On a Mushy Cell Tracking Method for Simulating Gallium Melting

Abstract

Gallium melting in a rectangular cavity heated from the side wall has been extensively studied. Since the previously simulated results were not consistent and the myth of a grid-converged solution remained, we reexamine this problem using the thermally driven mushy cell tracking method to clarify whether the solution is physically correct. In the study, the computational domain is separated into solid-phase and liquid-phase regions, with the mushy cell placed in between. The governing equations for the thermofluid transport are expressed in terms of the primitive variables and are discretized in the stationary unstructured grid using the finite-volume formulation. The mushy cell tracking equation is derived under the mass and energy balance laws to capture the mushy cell front. With the variables located in the cell centers, the distinguishing characteristic of the present tracking algorithm lies in the specification of constant melting or freezing temperature at the center of the mushy cells without consideration of the curvature and normal velocity effects in the dendritic solidification. Thanks to this feature, a straightforward and accurate evaluation of the boundary conditions at the interface of the mushy, solid, and liquid cells becomes feasible. The predicted moving interface and thermofluid field of gallium melting are shown to agree well with the results from other numerical solutions.

Acknowledgments

The authors would like to thank the National Science Council of Taiwan for funding this research (Project NSC 95-221-E-022-016).