## THERMAL SCIENCE

International Scientific Journal

### A COMPRESSIBILITY CORRECTIONS OF THE PRESSURE STRAIN LINEAR PART MODELS

**ABSTRACT**

The main focus of this paper is the analysis of the compressibility effects and the validation of some recent Reynolds stress models for computing compressible turbulent flows. The pressure strain correlation is one of the several terms appearing in the Reynolds stress equation which directly reflect the compressibility effects on the turbulence. For this reason, a special attention is paid to the modeling of this term in order to account for compressibility effects at high-speed. The models developed by Speziale Sarkar and Gatski (SSG) and Fu, Launder and Tselepidakis (FLT) for the pressure strain correlation are examined to be extended to compressible turbulent flows. A compressibility corrections of these models using the turbulent Mach number are proposed. The calculations have been performed for the compressible homogeneous shear flow and the turbulent plate mixing-layers. The comparison of the proposed compressibility modifications of the SSG and FLT models with its universal version shows some important ameliorations in results for the majority characteristic parameter of the structural compressibility effects. It’s found that the predicted results from the modified SSG and FLT models are in reasonable agreement with the accepted data.

**KEYWORDS**

PAPER SUBMITTED: 2015-12-14

PAPER REVISED: 2016-08-02

PAPER ACCEPTED: 2016-08-17

PUBLISHED ONLINE: 2016-09-05

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**Issue 1**, PAGES [453 - 466]

- Simone,S.,Coleman,G.N and Cambon,C., The effect of compressibility on turbulent shear flow: a rapid distorsion-theory and direct numerical simulation study, J.Fluid Mech.330(1997), pp.307-338.
- Aggarwal, A. K., Verma, A.: The Effect of Compressibility, Rotation and Magnetic field on thermal isstability of walters' fluid permeated with suspended particles in porous medium, Thermal Science 2014, Vol. 18, Suppl. 2, pp. S539-S550
- Fujihiro,H.,Effets of pressure fluctuations on turbulence growth compressible homogeneous shear flow,Phys.Fluid,A6(1999),1625.
- Vreman,A.W.,Sandham, N.D and Luo,K.H.,Compressible mixing layer growth rate and turbulence characteristics, J.Fluid Mech.,330(1996),pp.235-258.
- Pantano, C., Sarkar, S., A study of compressibility effects in the high speed turbulent shear layer using direct simulation, J. Fluid Mech., 451 (2002), pp. 329-371.
- Sarkar, S. , The stabilizing effects of compressibility in turbulent shear flows, Journal of Fluid Mech. 282(1995), pp.163-186.
- Goebel S.G., Dutton J.C., Experimental study of compressible mixing layers, AIAA Journal,29 (1991), pp. 538-546.
- Samimy M, Elliot G.S., Effects of compressibility on the characteristics of the free shear layers, AIAA Journal.89(1990),pp.439-445.
- Blaisdell, G.A. and Sarkar, S., Investigation of the pressure-strain correlation in compressible homogeneous turbulent shear flow, ASME FED,151(1993), pp.133-138.
- Speziale C.G, Sarkar S.,Second order closure models for supersonic turbulent flows, NASA Langley Research center ,Hampton,ICASE Report(1991).
- Speziale C.G, Sarkar S.,Gatski T.B.,Modelling the pressure strain correlation of turbulence an invariant dynamical systems approach, J.Fluid Mech.,227(1990),pp.245.
- Launder B E., Fu S., Tselepidakis S., Accomodating the effets of hig strain rates in modeling the pressure strain correlation TFD/5(1987).
- Adumitroiae V., Ristorcelli J.R and Taulbee D.B. ,Progress in Favre Reynolds stress closures for compressible flows, Phys.Fluids,A11(1999),pp.2696-2719.
- Hung S,Song Fu., Modelling of pressure strain correlation compressible turbulent flow., Acta Mech Sin24(2008),pp37-43.
- Hamed,M.,Hechmi,K.,Taieb,L.,Extension of the Launder Reece and Rodi on compressible Homogeneous shear flow, Eur.Phys. J.B,45(2005),pp.147-154.
- Hechmi,K., Taieb,L.,On the compressibility effects in mixing layers.,Thermal Sciences 2014,pp.59.
- Launder B.E., Reece G.J and Rodi, Progress in the development of a Reynolds-stress turbulence closure, J.Fluid Mech.,68(1975), pp.537-566.