Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests

This article reports on the potential of application of LES in the calculation of turbulent two-phase flows, in the case where each phase is resolved and interfaces remain much larger than the mesh size. In comparison with single-phase flow, successful application of LES to resolve two-phase flow problems should account for the complex interaction between turbulence and interfaces. Non-linear transfers of turbulent energy across the interface have to be accurately modeled. The derivation of the complete filtered two-phase flow governing equations has been formulated to deal with turbulence at the interface in a comprehensive and practical way. Explicit filtering of 2D direct numerical simulations has been employed to evaluate the order of magnitude of the new subgrid contributions. A parametric study on the academic test case of two counter-rotative vortices and a more complex test case of phase inversion in a closed box have been utilized to perform an order of magnitude analysis of different transport mechanisms. Important features of turbulent energy transfer across the interface have been discussed. Analyses of the numerical results have been conducted to derive conclusions on the relative importance of the different subgrid scale contributions, and modeling issues and solutions are provided.

[1]  G. Hetsroni.  Handbook of hydraulic resistance , 1990 .

[2]  F. Nicoud,et al.  Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor , 1999 .

[3]  John R. Fessler,et al.  Preferential concentration of particles by turbulence , 1991 .

[4]  Stéphane Vincent,et al.  TEST-CASE NO 15: PHASE INVERSION IN A CLOSED BOX (PC) , 2004 .

[5]  S. Zaleski,et al.  DIRECT NUMERICAL SIMULATION OF FREE-SURFACE AND INTERFACIAL FLOW , 1999 .

[6]  Kyle D. Squires,et al.  Preferential concentration of marine particles in isotropic turbulence , 1995 .

[7]  D. H. Peregrine,et al.  Breaking Waves on Beaches , 1983 .

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

[9]  Gretar Tryggvason,et al.  Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays , 1998, Journal of Fluid Mechanics.

[10]  Herve Lemonnier,et al.  TEST-CASE NO 5: OSCILLATION OF AN INCLUSION IMMERSED IN A QUIESCENT FLUID (PA) , 2004 .

[11]  M. Lance,et al.  Turbulence in the liquid phase of a uniform bubbly air–water flow , 1991, Journal of Fluid Mechanics.

[12]  Keith W. Bedford,et al.  Improved averaging method for turbulent flow simulation. Part II: Calculations and verification , 1986 .

[13]  Djamel Lakehal,et al.  Direct numerical simulation of turbulence in a sheared air–water flow with a deformable interface , 2003, Journal of Fluid Mechanics.

[14]  H. Blanch,et al.  Bubble coalescence and break‐up in air‐sparged bubble columns , 1990 .

[15]  Bernardus J. Geurts,et al.  A priori tests of large eddy simulation of the compressible plane mixing layer , 1995 .

[16]  Hiroshi Saeki,et al.  Velocity field after wave breaking , 2002 .

[17]  Djamel Lakehal,et al.  Large-eddy simulation of bubbly turbulent shear flows , 2002 .

[18]  J. M. Delhaye,et al.  Jump conditions and entropy sources in two-phase systems , 1974 .

[19]  Pierre Lubin,et al.  An adaptative augmented Lagrangian method for three-dimensional multimaterial flows , 2004 .

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

[21]  G. Batchelor,et al.  Transport Properties of Two-Phase Materials with Random Structure , 1974 .

[22]  D. Homescu,et al.  Forced Convection Condensation on a Horizontal Tube: Influence of Turbulence in the Vapor and , 1999 .

[23]  Pierre Lubin,et al.  Fully three-dimensional direct numerical simulation of a plunging breaker , 2003 .

[24]  K. Horiuti.  Assessment of the Subgrid-Scale Models at Low and High Reynolds Numbers , 1996 .

[25]  Pierre Sagaut,et al.  On the filtering paradigm for LES of flows with discontinuities , 2005 .

[26]  Benoît Mathieu.  Etudes physique, expérimentale et numérique des mécanismes de base intervenant dans les écoulements diphasiques , 2003 .

[27]  A. W. Vreman,et al.  Direct and Large-Eddy Simulation of the Compressible Turbulent Mixing Layer , 1995 .

[28]  Donald A. Drew,et al.  The virtual mass and lift force on a sphere in rotating and straining inviscid flow , 1987 .

[29]  P. Chassaing.  Turbulence en mécanique des fluides , 2000 .

[30]  D. Juric,et al.  Computations of Boiling Flows , 1998 .

[31]  Marcel Lesieur,et al.  Turbulence in fluids , 1990 .

[32]  K. Squires,et al.  On the prediction of gas–solid flows with two-way coupling using large eddy simulation , 2000 .

[33]  Erik Damgaard Christensen,et al.  Large eddy simulation of breaking waves , 2001 .

[34]  Y. Sato,et al.  Liquid velocity distribution in two-phase bubble flow , 1975 .

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

[36]  J. F. Harper,et al.  The Motion of Bubbles and Drops Through Liquids , 1972 .

[37]  P. Moin,et al.  A General Class of Commutative Filters for LES in Complex Geometries , 1998 .

[38]  Pascal Gardin,et al.  Numerical Simulation of Gas-Jet Wiping in Steel Strip Galvanizing Process , 2005 .

[39]  Lian Shen,et al.  Large-eddy simulation of free-surface turbulence , 2001, Journal of Fluid Mechanics.

[40]  Isao Kataoka,et al.  Local instant formulation of two-phase flow , 1986 .

[41]  Christophe Calvin,et al.  An object-oriented approach to the design of fluid mechanics software , 2002 .

[42]  Asghar Esmaeeli,et al.  An inverse energy cascade in two-dimensional low Reynolds number bubbly flows , 1996, Journal of Fluid Mechanics.

[43]  P. Sagaut.  Large Eddy Simulation for Incompressible Flows , 2001 .

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

[45]  S. Menon,et al.  Effect of subgrid models on the computed interscale energy transfer in isotropic turbulence , 1994 .

[46]  Wei Yao,et al.  Volumetric interfacial area prediction in upward bubbly two-phase flow , 2004 .

[47]  Keith W. Bedford,et al.  IMPROVED AVERAGING METHOD FOR TURBULENT FLOW SIMULATION. PART I: THEORETICAL DEVELOPMENT AND APPLICATION TO BURGERS' TRANSPORT EQUATION , 1986 .

[48]  Marcus Herrmann,et al.  A Eulerian level set/vortex sheet method for two-phase interface dynamics , 2005 .

[49]  Santiago Laín,et al.  Modelling hydrodynamics and turbulence in a bubble column using the Euler-Lagrange procedure , 2002 .

[50]  I. Eames,et al.  The Motion of High-Reynolds-Number Bubbles in Inhomogeneous Flows , 2000 .

[51]  Said Elghobashi,et al.  Prediction of the particle-laden jet with a two-equation turbulence model , 1984 .

[52]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[53]  J. Caltagirone,et al.  A One-Cell Local Multigrid Method for Solving Unsteady Incompressible Multiphase Flows , 2000 .

[54]  Pierre Sagaut,et al.  Assessment of some self-adaptive SGS models for wall bounded flows , 1999 .

[55]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[56]  Samuel W. J. Welch,et al.  Local simulation of two-phase flows including interface tracking with mass transfer , 1995 .

[57]  Isabelle Calmet,et al.  Statistical structure of high-Reynolds-number turbulence close to the free surface of an open-channel flow , 2003, Journal of Fluid Mechanics.