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.

Optimization of Tollmien-Schlichting waves control: comparison between a deep reinforcement learning and particle swarm optimization approach

“…This section outlines the numerical method and optimization techniques used to simulate the TS instabilities in an incompressible 2D laminar boundary layer and study their interaction with the AFC system. A non-linear Harmonic Navier-Stokes (HNS) solver [21] is implemented for this purpose, motivated by its ability to provide fast feedback for the optimization algorithms and also consider the TS waves in a frequency domain which facilitates the control strategy. A brief description of the HNS solver and a summary of the two methods of optimization (SDRL and PSO) implemented for the AFC are provided in this section.…”

“…These equations possess inherent nonlinearity, and they can be transformed into two distinct forms: the Nonlinear Harmonic Navier-Stokes (NLHNS) equations and the Linear Harmonic Navier-Stokes (LHNS) equations. The details regarding the corresponding LHNS and NLHNS equations are provided in [21] for the interested reader.…”

“…The solution of the harmonic Navier-Stokes equations is obtained using an in-house solver developed at the TU Delft Low-Speed Lab [22]. In the discretization process, a uniform grid is employed in the streamwise, 𝑥, direction.…”

“…Solving this system provides the desired perturbation velocity and pressure, enabling further analysis and investigation. The explicit form of the matrices and equations of HNS is available in [21].…”