Model Reduction and Analysis of NS-DBD Based Control of Stalled NACA0015 Airfoil

Recent years have seen increased emphasis on mathematical model reduction using modal decomposition techniques of high dimensional flow field data from experiments as well as numerical simulations. These tools decode the complex unsteady flow-field into several modes. Different tools highlight different flow dynamics. In the experimental community, Proper Orthogonal Decomposition (POD) has been the most commonly used technique, ranking modes by their relative energy content, without concern for temporal aspects. However, many dynamics are not highlighted by the most energetic structures. In transitional flows for example, structure growth is a more a more important indicator of the turbulent effects. The Dynamic Mode Decomposition (DMD) technique highlighted by Schmid [1] achieves this by ranking modes by the most dynamically varying flow features. In this work, we use DMD and POD to analyze flow past a NACA0015 airfoil at Reynolds number of 100,000 and AoA=15 degree, without and with control. The specific control technique employed is based on the Nano-second Pulsed Dielectric Barrier Discharge (NS-DBD) actuator. Experimentally validated high fidelity 3-D numerical simulations are employed to generate the required snapshots. From the DMD modes, the dominant time-varying flow structures associated with the two cases are identified, and their stability characteristics are compared. DMD and POD modes are compared to each other. The DMD modes highlight the dynamically varying nature of the flow-field. A Floquet stability analysis of the eigenvalues from DMD for both the no-control and control cases is presented. Further, the original flow field is reconstructed from the DMD modes and their individual modal behavior has been analyzed to show the effect of control authority on the flow.