超声速横向气流中液体射流的轨迹预测与连续液柱模型

周曜智; 李春; 李晨阳; 李清廉

doi:10.7498/aps.69.20200903

摘要

对于液体射流沿壁面法向喷注进入超声速横向气流中的射流轨迹开展了理论与实验研究, 建立了连续液柱三维实体模型. 基于液体微元受力分析建立了连续液柱沿喷注方向横截面的截面变形控制方程, 计算了液体射流轨迹与横截面变形, 合理考虑了液体射流因发生表面破碎所引起的质量损失, 提出适用于超声速横向气流的连续液柱模型. 利用高时空分辨率的显微成像方法拍摄超声速横向气流中连续液柱的瞬时图像, 研究的参数变量包括液体喷注压降(1—2 MPa)、液体喷嘴直径(0.5 mm/1.0 mm)及液气动量比(3.32—7.27). 研究结果表明, 采用连续液柱模型可以较好地预测中心面上的射流轨迹和三维空间上的液柱形态, 并可较为真实地反映实际流场特征, 预测结果与实验结果吻合良好.

关键词:

Abstract

The trajectory of the spray is studied theoretically and experimentally when a round liquid jet is injected into a supersonic crossflow vertically. A solid model of continuous liquid column is established in three-dimensional space. The cross-section deformation equation of the continuous liquid column along the injection direction is established using a method of micro-element analysis. The stress analysis of cross section is simplified into a two-dimensional droplet. The shape of the cross section is considered to continuously change from circular to elliptical shape. And the bow shock wave in front of the jet column is simplified into an oblique shock wave with a known shock angle. Based on this, the calculation of aerodynamic force is greatly simplified. A dimensionless parameter named effective deformation time of liquid column (the logogram is ${t_{\rm valid}}$) is defined and used to judge the end point of the liquid column quantitatively. The liquid jet trajectory and cross-section deformation can be calculated using MATLAB software. The instantaneous images of continuous liquid columns in supersonic crossflow are captured using high-spatial-resolution microscopic imaging methods. The microscopic imaging system is composed of a double pulse solid-state laser, computer, CCD camera, synchronous controller, microscope lens and laser diffuser. After passing through the laser diffuser, a plane background light with uniform distribution is formed on the scattering plate. The mean filtering method is used to filter the original image. After filtering, the range of gray distribution in the background area is obviously reduced. The distribution of gray value is more concentrated, and the background of the image is more uniform. Then the image edge detection function is used to obtain the near-field jet trajectory. The parameter variables studied include liquid injection pressure drop (1–2 MPa), liquid nozzle diameter (0.5 mm/1.0 mm), and liquid gas momentum ratio (3.32–7.27). The results show that the continuous liquid column model can better predict the jet trajectory on the center plane and the shape of the liquid column in three-dimensional space. It is indicated that the predictive result matches well with the experimental result. This study is of great significance for establishing the solid-particle coupling model of liquid jet in supersonic crossflows.

Keywords:

作者及机构信息

1.
国防科技大学空天科学学院, 长沙　410073

2.
国防科技大学, 高超声速冲压发动机技术重点实验室, 长沙　410073

通信作者: 李清廉, peakdreamer@163.com

基金项目: 国家自然科学基金(批准号: 11472303, 11402298, 11872375)和国家自然科学基金青年科学基金(批准号: 11902351)资助的课题

Authors and contacts

1.
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China

2.
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073, China

Corresponding author: Li Qing-Lian, peakdreamer@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11472303, 11402298, 11872375) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11902351)

