超声速风洞喷管冷却结构的多目标优化设计

杨洪涛; 游广飞; 徐亮; 阮麒成

doi:10.13224/j.cnki.jasp.20210590

超声速风洞喷管冷却结构的多目标优化设计

doi: 10.13224/j.cnki.jasp.20210590

1.
郑州机械研究所有限公司，郑州 450052
2.
西安交通大学机械制造系统工程国家重点实验室，西安 710049

基金项目: 国家自然科学基金（51876157）；陕西省自然科学基金（2019JM-096）

详细信息

作者简介:
杨洪涛（1989-），男，高级工程师，硕士，主要从事航空航天领域非标机电一体化装备设计研究

中图分类号: V211.74
计量
- 文章访问数: 129
- HTML浏览量: 42
- PDF量: 62
- 被引次数: 0
出版历程
- 收稿日期: 2021-10-16
- 网络出版日期: 2022-12-16

Multi-objective optimization design of supersonic wind-tunnel nozzle cooling structure

1.
Zhengzhou Research Institute of Mechanical Engineering Company, Limited，Zhengzhou 450052，China
2.
State Key Laboratory for Manufacturing Systems Engineering，Xi’an Jiaotong University，Xi’an 710049，China

摘要

摘要:
针对某风洞喷管提出了一种水冷结构，即在喷管前后段壁内设置了24组流道，而在喉部区域壁内错排布置扰流柱阵列。采用气热耦合-结构热分析的数值模拟方法对喷管整体结构的流动、换热、刚度性能进行了计算和分析。计算结果表明：冷却水量为1 kg/s时，与基础件相比，提出的冷却结构的概念件平均冷却效率提升0.68%，喉部等效应变减小5%左右。采用了响应面模型近似方法和多岛遗传算法对概念件进行了多目标优化计算，结果表明：冷却水量为2.1429 kg/s时，与概念件对比，优化件壁面最高温度可以降低1.6 K左右，喉部等效应变减小约10%。喷管冷却结构设计及其多目标优化方法为风洞喷管型面有效的热防护设计提供一定的参考。
- 超声速风洞喷管 /
- 多流道冷却结构 /
- 气热耦合-结构热分析 /
- 多目标优化设计 /
- 响应面模型近似方法
Abstract:
A cooling structure for nozzle of a wind tunnel was proposed, that is: 24 channels were set on walls of anterior and posterior segments of the nozzle while staggered pin-fin structure was set on wall of nozzle throat area. The numerical simulation method of the conjugated heat transfer-structural thermal analysis was used to calculate and analyze the fluid flow, heat transfer, and stiffness performances of the overall nozzle structure. The calculation results showed that under the cooling water mass flow rate of 1 kg/s, the averaged cooling efficiency of the proposed cooling structure of the conceptual nozzle was 0.68% higher than that of the basic structure, and equivalent elastic strain of throat area of the nozzle was reduced by around 5%. The response surface model approximation method and multi island genetic algorithm were used to perform multi-objective optimization calculation of the conceptual nozzle. The results showed that the maximum wall temperature of the optimized structure was about 1.6 K lower than that of the conceptual one under the cooling water mass flow rate of 2.142 9 kg/s, and equivalent elastic strain of throat area of the nozzle was reduced by around 10%. The cooling structure design of the nozzle and its multi-objective optimization method may provide a reference for an effective thermal protection design of nozzle of wind tunnel.

HTML

图 1 风洞喷管的几何模型^[15]

Figure 1. Geometric model of wind-tunnel nozzle^[15]

下载: 全尺寸图片幻灯片

图 2 风洞喷管壁面温度分布^[15]

Figure 2. Temperature distribution on wall of a wind-tunnel nozzle^[15]

下载: 全尺寸图片幻灯片

图 3 计算域网格绘制

Figure 3. Mesh generation for computational domain

下载: 全尺寸图片幻灯片

图 4 数值方法的验证

Figure 4. Validation of numerical method

下载: 全尺寸图片幻灯片

图 5 喷管壁面冷却的基础件和概念件模型

Figure 5. Basic nozzle and conceptual nozzle models for wall cooling

下载: 全尺寸图片幻灯片

图 6 固体域的非结构化网格

Figure 6. Unstructured mesh generation of solid domain

下载: 全尺寸图片幻灯片

图 7 多目标优化模型

Figure 7. Model of multi-objective optimization

下载: 全尺寸图片幻灯片

图 8 不同质量流量下概念件的流动换热性能比较

Figure 8. Flow and heat transfer performances comparison of conceptual nozzle under different mass flow rates

