Feedback control of flow separation using synthetic jets

摘要

The primary goal of this research is to assess the effect of synthetic jets on flow separationand provide a feedback control strategy for flow separation using synthetic jets.The feedback control synthesis is conducted based upon CFD simulation for a roundedbackward-facing step. The results of the synthetic jet experiments on an airfoil showedthat synthetic jets have the potential for controlling the degree of flow separation beyonddelaying the onset of flow separation. In the simulation, while the jet is ejected slightlyupstream from the separation point, the feedback pressure signal is acquired at a downstreamwall point where the vortex is fully developed. Due to the uniqueness of syntheticjets, i.e. "zero-net-mass flux", the profile of synthetic jet velocity cannot be arbitrarily generated.The possible control variables are the magnitude or frequency of the oscillating jetvelocity. Consequently, the fluidic system in simulation consists of the actuator model andthe NARMAX (Nonlinear Auto Regressive Moving Average with eXogenous inputs) flowmodel. This system shows a strong nonlinear pressure response to the input jet frequency.Low-pass filtering of the pressure response, introduced for pressure recovery, facilitatesa quasi-linear approximation of the system in the frequency domain using the describingfunction method. The low-pass filter effectively separates the pressure response into twofrequency bands. The lower frequency band below the filter pass frequency includes thequasi-linear response targeted by the feedback control and the higher band above the filterstop frequency contains the attenuated higher harmonics, which are treated as nonlinear disturbances. This quasi-linear approximation is utilized to design a PI controller for thefluidic system including the synthetic jet. To ensure one-to-one correspondence of the jetfrequency and the filtered pressure response, the upper bound of the jet frequency is set atthe frequency of the maximum pressure. The response of the resulting closed loop feedbackcontrol system, comprised of a PI controller, low-pass filter, SJA model and NARMAXmodel, is shown to track the desired pressure command with an improvement in thetransient response over the open-loop system.