Abstract
Classical numerical methods for solving solid–liquid phase change assume a constant density upon melting or solidification and are not efficient when applied to phase change with volume expansion or shrinkage. However, solid–liquid phase change is accompanied by a volume change and an appropriate numerical method must take this into account. Therefore, an efficient algorithm for solid–liquid phase change with a density change is presented. Its performance for a one-dimensional solidification problem and for the quasi two-dimensional melting of octadecane in a cubic cavity was tested. The new algorithm requires less than 1/9 of the iterations compared to the source based method in one dimension and less than 1/7 in two dimensions. Moreover, the new method is validated against PIV measurements from the literature. A conjugate heat transfer simulation, which includes parts of the experimental setup, shows that parasitic heat fluxes can significantly alter the shape of the phase front near the bottom wall.
Highlights
Melting and solidification processes receive scientific interest as they are fundamental to many phenomena in nature and technical applications
We developed a new algorithm for melting and freezing of phase change material (PCM) with density change, which minimizes the number of iterations required and is based on the optimum approach
This paper describes the new algorithm and compares its performance to the source based method
Summary
Melting and solidification processes receive scientific interest as they are fundamental to many phenomena in nature and technical applications. Multiple approaches exist to solve solid–liquid phase change in the framework of continuum theory numerically. These approaches are classified by the way they treat the moving phase boundary into deforming and fixed grid schemes [4,5]. Multiple approaches were developed to describe convective phase change on fixed grids [10,11,12]. Great effort was put into the development of efficient algorithms, especially by Voller and his coauthors [13,14]. This resulted in a numerical scheme, based on Newton linearization, with a minimized number of iterations. The numerical scheme was named the optimum approach and the idea of linearizing phase change problems has triggered further research [15]
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