﻿ 低空风切变系统建模及其对直升机飞行安全威胁定性分析
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Systematical modelling of low-altitude windshear and its qualitative threat analysis to helicopter flight safety
ZHAO Yanqin, CHEN Renliang
National Key Laboratory of Science and Technology on Rotorcraft Aeromechanics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Abstract: The model of three-dimensional low-altitude windshear with turbulence is systematically established, its threat to helicopter flight safety is comprehensively analyzed. A windshear model composed of microburst and atmosphere turbulence is developed. Without increasing the amount of calculation, a helicopter flight dynamic model integrated with wind velocity and windshear items is proposed, which optimizes the simulation precision of helicopter dynamic response through the windshear. Then a flight control system with attitude holding is synthesized into this model to correspond to the general helicopter flight state and to improve the response performance of helicopter. Following this, based on the characteristics of the windfield model, various flight velocities and windfield positions are selected and analyzed their relation between state changes and windfield. From the aspect of dynamics, the formula of response is derived theoretically with the vertical channel as the example. The results show that the turbulence mainly induces high frequency attitude response, while the windshear plays a dominant role in flight state influence, and the vertical downwind is the main inducement of threat. Based on the results, suggestions to avoid the windfiled threat are proposed.
Keywords: windshear    microburst    atmosphere turbulence    threat analysis    flight dynamics modelling    dynamic response

1 微下击暴流流场模型

 图 1 涡环法建模示意图 Fig. 1 Geometric schematic of ring-vortex model
1.1 涡环诱导速度场计算

 ${\phi _{\rm{v}}} = - \frac{\varGamma }{{2\pi }}({r_1} + {r_2})\frac{{0.788{k^2}}}{{0.25 + 0.75\sqrt {1 - {k^2}} }}$ （1）

 ${{v_x} = \frac{1}{{{r_M}}} \cdot \frac{{\partial {\phi _{\rm{v}}}}}{{\partial z}} \cdot \frac{{{x_M}}}{{{r_M}}}}$ （2）
 ${{v_y} = \frac{1}{{{r_M}}} \cdot \frac{{\partial {\phi _{\rm{v}}}}}{{\partial z}} \cdot \frac{{{y_M}}}{{{r_M}}}}$ （3）
 ${{v_z} = - \frac{1}{{{r_M}}} \cdot \frac{{\partial {\phi _{\rm{v}}}}}{{\partial {r_M}}}}$ （4）

 ${v_z} = \frac{\varGamma }{{2{R_{\rm{v}}}}} \cdot \frac{1}{{{{(1 + {{({z_M}/{R_{\rm{v}}})}^2})}^{1.5}}}}$ （5）

 $\overrightarrow {{O_r}N} = \lambda \overrightarrow {{O_r}M} \;\;\;{\kern 1pt} \lambda > 0$ （6）
 图 2 涡核示意图 Fig. 2 Schematic diagram of vortex core

 ${v_M} = \frac{{{v_N}}}{\lambda }$ （7）
1.2 地面风场建模

 $\left[ {\begin{array}{*{20}{l}} {{W_{Mx}}}\\ {{W_{My}}}\\ {{W_{Mz}}} \end{array}} \right] = \mathit{\boldsymbol{L}}({\phi _{\rm{v}}},{\theta _{\rm{v}}})\left[ {\begin{array}{*{20}{l}} {{v_{Px}}}\\ {{v_{Py}}}\\ {{v_{Pz}}} \end{array}} \right] + \mathit{\boldsymbol{L}}( - {\phi _{\rm{v}}}, - {\theta _{\rm{v}}})\left[ {\begin{array}{*{20}{l}} {{v_{Lx}}}\\ {{v_{Ly}}}\\ {{v_{Lz}}} \end{array}} \right]$ （8）

1.3 流场建模参数设置及其三维分布

 风切变特征参数 高频参数范围 模型参数 风切变尺度/m 1 830~3 660 1 800 最大水平风速变化(150 m处)/(km·h-1) 37~83 83.61 风速变化强度/(m·s-1·m-1) 0.016 7~0.026 7 0.01 7

 图 3 不同高度中心截面水平风与垂向风风速剖面 Fig. 3 Profile of horizontal and vertical wind velocities for various altitudes at central section

 图 4 不同方位侧向风风速剖面(h=300 m) Fig. 4 Profile of side wind velocity for various orientations(h=300 m)
1.4 风切变风场接口

