Characterization of synthetic jet resonant cavities

The scientific and technical literature about synthetic jet actuators includes a very wide field of applications such as flow control, heat transfer from limited-size surfaces, general enhancement of mixing between fluid currents, generation of micro-thrust for propulsion or attitude control. The overall design of the actuators needs practical modeling tools. The present work is aimed at characterizing the frequency response of a resonant cavity based synthetic jet actuator driven by a thin piezoelectric disk and represents an alternative contribution to the Persoons’s work [1]; in particular, it approaches the frequency response analysis from the same perspective of Sharma [2], who proposed a frequency-response model directly based on fluid dynamics equations, whereas Persoons [1] follows more directly the Gallas et al. [3] perspective based on the equivalent electric circuit approach. A lumped element mathematical model [4] of the operation of a synthetic jet actuator is both analytically and numerically investigated in order to obtain information about the frequency response of the device; the oscillating membrane is considered as a single-degree-of-freedom mechanical system, while the resonant cavity and orifice components are described by means of proper forms of the continuity and Bernoulli’s unsteady equations. The non-linear governing equations system has been numerically integrated in MATLAB environment. From the analytical viewpoint, it is found that the device behaves as a two-coupled oscillators system and, by solving the relevant eigenvalues problem, simply analytical formulas are given in order to predict the two modified peak frequencies, as functions of the uncoupled first-mode structural and Helmholtz resonance frequencies. The model is also validated through systematic experimental tests carried out on three devices having different mechanical and geometrical characteristics leading to an increasing coupling factor; it is found a very strict agreement between exit flow velocity measurements and numerical simulations for any tested device, for different supply voltages; moreover, the analytical formulas yield predictions in close agreement with numerical and experimental findings as well. References [1] Persoons, T., “General Reduced Order Model to Design and Operate Synthetic Jet Actuators", AIAA Journal, Vol. 50, No. 4, 2012, pp. 916-927. [2] Sharma, R. N., “Fluid Dynamics Based Analytical Model for Synthetic Jet Actuators,” AIAA Journal, Vol. 45, No. 8, Aug. 2007, pp. 1841-1847. [3] Gallas, Q., Holman, R., Nishida, T., Carroll, B., Sheplak, M., and Cattafesta, L., “Lumped Element Modeling of Piezoelectric-Driven Synthetic Jet Actuators,” AIAA Journal., Vol. 41, No. 2, 2003, pp. 240-247. [4] de Luca, L., Girfoglio, M., and Coppola, G., “Modeling and Experimental Validation of the Frequency Response of Synthetic Jet Actuators,” under revision for AIAA Journal, 2013.