Finite element models of piezoelectric actuators for active flow control

A numerical procedure, based on the finite element method, capable to simulate the interaction of active structures with an incompressible fluid flow is discussed. In particular the active functionality of such structures is demanded to piezoelectric type actuators. The development of this interaction is connected to the study of problems that involve an active flow control for different potential applications as drag reduction, noise abatement, separation control, mixing enhancement, etc. Two kind of finite element models, one for the electromechanical field and the other for the fluid dynamic field, are built. The analyses are performed with a coupled iterative solver and they are based on the Arbitrarian Lagrangian-Eulerian (ALE) description. A Reynolds Averaged Navier-Stokes Equations (RANS) formulation for the model of turbulent fluid is adopted. The results of some numerical analyses are correlated to an experimental benchmark case founded in literature with the aim to validate the procedure. A sample application to control of separated flow from a backward-facing step is described, in which a piezoelectric unimorph actuator is patched on a Euler-Bernoulli beam installed at the upper corner of the step. The numerical model describes the displacement of the incoming shear layer and the velocity perturbation produced by the periodic oscillations of the actuator and how these parameters are related each other. In order to produce sensible amplitude for the oscillations, the actuator is driven near its natural frequency. A preliminary response analysis to examine the effects of the fluid on the resonant behaviour of the structure is done.