A numerical investigation of phase-change in axi-symmetric geometry

This study is a numerical investigation of a heat transfer problem involving a change of phase. The enthalpy model for phase-change is employed to obtain solutions for two sets of problems in an axi-symmetric geometry. In both problems, it is assumed that the phase change occurs at a discrete temperature and that there is no change in density upon melting or freezing. The enthalpy model is a mathematical model based on global energy conservation. Enthalpy and temperature are both used as dependent variables, and the relationship between enthalpy and temperature for the phase-change material is required to carry out the solution. This model can be used to solve heat transfer problems with or without phase change; however, it is ideal for problems involving a change of phase because it is not necessary to track the interface. In other words, the location of the solid-liquid interface can be obtained after the solution is complete by knowing the location of two-phase elements. In most other numerical techniques it is necessary to know the exact location of the interface to carry out the computations at any instant of time, making the numerical method impractical for many problems. The general form of the enthalpy equation, along with its non-dimensionalized form and its finite difference form are presented. A discussion of various numerical procedures used for solving phase-change problems is presented which includes a summary of the advantages and disadvantages of various -schemes such as the explicit scheme, the fully implicit scheme and the Crank-Nicolson scheme. In addition, a survey of methods available for solving the resulting set of simultaneous equations is also presented. The enthalpy algorithm is developed and applied to two sample problems. In these problems, the freezing of a solid cylinder with either an imposed boundary temperature or a convective boundary heat flux is considered. The results obtained for the imposed boundary temperature case are checked against the known solution with excellent agreement resulting. The problem of freezing in a more complex axi-symmetric geometry (a tear-drop shaped container) is also studied, the effects of the curved boundary on the finite difference form of the enthalpy equation is considered, and a general algorithm is devised to employ the appropriate form of the enthalpy equation for a given case, considering various situations that may exist for nodes near the curved boundary. Limited experimental data are obtained and compared with the numerical results. The comparison showed agreement between the experimental and the numerical results.