Model reduction and analysis of deep dynamic stall on a plunging airfoil

Abstract

The ability to generate massive amounts of high-resolution data, both experimentally and computationally, has led to a surge of interest in mathematical model reduction using modal decomposition algorithms. When applied to complex unsteady flows, different techniques highlight different flow dynamics which are difficult to extract directly from large datasets. A widely used technique is Proper Orthogonal Decomposition (POD) which ranks modes by their relative energy content. A newer method, Dynamic Mode Decomposition (DMD), focuses on rates of growth of different modes, thus retaining temporal information pertinent to dynamic events which dominate highly transient flows. In this paper, we employ these techniques, with emphasis on DMD, to analyze flow past an SD7003 airfoil undergoing periodic plunging motion representative of small unmanned vehicles. Snapshots are obtained from a high-fidelity, experimentally validated Large-Eddy Simulation (LES). The stability characteristics of DMD modes show that the flow structure associated with the leading edge vortex (LEV) in dynamic stall is unstable. The influence of DMD modes in local regions of the flow provide insight into which flow frequencies may be targeted by leading edge actuators to have maximum impact in controlling the unstable flow structures inducing stall. Dominant POD modes, each of which can have multiple frequency components, are shown to be comprised primarily of the dominant DMD mode contributions. A practical framework is introduced to identify components of a global flow structure across different velocity components. The method is shown to successfully reproduce the global flow structure. A few dominant DMD modes are used to reconstruct the flow near the leading edge, where rapid changes occur during parts of the plunging cycle and the ability of individual probe to provide insight into global phenomena is assessed. Finally, a stability analysis of each mode is performed to identify flow instabilities near the leading edge.