Active Control of Vibration and NoiseOPTIMAL CONTROL OF TURBULENT CHANNEL

Feedback control equations are developed and tested using optimal control theory for two diierent ow control problems. In the rst, wall-normal blowing and suction distributions are computed to eeciently reduce drag. The technique used to compute the control is the minimization of a \cost functional" which is constructed to represent some balance of the drag integrated over the walls and the net control eeort. Minimization of this cost functional is achieved by utilizing an adjoint problem to determine the sensitivity of the ow to control , then updating the control with a gradient algorithm. A distribution of wall velocities is thus found which minimizes the cost functional over a short time interval based on current observations of the ow near the wall. Preliminary numerical simulations of this scheme applied to turbulent channel ow indicates it provides approximately 17% drag reduction with small levels of control input. The mechanism apparent when the scheme is applied to a simpliied ow is also discussed. The second problem considered is the computation of eecient internal forcing distributions to reduce pressure uctuations on the walls of a channel. The internal forcing simulated is of a type which might be produced by appropriately placed magnets and electrodes in a wall acting on near-wall uid, referred to in recent literature as ElectroMagnetic Turbulence Control (EMTC). The optimal formulation for this problem is similar to that in the drag reduction by wall transpiration problem. Computational results of this scheme, which were not available at the time of printing, will be presented at the conference.