基于浸入边界法的翼型俯仰振摆动态特性

为了探究翼型振摆运动时的动态特性以及升力波动形成机制，采用基于浸入边界法的自编求解器，对NACA0012翼型在1 000雷诺数作不同起始攻角、不同振摆频率、不同振摆幅值的俯仰振摆运动进行了直接数值模拟，并分析了升力系数的波动特性和其与流场演变的相关性。结果表明：翼型的高频振摆（2.92 Hz）较低频振摆（1.46 Hz）平均升力增加范围在5.2%～17.2%之间，且对于大初始攻角（15°）升力增加更为显著，增加17.2个百分点；翼型振摆过程中升力系数的波动趋势主要受翼型俯仰振摆频率由1.46 Hz增加至2.92 Hz的影响，压力面的流动分离及尾缘处负压梯度回流引起尾缘旋涡卷起后脱落是引起翼型压力波动的主要原因，并且进一步导致了翼型整体升力出现幅值较大，频率高于3 Hz次频的波动。研究结果为工程中风力机等流体机械翼型颤振引起的流动不稳定性研究提供理论参考和工程依据。

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.