Cluster-based feedback control of turbulent post-stall separated flows

Abstract

We propose a novel model-free self-learning cluster-based control strategy for general nonlinear feedback flow control technique, benchmarked for high-fidelity simulations of post-stall separated flows over an airfoil. The present approach partitions the flow trajectories (force measurements) into clusters, which correspond to characteristic coarsegrained phases in a low-dimensional feature space. A feedback control law is then sought for each cluster state through iterative evaluation and downhill simplex search to minimize power consumption in flight. Unsupervised clustering of the flow trajectories for in-situ learning and optimization of coarse-grained control laws are implemented in an automated manner as key enablers. Re-routing the flow trajectories, the optimized control laws shift the cluster populations to the aerodynamically favorable states. Utilizing limited number of sensor measurements for both clustering and optimization, these feedback laws were determined in only O(10) iterations. The objective of the present work is not necessarily to suppress flow separation but to minimize the desired cost function to achieve enhanced aerodynamic performance. The present control approach is applied to the control of two and three-dimensional separated flows over a NACA 0012 airfoil with large-eddy simulations at an angle of attack of 9 • , Reynolds number Re = 23, 000 and free-stream Mach number M ∞ = 0.3. The optimized control laws effectively minimize the flight power consumption enabling the flows to reach a low-drag state. The present work aims to address the challenges associated with adaptive feedback control design for turbulent separated flows at moderate Reynolds number.

Randomized methods to characterize large-scale vortical flow networks

“…Network analysis has also been used by Meena et al [19] for community detection and force prediction in an unsteady wake. More recently, interaction networks based on the energy transfer between modes has been used for modeling and control [35,41]. These studies provide compelling evidence that the emerging network perspective may complement well-established flow modeling techniques.…”

Deep model predictive flow control with limited sensor data and online learning

“…In a flow control problem, these can be the lift and drag coefficients of a wing, for instance. Such an approach has successfully been used in combination with surrogate models based on dynamic mode decomposition [33] or clustering [31]. We thus aim at directly approximating the dynamics for the observable z = f (y) and replacing the constraint in Problem (1) by a surrogate model.…”

“…A combination of the representational power of deep neural networks with the flexible optimization framework of MPC, called DeepMPC, is also a promising strategy. There exist various approaches for using data-driven surrogate models for MPC (e.g., based on the Koopman operator [15,16,20,[31][32][33]), and DeepMPC has considerable potential [3,24,30]. The ability of DeepMPC to control the laminar flow past a circular cylinder was recently demonstrated in [30]; the flow considered in this work is nearly linear and may be well approximated using more standard linear modeling and control techniques.…”

Cartographing dynamic stall with machine learning

“…DTW allows for the time series to be stretched and squashed a small amount to allow for an effective comparison between experimental repetitions. The approach of using a cycle to cycle distance metric (in this case DTW) is different to making time independent clusters used in the work of Nair et al (2018). The difference in approach comes from intended application.…”

“…Nair et al (2018) have demonstrated one approach to clustering for separated flows in the context of cluster-based feedback control Cao et al (2014). also demonstrated the use of time series clustering in the context of combustion.…”