Abstract: In agricultural aviation, quantitative acquisition of wind field (flow field) velocity distribution is important for singlerotor helicopterassisted pollination operations and pesticide application efficiency improvement. As a complement to the wind field computational fluid dynamics simulation, field or laboratory measurement methods, this paper applies a semianalytical theoretical method to rapidly and completely calculate the singlerotor flow field velocity. Based on the vortex ring model, the trailing vortex by the tip of the helicopters highspeed rotating propeller is equated to a vortex ring, and the wake vortices system under the propeller disk is equated to a cylindrical vortex surface formed by the continuous superposition of vortex rings. The wake shape is judged according to the motion state, and the vortex ring position and radius are determined by the fixed wake or predetermined wake, and the velocity of each point in helicopter rotor space is calculated analytically or semianalytically by the vortex ring velocity induction equation. The comparison of the theoretical model with the computational fluid dynamics simulation and literature test data shows that the vortex ring model is simple and fast, and the calculation is completed in 2.8 s on an ordinary computer (CPU 2 GHz, memory 2 GB). The average error in radial direction is less than 1.71 m/s, the average relative error is less than 39.1%, the average error in axial direction is less than 2.26 m/s, and the average relative error is less than 54.6%. When hovering, the induced velocity increases from the center to the tip of the rotor. In forward flight, the higher the leveling speed, the lower the induced velocity, and the lower the forward flight speed, the airflow outside the slipstream below the rotor changes from upwash to horizontal flow to downwash. The main factors affecting the flow field are forward flight speed, rotor radius, gross weight of the aircraft, and air density in that order. This model and results can provide a quick method and reference for quantitative calculation of rotor wind field to assist pollination operation and field application nozzle arrangement.

Key words: singlerotor helicopter, rotor flow field, vortex ring, impact factors of flow field； agricultural aviation

摘要： 农业航空领域中，定量获取风场(流场)速度分布对单旋翼直升机辅助授粉作业、农药施用效率提升具有重要意义。基于此提出一种半解析理论方法能够快速完整计算单旋翼流场速度。以涡环模型为基础，将农用直升机旋转桨盘下的尾涡系等效为涡环连续叠加所形成的圆柱涡面，再由涡环速度诱导公式半解析计算直升机旋翼空间各点速度。理论模型与仿真和文献试验数据比较，结果表明：涡环模型简单快速，普通计算机(CPU 2 GHz，内存2 GB)上2.8 s完成计算；悬停时与计算流体力学仿真结果下洗速度径向平均误差小于1.9 m/s，平均相对误差小于39.1%，轴向平均误差小于2.26 m/s，平均相对误差小于54.6%；悬停时，诱速从中央往桨尖递增；前飞时，平飞速度越大诱速越小；流场主要影响因素依次为前飞速度、旋翼半径、飞机总重、空气密度。为定量计算农用直升机旋翼风场、辅助授粉作业和田间施药喷头布置提供一种快速方法和参考。

关键词: 农用单旋翼直升机, 流场计算, 涡环模型, 流场影响因素, 农业航空