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The high-frequency pulsation noise generated by the turbulent boundary layer on the wall of a Laval nozzle can significantly affect the quality of the flow field at the nozzle outlet. In this study, a supersonic wind tunnel with visible internal flow is designed and fabricated to observe the development and evolution of the boundary layer on the contraction and expansion surfaces of a Laval nozzle, as well as to study the flow field inside the supersonic nozzle. The subsonic, transonic and supersonic profiles of the nozzle are designed by bicubic curve, Hall method and classical characteristic line method respectively. The results of numerical calculation and total pressure measurement show that the flow field at the nozzle outlet of the wind tunnel is uniform and stable, and the deviation of Mach-number-root mean square is better than the qualified level of China’s national military standard. Nanoparticle-tracer based planar laser scattering (NPLS) technology is used to carry out the flow display test of the internal flow visual supersonic nozzle, and the fine structure image of the whole flow field in the nozzle is obtained. The image clearly shows the development and evolution of the boundary layer in the nozzle. The interface between boundary layer and main stream and the wall curve of nozzle transition region are extracted by image processing technology. The fractal dimension of the extracted boundary layer contour is calculated, thereby establishing the corresponding relationship between the fractal dimension and the boundary layer state, and determining the transition position of the boundary layer. The results show that the transition position of the nozzle profile is closer to downstream than that of the nozzle straight wall. The fractal dimension can qualitatively judge the flow state of the boundary layer; however, it is necessary to distinguish between laminar boundary layers and hairpin vortices in the initial transition stage by considering the thickness of boundary layer.
[1] Schneider S P 2008 J. Spacecraft Rockets 45 641
Google Scholar
[2] Lobb R K, Winkler E M, Persh J 1955 J. Aeronaut. Sci. 22 1
Google Scholar
[3] Stainback P C, Anders J B, Harvey W D, Cary A M, Harris J E 1974 AIAA Paper 74 136
[4] Harvey W, Stainback P, Anders J B, Cary A 1975 AIAA J. 13 307
Google Scholar
[5] 于淼 2007 硕士学位论文 (合肥: 中国科学技术大学)
Yu M 2007 M. S. Thesis (Hefei: University of Science and Technology of China
[6] 何成军, 李建强, 范召林, 李耀华, 高荣钊, 梁锦敏, 苗磊 2020 推进技术 41 537
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[7] 王成鹏, 杨锦富, 程川, 王文硕, 徐培, 杨馨, 焦运, 程克明 2019 实验流体力学 33 11
Google Scholar
Wang C P, Yang J F, Cheng C, Wang W S, Xu P, Yang Q, Jiao Y, Cheng K M 2019 J. Exp. Fluid Mech. 33 11
Google Scholar
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Google Scholar
[9] 荣臻, 胡文杰, 邱云龙, 张玉剑, 王亦庄, 江中正, 陈伟芳 2022 空天防御 5 58
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Rong Z, Hu W J, Qiu Y L, Zhang Y J, Wang Y Z, Jiang Z Z, Chen W F 2022 Air Space Defense 5 58
Google Scholar
[10] 唐志共, 陈德江, 朱超, 曾令国, 吴锦水 2023 空气动力学学报 41 28
Google Scholar
Tang Z G, Chen D J, Zhu C, Zeng L G, Wu J S 2023 Acta Aerodyn. Sin. 41 28
Google Scholar
[11] 谢飞, 郭雷涛, 许晓斌, 凌岗 2022 推进技术 43 200806
Google Scholar
Xie F, Guo L T, Xu X B, Ling G 2022 J. Propul. Technol. 43 200806
Google Scholar
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Lu X G 2020 Ph. D. Dissertation (Changsha: National University of Defense Technology
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Lu L, Wang Y, Yan G W, Fan X Q, Su D 2019 J. Propul. Technol. 40 2654
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Lin X D, Hu X P, Wang H, Xiong B, Wu C J, Wang R B 2012 GJB1179A-2012 Requirement for Flow Quality of Low and High Speed Wind Tunnels
[16] 易仕和, 赵玉新, 何霖, 张敏莉 2013 超声速与高超声速喷管设计(北京: 国防工业出版社) 第41页
Yi S H, Zhao Y X, He L, Zhang M L 2013 Supersonic and Hypersonic Nozzle Design (Beijing: National Defense Industry Press) p41
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Wang X H, Yi S H, Fu J, Lu X G, He L 2015 Acta Phys. Sin. 64 054706
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Zhu Y Z, Yi S H, Kong X P, Quan P C, Chen Z, Tian L F 2014 Acta Phys. Sin. 63 134701
Google Scholar
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Xu X W 2019 M. S. Thesis (Changsha: National University of Defense Technology
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Google Scholar
[25] 何霖 2011 博士学位论文 (长沙: 国防科学技术大学)
He L 2011 Ph. D. Dissertation (Changsha: National University of Defense Technology
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图 1 喷管网格结构
Figure 1. Nozzle grid structure.
