Review of turbulent mixing models

Acta Mathematica Scientia

Volumn 29, Issue 6, 2009, Pages 1703-1720

  Cheng, Baolian ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

76E17; 76F25; hydrodynamic instabilities; turbulent mixing

Indexed keywords

EID: 73549098710     PISSN: 02529602     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0252-9602(10)60012-4     Document Type: Article

References (63)

1. Rayleigh L. Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Scientific Papers Volume II (1900), Cambridge Univ Press, Cambridge 200
2. Taylor G.I. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes I. Proc R Soc London A 201 (1950) 192-196
3. Richtmyer R.D. Taylor instability in shock acceleration of compressible fluids. Comm Pure Appl Math 13 (1960) 297-319
4. Meshkov E.E. Izv Akad Nauk SSSR. Mekh Zhidk Gaz 5 (1969) 151
5. Andronov V., Bakhrakh B., Meshkov E., Mokhov V., Nikiforov V., Pevnitskii A., and Tolshmyakov A. An experimental investigation and numerical modeling of turbulent mixing in one-dimensional flows. Sov Phys Dokl 27 (1982) 393-396
6. Andronov V., Bakhrakh B., Meshkov E., Mokhov V., Nikiforov V., Pevnitskii A., and Tolshmyakov A. An experimental investigation and numerical modeling of turbulent mixing in one-dimensional flows. Sov Phys JETP 44 (1967) 424-427
7. Read K.I. Experimental investigation of turbulent mixing by Rayleigh-Taylor instability. Physica D 12 (1984) 45-58
8. Dimonte G. Nonlinear evolution of the RT and RM instabilities. Phys Plasmas 6 (1999) 2009-2015
9. Ramaprabhu G., and Andrews M.J. Experimental investigation of Rayleigh-Taylor mixing at small Atwood numbers. J Fluid Mech 502 (2004) 233-237
10. Sharp D.H. An overview of Rayleigh-Taylor instability. Physica D 12 (1984) 3-18
11. Youngs D.L. Modeling turbulent mixing by Rayleigh-Taylor instability. Physica D 37 (1989) 270-287
12. Numerical simulation of turbulent mixing by Rayleigh-Taylor instability. Physica D 12 (1984) 32-44
13. 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
14. Gauthier S., and Bonnet M. A k - ε model for turbulent mixing in shocktube flows induced by Rayleigh-Taylor instability. Phys Fluid A 2 (1990) 1685-1694
15. Dalziel S.B., Linden P.F., and Youngs D.L. Self-similarity and internal structure of turbulence induced by Rayleigh-Taylor instability. J Fluid Mech 399 (1999) 1-48
16. Llor A. Bulk turbulent transport and structure in Rayleigh-Taylor, and Richtmyer-Meshkov instabilities. Laser Part Beams 21 (2003) 305-310
17. Scannapieco A.J., and Cheng B. A multifluids interpenetra mix model. Phys Letts A 299 (2002) 49-64
18. Cranfill C W. A new multifluid turbulent-mix-model. LANL Report LA-UR-92-2484, 1992
19. Cheng B., Glimm J., Saltz D., and Sharp D.H. Boundary conditions for a two pressure two phase flow model. Physica D 133 (1999) 84-105
20. Livescu D., and Ristorcelli J.R. Buoyancy-driven variable-density turbulence. J Fluid Mech 591 (2006) 43-71
21. Dimotakis P.E. Turbulent mixing. Annu Rev Fluid Mech 37 (2005) 329-356
22. Abarzhi S.L. Review of nonlinear dynamics of the unstable fluid interface: Conservation laws and group theory. Phys Scr T132 (2008) 014012
23. Chen Y., Glimm J., Sharp D.H., and Zhang Q. A two-phase flow model of the Rayleigh-Taylor mixing zone. Phys Fluids 8 (1996) 816-825
24. Mikaelian K. RT and RM instabilities in multilayer fluids with surface tension. Phys Rev A 42 (1990) 7211-7225
25. Freed N., Ofer D., Shvarts D., and Orszag S. Two-phase flow analysis of self-similar turbulent mixing by Rayleigh-Taylor instability. Phys Fluids A 3 (1991) 912-918
26. Alon U., Hecht J., Ofer D., and Shvarts D. Power laws and similarity of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts at all density ratios. Phys Rev Lett 74 (1995) 534-538
27. Glimm J., Saltz D., and Sharp D.H. Two-phase modeling of a fluid mixing layer. J Fluid Mech 378 (1997) 119-143
28. Glimm J., and Sharp D.H. Chaotic mixing as a renormalization group fixed point. Phys Rev Lett 64 (1990) 2137-2139
29. Cheng B., Glimm J., and Sharp D. Density dependence of RT and RM mixing fronts. Phys Lett A 268 (2000) 366-374
30. Cheng B., Glimm J., and Sharp D.H. Dynamical evolution of the RT and RM mixing fronts. Phys Rev E 66 (2002) 036312
