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. | Vietnam Journal of Mechanics, VAST, Vol. 38, No. 4 (2016), pp. 295 – 306 DOI: NUMERICAL SIMULATION OF SOLIDIFICATION AROUND A CIRCULAR CYLINDER WITH NATURAL CONVECTION Vu Van Truong∗ , Truong Viet Anh, Hoang Thi Bich Ngoc Hanoi University of Science and Technology, Vietnam ∗ E-mail: Received November 21, 2015 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. Keywords: Solidification, cylinder, natural convection, front tracking, immersed boundary method. 1. INTRODUCTION Solid-liquid phase change finds application in many systems and in nature including latent heat energy storage, metallurgy, and food and pharmaceutical processing. Solidification around cooled cylinders appears in thermal energy storage systems, freezing of soil and others. Therefore, understanding solidification heat transfer around cooled cylinders plays an important role in designing and operating such systems. Accordingly, there have been many works concerned with solidification around .
