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Based on the large eddy simulation, the boundary of a vortex and the coordinates of its core are both obtained by using the Lagrangian coherent structure method and the location extraction method of the vortex core, and thus the method of representing fluid density inside a vortex is proposed. The density distribution characteristics of fluid inside the vortex in a supersonic mixing layer are revealed by analyzing the changes in density of the fluid inside a vortex under different conditions (e.g. spatial size of the vortex, compressibility of the supersonic mixing layer, and merging process of the two paired vortices) as follows. For the weak and medium compressive supersonic mixing layers, the density distribution of the fluid inside a vortex is symmetrical about both the flow direction (x-axis) and longitudinal direction (y-axis), the fluid density at the vortex core is lowest while it is highest at the vortex boundary, and fluid density increases monotonically and nearly uniformly along the ray connecting the vortex core and the vortex boundary. For the strongly compressible supersonic mixing layer, however, the density distribution of the fluid inside the vortex is no longer symmetrical about any flow direction and moreover it shows the fluctuation characteristics of fluid density distribution. With the increase of the spatial size of a vortex and the compressibility of a supersonic mixing layer, the fluid density at the vortex core decreases (the maximum reduction is about 31%–56%) while it changes about 6%–27% at the vortex boundary. In the merging process of two adjacent vortices, the variation of fluid density in the two vortices is slight, which shows that the merging process is probably of a peer-to-peer combination of fluid inside the two adjacent vortices. Considering the practical engineering applications, the density distribution characteristics of fluid inside the vortex in the supersonic mixing layer with different inflow densities of its upper and lower layers are also investigated, and the results show that the density distribution of the fluid inside a vortex is symmetrical about the longitudinal direction (y-axis), but not the flow direction (x-axis). It is also found that the density distribution near the vortex boundary is determined by the inflow density there, so a good strategy of reducing the aero-optical effects caused by the supersonic mixing layer is that the difference in density between the upper and lower layers should be as small as possible.
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Keywords:
- density distribution /
- vortex /
- supersonic mixing layer /
- large eddy simulation
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Google Scholar
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Google Scholar
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Yin X L 2003 Principle of Aero-Optics (Beijing: China Astronautics Press) p2 (in Chinese)
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Google Scholar
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Google Scholar
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Yi S H, Chen Z, Zhu Y Z, He L, Wu Y 2015 Acta Aeronaut. Astronaut. Sin. 1 98
[9] 沈清, 袁湘江, 王强, 杨武兵, 关发明, 纪锋 2012 力学进展 42 252
Shen Q, Yuan X J, Wang Q, Yang W B, Guan F M, Ji F 2012 Adv. Mech. 42 252
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Google Scholar
[11] Zhang D D, Tan J G, Lv L 2015 Acta Astronaut. 117 440
Google Scholar
[12] 郭广明, 刘洪, 张斌, 张庆兵 2017 物理学报 66 084701
Google Scholar
Guo G M, Liu H, Zhang B, Zhang Q B 2017 Acta Phys. Sin. 66 084701
Google Scholar
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Google Scholar
Zhang D D, Tan J G, Yao X 2020 Acta Phys. Sin. 69 024701
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
Gan C J, Li L, Ma H D, Xiong H L 2014 Acta Phys. Sin. 63 054703
Google Scholar
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Google Scholar
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[21] 丁浩林, 易仕和, 赵鑫海, 易君如, 葛勇 2018 气体物理 6 26
Ding H L, Yi S H, Zhao X H, Yi J R, Ge Y 2018 Phys.Gases 6 26
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Google Scholar
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Guo G M, Liu H, Zhang B, Zhang Z Y, Zhang Q B 2016 Acta Phys. Sin. 65 074702
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Zheng Z H, Fan Z Q, Wang Z A, Yu B, Zhang B 2019 Acta Aeronaut. Astronaut. Sin. 41 123295
Google Scholar
[25] 秦苏洋 2016 硕士学位论文 (上海: 上海交通大学)
Qin S Y 2016 M S. Thesis (Shanghai: Shanghai Jiao Tong University) (in Chinese)
[26] Papamoschou D, Bunyajitradulya A 1997 Phys. Fluids 3 756
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图 1 (a)红外制导飞行器的气动光学效应; (b)涡结构引起光束波前畸变的示意图
Figure 1. (a) Schematic of aero-optic effects of an infrared guidance vehicle; (b) wavefront distortion caused by a vortex.
图 2 超声速混合层的涡量等值面
Figure 2. The vorticity contour of a supersonic mixing layer simulated by LES.
