A new approach to sub-grid surface tension for LES of two-phase flows

In two-phase flow, the presence of inter-phasal surface - the interface - causes additional terms to appear in LES formulation. Those terms were ignored in contemporary works, for the lack of model and because the authors expected them to be of negligible influence. However, it has been recently shown by a priori DNS simulations that the negligibility assumption can be challenged. In the present work, a model for one of the sub-grid two-phase specific terms is proposed, using deconvolution of the velocity field and advection of the interface using that field. Using the model, the term can be included into LES. A brief presentation of the model is followed by numerical tests that assess the model's performance by comparison with a priori DNS results.

[1]  Pierre Sagaut,et al.  Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests , 2007 .

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

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

[4]  Achi Brandt,et al.  Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, Revised Edition , 2011 .

[5]  Gaurav Tomar,et al.  Numerical simulation of bubble growth in film boiling using a coupled level-set and volume-of-fluid method , 2005 .

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

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

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

[9]  Artur Tyliszczak,et al.  LES of Variable Density Bifurcating Jets , 2007 .

[10]  C. Hirsch The Basic Equations of Fluid Dynamics , 2007 .

[11]  Jean-Luc Estivalezes,et al.  Direct numerical simulation of a freely decaying turbulent interfacial flow , 2010 .

[12]  R. Fletcher Conjugate gradient methods for indefinite systems , 1976 .

[13]  S. Osher,et al.  A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method) , 1999 .

[14]  D. Youngs,et al.  Numerical simulation of turbulent mixing by Rayleigh-Taylor instability , 1984 .

[15]  S. Osher,et al.  Spatially adaptive techniques for level set methods and incompressible flow , 2006 .

[16]  A. D. Gosman,et al.  Large Eddy Simulation of Primary Diesel Spray Atomization , 2004 .

[17]  Gian Marco Bianchi,et al.  3D Large Scale Simulation of the High-Speed Liquid Jet Atomization , 2007 .

[18]  Mark Sussman,et al.  A sharp interface method for incompressible two-phase flows , 2007, J. Comput. Phys..

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

[20]  T. Ménard,et al.  Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet , 2007 .

[21]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[22]  Frank Losasso,et al.  A fast and accurate semi-Lagrangian particle level set method , 2005 .

[23]  Michel Stanislas,et al.  Progress in Wall Turbulence 2 : Understanding and Modelling , 2011 .

[24]  Bernardus J. Geurts,et al.  Numerically induced high-pass dynamics in large-eddy simulation , 2005 .

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

[26]  S. Drobniak,et al.  Quality of LES Predictions of Isothermal and Hot Round Jet , 2008 .

[27]  Ebrahim Shirani,et al.  Turbulence Models for Flows with Free Surfaces and Interfaces , 2004 .

[28]  Wojciech Aniszewski,et al.  SIMPLIFIED VOLUME OF FLUID METHOD (SVOF) FOR TWO-PHASE FLOWS , 2008 .

[29]  Mikhael Gorokhovski,et al.  Modeling Primary Atomization , 2008 .

[30]  Gretar Tryggvason,et al.  Direct Numerical Simulations of Gas–Liquid Multiphase Flows: Preface , 2011 .

[31]  Hervé Jeanmart,et al.  Investigation of eddy-viscosity models modified using discrete filters : A simplified regularized variational multiscale model and an enhanced field model , 2007 .

[32]  M. Sussman,et al.  A Coupled Level Set and Volume-of-Fluid Method for Computing 3D and Axisymmetric Incompressible Two-Phase Flows , 2000 .

[33]  Olivier Simonin,et al.  DNS of the interaction between a deformable buoyant bubble and a spatially decaying turbulence: A priori tests for LES two-phase flow modelling , 2008 .

[34]  L. M. Albright Vectors , 2003, Current protocols in molecular biology.

[35]  Gaël Varoquaux,et al.  Mayavi: 3D Visualization of Scientific Data , 2010, Computing in Science & Engineering.

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

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

[38]  N. Adams,et al.  An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows , 2001 .

[39]  Michel Stanislas,et al.  Progress in Wall Turbulence: Understanding and Modeling Proceedings of the WALLTURB International Workshop held in Lille, France, April 21-23, 2009 , 2012 .

[40]  Gaurav Tomar,et al.  Multiscale simulations of primary atomization , 2010 .

[41]  Thomas Williams,et al.  Gnuplot 4.4: an interactive plotting program , 2010 .

[42]  Feng Xiao,et al.  A simple algebraic interface capturing scheme using hyperbolic tangent function , 2005 .

[43]  Greg Humphreys,et al.  Remote rendering for ultrascale data. , 2008 .

[44]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

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

[46]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

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

[48]  Gretar Tryggvason,et al.  Direct Numerical Simulations of Gas–Liquid Multiphase Flows: Introduction , 2011 .

[49]  R. Lathe Phd by thesis , 1988, Nature.

[50]  Nikolaus A. Adams,et al.  An adaptive local deconvolution method for implicit LES , 2005, J. Comput. Phys..

[51]  Mark Sussman,et al.  A Discontinuous Spectral Element Method for the Level Set Equation , 2003, J. Sci. Comput..

[52]  R. Marcer,et al.  A validated numerical simulation of diesel injector flow using a vof method , 2000 .

[53]  M. Sussman A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles , 2003 .

[54]  Heinz Pitsch,et al.  DETAILED NUMERICAL INVESTIGATION OF TURBULENT ATOMIZATION OF LIQUID JETS , 2010 .

[55]  Stéphane Popinet,et al.  An accurate adaptive solver for surface-tension-driven interfacial flows , 2009, J. Comput. Phys..

[56]  Delphine Lacanette,et al.  Parametric study of LES subgrid terms in a turbulent phase separation flow , 2010 .

[57]  Ronald Fedkiw,et al.  Animation and rendering of complex water surfaces , 2002, ACM Trans. Graph..

[58]  Pierre Sagaut,et al.  Numerical simulation of phase separation and a priori two-phase LES filtering , 2008 .

[59]  D. Lakehal,et al.  INTERFACE-TURBULENCE INTERACTIONS AND BUBBLE DYNAMICS , 2009 .