0.01ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing.
4
Temperature = 294K, Pressure = 82kPa. E = 60mJ. No relief hole.
ign
Figure 6.33 Temperature contours of the 2D 12cm diameter reactor model showing flame
propagation across an obstacle for a closed-end ignition. Obstacle: a solid rectangle H=2cm
L=30cm located 44cm from the open end, and a 1cm diameter sphere gob H = 2 spheres L=30cm
located 44cm from the open end. Ignition location is 1.39cm from the open end. Simulation Time
= 24ms. Time step = 0.01ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing.
4
Temperature = 294K, Pressure = 82kPa. E = 60mJ. No relief hole.
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Figure 6.34 Turbulent intensity contours of the 2D 12cm diameter reactor model showing flame
propagation across an obstacle for a closed-end ignition. Obstacle: a solid rectangle H=2cm
L=30cm located 44cm from the open end, and a 1cm diameter sphere gob H = 2 spheres L=30cm
located 44cm from the open end. Ignition location is 1.39cm from the open end. Simulation Time
= 16ms. Time step = 0.01ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing.
4
Temperature = 294K, Pressure = 82kPa. E = 60mJ. No relief hole.
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6.1.5 In-gob Modeling
The main purpose of the in-gob ignition experiments presented in Section 4.3 was to
understand how a flame propagates between obstacles. This is important for longwall coal
mining because EGZs can exist within the gob and have the potential to be ignited by rock-on-
rock friction (Brune, 2014). In order to model the in-gob ignition experiments shown in Figure
4.39, the checkerboard geometries were modeled as spheres, granite rock, and hexagons centered
on a vertical line 7.62cm on either side of the spark location 25cm from the open end. The
spheres and hexagons were modeled with a hydraulic diameter of 6.35mm and a no slip,
adiabatic boundary condition on the surface. The granite pebbles were modeled as irregular
shapes as shown in Figure 6.35 with no additional surface roughness and a no slip boundary
condition. The diameter of the circle enclosed inside the rock is 4.6mm and the average length,
L, of the irregularities is 1.7 ± 0.3mm, bringing the size of the irregular granite rock to within the
size of the spheres and hexagons. Also to note, these simulations were run using the EM model
and were initialized assuming zero-flow laminar flame expansion, k = 0.001 m2/s2 and ω = 0.001
1/s. These same simulations were run using the SM, but because the SM overpredicts the kernel
expansion, the resulting flame shapes were unrealistic. Future work must be done to rerun these
simulations with the SM and appropriate turbulence initialization parameters.
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Figure 6.35 Image of irregularly shaped granite rock (left) and glass spheres (right) used for
comparison of in-gob ignition models. Sphere diameter = 6.35mm. Thermal properties of glass
were used for direct comparison between all cases. Note: not to scale.
Figure 6.36 Temperature contours of the 2D 12cm diameter reactor model showing flame
propagation during an in-gob ignition. Obstacle: spheres with diameter 6.35mm, rock with an
average diameter of 4.6mm, and hexagons with diameter 6.35mm. Obstacles located 15cm apart
on center with ignition. Ignition location is 25cm from the open end. Simulation Time = 0.11s.
Time step = 0.01ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing. Temperature =
4
294K, Pressure = 82kPa. EM E = 5mJ. No relief hole.
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Results of modeling the in-gob ignition experiments in 2D are shown in Figure 6.36,
Figure 6.37, and Figure 6.38. As can be seen in these figures, at the same time, the rock and
hexagons produced significantly more turbulence in the local gases than the spheres. Although
this only shows a single time step, this was confirmed at several time steps as the flame was
passing through the obstacles. Also interestingly, the rock and hexagons resulted in significantly
more CO production than the spheres which indicates there was incomplete combustion. It is
also likely the increased CO production is due to the 2-step chemistry mechanism. To investigate
this further would require a more complex chemistry mechanism capable of predicting the
intermediate species and radicals produced by the initial reaction of methane and air. This is not
within the scope of this research, but even these preliminary results show that modeling the gob
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as different shapes can impact methane flame propagation which will be important when
modeling a large-scale ignition from within the gob.
Figure 6.37 Turbulent intensity contours of the 2D 12cm diameter reactor model showing flame
propagation during an in-gob ignition. Obstacle: spheres with diameter 6.35mm, rock with an
average diameter of 4.6mm, and hexagons with diameter 6.35mm. Obstacles located 15cm apart
on center with ignition. Ignition location is 25cm from the open end. Simulation Time = 0.11s.
Time step = 0.01ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing. Temperature =
4
294K, Pressure = 82kPa. EM E = 5mJ. No relief hole.
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Figure 6.38 CO mass fraction contours of the 2D 12cm diameter reactor model showing flame
propagation during an in-gob ignition. Obstacle: spheres with diameter 6.35mm, rock with an
average diameter of 4.6mm, and hexagons with diameter 6.35mm. Obstacles located 15cm apart
on center with ignition. Ignition location is 25cm from the open end. Simulation Time = 0.11s.
Time step = 0.01ms. CH = 9.5%. Body mesh size = 1mm, 0.25mm edge sizing. Temperature =
4
294K, Pressure = 82kPa. EM E = 5mJ. No relief hole.
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6.1.6 Ignition Location Modeling
It is often thought that a faster flame means greater pressure generation, but the ignition
location experiments presented in Section 4.4 helped show that this is not always the case. For
example, an ignition in the center of the reactor resulted in greater pressure generation than a
closed-end ignition, but slower flame front propagation velocities. This is important to capture in
the CFD model because methane gas explosions can occur in a variety of places in a mine with
varying degrees of confinement.
Therefore, 2D models were run exploring the impact of ignition location on methane
flame front propagation. To directly compare the experimental results shown in Figure 4.43,
Section 4.4 to CFD results, the maximum flame front propagation velocity towards the closed
end of the reactor of each experiment (i.e. ignition in Port 1, ignition in Port 2, ignition in Port 3)
was normalized to the maximum flame front propagation velocity of ignition in Port 1. For
example, the maximum flame front propagation velocity towards the closed end in Port 1 was
148cm/s, thus 148cm/s divided by 148cm/s is 1. For ignition in Port 2, the maximum flame front
propagation velocity towards the closed end was 416cm/s; dividing 416cm/s by 148cm/s is 2.8.
And so-on for Port 3. The normalized experimental data was then compared to the normalized
CFD data, summarized in Table 6.3. The normalized data further demonstrates that as ignition is
moved further from the open end, the flame front velocity increases. The differences between the
experimental and numerical data from ignition in Port 2 and Port 3 can be attributed to the fact
that acoustic effects have not yet been considered in the model since the flame acceleration in
Port 2 and 3 was mainly due to acoustic-flame interactions. Since the acoustic model has not
been implemented, there are qualitative differences in flame shape and oscillation as shown in
Figure 6.39. As can be seen in this figure, in the experiments the flame tends to move forward
and then be pushed backwards (t=0.07s to t=0.08s) versus the model predicting the flame
continues towards the closed end. Overall, the model predicts faster flames propagations towards
the open end and slower towards the closed end, but will require an acoustic model to capture the
impact of pressure oscillations on flame front stretching observed in experiments.
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Figure 6.39 Comparison of numerical to experimental methane flame front propagation of
ignition in port 3 (75 cm from the open end). CH = 9.5%. Operating conditions 294K, 82kPa.
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EM E = 5mJ. One (1) relief hole.
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Table 6.3 Comparison of normalized experimental flame front propagation velocities at the
closed end of the quartz reactor compared to maximum flame front propagation velocities
predicted by the 2D model. CH = 9.5%. Body mesh size = 0.001m, 0.25mm edge sizing.
4
Temperature = 293K, Pressure = 82kPa.
