燃气舵流动性能及其材料烧蚀剥蚀行为研究进展

程经理; 桂业伟; 曾磊; 刘骁; 杨肖锋; 石友安

燃气舵流动性能及其材料烧蚀剥蚀行为研究进展

中国空气动力研究与发展中心计算空气动力研究所, 绵阳621000

基金项目: 国家重点研发计划(NO.2019YFA0405202)；国家自然科学基金(NO.52276168)；四川省科技计划资助(NO.2022YFG0051)

详细信息

通讯作者:
桂业伟，博士，研究员，博士生导师，研究方向为高超声速飞行器气动热与热防护，　E-mail：guiyewei777@126.com

中图分类号: TB332; V421.6+2
计量
- 文章访问数: 46
- HTML全文浏览量: 30
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-15
- 修回日期: 2024-06-29
- 录用日期: 2024-07-05
- 网络出版日期: 2024-07-24

Research progress on flow performance and material ablation and denudation behavior of jet vane

Computational Aerodynamics Institute of China Aerodynamics Research and Development Center,Mianyang 621000, China

Funds: National Key Research and Development Program of China (2019YFA0405202); National Natural Science Foundation of China (NO.52276168); The Science and Technology Planning Project of Sichuan Province (NO.2022YFG0051)

摘要

摘要: 燃气舵因能够快速响应、完成大幅度姿态角转动而被广泛地研究与应用，但燃气舵表面烧蚀剥蚀问题严重制约了其发展。本文讨论了燃气舵相关代表性工作研究进展，包括燃气舵流动性能问题、金属材料和复合材料燃气舵结构表面热化学烧蚀及机械剥蚀问题。此外，针对轻质化复合材料燃气舵是未来发展的必然趋势，就其面临的复杂环境下的烧蚀剥蚀问题，还讨论了其他相关复合材料结构烧蚀剥蚀代表性工作，以共借鉴。据此，最后提出了复合材料燃气舵未来的发展重点，以期为复合材料燃气舵在国内的研究、应用及发展提供参考。
- 燃气舵 /
- 气动传热特性 /
- 复合材料 /
- 烧蚀剥蚀 /
- 高焓颗粒
Abstract: Jet vane has been widely studied and applied because of its fast response and large attitude Angle rotation. However, the ablation and denudation of jet vane surface seriously restricts its development. In this paper, the typical research progress of jet vane is reviewed, including the flow performance of jet vane, the surface thermal chemical ablation and mechanical erosion of metal and composite materials jet vane structure. In addition, in view of the light composite jet vane is an inevitable trend in the future development, the paper also discusses the ablative and denudation of other relevant composite structures for reference. Based on this, the paper finally puts forward the future development focus of composite jet vane, in order to provide reference for the research, application and development of composite jet vane in China.
- Jet vane /
- Aerodynamic heat transfer characteristics /
- Composite materials /
- Ablation and erosion /
- High enthalpy particle

HTML全文

图 1 燃气舵示意图

Figure 1. Gas rudder diagram

下载: 全尺寸图片幻灯片

图 2 燃气舵受力计算结果^[48]

Figure 2. Calculation results of force of the gas rudder^[48]

下载: 全尺寸图片幻灯片

图 3 测量舵随舵偏角变化的升力和阻力曲线^[53]

Figure 3. The curve of lift and drag of a gas rudder with the rudder Angle^[53]

下载: 全尺寸图片幻灯片

图 4 燃气舵与楔形耳片组合方式示意图^[32]

Figure 4. Schematic diagram of combination mode of jet vane and wedge lug^[32]

下载: 全尺寸图片幻灯片

图 5 两种网格下阻力和升力随舵偏角变化^[57]

Figure 5. Resistance and lift of the two meshing methods vary with the rudder declination Angle^[57]

下载: 全尺寸图片幻灯片

图 6 喷管和燃气舵结构及其计算网格^[57]

Figure 6. Nozzle and vane structure and its calculation grid^[57]

下载: 全尺寸图片幻灯片

图 7 烧蚀过程^[67]

Figure 7. Ablation Process^[67]

下载: 全尺寸图片幻灯片

图 8 烧蚀量随时间的变化^[46]

Figure 8. Change of ablation amount with time^[46]

下载: 全尺寸图片幻灯片

图 9 燃气舵实验过程^[46]

Figure 9. Ablation Process^[46]

下载: 全尺寸图片幻灯片

图 10 颗粒轨迹图^[68]

Figure 10. Particle trajectory diagram^[68]

下载: 全尺寸图片幻灯片

图 11 特型燃气舵示意图^[71]

Figure 11. Special gas rudder diagram^[71]

下载: 全尺寸图片幻灯片

图 12 不同舵偏角舵面热化学烧蚀退移量分布曲线^[80]

Figure 12. Distribution curve of thermo-chemical ablation regression of vane surface at different deflection angles^[80]

下载: 全尺寸图片幻灯片

图 13 碳/酚醛燃气舵表面烧蚀量云图^[81]

Figure 13. Nephogram of ablation amount of carbon/phenolic vane surface^[81]

下载: 全尺寸图片幻灯片

图 14 试件烧蚀形貌变化过程^[82]

Figure 14. Change process of ablation morphology of specimen^[82]

下载: 全尺寸图片幻灯片

图 15 气固交界面的能量交换示意图^[99]

Figure 15. Schematic diagram of energy exchange at gas-solid interface^[99]

