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Suppression of shock-induced separation in fluids having large bulk viscosities

Published online by Cambridge University Press:  09 September 2014

F. Bahmani  and
M. S. Cramer
F. Bahmani
Affiliation:
Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
M. S. Cramer*
Affiliation:
Department of Engineering Science and Mechanics, 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 effect of large bulk viscosity on the classical problem of two-dimensional shock–boundary-layer interaction. The flow is taken to be steady and supersonic over a flat adiabatic plate. The boundary layer is taken to be laminar and the fluid is modelled as a perfect gas with a bulk viscosity that is large compared with its shear viscosity. The flow details are computed using a fifth-order weighted essentially non-oscillatory finite difference scheme and a third-order Runge–Kutta scheme for the spatial and temporal discretizations. The primary result of interest is the suppression of separation when the ratio of bulk to shear viscosity is sufficiently large.

JFM classification

Compressible Flows: Compressible boundary layers Compressible Flows: Compressible Flows Compressible Flows: Shock waves
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , R2
Copyright
© 2014 Cambridge University Press 

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References

Adamson, T. C. & Messiter, A. F. 1980 Analysis of two-dimensional interactions between shock waves and boundary layers. Annu. Rev. Fluid Mech. 12, 103–138.CrossRefGoogle Scholar
Bahmani, F.2013 Three problems involving compressible flow with large bulk viscosity and non-convex equations of state. Doctoral Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.Google Scholar
Chapman, S. & Cowling, T. G. 1970 Mathematical Theory of Non-Uniform Gases. Cambridge University Press.Google Scholar
Cramer, M. S. 2012 Numerical estimates for the bulk viscosity of ideal gases. Phys. Fluids 24, 066102.Google Scholar
Cramer, M. S. & Bahmani, F. 2014 Effect of large bulk viscosity on large-Reynolds-number flows. J. Fluid Mech. 751, 142–163.CrossRefGoogle Scholar
Cramer, M. S. & Park, S. 1999 On the suppression of shock-induced separation in Bethe–Zel’dovich–Thompson fluids. J. Fluid Mech. 393, 1–21.Google Scholar
Cramer, M. S., Park, S. & Watson, L. T. 1997 Numerical verification of scaling laws for shock–boundary layer interactions in arbitrary gases. J. Fluid Mech. 119, 67–73.Google Scholar
Emanuel, G. 1990 Bulk viscosity of a dilute polyatomic gas. Phys. Fluids A 2 (3), 2252–2254.CrossRefGoogle Scholar
Emanuel, G. 1992 Effect of bulk viscosity on a hypersonic boundary layer. Phys. Fluids A 4 (3), 491–495.CrossRefGoogle Scholar
Emanuel, G. & Argrow, B. A. 1994 Linear dependence of the bulk viscosity on shock wave thickness. Phys. Fluids 6 (9), 3203–3205.Google Scholar
Gonzalez, H. & Emanuel, G. 1993 Effect of bulk viscosity on Couette flow. Phys. Fluids A 2 (5), 1267–1268.CrossRefGoogle Scholar
Graves, R. E. & Argrow, B. A. 1999 Bulk viscosity: past to present. Intl J. Thermophys. 13, 337–342.Google Scholar
Hakkinen, R. J., Greber, L., Trilling, L. & Abarbanel, S. S.1959 The interaction of an oblique shock wave with a laminar boundary layer. Tech. Rep. 2-18-59W. NASA Mem.Google Scholar
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228.Google Scholar
Katzer, E. 1989 On the scales of laminar shock/boundary layer interaction. J. Fluid Mech. 206, 477–496.Google Scholar
Kluwick, A. 1998 Interacting laminar and turbulent boundary layers. In Recent Advances in Boundary Layer Theory (ed. Kluwick, A.), Springer.CrossRefGoogle Scholar
MacCormack, R. W. 1982 A numerical method for solving the equations of a compressible viscous flow. AIAA J. 20, 1275–1281.Google Scholar
Pletcher, R. H., Tannehill, J. C. & Anderson, D. A. 1984 Computational Fluid Mechanics and Heat Transfer. McGraw-Hill.Google Scholar
Thompson, P. A. 1972 Compressible-Fluid Dynamics. McGraw-Hill.CrossRefGoogle Scholar
Tisza, L. 1942 Supersonic absorption and Stokes’ viscosity relation. Phys. Rev. 61, 531–536.Google Scholar
Zhong, X. 1994 Application of essentially nonoscillatory schemes to unsteady hypersonic shock–shock interference heating problems. AIAA J. 32 (1–2), 1606–1616.CrossRefGoogle Scholar