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Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number

Published online by Cambridge University Press:  26 April 2006

C. Cambon ,
G. N. Coleman  and
N. N. Mansour
C. Cambon
Affiliation:
Laboratoire de Mécanique des Fluides et d'Acoustique, URA CNRS no. 263, Ecole Centrale de Lyon, 69130 Ecully, France
G. N. Coleman
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305-3030, USA
N. N. Mansour
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035-1000, USA
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Abstract

The effect of rapid mean compression on compressible turbulence at a range of turbulent Mach numbers is investigated. Rapid distortion theory (RDT) and direct numerical simulation results for the case of axial (one-dimensional) compression are used to illustrate the existence of two distinct rapid compression regimes. These regimes – the nearly solenoidal and the ‘pressure-released’ – are defined by a single parameter involving the timescales of the mean distortion, the turbulence, and the speed of sound. A general RDT formulation is developed and is proposed as a means of improving turbulence models for compressible flows. In contrast to the well-documented observation that ‘compressibility’ (measured, for example, by the turbulent Mach number) is often associated with a decrease in the growth rate of turbulent kinetic energy, we find that under rapid distortion compressibility can produce an amplification of the kinetic energy growth rate. We also find that as the compressibility increases, the magnitude of the pressure–dilation correlation increases, in absolute terms, but its relative importance decreases compared to the magnitude of the kinetic energy production.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 257 , December 1993 , pp. 641 - 665
Copyright
© 1993 Cambridge University Press

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References

Batchelor, G. K. & Proudman, I. 1954 The effect of rapid distortion on a fluid in turbulent motion. Q. J. Mech. Appl. Maths 7, 83.Google Scholar
Blaisdell, G. A., Mansour, N. N. & Reynolds, W. C. 1991 Numerical simulation of compressible homogeneous turbulence. Department of Mechanical Engineering, Stanford University, Thermo-sciences Division Rep. TF-50.
Cambon, C. 1982 Etude spectrale d'un champ turbulent incompressible soumis à des effets couplés de déformation et de rotation imposés extérieurement. Thése d'Etat, Université Claude-Bernard-Lyon I.
Cambon, C. 1990 Single and double point modeling of homogeneous turbulence. CTR Annual Research Briefs, Stanford University/NASA Ames.
Cambon, C. Coleman, G. N. & Mansour, N. N. 1992 Rapid distortion analysis and direct simulation of compressible homogeneous turbulence at finite Mach number. In Proc. 4th Summer Prog., NASA/Stanford Center for Turbulence Research.
Cambon, C. & Jacquin, L. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295.Google Scholar
Cambon, C., Teissèdre, C. & Jeandel, D. 1985 Etude d'effets couplés de déformation et de rotation sur une turbulence homogène. J. Méc. Théor. Appl. 4, 629.Google Scholar
Coleman, G. N. & Mansour, N. N. 1991 Modeling the rapid spherical compression of isotropic turbulence. Phys. Fluids A 3, 2255.Google Scholar
Craya, A. 1958 Contribution à l'analyse de la turbulence associée à des vitesses moyennes. P.S.T. No. 345.
Debiève, J. F., Gouin, H. & Gaviglio, J. 1982 Evolution of the Reynolds stress tensor in a shock wave turbulence interaction. Indian J. Tech. 20, 90.Google Scholar
Durbin, P. A. & Zeman, O. 1992 Rapid distortion theory for homogeneous compressed turbulence with application to modelling. J. Fluid Mech. 242, 349 (referred to herein as DZ.)Google Scholar
Eringen, A. C. 1967 Mechanics of Continua. Wiley.
Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hayes, W. D. 1957 The vorticity jump across a gasdynamic discontinuity. J. Fluid Mech. 2, 595.Google Scholar
Herring, J. R. 1974 Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17, 859.Google Scholar
Jacquin, L., Cambon, C. & Blin, E. 1993 Turbulence amplification by a shock wave and rapid distortion theory. Submitted to Phys. Fluids A
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537.Google Scholar
Lee, S., Moin, P. & Lele, S. K. 1992 Interaction of isotropic turbulence with a shock wave. Department of Mechanical Engineering, Stanford University, Thermosciences Division Rep. TF-52.
Mansour, N. N., Shih, T.-H. & Reynolds, W. C. 1991 The effects of rotation on initially anisotropic homogeneous flows. Phys. Fluids A 10, 2421.Google Scholar
Reynolds, W. C. 1992 Towards a structure-based turbulence modeling. In Studies in Turbulence (ed. T. B. Gatski et al.) Springer.
Ribner, H. S. 1953 Convection of a pattern of vorticity through a shock wave. NACA Rep. 1164.
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA TM 81315.
Sabel'nikov, V. A. 1975 Pressure fluctuations generated by uniform distortion of homogeneous turbulence. Fluid Mech. Soviet Res. 4, 46.Google Scholar
Sarkar, S., Erlebacher, G., Hussaini, Y. M. & Kreiss, H. O. 1989 The analysis and modeling of dilatational terms in compressible turbulence. ICASE Rep. 89-79.
Townsend, A. A. 1976 The Structure of Homogeneous Turbulence. Cambridge University Press.
Waleffe, F. 1990 On the origin of the streak spacing in turbulent shear flows. CTR Annual Research Briefs, Stanford, University/NASA Ames.
Waleffe, F. 1993 Inertial transfers in the helical decomposition. Submitted to Phys. Fluids A.
Zeman, O. 1990 Dilatational dissipation: the concept and application in modeling compressible mixing layers. Phys. Fluids A 2, 178.Google Scholar
Zeman, O. & Coleman, G. N. 1993 Compressible turbulence subjected to shear and rapid compsion. In Turbulent Shear Flows 8 (ed. F. Durst et al.) Springer.