The Effect of Increasing Rarefaction on the Edney Type IV Shock Interaction Problem

  • Craig White
  • Konstantinos Kontis
Conference paper


Two-dimensional direct simulation Monte Carlo simulations of the Edney Type IV shock interaction problem, where an oblique shock wave generated by a wedge encounters the bow shock from a cylinder, are carried out for three different Knudsen numbers using the dsmcFoam+ code. The numerical results for surface and flow properties are in good agreement with experiment for a Knudsen number of 0.0067. When the degree of rarefaction is increased, the oblique and normal shock waves become more diffuse and the bow shock standoff distance increases. The supersonic jet that forms in the interaction region becomes weaker as the Knudsen number increases and the point at where it impinges on the cylinder surface moves in a clockwise direction due to the jet being turned upward. The location of the peak heat transfer coefficient, peak pressure coefficient, and zero skin friction coefficient on the cylinder surface follow the supersonic jet impingement in a clockwise direction around the cylinder. The peak heat transfer and pressure coefficients decrease with increasing Knudsen number.


  1. 1.
    Edney, B.: Anomalous heat transfer and pressure distributions on blunt bodies at hypersonic speeds in the presence of an impinging shock. Technical report 115, Aeronautical Research Institute of Sweden (1968)Google Scholar
  2. 2.
    Watts, J.: Flight experience with shock impingement and interference heating on the X-15-2 research airplane. Technical report TM X-1669, NASA (1968)Google Scholar
  3. 3.
    Padilla, J.F., Boyd, I.D.: Assessment of gas-surface interaction models for computation of rarefied hypersonic flow. J. Thermophys Heat Transf. 23(1), 96–105 (2009)CrossRefGoogle Scholar
  4. 4.
    GadelHak, M.: The fluid mechanics of microdevices—the freeman scholar lecture. J. Fluids Eng. 121(1), 5–33 (1999)CrossRefGoogle Scholar
  5. 5.
    Bird, G.A.: Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford Science Publications, Oxford University Press Inc, New York (1994)Google Scholar
  6. 6.
    Ivanov, M.S., Markelov, G.N., Gimelshein S.F.: Statistical simulation of reactive rarefied flows—numerical approach and applications. In: 7th AIAA/ASME Joint Thermophysics and Heat Transfer Conference (1998)Google Scholar
  7. 7.
    Stefanov, S.K.: On DSMC calculations of rarefied gas flows with small number of particles in cells. SIAM J. Sci. Comput. 33(2), 677–702 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Hadjiconstantinou, N.G., Garcia, A.L., Bazant, M.Z., He, G.: Statistical error in particle simulations of hydrodynamic phenomena. J. Comput. Phys. 187(1), 274–297 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Scanlon, T.J., Roohi, E., White, C., Darbandi, M., Reese, J.M.: An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries. Comput. Fluids 39(10), 2078–2089 (2010)CrossRefzbMATHGoogle Scholar
  10. 10.
    White, C., Borg, M.K., Scanlon, T.J., Reese, J.M.: A DSMC investigation of gas flows in micro-channels with bends. Comput. Fluids 71, 261–271 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    OpenFOAM Foundation (2016).
  12. 12.
    Pot, T., Chanet, B., Lefebvre, M., Bouchardy, P.: Fundamental study of shock/shock interference in low density flow: flowfield measurements by DL-CARS. In: 21st Rarefied Gas Dynamics Symposium, pp. 545–552 (1998)Google Scholar
  13. 13.
    Moss, J.N., Pot, T., Chanetz, B., Lefebvre, M.: DSMC simulation of shock/shock interactions: emphasis on type IV interaction. In: Proceedings of the 22nd International Symposium on Shock Waves, vol. 3570, pp. 1337–1342. Imperial College, London, UK (1999)Google Scholar
  14. 14.
    Bird, G.A.: Definition of mean free path for real gases. Phys. Fluids 26(11), 3222–3223 (1983)CrossRefGoogle Scholar
  15. 15.
    Glass, C.E.: Numerical simulation of low density shock-wave interactions. NASA/TM-1999-209358 (1999)Google Scholar
  16. 16.
    White, C., Borg, M.K., Scanlon, T.J., Longshaw, S.M., John, B., Emerson, D.R., Reese, J.M.: dsmcFoam+: An OpenFOAM based direct simulation Monte Carlo solver. In press, Computer Physics Communications (2017)Google Scholar
  17. 17.
    Xiao, H., Shang, Y., Wu, D.: DSMC simulation and experimental validation of shock interaction in hypersonic low density flow. Sci. World J. 2014, 732765 (2014)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Aerospace Sciences Division, School of EngineeringUniversity of GlasgowGlasgowUK

Personalised recommendations