Normalized Flame Front Propagation Velocity
Port 2D Model Experiments
1 1 1.0
2 2.1 2.8
3 2.8 3.6
6.2 3D 12cm Diameter Quartz Reactor Modeling Results
Although the 2D 12cm diameter reactor model successfully captured methane flame
propagation trends, maximum speeds, and interaction with obstacles, turbulence is inherently a
3D process. Therefore, this research also developed a 3D model of the 12cm diameter. As
discussed in Chapter 5, a 2mm body mesh for the 3D 12cm diameter reactor is sufficient in
predicting the flame front location and capturing the local flow velocities as well. The 3D, 12cm
diameter reactor model uses similar settings to the 2D model, summarized in Section 5.1, except
for the following changes:
• 2 levels of mesh adaption on the gradient of temperature every 2 time steps
• Residuals set to 10-4, dropping at least 3 orders or magnitude
• Closed-end ignition: k = 1.5m2/s2 and ω = 250 1/s
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The main difference between the 2D and 3D model is that the 3D model does not include
modeling the relief hole on the closed end of the reactor. A comparison of the 2D model with
and without a relief hole versus the 3D model without a relief hole is shown in Figure 5.47,
Section 5.1. The relief hole was not modeled in 3D because modeling the relief hole resulted in
reverse flow in this region due to the pressure oscillations creating low pressure zones.
To begin comparing experimental trends with 3D modeling results, a model was
developed to capture the observed phenomena of a flame passing over an obstacle wall.
Experimental results show that an obstacle wall in the path of the flame will tend to increase the
velocity of the flame. Upstream of the obstacle the flame may be slightly retarded by the
pressure resistance felt by the obstacle. Downstream of the obstacle, the flame is accelerated by a
combination of the reduced void spacing and a large eddy of unburned gas trapped downstream
of the obstacle that feeds the flame.
Figure 6.40 3D 12cm diameter reactor results of investigating the impact of an obstacle on
methane flame front location versus time for a closed-end ignition. Obstacle: a wall H=6cm
L=2cm located 1.13m from the open end and a wall H=6cm L=2cm located 37cm from the open
end. Ignition location is 11cm from the closed end. Time step = 0.01ms. CH = 9.5% Body mesh
4
size = 2mm. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ. No relief hole.
ign
To model this in 3D, a solid obstacle wall with height H = 6cm and L = 2cm was located
37cm from the open end and then moved to 1.13m from the open end. Flame front propagation
results as a function of time are presented in Figure 6.40 and results indicate that an obstacle
closer to ignition source (0.37m) accelerates the flame over the entire length of the reactor.
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Results also show that when the obstacle wall is further from the ignition source (1.13m), the
pressure resistance from the obstacle slightly retards the flame, but once the flame passes over
the obstacle it is accelerated.
2D model results are presented in Figure 6.41, Figure 6.42, Figure 6.43, Figure 6.44, and
Figure 6.45 and predicts the flame shape and combustion acceleration mechanisms well,
referring to flow over a step and the fluid motion that is formed behind the obstacle. This is
important for model development as researchers continue to validate larger models in the
transition to a mine-scale model which will be discussed in Chapter 7. Additionally these figures
show that as time continues, the flame accelerates past the obstacle similar to flow over a step as
shown in Figure 6.46. This is important because it forms eddies on the downstream side of the
wall, which increases temperatures and fluid motion promoting flame acceleration.
Figure 6.41 Temperature contours of the 2D 12cm diameter reactor model investigating the
impact of an obstacle on methane flame front location versus time for a closed-end ignition.
Obstacle: a wall H=6cm L=2cm located 1.13m from the open end and a wall H=6cm L=2cm
located 37cm from the open end. Ignition location is 11cm from the closed end. Simulation Time
= 6ms. Time step = 0.01ms. CH = 9.5%. Body mesh size = 2mm. Temperature = 293K,
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Pressure = 82kPa. E = 60mJ. No relief hole.
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6.3 Experimental Box Modeling Results
As discussed in Chapter 3, Section 3.1.2, the main goal of the experimental box was to
understand the impact of reactor shape on methane flame propagation and interaction with a
porous medium. Experimental results showed that, similar to the cylindrical reactors, ignitions
from a more confined space results in much faster flame velocities than an unconfined space.
Additionally, images from the flame propagation in the box reactor showed residual burning of
methane-air mixture in the corners of the box (Section 4.6). Finally, experimental results with a
porous medium showed flame acceleration across the porous medium and the flame tended to
propagate faster through the porous medium than in the open spaces inside the reactor. These
results are important to capture in the 2D and 3D box models because in a real mine explosion,
the propagation direction will be unknown and so developing a validated, robust model will be
important for understanding flame propagation at the mine-scale.
6.3.1 2D Modeling Results
As discussed in Chapter 5, in 2D, the experimental box is modeled with a 7cm relief and
a mesh size of 1mm with 0.25mm edge sizing on walls and obstacles and uses the following
turbulence parameter settings: open-end ignition k = 0.001m2/s2 and ω = 0.1 1/s, closed-end
ignition k = 1.5m2/s2 and ω = 25 1/s.
In order to accurately model flame propagation across a porous medium or gob, it is first
important to understand how previous researchers have modeled the gob. Many of the
researchers using ANSYS Fluent to perform ventilation studies on the air and methane
distribution in a longwall coal mine typically model the gob as a Darcy flow porous medium
with varying permeabilities and resistances to account for the different levels of gob compaction
(Gilmore, et al., 2016; Ren & Edwards, 2000; Tanguturi, Balusu, & Bongani, 2017; Yuan,
Smith, & Brune, 2000). However, modeling the gob as a porous media with laminar flow
assumes Darcy flow where there is a linear relationship between flow through the porous media
and pressure drop (Whitaker, 1986). Evidence has shown that EGZs are likely to exist near the
gob fringes where the porosity can be almost 40% (Gilmore, et al., 2016; Marts, et al., 2014) and
assuming a laminar Darcy flow may not account for the differences in void space and rock
size/distribution in these areas. As this research has previously shown, the void spacings,
porosity, and location of voids can have a significant impact on the resulting methane gas
deflagration. This research has also shown that modeling a simulated gob bed requires discrete
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modeling of the spheres instead of a solid rectangle (Section 6.1.4). Therefore, a study was
performed to investigate whether the Darcy flow assumption is valid and if so, under what
conditions. To do this, the 2D experimental box model was first validated for ignition without a
porous medium and then the model was used to investigate how to best represent the porous
medium.
Results of an open-end ignition without a simulated gob shows that the flame propagates
freely in all directions in the experimental box (Figure 6.47). 2-D combustion model results
agree with this trend, but at later times slightly overpredicts the methane flame speed. This is to
be expected since the model is in 2-D and assumes a 2-step methane-air mechanism. Also, as
previously mentioned these slight differences may also be attributed to the spark kernel diameter
and/or the turbulence initialization parameters. However, in general, the model is able to
accurately predict flame trends and even though it is still in 2D, it is capable of predicting flame
front wrinkling observed in experiments.
Figure 6.47 Temperature contours of the experimental box setup compared to the 2-D
combustion model for an open ignition with no gob. CH = 9.5%. Body mesh size = 1mm.
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Temperature = 294K, Pressure = 82kPa. SM E = 60mJ.
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Figure 6.48 Temperature contours of the box setup comparing modeling the gob as a Darcy flow
porous media with 66% porosity (left), porous media with opening 66% porosity (center), versus
modeling the gob as discrete spheres with 66% porosity (right). Center ignition. Simulation time
= 15ms. Time step = 0.01ms. CH = 9.5%. Body mesh size = 1mm, 0.5mm edge sizing.
4
Temperature = 294K, Pressure = 82kPa. E = 60mJ.
