A nonlinear reduced-order model evaluated with a comprehensive index for dual-excitation flow separation control

Single periodic excitation is widely used in unsteady flow separation control. However, in some two-dimensional (2D) or three-dimensional (3D) flow separation scenarios, dual excitations are necessary or advantageous. Referring to dual-excitation flow separation control, a nonlinear reduced-order model is established in this study to describe the interaction between dual external excitations with the internal flow instability of the separated flow and to provide physical insight into flow control mechanisms. The model is based on the Navier-Stokes equation, flow images of typical 2D or 3D flow separation, and the Stuart–Landau model. Additionally, a comprehensive index is proposed to evaluate flow control performance reflected by the reduced-order model, which accounts for flow losses from time-averaged and fluctuating flow, thus providing a more comprehensive evaluation of the model characteristics. Furthermore, we compare the results of the model to some numerical and experimental results of typical 2D and 3D flow separation control with dual excitations. The agreement of the model results and the numerical and experimental results verify the reduced-order model and its comprehensive index to a certain degree.