Unsteady aerodynamic damping characteristics of a pitching airfoil under surging motion: A Hilbert–dynamic mode decomposition analysis

Abstract

Under coupled pitching and surging motions, the aerodynamic response of an airfoil undergoing dynamic stall exhibits strongly unsteady and transient characteristics and is prone to instability. However, existing methods still lack a quantitative framework capable of capturing such instantaneous behavior. To address this issue, this paper proposes a hybrid computational-fluid-dynamics and data-driven approach integrated with the Hilbert transform to quantify instantaneous aerodynamic stability. Using the DU25-A17 airfoil as the research object, a transient flow-field model is established using an overset-grid strategy and user-defined functions. A dimensionless parameter, the surge velocity ratio, is introduced to systematically evaluate the effects of different motion parameters on the instantaneous aerodynamic response. Lift and drag coefficients, transient pressure and velocity fields, vortex structures, and instantaneous aerodynamic damping are analyzed in both the temporal and spatial domains. To elucidate the underlying instability mechanism, dynamic mode decomposition is employed to reconstruct the transient pressure field, enabling calculation of the chordwise aerodynamic damping distribution and identification of spatial “hotspot” regions. The results demonstrate that the proposed method can effectively evaluate instantaneous aerodynamic stability, reveal the essential instability mechanisms under complex flow conditions, and identify critical flow regions.