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Second-order modelling of a variable-density mixing layer

Published online by Cambridge University Press:  21 April 2006

Tsan-Hsing Shih ,
John L. Lumley  and
J. Janicka
Tsan-Hsing Shih
Affiliation:
Sibley School of Mechanical & Aerospace Engineering, Cornell University. Ithaca, NY 14853, USA
John L. Lumley
Affiliation:
Sibley School of Mechanical & Aerospace Engineering, Cornell University. Ithaca, NY 14853, USA
J. Janicka
Affiliation:
Institut fur Technische Thermodynamik, RWTH-Aachen, West Germany Present address: Krupp-Koppers GmbH, Moltkestrasse 27, D-41 Essen, West Germany.
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Abstract

A conventional (non-density-weighted) averaging method is used to study variable-density turbulent flows, in particular, a helium-nitrogen mixing layer. A careful order-of-magnitude analysis is carried out, first in relative density fluctuations, and then in the ratio of cross-stream to streamwise lengthscales. In this way it is shown that, to lowest order, in jets and shear layers, the turbulence is unafffected by the density fluctuations, and conventional models can be used. The non-uniform density distribution influences only the mean-continuity and mean-momentum equations. Calculations (using a new form for the scalar-dissipation equation based on relaxation to an equilibrium timescale ratio) show good agreement with experiment. Calculation with a less truncated system indicates that neglected terms have little effect. We use a modified Patankar-Spalding method that overcomes numerical stability difficulties.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 180 , July 1987 , pp. 93 - 116
Copyright
© 1987 Cambridge University Press

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References

Borghi, R. & Dutoya, D. 1978 On the scales of the fluctuations in turbulent combustion. 17th Intl Symp. on Combustion, pp. 235–244. The Combustion Institute.
Bradshaw, P., Ferriss, D. H. & Johnson, R. F. 1964 Turbulence in the noise-producing region of a circular jet. J. Fluid Mech. 19, 591–624.Google Scholar
Chen, J. Y. & Lumley, J. L. 1984 Second-order modeling of a turbulent non-premixed H2–air jet flame with intermittency and conditional averaging. Rep. FDA-84-10. Cornell University.
Donaldson, C. D., Sullivan, R. & Rosenbaum, H. 1972 A theoretical study of the generation of atmospheric—clear air turbulence. AIAA J. 10, 162–170.Google Scholar
Favre, A. 1966 The equations of compressible turbulent gases. USAF Contract AF61(052)-772, AD622097.
Favre, A. 1969 Statistical equations of turbulent gases. In Problems of Hydrodynamics and Continuum Mechanics, pp. 231–266. Philadelphia: Society for Industrial and Applied Mathematics.
Ha Minh, H., Launder, B. E. & MacInnes, J. M. 1981 A new approach to the analysis of turbulent mixing in variable density flows. In Third Symp. on Turbulent Shear Flows (ed. L. J. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), pp. 19.19–19.25. Davis: The University of California.
Kent, J. H. & Bilger, R. W. 1976 The prediction of turbulent diffusion flame fields and nitric oxide formation. 16th Intl Symp. on Combustion, pp. 1643–1656. The Combustion Institute.
Janicka, J. & Kollmann, W. 1979 A prediction model for turbulent diffusion flows including NO-formation. AGARD Conf. Proc. CP-275, pp. 1–16.
Janicka, J. & Lumley, J. L. 1981 Second order modeling in non-constant density flows. Rep. FDA-81-01. Cornell University.
Jeans, J. H. 1954 The Dynamical Theory of Gases. Dover.
Jones, W. P. 1979 Models for turbulent flows with variable density and combustion. VKI Lecture Series, 1979–2.
Konrad, J. H. 1976 An experimental investigation of mixing layer in two-dimensional turbulent shear flows with applications to diffusion-limited chemical reactions. Ph.D. thesis, California Institute of Technology.
Libby, P. A. 1977 Studies in variable-density and reacting turbulent shear flows. In Studies in Convection, Vol. 2 (ed. B. E. Launder), pp. 1–43. Academic.
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulent closure. J. Fluid Mech. 68, 537–566.Google Scholar
Lumley, J. L. 1978 Computational modeling of turbulent flow. Adv. Appl. Mech. 18, 123–176.Google Scholar
Rebollo, R. M. 1973 Analytical and experimental investigation of a turbulent mixing layer of different gases in a pressure-gradient. Ph.D. thesis, California Institute of Technology.
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.
Shih, T.-H. 1984 Second order modeling of scalar turbulent flows. Ph.D. thesis, Cornell University, Ithaca, NY.
Shih, T.-H. & Lumley, J. L. 1986 Influence of timescale ratio on scalar flux relaxation: modeling Sirivat & Warhaft's homogeneous passive scalar fluctuations. J. Fluid Mech. 162, 211–222.Google Scholar
Shih, T.-H., Lumley, J. L. & Janicka, J. 1985 Second order modeling of a variable density mixing layer. Rep. FDA-85-08. Cornell University.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Vandromme, D. 1980 Turbulence modeling in variable density flow. Ph.D. thesis, Free University of Brussels.