图 2 喷管对称面马赫数云图
Figure 2. Mach number cloud image of nozzle symmetry surface.
图 3 喷管中心流线马赫数分布图
Figure 3. Mach number distribution of nozzle direction.
图 4 喷管出口截面速度云图
Figure 4. Velocity cloud image of nozzle exit section.
图 5 喷管内流可视的超声速风洞
Figure 5. Supersonic wind tunnel with visible flow in nozzle.
图 6 达到镜面效果的喷管型面
Figure 6. Nozzle profile to achieve mirror effect.
图 7 实验设备示意图
Figure 7. Schematic diagram of experimental equipment.
图 8 FADS系统
Figure 8. FADS system.
图 9 喷管出口马赫数分布图
Figure 9. Mach number distribution diagram of nozzle outlet.
图 10 喷管流场NPLS图像
Figure 10. NPLS image of nozzle flow field.
图 11 转捩区边界层分形维数计算结果(x = 140—260 mm) (a) 转捩区喷管下壁面NPLS图像; (b) 图(a)中边界层与主流的边界; (c) 分形维数沿流向的分布曲线
Figure 11. Fractal dimension of transition boundary layer (x = 140–260 mm): (a) NPLS images of the lower wall of the transition nozzle; (b) boundary between boundary layer and main stream in panel (a); (c) distribution curve of fractal dimension along flow direction.
图 12 边界层转捩位置分布图
Figure 12. Boundary layer transition location distribution diagram.
表 1 网格无关性验证结果
Table 1. Grid independence verification results.
$ \overline{\Delta M a} $ 网格数/106 z = 0 z = 30 z = 45 1.86 0 0 0 1.40 0.0011 0.0012 0.0159 0.79 0.0027 0.0034 0.0354 注: $ \overline{\Delta M a} $为与网格数=1.86×106结果的马赫数平均偏差 
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表 2 喷管对称面内壁面区域亚-跨-超声速区域的x轴坐标范围
Table 2. The x-axis coordinate range of the subsonic transonic supersonic region in the wall area of the nozzle symmetry plane.
划分区域 亚声速区域(Ma ≤ 0.8) 跨声速区域(0.8 < Ma ≤ 1.4) 超声速区域(Ma > 1.4) x轴坐标/mm –150 ≤x < –20 –20 ≤x < 20 20 ≤x < 550
DownLoad: CSV
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[1] Schneider S P 2008 J. Spacecraft Rockets 45 641
Google Scholar
[2] Lobb R K, Winkler E M, Persh J 1955 J. Aeronaut. Sci. 22 1
Google Scholar
[3] Stainback P C, Anders J B, Harvey W D, Cary A M, Harris J E 1974 AIAA Paper 74 136
[4] Harvey W, Stainback P, Anders J B, Cary A 1975 AIAA J. 13 307
Google Scholar
[5] 于淼 2007 硕士学位论文 (合肥: 中国科学技术大学)
Yu M 2007 M. S. Thesis (Hefei: University of Science and Technology of China
[6] 何成军, 李建强, 范召林, 李耀华, 高荣钊, 梁锦敏, 苗磊 2020 推进技术 41 537
Google Scholar
He C J, Li J Q, Fan Z L, Li Y H, Gao R Z, Liang J M, Miao L 2020 J. Propul. Technol. 41 537
Google Scholar
[7] 王成鹏, 杨锦富, 程川, 王文硕, 徐培, 杨馨, 焦运, 程克明 2019 实验流体力学 33 11
Google Scholar
Wang C P, Yang J F, Cheng C, Wang W S, Xu P, Yang Q, Jiao Y, Cheng K M 2019 J. Exp. Fluid Mech. 33 11
Google Scholar
[8] Kiselev N, Malastovskii N, Zditovets A, Vinogradov Y A 2023 High Temp. 61 535
