Numerical Solution of Transient Freezing Equations of a Laminar Water Flow in a Channel with Constant Wall Temperature in the Absence of Gravity

Abstract

In this study, the freezing of water inside the channel with constant wall temperature was studied numerically. At the entrance of the channel, the velocity profile is assumed. The thermophysical properties of the fluid, including density, thermal capacity, thermal expansion coefficient and viscosity, are function of the temperature and the volume fraction of ice. Nonlinear equations of continuity, momentum and energy are solved in a general form and solved with finite volume method. The SIMPLEC algorithm is employed to handle the pressure-velocity coupling for the continuity and momentum equations. The enthalpy-porosity method has been used to model the phase-change problem. In this technique, the interface between solid and liquid is called the mushy zone. In the mushy zone, due to the high viscosity of this zone, a Laplace equation for velocity is used to solve the equation of momentum. It was observed that with the advance along the channel, the continuous effect of the cooling of the walls created and increased the thickness of the ice layer. Creating the ice layer causes fluid flow obstruction and pressure drop, with the highest pressure drop in Fourier number 12.0. Investigating the thickness of the ice layer, it was shown that in the Re = 1800, when the wall temperature difference and the input fluid temperature is about 7 degrees, ice is not formed. However, when this difference reaches 12 degrees, the ice layer thickness in the steady state covers 20% of the channel diameter. By increasing the wall temperature difference and the input fluid to 17 degrees, this number is increased to about 35%. Also, the effect of gravity on the freezing of water inside the channel was investigated and it was observed that gravity has negligible affect on the freezing of water and can be discarded.