Validation of a numerical model with a benchmark experiment for melting governed by natural convection in latent thermal energy storage

We report a combined experimental and numerical investigation of a melting process representative of latent thermal energy storage systems. The purpose of the work is to assess the accuracy of numerical models of melting governed by natural convection with a benchmark experiment. The experiment consists of a rectangular box filled with a model liquid (n-octadecane) and heated symmetrically from both sides such as to allow access for shadowgraph imaging and particle image velocimetry to measure the phase state and velocities, respectively. Our numerical method for computing fluid flow, temperature, and phase state involves two different approaches: the first is a detailed model using variable thermophysical properties and the volume of fluid method to allow volume expansion in an additional air phase that we solve in two dimensions. The second is a simplified model using constant thermophysical properties and the Boussinesq approximation that we solve either in two or in three dimensions. In the first part of the work, we systematically compare the simplified (Boussinesq) with the detailed (volume of fluid) model. We find that for the given set of parameters (Ra = 2.10(8), A = 4, Ste = 0.092, Pr = 52), the difference between the detailed and the simplified model in predicting global quantities such as the liquid phase fraction and the total heat flow rate is smaller than 4%, whereas velocities differ up to 20%. In the second part of the work, we compare the simulations of the simplified Boussinesq model in three dimensions with the benchmark experiment. We find that the simulation predicts the liquid phase fraction and temperatures with deviations below 4%, but significantly overestimates the velocity magnitudes. Our experimental and numerical tools provide a rational framework in which the accuracy of latent thermal energy storage simulations can be systematically and comprehensively assessed.