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After demonstrating model performance without a gob, Figure 6.48 shows the
comparison of modeling the gob as a Darcy flow porous media with 66% porosity (left), with a
small opening and 66% porosity (center), to modeling the gob as discrete spheres (D=0.025m)
with a porosity of 66% (right). As can be seen, ignition within the Darcy porous media with a
porosity of 66% did not allow the methane flame to propagate even when a small opening is
made to help allow for flame expansion (center image). Additionally, porosities between 25-90%
have been tested, permeabilities between 1.5x10-3m2 and 4.7x10-11m2 have been tested, and spark
energies between 60mJ and 1kJ have been tested and also show no flame propagation. However,
when the porous media has a 100% porosity, meaning all fluid space, the flame is able to
propagate. This condition, however, is unrealistic for a longwall coal mine environment where
the porosities typically range between 14-40%. Also to note, the flame propagation through the
100% porous media does not take into account any void spacing and so the flame front is very
smooth compared to modeling the gob discretely as shown on the right of Figure 6.48. This is
important because flame front stretching can increase combustion rates thereby increasing flame
speed and overpressure.
Results of a closed-end ignition show that the flame travels much faster through the
simulated gob than in the open spaces (Figure 6.49). This is because the pressure waves from the
confined ignition are enough to disturb the upstream unburned gases in the gob area. This
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increased turbulence enhances mixing and transport of unburned mixture to the flame front, as
well as increases the flame surface area; thereby increasing combustion rates. The combustion
model captures this well, but overpredicts the speed of the flame as seen in the sequence of
images in Figure 6.49. This overprediction is mainly due to the fact that the model is still in 2D
and the initialization of turbulence results in an overprediction of flame speed since the model is
confined to two dimensions. Despite these differences, the 2D model performs fairly well at
capturing the general flame dynamics.
Figure 6.49 Temperature contours of the experimental box setup compared to the 2-D
combustion model for a closed ignition with a gob. Sphere diameter = 0.025m, porosity = 65.9%.
Time step = 0.01ms.CH = 9.5%. Body mesh size = 1mm, 0.5mm edge sizing. Temperature =
4
294K, Pressure = 82kPa. SM E = 60mJ.
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After determining that to accurately model methane flame propagation through a gob
requires modeling the rock discretely, a study was performed to determine the impact of discrete
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object shape on methane flame propagation through a simulated gob. The shapes investigated are
detailed in Table 6.4; circles, hexagons, and squares were compared and sizes were made to
match the same porous media bed porosity of 66%. Interestingly though, matching the porosity
resulted in similar sizes to the hydraulic diameter, which is typically used in fluid mechanics to
scale objects geometrically.
Table 6.4 Table summarizing the discrete objects compared in this study including the
size/number of the shapes, the porosity, and the index of sphericity. *Calculated based on
Ionescu-Tirgoviste et al. 2015 as the ratio of the perimeter to hydraulic diameter, divided by π
(Ionescu-Tirgoviste, et al., 2015).
Object Shape Circle Hexagon Square
Diameter/Side Length (m) 0.025 0.014 0.022
Hydraulic Diameter (m) 0.025 0.024 0.022
Number of Objects 42 42 42
Bed Porosity (%) 66 66 66
Index of Sphericity* 1 1.1 1.2
Figure 6.50, Figure 6.51, Figure 6.52, and Table 6.5 show results comparing how the
shape of the discrete object can affect methane flame propagation through the gob. In all cases,
the porosity of the discrete shape porous medium was 66%. As can be seen in Table 6.5, in all
cases, the average flame front propagation velocity with a discretely modeled gob is faster than a
closed-end ignition with a gob, matching experimental observations. Additionally, the shape of
the discrete object can significantly affect methane flame propagation; the squares produced the
fastest flame and most tortuous flame path, followed by the hexagons and the circles (increased
flame speeds with increasing index of sphericity). The squares also produced the highest
turbulent intensity ahead of the flame and the most eddies. This is important because higher
turbulent intensities mean there are larger fluctuations in the average flow, which can increase
unburned gas velocities and enhance methane flame propagation. The eddies produced by the
shapes is important because one major concern in longwall coal mining, are dead zones where
methane and air mix and accumulate (i.e. an EGZ). As can be seen, the square gob produced
much more eddies, which is due to the sharp corners of the shape disrupting the boundary layer
resulting in vortex shedding. This is important because typical rock found down in coal mines
may have sharp edges and sphericity not equal to 1. Thus far, results indicate that modeling the
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Table 6.5 Table summarizing the average methane flame front propagation velocity from the box
experiments compared to 2D modeling results with and without a simulated gob for a confined,
closed-end ignition (ignition in the top-right corner of the experimental box). CH = 9.5%.
4
Temperature = 293K, Pressure = 82kPa.
2D Model Results Experiments
Average Flame Simulated Gob Average Flame
Simulated Gob
Front Propagation (Porous Medium) Front Propagation
Shape
Velocity (m/s) Conditions Velocity (m/s)
None 26 No Gob 7.7 ± 1
Sphere Gob 44 Gob 12 ± 4
Hexagon Gob 54
Square Gob 68
The main advantage of CFD modeling is the ability to gain a better understanding of
methane flame interaction with the gob. Thus, in addition to investigating the average velocity of
the methane flame front propagation through the discretely modeled gob, this research also
investigated methane flame propagation in the open areas around the discretely modeled gob. To
do this, horizontal and vertical seeded lines were taken as shown in Figure 6.53 and results of
tracking the flame front location are presented in Figure 6.64 and Figure 6.65. As shown, in all
cases, the discretely modeled gob enhanced flame propagation in both the vertical and horizontal
directions around the gob. Complimentary to previous results, the squares had the fastest flame
propagation in the open spaces, followed by the hexagons, and finally the circles. These results
are important because they show that the gob can impact flame propagation in the open spaces
around the gob which is important for longwall coal mining because it shows that an ignition
near or around the gob may be impacted by the gob or nearby obstacles. This is also important
for future modeling of the gob because it helps to demonstrate how the discrete object used to
represent the gob area can impact flame propagation through and around the gob.
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Figure 6.55 2D box model results for a closed-end ignition investigating the impact of gob shape
on methane flame propagation in the ‘y’-vertical direction away from ignition. Simulated gob
with 66% porosity modeled as discrete circles (dashed green line), discrete hexagons (dotted blue
line), and discrete squares (dash-dot red line). Time step = 0.01ms. Ignition in the top-right. CH
4
= 9.5%. Body mesh size = 1mm, 0.5mm edge sizing. Temperature = 293K, Pressure = 82kPa.
SM E = 60mJ.
ign
In a typical laminar methane flame, the quenching distance of the flame can be as small
as 1-2mm depending on the ambient conditions, however, a turbulent flame has a much smaller
quenching distance. A concern in longwall coal mining is whether or not an ignition deep within
the gob can propagate towards the longwall face. Thus, researchers used the 2D CFD,
combustion model to investigate the smallest possible distance between objects that allowed for
flame propagation. Researchers investigated separation distances of 10, 5, and 1mm as shown in
Figure 6.56. It is important to note that the mesh in-between the obstacles had at least 2 cells and
in many cases 3-4 cells. Results show that a more turbulent flame propagation from a confined
space can propagate through much smaller void space than a typical laminar flame. This is
important because it is typically assumed that in a highly compacted area the flame cannot travel
from deep within the gob towards the face. However, results indicate that a highly turbulent
flame can propagate through small cracks less than a millimeter in size. Although these results
agree with turbulent flame theory, future work must be done to confirm these results are
physically accurate which will require future modeling of more complex chemistry mechanisms
as well as translation of the model to 3D. Also, the boundary conditions on the obstacles were
adiabatic, assuming no heat loss to the obstacle. Additional future work includes investigating
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the assumption of an adiabatic boundary condition because flame quenching can occur due to
heat loss to a solid.
