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Statistical interpretation of the turbulent dissipation rate in wall-bounded flows

Published online by Cambridge University Press:  26 April 2006

J. Jovanović ,
Q.-Y. Ye  and
F. Durst
J. Jovanović
Affiliation:
Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058 Erlangen, Germany
Q.-Y. Ye
Affiliation:
Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058 Erlangen, Germany
F. Durst
Affiliation:
Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058 Erlangen, Germany
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Abstract

Statistical analysis was performed for interpreting the dissipation correlations in turbulent wall-bounded flows. The fundamental issues related to the formulation of the closure assumptions are discussed. Using the two-point correlation technique, a distinction is made between the homogeneous and inhomogeneous parts of the dissipation tensor. It is shown that the inhomogeneous part contributes half of the dissipation rate at the wall and vanishes remote from the wall region. The structure of an analytically derived equation was analysed utilizing the results of direct numerical simulations of turbulent channel flow at low Reynolds number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 293 , 25 June 1995 , pp. 321 - 347
Copyright
© 1995 Cambridge University Press

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References

Bradshaw, P. & Perot, J. B. 1993 A note on turbulent energy dissipation in the viscous wall region. Phys. Fluids A 5, 3305–3306.Google Scholar
Chou, P. Y. 1945 On the velocity correlation and the solution of the equation of turbulent fluctuation. Q. Appl. Maths 3, 38–54.Google Scholar
Daly, B. J. & Harlow, F. H. 1970 Transport equations in turbulence. Phys. Fluids 13, 2634–2649.Google Scholar
Davydov, B. I. 1961 On the statistical dynamics of an incompressible turbulent fluid. Dok. Akad. Nauk SSSR 136, 47–50.Google Scholar
Gilbert, N. & Kleiser, L. 1991 Turbulence model testing with the aid of direct numerical simulation results. Proc. Eighth Symp. on Turbulent Shear Flows, Munich, pp. 26.1.1–26.1.6.Google Scholar
Hanjalić, K. & Jakirlić, S. 1993 Conventional turbulence models: Prospects, limitations, and possible directions for improvement. Mini-Workshop, Advanced Turbulence Modelling, The Brite-Euram Project, Universität Erlangen-Nürnberg.
Hanjalić, K., Jakirlić, S., Stošić, N., Vasić, S. & Hadžić, I. 1992 Collaborative testing of turbulence models. Universität Erlangen-Nürnberg Rep. LSTM 352/T/92.Google Scholar
Hanjalić, K. & Launder, B. E. 1976 Contribution towards a Reynolds-stress closure for low Reynolds number turbulence. J. Fluid Mech. 74, 693–610.Google Scholar
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
Harlow, F. H. & Hirt, W. C. 1969 Generalized transport theory of anisotropic turbulence. Los Alamos Scientific Laboratory Rep. LA–4086.Google Scholar
Harlow, F. H. & Nakayama, P. I. 1968 Transport of turbulence energy decay rate. Los Alamos Scientific Laboratory Rep. LA–3854.Google Scholar
Harlow, F. H. & Welch, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flows. Phys. Fluids 8, 2182–2189.Google Scholar
Hirt, C. W. 1969 Computer studies of time-dependent turbulent flows. Phys. Fluids, Suppl. II, 219–227.Google Scholar
Hinze, J. O. 1975 Turbulence, 2nd edn., pp. 323–331, McGraw-Hill.
Jovanović, J., Ye, Q.-Y. & Durst, F. 1992 Refinement of the equation for the determination of turbulent micro-scale. Universität Erlangen-Nürnberg Rep. LSTM 349/T/92.Google Scholar
Kessler, R. 1993 Near-wall modelling of the dissipation rate equation using DNS data. In Engineering, Turbulence Modelling and Experiments 2 (ed. W. Rodi & F. Martelli), p. 113. Elsevier.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in a fully developed channel flow at low Reynolds numbers. J. Fluid Mech. 177, 133–166.Google Scholar
Kolovandin, B. A. & Vatutin, I. A. 1969 On statistical theory of non-uniform turbulence. Intl Seminar on Heat and Mass Transfer, Herceg Novi, Yugoslavia.
Kolovandin, B. A. & Vatutin, I. A. 1972 Statistical transfer theory in non-homogeneous turbulence. Intl J. Heat. Mass Transfer 15, 2371–2383.Google Scholar
Laufer, J. 1953 The structure of turbulence fully developed pipe flow. NACA Tech. Note 2954.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
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123–176.Google Scholar
Lumley, J. L. 1992 Some comments on turbulence. Phys. Fluids A 4, 203–211.Google Scholar
Mansour, N. N., Kim, J. & Moin, P. 1987 Reynolds stress and dissipation rate budgets in a turbulent channel flow. NASA Tech. Mem. 89451.Google Scholar
Mansour, N. N., Kim, J. & Moin, P. 1989 Near-wall k-ε turbulence modeling. AIAA J. 27, 1068–1073.Google Scholar
Rodi, W. & Mansour, N. N. 1993 Low Reynolds number k — ε modelling with the aid of direct numerical simulation data. J. Fluid Mech. 250, 509–529.Google Scholar
Rotta, J. 1951 Statistische Theorie nichthomogener Turbulenz. Z. Physik 129, 547–572.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, pp. 143–144. Cambridge University Press.
Tselepidakis, D. P. 1991 Development and application of a new second-moment closure for turbulent flows near walls. PhD thesis, University of Manchester.