Numerical simulation of boundary-layer control using MEMS actuation

MEMS actuators and their effect on boundary layers is investigated using numerical simulation. The thesis is specifically focussed on jet actuators and their application to the targeted control of turbulent boundary layers. A complete numerical model of jet-type actuators, including the popular synthetic-jet actuator, is developed. The assumed input is the voltage signal to the piezocermic driver and the calculated output is the exit jet velocity. Thorough validation of the numerical code is presented and simulations performed to highlight the key issues in MEMS-actuator design. The three-dimensional boundary-layer disturbance created by the MEMS actuator is modelled using a velocity-vorticity formulation of the Navier-Stokes equations. The parallel code is rigorously validated against results from linear stability theory and transitional-streak measurements. The boundary-layer code is used to determine a performance criterion for MEMS jets; it is shown that the net mass flow from a jet best determines its effectiveness. The code is also used to demonstrate the macro-scale capabilities of MEMS-scale actuators; a grid-scaling method is described and employed to facilitate this calculation. A method is presented that enables high- and low-speed streaks to be modelled economically in otherwise undisturbed mean flows. Using this model, the fundamental principles of targeted control using MEMS actuation are explored. The MEMS-actuator and boundary-layer models are coupled, and an investigation into the interactive effects of the two systems is described. Using the coupled code, disturbances in the boundary layer are shown to induce velocities in inactive devices. One special case occurs when an oscillating pressure field creates Helmhotz resonance within the cavity of a MEMS actuator, thus causing large mass flow rates in and out of the device. It is also suggested that the MEMS device could strongly interact with the random fluctuations of a turbulent boundary layer, leading to highly unpredictable actuator responses.

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