Explicit algebraic Reynolds stress model for compressible flow turbulence

References

• Launder , B. E. , Reece , G. J. and Rodi , W. 1975 . Progress in the development of a Reynolds-stress turbulence closure . J. Fluid Mech. , 68 ( part 3 ) : 537 – 566 . doi: 10.1017/S0022112075001814
   Web of Science ®Google Scholar
• Rodi , W. 1976 . A new algebraic relation for calculating the Reynolds stresses . Z. Angew. Math. Mech. , 56 : 219 – 221 . doi: 10.1002/zamm.19760560510
   Web of Science ®Google Scholar
• Pope , S. B. 1975 . A more general effective-viscosity hypothesis . J. Fluid Mech. , 72 ( part 2 ) : 331 – 340 . doi: 10.1017/S0022112075003382
   Web of Science ®Google Scholar
• Gatski , T. B. and Speziale , C. G. 1993 . On explicit algebraic stress models for complex turbulent flows . J. Fluid Mech. , 254 : 59 – 78 . doi: 10.1017/S0022112093002034
   Web of Science ®Google Scholar
• Jongen , T. and Gatski , T. B. 1998 . A New approach to characterizing the equilibrium states of the reynolds stress anisotropy in homogeneous turbulence . Theoret. Comput. Fluid Dynamics , 11 : 31 – 47 . doi: 10.1007/s001620050079
   Web of Science ®Google Scholar
• Girimaji , S. S. 1996 . Fully explicit and self-consistent algebraic Reynolds stress model . Theoret. Comput. Fluid Dynamics , 8 : 387 – 402 .
   Web of Science ®Google Scholar
• Wallin , S. and Johansson , A. V. 2000 . An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows . J. Fluid Mech. , 403 : 89 – 132 . doi: 10.1017/S0022112099007004
   Web of Science ®Google Scholar
• Wilcox , D. C. 1992 . Dilatation-dissipation corrections for advanced turbulence models . J. AIAA , 30 : 2639 – 2646 . doi: 10.2514/3.11279
   Web of Science ®Google Scholar
• Zeman , O. 1990 . Dilatation dissipation: The concept and application in modeling compressible mixing layer . Phys. Fluids A , 2 ( 2 ) : 178 – 188 . doi: 10.1063/1.857767
   Web of Science ®Google Scholar
• Sarkar , S. , Erlebacher , G. , Hussain , M. Y. and Kreiss , H. O. 1991 . The analysis and modeling of dilatational terms in compressible turbulence . J. Fluid Mech. , 227 : 473 – 493 . doi: 10.1017/S0022112091000204
   Web of Science ®Google Scholar
• Sarkar , S. 1992 . The pressure-dilatation correlation in compressible flows . Phys. Fluids A , 4 : 2674 – 2682 . doi: 10.1063/1.858454
   Web of Science ®Google Scholar
• Ristorcelli , J. R. 1997 . A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory . J. Fluid Mech. , 347 : 37 – 70 . doi: 10.1017/S0022112097006083
   Web of Science ®Google Scholar
• Sarkar , S. 1995 . The stabilizing effect of compressibility in turbulent shear-flow . J. Fluid Mech. , 282 : 163 – 186 . doi: 10.1017/S0022112095000085
   Web of Science ®Google Scholar
• Vreman , A. W. , Sandham , N. D. and Luo , K. H. 1996 . Compressible mixing layer growth rate and turbulence characteristics . J. Fluid Mech. , 320 : 235 – 258 . doi: 10.1017/S0022112096007525
   Web of Science ®Google Scholar
• Hamba , F. 1999 . Effects of pressure fluctuations on turbulence growth in compressible homogeneous shear flow . Phys. Fluids , 11 : 1623 – 1635 . doi: 10.1063/1.870023
   Web of Science ®Google Scholar
• Freund , J. B. 1997 . Compressibility effects in a turbulent annular mixing layer . Ph.D. diss., Stanford University
   Google Scholar
• Pantano , C. and Sarkar , S. 2002 . A study of compressibility effects in the high-speed turbulent shear layer using direct simulation . J. Fluid Mech. , 451 : 329 – 371 . doi: 10.1017/S0022112001006978
   Web of Science ®Google Scholar
• Adumitroaie , V. , Ristorcelli , J. R. and Taulbee , D. B. 1998 . Progress in Favre-Reynolds stress closures for compressible flows . NASA/CR-1998-2078423, NASA
   Google Scholar
• Park , C. H. and Park , S. O. 2005 . A compressible turbulence model for the pressure-strain correlation . J. Turbul. , 6 ( 2 ) : 1 – 25 .
