We report the first comparative study of the phase-change Rayleigh–Bénard (RB) convection system and the classical RB convection system to systematically characterize the effect of the oscillating solid-liquid interface on the RB convection. Here, the role of Stefan number Ste (defined as the ratio between the sensible heat to the latent heat) and the Rayleigh number based on the averaged liquid height R a f is systematically explored with direct numerical simulations for low Prandtl number fluid (Pr = 0.0216) in a phase-change RB convection system during the stationary state. The control parameters R a f (3.96 × 104 ≤ R a f ≤ 9.26 × 107) and Ste (1.1 × 10−2 ≤ Ste ≤ 1.1 × 102) are varied over a wide range to understand its influence on the heat transport and flow features. Here, we report the comparison of large-scale motions and temperature fields, frequency power spectra for vertical velocity, and a scaling law for the time-averaged Nusselt number at the hot plate [Formula: see text] vs R a f for both the RB systems. The intensity of solid-liquid interface oscillations and the standard deviation of Nu h increase with the increase in Ste and R a f. There are two distinct RB flow configurations at low R a f independent of Ste. At low and moderate R a f, the ratio of the Nusselt number for phase-change RB convection to the Nusselt number for classical RB convection [Formula: see text] is always greater than one. However, at higher R a f, the RB convection is turbulent, and [Formula: see text] can be less than or greater than one depending on the value of Ste. The results may turn out to be of immense consequence for understanding and altering the transport characteristics in the phase-change RB convection systems.
Here, for the first time, we report the criterion for the onset of convection in a low Prandtl number phase-change Rayleigh–Bénard (RB) system with an upward moving melt interface in a two-dimensional square box for a wide range of Rayleigh number Ra and Stefan number Ste (defined as the ratio between the sensible heat to the latent heat). High fidelity simulations were performed to study the phenomenon of the onset of convection. Unlike the classical RB system in the phase-change RB system, it was found that the onset of convection depended on Ste and Fourier number τ, in addition to Ra. The phase-change RB system with upward moving melt interface can be classified into two groups: slow expanding phase-change RB system (Ra ≤ 104) and moderate/fast melting phase-change RB system (Ra > 104). The slow melting phase-change RB system becomes unstable when the effective Rayleigh number based on the melt height is ≈1295.78, consistent with the finding by Vasil and Proctor [“Dynamic bifurcations and pattern formation in melting-boundary convection,” J. Fluid Mech. 686, 77 (2011)]; however, moderate and fast melting phase-change RB systems become unstable when the product of the local Rayleigh number Ra based on the melt-layer height hyt and the Fourier number based on the melt-layer height reaches a threshold value. Interestingly, it is seen that the criteria for the onset of convection for moderate and fast melting phase-change RB systems show a power law kind of form such that Racrτcr = aSteb + c. In addition, during the initial conduction regime before the onset of convection, it is seen that the Nusselt number at the hot wall is Nuh ∼ τ0.5, and during the onset of convection, i.e., during the formation of the initial convection rolls, the Nusselt number at the hot wall is Nuh ∼ τd, where the value of the exponent d is 2 for low Rayleigh numbers and 4 for higher Rayleigh numbers. This study reports some general characteristics of the onset of convection and some organized behavior in the transient melting phase-change RB system, which are not yet explored and reported in the open literature. This work may lead to significant understanding of different applications of fluid-dynamical melting phase-change RB systems in both natural and engineering systems.
In this work, numerical experiments were performed to compare the heat transfer and thermodynamic performance of melting process inside the square-shaped thermal energy storage system with three different heating configurations: an isothermal heating from left side-wall or bottom-wall or top-wall and with three adiabatic walls. The hot wall is maintained at a temperature higher than the melting temperature of the phase change material (PCM), while all other walls are perfectly insulated. The transient numerical simulations were performed for melting Gallium (a low Prandtl number Pr = 0.0216, low Stefan number, Ste = 0.014, PCM with high latent heat to density ratio) at moderate Rayleigh number (Ra ≊ 105). The transient numerical simulations consist of solving coupled continuity, momentum, and energy equation in the unstructured formulation using the PISO algorithm. In this work, the fixed grid, a source-based enthalpy-porosity approach has been adopted. The heat transfer performance of the melting process was analyzed by studying the time evolution of global fluid fraction, Nusselt number at the hot wall, and volume-averaged normalized flow-kinetic-energy. The thermodynamic performance was analyzed by calculating the local volumetric entropy generation rates and absolute entropy generation considering both irreversibilities due to the finite temperature gradient and viscous dissipation. The bottom-heating configuration yielded the maximum Nusselt number but has a slightly higher total change in entropy generation compared to other heating configurations.
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