Dynamic characteristics of pitching airfoil based on immersed boundary method

Abstract: The pitching motion of airfoils can induce a significant nonlinear change of the flow field during the operation process of fluid machinery, such as the blades of the wind and hydraulic turbine. Therefore, it is a high demand to explore the dynamic characteristics of airfoils during the pitching motion. This study aims to investigate the dynamic characteristics of pitching airfoil using an immersed boundary method (IBM). The typical airfoil NACA0012 was also taken as the research object, in order to enhance the universality of the data. A self-developed computational fluid dynamics (CFD) solver with the direct numerical simulation (DNS) was utilized to simulate the flow field during operation. A finite difference method and staggered grid were then employed to discretize the flow field. The momentum equations were integrated using the second-order Rungee Kutta (RK2) method, where the divergence-free condition was satisfied using the projection method. Furthermore, the velocity near the boundary of fluid-solid was interpolated to meet the no-slip boundary condition using the IBM. As such, the dynamic characteristics and formation mechanism of the airfoil were achieved in the simulation of pitching motions under the various initial angle of attack, frequency, and amplitudes. Specifically, nine typical working conditions were selected under 1000 Reynolds number for the flow simulation, where the pitching amplitudes were 5° and 10°, the pitching frequencies were 1.46 and 2.92 Hz, and the initial angles of attack were 5°, 10°, and 15°, respectively. The results indicate that the average lift coefficient of airfoil during the whole pitching period increased significantly, with the increase of angle of attack. Additionally, the average lift coefficient of an airfoil with a high-frequency pitching increased from 5.2% to 17.2%, compared with the low-frequency pitching (1.46 Hz). Meanwhile, there was a significantly weak sub-frequency amplitude of lift coefficient, where the influence degree increased with the increase of initial angle of attack. Therefore, the pitching frequency of airfoil dominated the fluctuation of lift coefficient during the pitching process. Specifically, there was a more severe fluctuation of lift coefficient, due to the outstandingly increased number of high-order sub-frequencies in the spectrum, as the initial angle of attack increased. As such, the anticlockwise vortex on the pressure surface was rolled up from the trailing edge of the airfoil to the pressure surface, and then developed into a reverse pressure gradient flow, thus forming positive vorticity, which was strongly interacted with the negative vortex that separated from the flow on the suction surface of the airfoil. Correspondingly, the pressure distribution changed drastically on the airfoil wall in this process, resulting in the large-amplitude fluctuation of the lift. The findings can provide a theoretical and engineering reference for the flow instability caused by the flutter of the airfoil in the fluid machinery, such as wind turbine.