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Pressure-gradient-dependent logarithmic laws in sink flow turbulent boundary layers

Published online by Cambridge University Press:  25 November 2008

SHIVSAI AJIT DIXIT  and
O. N. RAMESH
SHIVSAI AJIT DIXIT
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
O. N. RAMESH
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
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Abstract

Experiments were done on sink flow turbulent boundary layers over a wide range of streamwise pressure gradients in order to investigate the effects on the mean velocity profiles. Measurements revealed the existence of non-universal logarithmic laws, in both inner and defect coordinates, even when the mean velocity descriptions departed strongly from the universal logarithmic law (with universal values of the Kármán constant and the inner law intercept). Systematic dependences of slope and intercepts for inner and outer logarithmic laws on the strength of the pressure gradient were observed. A theory based on the method of matched asymptotic expansions was developed in order to explain the experimentally observed variations of log-law constants with the non-dimensional pressure gradient parameter (Δp=(ν/ρU3τ)dp/dx). Towards this end, the system of partial differential equations governing the mean flow was reduced to inner and outer ordinary differential equations in self-preserving form, valid for sink flow conditions. Asymptotic matching of the inner and outer mean velocity expansions, extended to higher orders, clearly revealed the dependence of slope and intercepts on pressure gradient in the logarithmic laws.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 615 , 25 November 2008 , pp. 445 - 475
Copyright
Copyright © Cambridge University Press 2008

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