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Numerical study of sink-flow boundary layers

Published online by Cambridge University Press:  21 April 2006

Philippe R. Spalart
Philippe R. Spalart
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA
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Abstract

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 × 10−6 and 3.0 × 10−6, are presented. The three-dimensional, time-dependent Navier–Stokes equations are solved numerically using a spectral method, with about 106 degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones & Launder is observed. Two effects of the favourable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of Rθ for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 × 10−6, corresponding to a Reynolds number Rθ ≈ 330.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 172 , November 1986 , pp. 307 - 328
Copyright
© 1991 Cambridge University Press

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References

Badri Narayanan, M. A. & Ramjee, V. 1969 On the criteria for reverse transition in a two-dimensional boundary layer flow. J. Fluid Mech. 35, 225–241.Google Scholar
Bradshaw P.1967 The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625–645.Google Scholar
Bradshaw P. Ferriss, D, H. & Atwell, N. P. 1967 Calculation of boundary-layer development using the turbulent energy equation. J. Fluid Mech. 28, 593–616.Google Scholar
Clauser F.1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21, 91–108.Google Scholar
Coles D. E.1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
Coles D. E.1957 Remarks on the equilibrium turbulent boundary layer. J. Aero. Sci. 24, 495–506.Google Scholar
Galbraith, R. A. Mcd. & Head M. R.1975 Eddy viscosity and mixing length from measured boundary-layer developments. Aero. Quart. 26, 133–154.Google Scholar
Head, M. R. & Bradshaw P.1971 Zero and negative entrainment in turbulent shear flow. J. Fluid Mech. 46, 385–394.Google Scholar
Herring, H. J. & Norbury J. F.1967 Some experiments on equilibrium boundary layers in favourable pressure gradients. J. Fluid Mech. 27, 541–549.Google Scholar
Jones, W. P. & Launder B. E.1972 Some properties of sink-flow turbulent boundary layers J. Fluid Mech. 56, 337–351.Google Scholar
Klebanoff P. S.1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA T.N. 3178.
Launder, B. E. & Jones W. P.1969 Sink-flow turbulent boundary layers. J. Fluid Mech. 38, 817–831.Google Scholar
Loyd R. J. Moffat, R, J. & Kays, W. M. 1970 The turbulent boundary layer on a porous plate: an experimental study of the fluid dynamics with strong favorable pressure gradients and blowing. Stanford University, Thermo. Sci. Div. Rep. HMT-13.Google Scholar
Moser, R. S. & Moin P.1984 Direct numerical simulation of curved turbulent channel flow. NASA T.M. 85974.
Narasimha, R. & Sreenivasan K. R.1979 Relaminarization of fluid flows. Adv. Appl. Mech. 19, 221–309.Google Scholar
Schlichting H.1979 Boundary layer theory, 7th edn. McGraw-Hill.
Spalart P. R.1984a A spectral method for external viscous flows. Contemp. Maths 28, 315–335.Google Scholar
Spalart P. R. 1984b Numerical simulation of boundary-layer transition. 9th Intl Conf. on Num. Meth. in Fluid Dyn., Paris, June 1984 (ed. S. Soubbaramayer & J. P. Boujot), pp. 531–535. Springer.
Spalart P. R.1986 Numerical simulation of boundary layers: Part 1. Weak formulation and numerical method. NASA T.M. 88222.
Spalart, P. R. & Leonard A.1986 Direct numerical simulation of equilibrium turbulent boundary layers. In Proc. 5th Symp. on Turbulent Shear Flows, Ithaca, USA, August 7–9, 1985 (ed. F. J. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw). Springer (to appear).
Townsend A. A.1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11, 97–120.Google Scholar
Townsend A. A.1976 The structure of turbulent shear flow, 2nd edn. Cambridge University Press.