Skin drag in shear flows can be significantly reduced by maintaining laminar versus turbulent flow, rendering the control or delay of transition to turbulence of engineering interest. Controlling transition from laminar to turbulent plane Poiseuille flow serves as a model problem for more geometrically complex or realistic shear flows, such as boundary layers or pipe flow. In previous numerical studies, application of a linear systems approach to controlling transition to turbulence in plane Poiseuille flow has been shown to increase transition thresholds by at least several factors, depending on the type of flow perturbation assumed. Generally speaking, these studies have two primary shortcomings: large model order and assuming a continuum, or near continuum, of wall-mounted sensors and actuators.
This research attempts to address the aforementioned shortcomings and progress toward physically realizable actuation and sensing. Performance is measured by searching for controlled and uncontrolled transition thresholds in a pseudo-spectral direct numerical simulation (DNS) of the Navier-Stokes equations written in-house. Firstly, our research examines the degree to which peak transition threshold improvement can still be obtained both by controlling only a narrow range of wave-number pairs and by using sparsely distributed discrete actuators under the assumption of full-state feedback. Secondly, we investigate the use of sparsely distributed discrete sensors, which relies upon the assumption that only a narrow range of wave-number pairs is of interest for state estimation and control, and apply a heretofore unused technique for filtering the effects of sensor spillover caused by deliberate undersampling: state-augmentation. Finally, the use of sparsely distributed actuators and sensors together is tested against spatially continuous actuation and sensing, demonstrating the transition threshold performance recovery ability of state-augmentation for filtering spillover effects.
