Articles

REVIEW OF TURBULENT MIXING MODELS

  • Baolian Cheng
Expand
  • Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Received date: 2009-11-02

  Online published: 2009-11-20

Supported by

This work was performed under the auspices of the U.S. Department of Energy by the Los Alamos National Laboratory under contract number W-7405-ENG-36.

Abstract

Fluid mixing is an important phenomenon in many physical applications from supernova explosions to genetic structure formations. In this paper, we overview some theoretical and empirical dynamic mix models, which have been developed over the recent decades, in particular, the ensemble-average micro physical mix model,  the multifluid interpenetration mix model, the phenomenological and hybrid turbulent mix models, the buoyancy drag mix model, the single fluid turbulence mix model, and the large eddy simulation mix model. The similarities, distinctions, and connections between these models and their applications are discussed.

Cite this article

Baolian Cheng . REVIEW OF TURBULENT MIXING MODELS[J]. Acta mathematica scientia, Series B, 2009 , 29(6) : 1703 -1720 . DOI: 10.1016/S0252-9602(10)60012-4

References

[1]  Rayleigh L. Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density//Scientific Papers, Volume II.
Cambridge: Cambridge Univ Press, 1900: 200; Taylor G I. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes I.  Proc R Soc London A, 1950, 201: 192--196

[2]  Richtmyer R D. Taylor instability in shock acceleration of compressible fluids. Comm Pure Appl Math, 1960, 13:297--319; Meshkov E E. Izv Akad Nauk SSSR, Mekh Zhidk Gaz, 1969, 5: 151

[3]  Andronov V, Bakhrakh B, Meshkov E, Mokhov V, Nikiforov V, Pevnitskii A, Tolshmyakov A. An experimental investigation and numerical modeling of turbulent mixing in one-dimensional flows. Sov Phys Dokl, 1982, 27: 393--396; Sov Phys JETP, 1967, 44: 424--427

[4]  Read K I. Experimental investigation of turbulent mixing by Rayleigh-Taylor instability. Physica D, 1984, 12: 45--58

[5]  Dimonte G. Nonlinear evolution of the RT and RM instabilities. Phys Plasmas, 1999, 6: 2009--2015

[6]  Ramaprabhu G, Andrews M J. Experimental investigation of Rayleigh-Taylor mixing at small Atwood numbers. J Fluid Mech, 2004, 502: 233--237

[7]  Sharp D H.  An overview of Rayleigh-Taylor instability. Physica D, 1984, 12: 3--18

[8]  Youngs D L. Modeling turbulent mixing by Rayleigh-Taylor instability. Physica D, 1989, 37: 270--287; Numerical simulation of turbulent mixing by Rayleigh-Taylor instability. Physica D, 1984, 12: 32--44

[9]  Besnard D, Harlow F, Rauenzahn R, Zemach C. Turbulent transport equations for variable-density turbulence and their relationship to two-field models. LANL Report LA-12303-MS, 1992

[10]  Gauthier S, Bonnet M.  A k-ε model for turbulent mixing in shocktube flows induced by Rayleigh-Taylor instability. Phys Fluid A, 1990, 2: 1685--1694

[11]  Dalziel S B, Linden P F, Youngs D L. Self-similarity and internal structure of turbulence induced by Rayleigh-Taylor instability. J Fluid Mech, 1999, 399: 1-48

[12]  Llor A. Bulk turbulent transport and structure in Rayleigh-Taylor, and Richtmyer-Meshkov instabilities. Laser Part Beams, 2003, 21: 305--310

[13]  Scannapieco A J, Cheng B.  A multifluids interpenetra mix model. Phys Letts A, 2002, 299: 49--64

[14]  Cranfill C W.  A new multifluid turbulent-mix-model. LANL Report LA-UR-92-2484, 1992

[15]  Cheng B, Glimm J, Saltz D, Sharp D H. Boundary conditions for a two pressure two phase flow model. Physica D, 1999, 133: 84--105

[16]  Livescu D, Ristorcelli J R. Buoyancy-driven variable-density turbulence. J Fluid Mech, 2006, 591: 43--71

