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摘要: 深入理解低空复杂风环境, 推动基于非定常非均匀假设的低空空气动力学的发展, 对保障低空飞行安全具有重要的科学意义和应用价值. 本文阐述了低空非均匀非定常复杂风场的特点及成因, 总结了风洞模拟方法、气动响应理论及流动规律等方面取得的突出成果. 本文报告了他们建设的国际前沿的低空风洞——“风矩阵”, 该装置通过采用多风机阵列定制化设计非均匀非定常来流来模拟低空复杂风环境, 并展望当前该领域亟待解决的关键问题.Abstract: Deep understanding of complex low-altitude wind environments and promoting the development of low-altitude aerodynamics based on unsteady and non-uniform assumptions are of great scientific significance and practical value for ensuring the safety of low-altitude flight. This paper describes the characteristics and underlying causes of complex low-altitude wind fields that are non-uniform and unsteady, and summarizes the major advances in wind tunnel simulation methods, aerodynamic response theories, and flow mechanisms. The authors’ team has built an internationally cutting-edge low-altitude wind tunnel, the “Wind Matrix”. By adopting a multi-fan array, facility enables the customized generation of non-uniform and unsteady incoming flow to simulate complex low-altitude wind environments. Finally, the paper looks ahead to the key issues in this field that urgently need to be addressed.
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图 5 尖劈, 挡板, 表面粗糙程度单元(Aldereguía Sánchez C et al. 2023, Ludena et al. 2017)
图 6 一些典型的被动湍流格栅装置实物图. (a) 被动湍流格栅, (b) 分型格栅(Hearst 2015)
图 7 一些典型的阵风叶栅装置实物图. (a) 英国斯旺西大学风洞(Balatti et al. 2022), (b) 希腊雅典国立技术大学风洞(Manolesos et al. 2026), (c) 意大利米兰理工大学GVPM风洞(Fonte 2017)
图 8 一些典型的主动湍流格栅装置实物图. (a) 德国欧登堡大学风洞(Neuhaus 2022), (b) 加拿大多伦多大学风洞(Azzam & Lavoie 2023), (c) 美国约翰霍普金斯大学风洞(Rumple 2024)
图 9 一些典型的运动机翼装置实物图. (a) 美国马里兰大学水洞 (Biler et al. 2021), (b) 英国剑桥大学水洞 (Gehlert & Babinsky 2019), (c) 德国达姆施塔特工业大学风洞 (Widmann & Tropea 2017)
图 10 一些典型的旋转圆柱装置实物图. (a) 美国空军实验室水洞 (Rockwood & Medina 2020), (b) 美国戴顿大学水洞(Durgesh et al. 2026)
图 11 流动阻塞装置实物与示意图. (a) ~ (b) 美国陆军实验室MAWT风洞ARGGUS阵风发生装置(Stutz et al. 2022b); (c) ~ (d) 德国汉堡国防大学风洞阵风发生装置(Wood & Breuer 2025); (e) ~ (f)美国伊利诺伊大学大学香槟分校AFUWT风洞阵风发生装置(He et al. 2022)
图 12 风机矩阵实物图. (a) 瑞士西部应用科学与艺术大学风墙(Walpen et al. 2024), (b) 中国同济大学多风机阵列风洞(Cao et al. 2017), (c) 加拿大西安大略大学WindEEE风洞, (d) 中国电子科技大学深思实验室三维风洞
