Abstract:
Active wave cancellation has the potential to delay laminar-turbulent transition without requiring a large expenditure of control energy, with application to aircraft drag reduction. A methodology is presented for the determination of the optimal location for a synthetic jet actuator used to control Tollmien-Schlichting disturbances with a wave cancellation approach. A direct numerical simulation (DNS) scheme is developed to allow the effect of controls on an at-plate boundary layer to be investigated. Time-periodic wall normal transpiration is used to represent the effect of synthetic jet actuators. An upstream actuator is used to introduce disturbances into the flow and a downstream control actuator is used to cancel the disturbances by anti-phase superposition. A distributed representation of the actuator using a truncated Gaussian function is utilised to allow the actuator location to be varied continuously to facilitate optimisation. An objective function quantifies the disturbance level, which is determined by a solution of the DNS system. Non-linear optimisation algorithms are used to determine the values for design variables, representing the amplitude, frequency, phase and location of the control actuator, which minimise the objective function. Derivative-free optimisation algorithms are used to investigate the optimal actuator location and are shown to be capable of adjusting the actuator location to obtain improved disturbance reduction. A gradient-based optimisation algorithm is effective at finding controls for an actuator with a fixed location. However the objective function is not sufficiently smooth to allow optimisation of the actuator location with this method. The use of a global optimisation algorithm shows a minimum in the objective function occurs in a region approximately twenty eight displacement thicknesses downstream of the control actuator. Further exploration of this region demonstrates that the objective function has a low sensitivity to changes in actuator location near the optimal location.