31. Drew D.A. Mathematical modeling of two-phase flow. Ann Rev Fluid Mech 15 (1983) 261-291
32. Oron D., Arazi L., Kartoon D., Rikanati A., Alon U., and Sharts D. Dimensionality dependence of Rayleigh-Taylor and Richtmyer-Meshkov instability late-time scaling laws. Phys Plasmas 8 (2001) 2883-2889
33. Alon U., Hecht J., Ofer D., and Shvarts D. Power laws and similarity of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts at all density ratios. Phys Rev Lett 74 (1995) 534-537
34. Cheng B., Glimm J., and Sharp D.H. Multi-temperature multiphase flow model. Z Angew Math Phys 53 (2002) 211-238
35. Cheng B., Glimm J., and Sharp D.H. A three-dimensional renormalization group bubble merger model for Rayleigh-Taylor mixing. Chaos 12 (2002) 267-274
36. Cheng B., Glimm J., Sharp D.H., and Yu Y. Multiphase flow model for unstable mixing of layered materials. Phys of Fluid 17 (2005) 087102
37. Heng B., Glimm J., Sharp D.H., and Yu Y. A multiphase flow model for the layered incompressible materials. Physics Scripta T132 (2008) 014016
38. 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 10 (2003) 4427-4434
39. Wilson D.C., Scannapieco A.J., Cranfill C.W., and Christensen C.R. Multi-fluid interpenetration mixing in directly driven ICF capsule implosions. Phys Plasmas 11 (2004) 2723-2728
40. Christensen C.R., Wilson D.C., Barnes C.W., et al. The influence of asymmetry on mix in direct-drive ICF experiments. Phys Plasmas 11 (2004) 2771-2777
41. 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 112 (2008) 022015
42. Hoffman N.M., Wilson D.C., and Kyrala G.A. Diagnosing radiation drive asymmetry and absorbed energy in ignition Hohlraums using gas-filled capsules. Rev Sci Instrum 77 (2006) 10E705
43. 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 14 (2007) 056306
44. Rygg J R. Shock Convergence and Mix Dynamics in Inertial Confinement Fusion [D]. Department of Physics, MIT, 2006
45. Grim G.P., Bradley P.A., Bredeweg T.A., Keksis A.L., et al. Prompt radiochemistry at the national ignition facility. Rev Sci Instrum 79 (2008) 10E503
46. Wilson D.C., Bradley P.A., Cerjan C.J., Salmonson J.D., et al. Diagnosing ignition with DT reaction history. Rev Sci Instrum 79 (2008) 10E525
47. 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
48. Herrmann H.W., Langenbrunner J.R., Mack J.M., Cooley J.H., et al. Anomalous yield reduction in directdrive deuterium/tritium implosions due to He addition. Phys Plasmas 16 (2009) 056312
49. Scannapieco E, et al. In progress, 2009
50. Cheng B, Cranfill C W, Turner L. The characteristic analysis of a hybrid multifluid turbulent mix model. LA-13851, 2001
51. 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
52. Steinkamp M.J., Clark T.T., and Harlow F.H. Two-point description of two-fluid turbulent mixing I: Model formulation. Int J Multiph Flow 25 (1999) 599-637
53. Two-point description of two-fluid turbulent mixing II: Numerical solutions and comparisons with experiments. Int J Multiph Flow 25 (1999) 639-682
54. Dimonte G., and Tipton R. KL turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Phys Fluids 18 (2006) 085101
55. Jin H., Liu X.F., Lu T., Cheng B., Glimm J., and Sharp D.H. Rayleigh-Taylor mixing rate for compressible flow. Phys Fluids 17 (2005) 024104
56. Vreman B., Geurts B., and Kuerten H. Large-eddy simulation of the turbulent mixing layer. J Fluid Mech 339 (1997) 357-390
57. Grinstein F.F., and Karniadakis G. Alternative LES and hybrid RANS/LES for the turbulent flows. J Fluids Engineering 124 (2002) 821-824
58. Fureby C., and Tabor G. Mathematical and physical constraints on large-eddy simulations. Theoret Comput Fluid Dynamics 9 (1997) 85-102
59. Cheng B., and Scannapieco A.J. Buoyancy-drag mix model obtained by multifluid interpenetration equations. Phys Rev E 72 (2005) 046310
60. Lim H., Yu Y., Glimm J., Li X.L., and Sharp D.H. Chaos, transport, and mesh convergence for fluid mixing. Acta Mathematicae Applicatae Sinica 24 (2008) 355-368
61. Lim H., Yu Y., Glimm J., Li X.L., and Sharp D.H. Multi Scale Models for Fluid Mixing. Compu Methods Appl Mech Engrg 197 (2008) 3435-3444
62. 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.
63. 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.