FREE SURFACE FLOW AND HEAT TRANSFER IN CAVITIES: THE SEA ALGORITHM

• Published in: Numerical heat transfer. Part B, Fundamentals Fundamentals, 1995-06, Vol.27 (4), p.487-507
• Main Authors: Pericleous, K. A., Chan, K. S., Cross, M.
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Computer simulation; Convection and heat transfer; Cooling; Enthalpy; Equations of motion; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Gravitation; Gravity die casting and continuous casting; Heat transfer; Hydrodynamic waves; Interfaces (materials); Metals. Metallurgy; Numerical methods; Physics; Production of metals; Production of non ferrous metals. Process materials; Surfaces; Turbulent flows, convection, and heat transfer; Two phase flow
• ISSN: 1040-7790; 1521-0626
• DOI: 10.1080/10407799508914969

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.