Improving separation control with noise-robust variants of dynamic mode decomposition

Flow separation can lead to degraded performance in many engineered systems, which has led to sustained interest in developing strategies for suppressing and controlling flow separation. Separation control strategies based on open-loop forcing via synthetic jets have demonstrated a relative degree of success in various studies; however, many of these studies have relied upon trial-and-error “tuning” of a synthetic jet’s operating parameters for satisfactory performance with respect to a particular flow configuration. Subsequent work has focused on improving the general understanding of fluid flow separation from a dynamical systems perspective, with the aim of isolating key mechanisms that can be exploited for more systematic controller designs. Numerical studies have shown that dynamically dominant flow characteristics, identified by the dynamic mode decomposition (DMD), can be used to guide the design of open-loop separation control strategies. While these approaches have proven valuable for dynamical analyses in numerics, standard formulations of DMD have recently been shown to possess systematic errors that can lead to misleading results when the data are corrupted by some degree of measurement noise (e.g., sensor noise in experimental studies). Here, we make use of DMD to synthesize time-resolved particle image velocimetry (TR-PIV) data from a canonical separation experiment in an effort to inform the design of open-loop separation control strategies; to this end, we make use of a noise-aware version of DMD-introduced in Hemati et al. (2015)-to assess the impact of measurement noise on the conclusions drawn for informing open-loop controller design. Additionally, we extend the noise-aware framework to formulate a noise-robust version of the streaming DMD algorithm presented in Hemati et al. (2014). Dynamic characterizations afforded by DMD-based techniques are then used to inform open-loop separation control strategies that are tested in experiments. We find that open-loop forcing at a frequency associated with the dominant DMD mode reduces the mean height of the separation bubble, suggesting that DMD-based techniques may provide a systematic means of designing open-loop control strategies aimed at suppressing flow separation.