 图 5 风切变强度计算示意图 Fig. 5 Diagram of windshear intensity calculation

 ${{p_{{\rm{gs}}}} = \frac{{\partial {W_{{\rm{s}}z}}}}{{\partial y}} = \frac{{{W_{{\rm{s}}bz}} - {W_{{\rm{s}}dz}}}}{{2R}}}$ （9）
 ${{q_{{\rm{gs}}}} = - \frac{{\partial {W_{{\rm{s}}z}}}}{{\partial x}} = - \frac{{{W_{{\rm{s}}cz}} - {W_{{\rm{s}}az}}}}{{2R}}}$ （10）
 $\begin{array}{*{20}{c}} {{r_{{\rm{gs}}}} = {r_{{\rm{gs1}}}} + {r_{{\rm{gs2}}}} = - \frac{{\partial {W_{{\rm{s}}x}}}}{{\partial y}} + \frac{{\partial {W_{{\rm{s}}y}}}}{{\partial x}} = }\\ {\frac{{{W_{{\rm{s}}dx}} - {W_{{\rm{s}}bx}}}}{{2R}} + \frac{{{W_{{\rm{s}}cy}} - {W_{{\rm{s}}ay}}}}{{2R}}} \end{array}$ （11）

 $\left[ {\begin{array}{*{20}{l}} {{p_{\rm{g}}}}\\ {{q_{\rm{g}}}}\\ {{r_{\rm{g}}}} \end{array}} \right] = {\mathit{\boldsymbol{L}}_{{\rm{SB}}}}\left[ {\begin{array}{*{20}{l}} {{p_{{\rm{gs}}}}}\\ {{q_{{\rm{gs}}}}}\\ {{r_{{\rm{gs}}}}} \end{array}} \right]$ （12）

 ${\mathit{\boldsymbol{W}}_{{\rm{sH}}}} = \frac{1}{4}({\mathit{\boldsymbol{W}}_{{\rm{s}}a}} + {\mathit{\boldsymbol{W}}_{{\rm{s}}b}} + {\mathit{\boldsymbol{W}}_{{\rm{s}}c}} + {\mathit{\boldsymbol{W}}_{{\rm{s}}d}})$ （13）

 $\left[ {\begin{array}{*{20}{c}} {{p_{{\rm{rel}}}}}\\ {{q_{{\rm{rel}}}}}\\ {{r_{{\rm{rel}}}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {p - {p_{\rm{g}}}}\\ {q - {q_{\rm{g}}}}\\ {r - {r_{\rm{g}}}} \end{array}} \right]$ （14）

 $\mathit{\boldsymbol{x}} = {\left[ {\begin{array}{*{20}{l}} u&v&w&{{p_{{\rm{ rel }}}}}&{{q_{{\rm{ rel }}}}}&{{r_{{\rm{ rel }}}}}&\phi &\theta &\psi \end{array}} \right]^{\rm{T}}}$

2 湍流模型及其三维扩展

2.1 二维平面大气湍流流场的生成

 图 6 旋翼面二维湍流场的生成示意图 Fig. 6 Schematic of two-dimensional turbulent flow field on rotor surface

 $L = NV\Delta t$ （15）

 $m = (n + 1 - k)\% N$ （16）

 $\begin{array}{*{20}{l}} {{x_{i,j}} = R + {r_j}{\kern 1pt} {\rm{cos}}{\kern 1pt} {\kern 1pt} {\psi _i}}\\ {{y_{i,j}} = {r_j}{\kern 1pt} {\rm{sin}}{\kern 1pt} {\kern 1pt} {\psi _i}} \end{array}$ （17）

xi, j可以计算得到桨叶气动中心所在横截线与两边交点EF处的紊流速度分别为UA(mi, j)、UB(mi, j)，且

 ${m_{i,j}} = \left( {n - \left\lfloor {\frac{{{x_{i,j}}}}{{L/N}}} \right\rfloor + 1} \right)\% N + 1$ （18）

 $\begin{array}{*{20}{l}} {{\mathit{\boldsymbol{W}}_{{\rm{T}}i,j}} = }\\ {\quad \;\;\;\frac{{{\mathit{\boldsymbol{U}}_A}({m_{i,j}})/{{(R + {y_{i,j}})}^2} + {\mathit{\boldsymbol{U}}_B}({m_{i,j}})/{{(R - {y_{i,j}})}^2}}}{{1/{{(R + {y_{i,j}})}^2} + 1/{{(R - {y_{i,j}})}^2}}}} \end{array}$ （19）