下载: 全尺寸图片幻灯片

图 16 不同材料的力学响应^[100]((a、d)：温度响应；(b、e)：应力响应；(c、f)：裂纹扩展响应)

Figure 16. Mechanical responses of different materials^[100] ((a、d): denotes temperature response; (b、e): denotes stress response; (c、d): denotes crack growth response)

下载: 全尺寸图片幻灯片

图 17 烧蚀形貌数值仿真结果与分析结果对比

Figure 17. Comparison of numerical simulation results and analysis results of ablation morphology

下载: 全尺寸图片幻灯片

图 18 微观烧蚀机制^[101]

Figure 18. Microscopic ablation mechanism^[101]

下载: 全尺寸图片幻灯片

[1]	杨鑫. 基于ARM的燃气舵舵机控制系统的设计与分析[D]. 南京: 南京理工大学, 2017. YANG Xin. Design and analysis of gas rudder control system based on ARM [D]. Nanjing: Nanjing University of Science and Technology, 2017(in Chinese).
[2]	VERMEULEN A. Missile Design: a Challenging Example for Control Education[J]. IFAC Proceedings Volumes, 2010, 42(24): 65-70. doi: 10.3182/20091021-3-JP-2009.00014
[3]	宋永杰. 基于无刷直流电机的小型舵机驱动与自适应控制研究[D]. 南京: 南京理工大学, 2016. SONG Yongjie. Based on Brushless Dc Motor of Small Steering Gear Drive and the Adaptive Control Research[D]. Nanjing: Nanjing University of Science and Technology, 2016(in Chinese).
[4]	朱忠惠, 胡隆庆. 推力矢量控制伺服系统[M]. 北京: 中国宇航出版社, 1995: 16-20. ZHU Zhonghui, HU Longqing. Thrust vector control servo system [M]. Beijing: China Aerospace Press, 1995: 16-20(in Chinese).
[5]	王晓明, 刘辉, 韩龙柱, 等. 激波诱导推力矢量喷管不同气体喷注时性能分析[J]. 北京航空航天大学学报, 2018, 44(11): 24-29. WANG Xiaoming, LIU Hui, HAN Longzhu, et al. Performance analysis of shock induced thrust vectoring nozzle with different gas injection[J]. Journal of Beihang University, 2018, 44(11): 24-29(in Chinese).
[6]	林泳辰, 徐惊雷, 韩杰星, 等. 气动推力矢量无舵面飞翼的飞行实验[J]. 航空动力学报, 2019, 34(3): 701-707. LIN Yongchen, XU Jinglei, HAN Jiexing, et al. Flight test of a fluidic thrust vectoring flying wing without rudder[J]. Journal of Aerospace Power, 2019, 34(3): 701-707(in Chinese).
[7]	段冬冬, 沈小林. 推力矢量技术在空空导弹上的应用与分析[J]. 飞航导弹, 2012, 4: 84-87. DUAN Dongdong, SHEN Xiaolin. Application and analysis of thrust vector technology in air-to-air missile[J]. Aerodynamic Missile Journal, 2012, 4: 84-87 (in Chinese).
[8]	王献策, 陈雄, 葛中杰, 等. 基于扩张状态观测器的燃气舵舵机位置控制[J]. 推进技术, 2020, 41(10): 2341-2347. WANG Xianse, CHEN Xiong, GE Zhongjie, et al. Position Control of Gas rudder Steering Gear based on Extended State Observer[J]. Journal of Propulsion Technology, 2019, 41(10): 2341-2347(in Chinese).
[9]	王献策. 燃气舵伺服控制系统动态特性研究[D]. 南京: 南京理工大学, 2022. WANG Xiance. Research on Dynamic Characteristics of Servo Control System for Gas Rudder [D]. Nanjing: Nanjing University of Science and Technology, 2022(in Chinese).
[10]	李修明, 童悦, 占冬至, 等. 分离线扩张比对超音速分离线摆动喷管流场影响规律的数值与试验研究[J]. 固体火箭技术, 2024, 47(2): 216-221. doi: 10.7673/j.issn.1006-2793.2024.02.009 LI Xiuming, TONG Yue, ZHAN Dongzhi, et al. Numerical and experimental study on the influence of separation line expansion ratio on the flow field of supersonic separation line oscillating nozzle[J]. Journal of Solid Rocket Technology, 2024, 47(2): 216-221. doi: 10.7673/j.issn.1006-2793.2024.02.009
[11]	付玮, 孙颖, 王恩泽, 等. 摆动喷管与惯性器件超谐波耦合仿真研究[J]. 宇航总体技术, 2023, 7(6): 65-72. FU Wei, SUN Ying, WANG Enze, et al. Superharmonic Coupling Simulation of oscillating nozzle and inertial Device[J]. Aerospace System Engineering Technol- ogy, 2023, 7(6): 65-72(in Chinese).
[12]	周成宝, 周荻. 面向摆动喷管的导弹非线性姿态控制[J]. 系统工程与电子技术, 2016, 38(5): 1107-1113. doi: 10.3969/j.issn.1001-506X.2016.05.21 ZHOU Chengbao, ZHOU Di. Nonlinear attitude control of missile for swinging nozzle[J]. Journal of Systems Engineering and Electronics, 2016, 38(5): 1107-1113(in Chinese). doi: 10.3969/j.issn.1001-506X.2016.05.21
[13]	BARUZZIM D, DOMEL N, MILLER D N. Pulsed injection flow control for throttling in supersonic nozzles-a computational fluid dynamics design study[C]. AIAA 2007-4215. 37th AIAA Fluid Dynamics Conference and Exhibit. June 2007.
