Skip to main content

2015 | OriginalPaper | Buchkapitel

17. Shock Structure and Temperature Overshoot in Macroscopic Model of Mixtures

verfasst von : Tommaso Ruggeri, Masaru Sugiyama

Erschienen in: Rational Extended Thermodynamics beyond the Monatomic Gas

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter, we study the shock structure in a mixture on the basis of the model of multi-temperature mixtures explained in the previous Chap. 16 For simplicity, the study is restricted to weak and moderately strong shocks in a binary mixture of ideal gases without viscosity and heat conductivity. The model predicts the existence of the temperature overshoot of the heavier constituent, which was also predicted by other sophisticated approaches. This phenomenon is a consequence of weak energy exchange between the constituents, either due to large mass difference, or large rarefaction of the mixture. In the range of small Mach number, it is also shown that the shock thickness (or equivalently, the inverse of Knudsen number) decreases with the increase of the Mach number: a behavior similar to a single fluid.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat D. Madjarević, T. Ruggeri, S. Simić, Shock structure and temperature overshoot in macroscopic multi-temperature model of mixtures. Phys. Fluids 26, 106102 (2014)CrossRef D. Madjarević, T. Ruggeri, S. Simić, Shock structure and temperature overshoot in macroscopic multi-temperature model of mixtures. Phys. Fluids 26, 106102 (2014)CrossRef
2.
Zurück zum Zitat S. Kosuge, K. Aoki, S. Takata, Shock-wave structure for a binary gas mixture: finite-difference analysis of the boltzmann equation for hard sphere molecules. Eur. J. Mech. B Fluids 17, 87 (2001)CrossRef S. Kosuge, K. Aoki, S. Takata, Shock-wave structure for a binary gas mixture: finite-difference analysis of the boltzmann equation for hard sphere molecules. Eur. J. Mech. B Fluids 17, 87 (2001)CrossRef
3.
Zurück zum Zitat A. Raines, Study of a shock wave structure in gas mixtures on the basis of the boltzmann equation. Eur. J. Mech. B/Fluids 21, 599 (2002)MathSciNetCrossRefMATH A. Raines, Study of a shock wave structure in gas mixtures on the basis of the boltzmann equation. Eur. J. Mech. B/Fluids 21, 599 (2002)MathSciNetCrossRefMATH
4.
Zurück zum Zitat G.A. Bird, Aspects of the structure of strong shock waves. Phys. Fluids 13, 1172 (1970)CrossRef G.A. Bird, Aspects of the structure of strong shock waves. Phys. Fluids 13, 1172 (1970)CrossRef
5.
Zurück zum Zitat D. Madjarević, S. Simić, Shock structure in helium-argon mixture—a comparison of hyperbolic multi-temperature model with experiment. Europhys. Lett. 102, 44002 (2013)CrossRef D. Madjarević, S. Simić, Shock structure in helium-argon mixture—a comparison of hyperbolic multi-temperature model with experiment. Europhys. Lett. 102, 44002 (2013)CrossRef
6.
Zurück zum Zitat L.N. Harnet, E. Muntz, Experimental investigation of normal shock wave velocity distribution functions in mixtures of argon and helium. Phys. Fluids 10, 565 (1972)CrossRef L.N. Harnet, E. Muntz, Experimental investigation of normal shock wave velocity distribution functions in mixtures of argon and helium. Phys. Fluids 10, 565 (1972)CrossRef
7.
Zurück zum Zitat K. Abe, H. Oguchi, An analysis of shock waves in binary gas mixtures with special regard to temperature overshoot, Report No. 511. Institute of Space and Aeronautical Science, University of Tokyo (1974) K. Abe, H. Oguchi, An analysis of shock waves in binary gas mixtures with special regard to temperature overshoot, Report No. 511. Institute of Space and Aeronautical Science, University of Tokyo (1974)