[17]  Dimotakis P E. Turbulent mixing. Annu Rev Fluid Mech, 2005, 37: 329--356

[18]  Abarzhi S L. Review of nonlinear dynamics of the unstable fluid interface: Conservation laws and group theory. Phys Scr, 2008, T132: 014012

[19]  Chen Y, Glimm J, Sharp D H,  Zhang Q. A two-phase flow model of the Rayleigh-Taylor mixing zone. Phys Fluids, 1996, 8: 816--825

[20]  Mikaelian K. RT and RM instabilities in multilayer fluids with surface tension. Phys Rev A, 1990, 42: 7211--7225

[21]  Freed N, Ofer D, Shvarts D,  Orszag S. Two-phase flow analysis of self-similar turbulent mixing by {Rayleigh-Taylor instability. Phys Fluids A, 1991, 3: 912--918; Alon U, Hecht J, Ofer D, Shvarts D. Power laws and similarity of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts at all density ratios. Phys Rev Lett, 1995, 74: 534--538

[22]  Glimm J, Saltz D,  Sharp D H. Two-phase modeling of a fluid mixing layer. J Fluid Mech, 1997, 378: 119--143

[23]  Glimm J, Sharp D H. Chaotic mixing as a renormalization group fixed point. Phys Rev Lett, 1990, 64: 2137--2139

[24]  Cheng B, Glimm J,  Sharp D. Density dependence of RT and RM mixing fronts. Phys Lett A, 2000, 268: 366--374

[25]  Cheng B, Glimm J, Sharp D H. Dynamical evolution of the RT and RM mixing fronts. Phys Rev E, 2002, 66: 036312

[26]  Drew D A. Mathematical modeling of two-phase flow.  Ann Rev Fluid Mech, 1983, 15: 261--291

[27]  Oron D, Arazi L, Kartoon D, Rikanati A, Alon U,  Sharts D. Dimensionality dependence of Rayleigh-Taylor and Richtmyer-Meshkov   instability late-time scaling laws. Phys Plasmas, 2001, 8: 2883--2889

[28]  Alon U, Hecht J, Ofer D,  Shvarts D. Power laws and similarity of Rayleigh-Taylor and Richtmyer-Meshkov  mixing fronts at all density ratios.
Phys Rev Lett, 1995, 74: 534--537

[29]  Cheng B, Glimm J, Sharp D H. Multi-temperature multiphase flow model. Z Angew Math Phys, 2002, 53: 211--238

[30]  Cheng B, Glimm J, Sharp D H. A three-dimensional renormalization group  bubble merger model for Rayleigh-Taylor mixing. Chaos, 2002, 12: 267--274

[31]  Cheng B, Glimm J, Sharp D H, Yu Y. Multiphase flow model for unstable mixing of layered materials. Phys  of Fluid, 2005, 17: 087102

[32]  Heng B, Glimm J,  Sharp D H, Yu Y.  A multiphase flow model for the layered incompressible materials. Physics Scripta, 2008, T132: 014016

[33]  Wilson D C, Scannapieco A J, Cranfill C W, et al. Degradation of radiatively driven inertial confinement fusion capsule implosions by multifluid interpenetration mixing. Phys Plasmas, 2003, 10: 4427--4434

[34]  Wilson D C, Scannapieco A J, Cranfill C W, Christensen C R. Multi-fluid interpenetration mixing in directly driven ICF capsule implosions.
Phys Plasmas, 2004, 11: 2723--2728

[35]  Christensen C R, Wilson D C, Barnes C W, et al. The influence of asymmetry on mix in direct-drive ICF experiments. Phys Plasmas, 2004, 11: 2771--2777

[36]  Wilson D C, Kyrala G A, Benage J F, et al. The The effects of pre-mix on burn in ICF capsules. Journal of Physics: Conference Series, 2008, 112: 022015

[37]  Hoffman N M, Wilson D C, Kyrala G A. Diagnosing radiation drive asymmetry and absorbed energy in ignition Hohlraums using gas-filled capsules. Rev Sci Instrum, 2006, 77: 10E705

