Modal Force and Vortex Dynamics of an Oscillating Airfoil

Under symmetric oscillation, a sinusoidally heaving and pitching airfoil typically produces a lift force signal dominated by the forcing frequency and a thrust signal that is dominated by its second harmonic. These force histories reflect the symmetry of the motion and the resulting wake. Introducing a pitch bias perturbs this symmetry, producing net lift and thrust and leading to more complex, multimodal force responses. In this research, we experimentally investigate an oscillating NACA0012 airfoil at varying pitch biases in the Cornell Cyber-Physical Fluid Dynamics (CPFD) Facility. We record unsteady force time histories and capture the evolution of the vorticity field using Particle Image Velocimetry (PIV). Both signals are decomposed into constituent frequency modes: forces through Fourier analysis and vorticity via Dynamic Mode Decomposition (DMD). We show that each force mode can be related to a corresponding DMD mode through the vortex impulse formulation. This relation allows for modal vorticity structures to be meaningfully linked to their respective force components.