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On the prediction of equilibrium states in homogeneous turbulence

Published online by Cambridge University Press:  26 April 2006

Charles G. Speziale  and
Nessan Mac Giolla Mhuiris
Charles G. Speziale
Affiliation:
Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665, USA
Nessan Mac Giolla Mhuiris
Affiliation:
Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23665, USA Present address: Mathematics Department, Case Western Reserve University, Cleveland, OH 44106, USA.
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Abstract

A comparison of several commonly used turbulence models (including the K–ε model and three second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for these models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to predict equilibrium states accurately for a range of the parameter Ω/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler K–ε model for the unstable flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the K–ε model erroneously yields equilibrium states that are independent of Ω/S while the Launder, Reece & Rodi model and the Shih-Lumley model predict a flow relaminarization when Ω/S > 0.39 - a result that is contrary to numerical simulations and linear spectral analyses, which indicate flow instability for at least the range 0 [les ] Ω/S [les ] 0.5. The physical implications of the results obtained from the various turbulence models considered herein are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 209 , December 1989 , pp. 591 - 615
Copyright
© 1989 Cambridge University Press

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References

Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1983 Improved turbulence models based on large-eddy simulation of homogeneous, incompressible turbulent flows. Stanford University Tech. Rep. TF-19.Google Scholar
Bertoglio, J. P. 1982 Homogeneous turbulent field within a rotating frame. AIAA J. 20, 1175–1181.Google Scholar
Champagne, F. H., Harris, V. G. & Corrsin, S. 1970 Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41, 81–139.Google Scholar
Hanjalic, 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
Haworth, D. C. & Pope, S. B. 1986 A generalized Langevin model for turbulent flows. Phys. Fluids 29, 387–405.Google Scholar
Karnik, V. & Tavoularis, S. 1983 The asymptotic development of nearly homogeneous turbulent shear flow. In Turbulent Shear Flows, vol. 4 (ed. L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), pp. 14.18–14.22. Springer.
Launder, B. E., Reece, G. & Rodi, W. 1975 Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech. 68, 537–566.Google Scholar
Lee, M. J., Kim, J. & Moin, P. 1987 Turbulence structure at high shear rate. In Proc. Sixth Symp. on Turbulent Shear Flows, Toulouse, France, pp. 22.6.1–22.6.6.Google Scholar
Lumley, J. L. 1978 Turbulence modeling. Adv. Appl. Mech. 18, 123–176.Google Scholar
Mellor, G. L. & Herring, H. J. 1973 A survey of mean turbulent field closure models. AIAA J. 11, 590–599.Google Scholar
Mellor, G. L. & Yamada, T. 1974 A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31, 1791–1806.Google Scholar
Patera, A. T. & Orszag, S. A. 1981 Finite-amplitude stability of axisymmetric pipe flow. J. Fluid Mech. 112, 467–474.Google Scholar
Reynolds, W. C. 1987 Fundamentals of turbulence for turbulence modeling and simulation. Lecture Notes for Von Karman Institute, AGARD Rep. 755. NATO.Google Scholar
Rodi, W. 1972 The prediction of free turbulent boundary layers by use of a two-equation model of turbulence. Ph.D. thesis, University of London.
Rogallo, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA Tech. Mem. 81315.Google Scholar
Rohr, J. J., Itsweire, E. C., Helland, K. N. & Van Atta, C. W. 1988 An investigation of the growth of turbulence in a uniform mean shear flow. J. Fluid Mech. 187, 1–33.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.
Speziale, C. G. 1985 Second-order closure models for rotating turbulent flows. ICASE Rep. 85–49. NASA Langley Research Center.
Speziale, C. G. 1987 On nonlinear K-l and K-ε models of turbulence. J. Fluid Mech. 178, 459–475.Google Scholar
Speziale, C. G. 1989 Turbulence modeling in non-inertial frames of reference. Theor. Comp. Fluid Dyn. 1, 3–19.Google Scholar
Speziale, C. G. & MacGiolla Mhuiris, N. 1989 Scaling laws for homogeneous turbulent shear flows in a rotating frame. Phys. Fluids A 1, 294–301.Google Scholar
Tavoularis, S. 1985 Asymptotic laws for transversely homogeneous turbulent shear flows. Phys. Fluids 28, 999–1004.Google Scholar
Tavoularis, S. & Corrsin, S. 1981 Experiments in nearly homogeneous turbulent shear flows with a uniform mean temperature gradient. Part 1. J. Fluid Mech. 104, 311–347.Google Scholar
Tritton, D. J. 1977 Physical Fluid Dynamics. Van Nostrand.
Tucker, H. J. & Reynolds, A. J. 1968 The distortion of turbulence by irrotational plane strain. J. Fluid Mech. 32, 657–673.Google Scholar