使用高阶逆风通量差分裂格式的悬停旋翼流场数值模拟

Numerical Simulations for the Flowfield of Helicopter Rotors in Hovering Based on High-Order Upwind Flux-Difference Splitting Scheme

为减少Jameson二阶中心差分有限体积法导致的旋翼尾迹的数值耗散,将三阶逆风格式(MUSCL)与通量差分裂方法相结合,建立了一个三维雷诺平均N-S方程数值模拟悬停状态旋翼流场的方法。为了充分考虑旋翼尾迹对流场的影响,采用周期性边界条件和由动量理论导出的远场边界条件。为进一步减少尾迹数值耗散和便于添加上述边界条件,采用了嵌套网格方法。然后,进行了算例计算,给出了桨叶表面的压强分布,与可得到的试验数据及二阶中心差分方法的计算结果进行了对比,并针对几种不同桨尖形状的旋翼悬停流场进行计算,数值结果显示:后掠桨尖可减弱超临界流动。此外,还计算和分析了旋翼下方不同位置上的涡量分布。计算结果表明,本文方法能够有效地减少旋翼尾迹的数值耗散。

In order to reduce effectively the numerical dissipation of the rotor wake vorticity induced by Jameson's second-order cell-centered finite volume approach, with the combination of the third-order upwind scheme (MUSCL) and flux-difference splitting scheme, a numerical method based upon the solution of three-dimensional Reynolds-average N-S equations has been developed to simulate the flowfield around a lifting rotor in hovering. To incorporate the important effects of the rotor wake, the far-field boundary condition derived from the rotor momentum theory and the cyclic boundary condition have been used. The embedded grids methodology was adopted so as to weaken the numerical dissipation of the wake and be easy to apply the above mentioned boundary conditions. Several cases of the blade surface pressure distribution have been calculated using the present method and the second-order center difference. The calculated results were validated by comparing with available experimental data. Then flowfield simulations under rotor hovering conditions were performed for three different blade tip planforms. The numerical results demonstrate that the swept tips can suppress supercritical flow. Additionally, the vorticity contours were computed and the characteristics of distorted rotor wake were analyzed. It is shown that the present method can effectively reduce the numerical dissipation of the rotor wake.