Turbulent drag reduction: Studies of feedback control and flow over riblets

The objective of this study is to explore concepts for control of turbulent boundary layers leading to skin-friction reduction using the direct numerical simulation technique. This report is divided into three parts where three different control methods are investigated; a passive control by longitudinal riblets, an active control by sensing and perturbing structures near the wall, and a feedback control procedure guided by control theory.; In PART I significant drag reduction is achieved when the surface boundary condition is modified to suppress the dynamically significant coherent structures present in the wall region. The drag reduction is accompanied with significant reduction in the intensity of the wall-layer structures and reductions in the magnitude of Reynolds shear stress throughout the flow. Two essential drag reduction mechanisms are presented.; In PART II mathematical methods of control theory are applied to the problem of control of fluid flow. The procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory is presented through the formalism and language of control theory. Then a suboptimal control and feedback procedure are presented using methods of calculus of variations through the adjoint state and gradient algorithms. This suboptimal feedback control procedure is applied to the distributed and boundary controls of the stochastic Burgers equation. Most cases considered show significant reductions of the costs.; In PART III direct numerical simulation is performed to analyze turbulent flow over longitudinal riblets, and to educe the mechanism of drag reduction by riblets. The computed drags on the riblet surfaces are in good agreement with the existing experimental data. Differences in the mean-velocity profile and turbulence quantities are found to be limited to the inner region of the boundary layer. Velocity and vorticity fluctuations as well as the Reynolds shear stresses above the riblets are reduced in drag-reducing configurations. Instantaneous flow fields near the riblets are investigated in detail and a physical explanation for the observed drag reduction is proposed.