Maximum intensity of rarefaction shock waves for dense gases

Abstract

Modern thermodynamic models indicate that fluids consisting of complex molecules may display non-classical gasdynamic phenomena such as rarefaction shock waves (RSWs) in the vapour phase. Since the thermodynamic region in which non-classical phenomena are physically admissible is finite in terms of pressure, density and temperature intervals, the intensity of RSWs is expected to exhibit a maximum for any given fluid. The identification of the operating conditions leading to the RSW with maximum intensity is of paramount importance for the experimental verification of the existence of non-classical phenomena in the vapour phase and for technical applications taking advantage of the peculiarities of the non-classical regime. This study investigates the conditions resulting in an RSW with maximum intensity in terms of pressure jump, wave Mach number and shock strength. The upstream state of the RSW with maximum pressure drop is found to be located along the double-sonic locus formed by the thermodynamic states associated with an RSW having both pre-and post-shock sonic conditions. Correspondingly, the maximumMach thermodynamic and maximum-strength loci locate the pre-shock states from which the RSW with the maximum wave Mach number and shock strength can originate. The qualitative results obtained with the simple van der Waals model are confirmed with the more complex Stryjek-Vera-Peng-Robinson, Martin-Hou and Span-Wagner equations of state for selected siloxane and perfluorocarbon fluids. Among siloxanes, which are arguably the best fluids for experiments aimed at the generation and measurement of an RSW, the state-of-the-art Span-Wagner multiparameter equation of state predicts a maximum wave Mach number close to 1.026 for D 6 (dodecamethylcyclohexasiloxane, [O-Si-(CH 3 ) 2 ] 6 ). Such value is well within the capacity of the measurement system of a newly built experimental set-up aimed at the first-ever demonstration of the existence of RSWs in dense vapours.

Admissible shock waves and shock-induced phase transitions in a van der Waals fluid

“…It is worth noting that the curve L ÃÃ d is the locus of the unperturbed states for which exactly one rarefaction shock wave is admissible. This curve was first obtained by Zamfirescu, Guardone, and Colonna 11,12 and, since the velocity of the unique admissible rarefaction shock obtainable for u 0 2 L ÃÃ d equals the sound velocity in both the unperturbed and perturbed states, this curve was named double sonic locus (DSL) by those authors (see also Ref. 48).…”

“…6,[8][9][10][11][12] Propagation of a rarefaction shock wave is impossible in the ideal gas model, where only (and all) the compressive shock waves can exist and be stable. Thus, in the terminology of the theory of hyperbolic systems, only compressive shocks are admissible in ideal gases.…”

Computation of tail probabilities for non-classical gasdynamic phenomena

“…The initial conditions (IC) for the experiment (and for the simulation) are prescribed according to the theory described in [10], to maximize the Mach number of the rarefaction shock wave and facilitate the wave detection. The maximum achievable precision in controlling the temperature and pressure values in the charge tube has been estimated from the measurement instruments and hardware specifications to be 0.4% for the pressure and 0.1% for the temperature.…”

Neutron star collapse and gravitational waves with a non-convex equation of state

“…BZT fluids have drawn some attention in the last fifteen years due to their potential applications in industry (see, e.g. Cinnella 2008;Guardone et al 2010). Unlike a regular fluid, a BZT fluid might condense on isentropic compression 1 .…”