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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: [email protected]
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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

Bahmani, F.2013 Three problems involving compressible flow with large bulk viscosity and non-convex equations of state. PhD thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.Google Scholar
Cramer, M. S. 2012 Numerical estimates for the bulk viscosity of ideal gases. Phys. Fluids 24, 066102.CrossRefGoogle Scholar
Emanuel, G. 1992 Effect of bulk viscosity on a hypersonic boundary layer. Phys. Fluids A 4 (3), 491–495.Google Scholar
Gonzalez, H. & Emanuel, G. 1993 Effect of bulk viscosity on Couette flow. Phys. Fluids A 5, 1267–1268.Google Scholar
Graves, R. E. & Argrow, B. A. 1999 Bulk viscosity: past to present. Intl J. Thermophys. 13 (3), 337–342.Google Scholar
Lees, L. 1956 Laminar heat transfer over blunt-nosed bodies at hypersonic speeds. Jet Propul. 26, 259–269.CrossRefGoogle Scholar
Reid, R. C., Prausnitz, J. M. & Poling, B. E. 1987 The Properties of Gases and Liquids. Wiley.Google Scholar
Tisza, L. 1942 Supersonic absorption and Stokes’ viscosity relation. Phys. Rev. 61, 531–536.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.Google Scholar
White, F. M. 1974 Viscous Fluid Flow. McGraw-Hill.Google Scholar