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Modelling of rapid pressure—strain in Reynolds-stress closures

Published online by Cambridge University Press:  26 April 2006

Arne V. Johansson  and
Magnus Hallbäck
Arne V. Johansson
Affiliation:
Department of Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Magnus Hallbäck
Affiliation:
Department of Mechanics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
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Abstract

The most general form for the rapid pressure—strain rate, within the context of classical Reynolds-stress transport (RST) closures for homogeneous flows, is derived, and truncated forms are obtained with the aid of rapid distortion theory. By a classical RST-closure we here denote a model with transport equations for the Reynolds stress tensor and the total dissipation rate. It is demonstrated that all earlier models for the rapid pressure—strain rate within the class of classical Reynolds-stress closures can be formulated as subsets of the general form derived here. Direct numerical simulations were used to show that the dependence on flow parameters, such as the turbulent Reynolds number, is small, allowing rapid distortion theory to be used for the determination of model parameters. It was shown that such a nonlinear description, of fourth order in the Reynolds-stress anisotropy tensor, is quite sufficient to very accurately model the rapid pressure—strain in all cases of irrotational mean flows, but also to get reasonable predictions in, for example, a rapid homogeneous shear flow. Also, the response of a sudden change in the orientation of the principal axes of a plane strain is investigated for the present model and models proposed in the literature. Inherent restrictions on the predictive capability of Reynolds-stress closures for rotational effects are identified.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 269 , 25 June 1994 , pp. 143 - 168
Copyright
© 1994 Cambridge University Press

