﻿ 运输机尾流场的小型空投物资下落轨迹仿真
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 哈尔滨工程大学学报  2019, Vol. 40 Issue (2): 273-278  DOI: 10.11990/jheu.201708020 0

### 引用本文

GAO Jing, HONG Guanxin. The research on the track of light cargo airdrop under the influence of the wake flow field[J]. Journal of Harbin Engineering University, 2019, 40(2), 273-278. DOI: 10.11990/jheu.201708020.

### 文章历史

The research on the track of light cargo airdrop under the influence of the wake flow field
GAO Jing , HONG Guanxin
School of Aeronautic Science and Engineer, Beihang University, Beijing 100191, China
Abstract: This study aims to investigate the influence of airdrop trajectory under downwash flow field of transporter plane. Vortex lattice method based on potential flow theory is used to solve velocity distribution of the downwash flow field. An airdrop rigid dynamic model is established for trajectory simulation of small dropping supplies. Results show that the downwash flow field from the transporter causes the airdrop to move toward the flight direction of the transporter. Furthermore, deviation of the downwash flow on the dropping track is reduced when the plane flies faster.
Keywords: airdrop    transporter    downwash flow field    vortex lattice method    dynamic modeling    dynamic simulation    airdrop uajectory    downwash flow field

1 运输机尾流场求解

 Download: 图 1 某运输机气动力计算网格 Fig. 1 Lattice layout for a certain transport aircraft aerodynamic prediction

 $\left( {{\mathit{\boldsymbol{C}}_C} \times \mathit{\boldsymbol{ \boldsymbol{\varGamma} }} + {\mathit{\boldsymbol{V}}_\infty }} \right) \cdot \mathit{\boldsymbol{N}} = 0$ (1)

 ${\mathit{\boldsymbol{V}}_i} = {\mathit{\boldsymbol{C}}_{Vn}} \times \mathit{\boldsymbol{ \boldsymbol{\varGamma} }}$ (2)

2 空投物资动力学建模 2.1 空投模型描述

2.2 动力学坐标系定义

2.3 降落伞气动力求解

 $\left\{ \begin{gathered} {F_A} = \frac{1}{2}\rho V_A^2{S_A}{C_A} \hfill \\ {F_N} = \frac{1}{2}\rho V_N^2{S_N}{C_N} \hfill \\ \end{gathered} \right.$ (3)
 $\left\{ \begin{gathered} {V_A} = {w_1} \hfill \\ {V_N} = \sqrt {u_1^2 + v_1^2} \hfill \\ \end{gathered} \right.$ (4)
 ${\mathit{\boldsymbol{V}}_1} = \mathit{\boldsymbol{V}} + \mathit{\boldsymbol{\omega }} \times \mathit{\boldsymbol{r}} = {\left( {\begin{array}{*{20}{c}} {{u_1}}&{{v_1}}&{{w_1}} \end{array}} \right)^{\text{T}}}$ (5)

2.4 动力学方程

 $\left\{ \begin{gathered} m\frac{{{\text{d}}V}}{{{\text{d}}t}} = {\mathit{\boldsymbol{F}}_{{\text{aero}}}} + \mathit{\boldsymbol{G}} \hfill \\ \frac{{{\text{d}}\mathit{\boldsymbol{H}}}}{{{\text{d}}t}} = {\mathit{\boldsymbol{M}}_{{\text{aero}}}} \hfill \\ \end{gathered} \right.$ (6)

 $\left\{ \begin{gathered} m{\left( {\frac{{{\text{d}}V}}{{{\text{d}}t}}} \right)_b} = {\mathit{\boldsymbol{F}}_{{\text{aero}}, b}} + {\mathit{\boldsymbol{G}}_b} \hfill \\ {\left( {\frac{{{\text{d}}\mathit{\boldsymbol{H}}}}{{{\text{d}}t}}} \right)_b} = {\mathit{\boldsymbol{M}}_{{\text{aero}}, b}} \hfill \\ \end{gathered} \right.$ (7)

