Connecting Wake Vorticity with Fundamental Fourier Terms in Unsteady Thin Airfoil Theory

Unsteady aerodynamics has been a subject of extensive research for several decades due to its relevance across a wide range of applications involving complex, time-dependent fluid flow phenomena. This paper investigates unsteady airfoil flows to gain insight into the interplay between airfoil motion, wake dynamics, and various aerodynamic quantities of the airfoil. The study employs a combination of unsteady thin airfoil theory and high-fidelity unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations. Leading Fourier coefficients from the thin-airfoil-theory-based modeling framework, along with the airfoil-bound circulation, are estimated using data from the numerical simulations. Trends in the key aerodynamic quantities governing flowfield evolution are analyzed and the causes of discrepancies between theoretical predictions and numerical simulation results are identified. The findings from this work will contribute to bridging the gap between theoretical modeling and high-fidelity approaches and improving the existing physics-informed, low-order prediction frameworks for unsteady aerodynamic flows.