Numerical study of drag reduction through rotating actuators in a wall-bounded turbulent flow

The reduction of frictional drag generated by turbulent fluid flow on solid surfaces is an important problem in fluid mechanics, with the long-term potential to impact the energy efficiency and the performance of many engineering systems. This thesis consists of three essays that elaborate on turbulent drag reduction through wall-mounted rotating discs, originally introduced by Ricco and Hahn (2013). The proposed methods are evaluated via direct numerical simulation of turbulent channel flow using the high-performance solver Incompact3D. In the first, turbulent channel flow altered by the combination of flush-mounted spinning rings and vertical-velocity opposition control or hydrophobic surfaces is studied. The two types of distributed control are applied over the surface area that is not occupied by the spinning rings. Drag reduction is enhanced by the novel combined methods, with up to 27% reduction compared to 20% of the simple rotating rings. A idealized predictive model of the combined drag-reduction performance is presented. A spatially-dependent variant of the Fukagata-Iwamoto-Kasagi integral identity is developed to explain the influence of the highly non-uniform spatial structure of the flow on the skin-friction. The streamwise structures forming between discs have a drag-increasing contribution, while drag is highly reduced over the central region where the rings generate a triangular wave of spanwise velocity. The different outcome of combining the rings with the opposition control and the hydrophobic surface are clarified by the alteration to the elongated structures between rings. The second part investigates the dynamics of rigid discs that are free to rotate under a turbulent channel flow. Simple yet realistic models are introduced for the actuator geometry and the frictional torques that are generated by fluid motion in the cavity underneath the disc and in the support bearing, and the related assumptions are discussed critically. Firstly, the dynamics of isolated, passively rotating discs of increasing diameter is simulated, finding that the discs oscillate around rest under the action of the shear-stress fluctuations at the wall. The root-mean-square of the turbulence-induced torque and the disc velocity show power-law dependence on the disc diameter, respectively positive and negative in the large-diameter range. A uncoupled model of the disc dynamics, where the disc do not move, is used as a small-velocity approximation of the disc-fluid system, leading to better understanding of the frequency-domain response of the disc to the turbulent excitation and the root-mean-square dependence on the disc diameter. Furthermore, half discs i.e. semicircular free-to-move actuators aligned to the streamwise direction and arranged in a rectangular array are considered. This configuration simulates the concept developed experimentally by Kocha and Kozulovic (2013) of partially covered discs. The mean-shear generates a non-zero torque on the disc half and the discs rotate with a finite mean angular velocity, locally producing a slip velocity at the wall. Drag reduction is found to be directly correlated to the rotation rate of the discs, the fastest-rotating case yielding above 5% globally and 20% on the disc surface. Dependence of the rotation velocity on the disc model parameter is discussed and a series of simulations aimed at a more comprehensive investigation of the half-disc technique is laid out. The third part of the work proposes a simple proportional feedback-control scheme for the array of discs, whereby the motor-powered discs are switched on or off to maintain the discs within a pre-determined velocity range. The actuator model developed previously is augmented with the inclusion of a model of a typical electric motor, used to power the discs. The optimal values of the control parameters i.e. the velocity range bounds and the motor torque are investigated by means of a Bayesian Optimization algorithm, capable of efficiently performing an autonomous search of the three-dimensional parameter space with a minimal number of simulations. The motorised steadily-rotating case is also simulated and its performance compared to the ideal model and to the feedback-controlled flow, concluding that it is highly likely that net power saving can be achieved even accounting for realistic losses in the disc housing. The power-budget dependence on the feedback-control parameters is analysed extensively and special consideration is given to its correlation to the disc mean velocity and to the characteristics of the transients. Although the on-off control can achieve marginal improvements on the reference steady activation of the discs, an optimised constant-velocity control is superior.