Can the numerical simulations of melting in a differentially-heated rectangular cavity be rationally reduced to 2D? A comparative study between 2D and 3D simulation results

摘要

The commonly-adopted two-dimensional (2D) numerical simulations of melting in containers have been proved to lead to significant deviations from the experimental results on a real three-dimensional (3D) configuration. To give a quantitative comparison between the 2D and 3D results, melting in a differentially-heated rectangular cavity was taken as an example case. By manipulating the empirical parameters in the enthalpy-porosity model, it was found that the discrepancies between the 2D results and experimental data cannot be eliminated by only optimizing the computational parameters. The inherent sources for such discrepancies were then investigated with the aid of scaling analysis on melting. Several inferences were drawn from the scaling analysis, and the most important one states that the 3D melting case cannot be simplified to 2D unless the Prandtl number is much larger than 1 and the ratio of length to width is far less than 1. Moreover, the scaling correlations for melt fraction were well verified by eleven numerical cases, showing a good prediction in both quantitative and qualitative comparisons between 2D and 3D results. The comparisons and inferences concluded in this work could serve as guidelines for a rational model simplification of melting problems towards practical applications.