All you need is time to generalise the Goman-Khrabrov dynamic stall model

Abstract: Dynamic stall on airfoils negatively impacts their aerodynamic performance and can lead to structural damage. Accurate prediction and modelling of the dynamic stall loads are crucial for a more robust design of wings and blades that operate under unsteady conditions susceptible to dynamic stall and for widening the range of operation of these lifting surfaces. Many dynamic stall models rely on empirical parameters that need to be obtained from experimental or numerical data which limits their generalisability. Here, we introduce physically derived times scales to replace the empirical parameters in the Goman-Khrabrov dynamic stall model. The physics-based time constants correspond to the dynamic stall delay and the decay rate of post-stall load fluctuations. The dynamic stall delay is largely independent of the type of the motion, the Reynolds number, and the airfoil geometry and is described as a function of a normalised instantaneous pitch rate. The post-stall decay rate is independent of the motion kinematics and is directly related to the Strouhal number of the post-stall vortex shedding. The general validity of our physics-based time constants is demonstrated using three sets of experimental dynamic stall data covering various airfoil profiles, Reynolds numbers varying from 75'000 to 1'000'000, and sinusoidal and ramp-up pitching motions. The use of physics-based time constants generalises the Goman-Khrabrov dynamic stall model and extends its range of application.