Solid-liquid phase change around a tube with periodic heating and cooling: Scale analysis, numerical simulations and correlations

This work studies solid-liquid phase change around a tube in a latent energy storage unit with cyclic thermal loading and unloading (i.e. alternate heating and cooling), while taking into account natural convection. A scale analysis is used to predict the tube surface temperature and the extent of the molten and solidified zones around the tube as a function of the main governing dimensionless parameters (the Stefan and Rayleigh numbers, and the period of the imposed sinusoidal heat transfer rate). A numerical model is then developed to simulate the process under a periodic regime and verify the scale analysis. Temperature, liquid fraction and flow fields are reported as a function of the main governing parameters. A frequency analysis is also proposed to develop a better understanding of how the system behaves. It is shown that the dimensionless group Pr/(τ∼Ra1/5Ste) allows to determine the importance of natural convection in the system. Results indicate that the size of the zone affected by the alternate heating and cooling increases when the period or the Stefan number increased, but was less sensitive to the Rayleigh number. Correlations are proposed to determine the maximal dimensions reached by the melt and by the solid around the tube.