Experimental implementation of modal approaches for reattachment of separated flows

Methods for adaptive control of flow separation based on dynamic mode decomposition (DMD) are formulated and implemented on a canonical separated flow subjected to actuation by a zero-net mass-flux (ZNMF) jet actuator. Using a linear array of unsteady surface pressure measurements, dynamical characteristics of a laminar separation bubble subjected to forcing are extracted by online DMD. This method provides reliable updates of the modal characteristics of the separated flow as forcing is applied at a rate commensurate with the characteristic time scales of the flow. Therefore, online DMD applied to the surface pressure measurements provides a time-varying linear estimate of the nonlinear evolution of the controlled flow, thereby enabling closed-loop control. From this adaptive model, feedback control is implemented in which the Linear Quadratic Regulator gains are computed recursively as the model provided by online DMD is updated. The controller’s explicit objective is to reduce the unsteady pressure fluctuations measured by surface mounted microphones within the separated flow region. Since this approach relies solely on observations of the separated flow, it is potentially robust to variable flow conditions. The chord Reynolds number of these experiments is 10⁵ and the pulse-modulated zero-net mass-flux actuator slot is located just upstream of separation. It is found that applying adaptive feedback control using the LQR approach to determine the feedback gains results in slightly better flow reattachment (2% lower separation height) with a 5% reduction in actuator effort as compared with the best open loop forcing case. This approach does not require prior knowledge of the characteristics of the separated flow.