Active Control and Reduced-Order Modeling of Transition in Shear Flows

Abstract: In this thesis direct numerical simulation is used to investigate the possibilityto delay the transition from laminar to turbulent in boundary layer flows.Furthermore, modal analysis is used to reveal the coherent structures in highdimensional dynamical systems arising in the flow problems.Among different transition scenarios, the classical transition scenario isanalysed. In this scenario, the laminar-turbulent transition occurs when Tollmien-Schlichting waves are triggered inside the boundary layer and grow exponentiallyas they move downstream in the domain. The aim is to attenuate the amplitudeof these waves using active control strategy based on a row of spatiallylocalised sensors and actuators distributed near the wall inside the boundarylayer. To avoid the high dimensional system arises from discretisation of theNavier Stokes equation, a reduced order model (ROM) based on EigensystemRealisation Algorithm (ERA) is obtained and a linear controller is designed.A plasma actuator is modelled and implemented as an external forcing on theflow. To account for the limitation of the plasma actuators and to further reducethe complexity of the controller several control strategies are examinedand compared. The outcomes reveal successful performance in mitigating theenergy of the disturbances inside the boundary layer.To extract coherent features of the wind turbine wakes, modal decompositiontechnique is employed where a large scale dynamical system is reduced toa fewer number of degrees of freedom. Two decomposition techniques are employed:proper orthogonal decomposition and dynamic mode decomposition.In the former procedure, the flow is decomposed into a set of uncorrelated structureswhich are rank according to their energy. In the latter, the eigenvaluesand eigenvectors of the underlying approximate linear operator is computedwhere each mode is associated with a specific frequency and growth rate. Theresults revealed the structures which are dynamically significant to the onsetof instability in the wind turbine wakes.