Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T12:46:34.803Z Has data issue: false hasContentIssue false
  • English
  • Français

Admissibility region for rarefaction shock waves in dense gases

Published online by Cambridge University Press:  06 March 2008

CALIN ZAMFIRESCU ,
ALBERTO GUARDONE  and
PIERO COLONNA
CALIN ZAMFIRESCU
Affiliation:
Process and Energy Department, Delft University of Technology, Leghwaterstraat 44, Delft, 2628 CA, The Netherlands
ALBERTO GUARDONE
Affiliation:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, Milano, 20154, Italy
PIERO COLONNA
Affiliation:
Process and Energy Department, Delft University of Technology, Leghwaterstraat 44, Delft, 2628 CA, The Netherlands
Get access Rights & Permissions [Opens in a new window]

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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 599 , 25 March 2008 , pp. 363 - 381
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bethe, H. A. 1942 The theory of shock waves for an arbitrary equation of state. Tech. Rep. 545. Office of Scientific Research and Development.Google Scholar
Callen, H. B. 1985 Thermodynamics and an Introduction to Thermostatistics, 2nd edn. Wiley.Google Scholar
Colonna, P. & Guardone, A. 2006 Molecular interpretation of non-classical gasdynamics of dense vapors under the van der waals model. Phys. Fluids 18, 056101–1–14.CrossRefGoogle Scholar
Colonna, P., Guardone, A. & Nannan, N. R. 2007 Siloxanes: a new class of candidate Bethe-Zel'dovich-Thompson fluids. Phys. Fluids 19, 086102–1–12.Google Scholar
Colonna, P., Guardone, A., Nannan, N. R. & Zamfirescu, C. 2008a Design of the dense gas flexible asymmetric shock tube. Trans. ASME: J. Fluids Engng (In press).CrossRefGoogle Scholar
Colonna, P., Nannan, N. R. & Guardone, A. 2008b Multiparameter equations of state for siloxanes: [(CH3)3-Si-O1/2]2-[O-Si-(CH3)2]i = 1. . .3, and [O-Si-(CH3)2]6. Fluid Phase Equilib. (In press).CrossRefGoogle Scholar
Colonna, P., Nannan, R., Guardone, A. & Lemmon, E. W. 2006 Multiparameter equations of state for selected siloxanes. Fluid Phase Equilib. 244, 193–211.CrossRefGoogle Scholar
Colonna, P. & Silva, P. 2003 Dense gas thermodynamic properties of single and multicomponent fluids for fluid dynamics simulations. Trans. ASME: J. Fluids Engng 125, 414–427.Google Scholar
Cramer, M. S. 1989 Negative nonlinearity in selected fluorocarbons. Phys. FluidsA 1, 1894–1897.CrossRefGoogle Scholar
Cramer, M. S. & Sen, R. 1987 Exact solutions for sonic shocks in van der Waal's gases. Phys. Fluids 30, 377–385.CrossRefGoogle Scholar
Emanuel, G. 1987 Advanced Classical Thermodynamics. AIAA Education Series.CrossRefGoogle Scholar
Fergason, S. H., Ho, T. L., Argrow, B. M. & Emanuel, G. 2001 Theory for producing a single-phase rarefaction shock wave in a shock tube. J. Fluid Mech. 445, 37–54.CrossRefGoogle Scholar
Godlewski, E. & Raviart, P. A. 1994 Numerical Approximation of Hyperbolic Systems of Conservation Laws. Springer.Google Scholar
Guardone, A. & Argrow, B. M. 2005 Non-classical gasdynamic region of selected fluorocarbons. Phys. Fluids 17, 116102–1–17.CrossRefGoogle Scholar
Hayes, W. 1960 The basic theory of gasdynamic discontinuities. In Fundamentals of Gasdynamics (ed. Emmons, H. W.), High speed aerodynamics and jet propulsion, vol. 3, pp. 416–481. Princeton University Press.Google Scholar
Kluwick, A. 2001 Theory of shock waves. Rarefaction shocks. In Handbook of Shockwaves (ed. Ben-Dor, G., Igra, O., Elperin, T. & Lifshitz, A.), vol. 1, chap. 3.4, pp. 339–411. Academic.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Course of Theoretical Physics, Fluid Mechanics, vol. 6. Pergamon.Google Scholar
Lax, P. 1957 Hyperbolic systems of conservation laws, II. Commun. Pure Appl. Maths 10, 537–566.Google Scholar
Liu, T. P. 1975 The Riemann problem for general systems of conservation laws. J. Diffl Equat. 18, 218–234.CrossRefGoogle Scholar
Oleinik, O. 1959 Uniqueness and stability of the generalized solution of the Cauchy problem for a quasilinear equation. Uspehi Mat. Nauk 14, 165–170.Google Scholar
Smoller, J. 1983 Shock Waves and Reaction-Diffusion Equations. Springer.CrossRefGoogle Scholar
Span, R. & Wagner, W. 2003a Equations of state for technical applications. i. simultaneously optimized functional forms for nonpolar and polar fluids. Intl J. Thermophys. 24, 1–39.CrossRefGoogle Scholar
Span, R. & Wagner, W. 2003b Equations of state for technical applications. II. Results for nonpolar fluids. Intl J. Thermophys. 24, 41–109.Google Scholar
Tegeler, C., Span, R. & Wagner, W. 1999 A new equation of state for Argon coveringthe fluid region for temperatures from the melting line to 700 K at pressures up to 1000 MP. J. Phys. Chem. Ref. Data 28, 779–850.Google Scholar
Thompson, P. A. 1971 A fundamental derivative in gas dynamics. Phys. Fluids 14, 1843–1849.CrossRefGoogle Scholar
Thompson, P. A. & Lambrakis, K. C. 1973 Negative shock waves. J. Fluid Mech. 60, 187–208.Google Scholar
Zamfirescu, C., Guardone, A. & Colonna, P. 2006a Numerical simulation of the FAST dense gas Ludwieg tube experiment. In ECCOMAS CFD 2006 Conference, Egmond aan Zee, NL.CrossRefGoogle Scholar
Zamfirescu, C., Guardone, A. & Colonna, P. 2006b Preliminary design of the FAST dense gas Ludwieg tube. In 9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, San Francisco, CA.CrossRefGoogle Scholar
Zel'dovich, Y. B. 1946 On the possibility of rarefaction shock waves. Zh. Eksp. Teor. Fiz. 4, 363–364.Google Scholar