Numerical Investigation of Solidification around a Circular Cylinder with the Presence of the Free Surface in a Rectangular Cavity
Main Article Content
Abstract
This paper presents numerical simulation of solidification around a cooled circular cylinder with the presence of a free surface in a rectangular cavity. The free surface is introduced to account for volume change due to density difference between the solid and liquid phases during solidification. Pure tin with the solid-to-liquid density ratio ρsl = 1.05 (shrinkage) is investigated as a phase change material. The front-tracking method combined with an interpolation technique, in which the interface separating two phases is represented by connected elements laid on a stationary grid, is used for solving the problem. The case of no volume change, i.e., ρsl = 1.0, is also calculated and compared with the case of ρsl = 1.05 to see how volume shrinkage affects the solidification process. The numerical results show that shrinkage reduces the solidification rate, and thus results in a decrease in the form, i.e., the area, of the solid layer around the cylinder. In addition, the liquid level decreases in time due to volume shrinkage upon solidification.
Keywords
Numerical simulation, Front-tracking, Solidification, Shrinkage, Circular cylinder
Article Details
References
[1] K. Sasaguchi, K. Kusano, R. Viskanta, A numerical analysis of solid-liquid phase change heat transfer around a single and two horizontal, vertically spaced cylinders in a rectangular cavity, Int. J. Heat Mass Transfer. 40 (1997) 1343–1354.
[2] M. Sugawara, H. Beer, Numerical analysis for freezing/melting around vertically arranged four cylinders, Heat Mass Transfer. 45 (2009) 1223–1231.
[3] Y.-C. Shih, H. Chou, Numerical study of solidification around staggered cylinders in a fixed space, Numer. Heat Tr. A-Appl. 48 (2005) 239–260.
[4] T.V. Vu, A.V. Truong, N.T.B. Hoang, D.K. Tran, Numerical investigations of solidification around a circular cylinder under forced convection, J. Mech. Sci. Technol. 30 (2016) 5019–5028.
[5] S. Sablani, S.P. Venkateshan, V.M.K. Sastri, Numerical study of two-dimensional freezing in an annulus, J. Thermophys. Heat Tr. 4 (1990) 398–400.
[6] T.V. Vu, G. Tryggvason, S. Homma, J.C. Wells, H. Takakura, A front-tracking method for three-phase computations of solidification with volume change, J. Chem. Eng. Jpn. 46 (2013) 726–731.
[7] T.V. Vu, G. Tryggvason, S. Homma, J.C. Wells, Numerical investigations of drop solidification on a cold plate in the presence of volume change, Int. J. Multiphase Flow. 76 (2015) 73–85.
[8] H. Gan, J. Chang, J.J. Feng, H.H. Hu, Direct numerical simulation of the sedimentation of solid particles with thermal convection, J. Fluid Mech. 481 (2003) 385–411.
[9] F.H. Harlow, J.E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids. 8 (1965) 2182–2189.
[10] V.V. Truong, Direct numerical simulation of solidification with effects of density difference, Vietnam Journal of Mechanics. 38 (2016) 193–204.
[2] M. Sugawara, H. Beer, Numerical analysis for freezing/melting around vertically arranged four cylinders, Heat Mass Transfer. 45 (2009) 1223–1231.
[3] Y.-C. Shih, H. Chou, Numerical study of solidification around staggered cylinders in a fixed space, Numer. Heat Tr. A-Appl. 48 (2005) 239–260.
[4] T.V. Vu, A.V. Truong, N.T.B. Hoang, D.K. Tran, Numerical investigations of solidification around a circular cylinder under forced convection, J. Mech. Sci. Technol. 30 (2016) 5019–5028.
[5] S. Sablani, S.P. Venkateshan, V.M.K. Sastri, Numerical study of two-dimensional freezing in an annulus, J. Thermophys. Heat Tr. 4 (1990) 398–400.
[6] T.V. Vu, G. Tryggvason, S. Homma, J.C. Wells, H. Takakura, A front-tracking method for three-phase computations of solidification with volume change, J. Chem. Eng. Jpn. 46 (2013) 726–731.
[7] T.V. Vu, G. Tryggvason, S. Homma, J.C. Wells, Numerical investigations of drop solidification on a cold plate in the presence of volume change, Int. J. Multiphase Flow. 76 (2015) 73–85.
[8] H. Gan, J. Chang, J.J. Feng, H.H. Hu, Direct numerical simulation of the sedimentation of solid particles with thermal convection, J. Fluid Mech. 481 (2003) 385–411.
[9] F.H. Harlow, J.E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids. 8 (1965) 2182–2189.
[10] V.V. Truong, Direct numerical simulation of solidification with effects of density difference, Vietnam Journal of Mechanics. 38 (2016) 193–204.