下载: 全尺寸图片幻灯片

图 9 响应拟合关联式误差

Figure 9. Error of response fitting correlation formulas

下载: 全尺寸图片幻灯片

图 10 喷管喉部区域壁面温度（Q=1 kg/s）

Figure 10. Temperature of nozzle throat wall （Q =1 kg/s）

下载: 全尺寸图片幻灯片

图 11 喷管壁面的应力、应变云图（Q=1 kg/s）

Figure 11. Stress and strain diagram of nozzle walls （Q=1 kg/s）

下载: 全尺寸图片幻灯片

图 12 目标参数与输入参数的关系

Figure 12. Relations between outputs and inputs

下载: 全尺寸图片幻灯片

图 13 优化件和概念件壁面的温度云图（Q=2.1429 kg/s）

Figure 13. Temperature diagram of the optimized and the conceptual nozzle walls （Q=2.1429 kg/s）

下载: 全尺寸图片幻灯片

图 14 优化件和概念件壁面的应变云图（Q=2.1429 kg/s）

Figure 14. Strain diagram of the optimized and the conceptual nozzle walls （Q=2.1429 kg/s）

下载: 全尺寸图片幻灯片

表 1 喷管气热耦合计算边界条件及其湍流模型

Table 1. Boundary conditions and turbulence model of the coupled heat transfer calculation for nozzle

参数	数值及说明
燃气入口压力/10⁵ Pa	5.171
燃气入口温度/K	844.3
外壁面温度	式（1）
喷管出口	超声速出口
入口燃气密度/（kg/m³）	2.1306
燃气动力黏度	Sutherland方程
湍流模型	RNG k-ε

下载: 导出CSV

表 2 中心复合实验设计方案下气热耦合数值模拟计算结果

Table 2. Coupled heat transfer numerical simulation results of central composite experimental design schemes

运行序	Q/ （kg/s）	θ/ （°）	D/ mm	L/ mm	η	T_max/K	f
1	2.75	20	3	6	0.8929	400.9	0.00452
2	2.75	15	3	6	0.8929	400.4	0.00425
3	2.75	15	5	6	0.8929	401.9	0.00460
4	2.75	10	3	6	0.8933	399.5	0.00432
5	5.00	15	3	6	0.8997	395.9	0.00399
6	2.75	15	3	5	0.8929	400.6	0.00427
7	2.75	15	3	7	0.8931	400.1	0.00391
8	0.50	15	3	6	0.8426	437.0	0.00525
9	2.75	15	3	6	0.8929	400.4	0.00425
10	2.75	15	1	6	0.8923	402.5	0.00381
11	5.00	20	5	5	0.8995	398.4	0.00435
12	2.75	15	3	6	0.8929	400.4	0.00425
13	2.75	15	3	6	0.8929	400.4	0.00425
14	0.50	20	5	7	0.8444	430.4	0.00541
15	5.00	10	1	5	0.8993	396.8	0.00388
16	0.50	10	5	5	0.8472	418.2	0.00525
17	0.50	10	1	7	0.8389	449.9	0.00539
18	5.00	10	5	7	0.8988	398.5	0.00576
19	0.50	20	1	5	0.8341	468.5	0.00506
20	5.00	20	1	7	0.8995	396.2	0.00319
21	0.50	20	5	5	0.8449	425.4	0.00553
22	5.00	10	1	7	0.8995	396.8	0.00377
23	0.50	10	1	5	0.8391	447.1	0.00584
24	5.00	10	5	5	0.8988	400.7	0.00486
25	2.75	15	3	6	0.8929	400.4	0.00425
26	5.00	20	5	7	0.8995	398.0	0.00398
27	2.75	15	3	6	0.8929	400.4	0.00425
28	0.50	20	1	7	0.8381	452.5	0.00456
29	5.00	20	1	5	0.8953	414.4	0.00347
30	0.50	10	5	7	0.8479	419.0	0.00614

