Numerical simulation of solidification around a circular cylinder with natural convection

Abstract

An analysis is carried out for solidification around a cold cylinder in a rectangular cavity using numerical simulations. The transient influences of solidification accompanied by natural convection are investigated in detail. The governing equations, in terms of one-fluid formulation, including the Navier-Stokes and energy equations for incompressible Newtonian fluids are written for the whole domain. The no-slip and Dirichlet-type isothermal temperature boundary conditions are both implemented using a linear interpolation technique (immersed boundary method). The solidification interface is represented by connected elements that move on the fixed background grid. Code validations are carried out through various problems. Finally, the temporal dependence of the solid area ratio of the solid phase to the cylinder upon various dimensionless parameters, such as Rayleigh number, Prandtl number, Stefan number, thermal property ratios as well as a parameter indicating the effect of superheat is studied.