Cluster-based control for net drag reduction of the fluidic pinball

Abstract

We propose a Cluster-Based Control (CBC) strategy for model-free feedback drag reduction with multiple actuators and full-state feedback. CBC consists of three steps. First, the input of the feedback law is clustered from unforced flow data. Second, the feedback law is interpolated with actuation commands associated with the cluster centroids. Thus, centroids and these actuation commands facilitate a low-dimensional parameterization of the feedback law. Third, the centroid-based actuation commands are optimized, e.g., with a downhill simplex method. This framework generalizes the feature-based CBC from Nair et al. [“Cluster-based feedback control of turbulent post-stall separated flows,” J. Fluid Mech. 875, 345–375 (2019)] in three aspects. First, the control law input is the velocity field. Second, the control law output commands multiple actuators here. Third, a reformulation of the downhill simplex method allows parallelizing the simulations, thus accelerating the computation threefold. Full-state CBC is demonstrated on a multiple-input configuration, the so-called fluidic pinball in three flow regimes, including symmetric periodic at Re = 30, asymmetric periodic at Re = 100, and chaotic vortex shedding at Re = 150. The net drag reductions for the three cases amount to 33.06%, 24.15%, and 12.23%, respectively. CBC shows distinct advantages for robustness control at different flow conditions. The full-state CBC further reveals the evolution of the control flow associated with the centroids, which contributes to the physical interpretation of the feedback control process.