Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Numerical modelling of free interaction of shock waves in corner flows

Numerical modelling of free interaction of shock waves in corner flows 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Thermophysics and Aeromechanics Springer Journals

Numerical modelling of free interaction of shock waves in corner flows

Download PDF
17 pages

Loading next page...
 
/lp/springer-journals/numerical-modelling-of-free-interaction-of-shock-waves-in-corner-flows-6MWexcSYoC
Publisher
Springer Journals
Copyright
2006 Yu.P. Goonko and A.N. Kudryavtsev
ISSN
0869-8643
eISSN
1531-8699
DOI
10.1134/S0869864306020065
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Thermophysics and Aeromechanics – Springer Journals

Published: Jun 1, 2006

References

  • Supersonic inviscid flows with regular and irregular interaction of shocks in corner configurations
    Yu.P. Goonko, A.N. Kudryavtsev, R.D. Rakhimov
  • 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.
    Yu.P. Goonko, A.N. Kudryavtsev, and A. Chpoun,
  • . Book of Abstr.
    Yu.P. Goonko and A.N. Kudryavtsev, Different types of
  • On some properties of supersonic corner-flows formation
    A.N. Kudryavtsev
  • Efficient implementation of weighted ENO schemes
    G.-S. Jiang, C.-W. Shu
  • Vortical solutions in supersonic corner flows
    R. Marsilio
  • On initial-value and self-similar solutions of the compressible Euler equations
    R. Samtaney, D.I. Pullin
  • Shock Wave Reflection Phenomena
    G. Ben-Dor
  • Transition between regular and Mach reflection of shock waves: new numerical and experimental results
    M.S. Ivanov, D. Vandromme, V.M. Fomin, A.N. Kudryavtsev, A. Hadjadj, D.V. Khotyanovsky