Shock Wave Reflections in Unsteady Flows

  • Gabi Ben-Dor


Unlike the shock reflection phenomena in pseudo-steady flows (chapter 2) and in steady flows (chapter 3), where the flow fields basically depend on two independent variables, namely; x/t and y/t in the former and x and y in the latter, here the flow field depends on three parameters x, y and t. For this reason, the analytical consideration of the reflection phenomenon in unsteady flows is much more difficult and as a matter of fact very limited progress has been made.


Shock Wave Wedge Angle Incident Shock Wave Mach Stem Mach Reflection 

List of Symbols

Latin Letters


local speed of sound in state (i)




length of the Mach stem in MR


length of the reflected shock wave in TRR


flow mass in region (3) of a TRR


flow Mach number in state (i)


Mach stem Mach number


incident shock wave Mach number


radius of curvature of cylindrical wedges


coordinate along the cylindrical wedge surface


propagation distance of the corner-generated signals




flow velocity in state (i) with respect to R in RR and TRR andTinMR


flow velocity in state (i) in a laboratory frame of reference




normal shock wave velocity of a TRR with respect to the reflection point R


x coordinate of the MR→RR transition point


x coordinate of the triple point of an MR


distance from Q to P in a TRR


y coordinate of the triple point of an MR


distance from R to Q in a TRR

Greek Letters


angle between the incident shock wave and the reflecting wedge surface in a TRR


angle between the slipstream and the reflecting wedge surface in a TRR


specific heat capacities ratio


time interval


change of the slope of the reflecting surface of a double wedge


angular position of a flow particle


angular position of the triple point


reflecting wedge angle


wedge angle of the first surface of a double wedge


wedge angle of the second surface of a double wedge


wedge angle of a cylindrical concave or convex wedge


transition wedge angle


transition wedge angle for shock wave Mach number M


transition wedge angle from reflection A to reflection B


flow density in state (i)


angle of incidence between the flow and the oblique shock wave across which the flow enters state (i) with respect to R in RR and TRR and with respect to T in MR.


triple point trajectory angle


triple point trajectory angle at glancing incidence


triple point trajectory angle at transition



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, of an MR or the normal shock wave, n, of a TRR


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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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