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Maximum intensity of rarefaction shock waves for dense gases

Published online by Cambridge University Press:  23 December 2009

ALBERTO GUARDONE ,
CALIN ZAMFIRESCU  and
PIERO COLONNA
ALBERTO GUARDONE
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano Via La Masa 34, Milano 20156, Italy
CALIN ZAMFIRESCU
Affiliation:
Faculty of Engineering and Applied Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, ON L1H 74K, Canada
PIERO COLONNA*
Affiliation:
Process and Energy Department, Delft University of Technology Leghwaterstraat 44, Delft, 2628 CA, The Netherlands
*
†Email address for correspondence: P.Colonna@TUDelft.nl
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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 maximum-Mach 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 multi-parameter equation of state predicts a maximum wave Mach number close to 1.026 for D6 (dodecamethylcyclohexasiloxane, [O-Si-(CH3)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.

JFM classification

Compressible Flows: Gas dynamics Compressible Flows: Shock waves

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 127 - 146
Copyright
Copyright © Cambridge University Press 2010

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