High-amplitude freestream turbulence and surface roughness elements can excite a laminar boundary-layer flow sufficiently enough to cause streamwise-oriented vortices to develop. These vortices resemble elongated streaks having alternate spanwise variations of the streamwise velocity. Following the transient growth phase, the fully developed vortex structures downstream undergo an inviscid secondary instability mechanism and, ultimately, transition to turbulence. This mechanism becomes much more complicated in high-speed boundary layer flows due to compressibility and thermal effects, which become more significant for higher Mach numbers. In this research, we formulate and test an optimal control algorithm to suppress the growth rate of the aforementioned streamwise vortex system. The derivation of the optimal control algorithm follows two stages.
In the first stage, to optimize the computational cost of the analysis, the study develops an efficient numerical algorithm based on the nonlinear boundary region equations (NBREs), a reduced form of the compressible Navier-Stokes equations in a high-Reynolds-number asymptotic framework. The NBREs algorithm results agree well with direct numerical simulation (DNS) results. The numerical simulations are substantially less computationally costly than a full DNS and have a more rigorous theoretical foundation than parabolized stability equation (PSE) based models. The substantial reduction in computational time required to predict the full development of a G\"{o}rtler vortex system in high-speed flows allows investigation into feedback control in reasonable total computational time, which is the focus of the second part of the study.
In the second stage, the method of Lagrange multipliers is utilized -- via an appropriate transformation of the original constrained optimization problem into an unconstrained form -- to obtain the adjoint compressible boundary-region equations (ACBREs) and corresponding optimality conditions, which constitute the basis of the optimal control approach. Numerical solutions for high-supersonic and hypersonic flows reveal a significant decrease in the kinetic energy and wall shear stress for all configurations considered. Streamwise velocity contour plots illustrate the qualitative effect of the optimal control iterations, demonstrating a significant decrease in the amplitude of the primary vortex instabilities.
| Identifer | oai:union.ndltd.org:MSSTATE/oai:scholarsjunction.msstate.edu:td-7061 |
| Date | 08 December 2023 |
| Creators | Es-Sahli, Omar |
| Publisher | Scholars Junction |
| Source Sets | Mississippi State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations |
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