Admissibility region for rarefaction shock waves in dense gases

Abstract

In the vapour phase and close to the liquid–vapour saturation curve, fluids made of complex molecules are expected to exhibit a thermodynamic region in which the fundamental derivative of gasdynamic Γ is negative. In this region, non-classical gasdynamic phenomena such as rarefaction shock waves are physically admissible, namely they obey the second law of thermodynamics and fulfil the speed-orienting condition for mechanical stability. Previous studies have demonstrated that the thermodynamic states for which rarefaction shock waves are admissible are however not limited to the Γ<0 region. In this paper, the conditions for admissibility of rarefaction shocks are investigated. This results in the definition of a new thermodynamic region – the rarefaction shocks region – which embeds the Γ<0 region. The rarefaction shocks region is bounded by the saturation curve and by the locus of the states connecting double-sonic rarefaction shocks, i.e. shock waves in which both the pre-shock and post-shock states are sonic. Only one double-sonic shock is shown to be admissible along a given isentrope, therefore the double-sonic states can be connected by a single curve in the volume–pressure plane. This curve is named the double sonic locus. The influence of molecular complexity on the shape and size of the rarefaction shocks region is also illustrated by using the van der Waals model; these results are confirmed by very accurate multi-parameter thermodynamic models applied to siloxane fluids and are therefore of practical importance in experiments aimed at proving the existence of rarefaction shock waves in the single-phase vapour region as well as in future industrial applications operating in the non-classical regime.