Identifier: 2009-7
Author(s): S. Zhang, H. Zhang, and C.-W. Shu
Title: Topological structure of shock induced vortex breakdown
Page count: 39 pp.
Date: 2009-02-18
Abstract:
Using a combination of critical point theory of partial differential equations and numer- ical simulation for the three dimensional unsteady Navier-Stokes equations, we study the possible flow structures of the vortical flow, especially the unsteady vortex breakdown in the interaction between a normal shock wave and a longitudinal vortex. The topological struc- ture contains two parts. One is the streamline pattern in the cross section perpendicular to the vortex axis. The other is the streamline pattern in the symmetrical plane. In the cross section perpendicular to the vortex axis, the streamlines take spiral or central patterns depending on the parameter λ(x, t) = 1 ρ ( ∂ ρ ∂ t + ∂ ρu ∂ x ) where x is the vortex axis. If λ > 0, the streamlines spiral inward in the near region of the center. If λ < 0, the streamlines spiral outward in the same region. If λ = 0, the streamlines take a central shape. If λ changes its sign along the vortex axis, one or more limit cycles appear in the streamlines in the cross section perpendicular to the vortex axis. Numerical simulation for two typical cases of shock induced vortex breakdown (Erlebacher G., Hussaini M.Y and Shu C.-W., Interaction of a shock with a longitudinal vortex, J. Fluid Mech. 337 (1997) 129-153) is performed. The onset and time evolution of the vortex breakdown are studied. It is found that there are more limit cycles for the streamlines in the cross section perpendicular to the vortex axis. In addition, we find that there are quadru-helix structure in the tail of the vortex breakdown.
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