图 3 涡边界椭圆模型的建立过程示意图 (a)两个涡结构; (b) LCS; (c)涡边界的椭圆模型
Figure 3. Process of establishing an elliptic model for the vortex boundary: (a) Two vortices; (b) LCS; (c) elliptic model of vortex boundary
图 4 计算涡核位置坐标的原理图
Figure 4. Schematic of calculating position coordinates of a vortex core.
图 5 基于涡边界和涡核位置的涡结构内部流体密度分布表示方法
Figure 5. Method of representing fluid density distribution inside a vortex based on its boundary and core location.
图 6 (a)对流马赫数0.5的超声速混合层; (b)涡结构 A; (c)涡结构B; (d)涡结构C
Figure 6. (a)The supersonic mixing layer with Mc = 0.5; (b) Vortex A; (c) Vortex B; (d) Vortex C.
图 7 不同尺寸涡结构内部流体的密度分布曲线 (a) Vortex A内部流体的密度随流向(x)距离变化的曲线图; (b) Vortex A内部流体密度随纵向(y)距离变化的曲线图; (c) Vortex B内部流体密度随流向(x)距离变化的曲线图; (d) Vortex B内部流体密度随纵向(y)距离变化的曲线图; (e) Vortex C内部流体密度随流向(x)距离变化的曲线图; (f) Vortex C内部流体密度随纵向(y)距离变化的曲线图
Figure 7. Density distribution of fluid inside three vortices: (a) Density distribution of fluid inside Vortex A along the flow direction (x-axis); (b) density distribution of fluid inside Vortex A along the longitudinal direction (y-axis); (c) density distribution of fluid inside Vortex B along the flow direction (x-axis); (d) density distribution of fluid inside Vortex B along the longitudinal direction (y-axis); (e) density distribution of fluid inside Vortex C along the flow direction (x-axis); (f) density distribution of fluid inside Vortex C along the longitudinal direction (y-axis).
图 8 不同压缩性的超声速混合层
Figure 8. Supersonic mixing layers with different compressibilities
图 9 不同压缩性流场中涡结构内部流体的密度分布曲线
Figure 9. Density distribution of fluid inside two vortices in the supersonic mixing layers with different compressibilities.
图 10 (a)弱压缩性的超声速混合层, Mc = 0.3; (b)其流场中相邻两个涡结构的融合过程
Figure 10. (a) Supersonic mixing layer with Mc = 0.3; (b) two adjacent vortices during their merging process.
图 11 涡a和涡b在长轴和短轴上的流体密度在涡融合过程中的变化曲线
Figure 11. Variation curve of the fluid density inside the vortex a and b during their merging process.
图 12 特征点密度在涡融合过程中的变化
Figure 12. Variation of fluid density at several characteristic points during their merging process.
图 13 (a)上下层来流密度不同的超声速混合层; (b)涡结构内部流体的密度沿纵向(y)分布曲线; (c)涡结构内部流体的密度沿流向(x)分布曲线
Figure 13. (a) The supersonic mixing layer with different inflow density of its upper and lower layers; (b) density distribution of fluid inside the vortex along the longitudinal direction (y-axis); (c) density distribution of fluid inside the vortex along the flow direction (x-axis).
表 1 超声速混合层的入流参数
Table 1. Inflow parameters of three supersonic mixing layers.
序号 混合层入流速度/m·s–1 T∞/K P∞/kPa ρ∞/kg·m–3 Mc 上层流体(U1) 下层流体(U2) 1 605.6 403.7 281 89.9 1.107 0.3 2 740.2 403.7 281 89.9 1.107 0.5 3 1009.3 403.7 281 89.9 1.107 0.9 
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表 2 不同空间尺寸涡结构的几何参数
Table 2. Geometric parameters of three vortices with different sizes.
涡结构 中心点 长半轴a/m 短半轴b/m 扁率e xc/m yc/m Vortex A 0.1136 –0.001762 0.003314 0.002703 0.1844 Vortex B 0.1858 0.001635 0.006231 0.003877 0.3778 Vortex C 0.2863 0.003296 0.010652 0.005091 0.5221
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表 3 不同压缩性超声速混合层涡结构的几何参数
Table 3. Geometric parameters of two vortices in the fields with different compressibilities.