 图 7 叶素湍流速度与近桨尖处特征点对比 Fig. 7 Turbulence velocities of elements and rotor hub

2.2 三维扩展

 ${\mathit{\boldsymbol{W}}_{{\rm{Tf}}}} = \frac{{\frac{{{\mathit{\boldsymbol{U}}_A}({k_{\rm{f}}})}}{{l_A^2}} + \frac{{{\mathit{\boldsymbol{U}}_B}({k_{\rm{f}}})}}{{l_B^2}} + \frac{{{\mathit{\boldsymbol{U}}_M}({k_{\rm{f}}})}}{{l_M^2}} + \frac{{{\mathit{\boldsymbol{U}}_N}({k_{\rm{f}}})}}{{l_N^2}}}}{{1/l_A^2 + 1/l_B^2 + 1/l_M^2 + 1/l_N^2}}$ （20）

 ${{k_{\rm{f}}} = \left( {n - \left\lfloor {\frac{{{x_{\rm{f}}}}}{{L/N}}} \right\rfloor + 1} \right)\% N + 1}$ （21）
 ${\left\{ {\begin{array}{*{20}{l}} {l_A^2 = {{(R + {y_{\rm{f}}})}^2} + z_{\rm{f}}^2}\\ {l_B^2 = {{(R - {y_{\rm{f}}})}^2} + z_{\rm{f}}^2}\\ {l_M^2 = {{(R + {y_{\rm{f}}})}^2} + {{({z_{\rm{H}}} - {z_{\rm{f}}})}^2}}\\ {l_N^2 = {{(R - {y_{\rm{f}}})}^2} + {{({z_{\rm{H}}} - {z_{\rm{f}}})}^2}} \end{array}} \right.}$ （22）

3 飞行动力学模型

 $\mathit{\boldsymbol{\dot x}} = f(\mathit{\boldsymbol{x}},\mathit{\boldsymbol{\delta }},t)$ （23）

3.1 模型验证

 图 8 配平姿态角与飞行试验对比 Fig. 8 Comparison of trim characteristics of attitude angle with flight test
 图 9 配平操纵杆量特性与飞行试验对比 Fig. 9 Comparison of trim characteristics of control stick with flight test
 图 10 配平旋翼需用功率与飞行试验对比 Fig. 10 Comparison of trim characteristics of main rotor power required with flight test

3.2 增稳控制系统

4 飞行动力学仿真 4.1 无湍流的风切变场

 图 11 不同速度穿越微下击暴流的姿态角变化历程 Fig. 11 History of attitude angle change for various velocities through microburst
 图 12 不同速度穿越微下击暴流的地速及高度变化历程 Fig. 12 History of ground speed and height change for various velocities through microburst

 图 13 不同高度穿越微下击暴流的姿态角变化历程 Fig. 13 History of attitude angle change for various altitudes through microburst
 图 14 不同高度穿越微下击暴流的地速及高度变化历程 Fig. 14 History of ground speed and height change for various altitudes and height through microburst

 图 15 不同方位穿越微下击暴流的姿态角变化历程 Fig. 15 History of attitude angle change for various orientations through microburst
 图 16 不同方位穿越微下击暴流的地速历程 Fig. 16 History of ground speed change for various orientations through microburst

4.2 飞行器运动与风场关系推导

 ${\mathit{\boldsymbol{\dot V}}_{\rm{a}}} + {\mathit{\boldsymbol{\omega }}_{\rm{a}}} \times {\mathit{\boldsymbol{V}}_{\rm{a}}} = \mathit{\boldsymbol{A}}/m + \mathit{\boldsymbol{g}} - ({\mathit{\boldsymbol{\dot W}}_{\rm{a}}} + {\mathit{\boldsymbol{\omega }}_{\rm{a}}} \times {\mathit{\boldsymbol{W}}_{\rm{a}}})$ （24）

