Exact solutions to non-classical steady nozzle flows of Bethe–Zel’dovich–Thompson fluids

Abstract

Steady nozzle flows of Bethe-Zel'dovich-Thompson fluids -substances exhibiting non-classical gasdynamic behaviour in a finite vapour-phase thermodynamic region in close proximity to the liquid-vapour saturation curve -are examined. Non-classical flow features include rarefaction shock waves, shock waves with either upstream or downstream sonic states and split shocks. Exact solutions for a mono-component single-phase fluid expanding from a reservoir into a stationary atmosphere through a conventional converging-diverging nozzle are determined within the quasi-onedimensional inviscid flow approximation. The novel analytical approach makes it possible to elucidate the connection between the adiabatic, possibly non-isentropic flow field and the underlying local isentropic-flow features, including the possible qualitative alterations in passing through shock waves. Contrary to previous predictions based on isentropic-flow inspection, shock disintegration is found to occur also from reservoir states corresponding to a single sonic point. The global layout of the flow configurations produced by a monotonic decrease in the ambient pressure, namely the functioning regime, is examined for reservoir conditions resulting in single-phase flows. Accordingly, a classification of steady nozzle flows into 10 different functioning regimes is proposed. Flow conditions determining the transition between the different classes of flow are investigated and each functioning regime is associated with the corresponding thermodynamic region of reservoir states.

Experimental evidence of non-ideal compressible effects in expanding flow of a high molecular complexity vapor

“…Current models predict that, for molecularly complex fluids, a thermodynamic region exists in the vapor phase where Γ < 1 and the flow behavior is non-ideal; if sub-regions of negative Γ are also present, the regime is non-classical and expansion shock waves are also admissible. A detailed discussion on different compressible fluid regimes in quasi one-dimensional nozzle expansions is given in Guardone and Vimercati (2016).…”

Experimental observation of oblique shock waves in steady non-ideal flows

“…The quasi-one-dimensional theory for isentropic nozzle flows (see e.g. Thompson 1988;Guardone and Vimercati 2016) predicts that, in the NICFD regime, the exhaust Mach number and the exhaust to total pressure ratio depend on the inlet total thermodynamic state. The experimental campaign documented by Spinelli et al (2018) provided evidence of this dependence, in that flows at different exhaust Mach number and exhaust to total pressure ratios were measured at varying inlet total thermodynamic state.…”

A unified description of oblique waves in ideal and non-ideal steady supersonic flows around compressive and rarefactive corners

“…The thermodynamic parameter Γ was named by Thompson [28] as the fundamental derivative of gasdynamics because of its paramount role in delineating the behaviour of compressible fluids. Among the others areas of compressible-fluid dynamics, the fundamental derivative is key in steady isentropic flows (see below), shock wave theory, nozzle flows and non-linear wave propagation [28,30,9,10,6,5,8,18,19,32,2,15,14]. In the references listed above, a distinction is devised between the classical gasdynamic regime if Γ is positive and the non-classical gasdynamic regime if Γ is negative or can possibly change its sign.…”