Figure 6.56 Temperature contours of methane flame propagation for closed end ignition across a
simulated gob consisting of squares with spacing of 10, 5, and 1mm. Simulation Time = 8.5ms.
Time step = 0.01ms. Ignition in the top-right. CH = 9.5%. Body mesh size = 1mm, 0.5mm edge
4
sizing. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ.
ign
In Figure 6.50, the methane flame had some room to propagate around the gob as well as
through the gob. Although the information from these types of simulations are important for
understanding flame propagation in and around the gob, it does not fully explain the entire
impact of shape on methane flame propagation. Therefore, a study was performed where the
entire box model was filled with discrete objects: circles, hexagons, and squares with the same
dimensions as shown in Table 6.4. Results of this study are shown in Figure 6.57, Figure 6.58,
Figure 6.59, and Figure 6.60. As expected, the square gob resulted in the fastest flame speeds
and turbulent intensities compared to the circles and hexagons.
Additionally, the square gob produces CO at a much faster rate than the hexagon and
circle gob, but after the flame has exited the reactor the amount of CO decays to almost the same
value for all cases. This is important because the model predicts a larger release of CO at a faster
rate for the square gob, however this is most likely an artifact of the methane-air 2-step
chemistry mechanism as shown in Table 5.1, Equation (5.1), and Equation (5.2) on page 109.
Note that in these equations, the methane and oxygen react to form CO and then the second
reaction is the reaction of CO with O to form CO . However, in a real situation, after methane
2 2
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reacts with oxygen there would be many intermediate species such as OH and other radicals. The
reaction of the OH radical with CO to form CO is a much faster process than the reaction of CO
2
and O to form CO . Although these results show there may be a trend of gob shape to CO
2 2
production, this must be reevaluated with more complex chemistry mechanisms that include
more intermediate species such as OH. Future recommended work includes investigating
different methane-air 2-step mechanisms as well as 13-step and full GRI methane air
mechanisms and repeating these experiments/modeling.
These results are important because they demonstrate that shape of the object can have a
large impact on methane gas combustion. This is extremely important for building the coupled,
mine-scale CFD combustion model because it shows that gob shape will be important in helping
predict the severity of the explosion. These results may also help investigative teams better
understand the heat damage or CO concentration in some of these large-scale explosions, leading
to better explosion prediction.
Figure 6.57 Temperature contours of methane flame propagation for closed end ignition across a
simulated gob modeled as discrete circles (left), discrete hexagons (center), and discrete squares
(right). Ignition in the top-right. Simulation Time = 4.5ms. Time step = 0.01ms.CH = 9.5%.
4
Body mesh size = 1mm, 0.5mm edge sizing. Temperature = 293K, Pressure = 82kPa. SM E =
ign
60mJ.
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Figure 6.60 Total moles of CO over time of methane flame propagation for a closed end ignition
2
across a simulated gob modeled as discrete circles (green dashed line), discrete hexagons (blue
dotted line), and discrete squares (red dash-dot line). Ignition in the top-right of the box. Time
step = 0.01ms.CH = 9.5%. Body mesh size = 1mm, 0.5mm edge sizing. Temperature = 293K,
4
Pressure = 82kPa. SM E = 60mJ.
ign
6.3.2 3D Modeling Results
The 3D, 12cm diameter reactor model uses the same ANSYS Fluent (v 17.2) as described
in Section 5.1 except for the following settings:
• Continuity/velocity residuals set to 10-4, Energy/turbulent 10-6
• 3 levels of mesh adaption on the gradient of temperature every 2 time steps
The 3D model the continuity and velocity residuals are set to 10-4 for model stability, but the
mesh adaption on the temperature gradient has been increased to 3 levels every 2 time steps.
These changes have been noted to help convergence and model predicted flame front location on
a coarse grid (5mm or 2.5mm) as discussed and shown in Chapter 5, Section 5.2.2 and Section
5.2.3.
The first experiment that was modeled was an open-end ignition without a simulated gob
as shown in Figure 4.53 on page 101. In the experiments, it was observed that the flame moved
in all directions and preferentially away from the relief opening. This was modeled in 2D and
compared to experiments in Figure 6.47 (page 219), concluding that the 2D model accurately
captured the flame propagation at early stages, but overestimated the flame progression later in
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development. Figure 6.61, Figure 6.63, Figure 6.64, Figure 6.65, and Figure 6.66 (pages 233-
236) show the 3D modeling results compared to the 2D model and experiments for an open-end
ignition. 3D results show similar flame propagation trends compared to the 2D model; the 3D
model predicts the flame propagation in all directions well, but compared to the 2D model the
3D flame propagating towards the closed end moves faster than towards the walls.
In general, the 3D model captures the early stages of flame development well, from t = 0s
to t = 0.15s, but at t = 0.20s the 3D flame tends to move faster than the 2D model and
experiments. Also, after t = 0.20s, the 3D model does not show any significant flame instabilities
along the flame front, which has been observed in experiments and captured in the 2D model.
This is likely due to the fact that the 3D model uses gradient adaption on temperature to resolve
the flame front location on a coarse, 2.5mm mesh; this method predicts the flame front location
well, but as shown in Chapter 5, Table 5.14 and Table 5.15 on page 165, temperature and the
flame front are resolved well, but the fluid velocities are not resolved as well. This is important
because in Chapter 2 it was shown that the fluid velocities change through a wrinkled flame front
(Figure 2.3 on page 11) and that hydrodynamic and thermo-diffusive instabilities are what can
lead to wrinkled flame fronts. It was concluded that the lack of flame front wrinkling in the 3D
model was due to the fact that the 3D model does not fully resolve the fluid velocities coupled
with the simplified chemistry mechanism not perfectly resolving the diffusive effects of species.
Overall, the 3D model does a good job of capturing the flame trends and flame shape despite the
coarse mesh and simplified chemistry mechanism.
Experiments of a closed-end ignition without a gob was shown in Figure 4.55 (page 102)
and results indicated a significantly faster flame than the open-end ignition. Figure 6.67, Figure
6.68, Figure 6.69, Figure 6.70, and Figure 6.71 (pages 236-238) compare experimental images to
2D and 3D modeling results of a closed-end ignition without a gob. Results show that at early
times, t = 2-6.3ms, the models predict the flame kernel expansion and propagation well. Due to
the overestimation of initial flame kernel expansion by the spark model (discussed in Chapter 5,
Section 5.1.2) the 2D and 3D model times are an order of magnitude different than the
experiments, but the acceleration of the flame at early times is estimated very well by the
models. Good estimation of the acceleration of a closed-end flame has also been observed in the
2D and 3D 12cm diameter reactor models, which also showed flame slow down near the reactor
outlet. In the 3D box model, after 6.3ms, the flame front location is underpredicted compared to
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experiments (Figure 6.70, page 238), which agrees with observations made in the 2D and 3D
12cm diameter reactor models. However, the shape of the flame in Figure 6.71 (page 238) at
time t = 12ms matches that observed in experiments and because the flame is resolved in the 3rd
dimension, researchers can see how the flame tends towards the relief which is near the bottom
of the box.
Overall, the 2D and 3D models of a closed-end ignition inside the experimental box
capture general flame propagation shapes and trends as well as acceleration rates at early stages
in the flame development. These results are important because as complexity, such as obstacles,
is added to the models it is important that general flame trends and propagation velocities are
captured in these simple cases. Also these results help show that as model volume increases, the
ability to resolve all flow quantities reduces and certain flame shapes or trends may be lost when
using more coarse meshes to reduce computational time.
Figure 6.61 Temperature contours of the experimental box setup compared to the 2D and 3D
combustion model for an open-end ignition with no gob. 3D isocontour at T=2200K. Simulation
time = 0.05s. Time step = 0.1ms. CH = 9.5%. 2D Body mesh size = 1mm, 0.25mm edge sizing.