[14]	DZIUBA M, ROSSMANN T. Active control of a sonic transverse jet in supersonic cross-flow using a powered resonance tube[C]. AIAA 2005-897. 43rd AIAA Aerospace Sciences Meeting and Exhibit. January 2005.
[15]	谢侃, 刘宇, 王一白. 圆孔喷嘴形成气动喉部的定常数值研究[J]. 航空动力学报, 2011, 26(4): 924-930. XIE Kan, LIU Yu, WANG Yibai. Steady numerical study of aerodynamic throat formed by round injectors[J]. Journal of Aerospace Power, 2011, 26(4): 924-930 (in Chinese).
[16]	谢侃, 王一白, 刘宇. 固体火箭发动机气动喉部非定常过程孔喷嘴形成气动喉部的定常数值研究[J]. 推进技术, 2011, 32(1): 103-108. XIE Kan, WANG Yibai, LIU Yu. Unsteady process of aerodynamic throat for solid rocket motor[J]. Journal of Propulsion Technology, 2011, 32(1): 103-108(in Chinese).
[17]	张建华, 谢侃. 流体喉部喷管二次流矢量控制方案[J]. 北京航空航天大学学报, 2012, 38(3): 309-318. ZHANG Jianhua, XIE Kan. Secondary flow thrust vector control study for fluidic throat nozzle[J]. Journal of Beijing University of Aeronautics and Astronautics, 2012, 38(3): 309-318(in Chinese).
[18]	谢永强, 李舜, 周须峰, 等. 推力矢量技术在空空导弹上的应用分析[J]. 科学技术与工程, 2009, 9(20): 6109-6113. doi: 10.3969/j.issn.1671-1815.2009.20.033 XIE Yongqiang, LI Shun, ZHOU Xufeng, et al. Application analysis of thrust vector technology in air-to-air missile[J]. Science Technology and Engineering, 2009, 9(20): 6109-6113 (in Chinese). doi: 10.3969/j.issn.1671-1815.2009.20.033
[19]	侯清海, 李剑. 推力矢量燃气舵在空空导弹上的应用研究[J]. 航空兵器, 2012, 1: 7-11. doi: 10.3969/j.issn.1673-5048.2012.01.003 HOU Qinghai, LI Jian. Application Study of Thrust Vector Jet Vanes on Air-to-Air Missiles[J]. Aviation Weaponry, 2012, 1: 7-11(in Chinese). doi: 10.3969/j.issn.1673-5048.2012.01.003
[20]	谢永强, 李舜, 周须峰, 等. 推力矢量技术在空空导弹上的应用分析[J]. 科学技术与工程, 2009, 9(20): 6109-6113. doi: 10.3969/j.issn.1671-1815.2009.20.033 XIE Yongqiang, LI Shun, ZHOU Xufeng et al. The Application Analysis of Thrust Vector Control Systems of Air to Air Missile[J]. Science, Technology and Engineering, 2009, 9(20): 6109-6113(in Chinese). doi: 10.3969/j.issn.1671-1815.2009.20.033
[21]	刘玉磊. 燃气舵流固耦合传热数值分析[J]. 航空兵器, 2013, 3: 41-43. doi: 10.3969/j.issn.1673-5048.2013.03.009 LIU Yulei. Heat Transmission Numerical Analysis for TVC Fluid-Solid Coupling[J]. Aviation Weaponry, 2013, 3: 41-43(in Chinese). doi: 10.3969/j.issn.1673-5048.2013.03.009
[22]	侯清海. 空空导弹燃气舵气动设计综述[J]. 航空兵器, 2000, 6: 37-40. HOU Qinghai. Aerodynamic design of gas rudder for air-to-air missile[J]. Aviation Ordnance, 2000, 6: 37-40(in Chinese).
[23]	王刚. 导弹垂直转弯燃气舵仿真研究[J] 电子测试, 2016, 8: 15-16. WANG Gang. Simulation of missile vertical turning gas rudder[J] Electronic Test, 2016, 8: 15-16(in Chinese).
[24]	薛凯, 刘鹏飞. 超声速导弹燃气舵系统设计与研究[J]. 战术导弹技术, 2008, 6: 65-68. doi: 10.3969/j.issn.1009-1300.2008.06.017 XUE Kai, LIU Pengfei. Investigation into the Jet Vane System of Supersonic Missile[J]. Tactical Missile Technology, 2008, 6: 65-68(in Chinese). doi: 10.3969/j.issn.1009-1300.2008.06.017
[25]	刘钧圣, 曾望, 汤江河, 等. 垂直发射多用途导弹发展现状与研究方向[J]. 弹箭与制导学报, 2019, 39(5): 172-177. LIU Junsheng, ZENG Wang, TANG Jianghe, et al. Development status and research direction of vertically launched multi-purpose missile[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2019, 39(5): 172-177 (in Chinese).
[26]	邢晓岚, 刘代军. 第四代红外近距格斗空空导弹关键技术探讨[J]. 航空兵器, 2001, 6: l-4. doi: 10.3969/j.issn.1673-5048.2001.06.012 XING Xiaolan, LIU Daijun. Discussion on the key technology of the fourth generation infrared short-range combat air-to-air missile[J]. Aviation Ordnance, 2001, 6: l-4(in Chinese). doi: 10.3969/j.issn.1673-5048.2001.06.012
[27]	高峰, 唐胜景, 师娇. 推力矢量控制技术在导弹上的应用[J]. 飞航导弹, 2010, 12: 52-59. GAO Feng, TANG Shengjing, SHI Jiao. Application of Thrust Vector Control Technology in Missile[J]. Aerodynamic Missile, 2010, 12: 52-59(in Chinese).
