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

• Published in: Journal of fluid mechanics 2018-11, Vol.855, p.445-468
• Main Authors: Vimercati, Davide, Kluwick, Alfred, Guardone, Alberto
• Format: Article
• Language: English
• Subjects: Configurations; Eigenvalues; Fluid flow; Fluids; Heat transmission; JFM Papers; Oblique shock waves; Ordinary differential equations; Ramps; Self-similarity; Shock waves; Specific volume; Supersonic flow; Upstream
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2018.633

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.