4
3D Body mesh size = 5mm. Temperature = 294K, Pressure = 82kPa. SM E = 60mJ.
ign
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Experiments of a confined methane gas explosion across a simulated gob was presented
in Figure 4.56 (page 102) and showed significant flame speed enhancement. It was also shown
that the flame moved through the gob significantly faster than around the gob in the open
passages. This is important because an ignition in or around the gob area might tend to interact
with the gob itself, other structures such as pillars, machinery, etc. enhancing combustion,
leading to more violent explosions. Complimentary 2D modeling was presented and it was found
that 1) the rock rubble must be modeled discretely to capture flame stretching and propagation
through the porous gob and 2) results in Figure 6.50, Figure 6.51, and Figure 6.52 (pages 223-
224) showed that the shape used to represent the rock rubble does affect local turbulence and
flame speed.
3D modeling of a confined ignition with rock rubble is presented in Figure 6.72, Figure
6.73, Figure 6.74, and Figure 6.75 on pages 239-240. Due to ease of meshing, the squares in the
3D model are 2x2x2cm instead of 2.2cm as shown in Table 6.4 on page 222. Despite this small
difference, the 3D model results follow the trends of the 2D model and experiments well. The 3D
model, similar to the 2D model, overestimates the actual time values of the flame expansion, but
the acceleration of the flame at early times, t = 2.5-4.2ms, matches the acceleration of the flame.
Compared to the 2D model, the 3D model better captures the impact of the third dimension on
flame propagation through the gob. For example, in Figure 6.73, the experiments show the flame
starting to propagate through the porous medium. The 2D model shows that some of the flame
passing through the obstacles, but most of the flame is still in the open regions. Compared to the
2D model, the 3D model flame is able to expand and freely propagate in the vertical direction,
showing significant flame propagation through the gob, matching experimental observations
better. This can also be observed in Figure 6.75; the 2D model shows significant flame stretching
versus the 3D model better predicting the bulk flame brush exiting the reactor.
Overall, the 3D model of the experimental box shows good agreement with experiments.
The 3D model better predicts the flame shape and flame front propagation trends for confined
ignitions compared to the 2D model, but due to the coarser mesh of the 3D model, does not
predict the local fluid velocities or instabilities observed in an unconfined ignition without a gob.
These results are important because they demonstrate the need to always balance model accuracy
and simulation time. Although a coarser 2.5mm cut cell body mesh was used with 3 levels of
mesh adaption on the gradient of temperature every 2 times steps to resolve the flame front, other
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flow quantities were not as well predicted resulting in certain flame inaccuracies. As the models
become larger and continue to scale, it will become more important to keep in mind the loss of
model accuracy to improve simulation times. However, this demonstrates why it is important to
continue to validate models across a variety of scales and conditions to ensure a robust model is
produced.
6.4 2D 71cm Steel Reactor Modeling Results
The main purpose of the 71cm diameter reactor is to develop an understanding of
methane flame dynamics at the large-scale for improved model development towards the mine-
scale. Experimental results in the 71cm diameter steel reactor showed that a rock pile at the back
of the reactor (closed end) resulted in faster flame front propagation velocities than a rock pile
located at the front (open end) of the reactor and faster velocities than no rock pile at all (Section
4.7, Figure 4.58 and Figure 4.59 on pages 104-105). In the experimental setup, the length of the
rock pile was L=1.8m and the height of the rock pile was 24cm. Previous results of modeling a
rock pile in the 2D, 12cm diameter quartz reactor showed that the obstacle must be modeled as
discrete objects (Section 6.1.4). Thus to model a rock pile in the 71cm diameter reactor, the rock
pile was modeled as idealized circles with a diameter of 10cm, which was based on the average
size of the rocks in the experiments. The discrete circles were spaced 2cm apart in the vertical
direction so that the total height of the simulated gob was 24cm.
Results of modeling a rock pile at the front and back of the 71cm are presented in Figure
6.76 and Figure 6.77 and flame shape and propagation trends are presented in Figure 6.78
through Figure 6.82. As can be seen in these figures, a rock pile at the back of the reactor results
in faster flame front propagation velocities than a rock pile at the front or no rock pile at all.
Compared to a rock pile at the front, a rock pile at the back of the reactor accelerates the flame
along the entire length of the reactor. When the rock pile is at the front, it only tends to accelerate
the flame across the obstacle. Also to note, the reason that the 2D model does not exactly match
the measured velocities of flame acceleration across a rock pile is because 1) the model uses a
coarse mesh with errors up to 15% as discussed in Section 5.3, 2) the discrete circles used to
represent the rock rubble does not fully capture the size/shape of the rock, 3) the spacing used
between the discrete circles is not representative of the actual void spaces in a pile of rock
rubble, and 4) the model is in 2D which means that turbulence is not fully resolved. Despite
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these differences, the 2D model does a good job at capturing the overall trends of methane flame
acceleration across a rock pile.
Figure 6.76 2D, 71cm diameter reactor model results for a closed-end ignition with a sphere gob
investigating the impact of gob location on methane flame front propagation velocity versus
distance. Obstacle: 10cm diameter sphere gob, H = 24cm, L = 1.8m. Time step = 0.01ms. CH =
4
9.5%. 2D Body mesh size = 5mm, 1mm edge sizing. Temperature = 295K, Pressure = 76kPa.
SM E = 60mJ.
ign
Figure 6.77 2D, 71cm diameter reactor model results for a closed-end ignition with a sphere gob
investigating the impact of gob location on methane flame front location versus time. Obstacle:
10cm diameter sphere gob, H = 24cm, L = 2m. Time step = 0.01ms. CH = 9.5%. 2D Body mesh
4
size = 5mm, 1mm edge sizing. Temperature = 295K, Pressure = 76kPa. SM E = 60mJ.
ign
Finally, although these researchers did not experiment with a rock pile in the middle of
the reactor (Fig, Strebinger, Bogin, & Brune, 2018; Fig M. , 2019), this condition is of
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Figure 7.1 Diagram showing the multiple pathways the ventilation model and combustion model
have been combined to simulate a 3D Sub-Section, a 3D Full-Scale, and a 2D methane gas
explosion.
As shown in Figure 7.1, three different full-scale models have been developed: 1) a 3D
full-scale sub-section model, 2) a 3D, full-scale mine model, and 3) a 2D mine model. The 3D,
sub-section models were developed to help balance computational time versus accuracy. As the
models have increased in size, it has become more and more difficult to determine mesh
independence, which has forced researchers to use mesh adaption on coarse grids as described in
Section 5.2.3 and Section 5.3. The sub-section models were built to model different methane gas
ignition scenarios as shown in Figure 7.2; the scenarios shall be described in subsequent sections.
The main idea is that once the flame propagates in this small domain, the information can be
translated over to the next domain, such that, researchers can track flame and pressure
propagation throughout the entire mine. In general, the sub-section models help prove the
viability of using detailed modeling to simulate a methane-gas explosion. Additionally, the sub-
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section models are run on a conservative number of cores, 8-12, on a single compute,
demonstrating that these models can run on a typical desktop computer.
Figure 7.2 Schematic taken from the 3D full-scale ventilation model showing dimensions, flow
directions and velocities, and sub-sections used for methane gas explosion modeling.
In addition to developing 3D, sub-section models, a 3D, full-scale simulation was also
performed. The main purpose of the full-scale simulation is to model a full-scale methane-gas
explosion in an underground coal mine, which has never been done to the knowledge of these
researchers. However, one of the drawbacks of this model is that it requires 96 cores over 4
compute on a supercomputer. Details of this model shall be given and results will be discussed in
Section 7.4.
