# Free-surface flow and heat transfer in cavities - The SEA algorithm

, Chan, K.S. and Cross, M. (1995) Free-surface flow and heat transfer in cavities - The SEA algorithm. Numerical Heat Transfer Part B, 27 (4). pp. 487-507. ISSN 1040-7790 (Print), 1521-0626 (Online) (doi:https://doi.org/10.1080/10407799508914969)

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## Abstract

This study concerns the mathematical modeling of heat transfer and free surface motion under gravity, in cavities partially filled with a liquid. This two-phase flow problem is solved using a single-phase technique that assumes the air and liquid occupying the volume of the cavity can be treated as a single fluid with a sharp property discontinuity at the interface. A two-valued scalar advection equation is solved to mark the extent of each fluid. This idea is simple in concept, but requires careful application for two reasons: (1) The interface must remain sharp throughout the simulation; and (2) the equations of motion have to be expressed in a way that prevents the numerical “smothering” of the lighter fluid by the heavy one during the iteration process. To satisfy (1), the Van Leer TVD differencing scheme is adopted for the scalar advection equation, with appropriate flux corrections in the momentum and enthalpy equations. To satisfy (2), the continuity equation is expressed in volumetric form.

The technique is incorporated in the scalar equation algorithm (SEA), It is applied to two problems, the first being the collapse of a liquid column in a sealed cavity with wall heat transfer, and the second the filling and simultaneous cooling of a mold with liquid aluminum.

Item Type: Article  First published online: 15 Mar 2007.  First published in print: June 1995. metal casting, free surface flow, heat transfer, solidification, CFD Q Science > QA Mathematics > QA76 Computer softwareQ Science > QC Physics School of Computing & Mathematical SciencesSchool of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis > Computational Science & Engineering Group 02 Mar 2019 15:52 None None None None http://gala.gre.ac.uk/id/eprint/5957 View Item