This paper is devoted to the second-order closure for compressible turbulent flows with special attention paid to modeling the pressure–strain correlation appearing in the Reynolds stress equation. This term appears as the main one responsible for the changes of the turbulence structures that arise from structural compressibility effects. From the analysis and DNS results of Simone et al. and Sarkar, the compressibility effects on the homogeneous turbulence shear flow are parameterized by the gradient Mach number. Several experiment and DNS results suggest that the convective Mach number is appropriate to study the compressibility effects on the mixing layers. The extension of the LRR model recently proposed by Marzougui, Khlifi and Lili for the pressure–strain correlation gives results that are in disagreement with the DNS results of Sarkar for high-speed shear flows. This extension is revised to derive a turbulence model for the pressure–strain correlation in which the compressibility is included in the turbulent Mach number, the gradient Mach number and then the convective Mach number. The behavior of the proposed model is compared to the compressible model of Adumitroiae et al. for the pressure–strain correlation in two turbulent compressible flows: homogeneous shear flow and mixing layers. In compressible homogeneous shear flows, the predicted results are compared with the DNS data of Simone et al. and those of Sarkar. For low compressibility, the two compressible models are similar, but they become substantially different at high compressibilities. The proposed model shows good agreement with all cases of DNS results. Those of Adumitroiae et al. do not reflect any effect of a change in the initial value of the gradient Mach number on the Reynolds stress anisotropy. The models are used to simulate compressible mixing layers. Comparison of our predictions with those of Adumitroiae et al. and with the experimental results of Goebel et al. shows good qualitative agreement.
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@article{CRMECA_2013__341_7_567_0,
author = {Hechmi Klifi and Taieb Lili},
title = {A compressibility correction of the pressure strain correlation model in turbulent flow},
journal = {Comptes Rendus. M\'ecanique},
pages = {567--580},
publisher = {Elsevier},
volume = {341},
number = {7},
year = {2013},
doi = {10.1016/j.crme.2013.04.003},
language = {en},
}
TY - JOUR AU - Hechmi Klifi AU - Taieb Lili TI - A compressibility correction of the pressure strain correlation model in turbulent flow JO - Comptes Rendus. Mécanique PY - 2013 SP - 567 EP - 580 VL - 341 IS - 7 PB - Elsevier DO - 10.1016/j.crme.2013.04.003 LA - en ID - CRMECA_2013__341_7_567_0 ER -
Hechmi Klifi; Taieb Lili. A compressibility correction of the pressure strain correlation model in turbulent flow. Comptes Rendus. Mécanique, Volume 341 (2013) no. 7, pp. 567-580. doi : 10.1016/j.crme.2013.04.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.04.003/
[1] Dilatation dissipation, the concept and application in modeling compressible mixing layers, Phys. Fluids A, Volume 2 (1990), p. 178
[2] The analysis and modeling of dilatational terms in compressible turbulence, J. Fluid Mech., Volume 227 (1991), p. 473
[3] The effect of compressibility on turbulent shear flow: a rapid distorsion-theory and direct numerical simulation study, J. Fluid Mech., Volume 330 (1997), pp. 307-338
[4] The stabilizing effects of compressibility in turbulent shear flow, J. Fluid Mech., Volume 282 (1995), p. 163
[5] Effects of pressure fluctuations on turbulence growth compressible homogeneous shear flow, Phys. Fluids A, Volume 6 (1999), p. 1625
[6] Compressible mixing layer growth rate and turbulence characteristics, J. Fluid Mech. (1996), pp. 320-325
[7] A study of compressibility effects in the high-speed turbulent shear layer using direct simulation, J. Fluid Mech., Volume 451 (2002), pp. 329-371
[8] Extension of the Launder, Reece and Rodi on compressible homogeneous shear flow, Eur. Phys. J. B, Volume 45 (2005), pp. 147-154
[9] Progress in the development of a Reynolds-stress turbulence closure, J. Fluid Mech., Volume 68 (1975), p. 537
[10] Experimental study of compressible turbulent mixing layers, AIAA J., Volume 29 (1981), p. 538
[11] Progress in Favre Reynolds stress closures for compressible flows, Phys. Fluids A, Volume 9 (1999), p. 2696
[12] A compressible turbulence model for the pressure–strain correlation, J. Turbul., Volume 6 (2005) no. 2, pp. 1-25
[13] Modeling of compressible turbulent flows with emphasis on pressure–dilatation correlation, Eng. Turbulence Model. Exp., Volume 3 (1996), p. 151
[14] Statistical Mechanics of Turbulent Flows, Springer Verlag, Berlin, 2003
[15] The pressure–dilatation correlation in compressible flows, Phys. Fluids A, Volume 4 (1992), p. 2674
[16] Evaluation of Reynolds-stress turbulence closures in compressible homogeneous shear flow, ZAMPS, Volume 17 (1985)
[17] Second-order closure models for supersonic turbulent flows, 1991 (NASA Langley Research Center. Hampton, ICASE Report 91-9)
[18] Turbulent free shear layer mixing and combustion (S.N.B. Murthy; E.T. Curran, eds.), Progress in Astronautics and Aeronautics, vol. 137, AIAA, Washington, DC, 1991
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