Finally, complimentary to these 3D models, a 2D model has been developed using inlet,
outlet, dimensions, and gob conditions from the full-scale, 3D ventilation model. The main
purpose of the 2D model is to show the capabilities of a reduced order model to predict methane
flame and pressure propagation in a longwall coal mine. Additionally, this reduced order model
can be run on a typical desktop and takes less than 1 week to solve, making it a good predictive
tool for initial flame and pressure wave propagation.
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7.1 3D Full-Scale Sub-Section 1
After validating the 2D and 3D reactor CFD combustion models under a variety of
conditions, researchers have begun modeling a small methane gas ignition under a single
longwall coal mine shield as shown in Figure 7.3. This model is taken as a subsection of the full-
scale longwall ventilation model; the height of the coal face is 3m and the length of the shield is
6m. In the previously developed 3D models presented in this research, mesh independence was
typically found at a mesh size of 2.5-2mm for the smaller, laboratory-scale reactors.
Unfortunately meshing this large volume would require millions of cells and researchers have
found modeling the 3D 12cm diameter reactor with 1 million cells takes a little less than 2 weeks
on a supercomputing node with 8-12 cores, 2.7-3.02GHz, 24-64GB RAM. However, it was also
found that using aggressing mesh adaption can help in using larger cell sizes while still
predicting physically accurate methane flame behavior (Section 5.2.3). Therefore, the single
shield model was meshed with approximately 500,000 tetrahedral elements, size 7-10cm. To
accurately model the deflagration physics, researchers are using the following settings in
ANSYS Fluent (v17.2):
• Pressure-Based Solver
• Energy Equation
• Viscous Standard k-ω Turbulence Model
o Low Re Corrections
o Shear Flow Corrections
• Species Transport
o Volumetric Reactions
o Stiff Chemistry Solver
o Finite Rate Chemistry
▪ Density solved using ideal gas theory
▪ Diffusion solved using kinetic theory
▪ Metghalchi and Keck laminar flame speed theory
• Spark Ignition Model
o Initial kernel radius = 5mm
o Duration = 1ms
o Energy = 60mJ
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Results of ignition underneath the single shield are shown in Figure 7.4, Figure 7.5,
Figure 7.6, and Figure 7.7 and took approximately 15 days to model flame expansion to the
model boundaries (note that parallelization across computes can help speed-up this simulation
time). As can be seen, the flame extends towards the path of least resistance, along the longwall
face in the x directions. Calculations of the average flame speed predicts a flame expanding at
30m/s. According to the Upper Big Branch explosion in 2010, investigators estimated the flame
speeds directly near the explosion to be close to 90m/s (Page, et al., 2011). What is positive
about these results is that the flame expansion is captured well and the approximate speed of
expansion is the same order of magnitude as the UBB explosion. As previously discussed, two
main reasons for the discrepancy in speeds is the large cells required to run this simulation and
the fact that the chemistry model assumes a 2-step methane-air mechanism. In general, 2-step
mechanism underestimates the flame speed as compared to more complex chemistry
mechanisms (13-step, full-GRI) as shown by Fig (2019). Additionally, the velocities and
pressures from the UBB were estimated based off investigative evidence, which means the error
bars on those values are not well known. Therefore, what this sub-section model shows is that
these full-scale methane gas explosions can be modeled in a reasonable amount of simulation
time on a typical desktop computer. Using ANSYS Fluent also allows data from this model to be
interpolated onto another model, or simply transferred to the next shield along the longwall face
(Figure 7.3).
7.2 3D Full-Scale Sub-Section 2
After running a preliminary simulation of ignition under a single shield, a second model
was developed which includes a discrete gob behind the shields as shown in Figure 7.9. 3D
hexagons were created to represent the gob and are 30cm in diameter. Some of the benefits of
modeling the gob as discrete hexagons is that 1) the hexagons capture the turbulence induced by
rock observed in experiments, 2) because they have flat faces they are easy to mesh, and 3) they
are easily arranged in different packing orientations to change gob porosity or resistance. The
mesh for this study is the same as the single shield model, 7-10cm tetrahedral cells,
approximately 1 million cells total. Model settings are the same as the sub-section 1 model
except for the following:
• Residuals set to 10-3, dropping at least 3 orders or magnitude
• Turbulence parameters: k = 1.5m2/s2 and ω = 25 1/s
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Figure 7.12 Isocontour of temperature at 2200K showing methane flame propagation behind the
longwall face within a discrete hexagonal gob. Ignition in the center of the gob. Simulation Time
= 8ms. Time step = 0.01ms.CH = 9.5%. Body mesh size = 7-10cm with 2 levels of mesh
4
adaption every 2 time steps. Temperature = 293K, Pressure = 82kPa. SM E = 60mJ.
ign
Results are shown in Figure 7.9 through Figure 7.12 and show the flame expanding at an
average velocity of 22m/s. Although these simulations are on-going, they demonstrate that
modeling these large-scale explosions is possible and requires a complete understanding of
model settings in addition to multiple points of model validation during development. In the
future, researchers are urged to investigate ways to obtain mesh independence, while also
maintaining reasonable simulations times, most likely by parallelization which is used in the full-
scale simulation presented in Section 7.4. Future work also includes testing these models using
an LES turbulence model in lieu of the k-ω turbulence model since the two-equation moment
models require an estimation of the initial turbulence. Since the initial turbulence is unknown
and the scales of these models are significantly larger than previously modeled, the LES
turbulence model may be more appropriate for higher fidelity simulations.
7.3 3D Full-Scale Sub-Section 3
The previous sub-section models described in Section 7.1 and Section 7.2 modeled a
methane gas explosion under stagnant conditions under a single shield along the longwall face
and in the gob behind the shields. These models helped demonstrated that the sub-section models
can be used to simulate methane-gas ignitions and solved on a typical-sized desktop computer.
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However, these models do not include the high velocity airflow typical along the longwall face
(5-7m/s) which can change the local initial turbulence and thus, solution. Therefore, a 3rd sub-
section model was created to more realistically model a methane gas explosion. For example, in
the UBB explosion, the shearer was at the tailgate and hot streaks left from worn shearer bits
ignited a pocket of methane at the tailgate (Page, et al., 2011). Thus, the sub-section modeled is
at the tailgate corner of the longwall face as shown in Figure 7.2 and Figure 7.13.
The settings for this model were the same as the sub-section 2 model (Section 7.2) except
for the model initialization. The model was no longer initialized to stagnant conditions; instead,
the 3D full-scale ventilation model was run to steady state and the flow and pressure data was
extracted. This data was then interpolated onto the sub-section model and the pressure profiles
from the steady state model were used as boundary conditions for the pressure inlet and outlets.
In the ventilation model used for this condition, there was not any methane at the tailgate corner,
so to simulate an EGZ a small box (0.5m cube) was filled with stoichiometric methane and was
ignited inside the box (volume of methane = 0.125m3). An example of the pressure profiles and
flow conditions are shown in Figure 7.13 and Figure 7.14.
Figure 7.13 Schematic of the 3D, Sub-Section 3 model showing the geometry used to simulate a
methane gas explosion at the tailgate corner. Pressure profiles were extracted from the 3D,
ventilation model and used as pressure boundary conditions as shown. Ignition is initiated in a
small methane box (0.5m cube) was initialized at 9.5% methane by volume.
