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针对旋翼自由尾迹分析的计算效率问题,对快速多极展开算法(Fast multipole method,FMM)在基于直线涡元的尾迹互诱导速度计算中的应用开展了研究。分别构建了悬停和前飞状态下诱导速度多极展开计算的定义域;在进行远场诱导速度计算时,将直线涡元等效为涡粒,推导了诱导速度的多极展开表达式。通过对悬停和前飞状态下旋翼尾迹中涡元诱导速度的计算,分析了该方法的加速特性和准确性。在此基础上,采用多极展开算法求解了旋翼模型在悬停和前飞状态下的自由尾迹几何形状和桨盘诱导入流分布,并与直接计算结果和实验数据进行了对比,表明FMM算法在提高计算效率的同时能够保持较高的精度。
Aiming at the computational efficiency of rotor free wake analysis, the application of fast multipole method (FMM) in the calculation of wake mutual induction velocity based on linear vortex was studied. The domain of induced multi-polar velocity in hovering and pre-fly state is constructed respectively. In the calculation of far-field induced velocity, the straight-line vortex is equivalent to the vortex particle, and the multi-polar expansion expression of induced velocity is derived. Based on the calculation of vortex induced velocity in the wake of hovering and pre-flight, the acceleration characteristic and accuracy of this method are analyzed. On this basis, the multi-pole expansion algorithm is used to solve the free wake geometry and the induced flow distribution of the rotor blade in the hovering and pre-fly state. The results are compared with the direct calculation and experimental data. Improve computational efficiency while maintaining high accuracy.