文章全文 : translate this paragraph

参考文献

[1]	Xiao F, Dianat M, Mcguirk J J 2013 AIAA J. 51 2878 Google Scholar
[2]	夏同军, 董永强, 曹义刚 2013 物理学报 62 214702 Google Scholar Xia T J, Dong Y Q, Cao Y G 2013 Acta Phys. Sin. 62 214702 Google Scholar
[3]	Heister S D 2011 Handbook of Atomization and Sprays: Theory and Applications (New York: Springer) pp65−660
[4]	Li C Y, Li C, Xiao F, Li Q L, Zhu Y H 2019 Aerosp. Sci. Technol. 95 105426 Google Scholar
[5]	Dixon D R, Gruber M R, Jackson T A, Lin K C 2005 43th AIAA Aerospace Sciences Meeting & Exhibit Reno, America, January 10−13, 2005 p733
[6]	Wu L Y, Wang Z G, Li Q L, Li C 2016 J. Visualization 3 337 Google Scholar
[7]	Hu R S, Li Q, Li C Y, Li C 2019 Acta Astronaut. 159 440 Google Scholar
[8]	Lin K C, Kennedy P J 2002 40 th AIAA Aerospace Sciences Meeting & Exhibit Reno, America, January 14−17, 2002 p873
[9]	Lin K C, Kennedy P J, Kennedy P J, Jackson T A 2004 42th AIAA Aerospace Sciences Meeting & Exhibit Reno, America, January 5−8, 2004 p971
[10]	刘静, 王辽, 张佳, 韦宝禧, 徐旭 2008 航空动力学报 4 146 Google Scholar Liu J, Wang L, Zhang J, Wei B X, Xu X 2008 J. Aerosp. Power 4 146 Google Scholar
[11]	仝毅恒, 李清廉, 吴里银 2012 国防科技大学学报 2 73 Google Scholar Tong Y H, Li Q L, Wu L Y 2012 J. Natl. Univ. Def. Technol. 2 73 Google Scholar
[12]	李春 2014 硕士学位论文 (长沙: 国防科学技术大学) Li C 2012 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese)
[13]	吴里银, 王振国, 李清廉, 李春中国专利 zl201410800056.5 [2018-2-2] Wu L Y, Wang Z G, Li Q L, Li C Chinese Patent zl201410800056.5 [20218-2-2] (in Chinese)
[14]	胡润生, 朱元昊, 张翔宇, 李清廉 2019 工程热物理学报 7 1659 Google Scholar Hu R S, Zhu Y H, Zhang X Y, Li Q L 2019 J. Eng. Therm. 7 1659 Google Scholar
[15]	吴里银, 王振国, 李清廉, 李春 2016 物理学报 68 094701 Google Scholar Wu L Y, Wang Z G, Li Q L, Li C 2016 Acta Phys. Sin. 68 094701 Google Scholar
[16]	周曜智, 李清廉, 李晨阳 2020 推进技术 41 7 Google Scholar Zhou Y Z, Li Q L, Li C Y 2020 J. Propul. Technol. 41 7 Google Scholar
[17]	Mashayek A, Behzad M, Ashgriz N 2011 AIAA J. 49 2407 Google Scholar
[18]	李春 2020 博士学位论文 (长沙: 国防科技大学) Li C 2020 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[19]	Xiao F, Wang Z G, Sun M B, Liang J H, Liu N 2016 Int. J. Multiphase Flow 87 229 Google Scholar
[20]	李佩波, 王振国, 孙明波, 汪洪波 2016 宇航学报 37 79 Google Scholar Li P B, Wang Z G, Sun M B, Wang H B 2016 J. Astronautics 37 79 Google Scholar
[21]	Zhu Y X, Xiao F, Li Q L, Li C Y, Lin S 2018 Acta Astronaut. 154 119 Google Scholar
[22]	Liu N, Wang Z G, Sun M B, Deiterding R, Wang H B 20191 Aerosp. Sci. Technol. 91 456 Google Scholar
[23]	Douglas H F, Vitor V, Lucas S M, Francisco J S 2019 Int. J. Multiphase Flow 114 98 Google Scholar
[24]	Li P B, Li C Y, Wang H B, Sun M B, Liu C Y, Wang Z G, Huang Y H 2019 Aerosp. Sci. Technol. 94 105401 Google Scholar
[25]	Nguyen T, Karagozian A R 1992 J. Propul. Power 8 21 Google Scholar
[26]	Clark M M 1988 Chem. Eng. Sci. 43 671 Google Scholar
[27]	Inamura T 2000 J. Propul. Power 16 155 Google Scholar
[28]	Sallam K A, Aalburg C, Faeth G M 2004 AIAA J. 42 2529 Google Scholar
[29]	Wu P K, Kirkendall K A, Fuller R P, Nejad A S 1997 J. Propul. Power 13 64 Google Scholar
[30]	吴里银 2016 博士学位论文 (长沙: 国防科学技术大学 Wu L Y 2016 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[31]	Lee K, Aalburg C, Diez F J, Faeth G M, Sallam K A 2007 AIAA J. 45 1907 Google Scholar
[32]	Ranger A A, Nicholls J A 1969 AIAA J. 7 285 Google Scholar
[33]	Chryssakis C A, Assanis, D N 2005 18th Annual Conference on Liquid and Atomization and Spray Systems, Irvine, America, May 15−18, 2005 p283

