Saddle point of attachment in jet–crossflow interaction

Abstract

Numerical simulation and theoretical analysis were performed to investigate the upstream topology of a jet–crossflow interaction. The numerical results were validated with mathematical theory as well as a juncture flow structure. The upstream critical point satisfies the condition of occurrence for a saddle point of attachment in the horseshoe vortex system. In addition to the classical topology led by a saddle point of separation, a new topology led by a saddle point of attachment was found for the first time in a jet–crossflow interaction. The degeneration of the critical point from separation to attachment is determined by the velocity ratio of the jet over the crossflow, and the boundary layer thickness of the flat plate. When the boundary layer thickness at the upstream edge of the jet is close to one diameter of the jet, the flow topology is led by a saddle point of attachment. Variation of the velocity ratio does not change the topology but the location of the saddle point. When the boundary layer thickness is less than 0.255 of the jet flow diameter, large velocity ratio can generate a saddle point of attachment without spiral horseshoe vortex; continuously decreasing the velocity ratio will change the flow topology to saddle point of the separation. The degeneration of the critical point from attachment to separation was observed.