Navier-Stokes simulation of quasi-axisymmetric and three-dimensional supersonic vortex breakdown.

摘要

Computational simulation of supersonic vortex breakdown is considered for internal and external flow applications. The interaction of a supersonic swirling flow with a shock wave in bounded and unbounded domains is studied. The problem is formulated using the unsteady, compressible, full Navier-Stokes equations which are solved using an implicit, flux-difference splitting, finite-volume scheme. Solutions are obtained for quasi-axisymmetric and three-dimensional flows. The quasi-axisymmetric solutions are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity to each other. For the flow in a bounded domain, a supersonic swirling flow is introduced into a configured circular duct. The duct is designed such that a shock wave intersects with the incoming swirling flow in the inlet portion. For the quasi-axisymmetric flow problem, a parametric study is performed which includes the effects of the Reynolds number, Mach number, swirl ratio and the type of exit-boundary conditions on the development and behavior of vortex breakdown. The effect of the duct wall boundary-layer flow on the vortex breakdown is also investigated. For the same duct geometry, three-dimensional effects are studied along with the effect of the duct wall boundary-layer flow. For the external flow application, a supersonic swirling jet is issued from a nozzle into a uniform supersonic flow of lower Mach number. For the quasi-axisymmetric flow problem, the effects of the Reynolds number and the type of downstream-boundary conditions are studied. For the three-dimensional flow problem, the effects of the grid fineness, grid-point distribution, grid shape and swirl ratio on the vortex breakdown are studied.;The results show several modes of vortex breakdown such as no-breakdown, transient single-bubble breakdown, transient multi-bubble breakdown, periodic multi-bubble multi-frequency breakdown and helical spiral breakdown.;In another application, a subsonic steady quasi-axisymmetric flow of an isolated slender vortex core is considered. The solution is obtained using a simple set of parabolic equations. The results are in excellent agreement with those of the full Navier-Stokes equations.