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References

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
Bradshaw, P., Mansour, N. N. & Piomelli, U. 1987 On local approximations of the pressure-strain term in turbulence models. Summer Program, Center for Turbulence Research, NASA Ames-Stanford University.
Cambon, C. & Jacquin, L. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317.Google Scholar
Cambon, C., Jacquin, L. & Lubrano, J. L. 1992 Toward a new Reynolds stress model for rotating turbulent flows. Phys. Fluids A 4, 812–824.Google Scholar
Cambon, C., Jeandel, D. & Mathieu, J. 1981 Spectral modelling of homogeneous non-isotropic turbulence. J. Fluid Mech. 104, 247–262.Google Scholar
Chou, P. Y. 1945 On velocity correlations and the solutions of the equations of turbulent fluctuation. Q. Appl. Maths 3, 38–54.Google Scholar
Crow, S. C. 1968 Viscoelastic properties of fine-grained incompressible turbulence. J. Fluid Mech. 33, 1–20.Google Scholar
Fu, S., Launder, B. E. & Tselepidakis, D. P. 1987 Accommodating the effects of high strain rates in modelling the pressure-strain correlations. UMIST Mech. Engng Dept Rep. TFD/87/5.
Hallbäck, M., Groth, J. & Johansson, A. V. 1990 An algebraic model for non-isotropic turbulent dissipation rate in Reynolds stress closures. Phys. Fluids A 2, 1859–1866.Google Scholar
Hallbäck, M., Sjögren, T. & Johansson, A. V. 1993 Modeling of intercomponent transfer in Reynolds stress closures of homogeneous turbulence. In Turbulent Shear Flows IX (ed. F. Durst, N. Kasagi, B. E. Launder, F. W. Schmidt & J. H Whitelaw). Springer (to appear).
Hanjalić, K. & Launder, B. E. 1972 A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52, 609–638.Google Scholar
Hunt, J. C. R. 1978 A review of the theory of rapidly distorted turbulent flows and its applications. Fluid Dyn. Trans. 9, 121–152.Google Scholar
Launder, B. E. 1989 Second-moment closure: present⃛ and future? Intl J. Heat Fluid Flow 10, 282–300.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech. 68, 537–566.Google Scholar
Launder, B. E., Tselepidakis, D. P. & Younis, B. A. 1987 A second-moment closure study of rotating channel flow. J. Fluid Mech. 183, 63–75.Google Scholar
Lee, M. J. 1986 Useful formulas in the rapid distortion theory of homogeneous turbulence. Phys. Fluids 29, 3471–3474.Google Scholar
Lee, M. J. 1989 Distortion of homogeneous turbulence by axisymmetric strain and dilatation. Phys. Fluids A 1, 1541–1557.Google Scholar
Lee, M. J. 1990 A contribution toward rational modeling of the pressure-strain-rate correlation. Phys. Fluids A 2, 630–633.Google Scholar
Lee, M. J., Kim, J. & Moin, P. 1989 Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561–583.Google Scholar
Lee, M. J. & Reynolds, W. C. 1985 Numerical experiments on the structure of homogeneous turbulence. Stanford Univ. Tech. Rep. TF-24.
Le Penven, L. & Gence, J.-N. 1983 Une méthode de construction systematique de la relation de fermeture liant la partie linéaire de la corrélation pression-déformation au tenseur de Reynolds dans une turbulence homogéne soumise à une déformation uniforme. C. R. Acad. Sci. Paris II 297, 309–312.Google Scholar
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123–177.Google Scholar
Lundbladh, A. & Johansson, A. V. 1991 Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499–516.Google Scholar
Mansour, N. N., Shih, T.-H. & Reynolds, W. C. 1991 The effects of rotation on initially anisotropic homogeneous flows. Phys. Fluids A 3, 2421–2425.Google Scholar
Maxey, M. R. 1982 Distortion of turbulence in flows with parallel stream lines. J. Fluid Mech. 124, 261–282.Google Scholar
Morris, P. J. 1984 Modeling the pressure redistribution terms. Phys. Fluids 27, 1620–1623.Google Scholar
Naot, D., Shavit, A. & Wolfshtein, N. 1973 Two-point correlation model and the redistribution of Reynolds stresses. Phys. Fluids 16, 738–743.Google Scholar
Pope, S. B. 1985 PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11, 119.Google Scholar
Reynolds, W. C. 1976 Computation of turbulent flows. Ann. Rev. Fluid Mech. 8, 183–208.Google Scholar
Reynolds, W. C. 1987 Fundamentals of turbulence for turbulence modelling and simulation. Lecture Notes for Von Karman Institute, AGARD-CP-93. NATO.
Reynolds, W. C. 1989 Effects of rotation on homogeneous turbulence. In Proc. 10th Australasian Fluid Mechanics Conf., Melbourne, December 1989, Paper KS-2.
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA TM 81315.
Rotta, J. 1951 Statistische Theorie nichthomogener Turbulenz. Z. Physik 129, 547–572.Google Scholar
Schumann, U. 1977 Realizability of Reynolds-stress models. Phys. Fluids 20, 721–725.Google Scholar
Shih, T.-H. & Lumley, J. L. 1985 Modeling of pressure correlation terms in Reynolds stress and scalar flux equations. Tech. Rep. FDA-85-3. Cornell University.
Shih, T.-H. & Lumley, J. L. 1993 Critical comparison of second-order closures with direct numerical simulations of homogeneous turbulence. AIAA J. 31, 663–670.Google Scholar
Shih, T.-H., Mansour, N. N. & Chen, J. Y. 1987 Reynolds stress models of homogeneous turbulence. In Proc. 1987 Summer Program, Center for Turbulence Research, NASA Ames—Stanford University.
Shih, T.-H., Reynolds, W. C. & Mansour, N. N. 1990 A spectrum model for weakly anisotropic turbulence. Phys. Fluids A 2, 1500–1502.Google Scholar
Spencer, A. J. M. & Rivlin, R. S. 1958 The theory of matrix polynomials and its application to the mechanics of isotropic continua. Arch. Rat. Mech. Anal. 2, 309–336.Google Scholar
Speziale, C. G., Gatski, T. B. & Mac Giolla Mhuiris, N. 1990 A critical comparison of turbulence models for homogeneous shear flows in a rotating frame. Phys. Fluids A 2, 1678–1684.Google Scholar
Speziale, C. G., Sarkar, S. & Gatski, T. B. 1991 Modelling the pressure-strain correlation of turbulence: an invariant dynamical systems approach. J. Fluid Mech. 227, 245–272.Google Scholar
Townsend, A. A. 1970 Entrainment and the structure of turbulent flow. J. Fluid Mech. 41, 13–46.Google Scholar