Topology transition description of horseshoe vortex system in juncture flows with velocity characteristic lines

Particle image velocimetry and numerical simulation results of juncture flows were analyzed to parametrically investigate topology transition. The vortex system evolutions from non-vortex to multi-vortex with variations in obstacle bluntness, obstacle width, flow velocity, and boundary layer thickness are discussed from the perspective of velocity characteristic lines. The velocity characteristic lines of u = 0, υ = 0, and ?2 υ = 0 are adopted to describe the vortex system evolution. The motions of the characteristic lines with juncture flow parameters are described in detail, and the corresponding reflections of the vortex system patterns are illustrated. A panoramic picture of the development of velocity characteristic lines corresponding to the HSV topology transition from a non-vortex to a multi-vortex system with variations in the juncture flow parameter is established. Two methods for determining the attachment/separation pattern of the most upstream singularity are proposed. One method is based on the number of intersections of the u = 0 and υ = 0 velocity characteristic curve lines, and the other is based on the relative positions of the most upstream feet of the u = 0 and υ = 0 loop curves with both feet attached to the wall.