谐波平衡法在旋翼前飞绕流数值模拟中的应用研究

Application of harmonic balance method in forward flight simulation for helicopter rotors

采用谐波平衡方法,以Euler方程为控制方程,数值模拟了旋翼前飞绕流。由于旋翼前飞绕流的周期特性,流动变量可以展开为关于时间的傅里叶级数,从而将时域下的非定常流动控制方程转换为频域下的定常方程。采用现有的数值方法求得定常解即可得到旋翼绕流的非定常解。与传统的双时间推进法相比,谐波平衡法采用周期性边界条件,只需计算一片桨叶,因而极大地提高了非定常流动求解的计算效率。计算的压力分布、拉力系数均与实验值或双时间推进法的计算结果吻合良好。为了进一步提高计算效率,还实现了基于MPI(Message Passing Interface)的并行计算。

The unsteady flow around helicopter rotor in forward flight is simulated by using harmonic bal- ance method based on Euler equations. For the periodical characteristics in forward flight, the flow variables can be represented by Fourier series in time. Thus, the unsteady governing equations in time domain can be converted to steady equations in frequency domain, so the well-developed steady computational fluid dynam- ics（CFD） techniques can be used to solve the steady equations in frequency domain, and the unsteady solu- tion is obtained. The main advantage of the present method is that only one blade needs to be simulated by implementation of the periodical condition. Compared with the traditional dual-time stepping method, har- monic balance method improves unsteady calculation efficiency greatly. The calculated pressure distributions and thrust coefficients agree well with the results of experimental data or dual-time stepping method. Mes- sage passing interface（MPI） parallel computing technique is utilized to improve the computational efficiency further.