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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
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: [email protected]

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.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

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