 $\left\{ \begin{gathered} m\frac{{{\text{d}}{\mathit{\boldsymbol{V}}_b}}}{{{\text{d}}t}} + {\mathit{\boldsymbol{\omega }}_b} \times {\mathit{\boldsymbol{V}}_b} = \hfill \\ {\mathit{\boldsymbol{F}}_{{\text{aero}}, b}} + {\mathit{\boldsymbol{G}}_b} \hfill \\ \frac{{{\text{d}}{\mathit{\boldsymbol{H}}_b}}}{{{\text{d}}t}} + {\mathit{\boldsymbol{\omega }}_b} \times {\mathit{\boldsymbol{H}}_b} = {\mathit{\boldsymbol{M}}_{{\text{aero}}, b}} \hfill \\ \end{gathered} \right.$ (8)

 $\left\{ \begin{gathered} \frac{{{\text{d}}{\mathit{\boldsymbol{V}}_b}}}{{{\text{d}}t}} = \hfill \\ \frac{1}{m}\left( {{\mathit{\boldsymbol{F}}_{{\text{aero}}, b}} + {\mathit{\boldsymbol{G}}_b}-{\mathit{\boldsymbol{\omega }}_b} \times {\mathit{\boldsymbol{V}}_b}} \right) \hfill \\ \frac{{{\text{d}}{\mathit{\boldsymbol{\omega }}_b}}}{{{\text{d}}t}} = \hfill \\ \mathit{\boldsymbol{I}}_b^{-1}\left( {{\mathit{\boldsymbol{M}}_{{\text{aero}}, b}}-{\mathit{\boldsymbol{\omega }}_b} \times {\mathit{\boldsymbol{I}}_b}{\mathit{\boldsymbol{\omega }}_b}} \right) \hfill \\ \end{gathered} \right.$ (9)

 $\begin{gathered} {\mathit{\boldsymbol{V}}_b} = {\left[{\begin{array}{*{20}{c}} u&v&w \end{array}} \right]^{\text{T}}} \hfill \\ {\mathit{\boldsymbol{\omega }}_b} = {\left[{\begin{array}{*{20}{c}} p&q&r \end{array}} \right]^{\text{T}}} \hfill \\ {\left( \mathit{\boldsymbol{I}} \right)_b} = \left[{\begin{array}{*{20}{c}} {{I_x}}&{-{I_{xy}}}&{-{I_{zx}}} \\ {-{I_{xy}}}&{{I_y}}&{ - {I_{yz}}} \\ { - {I_{zx}}}&{ - {I_{yz}}}&{{I_z}} \end{array}} \right] = \left[{\begin{array}{*{20}{c}} {{I_x}}&0&0 \\ 0&{{I_y}}&0 \\ 0&0&{{I_z}} \end{array}} \right] \hfill \\ \end{gathered}$ (10)
3 空投仿真算例

 Download: 图 5 空投物资运动平面的轨迹 Fig. 5 Path of airdrop on motion plane

 Download: 图 7 在考虑尾流场前后空投物资在x方向上的位移偏差 Fig. 7 Difference of displacement on x-axis between wake field on or off

 Download: 图 8 不同平飞迎角下空投物资的x方向的偏移量 Fig. 8 Displacement on x-axis with different angle of attack

 Download: 图 9 不同平飞速度下空投物资的x方向的偏移量 Fig. 9 Difference of displacement on x-axis between wake field on or off with different speed
4 结论

1) 运输机尾流场对空投物资的质心下落轨迹影响较大，对下落过程中空投物资的姿态影响不大。

2) 运输机尾流场会使空投物资下落轨迹向飞机飞行方向整体偏移，这种偏移影响随着运输机平飞迎角的增加而增加。

3) 在运输机飞行重量一定的情况下，空投时的平飞速度越大，尾流场对空投物资下落轨迹的偏移量反而越小。

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