Shock Waves

, Volume 23, Issue 4, pp 317–324 | Cite as

Imploding conical shock waves

  • R. T. PatonEmail author
  • B. W. Skews
  • S. Rubidge
  • J. Snow
Original Article


The behaviour of conical shock waves imploding axisymmetrically was first studied numerically by Hornung (J Fluid Mech 409:1–12, 2000) and this prompted a limited experimental investigation into these complex flow patterns by Skews et al. (Shock Waves 11:323–326, 2002). Modification of the simulation boundary conditions, resulting in the loss of self-similarity, was necessary to image the flow experimentally. The current tests examine the temporal evolution of these flows utilising a converging conical gap of fixed width fed by a shock wave impinging at its entrance, supported by CFD simulations. The effects of gap thickness, angle and incident shock strength were investigated. The wave initially diffracts around the outer lip of the gap shedding a vortex which, for strong incident shock cases, can contain embedded shocks. The converging shock at exit reflects on the axis of symmetry with the reflected wave propagating outwards resulting in a triple point developing on the incident wave together with the associated shear layer. This axisymmetric shear layer rolls up into a mushroom-shaped toroidal vortex ring and forward-facing jet. For strong shocks, this deforms the Mach disk to the extent of forming a second triple point with the primary shock exhibiting a double bulge. Separate features resembling the Richtmeyer–Meshkov and Kelvin–Helmholtz instabilities were noted in some tests. Aside from the incident wave curvature, the reflection patterns demonstrated correspond well with the V- and DV-types identified by Hornung although type S was not clearly seen, possibly due to the occlusion of the reflection region by the outer diffraction vortex at these early times. Some additional computational work explicitly exploring the limits of the parameter space for such systems has demonstrated the existence of a possible further reflection type, called vN-type, which is similar to the von Neumann reflection for plane waves. It is recommended that the parameter space be more thoroughly explored experimentally.


Conical shock wave Vortex von Neumann Kelvin–Helmholtz 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

ESM 1 (MPG 1208 kb)

ESM 2 (MPG 1228 kb)


  1. 1.
    Hornung H.G.: Oblique shock reflection from an axis of symmetry. J. Fluid Mech. 409, 1–12 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Hornung H.G., Schwendeman D.W.: Oblique shock reflection from an axis of symmetry: shock dynamics and relation to the Guderley singularity. J. Fluid Mech. 438, 231–245 (2001)zbMATHCrossRefGoogle Scholar
  3. 3.
    Skews B.W., Menon N., Bredin M., Timofeev E.V.: An experiment on imploding conical shock waves. Shock Waves 11, 323–326 (2002)CrossRefGoogle Scholar
  4. 4.
    Takayama K., Kleine H., Grönig H.: An experimental investigation of the stability of converging cylindrical shock waves in air. Exp. Fluids 5, 315–322 (1987)CrossRefGoogle Scholar
  5. 5.
    Mölder, S., Gulamhussein, A., Timofeev, E., Voinovich, P.: Focusing of conical shocks at the center-line of symmetry. In: Houwing, A.F.P., Paull, A. (eds.) Shock Waves Proceedings of 21st International Symposium on Shock Waves, pp. 875–880. Panther Publishing and Printing, Canberra (1997)Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • R. T. Paton
    • 1
    Email author
  • B. W. Skews
    • 1
  • S. Rubidge
    • 1
  • J. Snow
    • 1
  1. 1.Flow Research Unit, School of Mechanical, Industrial and Aeronautical EngineeringUniversity of the WitwatersrandJohannesburgSouth Africa

Personalised recommendations