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An Integral Method for the Oscillating Turbulent Boundary Layer

Published online by Cambridge University Press:  07 June 2016

M.H. Patel*
Affiliation:
Department of Mechanical Engineering, University College, London
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Summary

The linearised time dependent momentum integral equation is used in conjunction with assumed velocity profiles and a quasi-static skin friction approximation to predict the turbulent boundary layer response to sinusoidal streamwise velocity fluctuations in the freestream. The mean zero pressure gradient case, corresponding to flat plate flow, is presented in detail and verified by comparison with experimental data and alternative calculations. The asymptotic turbulent boundary layer response to very high frequency perturbations is also derived. It is shown that a travelling wave component in the freestream, with its associated time dependent streamwise pressure gradient, has a dominant effect on the turbulent boundary layer response.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1981

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References

1 Bradshaw, P. Calculation of boundary layer development using the turbulent energy equation - Unsteady flow. National Physical Laboratory, Aero Rpt 1288, February 1969 Google Scholar
2 Bradshaw, P., Ferris, D. and Attwell, N. Calculation of boundary layer development using the turbulent energy equation. JFM 28, pt 3, p 596616, 1967 CrossRefGoogle Scholar
3 Cebeci, T., Smith, A.M.O. and Mosinkis, G. Calculation of compressible adiabatic turbulent boundary layers. AIM Journal, Vol. 8, No. 11, pp 197482, November t1970 Google Scholar
4 Karlsson, S.K.F. An unsteady turbulent boundary layer. JFM, Vol. 5, pt 4, pp 62236, May 1959 CrossRefGoogle Scholar
5 Kenison, R.C. An experimental study of the effect of oscillatory flow on the separation region in a turbulent boundary layer. Proc. of AGARD Conf. on Unsteady Aerodynamics, AGARD-CP-227, pp 201 to 20-12, September 1977 Google Scholar
6 Ludwieg, H. and Tillmann, W. Untersuchungen über die Wandschubspannung in turbulenten Reibungsschichten, Ing.-Arch. 17, pp 28899, 1949 Google Scholar
7 McCroskey, W.J. Some current research in unsteady fluid dynamics. J. of Fluids Eng., Trans, of ASME, Ser. 1, p 839, March 1977 CrossRefGoogle Scholar
8 McCroskey, W.J. and Phillipe, J.J. Unsteady viscous flow on oscillating aerofoils. AIAA J., Vol. 13, No. 1, p 719, January 1975CrossRefGoogle Scholar
9 McDonald, H. and Shamroth, S.J. An analysis and application of the time dependent turbulent boundary layer equations. AIAA J., Vol. 9, No. 8, pp 155360, August 1971 CrossRefGoogle Scholar
10 Nash, J.F., Carr, L.W. and Singleton, R.E. Unsteady turbulent boundary layers in two dimensional incompressible flow. AIAA J., Vol. 13, No. 2, p 167173, February 1975 CrossRefGoogle Scholar
11 Patel, M.H. and Hancock, G.J. A gust tunnel facility. A.R.C. R & M., No. 3802, 1977 Google Scholar
12 Patel, M.H. On laminar boundary layers in oscillatory flow. Proc. Roy. Soc. A347, pp 99123, 1975 Google Scholar
13 Patel, M.H. On turbulent boundary layers in oscillatory flow. Proc. Roy. Soc. A353, pp 12144, 1977 Google Scholar
14 Pericleous, K.A. An oscillating turbulent boundary layer in an adverse pressure gradient. Ph.D. Thesis, University of London, 1977 Google Scholar
15 Rosenhead, L. Laminar boundary layers. Oxford University Press, 1963 Google Scholar
16 Schachemmann, A.A. and Rockwell, D.O. Oscillating turbulent flow in a conical diffuser. ASME J. of Fluids, p 695701, December 1976 CrossRefGoogle Scholar
17 Singleton, R.E. and Nash, J.F. Method for calculating unsteady turbulent boundary layers in two and three dimensional flows. AIAA J,, Vol. 12, No. 5, pp 5905, May 1974 CrossRefGoogle Scholar