Skip to main content
SpringerLink
Log in

Numerical modelling of free interaction of shock waves in corner flows

  • Published:
Thermophysics and Aeromechanics Aims and scope

Abstract

The inviscid supersonic flows in corners between intersecting compression wedges were studied numerically. Under usual conditions, the flows in such corner configurations are conically self-similar. Besides, shock waves formed by wedges are plane and they interact with one another in these flows and the downstream development of the shock interaction structure at that occurs in a region which is bounded in cross-sectional directions by the walls and contracts towards the corner rib, and in this sense the above interaction of shocks may be subjected to influence of the rib. The corner flows of another type with an interaction of shocks not subjected to the “rib effect”, in other words free, were considered. This was ensured by that the corner configurations were designed with a gradually expanding gap along the rib in a way that the reflected shocks arising as a result of interaction passed through the gap without falling onto the walls. This eliminated the influence of a local flow near the corner rib on the interaction of plane shock waves formed by the wedges.

The inviscid flows symmetric with respect to the bisector plane of the corner dihedral angle were considered. The computations showed that, in the gapped corner configurations with the free interaction of shocks, if these interactions were irregular, the cross-flow patterns were practically the same as in the original corner configurations without a gap.

The conditions for the flows over corner configurations were also considered under which the interaction of shocks corresponded to the Neumann criterion of mechanical equilibrium. These conditions are equivalent to those, which take place in two-dimensional steady flows, when a hysteresis phenomenon is possible, which manifests itself in changing the moment of transition from a regime of regular reflection of shocks to an irregular one and conversely at a direct and inverse courses of varying the flow parameters—the Mach number and the inclination angle of the wedges. The conducted computations showed that a hysteresis is possible for considered corner flows in gapped configurations, but it must be followed by a detachment of shocks from the corner apex and a breakdown of the conical flow structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Yu.P. Goonko, A.N. Kudryavtsev, and R.D. Rakhimov, Supersonic inviscid flows with regular and irregular interaction of shocks in corner configurations, Fluid Dyn., 2004, Vol. 39, No. 2, P. 153–169.

    Google Scholar 

  2. Yu.P. Goonko, A.N. Kudryavtsev, and A. Chpoun, 3D interaction of shock waves in corner flows, Proc. 24th Intern. Symp. on Shock Waves (Beijing, China, July 11–16, 2004), Z.L. Jiang (Ed.), Tsinghua Univ. Press, Paper No. 3071.

  3. Yu.P. Goonko and A.N. Kudryavtsev, Different types of 3D shock wave interaction in supersonic corner flows, The 1st Intern. Mach Reflection Symp. on Shock-Vortex Interaction (Jeju Island, Korea, November 1–4, 2004). Book of Abstr., P. 11–12.

  4. Y.P. Goonko and A.N. Kudryavtsev, On some properties of supersonic corner-flows formation. Proc. XII Intern. Conf. on the Methods of Aerophysical Research (ICMAR 2004), 28 June–3 July, 2004, Russia, Novosibirsk, Publ. House “Nonparel”, 2004, Pt 1, P. 100–105.

    Google Scholar 

  5. G.-S. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 1996, Vol. 126, P. 202–228.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  6. R. Marsilio, Vortical solutions in supersonic corner flows, AIAA J., 1993, Vol. 31, No. 9, P. 1651–1658.

    Article  MATH  ADS  Google Scholar 

  7. R. Samtaney and D.I. Pullin, On initial-value and self-similar solutions of the compressible Euler equations, Phys. Fluids, 1996, Vol. 8, No. 10, P. 2650–2655.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. G. Ben-Dor, Shock Wave Reflection Phenomena, Springer-Verlag, New York Berlin et al., 1992.

    MATH  Google Scholar 

  9. M.S. Ivanov, D. Vandromme, V.M. Fomin, A.N. Kudryavtsev, A. Hadjadj, and D.V. Khotyanovsky, Transition between regular and Mach reflection of shock waves: new numerical and experimental results, Shock Waves, 2001, Vol. 11, No. 3, P. 199–207.

    Article  MATH  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia

    Yu. P. Goonko & A. N. Kudryavtsev

Authors
  1. Yu. P. Goonko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. N. Kudryavtsev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goonko, Y.P., Kudryavtsev, A.N. Numerical modelling of free interaction of shock waves in corner flows. Thermophys. Aeromech. 13, 221–237 (2006). https://doi.org/10.1134/S0869864306020065

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0869864306020065

Keywords

Search

Navigation