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Figure 7.20 3D sub-section 3 results of the first pressure wave expansion location as a function
of time. Time step = 0.01ms.CH = 9.5%. Body mesh size = 7-10cm with 2 levels of mesh
4
adaption every 2 time steps. SM E = 60mJ.
ign
Figure 7.21 3D sub-section 3 results of the maximum overpressure of the first pressure wave as a
function of time. Time step = 0.01ms.CH = 9.5%. Body mesh size = 7-10cm with 2 levels of
4
mesh adaption every 2 time steps. SM E = 60mJ.
ign
Results from this study are presented in Figure 7.15 through Figure 7.21. Results show
that the pressure wave expands towards the boundaries of the domain much faster than the flame
itself. Calculations of the expansions reveal that the flame front expands at approximately 22m/s
and the pressure wave expands at 350m/s. The overpressure of the first expanding pressure wave
is plotted as a function of time in Figure 7.21 and results show an initial pressure wave of
approximately 18kPa at 2ms. However, it is important to note that there may have been higher
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pressures generated between spark initiation and 2ms. Therefore, this research recommends
future work saving time steps more frequently during the initial kernel expansion in order show
the initial pressure rise likely missed here. Additionally, results show that the expanding pressure
wave disturbs the flow in nearby areas, such that by 30ms there is no flow from the longwall face
to the tailgate entries. This can also be seen in Figure 7.19 which shows that the model is able to
predict the pressure wave reflection off the mine walls and pressure wave interaction. From the
UBB explosion it was estimated that near the ignition the flame front propagation velocity was
near 90m/s and the overpressure was 27kPa (Page, et al., 2011). Although this initial simulation
predicts overpressure slightly less than 27kPa, they are still the same order of magnitude and
again, the actual peak overpressure may have been between 0-2ms. More importantly these
results show that even for these small overpressures, they are enough to change the airflow
patterns in this area. These results are important because they demonstrate the viability of
modeling methane gas explosions using data interpolated from a steady state ventilation model.
These results also show how the flow in the tailgate can be disturbed from the explosion
overpressure, which can be important for understanding movement of EGZs or even entrainment
of coal dust (which would require a multiphase model). Additionally, models such as this can be
used to help estimate the amount of impact force on nearby mine structure, which may help in
the design of pillars or seals.
In general, all of the sub-section models have demonstrated the potential for modeling
these explosions on smaller domains. They have shown reasonable results under totally stagnant
conditions and have proven that steady state results can be used to initialize and model a methane
gas explosion. They have also demonstrated the need to continue improving the models by
investigating the use of an LES model, more complex chemistry mechanisms, sensitivity analysis
on turbulence parameters, parallelization, and coupling with the ANSYS Mechanical to
understand the stresses on nearby mine equipment/structure. Altogether, these results have
enormous potential for accurately predicting methane gas explosions in a full-scale, sub-section
model. Data extracted from these models could even be used to help further track the flame and
pressure waves in the 2D mine model, which will be discussed in Section 7.5.
7.4 3D Full-Scale Simulations
Researchers have also simulated an ignition and subsequent flame propagation in the full-
scale ventilation model. The ventilation model contains the full longwall face (300m long), 6m
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of gob behind the shields (152 shields), and part of tailgate and tailgate bleeder entries. The
height of the coal seam is 3m and the distance from the coal face to the back of the shields is
6.5m. Pressure profiles obtained from the steady state ventilation model are used as boundary
conditions for the inlets and outlets, to maintain model accuracy. For the ventilation scenario, it
is assumed that the flow at the tailgate corner is directed toward the open crosscut outby the face
due to the tailgate entry inby the face blocked by the roof fall. The shearer is cutting the tailgate
corner, with half of the tailgate drum exposed at the tailgate entry. Both shearer drums are 1.8m
in diameter and are rotating at 30 rpm (shearer cowls are also modeled). For ventilation, 85,000
cfm of fresh air enters the longwall face at the headgate. The majority of the air leaks into the
gob, resulting in 30,000 cfm remains inside the face by the time it reaches the tailgate side.
Figure 7.22 shows the ventilation condition used for this test, while Figure 7.23 shows volume
rendering of methane mass fraction around shearer drums. The rendering is limited to methane
around shearer drums for visual purposes.
Figure 7.22 Volume rendering of velocity inside longwall face from plan view (top) and velocity
contour plot showing close-up view of flow around shearer drums (bottom). Blue arrows indicate
flow direction.
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Figure 7.23 Volume rendering of methane mass fraction near the shearer drums.
This scenario represents the case when there is insufficient fresh air to dilute the methane
inflow from the coal face, resulting in the formation of explosive gas zones of methane and air
around the shearer drums. From the figure, methane accumulation can be observed in the small
gap between the shearer body and uncut coal face. There is also notable methane accumulation in
areas between the headgate drum and coal face, and between the tailgate drum and cowl. For this
test, it is assumed that the ignition occurred when the headgate drum is cutting the coal face, as
shown in Figure 7.23. This ignition location is chosen to test the viability of initiating
combustion in a region of high turbulence. Before ignition, the shearer drums are rotating until
the flow is fully developed. After the onset of ignition, the drums are switched to stationary and
considering the time scale of the explosion, the continuous rotation of the drums should not have
any significant impact on the flame expansion. The combustion model settings for this
simulation are the same as those used for the sub-section 3 model (Section 7.3) except for the
following:
• First order implicit time stepping (for simulation stability)
• 3 levels of mesh adaption on the gradient of temperature every time step (for increased
accuracy in predicting the flame front)
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• Initial spark kernel radius is 2cm which matches the mesh size near ignition
• Spark duration is 2ms
Figure 7.24 through Figure 7.28 shows volume rendering of the total pressure and
temperature after ignition near the headgate drum, looking from inside the longwall face towards
the uncut coal face. As can be seen in these images, the overpressure from the explosion
develops very quickly at 350m/s and expands to a much larger radius than the main flame front
which is moving at approximately 30-35m/s as shown by the expansion of temperature in Figure
7.28. This is important because the quickly expanding pressure wave is increasing the pressures
and temperatures inside the volume such that as the main flame front expands, the unburned
upstream gases are slightly preheated. Subsequently, increased preheating in the unburned gases
can increase combustion rates and flame acceleration, which is well known from fundamental
flame theory (Andrews & Bradley, 1972). If these processes continue, this can lead to significant
flame acceleration and possible transition to a detonation as described in Section 2.3.
Figure 7.24 Volume rendering of total pressure showing ignition and explosion overpressure.
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Figure 7.25 Volume rendering of total pressure showing ignition at the headgate drum and
explosion overpressure overlaid with black streamlines for flow visualization.
Also shown in Figure 7.25 and Figure 7.26 are black streamlines used to visualize the
flow in the longwall face. As can be seen in these figures, the overpressure from the explosion
diverts the main airflow in the longwall face such that there is little airflow near the coal face and
tailgate drum. This is important because this pushes more flow into the gob area, which can
potentially mix with pockets of methane creating more areas of EGZs. The diverted flow around
the shield can also entrain more methane from the face, creating an environment which could
lead to secondary or tertiary explosions.
Figure 7.27 shows the decrease in pressure of the first pressure wave as it expands away
from ignition. At 1ms the model predicts an overpressure of approximately 13kPa which
decreases proportionally to the inverse of distance from ignition squared, as expected from a
pressure wave. Similar to the full-scale sub-section 3 model presented in Section 7.3, the
maximum overpressure is the same order of magnitude as those estimated from the UBB
explosion (27kPa) (Page, et al., 2011). Also, although 13kPa was recorded at 1ms, there may
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have been higher pressures generated between 0-1ms. Thus, researchers again recommend future
work recording more frequent time steps in the initial flame kernel expansion in order to more
accurately capture overpressure of the explosion as a function of time.
This test successfully demonstrates the viability of integrating the combustion model into
the full-scale bleeder ventilation model. One major issue that needs to be addressed is balancing
computational time versus model accuracy. This current simulation has taken approximately 4
days to simulate 2.25ms of methane gas combustion using 4 x 24 cores nodes of computational
power. It is important to note that this model has ~22.5 million base cells before using mesh
adaptation. Mesh adaption is employed on the gradient of temperature to better resolve the flame
front on such a coarse grid, but this increases the total simulation time. In the future, mesh
coarsening and dynamic meshing can be used so that, as cells are added to the model to refine
flow/temperature gradients, other mesh areas are coarsened thereby reducing the total number of
cells in the model while still maintaining model accuracy and reasonable simulation times.
