How a wing-tip vortex escapes the streamwise impingement onto a downstream-located obstacle

Impingement of vortices on surfaces can take place with the vortex axis aligned either normal or parallel to the obstacle. The latter case is considered, which could be encountered in turbomachinery blade cascade or in formation flight, possibly affecting the efficiency or the flight performance. More precisely, the focus is on the dynamics governing the escape of the vortex from a downstream-located obstacle, which is slightly displaced from the vortex centreline. To this end, a Batchelor vortex impinging a downstream sphere is numerically investigated. Above a specific swirl number, defined as the ratio between the maximum tangential velocity and the centreline axial velocity, the vortex impinging the sphere breaks down with the development of a self-sustained instability. However, the breakdown disappears when a sufficient lateral displacement of the sphere is introduced, resulting in a fixed and steady deflection of the vortex circumventing the sphere. The interactions of the instability and the sphere lateral displacement are investigated by a weakly nonlinear analysis coupled to a domain perturbation method.