Far-field momentum flux of high-frequency axisymmetric synthetic jets

Abstract

This study focuses on predicting the far-field momentum flux for axisymmetric synthetic jets, which is an important parameter that characterizes the performance of such jets in flow-control applications. Previous researchers have found that a negative pressure gradient near the jet orifice is responsible for the observed decrease in the momentum flux in the streamwise direction. As a result, prediction of the far field momentum flux of synthetic jets has encountered serious challenges. In this paper, the far-field momentum flux is modeled by calculating the hydrodynamic impulse of the vortical structure formed during one actuation cycle, under the assumption that the jet is fully developed and periodic. In this manner, the complex near-field effect of a synthetic jet is explicitly captured by the interactions between the vortices and the actuator. Furthermore, the impulse of these vortical structures is predicted using only the actuation parameters of the synthetic jet, namely, the stroke length, L, the orifice diameter, d, and the actuation frequency, f. For a synthetic jet with a stroke ratio, L/d, larger than the formation number, L*/d, this model predicts that the normalized far-field momentum flux, K/Ks, decreases when L/d increases. This can be explained by an increasing circulation fraction of the trailing jet, which contains less impulse per unit circulation compared with the leading vortex. This model is validated using hot-wire anemometry measurement of a series of synthetic jets. Moreover, by comparing with experimental data that have large L/d, this model suggests that the contribution of trailing jet to the overall far-field momentum flux is not negligible.