施引文献

图 1 超声速风洞系统示意图^[18]

Fig. 1. Schematic diagram of supersonic wind tunnel system^[18]

下载: 全尺寸图片幻灯片

图 2 显微成像系统原理图

Fig. 2. Schematic diagram of microscopic imaging system

下载: 全尺寸图片幻灯片

图 3 显微成像系统原理图　(a) QM1镜头; (b) QM1镜头工作特性曲线

Fig. 3. Schematic diagram of microscopic imaging system: (a) QM1 camera lens; (b) QM1 microscopy camera lens working characteristic curve

下载: 全尺寸图片幻灯片

图 4 液体微元的受力分析示意图

Fig. 4. Aerodynamic drag coefficient calculation domain

下载: 全尺寸图片幻灯片

图 5 二维液滴附近网格

Fig. 5. Grids near the 2D droplet

下载: 全尺寸图片幻灯片

图 6 对称面流向速度分布

Fig. 6. Symmetrical flow velocity distributions

下载: 全尺寸图片幻灯片

图 7 二维液滴表面静压分布

Fig. 7. Surface static pressure distributions of 2D droplet

下载: 全尺寸图片幻灯片

图 8 连续液柱变形分区示意图

Fig. 8. Schematic diagram of continuous liquid column deformation partition

下载: 全尺寸图片幻灯片

图 9 模型假设示意图(粉色为液体射流一次破碎大涡模拟结果^[19-22])

Fig. 9. Schematic diagram of model hypothesis (The pink region is the result of large eddy simulation of liquid jet primary breakup^[19-22])

下载: 全尺寸图片幻灯片

图 10 液体微元横截面变形示意图

Fig. 10. Schematic diagram of cross-section deformation of liquid microelements

下载: 全尺寸图片幻灯片

图 11 液体微元的受力分析示意图

Fig. 11. Schematic diagram of force analysis of liquid microelements

下载: 全尺寸图片幻灯片

图 12 二维液滴附近流向速度分布

Fig. 12. Flow velocity distribution of 2D droplets

下载: 全尺寸图片幻灯片

图 13 二维液滴气动阻力系数C_D

Fig. 13. Aerodynamic drag coefficient of 2D droplet C_D

下载: 全尺寸图片幻灯片

图 14 斜激波简化示意图

Fig. 14. Simplified schematic diagram of oblique shock

下载: 全尺寸图片幻灯片

图 15 斜激波波前/波后速度分解示意图

Fig. 15. Schematic diagram of velocity decomposition of oblique shock wave front/back wave

下载: 全尺寸图片幻灯片

图 16 液体微元横截面椭圆率计算结果

Fig. 16. Calculation results of eccentricity of liquid microelement cross section

