Melting and solidification in periodically modulated thermal convection

Melting and solidification in periodically time-modulated thermal convection are relevant for numerous natural and engineering systems, for example, glacial melting under periodic sun radiation and latent thermal energy storage under periodically pulsating heating. It is highly relevant for the estimation of melt rate and melt efficiency management. However, even the dynamics of a solid–liquid interface shape subjected to a simple sinusoidal heating has not yet been investigated in detail. In this paper, we offer a better understanding of the modulation frequency dependence of the melting and solidification front. We numerically investigate periodic melting and solidification in turbulent convective flow with the solid above and the melted liquid below, and sinusoidal heating at the bottom plate with the mean temperature equal to the melting temperature. We investigate how the periodic heating can prevent the full solidification, and the resulting flow structures and the quasi-equilibrium interface height. We further study the dependence on the heating modulation frequency. As the frequency decreases, we found two distinct regimes, which are ‘partially solid’ and ‘fully solid’. In the fully solid regime, the liquid freezes completely, and the effect of the modulation is limited. In the partially solid regime, the solid partially melts, and a steady or unsteady solid–liquid interface forms depending on the frequency. The interface height can be derived based on the energy balance through the interface. In the partially solid regime, the interface height oscillates periodically, following the frequency of modulation. Here, we propose a perturbation approach that can predict the dependency of the oscillation amplitude on the modulation frequency.