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Characteristics of turbulent boundary layers at low Reynolds numbers with and without transpiration

Published online by Cambridge University Press:  29 March 2006

Roger L. Simpson
Roger L. Simpson
Affiliation:
Institute of Technology, Southern Methodist University, Dallas, Texas
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Abstract

An extension to Coles's (1956) ‘law of the wall–law of the wake’ formulation for incompressible unblown boundary layers with momentum thickness Reynolds number Reθ > 6000. is made for Reθ < 6000. It is found that κ = 0·40, the von Kármán constant for Reθ > 6000, is replaced by Ω = 0·40 (Reθ/6000)⅛ for Reθ < 6000. Based upon the data of Simpson (1967) this formulation is extended to injection and undersucked (dθ/dx > 0) flows in ‘law of the wall’ and ‘velocity-defect’ representations. This law of the wall for the logarithmic turbulent region and Reichardt's sublayer variation of εM/ν are used to obtain a continuous expression for εM/ν as a function of U+, V+w, and Reθ for the wall region. This expression is in reasonable agreement with the generated εM/ν blowing results and in less agreement with the unblown and suction results. Eddy viscosity and mixing length results confirm that εM/δ*U∞ ∝ Ω2 and l/δ ∝ Ω for the outer region and that εM/δ*U∞ and l/δ are substantially independent of blowing and moderate suction, as also reflected by the velocity defect representation for injection and suction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 4 , 30 July 1970 , pp. 769 - 802
Copyright
© 1970 Cambridge University Press

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