tailieunhanh - Direct numerical simulation of solidification with effects of density difference

In this paper, direct numerical simulations are presented for solidification with the effects of density difference between the solid and liquid phases. A front-tracking method is used. The solidification front, . the solid-liquid interface separating solid and liquid, is represented by connected elements that move on a rectangular and stationary grid. | Vietnam Journal of Mechanics, VAST, Vol. 38, No. 3 (2016), pp. 193 – 204 DOI: DIRECT NUMERICAL SIMULATION OF SOLIDIFICATION WITH EFFECTS OF DENSITY DIFFERENCE Vu Van Truong Hanoi University of Science and Technology, Vietnam E-mail: Received April 15, 2015 Abstract. In this paper, direct numerical simulations are presented for solidification with the effects of density difference between the solid and liquid phases. A front-tracking method is used. The solidification front, . the solid-liquid interface separating solid and liquid, is represented by connected elements that move on a rectangular and stationary grid. The Navier-Stokes equations are solved by a projection method on the entire domain including the solid phase. An indicator function reconstructed from the front information is used to set the velocities in the solid phase to zero, and thus to enforce the no-slip condition at the interface. The method is validated through comparisons with exact solutions for one- and two-dimensional problems. The method is then used to simulate the solidification processes with the effects of volume change due to density difference. Keywords: Direct numerical simulation, front-tracking, solidification, density difference. 1. INTRODUCTION Solidification problems occur in many industrial applications, and have thus received much attention, through experimental, theoretical and simulation investigations [1]. Experiments can be found in [2–5], in which the authors mentioned the effects of volume change on the phase change process. Many phase change materials such as water, silicon (Si), germanium (Ge), . . . have density difference between the solid and liquid phases. Accordingly, volume change always appears during the solidification process, and considerably affects the final products of the phase change process [3]. Phase change problems are non-linear due to the presence of a moving interface between the solid .