A FULL 3-DIMENSIONAL ADAPTIVE FINITE VOLUME SCHEME FOR TRANSPORT AND PHASE-CHANGE PROCESSES, PART I: FORMULATION AND VALIDATION

Abstract

A full three-dimensional (3-D) numerical formulation for accurate simulation of transport and phase-change processes is presented. These processes are characterized by a variety of flow and heat transfer mechanisms in irregular domains with or without the movement of phase-change interfaces and free surfaces. A generalized 3-D nonorthogonal curvilinear finite volume formulation is developed in conjunction with a robust mesh generation scheme known as multizone adaptive grid generation (MAGG) to tackle such problems. The coupling between the interfacial dynamics and transport phenomena in the bulk of the phases is inherent in this formulation. A 3-D k-epsilon model is also incorporated to tackle the turbulent flows in these applications. The unified numerical model is validated against classical 3-D problems such as turbulent natural convection in a differentially heated cube, solidification in a cavity, and so on. In a companion paper, Part II (see this issue), application of this formulation to 3-D simulation of hydrothermal crystal growth and low and high pressure Czochralski (Cz) crystal growth is presented.