A coupled model for simulation of the gas–liquid two-phase flow with complex flow patterns

Abstract A new model coupling two basic models, the model based on interface tracking method and the two-fluid model, for simulating gas–liquid two-phase flow is presented. The new model can be used to simulate complex multiphase flow in which both large-length-scale interface and small-length-scale gas–liquid interface coexist. By the physical state and the length scale of interface, three phases are divided, including the liquid phase, the large-length-scale-interface phase (LSI phase) and the small-length-scale-interface phase (SSI phase). A unified solution framework shared by the two basic models is built, which makes it convenient to perform the solution process. Based on the unified solution framework, the modified MCBA–SIMPLE algorithm is employed to solve the Navier–Stokes equations for the proposed model. A special treatment called “volume fraction redistribution” is adopted for the special grids containing all three phases. Another treatment is proposed for the advection of large-length-scale interface when some portion of SSI phase coalesces into LSI phase. The movement of the large-length-scale interface is evaluated using VOF/PLIC method. The proposed model is equivalent to the two-fluid model in the zone where only the liquid phase and the SSI phase are present and to the model based on interface tracking method in the zone where only the liquid phase and the LSI phase are present. The characteristics of the proposed model are shown by four problems.

[1]  David H. Sharp,et al.  The dynamics of bubble growth for Rayleigh-Taylor unstable interfaces , 1987 .

[2]  E. Puckett,et al.  A High-Order Projection Method for Tracking Fluid Interfaces in Variable Density Incompressible Flows , 1997 .

[3]  G. Kreiss,et al.  A conservative level set method for two phase flow II , 2005, Journal of Computational Physics.

[4]  D. Drew,et al.  Theory of Multicomponent Fluids , 1998 .

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

[6]  Donald A. Drew,et al.  Phase-distribution mechanisms in turbulent low-quality two-phase flow in a circular pipe , 1982, Journal of Fluid Mechanics.

[7]  Stojan Petelin,et al.  Coupling of the interface tracking and the two-fluid models for the simulation of incompressible two-phase flow , 2001 .

[8]  I. Zun,et al.  A three-dimensional particle tracking method for bubbly flow simulation , 1997 .

[9]  Lev Shemer,et al.  On the interaction between two consecutive elongated bubbles in a vertical pipe , 2000 .

[10]  G. Wallis.  One Dimensional Two-Phase Flow , 1969 .

[11]  Andrea Prosperetti,et al.  Ensemble phase‐averaged equations for bubbly flows , 1994 .

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

[13]  H. Bruce Stewart,et al.  Two-phase flow: Models and methods , 1984 .

[14]  M. Darwish,et al.  A pressure-based algorithm for multi-phase flow at all speeds , 2003 .

[15]  D. Drew,et al.  Application of general constitutive principles to the derivation of multidimensional two-phase flow equations , 1979 .

[16]  Mark Sussman,et al.  A computational study of the effect of initial bubble conditions on the motion of a gas bubble rising in viscous liquids , 2005 .

[17]  On the multidimensional modeling of gas-liquid slug flows , 2002 .

[18]  Martin E. Weber,et al.  Bubbles in viscous liquids: shapes, wakes and velocities , 1981, Journal of Fluid Mechanics.

[19]  Qiang Song,et al.  Phase distributions for upward laminar dilute bubbly flows with non-uniform bubble sizes in a vertical pipe , 2001 .

[20]  Wing Kam Liu,et al.  Lagrangian-Eulerian finite element formulation for incompressible viscous flows☆ , 1981 .

[21]  M. Ishii.  Thermo-fluid dynamic theory of two-phase flow , 1975 .

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

[23]  D. Drew.  Mathematical Modeling of Two-Phase Flow , 1983 .

[24]  N. Zuber,et al.  Drag coefficient and relative velocity in bubbly, droplet or particulate flows , 1979 .

[25]  Donghong Zheng,et al.  CFD simulations of hydrodynamic characteristics in a gas-liquid vertical upward slug flow , 2007 .

[26]  Stanley Osher,et al.  Level Set Methods , 2003 .

[27]  C. W. Hirt,et al.  An Arbitrary Lagrangian-Eulerian Computing Method for All Flow Speeds , 1997 .

[28]  J. Flaherty,et al.  Analysis of phase distribution in fully developed laminar bubbly two-phase flow , 1991 .

[29]  Michio Sadatomi,et al.  Momentum and heat transfer in two-phase bubble flow—I. Theory , 1981 .

[30]  M. Darwish,et al.  A UNIFIED FORMULATION OF THE SEGREGATED CLASS OF ALGORITHMS FOR FLUID FLOW AT ALL SPEEDS , 2000 .

[31]  P. Colella,et al.  An Adaptive Level Set Approach for Incompressible Two-Phase Flows , 1997 .

[32]  S. G. Bankoff,et al.  Structure of air-water bubbly flow in a vertical pipe—I. liquid mean velocity and turbulence measurements , 1993 .

[33]  Fabián J. Bonetto,et al.  Lateral forces on spheres in turbulent uniform shear flow , 1999 .

[34]  F. Harlow,et al.  Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface , 1965 .

[35]  Mamoru Ishii,et al.  Two-fluid model and hydrodynamic constitutive relations , 1984 .

[36]  J. G. Hnat,et al.  Spherical cap bubbles and skirt formation , 1976 .

[37]  S. Zaleski,et al.  Volume-of-Fluid Interface Tracking with Smoothed Surface Stress Methods for Three-Dimensional Flows , 1999 .

[38]  Robert I. Nigmatulin,et al.  Spatial averaging in the mechanics of heterogeneous and dispersed systems , 1979 .