 $\begin{array}{l} {V_{{\rm{a}}z}} + {p_{\rm{a}}}{V_{{\rm{a}}x}} - {q_{\rm{a}}}{V_{{\rm{a}}y}} = g{\rm{cos}}{\theta _{\rm{w}}}{\rm{cos}}{\phi _{\rm{w}}} - {L_{\rm{a}}}/m + \\ {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {W_{{\rm{a}}z}} + {p_{\rm{a}}}{W_{{\rm{a}}x}} - {q_{\rm{a}}}{W_{{\rm{a}}y}} \end{array}$ （25）

 ${L_{\rm{a}}} \approx T = \frac{1}{2}\rho \pi {R^2}{(\varOmega R)^2}{C_T}$ （26）

 ${C_T} = F({\theta _0}) + \frac{1}{2}\kappa {a_\infty }\sigma \left( {\frac{{{V_{{\rm{a}}z}} - {W_{{\rm{a}}z}}}}{{\varOmega R}}} \right)$ （27）

 $\begin{array}{*{20}{l}} {{P_{{\rm{ const }}}} = \frac{1}{2}\rho \pi {R^2}(\varOmega R)2F({\theta _0}) - g{\rm{cos}}{\theta _{\rm{w}}}{\rm{cos}}{\phi _{\rm{w}}}}\\ {{P_{{\rm{ varia }}}} = \frac{1}{{4m}}\kappa {a_\infty }\rho \pi {R^2}(\varOmega R)} \end{array}$ （28）

 ${\dot V_{{\rm{a}}z}} - {\dot W_{{\rm{a}}z}} = - {P_{{\rm{ const }}}} - {P_{{\rm{ varia }}}}({V_{{\rm{a}}z}} - {W_{{\rm{a}}z}})$ （29）

 $({V_{{\rm{a}}z}} - {W_{{\rm{a}}z}})(t) = - \frac{{{P_{{\rm{ const }}}}}}{{{P_{{\rm{ varia }}}}}} + {P_{{\rm{ coef }}}}{{\rm{e}}^{ - {P_{{\rm{ varia }}}}^t}}$ （30）

 $\begin{array}{*{20}{l}} {{V_{{\rm{a}}z}} = {W_{{\rm{a}}z}} = 0{\kern 1pt} {\kern 1pt} {\kern 1pt} {\rm{m/s}}}\\ {T \approx mg{\kern 1pt} {\kern 1pt} {\rm{cos}}{\theta _{\rm{w}}}{\rm{cos}}{\phi _{\rm{w}}}} \end{array}$ （31）

 ${P_{{\rm{ const }}}} = 0$ （32）

 ${V_{{\rm{a}}z}}(t) = - {W_{{\rm{a}}z0}}{{\rm{e}}^{ - {P_{{\rm{ varia }}}}^t}} + {W_{{\rm{a}}z}}(t)$ （33）

4.3 叠加湍流的风切变场

 图 17 飞越含湍流的风切变俯仰角、地速变化历程 Fig. 17 History of pitch angle and ground velocity change through windshear with turbulence

5 结 论

1) 为捕捉风切变的切变项，在不增加计算量的前提下，发展了可适用于直升机飞行动力学的三维风切变风场模型，并在风场中加入了三维湍流模型，提高了直升机在风切变气流场中的动态响应计算精度。

2) 分析了不同风场位置、飞行速度等直升机的响应。在增稳系统的辅助作用下，水平风及侧向风对飞行安全威胁较小。垂直气流是直升机在微下击暴流中的主要威胁来源，可导致同等幅度的机体下降速度，且与机体飞行速度无关，因此，水平飞行速度越慢，下降高度越多，坠地威胁越强。

3) 遭遇风切变时，提高飞行高度以及向侧向远离风场中心可有效降低风场对直升机威胁。提高飞行高度可增加高度裕度，降低坠地可能性；向风场侧向规避可有效减弱水平风尤其是垂向风的影响，侧向风的威胁较弱。

4) 湍流与微下击暴流风场对直升机的影响相互独立，且湍流主要引起高频小幅姿态角的震荡，总体而言对直升机的威胁次于微下击暴流对速度等状态量的作用。

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http://dx.doi.org/10.7527/S1000-6893.2020.23413

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#### 文章信息

ZHAO Yanqin, CHEN Renliang

Systematical modelling of low-altitude windshear and its qualitative threat analysis to helicopter flight safety

Acta Aeronautica et Astronautica Sinica, 2020, 41(7): 123413.
http://dx.doi.org/10.7527/S1000-6893.2020.23413