Optimal cluster-based feedback control for separated flows*

We propose a model-free self-learning cluster-based feedback control strategy from sensor measurements benchmarked for separation control simulations. Here, we leverage unsupervised clustering for in-situ learning  and optimization of coarse-grained control laws to manipulate turbulent post-stall flows over an airfoil in high-fidelity simulations. The approach partitions the baseline flow trajectories (force measurements) into clusters, which correspond to characteristic coarse-grained phases in a low-dimensional feature space.  A feedback control law is sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption for aerodynamic flight. Re-routing the flow trajectories modifies the baseline Markov transition network to achieve aerodynamically favorable states with control. The approach is applied to two and three-dimensional separated flows over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of $9^\circ$, Reynolds number $Re = 23,000$ and free-stream Mach number $M_\infty = 0.3$. The optimized control laws effectively minimize the power consumption for flight enabling the flows to reach a low-drag state.