Accuracy of Local and Nonlocal Linear Stability Theory in Swept Separation Bubbles

Abstract

A series of swept laminar separation bubbles is used to investigate the principle applicability of the e N method to laminar separation bubbles in swept configurations. To this end the effect of sweep and of the propagation direction of disturbance waves on the accuracy of linear stability theory and solutions of the parabolized stability equations is studied systematically. Direct comparisons of spatial linear stability theory and linear parabolized stability equation solutions to results of direct numerical simulations allow for a qualitative and quantitative evaluation of their performance in the presence of sweep, flow separation, and local backflow. A variety of Tollmien-Schlichting waves as well as the most amplified stationary crossflow vortex is analyzed within a sweep angle range between 0 and 45 deg. It turns out that even though linear stability theory works satisfactorily, parabolized stability equations are clearly preferable in terms of accuracy, especially for very oblique modes or larger sweep angles.