8.
Zurück zum Zitat G. Bird, The structure of normal shock waves in a binary gas mixture. J. Fluid Mech. 31, 657 (1968)CrossRef G. Bird, The structure of normal shock waves in a binary gas mixture. J. Fluid Mech. 31, 657 (1968)CrossRef
9.
Zurück zum Zitat T. Ruggeri, The binary mixtures of euler fluids: a unified theory of second sound phenomena, in Continuum Mechanics and Applications in Geophysics and the Environment, ed. by B. Straughan, R. Greve, H. Ehrentraut, Y. Wang (Springer, Berlin, 2001), pp. 79–91CrossRef T. Ruggeri, The binary mixtures of euler fluids: a unified theory of second sound phenomena, in Continuum Mechanics and Applications in Geophysics and the Environment, ed. by B. Straughan, R. Greve, H. Ehrentraut, Y. Wang (Springer, Berlin, 2001), pp. 79–91CrossRef
10.
Zurück zum Zitat G. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, Oxford, 1994) G. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, Oxford, 1994)
11.
Zurück zum Zitat T. Ruggeri, S. Simić, On the hyperbolic system of a mixture of eulerian fluids: a comparison between single and multi-temperature models. Math. Methods Appl. Sci. 30, 827 (2007)MathSciNetCrossRefMATH T. Ruggeri, S. Simić, On the hyperbolic system of a mixture of eulerian fluids: a comparison between single and multi-temperature models. Math. Methods Appl. Sci. 30, 827 (2007)MathSciNetCrossRefMATH
12.
Zurück zum Zitat S. Simić, Shock structure in continuum models of gas dynamics: stability and bifurcation analysis. Nonlinearity 22, 1337 (2009)MathSciNetCrossRefMATH S. Simić, Shock structure in continuum models of gas dynamics: stability and bifurcation analysis. Nonlinearity 22, 1337 (2009)MathSciNetCrossRefMATH
13.
Zurück zum Zitat S. Simić, Shock structure in the mixture of gases: stability and bifurcation of equilibria, in Thermodynamics – Kinetics of Dynamic Systems, Chap. 8, ed. by J.C.M. Pirajãn (InTech, Rijeka, 2011) S. Simić, Shock structure in the mixture of gases: stability and bifurcation of equilibria, in Thermodynamics – Kinetics of Dynamic Systems, Chap. 8, ed. by J.C.M. Pirajãn (InTech, Rijeka, 2011)
14.
Zurück zum Zitat G. Boillat, T. Ruggeri, Hyperbolic principal subsystems: entropy convexity and subcharacteristic conditions. Arch. Ration. Mech. Anal. 137, 305 (1997)MathSciNetCrossRefMATH G. Boillat, T. Ruggeri, Hyperbolic principal subsystems: entropy convexity and subcharacteristic conditions. Arch. Ration. Mech. Anal. 137, 305 (1997)MathSciNetCrossRefMATH
15.
Zurück zum Zitat W. Weiss, Continuous shock structure in extended thermodynamics. Phys. Rev. E 52, R5760 (1995)CrossRef W. Weiss, Continuous shock structure in extended thermodynamics. Phys. Rev. E 52, R5760 (1995)CrossRef
16.
Zurück zum Zitat R. Monaco, Shock-wave propagation in gas mixtures by means of a discrete velocity model of the boltzmann equation. Acta Mech. 55, 239 (1985)MathSciNetCrossRefMATH R. Monaco, Shock-wave propagation in gas mixtures by means of a discrete velocity model of the boltzmann equation. Acta Mech. 55, 239 (1985)MathSciNetCrossRefMATH
17.
Zurück zum Zitat I. Müller, T. Ruggeri, Rational Extended Thermodynamics, 2nd edn. (Springer, New York, 1998)CrossRefMATH I. Müller, T. Ruggeri, Rational Extended Thermodynamics, 2nd edn. (Springer, New York, 1998)CrossRefMATH
Metadaten
Titel
Shock Structure and Temperature Overshoot in Macroscopic Model of Mixtures
verfasst von
Tommaso Ruggeri
Masaru Sugiyama
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-13341-6_17

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.