Effect of density change during solidification using variable time step method

Abstract

A numerical solution has been developed for variable density phase change with shrinkage or expansion using the variable time step method, where the grid spacing is kept constant while the time step is kept as a variable. The temperature distribution has been studied as a function of position and time for different partition coefficient, initial and boundary temperatures. The key effect that has been investigated is the effect of the density variation due to phase change during solidification. The numerical solution obtained has been compared with that of the analytical solution for validation. It is found that with increase in density ratio, the interface moves slower for undercooled initial temperature and vice versa for superheated initial temperature. It is also seen that with a decrease in initial and boundary temperature, the interface moves faster.