Reduced-order model for efficient simulation of synthetic jet actuators

A new reduced-order model of multidimensional synthetic jet actuators that combines the accuracy and conservation properties of full numerical simulation methods with the efficiency of simplified zero-order models is proposed. The multidimensional actuator is simulated by the solution of the time-dependent compressible quasi-one-dimensional Euler equations, whereas the diaphragm is modeled as a moving boundary. The governing equations are approximated with a fourth-order finite difference scheme on a moving mesh, such that one of the mesh boundaries coincides with the diaphragm. The reduced-order model of the actuator has several advantages. In contrast to the zero-dimensional models, this approach provides conservation of mass, momentum, and energy. Furthermore, the new method is computationally much more efficient than the two-dimensional Navier-Stokes simulation of the actuator cavity flow, while providing practically the same accuracy in the exterior flowfield. The most distinctive feature of the present model is its ability to predict the resonance characteristics of synthetic jet actuators; this is not practical when the three-dimensional models are used because of the computational cost involved. Numerical results demonstrating the accuracy of the new reduced-order model and its limitations are presented.