Comptes Rendus
A priori evaluation of the Pantano and Sarkar model in compressible homogeneous shear flows
Comptes Rendus. Mécanique, Volume 339 (2011) no. 1, pp. 27-34.

In this study, a Reynolds stress closure, including the Pantano and Sarkar model of the mean part of the pressure–strain correlation is used for the computation of compressible homogeneous at high-speed shear flow. Several studies concerning the compressible homogeneous shear flow show that the changes of the turbulence structures are principally due to the structural compressibility effects which significantly affect the pressure field and then the pressure–strain correlation. Eventually, this term appears as the main term responsible for the changes in the magnitude of the Reynolds stress anisotropies. The structure of the gradient Mach number is similar to that of turbulence, therefore this parameter may be appropriate to study the changes in turbulence structures that arise from structural compressibility effects. Thus, the incompressible model of the pressure strain correlation and its corrected form by using the turbulent Mach turbulent only, fail to correctly evaluate the compressibility effects at high shear flow. An extension of the widely used incompressible Launder, Reece and Rodi model on compressible homogeneous shear flow is the major aim of the present work. From this extension, the standard coefficients Ci become a function of the extra compressibility parameters (the turbulent Mach number Mt and the gradient Mach number Mg) through the Pantano and Sarkar model. Application of the model on compressible homogeneous shear flow by considering various initial conditions shows reasonable agreement with the DNS results of Simone et al. and Sarkar. The observed trend of the dramatic increase in the normal Reynolds stress anisotropies, the significant decrease in the Reynolds shear stress anisotropy and the increase of the turbulent kinetic energy amplification rate with increasing the gradient Mach number are well predicted by the model. The ability of the model to predict the equilibrium states for the flow in cases A1 to A4 from DNS results of Sarkar is examined, the results appear to be very encouraging. Thus, both parameters Mt and Mg should be used to model significant structural compressibility effects at high-speed shear flow.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2010.12.008
Mots-clés : Turbulence, Compressible, Homogeneous, Shear flow, Pressure strain

Hechmi Khlifi 1; J. Abdallah 1; H. Aïcha 1; L. Taïeb 1

1 Département de physique, faculté des sciences de Tunis, campus universitaire, 1060, Tunis, Tunisia
@article{CRMECA_2011__339_1_27_0,
     author = {Hechmi Khlifi and J. Abdallah and H. A{\"\i}cha and L. Ta{\"\i}eb},
     title = {A priori evaluation of the {Pantano} and {Sarkar} model in compressible homogeneous shear flows},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {27--34},
     publisher = {Elsevier},
     volume = {339},
     number = {1},
     year = {2011},
     doi = {10.1016/j.crme.2010.12.008},
     language = {en},
}
TY  - JOUR
AU  - Hechmi Khlifi
AU  - J. Abdallah
AU  - H. Aïcha
AU  - L. Taïeb
TI  - A priori evaluation of the Pantano and Sarkar model in compressible homogeneous shear flows
JO  - Comptes Rendus. Mécanique
PY  - 2011
SP  - 27
EP  - 34
VL  - 339
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crme.2010.12.008
LA  - en
ID  - CRMECA_2011__339_1_27_0
ER  - 
%0 Journal Article
%A Hechmi Khlifi
%A J. Abdallah
%A H. Aïcha
%A L. Taïeb
%T A priori evaluation of the Pantano and Sarkar model in compressible homogeneous shear flows
%J Comptes Rendus. Mécanique
%D 2011
%P 27-34
%V 339
%N 1
%I Elsevier
%R 10.1016/j.crme.2010.12.008
%G en
%F CRMECA_2011__339_1_27_0
Hechmi Khlifi; J. Abdallah; H. Aïcha; L. Taïeb. A priori evaluation of the Pantano and Sarkar model in compressible homogeneous shear flows. Comptes Rendus. Mécanique, Volume 339 (2011) no. 1, pp. 27-34. doi : 10.1016/j.crme.2010.12.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.12.008/

[1] C.G. Spezial; R. Abid; N. Mansour Evaluation of Reynolds-stress turbulence closures in compressible homogeneous shear flow, ZAMPS, Volume 17 (1985)

[2] O. Zeman Dilatation dissipation, the concept and application in modeling compressible mixing layers, Phys. Fluids A, Volume 2 (1990), p. 178

[3] S. Sarkar; G. Erlebacher; M.Y. Hussaini; H.O. Kreiss The analysis and modeling of dilatational terms in compressible turbulence, J. Fluid Mech., Volume 227 (1991), p. 473

[4] G.A. Blaisdell; S. Sarkar Investigation of the pressure strain correlation in compressible homogeneous shear flow, Transitional and turbulent compressible flow, ASME, Volume 151 (1993), pp. 133-138

[5] S. Sarkar The stabilizing effects of compressibility in turbulent shear flow, J. Fluid Mech., Volume 282 (1995), p. 163

[6] A. Simone; G.N. Coleman; C. Cambon The effect of compressibility on turbulent shear flow: a rapid distortion—theory and direct numerical simulation study, J. Fluid Mech., Volume 330 (1997), pp. 307-338

[7] H. Marzougui; H. Khlifi; T. Lili Extension of the Launder, Reece and Rodi on compressible homogeneous shear flow, Eur. Phys. J. B, Volume 45 (2005), pp. 147-154

[8] C. Pantano; S. Sarkar A study of compressibility effects in the high-speed turbulent shear layer using direct simulation, J. Fluid Mech., Volume 451 (2002), pp. 329-371

[9] B.E. Launder; G.J. Reece; W. Rodi Progress in the development of a Reynolds-stress turbulence closure, J. Fluid Mech., Volume 68 (1975), p. 537

[10] J.R. Ristorcelli A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory, J. Fluid Mech., Volume 347 (1997), p. 37

[11] V. Adumitroaie; J.R. Ristorcelli; D.B. Taulbee Progress in Favre Reynolds stress closures for compressible flows, Phys. Fluids A, Volume 9 (1999), p. 2696

[12] F. Hamba Effects of pressure fluctuations on turbulence growth compressible homogeneous shear flow, Phys. Fluids A, Volume 6 (1999), p. 1625

[13] H. Stefan Statistical Mechanics of Turbulent Flows, Springer-Verlag, Berlin, 2003

[14] C.G. Spezial, S. Sarkar, Second-order closure models for supersonic turbulent flows, ICASE Report 91-9, NASA Langley Research Center, Hampton, 1991.

[15] A.W. Vreman; N.D. Sandham; K.H. Luo Compressible mixing layer growth rate and turbulence characteristics, J. Fluid Mech., Volume 320 (1996), p. 325

Cited by Sources:

Comments - Policy