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On near-wall turbulent flow modelling

Published online by Cambridge University Press:  26 April 2006

Y. G. Lai  and
R. M. C. So
Y. G. Lai
Affiliation:
Mechanical and Aerospace Engineering, Arizona State University. Tempe, AZ 85287, USA
R. M. C. So
Affiliation:
Mechanical and Aerospace Engineering, Arizona State University. Tempe, AZ 85287, USA
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Abstract

The characteristics of near-wall turbulence are examined and the result is used to assess the behaviour of the various terms in the Reynolds-stress transport equations. It is found that all components of the velocity-pressure-gradient correlation vanish at the wall. Conventional splitting of this second-order tensor into a pressure diffusion part and a pressure redistribution part and subsequent neglect of the pressure diffusion term in the modelled Reynolds-stress equations leads to finite near-wall values for two components of the redistribution tensor. This, therefore, suggests that, in near-wall turbulent flow modelling, the velocity-pressure-gradient correlation rather than pressure redistribution should be modelled. Based on this understanding, a methodology to derive an asymptotically correct model for the velocity-pressure-gradient correlation is proposed. A model that has the property of approaching the high-Reynolds-number model for pressure redistribution far away from the wall is derived. A similar analysis is carried out on the viscous dissipation term and asymptotically correct near-wall modifications are proposed. The near-wall closure based on the Reynolds-stress equations and a conventional low-Reynolds-number dissipation-rate equation is used to calculate fully-developed turbulent channel and pipe flows at different Reynolds numbers. A careful parametric study of the model constants introduced by the near-wall closure reveals that one constant in the dissipation-rate equation is Reynolds-number dependent, and a preliminary expression is proposed for this constant. With this modification, excellent agreement with near-wall turbulence statistics, measured and simulated, is obtained, especially the anisotropic behaviour of the normal stresses. On the other hand, it is found that the dissipation-rate equation has a significant effect on the calculated Reynolds-stress budgets. Possible improvements could be obtained by using available direct simulation data to help formulate a more realistic dissipation-rate equation. When such an equation is available, the present approach can again be used to derive a near-wall closure for the Reynolds-stress equations. The resultant closure could give improved predictions of the turbulence statistics and the Reynolds-stress budgets.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 221 , December 1990 , pp. 641 - 673
Copyright
© 1990 Cambridge University Press