Figure 7.26 Volume rendering of total pressure showing ignition at the headgate drum and black
streamlines showing how the flow is diverted away from the coal face and tailgate drum.
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7.4.1 Discussion of Potential Future Work
To the knowledge of these researchers, the simulations presented in this Chapter are the
first 3D, full-scale simulations of methane gas explosions in an underground longwall coal mine.
More specifically, the simulations presented in Section 7.4 are monumental because they show
that modeling a methane gas explosion in a longwall coal mine is feasible using a commercial
CFD software, which has enormous potential for future research areas including:
• Explosion prevention and mitigation
• Design of mine layout
• Shearer and drum design
• Design of mine structures and seals
• Design of water spray systems
For explosion prevention and mitigation, for example, if there is an EGZ in a hanging
roof behind the longwall shields, researchers could model different explosion scenarios to
estimate flame speeds and overpressures. This type of information could be used to better
distribute inert rock dust in these areas or perhaps include water sprays, increasing the humidity
thereby decreasing the flame speed and pressure. Inclusion of a multiphase model (which is an
option in ANSYS Fluent) could help in modeling the transition of a gaseous explosion to a coal
dust explosion, like what happened in the UBB explosion (Page, et al., 2011).
Running different mine explosion scenarios can also help research understand the
potential transition of a deflagration to a detonation for improved mine design and layout. As
described in Section 2.3, a deflagration can transition to a detonation by different flame
acceleration mechanisms. For example, flame stretching can increase combustion rates,
accelerating the flame. If there was an explosion in the gob, the turbulence induced by the nearby
rock rubble and mine equipment could potentially aid in DDT. Also, deflagrations can transition
to detonations if there is enough run-up distance; for methane-air mixtures this is typically
around a L/D ratio of 50, but can be shortened by roughened walls (Ciccarelli & Dorofeev, 2008;
Lee J. , 1984). In a mine, the entryways are typically 6m wide and can be 3m high, which means
the hydraulic diameter of the entryways are 4m. Active longwall panels continue to get longer,
and can be upwards of 1000m, corresponding to an L/D ratio of 250. In general this demonstrates
how a mine environmental can be inherently dangerous, but the models developed in this work
can aid in better designing certain areas of the mine with potential for methane gas explosions.
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The models developed can also aid in the design of the shearer, drums, mine structures,
and seals. ANSYS also owns ANSYS Mechanical which is a program that can estimate
mechanical stresses and strains on solid objects. This can be coupled with ANSYS Fluent quite
easily, such that researchers can estimate the forces and impacts of an explosion on nearby mine
equipment and structure. This kind of information can also aid in designing better seals or
perhaps the layout of seals.
Finally, another potential research area could be the design of water spray systems either
on the shearer, along the longwall face, or in the gob. Water sprays are important because they
can capture entrained coal dust reducing the risk of a coal dust explosion. Water sprays can also
provide enough pressure to mitigate the accumulation of EGZs and they can also make the
nearby air humid, thereby decreasing the potential explosion hazard. In ANSYS Fluent, this
could be done by incorporating the multiphase model in Fluent and running different spray
scenarios.
7.5 2D Mine Model Simulation
Section 7.1 through Section 7.4 presented high-fidelity, 3D models of methane gas
explosions in underground coal mines. The models and simulations presented thus far have
shown great potential in modeling these large-scale explosions in 3D, capturing the flame and
pressure wave propagation trends as well as predicting reasonable flame speeds. However, they
take a significant amount of simulation time and computational resources. Therefore, researchers
have also created a 2D model of the ventilation conditions in a underground longwall coal mine
and have combined it with the 2D combustion model developed in this research. The main
purpose of this model is to simulate the flame and pressure wave propagation throughout the
entire mine, but in a more user-friendly, reasonable amount of time.
To begin, the 2D mine model was run as a steady state to obtain the velocity profiles in
the mine; a diagram of the setup is shown in Figure 7.29. Airflow was initialized as a fluid with
no methane while the gob was a porous media with 9.5% methane by volume (stoichiometric).
With the velocity profile from the steady state case imported, the ANSYS Spark Model was
turned on with an initial radius of 10cm at the location marked with a yellow star in Figure 7.29.
As shown in Section 6.3.1, a flame cannot propagate in a Darcy flow porous media unless the
porosity is set to 100%. Therefore, to obtain realistic flame propagation in this area, the box in
the gob around the spark location was set as a fluid zone to allow the flame kernel to expand.
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Figure 7.31 Absolute pressure contours of the 2D mine model with an ignition behind the
shields, in an area of the gob which is not fully caved. Black lines are the forward and
backwards streamlines of airflow along the longwall face. Time step = 0.01ms. CH = 9.5%.
4
Body mesh size = 10cm. Temperature = 293K, Pressure = 82kPa. E = 60mJ.
ign
Initial results at 10ms show that the flame propagates through the fluid zone of the gob
and has resistance as it reaches the porous zone of the gob, shown in Figure 7.30. The black
regions in Figure 7.30 are the areas where methane reacts with oxygen, representing the flame
front. The pressure contour in Figure 7.31 shows that at a given time, a large pressure wave will
propagate ahead of the flame front by several meters. As time progresses, the difference between
the flame front and pressure front increases. Additionally, the black lines in Figure 7.31 represent
velocity streamlines, showing that the pressure wave diverts the flow along the longwall face.
These results were also observed modeling an explosion using the sub-section 3 model (Section
7.3) and the full-scale methane explosion model (Section 7.4). This is important because even in
2D, the model predicts general flame and pressure wave propagation trends observed in high-
fidelity simulations, and in a fraction of the time, approximately 5 days.
The 2D model is on-going, but future modeling will include a mesh independence study
and a study investigating model parallelization for reduced computational times. Further studies
including discrete modeling of obstacles in the gob rather than using a porous media as well as
adding obstacles representing the hydraulic roof jacks along the longwall face. However, what is
positive about this initial 2D model is that researchers will be able to run a variety of mine
explosion scenarios and evaluate general flame and pressure wave propagation trends in under a
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CHAPTER 8
SUMMARY OF IMPACTFUL RESULTS
8.1 Summary of Impactful Experimental Results
Open-End Ignition versus Closed-End Ignition – Section 4.1
➢ Purpose: These experiments demonstrate the difference between an un-confined (OEI)
and a fully confined (CEI) methane gas explosion.
➢ Outcomes:
• Ignition from a confined space increases flame speeds 5000% and peak overpressures
1200%. This increase is due to increased temperatures and pressures during flame
kernel expansion, which increases fluid motion ahead of the flame thereby increasing
turbulence and combustion rates.
• CEI results in large overpressures and pressure oscillations, over 6 times greater than
an OEI.
➢ Impact: In longwall coal mining, EGZs typically exist near the working face, behind the
shields, and the corridors. Therefore, ignitions can occur in variety of locations and it is
extremely important to capture these effects in the combustion model. Additionally, large
overpressures from a methane gas explosion can cause serious damage to nearby workers
and large pressure oscillations can damage ventilation controls and reverse airflow in a
mine which will be important to capture in the combustion model.
➢ Novelty: Many researchers have compared open- versus closed-end ignition, but not
across the wide range of scales under investigation in this project. Due to the variety of
experimental setups and methods of measuring flame speed and overpressure, it would be
extremely difficult to develop a comprehensive combustion model using other
researcher’s experimental data. Even for those researchers who use different sized
reactors, many of them have a different ratio of length to diameter, which makes scaling
difficult and many of them did not have optical access to the flame. These results are
novel in that they help us further complete our understanding of the effect of scale on
methane flame dynamics as we continue validating larger combustion models.
➢ Presented at the SME Annual Conference, Minneapolis, Minnesota, 2018:
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