下载: 全尺寸图片幻灯片

图 17 液体微元当地韦伯数计算结果

Fig. 17. Schematic diagram of cross-section deformation of liquid microelements

下载: 全尺寸图片幻灯片

图 18 剥离液滴质量计算结果

Fig. 18. Schematic diagram of cross-section deformation of liquid microelements

下载: 全尺寸图片幻灯片

图 19 CLC模型预测得到的连续液柱结构　(a) 侧视图; (b) 正视图

Fig. 19. Continuous liquid column structure predicted by CLC model: (a) Side view; (b) front view

下载: 全尺寸图片幻灯片

图 20 射流轨迹叠加结果

Fig. 20. Superposition result of jet trajectory

下载: 全尺寸图片幻灯片

图 21 喷嘴出口位置射流显微成像结果(基准工况)

Fig. 21. Jet microscopic imaging results at the nozzle outlet (basic condition).

下载: 全尺寸图片幻灯片

图 22 不同喷注压降射流显微图像　(a)$\Delta p$ = 0.97 MPa; (b)$\Delta p$ = 1.49 MPa; (c)$\Delta p$ = 2.05 MPa

Fig. 22. Microscopic images of jets with different injection pressure drops: (a)$\Delta p$ = 0.97 MPa; (b)$\Delta p$ = 1.49 MPa; (c)$\Delta p$ = 2.05 MPa.

下载: 全尺寸图片幻灯片

图 23 CLC模型预测得到的射流轨迹结果与实验结果(基准工况)

Fig. 23. Jet trajectory results and experimental results predicted by the CLC model (basic condition)

下载: 全尺寸图片幻灯片

图 24 超声速横流中液柱破碎位置与文献结果对比

Fig. 24. Comparison of the broken position of liquid column in supersonic cross-flow with literature results

下载: 全尺寸图片幻灯片

图 25 不同动量比和不同喷嘴直径下射流轨迹计算结果与本文实验结果比较　(a) d = 0.5 mm; (b) q = 3.32

Fig. 25. Calculations for different momentum ratios and diffent nozzle diameters in comparison with experiments: (a) d = 0.5 mm; (b) q = 3.32

下载: 全尺寸图片幻灯片

表 1 超声速横流参数

Table 1. Supersonic cross flow parameters

	Ma = 2.1	Ma = 2.85
总温T₀/K	300	300
总压P₀/kPa	891	1410
静温T/K	159.4	114.3
静压P/kPa	97.7	48.1
密度/kg·m^–3	2.13	1.47
声速/m·s^–1	253	214
速度/m·s^–1	531	611

下载: 导出CSV

表 2 不同网格计算得到的气动阻力系数

Table 2. Aerodynamic drag coefficients calculated from different grids.

类别	最小网格尺寸/d	网格量	气动阻力系数
Coarse	0.020	50840	1.372
Middle	0.010	225448	1.350
Fine	0.005	488752	1.349

下载: 导出CSV

表 3 理论计算参数

Table 3. Theoretical calculation parameters.

编号	横向气流 (T₀ = 300 K)			水射流 (密度: 998 kg·m^–3)
编号	Ma	P₀/kPa	ρ_g/kg·m^–3	u_j/m·s^–1	d/mm	$\Delta P$/MPa	q
Case 1	2.85	1410	1.47	44.7	0.5/1.0	1.0	3.323
Case 2	2.85	1410	1.47	54.8	0.5/1.0	1.5	4.985
Case 3	2.85	1410	1.47	63.2	0.5/1.0	2.0	6.647
Case 4	2.1	891	2.13	44.7	0.5/1.0	1.0	3.637
Case 5	2.1	891	2.13	54.8	0.5/1.0	1.5	5.456
Case 6	2.1	891	2.13	63.2	0.5/1.0	2.0	7.274

下载: 导出CSV

表 4 三维连续液柱模型参数

Table 4. 3D continuous liquid column model parameters.