图 13 风机矩阵控制算法示意图. (a) 美国加州理工学院数据驱动建模(Stefan-Zavala et al. 2026), (b) 美国布法罗大学深度学习方法和DDPG方法 (Li et al. 2021)
图 14 风矩阵的构造及水平流模拟能力. (a) 风矩阵装置构造HFA 水平风机阵列VFA 垂直风机阵列SFA旋流风机阵列, (b) HFA生成的强湍流沿流向的演化, (c) HFA生成的风切变沿流向的演化(Wang et al. 2026)
图 15 最小域冲量理论示意图 (改自文献(Kang et al. 2018))
图 16 不同攻角下升力幅值随减缩频率的变化 (数据来自文献(Granlund et al. 2014))
图 17 (a) 实验装置示意图, (b) 定常升力系数傅里叶频谱(Ma et al. 2021), (c) 气动导纳幅值理论与试验对比图(Yang et al. 2017)
图 18 静止起步 (灰色) 与基准来流U0加速 (橙色) 工况的升力响应(Mulleners et al. 2017)
图 19 在UMD拖曳水槽中的“正弦平方阵风”作用下的实验结果, 实验模型为攻角α = 0°、10°和20°的平板机翼, 穿越阵风比$ \sigma $ = 0.5的阵风区域. (a) “正弦平方阵风”速度剖面, (b)升力系数CL随时间变化的历程, (c) ~ (e)对应(b)中标记时刻的流场结构(Biler & Jones 2020)
图 20 阵风因子对气动特性的影响. (a) 涡量分布云图, (b) 最大升力系数, (c) LEV垂直于翼面的位置, (d) LEV脱落角(注: t*表示翼型穿过阵风区域的对流时间, Bonnet et al. 2024)
图 22 减缩频率对(a)流场特性(Du et al. 2024)和(b)气动特性的影响(Young & Smyth 2021)
图 21 雷诺数对气动特性的影响, 改编自文献(Gementzopoulos et al. 2022)
图 25 翼型攻角(a)和涡阵风半径(b)对气动响应及流场结构的影响(Lopez-Doriga et al. 2025)
图 24 不同阵风作用下CL及诱导攻角随对流时间的演化对比. (a1), (b1)不同阵风因子横向阵风; (a2), (b2)涡阵风($ \sigma $= 1)在不同横向位置 Δy/c 条件下的响应(Biler et al. 2021)
图 26 翼型弯度(a)与厚度(b)对涡阵风气动响应及流场结构的影响(Lopez-Doriga et al. 2025)
图 27 正弦轴向阵风工况下, 0.6倍桨盘半径位置的(a)稳态与动态推力、(d)诱导速度 (数据来自原始及改进Øye 动态入流模型)、(b)、(e)对应试验测量与(c)、(f) FVWM仿真(Berger et al. 2022)
图 28 需要对动态入流模型进行修正的几种尾流形态(Zhao et al. 2004)
图 29 悬停情况下, Harrington旋翼受轴向阵风影响下旋翼攻角和尾流涡结构的演化过程(Narayanan & Govindarajan 2024)
图 30 悬停情况下, Harrington共轴旋翼受离散侧向阵风影响下尾流涡结构的演化过程(Narayanan & Govindarajan 2024)
图 31 旋翼遭遇不同强度锐边阵风 (a) 计算模型 (b) 不同阵风因子下全周期拉力响应 (c) 旋翼阵风遭遇全过程涡结构的时间演化(Liu et al. 2026)
图 32 旋翼气动载荷随阵风因子的变化. (a) 阵风工况与定常来流推力系数之比, (b) 推力系数标准差(Finnemore et al. 2026a)
图 33 左: 在4 Hz连续阵风下, 不同旋翼转速的旋翼推力功率谱密度; 右: 旋翼下游0.2倍桨半径处 y-z平面流场湍动能分布: (a) 稳态来流, (b) 连续阵风 (Finnemore et al. 2026a)
图 34 (a) 基于涡管模型对旋翼机的尾流进行三维建模(b)涡管12方位基准点(Park et al. 2023a)
图 35 APC四旋翼无人机遭遇离散侧阵风时尾流涡的演化过程(Narayanan & Govindarajan 2024)
表 1 水平风的垂直切变(崔海洋 等 2024)
强度等级 风切变数值标准/
(海里·hr−1·30 m−1)风切变数值标准/
(m·s−1·30 s−1)风切变数值标准/
(s−1)对飞行的影响 轻度 ≤ 4 0 ~ 2 0 ~ 0.07 飞行航迹和空速稍有变化 中度 5 ~ 8 2.1 ~ 4 0.08 ~ 0.13 对飞机操纵造成很大的困难 强烈 9 ~ 12 4.1 ~ 6 0.14 ~ 0.20 有使飞机失去操纵的危险 严重 > 12 > 6 > 0.20 造成严重的危害 
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表 2 被动和主动的风洞模拟方法对比
