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Effect of large bulk viscosity on large-Reynolds-number flows

Published online by Cambridge University Press:  17 June 2014

M. S. Cramer  and
F. Bahmani
M. S. Cramer*
Affiliation:
Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
F. Bahmani
Affiliation:
Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
*
†Email address for correspondence: macramer@vt.edu
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Abstract

We examine the inviscid and boundary-layer approximations in fluids having bulk viscosities which are large compared with their shear viscosities for three-dimensional steady flows over rigid bodies. We examine the first-order corrections to the classical lowest-order inviscid and laminar boundary-layer flows using the method of matched asymptotic expansions. It is shown that the effects of large bulk viscosity are non-negligible when the ratio of bulk to shear viscosity is of the order of the square root of the Reynolds number. The first-order outer flow is seen to be rotational, non-isentropic and viscous but nevertheless slips at the inner boundary. First-order corrections to the boundary-layer flow include a variation of the thermodynamic pressure across the boundary layer and terms interpreted as heat sources in the energy equation. The latter results are a generalization and verification of the predictions of Emanuel (Phys. Fluids A, vol. 4, 1992, pp. 491–495).

JFM classification

Aerodynamics: Aerodynamics Compressible Flows: Compressible boundary layers Compressible Flows: Compressible Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , pp. 142 - 163
Copyright
© 2014 Cambridge University Press 

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References

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