发表机构
Brown University（布朗大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过PIV测量小型悬停四旋翼的下洗尾流，明确了四股旋翼射流的合并位置与自相似演化规律，验证了低雷诺数下其仍符合经典圆形射流标度律，并揭示了湍流正应力的双峰截面特征。
AI 中文摘要
悬停四旋翼飞行器的下洗尾流既决定着飞行器自身的性能，也关系到多旋翼编队的安全间距。此前的测量主要通过单点风速测量、体积跟踪或对旋翼系统局部进行平面切片的方式，表征了平均流场特性。合并尾流的高阶湍流统计特征，以及它们与经典射流标度律的关联，仍未得到明确解析，尤其是针对尺寸范围中低雷诺数端的小型四旋翼飞行器。\n本文开展了详细的粒子图像测速（PIV）研究，测量对象为悬停状态的Crazyflie 2.1四旋翼飞行器（臂长$l = 46$ mm），采样沿两个截面进行：一是沿四旋翼对称轴穿过旋翼的对角截面，二是穿过相邻旋翼的前旋翼截面。四股旋翼射流在$z/l \approx 5$的位置合并为单股柱形射流，在此之后，平均速度剖面逐渐趋近于经典圆形射流的自相似形式；当以当地中心线速度和半宽度进行标度时，剖面在$z/l \approx 13$的位置实现坍缩。\n中心线速度衰减和半宽度增长遵循经典标度律，有效源直径$D_\text{eff} = 2.29\\\\,l$，有效雷诺数$Re_{D_\text{eff}} = 3 \times 10^4$，处于经典射流标度律已被验证的雷诺数范围的下限，但其扩散和衰减常数仍在经典圆形射流的取值范围内。对两个截面的解析表明，在整个测量域内，湍流正应力保留着四旋翼源的双峰、截面相关的特征。
英文摘要
The downwash wake of a hovering quadrotor governs both the vehicle's own performance and the safe spacing of multi-rotor formations. Prior measurements have largely characterized the mean flow, using single-point anemometry, volumetric tracking, or planar cuts through part of the rotor system. Higher-order turbulent statistics of the merged wake, and how they relate to canonical jet scaling, have remained unresolved, particularly for small quadrotors at the low-Reynolds-number end of the size range. Here, we present a detailed particle image velocimetry (PIV) study of the downwash of a hovering Crazyflie 2.1 quadrotor (arm length, $l = 46$ mm), sampled along a diagonal cut, passing through rotors along the symmetry axis of the quadrotor, and a front-rotor cut, passing through adjacent rotors. The four rotor jets merge into a single column by $z/l \approx 5$, beyond which the mean velocity profiles progressively approach the canonical round-jet self-similar form, collapsing by $z/l \approx 13$ when scaled by the local centerline velocity and half-width. Centerline decay and half-width growth follow canonical scaling laws with an effective source diameter $D_\text{eff} = 2.29\,l$, effective Reynolds number $Re_{D_\text{eff}} = 3 \times 10^4$, at the low end of the range over which canonical jet scaling has been established, and spreading and decay constants nonetheless within the canonical round-jet range. Resolving both cuts shows that the turbulent normal stresses retain a bimodal, cut-dependent signature of the four-rotor source throughout the measurement domain.
Comments20 pages, 11 figures
