Title: Dynamic of plumes and scaling during the melting of a Phase Change Material heated from below,
Abstract: We identify and describe the main dynamic regimes occurring during the
melting of the PCM n-octadecane in horizontal layers of several sizes heated
from below. This configuration allows to cover a wide range of effective
Rayleigh numbers on the liquid PCM phase, up to $\sim 10^9$, without changing
any external parameter control. We identify four different regimes as time
evolves: (i) the conductive regime, (ii) linear regime, (iii) coarsening regime
and (iv) turbulent regime. The first two regimes appear at all domain sizes.
However the third and fourth regime require a minimum advance of the
solid/liquid interface to develop, and we observe them only for large enough
domains.
The transition to turbulence takes places after a secondary instability that
forces the coarsening of the thermal plumes. Each one of the melting regimes
creates a distinct solid/liquid front that characterizes the internal state of
the melting process. We observe that most of the magnitudes of the melting
process are ruled by power laws, although not all of them. Thus the number of
plumes, some regimes of the Rayleigh number as a function of time, the number
of plumes after the primary and secondary instability, the thermal and kinetic
boundary layers follow simple power laws. In particular, we find that the
Nusselt number scales with the Rayleigh number as $Nu \sim Ra^{0.29}$ in the
turbulent regime, consistent with theories and experiments on Rayleigh-Bénard
convection that show an exponent $2/7$.