Skip to main content
SpringerLink
Log in

Effect of the dynamic pressure on nozzle gas-flows

  • Published:
Ricerche di Matematica Aims and scope Submit manuscript

Abstract

Flows of a rarefied polyatomic gas confined in a nozzle with simple geometry are numerically studied based on the rational extended thermodynamics theory with six independent fields (RET\(_6\)). Using the theory, we can focus on, in particular, the effect of the dynamic pressure (nonequilibrium part of the pressure) on nozzle gas-flows. Development of a nonequilibrium state of a gas along the flow is studied by comparing the flow profiles to the ones predicted by the Euler theory of perfect fluids. Under some conditions, we find flow profiles that are qualitatively different from those by the Euler theory. Choking phenomena are also observed on the basis of RET\(_6\). From these findings we confirm that the RET\(_6\) theory is useful also for the analysis of nozzle gas-flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Landau, L.D., Lifshitz, E.M.: Fluid Mechanics. Pergamon, Oxford (1959)

    Google Scholar 

  2. Liepmann, H.W., Roshko, A.: Elements of Gasdynamics. Wiley, London (1960)

    Google Scholar 

  3. Vincenti, W.G., Kruger, C.H.: Introduction to Physical Gas Dynamics. Wiley, New York (1965)

    Google Scholar 

  4. Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Extended thermodynamics of dense gases. Contin. Mech. Thermodyn. 24, 271–292 (2011)

    Article  ADS  Google Scholar 

  5. Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics. Contin. Mech. Thermodyn. 25, 727–737 (2013)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  6. Taniguchi, S., Arima, T., Ruggeri, T., Sugiyama, M.: Thermodynamic theory of the shock wave structure in a rarefied polyatomic gas: beyond the Bethe–Teller theory. Phys. Rev. E 89, 013025 (2014)

    Article  ADS  Google Scholar 

  7. Arima, T., Barbera, E., Brini, F., Sugiyama, M.: The role of the dynamic pressure in stationary heat conduction of a rarefied polyatomic gas. Phys. Lett. A 378, 2695–2700 (2014)

    Article  CAS  ADS  Google Scholar 

  8. Müller, I., Ruggeri, T.: Rational Extended Thermodynamics, 2nd edn. Springer, New York (1998)

    Book  Google Scholar 

  9. Ruggeri, T., Sugiyama, M.: Rational Extended Thermodynamics Beyond the Monatomic Gas. Springer, Heidelberg (2015)

    Book  Google Scholar 

  10. Ruggeri, T., Sugiyama, M.: Classical and Relativistic Rational Extended Thermodynamics of Gases. Springer, Cham (2021)

    Book  Google Scholar 

  11. Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Extended thermodynamics of real gases with dynamic pressure: an extension of Meixner’s theory. Phys. Lett. A 376, 2799–2803 (2012)

    Article  MathSciNet  CAS  ADS  Google Scholar 

  12. Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: A study of linear waves based on extended thermodynamics for rarefied polyatomic gases. Acta Appl. Math. 132, 15–25 (2014)

    Article  MathSciNet  Google Scholar 

  13. Taniguchi, S., Arima, T., Ruggeri, T., Sugiyama, M.: Effect of dynamic pressure on the shock wave structure in a rarefied polyatomic gas. Phys. Fluids 26, 016103 (2014)

    Article  ADS  Google Scholar 

  14. Arima, T., Ruggeri, T., Sugiyama, M., Taniguchi, S.: Nonlinear extended thermodynamics of real gases with 6 fields. Int. J. Non-Linear Mech. 72, 6–15 (2015)

    Article  ADS  Google Scholar 

  15. Arima, T., Sugiyama, M.: Extended thermodynamics of dense polyatomic gases: modeling of molecular energy exchange. Ric. Mat. 68, 91–101 (2019)

    Article  MathSciNet  Google Scholar 

  16. Arima, T., Sugiyama, M.: Nonequilibrium pressure and temperatures in extended thermodynamics of gases with six fields. Ric. Mat. 68, 211–224 (2019)

    Article  MathSciNet  Google Scholar 

  17. Arima, T., Ruggeri, T., Sugiyama, M.: Rational extended thermodynamics of a rarefied polyatomic gas with molecular relaxation processes. Phys. Rev. E 96, 042143 (2017)

    Article  PubMed  ADS  Google Scholar 

  18. Arima, T., Ruggeri, T., Sugiyama, M.: Duality principle from rarefied to dense gas and extended thermodynamics with six fields. Phys. Rev. Fluids 2, 013401 (2017)

    Article  ADS  Google Scholar 

  19. Boillat, G., Ruggeri, T.: Hyperbolic principal subsystems: entropy convexity and subcharacteristic conditions. Arch. Ration. Mech. Anal. 137, 305–320 (1997)

    Article  MathSciNet  Google Scholar 

  20. Sugiyama, M.: A study of steady flow of a polyatomic gas by extended thermodynamics with six fields. J. Phys. Conf. Ser. 1035, 012008 (2018)

    Article  Google Scholar 

  21. Arima, T., Ruggeri, T., Sugiyama, M.: Rational extended thermodynamics of dense polyatomic gases incorporating molecular rotation and vibration. Philos. Trans. R. Soc. A 378, 20190176 (2020)

    Article  MathSciNet  CAS  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by JSPS KAKENHI Grant Number 22K03912 (T.A.).

Author information

Authors and Affiliations

  1. Department of Engineering for Innovation, National Institute of Technology, Tomakomai College, Tomakomai, 059-1275, Japan

    Takashi Arima

  2. Nagoya Institute of Technology, Nagoya, 466-8555, Japan

    Masaru Sugiyama

Authors
  1. Takashi Arima
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masaru Sugiyama
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Data collection and analysis were performed by TA. The first draft of the manuscript was written by all authors and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding authors

Correspondence to Takashi Arima or Masaru Sugiyama.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

In memory of Prof. Salvatore Rionero, the authors dedicate the present paper to him.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arima, T., Sugiyama, M. Effect of the dynamic pressure on nozzle gas-flows. Ricerche mat 73 (Suppl 1), 15–28 (2024). https://doi.org/10.1007/s11587-023-00784-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11587-023-00784-y

Keywords

Mathematics Subject Classification

Search

Navigation