类别 代表方法 基本实现思路 主要控制能力 可模拟特征 被动方法 尖劈、粗糙元、挡板、
被动格栅通过固定几何构件对来流产生
阻塞, 剪切层发展无主动控制能力 平均速度剖面、湍流强度、
积分尺度、能量谱主动方法 阵风叶栅、主动格栅、运动
翼型、旋转圆柱、风墙等动过电机驱动的随机或周期性
运动, 对流动施加时间变化扰动时间和空间可控 非定常、非均匀流动,
低频大尺度结构
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表 3 近年来的阵风叶栅装置主要结构参数
机构 试验段尺寸
(宽 × 高 × 长, m)流速/
(m·s−1)叶栅参数 摆动角
度/°摆动频
率/Hz阵风类型 典型参数 (范围) 米兰理工大学 (Fonte et al. 2016) 4 × 3.84 × 6 3 ~ 55 NACA 0012, $ N=6 $
$ c=0.4\; \text{m} $, $ \mathrm{AR}=8.9 $6 ~ 12 最大5 横向: 离散
(1−cos)、连续
(正弦)$ {U}_{\infty }=35\; \text{m/s} $,
$ \mathrm{GR}=0.04 \sim 0.087 $,
$ k=0.025 $代尔夫特大学 (Lancelot
et al. 2017)2.85 × 2.85
(开口)最大 35 NACA 0014, $ N=2 $
$ c=0.3\; \text{m} $, $ \mathrm{AR}=9.6 $2.5 ~ 10 0.6 ~ 5 横向: 离散
(1−cos)、连续
(正弦)$ {U}_{\infty }=15 \sim 25\; \text{m/s} $,
$ \mathrm{GR}=0.014 \sim 0.017 $,
$ k=0.0377 \sim 0.1884 $布里斯托大学 (Wood et al. 2017) 2.14 × 1.525 × 3.2 最大60 NACA 0015, $ N=2 $
$ c=0.3\; \text{m} $, $ \mathrm{AR}=7.1 $最大30 最大20 横向: 离散
(1−cos)、连续
(正弦)、随机$ {U}_{\infty }=8 \sim 24\; \text{m/s} $,
$ \mathrm{GR}=0.014 \sim 0.23 $,
$ k=0.0377 \sim 0.1884 $缅因大学 (French et al. 2021) 0.75 ×
0.75 × 2最大约24 NACA 0018, $ N=2 $
$ c=0.15\; \text{m} $, $ \mathrm{AR}=5 $15 ~ 45 0.5 ~ 2 流向: 离散、连续 $ {U}_{\infty }=9 \sim 18\; \text{m/s} $,
$ \mathrm{GR}=0.083 \sim 0.22 $,
$ k=0.013 \sim 0.105 $北京航空航天大学 (Wang & Feng 2022) 1 × 1.2 × 18
(水洞)最大1 NACA 0015, $ N=2 $
$ c=0.24\; \text{m} $, $ \mathrm{AR}=2.5 $4 ~ 6 小于1 横向: 连续
(正弦)
流向: 连续
(正弦)$ {U}_{\infty }=0.5\; \text{m/s} $,
$ {\mathrm{G{R}}}_{{\mathrm{v}}}=0.02 \sim 0.09 $,
$ {\mathrm{G{R}}}_{{\mathrm{u}}}=0.025 \sim 0.1 $,
$ k=0.2 \sim 0.8 $中东科技大学 (Yigili 2022) 0.34 ×
0.34 × 1最大25 NACA 0015, $ N=2 $
$ c=0.08\; \text{m} $, $ \mathrm{AR}=4.1 $8 ~ 16 2.5 ~ 10 横向: 离散、连续
流向: 离散、连续$ {U}_{\infty }=5 \sim 15\; \text{m/s} $,
$ {\mathrm{G{R}}}_{{\mathrm{v}}}=0.04 \sim 0.14 $,
$ {\mathrm{G{R}}}_{{\mathrm{u}}}=0.01 \sim 0.03 $,
$ k=0.06 \sim 0.5 $斯旺西大学 (Balatti 2023) 1.5 × 1 × 2.36 10 ~ 50 NACA 0015, $ N=2 $
$ c=0.2\; \text{m} $, $ \mathrm{AR}=7.5 $5 ~ 12 最大14 横向: 离散
(1−cos)、连续
(正弦)、自定义$ {U}_{\infty }=10 \sim 26\; \text{m/s} $,
$ \mathrm{GR}=0.01 \sim 0.15 $
$ k=0.06 \sim 0.88 $亚利桑那大学 (Nietzel 2024) 0.91 × 1.22 × 3.66 最大80 NACA 0015, $ N=2 $