[28]	HERVAS J, REYHANOGLU M. Thrust Vector Control of an Upper-Stage Rocket with Multiple Propellant Slosh Modes[J]. Mathematical Problems in Engineering, 2012, 2012(8): 603-621.
[29]	KONG F, JIN Y, KIM H D. Thrust vector control of supersonic nozzle flow using a moving plate[J]. Journal of Mechanical Science and Technology, 2016, 30(3): 1209-1216. doi: 10.1007/s12206-016-0224-4
[30]	RAHAIM C, CAVALLERI R, MCCARTHY J, et al. Jet vane thrust vector control-A design effort[C]. AIAA 1996-2904. 32nd Joint Propulsion Conference and Exhibit. July 1996.
[31]	李静. 箱式垂直热发射燃气流场与结构相容性研究[D]. 北京: 北京理工大学, 2021. LI Jing. Research on Gas Flow and Compatibility of Vertical Launching System of Container-launched Missile [D]. Beijing: Beijing Institute of Technology, 2021(in Chinese).
[32]	孙宇航, 杨晨. 燃气舵推矢装置的改进设计及其气动特性分析[J]. 兵器装备工程学报, 2020, 41(12): 77-81. doi: 10.11809/bqzbgcxb2020.12.014 SUN Yuhang, YANG Chen. Improved design and aerodynamic characteristics analysis of jet vane thruster[J]. Journal of Ordnance Equipment Engineering, 2020, 41(12): 77-81 (in Chinese). doi: 10.11809/bqzbgcxb2020.12.014
[33]	KOSTIĆ O, STEFANOVIĆ Z, KOSTIĆ I. Comparative CFD Analyses of a 2D Supersonic Nozzle Flow with Jet Tab and Jet Vane[J]. Tehnicki Vjesnik, 2017, 24(5): 1335-1344.
[34]	张新桥, 李清廉, 沈赤兵, 等. 燃气发生器低频非稳态燃烧统计分析[J]. 国防科技大学学报, 2016, 38(2): 6-11. doi: 10.11887/j.cn.201602002 ZHANG Xinqiao, LI Qinglian, SHEN Chibing, et al. Statistical Analysis of Low-frequency unsteady combustion of Gas Generator[J]. Journal of National University of Defense Technology, 2016, 38(2): 6-11(in Chinese). doi: 10.11887/j.cn.201602002
[35]	万家欢. 面向燃烧振荡的参数化建模和主动控制技术研究[D]. 南京: 南京航空航天学, 2020. WAN Jiahuan. Research on Parametric Modeling and active Control Technology for combustion Oscillation [D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2020(in Chinese).
[36]	YAGLA J, ANDERSON L. Internal ballistics and missile launch environment for the vertical launching system. 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference, Fluid Dynamics and Co-located Conferences [C]. AIAA 1982-855. 3rd Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference. June 1982.
[37]	莫展, 白涛涛, 郭颜红. 带燃气舵的固体火箭发动机尾流仿真[J]. 弹箭与制导学报, 2011, 31(2): 120-122. doi: 10.3969/j.issn.1673-9728.2011.02.038 MO Zhan, BAI Taotao, GUO Yanhong. Numerical Analysis of Plume Field for SRM with Gas Vane[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2011, 31(2): 120-122(in Chinese). doi: 10.3969/j.issn.1673-9728.2011.02.038
[38]	BURAK S, BULENT S. Experim- ental and Numerical Investigation of a Jet Vane of Thrust Vector Control System [C]. AIAA 2019-3880. AIAA Propulsion and Energy 2019 Forum. August 2019.
[39]	郑兴宇. 固体火箭发动机钨渗铜燃气舵流固耦合仿真与烧蚀冲刷特性研究[D]. 长沙: 国防科学技术大学, 2019. ZHENG Xingyu. Fluid-structure coupling simulation and ablation and scouring characteristics of tungsten copper infiltrated jet vane of solid rocket motor[D]. Changsha: National University of Defense Technology, 2019 (in Chinese).
[40]	薛海峰. 碳/酚醛燃气舵传热烧蚀数值仿真与实验研究[D]. 南京: 南京理工大学, 2019. XUE Haifeng. Numerical simulation and experimental study on heat transfer and ablation of carbon/phenolic jet vane[D]. Nanjing: Nanjing University of Science and Technology, 2019 (in Chinese).
[41]	LI W, Fang G D, Li W J, et al. Role of mesoscopic features on thermo-chemical ablative behavior of 3D C/C braided composites[J]. Int. J. Heat Mass Transf, 2019, 144: 118602. doi: 10.1016/j.ijheatmasstransfer.2019.118602
[42]	杜瑞泽, 何厚辛, 刘永利. 燃气舵仿真与实验研究综述[J]. 现代防御技术, 2022, 50(6): 132-140. DU Ruize, HE Houxin, LIU Yongli. Summary of simulation and experimental research on gas rudder[J]. Modern Defense Technology, 022, 50(6): 132- 140(in Chinese).
