Spatiotemporal Waveform Observers and Feedback in Shear Layer Control

Active control enhances shear layer mixing by exciting natural instabilities. Harmonizing the periodic actuation with vortex release can be used to manipulate and improve the mixing effect. This type of feedback requires tracking large shear layer vortices. We propose an observer structure based on a very simple model, representing the collective signal of a set of sensors as a spatiotemporal waveform. The observer tracks the slow drift and abrupt changes in the spatiotemporal phasors (local Fourier coefficients). Benefiting from a much longer time constant than the period of vortex release, it naturally filters spatial and temporal high frequency noise. The discussion is illustrated by simulations and wind tunnel experiments for the flow over a backward facing step, where the design objective is shortening the recirculation bubble. Simulations of the free shear layer are used to illustrate means to track asynchronous vortex merging events.

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