高超声速再入飞行器气动布局多目标优化

樊博璇; 陈桂明; 曹逸群

doi:10.13700/j.bh.1001-5965.2021.0566

高超声速再入飞行器气动布局多目标优化

doi: 10.13700/j.bh.1001-5965.2021.0566

樊博璇^{1, 2, ,},
陈桂明¹,
曹逸群²

1.
火箭军工程大学，西安 710025
2.
火箭军装备部驻西安地区第一军事代表室，西安 710025

基金项目: 国家自然科学基金(71601180)

详细信息

通讯作者:
E-mail：1092442646@qq.com

中图分类号: V221⁺.3；TB553
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出版历程
- 收稿日期: 2021-09-23
- 录用日期: 2022-01-05
- 网络出版日期: 2022-02-14
- 整期出版日期: 2023-07-31

Multi-objective optimization of aerodynamic layout for hypersonic reentry vehicle

FAN Boxuan^{1, 2
, ,},
CHEN Guiming¹,
CAO Yiqun²

1.
Rocket Army Engineering University，Xi’an 710025，China
2.
The First Military Representative Office of Rocket Army Equipment Department in Xi’an，Xi’an 710025，China

Funds: National Natural Science Foundation of China (71601180)

More Information

Corresponding author: E-mail：1092442646@qq.com

摘要

摘要:
气动布局的多目标优化是飞行器设计中的关键技术。提出一种新的高超声速再入飞行器气动外形参数的多目标优化方法，证明外形优化对高超声速流下飞行器性能的影响。通过实例仿真对飞行器所受阻力和升力对制导性能影响进行详细验证分析，将飞行器落点圆概率偏差、末速大于500 m/s的占比、最大飞行过载小于60g的占比这3个性能指标作为优化目标，将升力特性作为中间参数，将气动布局优化问题分解为2个子问题，通过基于搜索算法的升力特性优化和基于改进的模拟退火算法的外形参数优化，减少优化计算时间、提升计算效率、实现对飞行器主体和襟翼的气动布局优化、获得高超声速流下的最佳飞行器外形。仿真结果表明：在确定的约束条件下，优化算法增加了飞行器在超音速流下的气动升力，有效提高了升阻比。在不影响最大飞行过载的前提下，优化后的飞行器表现出更高的气动性能，显著提升了命中精度，同时末速也满足指标要求，制导系统性能得到有效改善。
- 高超声速再入飞行器 /
- 气动布局 /
- 升力特性 /
- 模拟退火组合优化算法 /
- 优化设计
Abstract:
Multi-objective optimization of aerodynamic layout is a key technology in aircraft design. A new multi-objective optimization method is proposed for aerodynamic shape parameters of hypersonic reentry vehicle, and then the influence of the method on the performance of hypersonic reentry vehicle is proved. Through example simulation, the influence of drag and lift on guidance performance is verified and analyzed in detail, with 3 performance indicators, including circular error probable of aircraft landing point, proportion of landing speed greater than 500 m/s, and proportion of maximum flight overload less than 60g, set as the optimization objective. By taking lift characteristics as intermediate parameters, the aerodynamic layout optimization problem divided into two sub problems. Through the lift characteristic optimization based on search algorithm and the shape parameter optimization based on an improved simulated annealing algorithm, the optimization calculation time is reduced, the calculation efficiency is improved, thus optimizing the overall aerodynamic layout of the main body and flap of the aircraft, and obtaining the best aircraft shape under hypersonic flow. The simulation results show that under determined constraints, the optimization algorithm increases the aerodynamic lift of the aircraft under supersonic flow and effectively improves the lift drag ratio. On the premise of not affecting the maximum flight overload, the optimized aircraft shows higher aerodynamic performance, and significantly improved hit accuracy, with the landing speed in compliance with the index requirements, and the performance of the guidance system effectively improved.
- hypersonic reentry vehicle /
- pneumatic layout /
- lift characteristic /
- simulated annealing combinatorial optimization algorithm /
- optimal design

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图 1 高超声速再入飞行器外形三视图

Figure 1. Three views of hypersonic reentry vehicle

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图 2 飞行器无襟翼状态几何模型

Figure 2. Geometric model of aircraft without flap

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图 3 飞行器几何模型

Figure 3. Aircraft geometric model

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图 4 数值仿真对比

Figure 4. Comparison of numerical simulation

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图 5 残差相对偏差e

Figure 5. Relative error of residual e

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图 6 算法流程

Figure 6. Algorithm process

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图 7 标称条件下优化前后仿真曲线

Figure 7. Simulation curves before and after optimization under nominal conditions