[43]	熊瑛, 夏薇, 高云昊, 等. 2020 年国外导弹防御发展综述[J]. 飞航导弹, 2021, 1: 6-11. XIONG Ying, XIA Wei, GAO Yunhao, et al. Over view of Foreign Missile Defense Development in 2020[J]. Aerodynamic Missile Journal, 2021, 1: 6-11(in Chinese).
[44]	卜庆伟, 陈雄, 崔二伟. 推力矢量发动机燃气舵系统设计与分析[J]. 科学技术与工程, 2017, 17(33): 182-187. doi: 10.3969/j.issn.1671-1815.2017.33.026 BU Qingwei, CHEN Xiong, CUI Erwei. Design andAnalysis on Jet Vane System of Thrust-Vector Motor[J]. Science Technology and Engineering, 2017, 17(33): 182-187(in Chinese). doi: 10.3969/j.issn.1671-1815.2017.33.026
[45]	SABOURIN J L, YETTER R A. High- Temperature Heterogeneous Reaction Kinetics of Tungsten Oxidation by CO₂, CO, and O₂[J]. Jouranal of Propulsion and Power, 2009, 25(2): 490-498(in Chinese). doi: 10.2514/1.38123
[46]	HARRISSION V, CHAMPLAIN A, KRETSCHMER D. Optical technique to quantify erosion on jet vanes for thrust vector control[C]. AIAA 2002-4190. 38th AIAA/ASME/SAE/ASEE Joint Propul- sion Conference & Exhibit. July 2002.
[47]	RAINVILLE P A, DECHAMPLAIN A, KRETSCHMER D. Unsteady CFD calculation for validation of a multi-vane thrust vector control system[C]. AIAA 2004-3384. 40th AIAA/ASME/SAE/ ASEE Joint Propulsion Conference and Exhibit. July 2004.
[48]	ROGER R, CHAN S, HUNLEY J. CFD analysis for the lift and drag on a fin/mount used as a jet vane tvc for boost control[C]. AIAA 1995-83. 33rd Aerospace Sciences Meeting and Exhibit. January 1995.
[49]	谢玲玲, 陈文亮, 牛亚然, 等. 燃气舵的绕流场及气动特性数值研究[J]. 航空计算技术, 2015, 45(6): 79-82+86. doi: 10.3969/j.issn.1671-654X.2015.06.020 XIE Lingling, CHEN Wenliang, NIU Yaran, et al. Numerical study on Flow Field and Aerodynamic Characteristics of a gas Rudder[J]. Aeronautical Computing Technique, 2015, 45(6): 79-82+86(in Chinese). doi: 10.3969/j.issn.1671-654X.2015.06.020
[50]	孙晓娇. 超声速稠密两相流条件下燃气舵绕流特性研究[D]. 南京: 南京理工大学, 2012. SUN Xiaojiao. Study on Flow Characteristics of gas rudder under Supersonic Dense two-phase flow [D]. Nanjing: Nanjing University of Science and Technology, 2012(in Chinese).
[51]	常见虎, 周长省, 李军, 等. 推力矢量燃气舵特性的机制分析[J]. 弹道学报, 2009, 21(2): 23-26. CHANG Jianhu, Zhou ChangSheng, Li Jun, et al. Mechanism analysis of thrust vector jet vane characteristics[J]. Journal of Ballistics, 2009, 21(2): 23-26 (in Chinese).
[52]	宋扬. 燃气舵推矢装置稳态及动态气动特性研究[J]. 航空兵器, 2014, 2: 41-43. doi: 10.3969/j.issn.1673-5048.2014.02.010 SONG Yang. Study on steady-state and dynamic aerodynamic characteristics of jet vane thruster[J]. Aero Weaponry, 2014, 2: 41-43 (in Chinese). doi: 10.3969/j.issn.1673-5048.2014.02.010
[53]	常见虎, 李军, 周长省, 等. 推力矢量发动机燃气舵舵间干扰的数值分析[J]. 固体火箭技术, 2008, 2: 141-144. doi: 10.3969/j.issn.1006-2793.2008.02.010 CHANG Jianhu, LI Jun, ZHOU Changsheng, et al. Numerical analysis of jet vane-rudder interference of thrust vector engine[J]. Journal of Solid Rocket Technology, 2008, 2: 141-144 (in Chinese). doi: 10.3969/j.issn.1006-2793.2008.02.010
[54]	汪学江. 燃气舵的舵间气动干扰分析[J]. 宇航学报, 1994, 3: 50-54+63+104. WANG Xuejiang. Analysis of interrudder aerodynamic Interference in gas-powered rudder[J]. Journal of Astronautics, 1994, 3: 50-54+63+104(in Chinese).
[55]	李军, 刘献伟, 李飞. 推力矢量发动机燃气舵气动特性设计[J]. 南京航空航天大学学报, 2007, 5: 646-649. doi: 10.3969/j.issn.1005-2615.2007.05.019 LI Jun, LIU Xianwei, LI Fei. Aerodynamic design of jet vane for thrust vector engine[J]. Journal of Nanjing University of Aeronautics and Astronautics, 2007, 5: 646-649 (in Chinese). doi: 10.3969/j.issn.1005-2615.2007.05.019
[56]	李军. 推力矢量发动机燃气舵气动性能分析[J]. 航空学报, 2006, 6: 1005-1008. doi: 10.3321/j.issn:1000-6893.2006.06.003 LI Jun. Aerodynamic performance analysis of jet vane of thrust vector engine[J]. Acta Aeronautica Et Astronautica Sinica, 2006, 6: 1005-1008 (in Chinese). doi: 10.3321/j.issn:1000-6893.2006.06.003