$ c=0.174\; \text{m} $, $ \mathrm{AR}=6.9 $5 ~ 20 10 ~ 50 横向: 离散
(1−cos)、连续
(正弦)、随机$ {U}_{\infty }=6 \sim 25\; \text{m/s} $,
$ \mathrm{GR}=0.005 \sim 1 $雅典国立技术大学 (Manolesos
et al. 2026)1.8 × 1.4 × 3.2 最大60 NACA 0015, $ N=4 $
$ c=0.2\; \text{m} $, $ \mathrm{AR}=7.0 $最大20 最大20 横向: 离散
(1−cos)、
自定义$ {U}_{\infty }=10 \sim 20\; \text{m/s} $,
$ \mathrm{GR}=0.014 \sim 0.23 $,
$ k=0.31 \sim 1.26 $
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表 4 近年主动湍流格栅装置主要结构参数
机构 试验段尺寸
(宽 × 高 × 长, m)流速/
(m·s−1)格栅数
(行 × 列)格栅尺寸
M/mm最大雷诺数
$ {\mathrm{R{e}}}_{\lambda } $湍流强度 加利福尼亚大学尔湾
分校 (Marti et al. 2017)0.15 × 0.15 × 2 16 8 × 8 30 717 3.92% ~ 25.1% 乔治亚理工 (Fries et al. 2017) 0.146 × 0.146 × 1.372 15 ~ 30 5 × 6 24.1 1242 — 新墨西哥州州立大学
(Talavera & Shu 2017)1.2 × 1.2 × 14.6 最大35 6 × 6 190 — 0.5% ~ 8% 斯坦福大学 (Quinn
et al. 2017)1 × 0.82 × 1.73 最大50 7 × 8 100 — — 格勒诺布尔阿尔卑斯
大学 (Mora et al. 2019)0.75 × 0.75 × 4 5 ~ 50 8 × 8 100 50 ~ 200
(全开静止)
200 ~ 950
(三重随机)2% ~ 10%
12.5% ~ 15%欧德堡大学 (Neuhaus
et al. 2021)3 × 3 × 6 最大42 (闭口),
32 (开口)20 × 20 轴
(80个电机)140 14000 — 多伦多大学 (Azzam & Lavoie 2023) 1.2 × 0.8 × 5 最大 20 × 30
(双层, 每层10 × 15,
间距40 mm)80 486 — 南安普顿大学 (Thompson 2024) 1.2 × 1 × 2.4 最大10 11 × 13 85 760 12.6% ~ 19.6% 怀俄明大学 (Rumple 2024) 0.61 × 0.61 × 1.22 最大33 20 × 20
(双层, 每层10 × 10,
间距76 mm)106 — 0.4% ~ 11% 挪威科技大学
(Kidal 2025)2.71 × 1.8 × 11 最大30 18 × 10 101.6 × 71.12 — —
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表 5 近年运动机翼装置主要结构参数
机构和设施 试验段尺寸
(宽 × 长 × 高, m)相对流速/
(m·s−1)机翼尺寸 实验条件 产生流动 研究问题 达姆施塔特工业大学 (Widmann & Tropea 2017) 0.45 ×
0.45 × 2
(风洞)0 ~ 68 平板, 弦长120 mm,
厚度5 mmRe = 10 000 ~ 80 000
k = 0.25
$\alpha $ = $ 0^{\circ } \sim{30}^{\circ } $前缘涡 $ {\mathrm{Re}} $对俯仰平板前缘涡生成
的影响剑桥大学 (Corkery
et al. 2018)1 × 1 × 9
(水槽)0.4 平板, 弦长120 mm, 展长480 mm, 厚度
4 mmRe = 20 000
GR = 1
$ \alpha $ = ${0}^{\circ } $阶跃型
横阵风Küssner
模型修正伊斯坦布尔科技大学 (Zaloglu et al. 2020) 1.01 × 0.79
(水洞)0.1 NACA 0012 弦长100 mm, 展长
300 mm
平板, 弦长100 mm, 展长400 mm,
厚度5 mmRe = 10 000
GR = 0.3 ~ 1
f = 0.25 ~ 0.5 Hz连续涡阵风或瞬态
涡阵风涡阵风气
动响应马里兰大学 (Biler et al. 2021a) 1.5 × 1 × 7
(水槽)0.8 平板, 弦长76.2 mm, 展长304.8 mm,
厚度3.28 mmGR = 0.5 ~ 1.5
$\alpha $ = $ {0}^{\circ }\sim{45}^{\circ } $离散正弦型