[38]  Rygg J R, Frenje J A, Li C K, Seguin F H, et al. Nuclear measurements of fuel-shell mix in inertial confinement fusion implosions at OMEGA. Phys Plasmas, 2007, 14: 056306

[39]  Rygg J R.  Shock Convergence and Mix Dynamics in Inertial Confinement Fusion[D]. Department of Physics, MIT, 2006

[40]  Grim G P, Bradley P A, Bredeweg T A,  Keksis A L, et al. Prompt radiochemistry at the national ignition facility. Rev Sci Instrum, 2008, 79: 10E503

[41]  Wilson D C, Bradley P A, Cerjan C J, Salmonson J D, et al. Diagnosing ignition with DT reaction history. Rev Sci Instrum, 2008, 79: 10E525

[42]  Wilson D C, Marshall F J, McKenty P W, et al. Mixing in thick-walled and pulse-shaped directly driven ICF capsule implosions. Proceedings of the 9th International Workshop on the Physics of Compressible Turbulent Mixing, Cambridge, UK, July, 2004

[43]  Herrmann H W, Langenbrunner J R, Mack J M, Cooley J H, et al. Anomalous yield reduction in direct-drive deuterium/tritium  implosions due to He addition. Phys Plasmas, 2009, 16: 056312

[44]  Scannapieco E, et al. In progress, 2009

[45]  Cheng B, Cranfill C W,  Turner L. The characteristic analysis of a hybrid multifluid turbulent mix model. LA-13851, 2001

[46]  Cheng B, Cranfill C W. Using the Green's function method to calculate pressure fluctuations in compressible multifluids. The Proceedings of the 9th International Conference on the Physics of Compressible Turbulent Mixing, Paris, July 2004

[47]  Steinkamp M J, Clark T T, Harlow F H. Two-point description of two-fluid turbulent mixing I: Model formulation. Int J Multiph Flow, 1999, 25:599-637; Two-point description of two-fluid turbulent mixing II: Numerical solutions and comparisons with experiments. Int J Multiph Flow, 1999, 25: 639--682

[48]  Dimonte G, Tipton R. KL turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Phys Fluids, 2006, 18: 085101

[49]  Jin H, Liu X F, Lu T, Cheng B, Glimm J, Sharp D H. Rayleigh-Taylor mixing rate for compressible flow. Phys Fluids, 2005, 17: 024104

[50]  Vreman B, Geurts B,  Kuerten H. Large-eddy simulation of the turbulent mixing layer. J Fluid Mech, 1997, 339: 357--390

[51]  Grinstein F F, Karniadakis G. Alternative LES and hybrid RANS/LES for the turbulent flows. J Fluids Engineering, 2002, 124: 821--824;
Fureby C,  Tabor G. Mathematical and physical constraints on large-eddy simulations.  Theoret Comput Fluid Dynamics, 1997,  9: 85--102

[52]  Cheng B, Scannapieco A J. Buoyancy-drag mix model obtained by multifluid interpenetration equations. Phys Rev E, 2005, 72: 046310

[53]  Lim H, Yu Y, Glimm J, Li X L, Sharp D H. Chaos, transport, and mesh convergence for fluid mixing. Acta Mathematicae Applicatae Sinica, 2008, 24: 355--368

[54]  Lim H, Yu Y, Glimm J, Li X L, Sharp D H. Multi Scale Models for Fluid Mixing. Compu Methods Appl Mech Engrg, 2008, 197: 3435--3444

[55]  Lim H, Yu Y, Glimm J, Li X L, Sharp D H. Subgrid models for mass and thermal diffusion in turbulent mixing. Phys Fluids, 2008, Stony Brook Preprint SUNYSB-AMS-08-07 and Los Alamos National Laboratory Preprint LA-UR 08-07725; Submitted for Publication.

[56]  Lim H, Yu Y, Glimm J, Li X L,  Sharp D H. Nearly discontinuous chaotic mixing. J High Energy Physics, 2008, {Stony Brook Preprint SUNYSB-AMS-09-02 and Los Alamos National Laboratory Preprint LA-UR 09-01364; Submitted for Publication.

Outlines

/