类别	$x{\rm{/}}d$	$y{\rm{/}}d$	$z/d$
考虑质量损失	0—1.92	0—4.17	–1.03—1.03

下载: 导出CSV

[1]	Xiao F, Dianat M, Mcguirk J J 2013 AIAA J. 51 2878 Google Scholar
[2]	夏同军, 董永强, 曹义刚 2013 物理学报 62 214702 Google Scholar Xia T J, Dong Y Q, Cao Y G 2013 Acta Phys. Sin. 62 214702 Google Scholar
[3]	Heister S D 2011 Handbook of Atomization and Sprays: Theory and Applications (New York: Springer) pp65−660
[4]	Li C Y, Li C, Xiao F, Li Q L, Zhu Y H 2019 Aerosp. Sci. Technol. 95 105426 Google Scholar
[5]	Dixon D R, Gruber M R, Jackson T A, Lin K C 2005 43th AIAA Aerospace Sciences Meeting & Exhibit Reno, America, January 10−13, 2005 p733
[6]	Wu L Y, Wang Z G, Li Q L, Li C 2016 J. Visualization 3 337 Google Scholar
[7]	Hu R S, Li Q, Li C Y, Li C 2019 Acta Astronaut. 159 440 Google Scholar
[8]	Lin K C, Kennedy P J 2002 40 th AIAA Aerospace Sciences Meeting & Exhibit Reno, America, January 14−17, 2002 p873
[9]	Lin K C, Kennedy P J, Kennedy P J, Jackson T A 2004 42th AIAA Aerospace Sciences Meeting & Exhibit Reno, America, January 5−8, 2004 p971
[10]	刘静, 王辽, 张佳, 韦宝禧, 徐旭 2008 航空动力学报 4 146 Google Scholar Liu J, Wang L, Zhang J, Wei B X, Xu X 2008 J. Aerosp. Power 4 146 Google Scholar
[11]	仝毅恒, 李清廉, 吴里银 2012 国防科技大学学报 2 73 Google Scholar Tong Y H, Li Q L, Wu L Y 2012 J. Natl. Univ. Def. Technol. 2 73 Google Scholar
[12]	李春 2014 硕士学位论文 (长沙: 国防科学技术大学) Li C 2012 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese)
[13]	吴里银, 王振国, 李清廉, 李春中国专利 zl201410800056.5 [2018-2-2] Wu L Y, Wang Z G, Li Q L, Li C Chinese Patent zl201410800056.5 [20218-2-2] (in Chinese)
[14]	胡润生, 朱元昊, 张翔宇, 李清廉 2019 工程热物理学报 7 1659 Google Scholar Hu R S, Zhu Y H, Zhang X Y, Li Q L 2019 J. Eng. Therm. 7 1659 Google Scholar
[15]	吴里银, 王振国, 李清廉, 李春 2016 物理学报 68 094701 Google Scholar Wu L Y, Wang Z G, Li Q L, Li C 2016 Acta Phys. Sin. 68 094701 Google Scholar
[16]	周曜智, 李清廉, 李晨阳 2020 推进技术 41 7 Google Scholar Zhou Y Z, Li Q L, Li C Y 2020 J. Propul. Technol. 41 7 Google Scholar
[17]	Mashayek A, Behzad M, Ashgriz N 2011 AIAA J. 49 2407 Google Scholar
[18]	李春 2020 博士学位论文 (长沙: 国防科技大学) Li C 2020 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[19]	Xiao F, Wang Z G, Sun M B, Liang J H, Liu N 2016 Int. J. Multiphase Flow 87 229 Google Scholar
[20]	李佩波, 王振国, 孙明波, 汪洪波 2016 宇航学报 37 79 Google Scholar Li P B, Wang Z G, Sun M B, Wang H B 2016 J. Astronautics 37 79 Google Scholar
[21]	Zhu Y X, Xiao F, Li Q L, Li C Y, Lin S 2018 Acta Astronaut. 154 119 Google Scholar
[22]	Liu N, Wang Z G, Sun M B, Deiterding R, Wang H B 20191 Aerosp. Sci. Technol. 91 456 Google Scholar
[23]	Douglas H F, Vitor V, Lucas S M, Francisco J S 2019 Int. J. Multiphase Flow 114 98 Google Scholar
[24]	Li P B, Li C Y, Wang H B, Sun M B, Liu C Y, Wang Z G, Huang Y H 2019 Aerosp. Sci. Technol. 94 105401 Google Scholar
[25]	Nguyen T, Karagozian A R 1992 J. Propul. Power 8 21 Google Scholar
[26]	Clark M M 1988 Chem. Eng. Sci. 43 671 Google Scholar
[27]	Inamura T 2000 J. Propul. Power 16 155 Google Scholar
[28]	Sallam K A, Aalburg C, Faeth G M 2004 AIAA J. 42 2529 Google Scholar
[29]	Wu P K, Kirkendall K A, Fuller R P, Nejad A S 1997 J. Propul. Power 13 64 Google Scholar
[30]	吴里银 2016 博士学位论文 (长沙: 国防科学技术大学 Wu L Y 2016 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)
[31]	Lee K, Aalburg C, Diez F J, Faeth G M, Sallam K A 2007 AIAA J. 45 1907 Google Scholar
[32]	Ranger A A, Nicholls J A 1969 AIAA J. 7 285 Google Scholar
[33]	Chryssakis C A, Assanis, D N 2005 18th Annual Conference on Liquid and Atomization and Spray Systems, Irvine, America, May 15−18, 2005 p283

