Model Reduction and Analysis of Deep Dynamic Stall on a Plunging Airfoil using Dynamic Mode Decomposition

Abstract

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, thereby losing temporal information. However, many dynamics are not highlighted by the most energetic structures. In transitional flows for example, growth of flow structures is a more important indicator. The Dynamic Mode Decomposition (DMD) technique highlighted by Schmid1 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 SD7003 airfoil undergoing periodic plunging motion, which is representative of a wide variety of phenomena present in MAVs and UAVs.The DMD modes highlight the dynamically varying nature of highly transient low Reynolds number flows and identify the specific flow structures associated with the plunging motion.A stability analysis of the computed DMD modes is performed and unstable flow structures are identified. Flow structures which are common to the dominant modes in both POD and DMD are identified using the two techniques in conjunction with each other. Further, the original flow field is reconstructed from the DMD modes and their individual modal behavior is analyzed to understand the net contribution of the mode to the total flow field.Finally, DMD modes in local regions are used to decide optimum probe placement locations, which capture majority of the flow dynamics based on sparse available time signals.