A computational analysis and design methodology is presented for effective microflow control using synthetic jets. The membrane is modeled as a moving boundary to accurately compute the flow inside the jet cavity. Compressible Navier-Stokes equations are solved with boundary conditions for the wall slip and the temperature jump conditions encountered for a specific range of Knudsen numbers. For validation, microchannel flow and microfilter flow are successfully computed. Then, flow past a backward-facing step in a microchannel is considered. Analysis is coupled with a design methodology to improve the actuator effectiveness. The objective function is selected to be the square of the vorticity (enstrophy) integrated over a separated region. First, from a design of experiments study, orifice and actuator cavity widths are identified as the most effective design variables. Then, a response surface method is constructed to find the improved control of the flow. This optimization results in more than 83% reduction of the enstrophy of the recirculation region.

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