下载: 导出CSV

表 3 拟合公式系数表

Table 3. Table of fitting formula coefficient

多项式分项	分项系数	系数值
多项式分项	分项系数	η	T_max	f
常数项	c₀	8.19×10⁻¹	4.57×10²	3.13×10⁻³
x₁	c₁	3.71×10⁻²	−2.68×10¹	−8.14×10⁻⁴
x₂	c₂	−8.63×10⁻⁴	3.64×10⁰	−1.15×10⁻⁴
x₃	c₃	4.00×10⁻³	−1.56×10¹	−4.27×10⁻⁴
x₄	c₄	1.58×10⁻³	−2.20×10⁰	1.43×10⁻³
x₁²	c₁₁	−4.35×10⁻³	3.25×10⁰	8.34×10⁻⁵
x₂²	c₂₂	−1.93×10⁻⁶	8.00×10⁻³	8.88×10⁻⁶
x₃²	c₃₃	−1.27×10⁻⁴	5.50×10⁻¹	2.96×10⁻⁶
x₄²	c₄₄	−1.40×10⁻⁴	3.50×10⁻¹	−1.04×10⁻⁴
x₁·x₂	c₁₂	4.90×10⁻⁵	−1.58×10⁻¹	−6.78×10⁻⁶
x₁·x₃	c₁₃	−4.34×10⁻⁴	1.62×10⁰	4.41×10⁻⁵
x₁·x₄	c₁₄	1.02×10⁻⁵	−3.72×10⁻¹	8.06×10⁻⁶
x₂ x₃	c₂₃	3.44×10⁻⁵	−1.57×10⁻¹	−8.36×10⁻⁷
x₂·x₄	c₂₄	8.73×10⁻⁵	−3.87×10⁻¹	−3.13×10⁻⁵
x₃·x₄	c₃₄	−2.53×10⁻⁴	1.08×10⁰	8.21×10⁻⁵

下载: 导出CSV

表 4 响应面模型拟合公式的精度

Table 4. Accuracy of response surface model fitting formula

响应参数	R²/%
η	99.91
T_max	97.77
f	93.05

下载: 导出CSV

表 5 喷管的流动换热性能对比

Table 5. Flow and heat transfer performances comparison of nozzle

流动换热指标	概念件	基础件
最高温度T_max/K	416.0	426.7
平均冷却效率η	0.8716	0.8648
摩擦因数f	0.00479	0.00351

下载: 导出CSV

表 6 优化计算和仿真验算结果的比较

Table 6. Comparison of optimization calculation and simulation verification results

结果比较	输入参数				响应参数
结果比较	Q/（kg/s）	θ/（°）	D/mm	L/mm	η	T_max/K	f
优化件的优化计算结果	2.1429	10.0233	3.3222	5.8480	0.8850	401.8	0.00493
优化件的仿真验算结果	2.1429	10.0233	3.3222	5.8480	0.8896	401.4	0.00453
误差/%					0.52	0.10	8.11
概念件的仿真验算结果	2.1429	15	3	6	0.8890	403.0	0.00437

下载: 导出CSV

参考文献(19)