涡结构 中心点 长半轴a/m 短半轴b/m 扁率e xc/m yc/m Vortex D (Mc = 0.3) 0.1824 –0.0008203 0.004854 0.003128 0.3556 Vortex E (Mc = 0.9) 0.2607(0.2589) –0.0012338(–0.0001429) 0.013673 0.006051 0.5574
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[1] Niu Q L, Gao P, Yuan Z C, He Z H, Dong S K 2019 Infrared Phys. Technol. 97 74
Google Scholar
[2] Jumper E J, Gordeyev S 2017 Annu.Rev.Fluid Mech. 49 419
Google Scholar
[3] 殷兴良 2003 气动光学原理 (北京: 中国宇航出版社) 第2页
Yin X L 2003 Principle of Aero-Optics (Beijing: China Astronautics Press) p2 (in Chinese)
[4] Rogers M M, Moser R D 1992 J.Fluid Mech. 243 183
Google Scholar
[5] Mungal M G, Hermanson J C, Dimotakis P E 1985 AIAA J. 23 1418
Google Scholar
[6] Brown G L, Roshko A 1974 J.Fluid Mech. 64 775
Google Scholar
[7] 朱杨柱, 易仕和, 孔小平, 何霖 2015 物理学报 64 064701
Google Scholar
Zhu Y Z, Yi S H, Kong X P, He L 2015 Acta Phys. Sin. 64 064701
Google Scholar
[8] 易仕和, 陈植, 朱杨柱, 何霖, 武宇 2015 航空学报 1 98
Yi S H, Chen Z, Zhu Y Z, He L, Wu Y 2015 Acta Aeronaut. Astronaut. Sin. 1 98
[9] 沈清, 袁湘江, 王强, 杨武兵, 关发明, 纪锋 2012 力学进展 42 252
Shen Q, Yuan X J, Wang Q, Yang W B, Guan F M, Ji F 2012 Adv. Mech. 42 252
[10] Wang B, Wei W, Zhang Y L, Zhang H Q, Xue S Y 2015 Comput. Fluids 123 32
Google Scholar
[11] Zhang D D, Tan J G, Lv L 2015 Acta Astronaut. 117 440
Google Scholar
[12] 郭广明, 刘洪, 张斌, 张庆兵 2017 物理学报 66 084701
Google Scholar
Guo G M, Liu H, Zhang B, Zhang Q B 2017 Acta Phys. Sin. 66 084701
Google Scholar
[13] 张冬冬, 谭建国, 姚霄 2020 物理学报 69 024701
Google Scholar
Zhang D D, Tan J G, Yao X 2020 Acta Phys. Sin. 69 024701
Google Scholar
[14] Catrakis H J, Aguirre R C 2004 AIAA J. 42 1973
Google Scholar
[15] Dimotaksi P, Catrakis H, Fourguette D 2001 J. Fluid Mech. 433 105
Google Scholar
[16] Chew L, Christiansen W 1993 AIAA J. 31 2290
Google Scholar
[17] 甘才俊, 李烺, 马汉东, 熊红亮 2014 物理学报 63 054703
Google Scholar
Gan C J, Li L, Ma H D, Xiong H L 2014 Acta Phys. Sin. 63 054703
Google Scholar
[18] Guo G M, Liu H, Zhang B 2016 Appl. Opt. 55 2708
Google Scholar
[19] Visbal M R, Rizzeta D P 2008 AIAA Paper 2008-1074
[20] Rennie R M, Duffin D A, Jumper E J 2008 AIAA J. 46 2787
Google Scholar
[21] 丁浩林, 易仕和, 赵鑫海, 易君如, 葛勇 2018 气体物理 6 26
Ding H L, Yi S H, Zhao X H, Yi J R, Ge Y 2018 Phys.Gases 6 26
[22] Guo G M, Luo Q 2019 Opt.Commun. 452 48
Google Scholar
[23] 郭广明, 刘洪, 张斌, 张忠阳, 张庆兵 2016 物理学报 65 074702
Google Scholar
Guo G M, Liu H, Zhang B, Zhang Z Y, Zhang Q B 2016 Acta Phys. Sin. 65 074702
Google Scholar
[24] 郑忠华, 范周琴, 王子昂, 余彬, 张斌 2019 航空学报 41 123295
Google Scholar
Zheng Z H, Fan Z Q, Wang Z A, Yu B, Zhang B 2019 Acta Aeronaut. Astronaut. Sin. 41 123295
Google Scholar
[25] 秦苏洋 2016 硕士学位论文 (上海: 上海交通大学)
Qin S Y 2016 M S. Thesis (Shanghai: Shanghai Jiao Tong University) (in Chinese)
[26] Papamoschou D, Bunyajitradulya A 1997 Phys. Fluids 3 756
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