Skip to main content
SpringerLink
Log in

Numerical study of shock wave interaction in steady flows of a viscous heat-conducting gas with a low ratio of specific heats

  • Published:
Thermophysics and Aeromechanics Aims and scope

Abstract

Specific features of shock wave interaction in a viscous heat-conducting gas with a low ratio of specific heats are numerically studied. The case of the Mach reflection of shock waves with a negative angle of the reflected wave with respect to the free-stream velocity vector is considered, and the influence of viscosity on the flow structure is analyzed. Various issues of nonuniqueness of the shock wave configuration for different Reynolds numbers are discussed. Depending on the initial conditions and Reynolds numbers, two different shock wave configurations may exist: regular configuration interacting with an expansion fan and Mach configuration. In the dual solution domain, a possibility of the transition from regular to the Mach reflection of shock waves is considered.

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

Similar content being viewed by others

References

  1. E. Mach, Über den Verlauf von Funkenwellen in der Ebene und im Raume, Sitzungsber. Acad. Wiss. Wien, 1878, Vol. 78, S. 819–838.

    Google Scholar 

  2. J. von Neumann, Oblique reflection of shock waves, Explosive Research Report12, Navy Dept. Bureau of Ordonance, Washington DC. US Dept. Comm. Off. Tech. Serv. PB37079, 1943 (reproduced in Collected Works of J. von Neumann. Pergamon Press, 1963, Vol. 6, P. 238–299).

    Google Scholar 

  3. K. G. Guderley, The Theory of Transonic Flow (Translated from German by J. R. Moszynski), Pergamon Press, Oxford, New York, 1962.

  4. H. Hornung, Regular and Mach reflection of shock waves, Annu. Rev. Fluid Mech., 1986, Vol. 180, P. 33–58.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. G. Ben-Dor, Shock Wave Reflection Phenomena, Springer Verlag, New York, 1991.

    MATH  Google Scholar 

  6. H. Ogawa, S. Mölder, and R. Boyce, Effects of leading-edge truncation and stunting on drag and efficiency of Busemann intakes for axisymmetric scramjet engines, J. Fluid Sci. and Technology, 2013, Vol. 8, No. 2, P. 186–199.

    Article  ADS  Google Scholar 

  7. Yu. P. Gounko and I. I. Mazhul, Numerical modeling of the conditions for realization of flow regimes in supersonic axisymmetric conical inlets of internal compression, Thermophysics and Aeromechanics, 2015, Vol. 22, No. 5, P. 545–558.

    Article  ADS  Google Scholar 

  8. H. Hornung, H. Oertel, and R. Sandeman, Transition to Mach reflection of shock waves in steady and pseudosteady flows with and without relaxation, J. Fluid Mech., 1979, Vol. 90, P. 541–560.

    Article  ADS  Google Scholar 

  9. M. S. Ivanov, S. F. Gimelshein, and A. E. Beylich, Hysteresis effect in stationary reflection of shock waves, Phys. Fluids, 1995, Vol. 7, P. 685–687.

    Article  ADS  MATH  Google Scholar 

  10. M. S. Ivanov, G. Ben-Dor, T. Elperin, A. N. Kudryavtsev, and D. V. Khotyanovsky, The reflection of asymmetric shock waves in steady flows: a numerical investigation, J. Fluid Mech., 2002, Vol. 469, P. 71–87.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. M. S. Ivanov, D. Vandromme, V. M. Fomin, A. N. Kudryavtsev, A. Hadjadj, and D. V. Khotyanovsky, Transition between regular and Mach reflection of shock waves: new numerical and experimental results, Shock Waves, 2001, Vol. 11, No. 3, P. 199–207.

    Article  ADS  MATH  Google Scholar 

  12. A. Chpoun, D. Passerel, H. Li, and G. Ben-Dor, Reconsideration of oblique shock wave reflections in steady flows. Part 1. Experimental investigation, J. Fluid Mech., 1995, Vol. 301, P. 19–35.

    Article  ADS  Google Scholar 

  13. M. S. Ivanov, A. N. Kudryavtsev, S. B. Nikiforov, D. V. Khotyanovsky, and A. A. Pavlov, Experiments on shock wave reflection transition and hysteresis in low-noise wind tunnel, Physics Fluids, 2003, Vol. 15, No. 6, P. 1807–1810.