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References

Amano, R. S. & Goel, P., 1987 Investigation of third-order closure model of turbulence for the computation of incompressible flows in a channel with a backward-facing step. Trans. ASME I: J. Fluids Engng 109, 424–428.Google Scholar
Chien, K. Y.: 1982 Predictions of channel and boundary layer flows with a low-Reynolds-number two-equation model of turbulence. AIAA J. 20, 33–38.Google Scholar
Cormack, D. E., Leal, L. G. & Steinfeld, J. H., 1978 An evaluation of mean Reynolds stress turbulence models: the triple velocity correlation. Trans. ASME I: J. Fluids Engng 100, 47–54.Google Scholar
Daly, B. J. & Harlow, F. H., 1970 Transport equations in turbulence. Phys. Fluids 13, 2634–2649.Google Scholar
Van Driest, E. R.: 1956 On turbulent flow near a wall. J. Aero. Sci. 23, 1007–1011.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
Hanjalic, K. & Launder, B. E., 1976 Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence. J. Fluid Mech. 74, 593–610.Google Scholar
Hoffmann, G. H.: 1975 Improved form of the low-Reynolds number k-ε turbulence model. Phys. Fluids 18, 309–312.Google Scholar
Jones, W. P. & Launder, B. E., 1972 The prediction of laminarization with a two-equation model of turbulence. Intl J. Heat Mass Transfer 15, 301–314.Google Scholar
Kebede, W., Launder, B. E. & Younis, B. A., 1985 Large amplitude periodic pipe flow: a second-moment closure study. Proc. 5th Symp. Turbulent Shear Flows, Ithaca, NY, pp. 16.23–16.29.Google Scholar
Kim, J., Moin, P. & Moser, R., 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–186.Google Scholar
Kolmogorov, A. N.: 1941 Local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 299–303.Google Scholar
Kreplin, H. P. & Eckelmann, H., 1979 Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow. Phys. Fluids 22, 1233–1239.Google Scholar
Lai, Y. G. & So, R. M. C. 1990 Near-wall modelling of turbulent heat fluxes. Intl J. Heat Mass Transfer 33, 1429–1440.Google Scholar
Lai, Y. G., So, R. M. C., Anwer, M. & Hwang, B. C., 1990 Modelling of turbulent curved-pipe flows. Presented at the Intl Symp. on Engineering Turbulence Modelling and Measurements, Dubrovnik, Yugoslavia, September 24–28.Google Scholar
Lai, Y. G., So, R. M. C. & Hwang, B. C. 1989 Calculation of planar and conical diffuser flows. AIAA J. 27, 542–548.Google Scholar
Lam, C. K. G. & Bremhorst, K. A. 1981 Modified form of the k-ε model for predicting wall turbulence. Trans. ASME I: J. Fluids Engng 103, 456–460.Google Scholar
Laufer, J.: 1954 The structure of turbulence in fully developed pipe flow. NACA Rep. 1174.Google Scholar
Launder, B. E.: 1986 Low-Reynolds number turbulence near walls. UMIST, Mech. Engng Dept Rep. TFD/86/4.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. & Reynolds, W. C., 1983 Asymptotic near-wall stress dissipation rates in a turbulent flow. Phys. Fluids 26, 1157–1158.Google Scholar
Launder, B. E. & Tselepidakis, D. P., 1988 Contribution to the second-moment modelling of sublayer turbulent transport. Zaric Memorial Intl Seminar on Near-Wall Turbulence, Dubrovnik, Yugoslavia, May 16–20.Google Scholar
Lumley, J. L.: 1980 Second order modelling of turbulent flow. Prediction Methods for Turbulent Flows (ed. W. Kollmann), pp. 1–31. Hemisphere.
Mansour, N. N., Kim, J. & Moin, P., 1988 Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 192, 15–44.Google Scholar
Mansour, N. N., Kim, J. & Moin, P., 1989 Near-wall k-ε turbulence modelling. AIAA J. 27, 1068–1073.Google Scholar
Na, T. Y.: 1979 Computation Methods in Engineering Boundary Value Problems. Academic.
Nikjooy, M. & So, R. M. C. 1989 On the modelling of scalar and mass transport in combustor flows. Intl J. Numer. Meth. Engng 28, 861–877.Google Scholar
Patel, V. C., Rodi, W. & Scheuerer, G., 1985 Turbulence models for near-wall and low-Reynolds-number flows: a review. AIAA J. 23, 1308–1319.Google Scholar
Prud'Homme, M. & Elghobashi, S. 1983 Prediction of wall-bounded turbulent flows with an improved version of a Reynolds-stress model. Proc. 4th Symp. Turbulent Shear Flows, Karlsruhe, FRG, pp. 1.7–1.12.Google Scholar
Reynolds, W. C.: 1976 Computation of turbulent flows. Ann. Rev. Fluid Mech. 8, 183–208.Google Scholar
Rotta, J. C.: 1951 Statistiche Theorie Nichthomogener Turbulenz. Z. Phys. 129, 547–572; also 131, 51–77.Google Scholar
Schildknecht, M., Miller, J. A. & Meier, G. E. A. 1979 The influence of suction on the structure of turbulence in fully-developed pipe flow. J. Fluid Mech. 90, 67–107.Google Scholar
Shima, N.: 1988 A Reynolds-stress model for near-wall and low-Reynolds-number regions. J. Fluids Engng 110, 38–44.Google Scholar
Shir, C. C.: 1973 A preliminary numerical study of atmospheric turbulent flows in the idealized planetary boundary layer. J. Atmos. Sci. 30, 1327–1339.Google Scholar
So, R. M. C., Lai, Y. G., Hwang, B. C. & Yoo, G. J., 1988 Low-Reynolds-number modelling of flows over a backward-facing step. Z. angew. Math. Phys. 39, 13–27.Google Scholar
So, R. M. C. & Yoo, G. J. 1986 On the modelling of low-Reynolds-number turbulence. NASA CR-3994.Google Scholar
So, R. M. C. & Yoo, G. J. 1987 Low-Reynolds-number modelling of turbulent flows with and without wall transpiration. AIAA J. 25, 1556–1564.Google Scholar
Yoo, G. J. & So, R. M. C. 1989 Variable density effects on axisymmetric sudden-expansion flows. Intl J. Heat Mass Transfer 32, 105–120.Google Scholar
Yoo, G. J., So, R. M. C. & Hwang, B. C. 1991 Calculation of developing turbulent flows in a rotating pipe. J. Turbomachinery, to appear.Google Scholar