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表 1 飞行器气动外形尺寸

Table 1. Aircraft aerodynamic dimensions

飞行器编号	$\vartheta $/(°)	$l$/mm	$\delta $/(°)	$h$/mm
1	7.5
2	7.5	400	45	60
3	7.5	400	45	85
4	7.5	400	60	60
5	7.5	400	60	85
6	7.5	600	45	60
7	7.5	600	45	85
8	7.5	600	60	60
9	7.5	600	60	85
10-18	8.5
19-27	9.5

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表 2 计算选取的飞行器无襟翼下气动特性状态

Table 2. Aerodynamic characteristic states of aircraft without flap selected for calculation

高度H/km	马赫数$Ma$	迎角$\alpha $ /(°)
80	29,28,27,26	10,9,8,7,5,4,3,2,1,0
70	28,27,26,25	10,9,8,7,5,4,3,2,1,0
60	27,26,25,24,23	10,9,8,7,5,4,3,2,1,0
50	26,25,24,23,22,21	10,9,8,7,5,4,3,2,1,0
40	26,25,24,23,22,21	10,9,8,7,5,4,3,2,1,0
30	26,25,24,23,22,21	10,9,8,7,5,4,3,2,1,0
25	23,21,20,18,16	13,12,10,9,8,7,5,4,3,2,1,0
20	20,19,18,17,16,15	13,12,10,9,8,7,5,4,3,2,1,0
15	16,14,13,12,10	13,12,10,9,8,7,5,4,3,2,1,0
10	14,13,12,11,10	13,12,10,9,8,7,5,4,3,2,1,0
5	8,7,6,5,4	16,15,13,12,10,9,8,7,5,4,3,2,1,0
0	5,4,3,2	20,18,16,15,13,12,10,9,8,7,5,4,2,0

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表 3 带襟翼飞行器气动特性计算结果

Table 3. Calculation results aerodynamic characteristic of aircraft with flap

高度H/km	马赫数$Ma$	迎角$\alpha $ /(°) （$\beta {\text{ = }}0^\circ $）	侧滑角$\beta $ /(°) （$\alpha {\text{ = }}0^\circ $）
80	28	−10,0,10	5,10
60	26	−10,0,10	5,10
40	25,23	−10,0,10	5,10
30	24,22	−10,0,10	5,10
20	17,15	−10,0,10	5,10
10	12,10	−10,0,10	5,10

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表 4 优化前后的设计变量取值

Table 4. Value of design variables before and after optimization

阶段	$\vartheta $ /(°)	$l$ /mm	$\delta $ /(°)	$h$ /mm
优化前	7.5	900	56	120
优化后	7.5473	864	58.1741	119.3

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表 5 优化前后的升阻特性

Table 5. Lift and drag characteristics before and after optimization

Ma	阻力系数		升力系数
Ma	优化前	优化后	优化前	优化后
1	0.557 3	0.558 9	0.263 4	0.288 5
2	0.430 1	0.431 1	0.217 8	0.240 0
4	0.243 0	0.243 6	0.143 6	0.160 2
6	0.187 4	0.188 1	0.126 0	0.143 0
8	0.169 4	0.170 6	0.106 5	0.123 6
10	0.151 5	0.152 9	0.094 5	0.113 1
12	0.131 3	0.132 2	0.057 5	0.073 8
14	0.158 1	0.159 3	0.099 2	0.113 1
16	0.168 3	0.169 5	0.110 4	0.124 2
18	0.153 5	0.154 7	0.087 5	0.096 8
20	0.123 3	0.124 4	0.110 4	0.121 8

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表 6 随机偏差取值范围

Table 6. Range of random deviation

随机偏差变量	取值范围
初始弹道倾角偏差$ \Delta {\theta _0} $/(°)	$[ - {0.4 },{0.4 }]$
大气密度偏差比例系数$ \Delta {P_\rho } $/%	$[ - 10 ,10]$
法向力系数偏差比例系数$ \Delta {P_{{\text{CN}}}} $/%	$[ - 15 ,15]$
轴向力系数偏差比例系数$ \Delta {P_{{\text{CA}}}} $/%	$[ - 15 ,15 ]$
配平迎角偏差$ \Delta {\alpha _{\text{T}}} $/(°)	$[ - {2.8 },{2.8 }]$
法向力系数常值偏差$ \Delta {\text{C}}{{\text{N}}_0} $	$ [ - 0.015,0.015] $
轴向力系数常值偏差$ \Delta {\text{C}}{{\text{A}}_0} $	$ [ - 0.015,0.015] $