横阵风大阵风因子横阵风和涡阵风对气动影响的对比 北京航空航天大学 (Feng & Wang 2014) 1 × 1.2 × 18
(水洞)0.2 NACA 0012, 弦长120 mm, 展长
600 mm$ {f}_{{\mathrm{g}}}=0.11\;\text{Hz} $ (阵风频率);
$ {f}_{{\mathrm{m}}} $ = 0.055 ~ 0.22 Hz
(俯仰频率), $ {\alpha }_{{\mathrm{m}}}={4}^{\circ } $
(最大迎角); $ {f}_{{\mathrm{m}}}=0.11 \; \text{Hz} $
(俯仰频率), $ {\alpha }_{{\mathrm{m}}}={24}^{\circ } $连续正弦型
横阵风Theodorsen和Sears模型
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表 6 近年多风机阵列装置主要结构参数
机构 风扇大
小/mm阵列规模 成风尺寸
(宽 × 高, m)最大速度/
(m·s−1)应用方向 流场/阵风能力 控制策略/
算法西安大略大学 (Hangan 2014) 800 15 × 4 14 × 5
(内舱直径25 m)16 (龙卷风) 35 (下击暴流) 31 (直流) 复杂风场生成, 城市风场表征, 风力发电机优化 龙卷风、下击暴流、直流、剪切流 复杂开环控制 布法罗大学 (Li et al. 2021) 250 8 × 8 1 × 1.2 20 下击暴流风
场模拟风墙响应频率最大
12 Hz; 流向阵风6 Hz, 阵风因子0.14深度强化学习, 全理解
深层网络瑞士西部应用科学与艺术大学 (Walpen et al. 2023) 80 36 ×
24 × 22.88 × 1.92 16 模拟大气扰动生成, 无人机抗风研究 均匀、水平/垂直剪切、点阵; 连续阵风 (正弦0.2 Hz, 左右同向/异相); 随机 五孔探针
测量反馈同济大学 (Cao et al. 2024) 270 10 × 12 1.5 × 1.8 18 (有阻尼段) 24 (无阻尼段) 大气边界层模拟, 剪切、速度突变流动 剪切流动; 瞬态加/减速流动 (12 ~ 17 m/s用时0.3 ~ 0.6 s; 连续 (简谐) 阵风, 动态范围 < 3 Hz 开环控制, 预先设定输
入信号哈尔滨工业大学深圳 (Li
et al. 2024)40 10 × 10 0.4 × 0.4 12 风墙流场表征 均匀流动 开环控制, 均匀占空比 深圳技术大学 (Liu et al. 2024) 80 40 × 40 3.25 × 3.25 12.5 无人机抗风
性测试均匀流动; 脉冲流动: 静止−全速响应2 s; 全速−静止响应10 s 开路脉冲宽度调制 加州理工学院 (Stefan-Zavala et al. 2026) 120 10 × 10 1.2 × 1.2 11 火星无人机测试, 风墙控制算法 均匀、单行、缺行、自由剪切、间行、随机 数据驱动建模 (LASSO线性回归) 电子科技大学深圳高等研究院 (Wang
et al. 2026)300 9 × 9 3 × 3
(舱体直径10 m)50 无人机抗风
性测试三维多物理场风、龙卷风、下击暴流 分布式控制
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表 7 典型线性气动模型的理论基础及适用性对比
模型类别 代表模型 理论假设与建模基础 来流/激励类型 适用范围 局限性 线性定常模型 Kutta-Joukowski/
薄翼理论二维薄翼、无黏势流、小攻角 定常均匀流 基础升力估计 无法描述非定常与分离 线性非定常模型 Theodorsen 1935 二维薄翼、无黏势流、小扰动、频域函数 均匀流 + 翼型
简谐运动颤振、气动弹性分析 不考虑阵风输入 线性非定常模型 von Kármán &
Sears 1938二维薄翼、势流、涡系分解、连续尾流 任意加速运动 一般非定常升力问题 尾流积分复杂 横向阵风模型 Sears 1941 二维薄翼、势流、小扰动、正弦阵风输入 横向阵风 阵风升力响应
分析仅适用于二维理想阵风 流向阵风模型 Isaacs 1945/ Greenberg 1947 二维薄翼、小攻角、附加质量、尾流耦合 流向阵风 来流脉动主导
问题物理机理较复杂 三维非定常模型 Graham 1971 薄升力面理论、双波数展开、小扰动 三维湍流阵风 三维机翼气动
响应数学形式复杂 三维导纳模型 Massaro & Graham 2015 频谱分析、统计湍流假设、展弦比效应 三维湍流场 气动导纳分析 依赖湍流统计
模型高阶非定常模型 Atassi 1984/ Goldstein &
Atassi 1976薄翼、二阶摄动、阵风畸变、弱非线性 周期阵风 高精度非定常气动分析 仍基于小扰动
假设
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