CFD verification and weak compressibility correction of unsteady aerodynamic force models applied to high-amplitude oscillating incoming flows

The two-dimensional airfoil theories of Isaacs and Greenberg for unsteady aerodynamic forces are widely adopted to estimate the aerodynamic performance of wind-turban blades and helicopter blade loads. The models are established under the assumption that the incoming flow is incompressible and without viscosity. However, the viscosity and compressibility are inevitable and the applicability of the model to predict the aerodynamic force in real flows needs to be checked. For the viscous effects, Strangfeld et al. verified the models experimentally using the data of NACA 0018 from wind tunnel at Reynolds number 0.25 million in 2014. The Mach number of the experiment is near 0.0326, which makes the flow almost incompressible. To check the effects of compressibility, a numerical simulation of NACA 0018 is conducted. For verification, the result of Strangfeld et al. at Mach number 0.0326 is repeated using CFD. The simulation further extends to the Mach number 0.1, 0.2 and 0.3 cases to investigate performance of the model at higher Mach numbers. The results show that maximum lift coefficient increases and the phase lags with Mach number increasing. Maximum overshot is at Mach number 0.3, which is over 50% more than the prediction of the models. The results show that the compressibility is non-negligible and the Mach number is needed to be taken into account as a sensitive factor. To extend the application range of Mach number, a correction is added to the models to account the influence of weak compressibility. The correction relates the variation of density of the incoming flow to the Mach number changing, which changes the density near the airfoil. As the aerodynamic force are proportional to the density, the correction would increase the aerodynamic force as Mach number increases. Using the correction, the differences of the models and simulation is within 5%.