Design approach to predict synthetic jet formation and resonance amplifications

A predictive approach for the Synthetic Jet (SJ) formation, which couples formation criteria already available from the literature, with outcome to Lumped Element Modeling (LEM), which is able to predict the resonance velocity amplifications, is presented. In this respect, the formation criteria yield the minimum jet velocity to obtain an experimentally observable jet, whereas the LEM approach predicts the jet velocity, to be compared with the minimum one of the formation criterion. A deep experimental investigation is carried out to detect jet formation and to measure resonance velocity amplifications on various types of actuators manufactured in house, including, among others, the influence of single and double orifices. Jet velocity is recorded by means of hot-wire anemometry, at both the device orifice exit and one orifice diameter downstream, i.e. downstream of the expected stagnation (saddle) point. Jet formation and resonance amplification thresholds are identified in terms of the dimensionless Stokes and Strouhal parameters. Based on the experimental finding, a description of the relevant modeling is reported, devoted to the evaluation of the velocity magnification factor with respect to the so-called incompressible (static) solution. It takes advantage from the physical consideration that the actuator behaves as a driven system of two-coupled mechanical oscillators, the Helmholtz’s one and the structural one, for which resonance frequencies are predicted by means of simple relationships, together with appropriate damping factors. Jet formation thresholds closely agree with the present experimental findings. The predicted overdamped conditions are compared with classic analytic boundary correlations of the literature and previous experimental results as well. Practical and simple relationships, that can help the designer to manufacture a device having desired performances, are presented.