Modal Phase Study on Lift Enhancement of a Locally Flexible Membrane Airfoil Using Dynamic Mode Decomposition

The dynamic mode decomposition serves as a useful tool for the coherent structure extraction of the complex flow fields with characteristic frequency identification, but the phase information of the flow modes is paid less attention to. In this study, phase information around the locally flexible membrane airfoil is quantitatively studied using dynamic mode decomposition (DMD) to unveil the physical mechanism of the lift improvement of the membrane airfoil. The flow over the airfoil at a low Reynolds number (Re = 5500) is computed parametrically across a range of angles of attack (AOA = 4°–14°) and membrane lengths (LM = 0.55c–0.70c) using a verified fluid–structure coupling framework. The lift enhancement is analyzed by the dynamic coherent patterns of the membrane airfoil flow fields, which are quantified by the DMD modal phase propagation. A downstream propagation pressure speed (DPP) on the upper surface is defined to quantify the propagation speed of the lagged maximal pressure in the flow separation zone. It is found that a faster DPP speed can induce more vortices. The correlation coefficient between the DPP speed and lift enhancement is above 0.85 at most cases, indicating the significant contribution of vortex evolution to aerodynamic performance. The DPP speed greatly impacts the retention time of dominant vortices on the upper surface, resulting in the lift enhancement.