[1]	MEYER O,NITSCHE W. Update on progress in adaptive wind tunnel wall technology[J]. Progress in Aerospace Sciences,2004,40(3): 119-141. doi: 10.1016/j.paerosci.2004.02.001
[2]	OWEN F K,OWEN A K. Measurement and assessment of wind tunnel flow quality[J]. Progress in Aerospace Sciences,2008,44(5): 315-348. doi: 10.1016/j.paerosci.2008.04.002
[3]	MUNGIGUERRA S,MARTINO G D D,SAVINO R,et al. Characterization of novel ceramic composites for rocket nozzles in high-temperature harsh environments[J]. International Journal of Heat and Mass Transfer,2020,163: 120492.1-120492.18. doi: 10.1016/j.ijheatmasstransfer.2020.120492
[4]	范志鹏,徐惊雷,吕郑,等. 型面旋转变马赫数风洞喷管的优化设计[J]. 航空学报,2014,35(5): 1216-1225. FANG Zhipeng,XU Jinglei,LÜ Zheng,et al. Optimization design of variable mach number wind tunnel nozzle by rotating profile[J]. Acta Aeronautica et Astronautica Sinica,2014,35(5): 1216-1225. (in Chinese)
[5]	CHEN Pengfei,WU Feng,XU Jinglei,et al. Design and implementation of rigid-flexible coupling for a half-flexible single jack nozzle[J]. Chinese Journal of Aeronautics,2016,29(6): 1477-1483. doi: 10.1016/j.cja.2016.09.002
[6]	齐伟呈,徐惊雷,范志鹏,等. 马赫数2~4连续可调风洞数值模拟及静态标定试验[J]. 航空学报,2017,38(1): 86-94. QI Weicheng,XU Jinglei,FAN Zhipeng,et al. Numerical simulation and experimental calibration of continuously adjustable wind tunnel with Mach number 2 to 4[J]. Acta Aeronautica et Astronautica Sinica,2017,38(1): 86-94. (in Chinese)
[7]	LÜ Zheng. , XU Jinglei, WU Feng, et al. Design of a variable Mach number wind tunnel nozzle operated by a single jack[J]. Aerospace Science and Technology,2018,77: 299-305. doi: 10.1016/j.ast.2018.03.011
[8]	金韶山,姜培学,孙纪国. 液体火箭发动机喷管发汗冷却研究[J]. 航空动力学报,2008,23(7): 1334-1340. JIN Shaoshan,JIANG Peixue,SUN Jiguo. Investigation on the transpiration cooling of a liquid rocket nozzle[J]. Journal of Aerospace Power,2008,23(7): 1334-1340. (in Chinese)
[9]	金韶山. 液体火箭发动机推力室及钝体头锥发汗冷却研究[D]. 北京: 清华大学, 2008. JIN Shaoshan. Research on transpiration cooling of liquid rocket thrust chamber and blunt nose cone[D]. Beijing: Tsinghua University, 2008. (in Chinese)
[10]	张宏伟,陶文铨,何雅玲,等. 再生冷却推力室耦合传热数值模拟[J]. 航空动力学报,2006,21(5): 148-154. doi: 10.3969/j.issn.1000-8055.2006.05.025 ZHANG Hongwei,TAO Wenquan,HE Yaling,et al. Numerical study on coupled heat transfer of thrust chamber with regenerative cooling[J]. Journal of Aerospace Power,2006,21(5): 148-154. (in Chinese) doi: 10.3969/j.issn.1000-8055.2006.05.025
[11]	康玉东,孙冰. 气壁镀镍和冷却剂入口对再生冷却的影响[J]. 航空动力学报,2010,25(12): 2834-2838. KANG Yudong,SUN Bing. Effects of hot-gas wall nickelage and cooling channel inflow on regenerative cooling[J]. Journal of Aerospace Power,2010,25(12): 2834-2838. (in Chinese)
[12]	RALF S,CHLOÉ G,CHRISTIAN M,et al. Design of a film cooled dual-bell nozzle[J]. Acta Astronautica,2019,158: 342-350. doi: 10.1016/j.actaastro.2018.05.056
[13]	MAYANK V,NITISH A,ASHOKE D. Investigation of flow characteristics inside a dual bell nozzle with and without film cooling[J]. Aerospace Science and Technology,2020,99: 105741.1-105741.14. doi: 10.1016/j.ast.2020.105741
[14]	KIM K S,LEE S H,NGUYEN V Q,et al. Ablation characteristics of rocket nozzle using HfC-SiC refractory ceramic composite[J]. Acta Astronautica,2020,173: 31-44. doi: 10.1016/j.actaastro.2020.03.050
[15]	BACK L H, MASSIER P F, GIER H L. Convective heat transfer in a convergent-divergent nozzle[J]. International Journal of Heat and Mass Transfer 1964, 7(5): 549-568.
[16]	何宁,杨海波,孙冬柏. 高温长时间风洞喷管冷却结构CFD研究[J]. 工程科学学报,2016,38(4): 568-574. HE Ning,YANG Haibo,SUN Dongbai. CFD study on nozzle cooling structure for a wind tunnel of high temperature and long operation time[J]. Chinese Journal of Engineering,2016,38(4): 568-574. (in Chinese)
[17]	黄祯君,张涛,王杰. 高焓高热流条件下半椭圆喷管冷却结构设计与分析[J]. 机械工程学报,2019,55(18): 157-164. doi: 10.3901/JME.2019.18.157 HUANG Zhenjun,ZHANG Tao,WANG Jie. Cooling structural design and thermodynamic analysis of semi-elliptic nozzle under high enthalpy and high heatflux conditions[J]. Journal of Mechanical Engineering,2019,55(18): 157-164. (in Chinese) doi: 10.3901/JME.2019.18.157
[18]	PAL S, TUCKER K, LEHMAN M, et al. Experimental studies of the heat transfer to RBCC rocket nozzles for CFD application to design methodology[C]//Proceedings of the 33rd ASME/AIChE/ANS/AIAA National Heat Transfer Conference. Reston, US: AIAA, 1999: 168-177.
[19]	LIU Q Y,LUKE E A,CINNELLA P. Coupling heat transfer and fluid flow solvers for multidisciplinary simulations[J]. Journal of Thermophysics and Heat Transfer,2005,19(4): 417-427. doi: 10.2514/1.13522