title: Criterion for vortex breakdown on shock wave and streamwise vortex interactions.
abstract: The interactions between supersonic streamwise vortices and oblique shock waves are theoretically and numerically investigated by three-dimensional (3D) Navier-Stokes equations. Based on the two inequalities, a criterion for shock-induced breakdown of the streamwise vortex is proposed. The simple breakdown condition depends on the Mach number, the swirl number, the velocity deficit, and the shock angle. According to the proposed criterion, the breakdown region expands as the Mach number increases. In numerical simulations, vortex breakdown appeared under conditions of multiple pressure increases and the helicity disappeared behind the oblique shock wave along the line of the vortex center. The numerical results are consistent with the predicted breakdown condition at Mach numbers 2.0 and 3.0. This study also found that the axial velocity deficit is important for classifying the breakdown configuration.
authors.affiliation: Department of Aerospace Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japan.
authors.forename: Toshihiko
authors.initials: T
authors.lastname: Hiejima