An experimental and analytical study of solidification around an array of horizontal cylinders subjected to free convection flow

Abstract

In this paper the solidification of a liquid around an array of cooled horizontal cylinders has been investigating experimentally and analytically. The horizontal cylinders can be arranged in various configurations. In this paper one typical example for such a configuration is studied. This is a cyclic system cylinders with cylinders of a diameter of 54 mm a length of 1793 mm and a spacing between them of 100 mm. The cylinders are arranged in an equilateral triangular array. The theoretical part of the paper deals with a simplified solution of the problem of liquid solidification around the horizontal cylinders under the influence of a free convection flow. A simple quasi steady-state model for the solidification process is derived. The model describes the phase change phenomenon with an imposed boundary condition on the solidification front which assumes a distribution of the heat transfer coefficient from the surrounding free convection flow. The simplified theoretical model, which is based on the Happel-Brenner cell method, can be used for a fast preliminary design of latent heat storage devices. In addition, the model considers the effect of a contact layer between the cooled cylinders and the surrounding ice layers. It can be shown, that the solution of the problem can be reduced to the solution of a system of integro-differential equations, which has been solved numerically. In the experimental part of this work, the thickness of the solidified layer was measured by using a newly built test apparatus. Both, the thickness of the solidified layer and the average liquid temperature depend on time. The local heat transfer coefficient at the solidification front was also determined experimentally. Experiments have been done with timely varying fluid temperatures between 293 K to 274 K. The experimental results are found in good agreement with the theoretical model for the obtained results for time dependent thickness of the frozen crust.