Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition

Adaptive control of flow separation based on online dynamic mode decomposition (DMD) is formulated and implemented on a canonical separated laminar boundary layer via a pulse-modulated zero-net mass-flux jet actuator located just upstream of separation. Using a linear array of thirteen flush-mounted microphones, dynamical characteristics of the separated flow subjected to forcing are extracted by online DMD. This method provides updates of the modal characteristics of the separated flow while forcing is applied at a rate commensurate with the characteristic time scales of the flow. In particular, online DMD provides a time-varying linear estimate of the nonlinear evolution of the controlled flow without any prior knowledge. Using this adaptive model, feedback control is then implemented in which the linear quadratic regulator gains are computed recursively. This physics-based, autonomous approach results in more efficient flow reattachment compared with commensurate open-loop control. Four Reynolds numbers are tested to assess robustness, Rec = 0.9× 10⁵, Rec = 1× 10⁵, Rec = 1.1× 10⁵ and Rec = 1.25× 10⁵. All controlled cases exhibit a significant reduction in mean separation bubble height, requiring approximately 10 characteristic time periods to establish control.