Linear and Nonlinear Stability Analysis of a Three-Dimensional Boundary Layer over a Hump

Abstract

The Parabolized Stability Equations (PSE), Adaptive Harmonic Linearized Navier-Stokes (AHLNS) and Harmonic Navier-Stokes (HNS) solvers are used to analyze the linear and nonlinear stability of swept-wing boundary layers under the influence of smooth wall deformations of varying size and geometry. Special attention is given to the validity of the slowly varying flow assumption of PSE via a comparison with AHLNS and HNS results. The surface deformations analyzed in this work are found to affect the development of the primary stationary crossflow instability mode as well as higher harmonics. Analysis of the locally most amplified mode reveals successive modulation of the growth rate in the vicinity of the surface deformation. This process was found to be largely governed by linear terms and driven by the base flow modification due to the deformed wall. Similarly, the base flow modification causes higher harmonics to experience a significant destabilization. This is followed by stabilization as nonlinear interactions become dominant. The PSE methodology proved capable of predicting the stability response for small wall deformations with only minor amplitude discrepancies compared to HNS results. The main difference was found to occur in the wall-normal velocity profiles of the mean flow distortion mode. The deviations of the PSE results compared to harmonic stability methods increased as the protuberance was made steeper. Moreover, the PSE framework was not able to converge for all cases nonlinearly.