Motivated by closed-loop flow control applications, a formulation of the proper orthogonal decomposition (POD) is demonstrated, which is capable of characterizing not only the controlled and natural states of a given flow, but also the transient behavior between these states. This approach, which is termed temporal POD (TPOD), extracts the optimum frame of reference and the temporal information regarding the dynamics of the flow in the natural, controlled and transient states. In this paper, the TPOD concept is developed and is subsequently demonstrated in two experiments using dielectric barrier discharge plasma flow control: (1) flow over a circular cylinder at subcritical Reynolds number and (2) flow over a NACA 0015 airfoil at a large post-stall angle of attack. Both flows exhibit well-defined and distinct natural and controlled flow states. For the cylinder flow, the TPOD technique is used to develop a low-order dynamical systems model that is shown to properly capture the dynamics of the first TPOD mode, including the natural, forced and transient regimes. In the airfoil experiment, the TPOD approach is shown to provide the unique ability to conditionally examine the families of flow trajectories between natural and controlled states for user-selected initial conditions. This can be extremely useful in order to understand the physical mechanisms of flow control in complex flows where there may be very little a priori knowledge regarding the system behavior.
Experiments in Fluids – Springer Journals
Published: Mar 3, 2013
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