Numerical simulation of the interaction of microactuators and boundary layers

A technique is presented for carrying out relatively low-cost numerical simulations of the interaction between three-dimensional microelectromechanical systems (MEMS)- and mesoscale actuators and a laminar boundary layer. The jet-type actuators take the form of a diaphragmlocated at the bottom of a cavity. When the diaphragm is driven by piezoceramic, for example, it de� ects, reduces the cavity volume, and drives air out of an ori� ce as a jet into the boundary layer. In an attempt to avoid an in� ow phase into the cavity, we study the effects of a “puff-like” jet produced when the diaphragmis driven by a short-duration constant force, or the cavity pressure is suddenly increased by providing air from a microvalve. The theoretical model for the actuator is based on classic thin-plate theory for the diaphragmdynamics andmodi� ed unsteady pipe-� owtheory for the � uid dynamics in the ori� ce/nozzle leading to the boundary layer. The cavity � uid dynamics is not modeled in detail; the compressible � owinit is neglected, and the instantaneouspressure there is determined viathe perfect gas law.A velocity–vorticity method is used to compute the perturbation � ow� eld created in the boundary layer. This method is capable of full direct numerical simulations, but for the present results the governing equations were linearized. The cavity and boundary-layer � ow� elds are linked by requiring continuity of velocity and pressure at the ori� ce exit. The computational methods are used to investigate such questions as the need for fully interactive computations and the differences between meso- and MEMS-scale actuators.