Some Insights into Synthetic Jet Actuation From Analytical Modelling

An analytical model based on the laws of fluid dynamics for synthetic jet actuation into quiescent air as well as into external flow fields is presented. A synthetic jet actuator consists of a cavity with a driven wall and an orifice. Under actuation, the wall is oscillated resulting in an oscillatory flow through the orifice. In the model, the driven wall is modelled as a single degree of freedom mechanical system, which is pneumatically coupled to the cavity-orifice arrangement acting as a Helmholtz resonator. The latter has been modelled using the unsteady form of the continuity and Bernoulli equations with a loss term. External flow field effects are represented by fluctuating external pressure at the actuator orifice. The model has been validated against experimental data available in the published literature, and excellent agreement is obtained between the predicted and measured frequency responses as well as the phase relationships between velocities and pressures. The model and analysis based on it provides valuable insights into the behaviour of synthetic jet actuators, and reveals amongst other things, that air in the actuator cavity exhibits compressibility at all frequencies beyond the Helmholtz resonance frequency. Furthermore, the actuator output velocity is maximised when cavity Helmholtz and wall natural frequencies are brought together. The presence of an external flow field could either aid or hinder actuation depending on the phase relationship between, and the relative frequencies of, the wall forcing and external pressure fluctuations.