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表 7 随机偏差变量的正态分布规律

Table 7. Normal distribution law of random deviation variables

随机偏差变量	正态分布规律
初始弹道倾角偏差	$ \Delta {\theta _0} \sim N\left( {0,\sigma _{{\theta _0}}^2} \right) $，$ {\sigma _{{\theta _0}}} = 0.4/3 $
大气密度偏差比例系数	$ \Delta {P_\rho } \sim N\left( {0,\sigma _{{P_\rho }}^2} \right) $，$ {\sigma _{{P_\rho }}} = 0.1/3 $
法向力系数偏差比例系数	$ \Delta {P_{{\text{CN}}}} \sim N\left( {0,\sigma _{{P_{{\text{CN}}}}}^2} \right) $，$ {\sigma _{{P_{{\text{CN}}}}}} = 0.15/3 $
轴向力系数偏差比例系数	$ \Delta {P_{{\text{CA}}}} \sim N\left( {0,\sigma _{{P_{{\text{CA}}}}}^2} \right) $，$ {\sigma _{{P_{{\text{CA}}}}}} = 0.15/3 $
配平迎角偏差	$ \Delta {\alpha _{\text{T}}} \sim N\left( {0,\sigma _{{\alpha _{\text{T}}}}^2} \right) $，${\sigma _{ {\alpha _{\text{T} } } } } = {2.8}/3$
法向力系数常值偏差	$ \Delta {\text{C}}{{\text{N}}_0} \sim N\left( {0,\sigma _{{\text{C}}{{\text{N}}_0}}^2} \right) $，$ {\sigma _{{\text{C}}{{\text{N}}_{\text{0}}}}} = 0.015/3 $
轴向力系数常值偏差	$ \Delta {\text{C}}{{\text{A}}_0} \sim N\left( {0,\sigma _{{\text{C}}{{\text{A}}_0}}^2} \right) $，$ {\sigma _{{\text{C}}{{\text{A}}_0}}} = 0.015/3 $

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表 8 优化前仿真数据统计

Table 8. Statistics of simulation data before optimization

落点偏差/km	落点偏差分布占比/%	末速/(m·s⁻¹)	末速分布占比/%	末弹道倾角/(°)	末弹道倾角分布占比/%	最大过载	最大过载分布占比/%
[0,0.1)	88.11	[0,200)	0	[−90,−70)	0	[20g,40g)	53.15
[0.1,0.2)	5.59	[200,300)	0	[−70,−55)	6.29	[40g,50g)	26.57
[0.2,0.5)	0.70	[300,400)	0	[−55,−40)	28.67	[50g,55g)	9.79
[0.5,1)	0	[400,500)	0	[−40,−30)	46.85	[55g,60g)	6.99
[1,3)	2.10	[500,600)	5.59	[−30,−20)	18.18	[60g,65g)	2.10
[3,∞)	3.50	[600,∞)	94.41	[−20,0)	0	[65g,∞)	1.40

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表 9 优化后仿真数据统计

Table 9. Statistics of simulation data before optimization

落点偏差/km	落点偏差分布占比/%	末速/(m·s⁻¹)	末速分布占比/%	末弹道倾角/(°)	末弹道倾角分布占比/%	最大过载	最大过载分布占比/%
[0,0.1)	88.61	[0,200)	0	[−90,−70)	1.27	[20g,40g)	53.16
[0.1,0.2)	8.23	[200,300)	0	[−70,−55)	6.96	[40g,50g)	24.05
[0.2,0.5)	1.27	[300,400)	0	[−55,−40)	29.11	[50g,55g)	11.39
[0.5,1)	0.63	[400,500)	0.63	[−40,−30)	46.20	[55g,60g)	6.33
[1,3)	0.63	[500,600)	3.80	[−30,−20)	16.46	[60g,65g)	3.80
[3,∞)	0.63	[600,∞)	95.57	[−20,0)	0	[65g,∞)	1.27

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表 10 制导性能评估结果

Table 10. Guidance performance evaluation results

类型	CEP /m	末速低于500 m/s 的占比/%	最大飞行过载
理想值	≤200	2	6g
优化前	526.8	0	3.7g
优化后	215.4	0.61	5.2g

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