   Google Scholar
• Yoshizawa , A. , Fujiwara , H. , Hamba , F. , Nisizima , S. and Kumagai , Y. 2003 . Nonequilibrium turbulent-viscosity model for supersonic free-shear layer /wall-bounded flows . J. AIAA , 41 : 1029 – 1036 . doi: 10.2514/2.2069
   Web of Science ®Google Scholar
• Yoshizawa , A. , Nisizima , S. , Shimomura , Y. , Kobayashi , H. , Matsuo , Y. , Abe , H. and Fujiwara , H. 2006 . A new methodology for Reynolds-averaged modeling based on the amalgamation of heuristic-modeling and turbulence theory methods . Phys. Fluids , 18 : 1 – 17 . doi: 10.1063/1.2186669
   Web of Science ®Google Scholar
• Kim , J. Y. and Park , S. O. 2010 . New compressible turbulence model for free and wall-bounded shear layers . J. Turbul , 11 : 1 – 20 . doi: 10.1080/14685241003627760
   Web of Science ®Google Scholar
• Gomez , A. and Girimaji , S. S. Algebraic Reynolds Stress Model (ARSM) for Compressible Shear Flows . 41st AIAA Fluid Dynamics Conference and Exhibit , Honolulu , Hawaii
   Google Scholar
• Bertsch , R. L. , Suman , S. and Girimaji , S. S. 2012 . Rapid distortion analysis of high Mach number homogeneous shear flows: Characterization of flow-thermodynamics interaction regimes . Phys. Fluids , 24 : 125106–1-24 doi: 10.1063/1.4772193
   Google Scholar
• Batchelor , G. K. 1951 . Pressure fluctuations in isotropic turbulence . Proc. Cambridge Philos. Soc. , 27 : 359 – 374 . doi: 10.1017/S0305004100026712
   Google Scholar
• Lavin , T. A. , Girimaji , S. S. , Suman , S. and Yu , H. 2012 . Flow-thermodynamics interactions in rapidly-sheared compressible turbulence . Theor. Comput. Fluid Dyn. , 26 : 501 – 522 . doi: 10.1007/s00162-011-0243-9
   Web of Science ®Google Scholar
• Mathematica . Wolfram, Champaign, IL, US; software available at http://www.wolfram.com/mathematica
   Google Scholar
• Park , C. H. and Park , S. O. 2005 . On the limiters of two-equation turbulence models . Int. J. Comput. Fluid Dyn. , 19 : 79 – 86 . doi: 10.1080/10618560412331286292
   Web of Science ®Google Scholar
• Yoon , S. and Jameson , A. 1988 . Lower-upper symmetric-gauss-seidel method for the euler and navier-stokes equations . J. AIAA , 26 : 1025 – 1026 . doi: 10.2514/3.10007
   Web of Science ®Google Scholar
• Menter , F. R. 1994 . Two-equation eddy-viscosity turbulence models for engineering applications . J. AIAA , 32 ( 8 ) : 1598 – 1605 . doi: 10.2514/3.12149
   Web of Science ®Google Scholar
• Kurganov , A. and Tadmor , E. 2000 . New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations . J. Comp. Phys. , 160 : 214 – 282 .
   Google Scholar
• Bogdanoff , D. W. 1983 . Compressibility effects in turbulent shear layers . J. AIAA , 21 : 926 – 927 . doi: 10.2514/3.60135
   Web of Science ®Google Scholar
• Papamoschou , D. and Roshko , A. 1988 . The compressible turbulent shear layer: An experimental study . J. Fluid Mech. , 197 : 453 – 477 . doi: 10.1017/S0022112088003325
   Web of Science ®Google Scholar
• Goebel , S. G. and Dutton , J. C. 1991 . Experimental study of compressible turbulent mixing layers . J. AIAA , 29 : 538 – 546 . doi: 10.2514/3.10617
   Web of Science ®Google Scholar
• Clemens , N. T. and Mungal , M. G. 1995 . Large-scale structure and entrainment in the supersonic mixing layer . J. Fluid Mech , 284 : 171 – 219 . doi: 10.1017/S0022112095000310
   Web of Science ®Google Scholar
• Elliot , G. S. and Samimy , M. 1990 . Compressibility effects in free shear layers . Phys. Fluids A , 2 : 1231 – 1240 . doi: 10.1063/1.857816
   Web of Science ®Google Scholar
• Guarini , S. E. , Moser , R. D. , Shariff , K. and Wray , A. 2000 . Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5 . J. Fluid Mech. , 414 : 1 – 33 . doi: 10.1017/S0022112000008466
   Web of Science ®Google Scholar
• Yee , H. C. 1987 . Construction of explicit and implicit symmetric TVD schemes and their applications . J. Comput. Phys. , 68 : 561 – 576 . doi: 10.1016/0021-9991(87)90049-0
   Web of Science ®Google Scholar
• Lagha , M. , Kim , J. , Eldredge , J. D. and Zhong , X. 2011 . A numerical study of compressible turbulent boundary layers . Phys. Fluids , 23 : 015106 – 112 . 015106 doi: 10.1063/1.3541841
   Web of Science ®Google Scholar
• Scarano , F. and Oudheusden , B. W. PIV investigation of a planar supersonic wake flow . 11th international symposium on applications of laser techniques to fluid mechanics , Lisbon , , Portugal
   Google Scholar
• Kim , M. H. and Park , S. O. 1998 . Supersonic base flow predictions using second-moment closure models of turbulence . CFD Journal , 6 ( 4 ) : 561 – 576 .
   Google Scholar
• Roache , P. J. 1976 . Computational Fluid Dynamics , 282 – 283 . New Maxico : Albuquerque .
   Google Scholar