Appropriate Formulations for Velocity and Pressure Calculations at Gas-liquid Interface with Collocated Variable Arrangement

A high-precision simulation algorithm for gas-liquid two-phase flows on unstructured meshes has been developed to simulate gas entrainment phenomenon in a sodium-cooled fast reactor. In this study, it became clear that unphysical behaviors near gas-liquid interfaces were caused by conventional algorithms. Then, physics-basis considerations were conducted for mechanical balances at gas-liquid interfaces to derive appropriate formulations. By defining momentum and velocity independently and developing the momentum transport equations for both gas and liquid phases, the physically appropriate formulation of momentum transport was derived, which eliminated the unphysical pressure distribution caused by the conventional formulation. In addition, the physically appropriate formulation was derived for the pressure gradient to satisfy the mechanical balances between pressure and surface tension at gas-liquid interfaces. As the validation test, the rising gas bubble in liquid was simulated by the developed simulation algorithm with the physically appropriate formulations, and the simulated terminal bubble shapes on the structured and highly-distorted unstructured meshes coincided with the experimental data under each simulation condition determined by the Morton and Eotvos numbers.

[1]  S. Zaleski,et al.  Analytical relations connecting linear interfaces and volume fractions in rectangular grids , 2000 .

[2]  Takumi KAWAMURA,et al.  Formulations and Validations of a High-Precision Volume-of-Fluid Algorithm on Nonorthogonal Meshes for Numerical Simulations of Gas Entrainment Phenomena , 2009 .

[3]  S. Cummins,et al.  Estimating curvature from volume fractions , 2005 .

[4]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[5]  G. Tryggvason,et al.  A front-tracking method for viscous, incompressible, multi-fluid flows , 1992 .

[6]  Sung-Eun Kim,et al.  A Multi-Dimensional Linear Reconstruction Scheme for Arbitrary Unstructured Mesh , 2003 .

[7]  Chia-Jung Hsu Numerical Heat Transfer and Fluid Flow , 1981 .

[8]  P. Woodward,et al.  SLIC (Simple Line Interface Calculation) , 1976 .

[9]  Yoshiaki Oka,et al.  Direct calculation of bubble growth, departure, and rise in nucleate pool boiling , 2001 .

[10]  E. Puckett,et al.  Second-Order Accurate Volume-of-Fluid Algorithms for Tracking Material Interfaces , 2013 .

[11]  H. Takewaki,et al.  The cubic-interpolated Pseudo particle (cip) method: application to nonlinear and multi-dimensional hyperbolic equations , 1987 .

[12]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[13]  W. Rider,et al.  Reconstructing Volume Tracking , 1998 .

[14]  Xiaofeng Yang,et al.  Analytic relations for reconstructing piecewise linear interfaces in triangular and tetrahedral grids , 2006, J. Comput. Phys..

[15]  Marius Paraschivoiu,et al.  Second order accurate volume tracking based on remapping for triangular meshes , 2003 .

[16]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[17]  D. Fletcher,et al.  A New Volume of Fluid Advection Algorithm , 2000 .

[18]  L YoungsD,et al.  Time-dependent multi-material flow with large fluid distortion. , 1982 .

[19]  A. A. Amsden,et al.  The SMAC method: A numerical technique for calculating incompressible fluid flow , 1970 .

[20]  Tomoaki Kunugi,et al.  MARS for multiphase calculation , 2000 .

[21]  J. López,et al.  An improved PLIC-VOF method for tracking thin fluid structures in incompressible two-phase flows , 2005 .

[22]  S. Koshizuka,et al.  Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid , 1996 .

[23]  Gang Wang,et al.  A computational Lagrangian–Eulerian advection remap for free surface flows , 2004 .