International Electronic Journal of Mathematics Education

Oblique Shock Reflection from the Wall
  • Article Type: Research Article
  • International Electronic Journal of Mathematics Education, 2016 - Volume 11 Issue 5, pp. 1205-1214
  • Published Online: 02 Aug 2016
  • Article Views: 915 | Article Download: 980
  • Open Access Full Text (PDF)
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Bulat PV, Upyrev VV. Oblique Shock Reflection from the Wall. Int Elect J Math Ed. 2016;11(5), 1205-1214.
APA 6th edition
In-text citation: (Bulat & Upyrev, 2016)
Reference: Bulat, P. V., & Upyrev, V. V. (2016). Oblique Shock Reflection from the Wall. International Electronic Journal of Mathematics Education, 11(5), 1205-1214.
Chicago
In-text citation: (Bulat and Upyrev, 2016)
Reference: Bulat, Pavel V., and Vladimir V. Upyrev. "Oblique Shock Reflection from the Wall". International Electronic Journal of Mathematics Education 2016 11 no. 5 (2016): 1205-1214.
Harvard
In-text citation: (Bulat and Upyrev, 2016)
Reference: Bulat, P. V., and Upyrev, V. V. (2016). Oblique Shock Reflection from the Wall. International Electronic Journal of Mathematics Education, 11(5), pp. 1205-1214.
MLA
In-text citation: (Bulat and Upyrev, 2016)
Reference: Bulat, Pavel V. et al. "Oblique Shock Reflection from the Wall". International Electronic Journal of Mathematics Education, vol. 11, no. 5, 2016, pp. 1205-1214.
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Bulat PV, Upyrev VV. Oblique Shock Reflection from the Wall. Int Elect J Math Ed. 2016;11(5):1205-14.

Abstract

Regular and Mach (irregular) reflection of oblique shock from the wall is discussed. The criteria for the transition from regular to irregular reflection: von Neumann criterion and the criterion of fixed Mach configuration are described. The dependences of specific incident shocks’ intensities corresponding to the two criteria for the transition from regular to irregular reflection are plotted. The article demonstrates ambiguity region in which both regular and Mach reflection are not prohibited by conditions of dynamic compatibility. The areas in which the transition from one reflection type to another is only possible via shock, as well as areas of possible a smooth transition are described. The dependences of magnitude of this shock change in reflected discontinuity’s intensity on the intensity of the incident shock are plotted. The article also provides dependences of reflected discontinuity’s intensity on the intensity of incident shock falling on the wall for all types of reflections.

References

  • Adrianov, A. L., Starykh, A. L. & Uskov, V. N. (1995) Interference of Stationary Gasdynamic Discontinuities. Novosibirsk: Publishing house “Nauka”. 180p.
  • Ben-Dor, G. (2007). Shock Wave Reflection Phenomena. Berlin, Springer. Direct access:
  • http://www.springer.com/us/book/9783540713814. DOI: 10.1007/978-3-540-71382-1
  • Ben-Dor, G., Ivanov, M., Vasilev, E.I. & Elperin, T. (2002) Hysteresis processes in the regular reflection. Mach reflection transition in steady flows. Progress in Aerospace Sciences, 38, 347-387.
  • Bulat, P. V., Uskov, V. N. (2014) Mach reflection of a shock wave from the symmetry axis of the supersonic nonisobaric jet. Research Journal of Applied Sciences, Engineering and Technology, 8(1), 135-142.
  • Gavrenkov, S. A. & Gvozdeva, L. G. (2011) Numeral investigation of triple shock configuration for steady cases in real gases. Proc. Physics of Extreme States of Matter. Direct access:  http://www.ihed.ras.ru/elbrus/compendiums/2011/1132
  • Guderley, K. G. (1960) Theory of Transonic Flows. Moscow: Publishing House of Foreign Literature. 419p.
  • Gvozdeva, L. G., Borsch, V. L. & Gavrenkov, S. A. (2012) Analytical and Numerical Study of Three Shock Configurations with Negative Reflection Angle. Proceedings of 28th International Symposium on Shock Waves, 587-592
  • Ivanov, M. S., Ben-Dor, G., Elperin, Т., Kudryavtsev, A. N., Khotyanovsky, D. V. (2002) The reflection of asymmetric shock waves in steady flows: A numerical investigation. Journal of Fluid Mechanics, 469, 71–87.
  • Ivanov, M. S., Vandromme, D., Fomin, V. M. & Kudryavtsev, A. N. (2001) Transition between regular and mach reflection of shock waves: New numerical and experimental results. Shock Waves, 11(3), 199-207.
  • Kawamura, R. & Saito, H. (1956) Reflection of Shock Waves-1. Pseudo-Stationary Case. Journal of the Physical Society of Japan, 11(5), 584-595.
  • Mach, E. (1978) Uber den Verlauf von Funkenwellen in der Ebene und im Raume. Sitzungsbr Akad Wien, 78, 819-838.
  • Uskov, V. N., Bulat, P. V. & Prodan, N. V. (2012) History of study of the irregular reflection shock wave from the symmetry axis with a supersonic jet mach disk. Fundamental Research, 9(2), 414-420.
  • Vasilev, E. I. (1999). Four-wave scheme of weak Mach shock waves interaction under the von Neumann paradox conditions. Fluid Dynamics, 34(3), 421-427.
  • Vasilev, E. & Olkhovsky, M. (2009). 27th ISSW: Book of proceedings. Direct access: http://istina.msu.ru/media/publications/article/f98/581/10902190/Istoriya_izucheniya_mahovskogo_otrazheniya_udarnoj_volnyi_ot_klina.pdf
  • von Neumann, J. (1943) Oblique reflection of shocks. In A.H. Taub (ed.) John von Neumann Collected Works, 4, 238-299
  • White, D. R. (1952). An experimental survey of shock waves. Proc. 2nd Midwest Conf. on Fluid Mechanics, 3, 253-262.

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.