Secondary instabilities of stationary crossflow vortices: Comparison of LST-2D and PSE-3D with DNS.

Abstract

Three-dimensional laminar boundary layers over swept wings are susceptible to crossflow instabilities that manifest themselves in the form of stationary and traveling crossflow vortices. The boundary layer distorted by the action of the crossflow vortices is prone to the growth of secondary instabilities. Discrepancies between direct numerical simulation (DNS) and stability methodologies on the development of secondary perturbations of stationary crossflow vortices over swept wings have been reported in the literature. To shed light on the origin of these inconsistencies, a comparison of DNS and linear stability theory is provided here. Unsteady secondary disturbances in a crossflow-dominated boundary layer are analyzed for two frequencies: the lower one ( f = 900 Hz) is dominated by a type III secondary instability, while the higher frequency ( f = 2200 Hz) is characterized by a type I instability. Results from linear stability theory (LST-2D) and linear parabolized stability equations (PSE-3D) formulated in a suitable non-orthogonal coordinate system correlate well with DNS data in terms of perturbation shape and location relative to the stationary crossflow vortices. Employing a non-orthogonal coordinate system is crucial for such base flows in order to simultaneously fulfill the spanwise periodicity and slow variation along the streamwise direction. However, the LST-2D results underestimate the integrated growth rate, while the PSE-3D computations closely match the DNS, highlighting the importance of including the streamwise gradients and the upstream history in the instability computations.