Shock Waves

, Volume 28, Issue 2, pp 311–319 | Cite as

Three-dimensional shock wave configurations induced by two asymmetrical intersecting wedges in supersonic flow

Original Article


This study explores the three-dimensional (3D) wave configurations induced by 3D asymmetrical intersecting compression wedges in supersonic and hypersonic inviscid flows. By using the “spatial dimension reduction” approach, the problem of 3D steady shock/shock interaction is converted to that of the interaction of two moving shock waves in the characteristic two-dimensional (2D) plane. Shock polar theory is used to analyze the shock configurations in asymmetrical situations. The results show that various shock configurations exist in 3D asymmetrical shock wave interactions, including regular interaction, transitioned regular interaction, single Mach interaction, inverse single Mach interaction, transitional double Mach interaction, weak shock interaction, and weak single Mach interaction. All of the above 3D steady shock/shock interactions have their corresponding 2D moving shock/shock interaction configurations. Numerical simulations are performed by solving the 3D inviscid Euler equations with the non-oscillatory, non-free parameters, dissipative (NND) numerical scheme, and good agreement with the theoretical analysis is obtained. Furthermore, the comparison of results show that the concept of the “virtual wall” in shock dynamics theory is helpful for understanding the mechanism of two-dimensional shock/shock interactions.


Supersonic flow 3D shock/shock interaction 3D asymmetrical wave configurations Spatial dimension reduction 



The project is supported by the National Natural Science Foundation of China (11372333). We would like to thank Changtong Luo and Zongmin Hu of our group for their support in the numerical simulations.


  1. 1.
    Ben-Dor, G.: Shock Wave Reflection Phenomena, 2nd edn. Springer, Berlin (2007). doi: 10.1007/978-3-540-71382-1
  2. 2.
    Edney, B.E.: Effects of shock impingement on the heat transfer around blunt bodies. AIAA J. 6(1), 15–21 (1968). doi: 10.2514/3.4435 CrossRefGoogle Scholar
  3. 3.
    Charwat, A.F., Redekeopp, L.G.: Supersonic interference flow along the corner of intersecting wedges. AIAA J. 5(3), 480–488 (1967). doi: 10.2514/3.4004 CrossRefGoogle Scholar
  4. 4.
    Stainback, P.C., Weinstein, L.M.: Aerodynamic heating in the vicinity of corners at hypersonic speeds. National Aeronautics and Space Administration, NASA-TN-D-4130 (1967)Google Scholar
  5. 5.
    Watson, R., Weinstein, L.: A study of hypersonic corner flow interactions. AIAA J. 9(7), 1280–1286 (1971). doi: 10.2514/3.49937 CrossRefGoogle Scholar
  6. 6.
    West, J.E., Korkegi, R.H.: Supersonic interaction in the corner of intersecting wedges at high Reynolds numbers. AIAA J. 10, 652–656 (1972). doi: 10.2514/3.50171 CrossRefGoogle Scholar
  7. 7.
    Skews, B.W., Mills, J.G., Quinn, P., Menon, N., Mohan, J.A.: Supersonic corner flow with fillets, camber, sweep and dihedral. In: 25th International Symposium on Shock Waves, Society for Shock Wave Research IIS, pp. 83–88. Bangalore, India (2005)Google Scholar
  8. 8.
    Naidoo, P.: Supersonic and transonic viscous corner flows. PhD Thesis, University of the Witwatersrand, Johannesburg (2011)Google Scholar
  9. 9.
    Naidoo, P., Skews, B.W.: Supersonic viscous corner flows. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 8, 950–965 (2011). doi: 10.1177/0954410011416709
  10. 10.
    Yang, Y., Wang, C., Jiang, Z.L.: Analytical and numerical investigations of the reflection of asymmetric nonstationary shock waves. Shock Waves 22, 435–449 (2012). doi: 10.1007/s00193-012-0392-9 CrossRefGoogle Scholar
  11. 11.
    Yang, Y.: The investigations on complex flow of three dimensional shock/shock interaction. PhD Thesis, Institute of Mechanics, Chinese Academy of Sciences (2012) (in Chinese) Google Scholar
  12. 12.
    Xiang, G.X., Wang, C., Teng, H.H., Yang, Y., Jiang, Z.L.: Study on Mach stem induced by interaction of planar shock waves on two intersecting wedges. Acta. Mech. Sin. 32(3), 362–368 (2016). doi: 10.1007/s10409-015-0498-2
  13. 13.
    Xiang, G.X., Wang, C., Teng, H.H., Jiang, Z.L.: Investigations of three-dimensional shock/shock interactions over symmetrical intersecting wedges. AIAA J. 54(5), 1472–1481 (2016). doi: 10.2514/1.J054672 CrossRefGoogle Scholar
  14. 14.
    Xiang, G.X., Wang, C., Hu, Z.M., Li, X.D., Jiang, Z.L.: Theoretical solutions to three-dimensional asymmetrical shock/shock interaction. Sci. China Technol. Sci. 59(8), 1208–1216 (2016). doi: 10.1007/s11431-016-6036-z CrossRefGoogle Scholar
  15. 15.
    Xie, P., Han, Z.Y., Takayama, K.: A study of the interaction between two triple points. Shock Waves 14(1), 29–36 (2005). doi: 10.1007/s00193-005-0245-x CrossRefMATHGoogle Scholar
  16. 16.
    Zhang, H.X.: A dissipaive difference scheme with non-oscillatory, non-free-parameters. Acta Aerodynamica Sinica 6(2), 143–165 (1988) (in Chinese) Google Scholar
  17. 17.
    Ben-Dor, G., Glass, I.I.: Nonstationary oblique shock wave reflections: actual isopycnics and numerical experiments. AIAA J. 16, 1146–1153 (1978). doi: 10.2514/3.61021 CrossRefGoogle Scholar
  18. 18.
    Smith, L.G.: Photographic investigation of the reflection of plane shocks in air. Phys. Rev. 69(11–12), 678–678 (1946). doi: 10.1103/PhysRev.69.674.2
  19. 19.
    Mach, E.: Über den Verlauf von Funkenwellen in der Ebene und im Raume. Sitzungsbr. Akad. Wiss. Wien. 78, 819–838 (1878)Google Scholar
  20. 20.
    Skews, B.W., Ashworth, J.T.: The physical nature of weak shock wave reflection. J. Fluid Mech. 542, 105–114 (2005). doi: 10.1017/S0022112005006543 MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Skews, B.W., Li, G., Paton, R.: Experiments on Guderley Mach reflection. Shock Waves 19, 95–102 (2009). doi: 10.1007/s00193-009-0193-y CrossRefGoogle Scholar
  22. 22.
    Vasilev, E.I., Elperin, T., Ben-Dor, G.: Analytical reconsideration of the von Neumann paradox in the reflection of a shock wave over a wedge. Phys. Fluids 20(4), 046101 (2008). doi: 10.1063/1.2896286 CrossRefMATHGoogle Scholar
  23. 23.
    Tesdall, A.M., Hunter, J.K.: Self-similar solutions for weak shock reflection. SIAM J. Appl. Math. 63, 42–61 (2002). doi: 10.1137/S0036139901383826 MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Chang’an Campus School of Mechanics, Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi’anChina
  2. 2.State Key Laboratory of High-temperature Gas Dynamics (LHD), Institute of MechanicsChinese Academy of SciencesBeijingChina

Personalised recommendations