[57]	孙宇航, 杨晨. 多面体网格在推力矢量燃气舵气动特性计算中的应用[J]. 航空兵器, 2018, 4: 95-99. SUN Yuhang, YANG Chen. Application of polyhedral mesh in aerodynamic characteristics calculation of thrust vector jet vane[J]. Aero Weaponry, 2018, 4: 95-99 (in Chinese).
[58]	MURTY M S R C, RAO M S, CHAKRABORTY D. Numerical Simulation of Nozzle Flow Field with Jet VaneThrust Vector Control[J]. Proceedings of the Institution of Mechanical Engineers, Part G;Journal of Aerospace Engineering, 2010, 224(5): 541-548.
[59]	李军. 非定常燃气舵绕流场的数值分析[J]. 南京航空航天大学学报, 2005, 4: 471-475. doi: 10.3969/j.issn.1005-2615.2005.04.015 LI JUN. Numerical Analysis of Flow Field around Unsteady gas rudder[J]. Journal of Nanjing University of Aeronautics and Astronautics, 2005, 4: 471-475(in Chinese). doi: 10.3969/j.issn.1005-2615.2005.04.015
[60]	HWANG K Y. An Analysis on 3-Dimensional Temperature Distribution of Jet Vanes for a Thrust Vector Control[C]. Proceedings of the Academic Conference of the Korean Society for Propulsion Engineering, 2011.
[61]	YU M S, JU C B, CHO H H, et al. Hybrid Method for Jet Vane Thermal Analysis in Supersonic Nozzle Flow[J]. Journal of Thermophysics and Heat Transfer, 2006, 20(3): 614-617. doi: 10.2514/1.17675
[62]	YU M S, LEE J W, CHO H H. Numerial study on a thermal response of the jet vane system in a rocket nozzle[C]. AIAA 2004-997. 42nd AIAA Aerospace Sciences Meeting and Exhibit. 2004.
[63]	BACK L H, CUFFEL R F. Turbulent Boundary Layer and Heat Transfer Measurements Along a Convergent-Divergent Nozzle[J]. Journal of Heat Transfer, 1971, (93): 397-407.
[64]	MASTANAIAH K. Prediction of Skin-Friction and Heat Transfer from Compressible Turbulent Boundary Layers in Rocket Nozzles[J]. International Journal of Heat and Mass Transfer, 1978, (21): 1403-1409.
[65]	刘丽丽, 李克智, 李贺军, 等. 碳/碳燃气舵热-结构数值模拟分析[J]. 机械科学与技术, 2011, 30(5): 793-796+803. LIU Lili, LI Kezhi, LI Hejun, et al. Numerical Simulation of Thermal Structure of Carbon/Carbon Gas Rudder[J]. Mechanical Science and Technology for Aerospace Engineering, 2011, 30(5): 793-796+803(in Chinese).
[66]	刘洋, 何国强, 刘佩进, 等. 固体火箭发动机燃气舵热分析数值研究[J]. 弹箭与制导学报, 2007, (3): 165-168. doi: 10.3969/j.issn.1673-9728.2007.03.049 LIU Yang, HE Guoqiang, LIU Peijin, et al. Numerical Study on Thermal Analysis of gas rudder of solid rocket Engine[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2007, (3): 165-168(in Chinese). doi: 10.3969/j.issn.1673-9728.2007.03.049
[67]	YU M S, CHO H H. A study on a surface ablation of the jet vane in a rocket nozzle[C]. AIAA 2004-2276. 37th AIAA Thermophysics Conference. 2004.
[68]	CHO H H, KIM B G, YU M S. Analysis of particle laden flows around a jet vane in a solid rocket motor[C]. AIAA 2001-3591. 37th Joint Propulsion Confer- ence and Exhibit. 2001.
[69]	李军 , 常见虎, 周长省, 等. 推力矢量燃气舵三维气-固两相流的数值分析[J]. 南京理工大学学报(自然科学版), 2008, 5: 565-569. LI Jun, CHANG Hu, ZHOU ChangSheng, et al. Numerical analysis of three dimensional gas-solid two-phase flow with thrust vector jet vane[J]. Journal of Nanjing University of Science and Technology (Natural Science), 2008, 5: 565-569(in Chinese).
[70]	曹熙炜, 刘宇, 谢侃, 等. 气-粒两相流对燃气舵工作性能的影响[J]. 航空动力学报, 2010, 25(10): 2358-2362. CAO Xiwei, LIU Yu, XIE Kan, et al. Effect of gas-particle two-phase flow on the performance of jet vane[J]. Journal of Aerospace Power, 2010, 25(10): 2358-2362(in Chinese).
[71]	曹熙炜, 刘宇, 谢侃, 等. 一种特型燃气舵数值模拟分析[J]. 固体火箭技术, 2011, 34(1): 5-8. doi: 10.3969/j.issn.1006-2793.2011.01.002 CAO Xiwei, LIU Yu, XIE Kan, et al. Numerical simulation analysis of a special gas rudder[J]. Journal of Solid Rocket Technology, 2011, 34(1): 5-8(in Chinese). doi: 10.3969/j.issn.1006-2793.2011.01.002