    Article  ADS  MATH  Google Scholar 

  14. D. Khotyanovsky, A. Kudryavtsev, M. Ivanov, B. Chanetz, A. Durand, M. Chernyshev, A. Omelchenko, and V. Uskov, Analytical, numerical and experimental investigation of shock wave reflection transition induced by variation of distance between wedges, West East High Speed Flowfield Conf., Marseille, France, April 22-26, 2002, P. 274–281.

    Google Scholar 

  15. D. V. Khotyanovsky, Y. A. Bondar, A. N. Kudryavtsev, G. V. Shoev, and M. S. Ivanov, Viscous effects in steady reflection of strong shock waves, AIAA J., 2009, Vol. 47, No. 5, P. 1263–1269.

    Article  ADS  MATH  Google Scholar 

  16. E. I. Vasilev, A. N. Kraiko, Numerical simulation of weak shock diffraction over a wedge under the von Neumann paradox conditions, Comput. Math. Math. Phys., 1999, Vol. 39, No. 8, P. 1335–1345

    MathSciNet  Google Scholar 

  17. M. S. Ivanov, Ye. A. Bondar, D. V. Khotyanovsky, A. N. Kudryavtsev, and G. V. Shoev, Viscosity effects on weak irrgular reflection of shock waves in steady flow, Progress in Aerospace Sci., 2010, Vol. 46, Nos. 2-3, P. 89–105.

    Article  ADS  MATH  Google Scholar 

  18. A. Sakurai, M. Tsukamoto, D. Khotyanovsky, and M. Ivanov, The flow field near the triple point in steady shock reflection, Shock Waves, 2011, Vol. 21, No. 3, P. 267–272.

    Article  ADS  Google Scholar 

  19. S. A. Gavrenkov and L. G. Gvozdeva, Formation of triple shock configurations with negative reflection angle in steady flows, Technical Physics Letters, 2012, Vol. 38, Is. 4, P. 372–374.

    Article  ADS  Google Scholar 

  20. S. A. Gavrenkov and L. G. Gvozdeva, Numerical investigation of the onset of instability of triple shock configurations in steady supersonic gas flows, Technical Physics Letters, 2012, Vol. 38, Is. 6, P. 587–589.

    Article  ADS  Google Scholar 

  21. M. S. Liou and C. J. Steffen, A new flux splitting scheme, J. Comput. Phys., 1993, Vol. 107, No. 1, P. 23–39.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. H. G. Hornung and M. L. Robinson, Transition from regular to Mach reflection of shock wave. Part 2. The steady-flow criterion, J. Fluid Mech., 1982, Vol. 123, P. 155–164.

    Article  ADS  Google Scholar 

  23. E. Martelli, B. Betti, F. Nasuti, and M. Onofri, Effect of the abiabatic index on the shock reflection in overexpanded nozzle flow, Program and abstracts, Intern. Symp. on Shock Waves, Tel Aviv, Israel, July 19-24, 2015, P. 166–168.

    Google Scholar 

  24. D. V. Khotyanovsky, A. N. Kudryavtsev, and M. S. Ivanov, Effects of a single-pulse energy deposition on steady shock wave reflection, Shock Waves, 2006, Vol. 15, No. 5, P. 353–362.

    Article  ADS  MATH  Google Scholar 

  25. A. N. Kudryavtsev, D. V. Khotyanovsky, M. S. Ivanov, A. Hadjadj, and D. Vandromme, Numerical investigations of transition between regular and Mach reflections caused by free-stream disturbances, Shock Waves, 2002, Vol. 12, No. 2, P. 157–165.

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia

    G. V. Shoev & M. S. Ivanov

  2. Novosibirsk State University, Novosibirsk, Russia

    G. V. Shoev

Authors
  1. G. V. Shoev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. S. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. V. Shoev.

Additional information

This work was supported by the Russian Foundation for Basic Research (Grant Nos. 15-58-52044 and 14-08-01252). Numerical simulations were performed on clusters of the Siberian Supercomputer Center of the Siberian Branch of the Russian Academy of Sciences and Novosibirsk State University.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shoev, G.V., Ivanov, M.S. Numerical study of shock wave interaction in steady flows of a viscous heat-conducting gas with a low ratio of specific heats. Thermophys. Aeromech. 23, 343–354 (2016). https://doi.org/10.1134/S0869864316030045

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0869864316030045

Keywords

Search

Navigation