Google Scholar
[9] 荣臻, 胡文杰, 邱云龙, 张玉剑, 王亦庄, 江中正, 陈伟芳 2022 空天防御 5 58
Google Scholar
Rong Z, Hu W J, Qiu Y L, Zhang Y J, Wang Y Z, Jiang Z Z, Chen W F 2022 Air Space Defense 5 58
Google Scholar
[10] 唐志共, 陈德江, 朱超, 曾令国, 吴锦水 2023 空气动力学学报 41 28
Google Scholar
Tang Z G, Chen D J, Zhu C, Zeng L G, Wu J S 2023 Acta Aerodyn. Sin. 41 28
Google Scholar
[11] 谢飞, 郭雷涛, 许晓斌, 凌岗 2022 推进技术 43 200806
Google Scholar
Xie F, Guo L T, Xu X B, Ling G 2022 J. Propul. Technol. 43 200806
Google Scholar
[12] 陆小革 2020 博士学位论文 (长沙: 国防科技大学)
Lu X G 2020 Ph. D. Dissertation (Changsha: National University of Defense Technology
[13] 陆雷, 王翼, 闫郭伟, 范晓樯, 苏丹 2019 推进技术 40 2654
Google Scholar
Lu L, Wang Y, Yan G W, Fan X Q, Su D 2019 J. Propul. Technol. 40 2654
Google Scholar
[14] Hall I M 1962 Q. J. Mech. Appl. Math. 15 487
Google Scholar
[15] 林学东, 胡向鹏, 王辉, 熊波, 巫朝君, 王瑞波 2012 GJB1179A-2012 低速风洞和高速风洞流场品质要求
Lin X D, Hu X P, Wang H, Xiong B, Wu C J, Wang R B 2012 GJB1179A-2012 Requirement for Flow Quality of Low and High Speed Wind Tunnels
[16] 易仕和, 赵玉新, 何霖, 张敏莉 2013 超声速与高超声速喷管设计(北京: 国防工业出版社) 第41页
Yi S H, Zhao Y X, He L, Zhang M L 2013 Supersonic and Hypersonic Nozzle Design (Beijing: National Defense Industry Press) p41
[17] 易仕和, 刘小林, 陆小革, 牛海波, 徐席旺 2020 空气动力学学报 38 348
Google Scholar
Yi S H, Liu X L, Lu X G, Niu H B, Xu X W 2020 Acta Aerodyn. Sin. 38 348
Google Scholar
[18] 刘小林, 易仕和, 牛海波, 陆小革, 赵鑫海 2018 物理学报 67 174701
Google Scholar
Liu X L, Yi S H, Niu H B, Lu X G, Zhao X H 2018 Acta Phys. Sin. 67 174701
Google Scholar
[19] 全鹏程, 易仕和, 武宇, 朱杨柱, 陈植 2014 物理学报 63 084703
Google Scholar
Quan P C, Yi S H, Wu Y, Zhu Y Z, Chen Z 2014 Acta Phys. Sin. 63 084703
Google Scholar
[20] 武宇, 易仕和, 陈植, 张庆虎, 冈敦殿 2013 物理学报 62 184702
Google Scholar
Wu Y, Yi S H, Chen Z, Zhang Q H, Gang D D 2013 Acta Phys. Sin. 62 184702
Google Scholar
[21] 王小虎, 易仕和, 付佳, 陆小革, 何霖 2015 物理学报 64 054706
Google Scholar
Wang X H, Yi S H, Fu J, Lu X G, He L 2015 Acta Phys. Sin. 64 054706
Google Scholar
[22] 朱杨柱, 易仕和, 孔小平, 全鹏程, 陈植, 田立丰 2014 物理学报 63 134701
Google Scholar
Zhu Y Z, Yi S H, Kong X P, Quan P C, Chen Z, Tian L F 2014 Acta Phys. Sin. 63 134701
Google Scholar
[23] 徐席旺 2019 硕士学位论文 (长沙: 国防科学技术大学)
Xu X W 2019 M. S. Thesis (Changsha: National University of Defense Technology
[24] Zhao Y X, Yi S H, Tian L F, Cheng Z Y 2009 Sci. China Ser. E: Technol. Sci. 52 3640
Google Scholar
[25] 何霖 2011 博士学位论文 (长沙: 国防科学技术大学)
He L 2011 Ph. D. Dissertation (Changsha: National University of Defense Technology
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