Shock Wave Reflections in Steady Flows

  • Gabi Ben-Dor


The analytical investigation of the reflection phenomenon of shock waves in steady flows is much simpler than that in pseudo-steady flows for the following reasons:
  1. 1)

    Unlike the reflection process in pseudo-steady flows, where it is coupled with an additional process, namely, the flow deflection process (see section 2.6.1), in steady flows the reflection process is independent.

  2. 2)

    Unlike the analysis of the reflection process in pseudo-steady flows, where there is a need to analytically predict the first triple point trajectory angle, χ, in order to transform the results from the (Ms, \(\theta _w^c\))-plane to the more physically meaningful and more applicable (Ms, θw)-plane, in steady flows the results are presented in the (M01)-plane. The presentation of the results in this plane can be done by solving equations (1.14) to (1.27) without the need for an additional expression for χ [equation (2.33)] as discussed in section 2.2.1.

  3. 3)

    Of the ten different shock wave reflection configurations mentioned in section 1.1 only two, namely, RR and SMR, are possible in steady flows.



Shock Wave Triple Point Incident Shock Incident Shock Wave Reflection Point 
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List of Symbols

Latin Letters


thermal conductivity


length of the Mach stem


length of the reflecting wedge


flow Mach number in state (i)


incident shock wave Mach number


static pressure in state (i)


flow velocity in state (i)

Greek Letters


specific heat capacities ratio


maximum deflection angle for a flow having Mach number M through an oblique shock wave


reflecting wedge angle


complementary wedge angle


dynamic viscosity


Mach angle of the flow having a Mach number Mi


flow density in state (i)


angle of incidence between the flow and the oblique shock wave across which the flow enters state (i)


limiting angle of incidence



flow state ahead of the incident shock wave, i.


flow state behind the incident shock wave, i.


flow state behind the reflected shock wave, r.


flow state behind the Mach stem, m.


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  1. Azevedo, D.J., “Analytic Prediction of Shock Patterns in a High-Speed, Wedge-Bounded Duct”, Ph.D. Thesis, Dept. Mech. & Aero. Eng., State Univ. N.Y. Buffalo, N.Y., U.S.A., 1989.Google Scholar
  2. Henderson, L.F., “The Reflection of a Shock Wave at a Rigid Wall in the Presence of a Boundary Layer”, J. Fluid Mech., Vol. 30, pp. 699–722, 1967.ADSzbMATHCrossRefGoogle Scholar
  3. Henderson, L.F. & Lozzi, A., “Experiments of Transition to Mach Reflection”, J. Fluid Mech., Vol. 68, pp. 139–155, 1975.ADSCrossRefGoogle Scholar
  4. Henderson, L.F. & Lozzi, A., “Further Experiments of Transition to Mach Reflection”, J. Fluid Mech., Vol. 94, pp. 541–560, 1979.ADSCrossRefGoogle Scholar
  5. Hornung, H.G., Oertel, H. Jr. & Sandeman, R.J., “Transition to Mach Reflection of Shock Waves in Steady and Pseudo-Steady Flow with and without Relaxation”, J. Fluid Mech., Vol. 90, pp. 541–560, 1979.ADSCrossRefGoogle Scholar
  6. Hornung, H.G. & Robinson, M.L., “Transition from Regular to Mach Reflection of Shock Waves. Part 2. The Steady-Flow Criterion”, J. Fluid Mech., Vol. 123, pp. 155–164, 1982.ADSCrossRefGoogle Scholar
  7. Mölder, S., “Reflection of Curved Shock Waves in Steady Supersonic Flow”, CASI Trans., Vol. 4, pp. 73–80, 1971.Google Scholar
  8. Mölder, S., “Particular Conditions for the Termination of Regular Reflection of Shock Waves”, CASI Trans., Vol. 25, pp. 44–49, 1979.Google Scholar
  9. Pant, J.C., “Reflection of a Curved Shock from a Straight Rigid Boundary”, Phys. Fluids, Vol. 14, pp. 534–538, 1971.ADSzbMATHCrossRefGoogle Scholar
  10. Shapiro, A.H., The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. II, The Ronald Press Co., New York, N.Y., U.S.A., 1953.Google Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Gabi Ben-Dor
    • 1
  1. 1.Department of Mechanical EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael

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