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Adjoint-based optimization of steady suction for disturbance control in incompressible flows
The optimal distribution of steady suction needed to control the
growth of single or multiple disturbances in quasi three-dimensional incompressible boundary layers on a flat plate is investigated. The evolution of disturbances is analyzed in the framework of the Parabolized Stability Equations (PSE).
A gradient based optimization procedure is used and the gradients are evaluated using the adjoint of the parabolized stability equations (APSE) and the adjoint of the boundary layer equations (ABLE). The accuracy of the gradient is increased by introducing a stabilization procedure for the PSE. Results show that a suction peak appears in the upstream part of the
suction region for optimal control of Tollmien-Schlichting (T-S)
waves, steady streamwise streaks in a two-dimensional boundary layer and oblique waves in a quasi three-dimensional boundary layer subject to an adverse pressure gradient. The mean flow modifications due to suction are shown to have a stabilizing effect similar to that of a favorable pressure gradient. It is also shown that the optimal suction distribution for the disturbance of interest reduce the growth rate of other perturbations. Results for control of a steady cross-flow mode
in a three-dimensional boundary layer subject to a favorable pressure gradient show that not even large amounts of suction manages to completely stabilize the disturbance.