[72]	郑兴宇, 杨涛, 张青斌. 钨渗铜燃气舵化学烧蚀计算[J]. 兵器装备工程学报, 2016, 37(9): 166-170. doi: 10.11809/scbgxb2016.09.038 ZHENG Xingyu, YANG Tao, ZHANG Qingbin. Chemical ablation calculation of tungsten copper infiltrated jet vane[J]. Journal of Ordnance Equipment Engineering, 2016, 37(9): 166-170 (in Chinese). doi: 10.11809/scbgxb2016.09.038
[73]	郑兴宇. 燃气舵烧蚀地面模拟实验设计与计算[J]. 科技视界, 2016, 17: 105-106. doi: 10.3969/j.issn.2095-2457.2016.12.071 ZHENG Xingyu. Design and calculation of ground simulation experiment of jet vane ablation[J]. Science & Technology Vision, 2016, 17: 105-106(in Chinese). doi: 10.3969/j.issn.2095-2457.2016.12.071
[74]	马丽滨, 何洪庆. 燃气舵外围流场计算[J]. 推进技术, 1993, 01: 28-33. MA Libin, HE Hongqing. Calculation of flow field around jet vane[J]. Journal of Propulsion Technology, 1993, 01: 28-33 (in Chinese).
[75]	董晓芳. 固体火箭发动机燃气舵热分析研究[D]. 西安: 西北工业大学, 2005. DONG Xiaofang. Thermal analysis of solid rocket motor jet vane[D]. Xi’an Northwestern Polytechnical University, 2005 (in Chinese).
[76]	刘玉磊. 燃气舵矢量喷管流固热耦合数值研究[D]. 南京: 南京理工大学, 2012. LIU Yulei. Numerical study on fluid-solid-thermal coupling of jet vane vector nozzle[D]. Nanjing: Nanjing University of Science and Technology, 2012 (in Chinese).
[77]	TEWARI A, SRINIVASULU T, RAMESH A, et al. Development of Manufacturing Technology for C-SiC Jet Vanes[J]. Procedia Materials Science, 2014, 5: 1567-1573. doi: 10.1016/j.mspro.2014.07.344
[78]	KUMAR S, KUMAR A, SAMPATH K, et al. Fabrication and erosion studies of C-SiC composite Jet Vanes in solid rocket motor exhaust[J]. Journal of the European Ceramic Society 2011, 31(13): 2425-2431
[79]	薛海峰, 陈雄, 郑健, 等. 基于热解动力学炭/酚醛燃气舵流热耦合数值研究[J]. 固体火箭技术, 2015, 38(4): 503-509. XUE Haifeng, CHEN Xiong, ZHENG Jian, et al. Numerical research on flow- thermal coupling of carbon-phenolic jet-vane based on pyrolysis kinetics[J]. Journal of Solid Rocket Technology, 2015, 38(4): 503-509(in Chinese).
[80]	薛海峰, 陈雄, 周长省. 碳/酚醛燃气舵热化学烧蚀过程数值研究[J]. 推进技术, 2016, 37(10): 1900-1908. XUE Haifeng, CHEN Xiong, ZHOU Changsheng. Numerical Research of Thermochemical Ablation about Carbon-Phenolic Jet Vane in Solid Rocket Motors[J]. Journal of Propulsion Technology, 2016, 37(10): 1900-1908 (in Chinese).
[81]	薛海峰, 陈雄, 郑健, 等. 炭/酚醛燃气舵烧蚀性能[J]. 固体火箭技术, 2017, 40(6): 706-713. doi: 10.7673/j.issn.1006-2793.2017.06.006 XUE Haifeng, CHEN Xiong, ZHENG Jian, et al. Ablation performance of carbon/phenolic jet vane[J]. Journal of Solid Rocket Technology, 2017, 40(6): 706-713 (in Chinese). doi: 10.7673/j.issn.1006-2793.2017.06.006
[82]	陈俊. 碳/酚醛复合材料燃气舵烧蚀及工作特性研究[D]. 南京: 南京理工大学, 2013. CHEN Jun. Study on ablation and working characteristics of carbon/phen- olic composite jet vane[D]. Nanjing: Nanjing University of Science and Technology, 2013 (in Chinese).
[83]	朱燕伟, 孟松鹤, 易法军, 等. 碳/酚醛复合材料烧蚀行为预报方法[J]. 复合材料学报, 2016, 33(5): 984-990. ZHU Yanwei, MENG Songhe, YI Fajun, et al. Forecasting method for ablation behaviors of carbon/phenolic composites[J]. Acta Materiae Compositae Sinica, 2016, 33(5): 984-990 (in Chinese).
[84]	张拜, 李旭东. 碳/酚醛防热复合材料烧蚀行为的数值模拟[J]. 复合材料学报, 2018, 35(10): 2786-2792. ZHANG Bai, LI Xudong. Numerical simulation of ablation behavior of carbon/phenolic thermal protection system composite[J]. Acta Materiae Compositae Sinica, 2018, 35(10): 2786-2792 (in Chinese).
[85]	张亚妮, 徐永东, 高列义, 等. 基于酚醛树脂的碳/碳复合材料在高温分解过程的微结构演变[J]. 复合材料学报, 2006, 23(1): 37-43. doi: 10.3321/j.issn:1000-3851.2006.01.006 ZHANG Yani, XU Yongdong, GAO Lieyi, et al. Microstructural evolution of phenolic resin-based carbon/carbon composites during pyrolysis[J]. Acta Materiae Compositae Sinica, 2006, 23(1): 37-43 (in Chinese). doi: 10.3321/j.issn:1000-3851.2006.01.006
[86]	ASPA Y, LACHAUD J, VIGNOLES G L, et al. Simulation of C/C composites ablation using a VOF method with moving reactive interface[C]. ECCM12 proceedings (385) (2006).
