General Reduced-Order Model to Design and Operate Synthetic Jet Actuators

Abstract

Synthetic jets are used in various applications from flow control to thermal management of electronics. Controlling the jet operating point using a simple voltage to velocity calibration becomes unreliable in case of external pressure field disturbances or varying actuator characteristics. This paper presents a general lumped parameter model for a synthetic jet actuator with an electromagnetic or piezoelectric driver. The fluidic model accurately predicts the synthetic jet operating point (i.e., Reynolds number and stroke length) based on the measured cavity pressure. The model requires only two empirical coefficients characterizing nozzle fluid damping and inertia. These can be obtained via calibration or estimated from pressure loss correlations and the governing acoustic radiation impedance. The model has been validated experimentally for circular and rectangular orifices. The effect of nozzle damping on the nonlinear system response is discussed. Analytical expressions are given for the two resonance frequencies characterizing the system response as a function of the diaphragm and Helmholtz resonance frequencies. The optimal design of an impinging synthetic jet actuator is discussed in terms of the thermal and acoustic efficiencies. Guidelines for selecting the optimum combination of diaphragm and Helmholtz resonance frequency are presented and compared with previous studies.