Drag reduction by passive in-plane wall motions in turbulent wall-bounded flows

Losses associated with turbulent flows dissipate a significant amount of generated energy. Such losses originate from the drag force, which is often described as the sum of the pressure drag and the friction drag. This thesis sets out to explore the hypothesis that passive wall motions driven by fluid mechanical forces are able to reduce the friction drag in fully developed turbulent boundary layers. Firstly, the streamwise and spanwise opposition controls proposed by Choi et al. (1994, Journal of Fluid Mechanics) are revisited to identify beneficial wall motions. Near-wall streamwise or spanwise velocity fluctuations are measured along a detection plane parallel to the wall (sensing). For streamwise control, the wall velocities are set to be equivalent to the measured streamwise velocity fluctuations, whereas for spanwise control, the wall velocities are set to have the same magnitude but opposite direction as the measured spanwise velocity fluctuations (actuation). Direct numerical simulations of canonical turbulent channel flows are carried out at low (Reτ ≈ 180) and intermediate (Reτ ≈ 1000) Reynolds numbers to quantify the effect of the distance between the wall and the detection plane. The investigation reveals the primary differences between the mechanisms underlying the two active in-plane controls. The modified flow features and turbulence statistics show that the streamwise control amplifies the most energetic streamwise velocity fluctuations and damps the near-wall vorticity fluctuations. In comparison, the spanwise control induces near-wall vorticity in order to counteract the quasi-streamwise vortices of the near-wall cycle and suppress turbulence production. Although, the working principles of the active controls are fundamentally different, both achieve drag reduction by mitigating momentum transfer between the velocity components. Secondly, two theoretical passive compliant wall models are proposed, the aim being to sustain beneficial wall motions identified by active flow control simulations. In the proposed models, streamwise or spanwise in-plane wall motions are governed by an array of independent one-degree-of-freedom damped harmonic oscillators. Unidirectional wall motions are driven by local streamwise or spanwise wall shear stresses. A weak coupling scheme is implemented to investigate the interaction between the compliant surface models and the turbulent flow in the channel by means of direct numerical simulations. A linear analytical solution of the coupled differential equation system is derived for laminar pulsatile channel flows allowing verification and validation of the numerical model. The obtained analytical solution is utilised to map the parameter space of the passive controls and estimate the effect of the wall motions. It is shown that depending on the control parameters, the proposed compliant walls decrease or increase the vorticity fluctuations at the wall similarly to the active controls. This is confirmed by direct numerical simulations. On the one hand, when the control parameters are chosen appropriately, the passive streamwise control damps the