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Reynolds Stress Calculations for Pre-Transition Boundary Layers With Turbulent Free Streams

[+] Author Affiliations
R. E. Mayle, A. Schulz, H.-J. Bauer

Universität Karlsruhe, Karlsruhe, Germany

Paper No. GT2008-50109, pp. 1247-1254; 8 pages
doi:10.1115/GT2008-50109
From:
  • ASME Turbo Expo 2008: Power for Land, Sea, and Air
  • Volume 4: Heat Transfer, Parts A and B
  • Berlin, Germany, June 9–13, 2008
  • Conference Sponsors: International Gas Turbine Institute
  • ISBN: 978-0-7918-4314-7 | eISBN: 0-7918-3824-2
  • Copyright © 2008 by ASME

abstract

Equations are developed for calculating u′ u′ and u′ v′ in a laminar boundary layer when the free stream is turbulent. These equations are based on the ideas presented by the first two authors in their 1997 paper, where the crucial role of high frequency fluctuations in the free stream was first recognized. Solutions of these equations, which also include the effect of a variable free stream velocity, show that the intensity of the fluctuations in the boundary layer increase as separation is approached, that the initial growth rate of the shear stress component is substantially less than the normal component, that the maximum value of u′ u′ near transition is about the same as that in a turbulent boundary layer, and that, as is well known, free-stream turbulence increases the skin-friction coefficient. Overall, the calculations agree reasonably well with experimental results for all free-stream turbulence levels and velocity variations. In addition, upon examining Liepmann’s transition hypothesis, we show that transition from laminar to turbulent flow seems to occur at the streamwise position where the maximum of u′ v′ /uτ 2 first attains a value of about one-third. But other criteria also seem to apply.

Copyright © 2008 by ASME

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