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Oblique waves in steady supersonic flows of Bethe–Zel’dovich–Thompson fluids

Published online by Cambridge University Press:  19 September 2018

Davide Vimercati ,
Alfred Kluwick  and
Alberto Guardone Open the ORCID record for Alberto Guardone [Opens in a new window]
Davide Vimercati
Affiliation:
Department of Aerospace Science and Technology, Politecnico di Milano Via La Masa 34, 20156 Milano, Italy
Alfred Kluwick
Affiliation:
Institute of Fluid Mechanics and Heat Transfer, Vienna University of Technology, Getreidemarkt 9, 1060 Vienna, Austria
Alberto Guardone*
Affiliation:
Department of Aerospace Science and Technology, Politecnico di Milano Via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: alberto.guardone@polimi.it
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Abstract

Steady self-similar solutions to the supersonic flow of Bethe–Zel’dovich–Thompson fluids past compressive and rarefactive ramps are derived. Inviscid, non-heat-conducting, non-reacting and single-phase vapour flow is assumed. For convex isentropes and shock adiabats in the pressure–specific volume plane (classical gas dynamic regime), the well-known oblique shock and centred Prandtl–Meyer fan occur at a compressive and rarefactive ramp, respectively. For non-convex isentropes and shock adiabats (non-classical gas dynamic regime), four additional wave configurations may possibly occur; these are composite waves in which a Prandtl–Meyer fan is adjacent up to two oblique shock waves. The steady two-dimensional counterparts of the wave curves defined for the one-dimensional Riemann problem are constructed. In the present context, such curves consist of all the possible states connected to a given initial state (namely, the uniform state upstream of the ramp/wedge) by means of a steady self-similar solution. In addition to the classical case, as many as six non-classical wave-curve configurations are singled out. Moreover, the necessary conditions leading to each type of wave curves are analysed and a map of the upstream states leading to each configuration is determined.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Gas dynamics Compressible Flows: Shock waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 855 , 25 November 2018 , pp. 445 - 468
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Copyright
© 2018 Cambridge University Press 

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