Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-29T13:30:34.789Z Has data issue: false hasContentIssue false

On near-wall turbulent flow modelling

Published online by Cambridge University Press:  26 April 2006

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

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
Copyright
© 1990 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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, 424428.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, 3338.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, 4754.Google Scholar
Daly, B. J. & Harlow, F. H., 1970 Transport equations in turbulence. Phys. Fluids 13, 26342649.Google Scholar
Van Driest, E. R.: 1956 On turbulent flow near a wall. J. Aero. Sci. 23, 10071011.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, 609638.Google Scholar
Hanjalic, K. & Launder, B. E., 1976 Contribution towards a Reynolds-stress closure for low-Reynolds-number turbulence. J. Fluid Mech. 74, 593610.Google Scholar
Hoffmann, G. H.: 1975 Improved form of the low-Reynolds number k-ε turbulence model. Phys. Fluids 18, 309312.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, 301314.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. 16.2316.29.Google Scholar
Kim, J., Moin, P. & Moser, R., 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133186.Google Scholar
Kolmogorov, A. N.: 1941 Local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 299303.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, 12331239.Google Scholar
Lai, Y. G. & So, R. M. C. 1990 Near-wall modelling of turbulent heat fluxes. Intl J. Heat Mass Transfer 33, 14291440.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, 542548.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, 456460.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, 537566.Google Scholar
Launder, B. E. & Reynolds, W. C., 1983 Asymptotic near-wall stress dissipation rates in a turbulent flow. Phys. Fluids 26, 11571158.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. 131. Hemisphere.
Mansour, N. N., Kim, J. & Moin, P., 1988 Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 192, 1544.Google Scholar
Mansour, N. N., Kim, J. & Moin, P., 1989 Near-wall k-ε turbulence modelling. AIAA J. 27, 10681073.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, 861877.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, 13081319.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. 1.71.12.Google Scholar
Reynolds, W. C.: 1976 Computation of turbulent flows. Ann. Rev. Fluid Mech. 8, 183208.Google Scholar
Rotta, J. C.: 1951 Statistiche Theorie Nichthomogener Turbulenz. Z. Phys. 129, 547572; 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, 67107.Google Scholar
Shima, N.: 1988 A Reynolds-stress model for near-wall and low-Reynolds-number regions. J. Fluids Engng 110, 3844.Google Scholar
Shir, C. C.: 1973 A preliminary numerical study of atmospheric turbulent flows in the idealized planetary boundary layer. J. Atmos. Sci. 30, 13271339.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, 1327.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, 15561564.Google Scholar
Yoo, G. J. & So, R. M. C. 1989 Variable density effects on axisymmetric sudden-expansion flows. Intl J. Heat Mass Transfer 32, 105120.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