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Progress in the development of a Reynolds-stress turbulence closure

Published online by Cambridge University Press:  29 March 2006

B. E. Launder
Affiliation:
Department of Mechanical Engineering, Imperial College, London
G. J. Reece
Affiliation:
Department of Mechanical Engineering, Imperial College, London
W. Rodi
Affiliation:
Department of Mechanical Engineering, Imperial College, London Present address: Sonderforschungsbereich 80, University of Karlsruhe, Germany.

Abstract

The paper develops proposals for a model of turbulence in which the Reynolds stresses are determined from the solution of transport equations for these variables and for the turbulence energy dissipation rate ε. Particular attention is given to the approximation of the pressure-strain correlations; the forms adopted appear to give reasonably satisfactory partitioning of the stresses both near walls and in free shear flows.

Numerical solutions of the model equations are presented for a selection of strained homogeneous shear flows and for two-dimensional inhomogeneous shear flows including the jet, the wake, the mixing layer and plane channel flow. In addition, it is shown that the closure does predict a very strong influence of secondary strain terms for flow over curved surfaces.

Type
Research Article
Copyright
© 1975 Cambridge University Press

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References

Batchelor, G. K. & Proudman I. 1954 The effect of rapid distortion of a fluid in turbulent motion. Quart. J. Mech. Appl. Math. 7, 83.Google Scholar
Batchelor, G. K. & Townsend A. A. 1948 Decay of isotrophic turbulence in the initial period. Proc. Roy. Soc. A 193, 539.Google Scholar
Bradbury, L. J. S. 1965 The structure of a self-preserving turbulent plane jet. J. Fluid Mech. 23, 31.Google Scholar
Bradshaw P. 1972 The understanding and prediction of turbulent flow. Aero. J. 76, 403.Google Scholar
Bradshaw P. 1973a Effects of streamline curvature on turbulent flow. Agardograph, no. 169.Google Scholar
Bradshaw P. 1973b The strategy of calculation methods for complex turbulent flows. Imperial College Aero. Rep. no. 73–05.
Bradshaw P., Ferriss, D. H. & Johnson R. F. 1964 Turbulence in the noise-producing region of a circular jet. J. Fluid Mech. 19, 591.Google Scholar
Castro I. 1973 A highly distorted free shear layer. Ph.D. thesis, University of London.
Champagne F. H., Harris, V. G. & Corrsin S. 1970 Experiments on nearly homogeneous shear flow. J. Fluid Mech. 41, 81.Google Scholar
Chevray, R. & Kovasznay L. S. G. 1969 Turbulence measurements in the wake of a thin flat plate. A.I.A.A. J. 7, 1641.Google Scholar
Crou P. Y. 1945 On velocity correlations and the solutions of the equations of turbulent fluctuation. Quart. Appl. Math. 3, 38.Google Scholar
Comte-Bellot O. 1965 Ecoulement turbulent entre deux parois parallèes. Publ. Sci. Tech. Ministére de l'Air, no. 419.Google Scholar
Crow S. C. 1968 Viscoelastic properties of fine-grained incompressible turbulence. J. Fluid Mech. 41, 81.Google Scholar
Daly, B. J. & Harlow F.H. 1970 Transport equations of turbulence. Phys. Fluids, 13, 2634.Google Scholar
Donaldson C. DUP. 1968 A computer study of an analytical model of boundary layer transition. A.I.A.A. Paper, no. 68–38.Google Scholar
Donaldson C. DUP. 1971 A progress report on an attempt to construct an invariant model of turbulent shear flows. Proc. Agard Conf. on Turbulent Shear Flows, London, paper B-1.
Hanjalić K. 1970 Two-dimensional flow in an axisymmetric channel. Ph.D. thesis, University of London.
Hanjalić, K. & Launder B. E. 1972a Asymmetric flow in a plane channel. J. Fluid Mech. 51, 301.Google Scholar
Hanjalić, K. & Launder B. E. 1972b A Reynolds stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52, 609.Google Scholar
Irwin H. P. A. 1973 Measurements in a self-preserving plane wall jet in a positive pressure gradient. J. Fluid Mech. 61, 33.Google Scholar
Klebanoff P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. N.A.C.A. Rep. no. 1247.
Laufer J. 1951 Investigation of turbulent flow in a two-dimensional channel. N.A.C.A. Rep. no. 1053.
Lumley J. L. 1972 A model for computation of stratified turbulent flows. Int. Symp. on Stratified Floui, Novisibirsk.Google Scholar
Lumley, J. L. & Khajeh-Nouri B. 1974 Computational modelling of turbulent transport. Proc. 2nd IUGG-IUTAM Symp. on Atmos. Diffwion in Environmental Pollution, Academic.
Naot D., Shavit, A. & Wolfshtein M. 1970 Interactions between components of the turbulent velocity correlation tensor. Israel J. Tech. 8, 259.Google Scholar
Naot D., Shavit, A. & Wolfshtein M. 1972 Prediction of flow in square section ducts. Mech. Engng Dept., Technion, Haifa, Intern. Rep. no. 154.
Naot D., Shavit, A. & Wolfshtein M. 1973 Two-point correlation model and the redistribution of Reynolds stress. Phys. Fluids, 16, 738.Google Scholar
Patankar, S. V. & Spalding D. B. 1970 Heat and Mass Transfer on Boundary Layers. London: Intertext Books.
Patankar, S. V. & Spalding D. B. 1972 A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat Mass Transfer, 15, 1787.Google Scholar
Patel R. P. 1970 A study of two-dimensional symmetric and asymmetric turbulent shear flows. Ph.D. thesis, McGill University.
Reynolds W. C. 1970 Computation of turbulent flows-state-of-the-art, 1970. Stanford University Mech. Engng Dept. Rep. MD-27.
Robins A. 1971 The structure and development of a plane turbulent free jet. Ph.D. thesis, University of London.
Rodi W. 1972 The prediction of free turbulent boundary layers by use of a 2-equation model of turbulence. Ph.D. thesis, University of London.
Rotta J. C. 1951 Statistische Theorie nichthomogener Turbulent. J. Phys. 129, 547.Google Scholar
Rotta J. C. 1962 Turbulent boundary layers in incompressible flow. Prog. Aero. Sci. 2, 1.Google Scholar
Tennekes, H. & Lumley J. L. 1972 A First Course in Turbulence. M.I.T. Press.
Townsend A. A. 1954 The uniform distortion of homogeneous turbulence. Quart. J. Mech. Appl. Math. 7, 104.Google Scholar
Tucker H. J. 1970 The distortion of turbulence by irrotational strain. McGill University, Mech. Engng Dept. Rep. no. 70-7.Google Scholar
Tucker, H. J. & Reynolds A. J. 1968 The distortion of turbulence by irrotational plane strain. J. Fluid Mech. 32, 657.Google Scholar
Uberoi M. S. 1956 Effect of wind-tunnel contraction on free-stream turbulence. J. Aerospace Sci. 23, 754.Google Scholar
Uberoi M. S. 1957 Equipartition of energy and local isotropy in turbulent flows. J. Appl. Phys. 28, 1165.Google Scholar
Ubeboi M. S. 1963 Energy transfer in isotropic turbulence. Phys. Fluids, 6, 1048.Google Scholar
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