Doctoral Dissertations

Date of Award

8-1989

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mechanical Engineering

Major Professor

Masood Parang, Rao V. Arimilli

Committee Members

V. Alexiades, James A. Euler

Abstract

Transient heat transfer problems involving solid-liquid phase change moving boundaries have attracted a great deal of interest in recent years. Applications of phase change moving boundary problems in wide range of technologies have given the impetus and motivation for research in this area for many years. The solution methodologies for these problems can be classified into three broad categories, Analytical, Numerical and Experimental. Analytical methods are applicable only to relatively simple problems and only in one dimension. Limitations of analytical methods compell researchers to seek solutions numerically and observe the phenomenon experimentally.

The most versatile method for moving boundary problems is the enthalpy method. There have been a few studies which use enthalpy method and consider convective effects in the liquid. The present study uses a formulation developed by Voller, Markatos & Cross. The main feature of the formulation is that the latent heat effects are isolated in the so called 'source term'. The governing equations so formulated have the same general form as the conventional conservation equations of mass, momentum, and energy. Standard algorithms such as SIMPLE or SIMPLER, therefore can be used. In the present paper the problem of solidification in a rectangular cavity, cooled from one vertical side with remaining sides kept insulated, is solved. The velocities in the solid need to be made zero. This was done using Darcy source technique, which adds a 'Darcy source' to the leading coefficient to the velocity discretization equation. This allows for a gradual slow down of the velocities in the solid region. This technique produced a physically realistic velocity field and interface location.

The numerical technique utilized here is relatively new. For this reason, one of the focusses of this study is the experimental verification of this numerical model. An experimental apparatus is built with one copper wall ( cold wall) and other walls made of plexiglass (adiabatic walls). The liquid used for solidification experiments is Caprilic acid. Caprilic acid is used because of its less than ambient melting point 14° C) and low volume reduction upon solidification (3 - 4 %). Photographs of the interface location are presented at various times. The numerical solution is compared with the experimental data for the interface location and temperature. The numerical and experimental solutions are found to be in good agreement.

The numerical model is used to conduct a parametric study. The results are presented for a wide range of physical parameters. Low Prandtl number (0.01) signifying liquid metals (Aluminum, Iron, etc. ) and high Prandtl numbers (10, 100) signifying paraffins are considered. Rayleigh number range of 104 to 106 , aspect ratios of 0.1 to 10, a range of cold wall temperatures, a range of initial superheat levels for the liquid are also considered. A simple corelation is presented for the time for complete solidification.

The results show that for Rayleigh number of 104,when Prandtl number is 0.01 the interface is curved with solidification more advanced near the bottom than at the top of the enclosure. However, at Prandtl number of 100 the interface is essentially planar. Influence of aspect ratio on the volume fraction solidified is found to be weak. However, for lower aspect ratios (< 0.5 )the interface is planar and for higher aspect ratios(> 1) the interface is curved.

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