揭示小型四旋翼下洗流的湍流结构与经典射流规律的契合性。
The Structure of Merging Turbulent Jets Beneath a Small Quadrotor

- 通过粒子图像测速法,沿对角和前旋翼截面测量下洗流结构。
- 合并后5倍臂长处形成单柱流,13倍臂长处符合经典射流自相似性。
- 湍流应力具双峰特征,适合研究多旋翼编队与低雷诺数流动者参考。
悬停四旋翼的下洗尾迹决定了飞行器性能及多旋翼编队的安全间距。以往测量多聚焦平均流,采用单点测速、体积追踪或部分旋翼平面切片。对于小型四旋翼(如臂长46 mm的Crazyflie 2.1),其合并尾迹的高阶湍流统计特性及其与经典射流标度的关系仍未明确,尤其在低雷诺数范围。本文通过粒子图像测速(PIV)系统研究了沿对称轴对角切面及相邻旋翼前切面的下洗流。四个旋翼射流在$z/l \approx 5$处合并为单一流柱,此后平均速度剖面逐步趋近经典圆射流自相似形式,并在$z/l \approx 13$处以局部中心线速度和半宽归一化后实现坍缩。中心线衰减与半宽增长符合经典标度律,有效源直径$D_\text{eff} = 2.29\,l$,有效雷诺数$Re_{D_\text{eff}} = 3 \times 10^4$,处于经典射流标度成立的最低范围,但扩散与衰减常数仍在典型圆射流范围内。两组截面分析表明,湍流法向应力在整个测量域内仍保持源自四旋翼源的双峰、切面依赖特征。
原文摘要 · Abstract (English)
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.
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