| Summary: | The advances in the understanding of compressible turbulent flows challenge researchers to tackle more ambitious problems that surpass human intuition. Hence, it becomes necessary to rely on methods that give an insight into the underlying physical mechanisms that govern these turbulent flows to perform non-trivial tasks such as flow control. This thesis describes the development and application of an adjoint-based optimal flow control framework for compressible flows, which has been appended to an existing in-house DNS code (HiPSTAR).With minor coding effort, this framework is extended to permit the computation of both (stable and unstable) exact steady and periodic flow solutions in compressible flows over complex geometries. In this work we present for the first time a family of exact periodic solutions in compressible flows (Re = 2000), which we study in detail, paying special attention to the flow-acoustic interaction characteristic from cavity flows. Furthermore, a family of equilibrium flow solutions associated to these periodic orbits is also introduced, where it is shown that both families meet at the quasi-incompressible Mach number range. A stability analysis of both periodic and equilibrium solutions shows that the bifurcation is of subcritical Hopf type. Moreover, this flow-acoustic interaction is optimally controlled in a cavity flow of a higher Reynolds number (Re = 5000) by using the adjoint-based optimal flow control framework. The target of the flow actuation consists in reducing noise levels at the sensor location, by either reducing the overall sound radiation or altering the sound directivity. Lastly, we also carry out adjoint-based optimal flow control on a three-dimensional backward-facing step flow (Re = 3000). The investigation is oriented to cabin noise reduction, where we optimise an upstream flow actuation to reduce the flow impinging scales which present the largest impact on cabin noise. In addition, the complexity present in the flow studied pushes the adjoint-based approach at its limits. These intrinsic limitations of the method are discussed, where we also suggest and demonstrate a successful alternative which permits the use of adjoint-based optimisation methods in separated flows.
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