[87]	NEILSON J H, GILCHRIST A. Erosion by a stream of solid particles[J]. Wear, 1968, 11(2): 111-122. doi: 10.1016/0043-1648(68)90591-7
[88]	NEILSON J H, GILCHRIST A. An experimental investigation into aspects of erosion in rocket motor nozzles[J]. Wear, 1968, 11(2): 123-143. doi: 10.1016/0043-1648(68)90592-9
[89]	OKA Y I, OKAMURA K, YOSHIDA T. Practical estimation of erosion damage caused by solid particle impact: Part 1 effects of impact parameters on a predictive equation[J]. Wear, 2005, 259(1/2/3/4/5/6): 95-101.
[90]	OKA Y I, YOSHIDA T. Practical estimation of erosion damage caused by solid particle impact: Part 2 mechanical properties of materials directly associated with erosion damage[J]. Wear, 2005, 259(1/2/3/4/5/6): 102-109.
[91]	THAKRE P, RAWAT R, CLAYTON R, et al. Mechanical erosion of graphite nozzle in solid-propellant rocket motor[J]. Journal of Propulsion and Power, 2013, 29(3): 593-602. doi: 10.2514/1.B34630
[92]	YANG B C, CHEUNG F B, KOO J. Numerical investigation of thermos chemical and mechanical erosion of abl- ative materials[C]. AIAA 1993-2045. 29th Joint Propulsion Conference and Exhibit. June 1993.
[93]	YANG B C. A Theoretical Study of Thermome-chanical Erosion of High-Temperature Ablatives[D]. State College: The Pennsylvania State University, University Park, 1992.
[94]	YANG B C, CHEUNG F B, KOO J H. Prediction of thermos-mechanical erosion of high-temperature ablatives in the SSRM Facility[C]. AIAA 1995-254. 33rd Aerospace Sciences Meeting and Exhibit. January 1995.
[95]	KATO K. , UENO K. , SAWADA K. Estimation of Mechanical Erosion at Nozzle Inlet by Multiphase Flow Simulation in Solid Rocket Motor Considering Aluminum Droplets and Alumina Mist[C]. AIAA 2007-341. 45th AIAA Aerospace Sciences Meeting and Exhibit. January 2007.
[96]	黄海明, 徐晓亮, 章梓茂. 剥蚀引起的球锥体两相绕流效应[J]. 计算力学学报, 2011, 28(3): 366-370. doi: 10.7511/jslx201103011 HUANG Haiming, XU Xiaoliang, ZHANG Zimao. Effect of two-phase flow around spherical cone caused by erosion[J]. Chinese Journal of Computational Mechanics, 2011, 28(3): 366-370 (in Chinese). doi: 10.7511/jslx201103011
[97]	孙林, 白建强, 赵瑜, 等. 碳/碳复合材料喉衬烧蚀过程的数值分析及实验研究[J]. 固体火箭技术, 2021, 44(1): 83-89. doi: 10.7673/j.issn.1006-2793.2021.01.012 SUN Lin, BAI Jianqiang, ZHAO Yu, et al. Numerical analysis and experimental study on ablation process of throat lining of carbon/carbon composites[J]. Journal of Solid Rocket Technology, 2021, 44(1): 83-89 (in Chinese). doi: 10.7673/j.issn.1006-2793.2021.01.012
[98]	杨丰. 基于工程算法的材料烧蚀数值仿真[D]. 南京: 南京理工大学, 2017. YANG Feng. Numerical simulation of material ablation based on engineering algorithm[D]. Nanjing: Nanjing Universi- ty of Science and Technology, 2017 (in Chinese).
[99]	ZHANG X T, WANG Z K, WANG R Q, et al. Numerical simulation of chemical ablation and mechanical erosion in hybrid rocket nozzle[J]. Acta Astronautica, 2022, 192: 82-96. doi: 10.1016/j.actaastro.2021.12.012
[100]	Tang B, Rong Z C, Lu Z Y, et al. Numerical study on mechanical erosion behaviour of the burning-free Al₂O₃–C bottom nozzle during casting[J]. Ceramics International, 2022, 48(20): 30838-30845, doi: 10.1016/j.ceramint.2022.07.037
[101]	YANG J, LI W, GE J G, et al. A mesoscopic model of mechanical erosion for the characterization of ablation behavior of C/C woven composites[J]. International Journal of Heat and Mass Transfer, 2023, 206: 123962. doi: 10.1016/j.ijheatmasstransfer.2023.123962
[102]	LACHAUD J, ASPA Y, VIGNOLES G L. Analytical modeling of the steady state ablation of a 3D C/C composite[J]. Int. J. Heat Mass Transf, 2008, 51(9 /10): 2614–2627.
[103]	ZIERING M, DICRISTINA V. Thermomechanical erosion of ablative plastic composites[C]. AIAA 1972-299. 7th Thermophysics Conference. April 1972.