[1]	张洋, 张志豪, 王宇剑, 薛晓兰, 陈令修, 石礼伟. 偏振调制扫描光学显微镜方法. 物理学报, 2024, 73(15): 157801. doi: 10.7498/aps.73.20240688
[2]	韦芊屹, 倪洁蕾, 李灵, 张聿全, 袁小聪, 闵长俊. 超高时空分辨显微成像技术研究进展. 物理学报, 2023, 72(17): 178701. doi: 10.7498/aps.72.20230733
[3]	刘勇, 涂国华, 向星皓, 李晓虎, 郭启龙, 万兵兵. 横向矩形微槽抑制高超声速第二模态扰动波的参数化研究. 物理学报, 2022, 71(19): 194701. doi: 10.7498/aps.71.20220851
[4]	隋怡晖, 郭星奕, 郁钧瑾, Alexander A. Solovev, 他得安, 许凯亮. 生成对抗网络加速超分辨率超声定位显微成像方法研究. 物理学报, 2022, 71(22): 224301. doi: 10.7498/aps.71.20220954
[5]	张益溢, 吴佳琛, 郝然, 金尚忠, 曹良才. 基于数字全息的血红细胞显微成像技术. 物理学报, 2020, 69(16): 164201. doi: 10.7498/aps.69.20200357
[6]	王鹏, 沈赤兵. 等离子体合成射流对超声速混合层的混合增强. 物理学报, 2019, 68(17): 174701. doi: 10.7498/aps.68.20190683
[7]	许昊, 王聪, 陆宏志, 黄文虎. 水下超声速气体射流诱导尾空泡实验研究. 物理学报, 2018, 67(1): 014703. doi: 10.7498/aps.67.20171617
[8]	王建国, 杨松林, 叶永红. 样品表面银膜的粗糙度对钛酸钡微球成像性能的影响. 物理学报, 2018, 67(21): 214209. doi: 10.7498/aps.67.20180823
[9]	刘强, 罗振兵, 邓雄, 杨升科, 蒋浩. 合成冷/热射流控制超声速边界层流动稳定性. 物理学报, 2017, 66(23): 234701. doi: 10.7498/aps.66.234701
[10]	张孝石, 许昊, 王聪, 陆宏志, 赵静. 水流冲击超声速气体射流实验研究. 物理学报, 2017, 66(5): 054702. doi: 10.7498/aps.66.054702
[11]	刘双龙, 刘伟, 陈丹妮, 屈军乐, 牛憨笨. 相干反斯托克斯拉曼散射显微成像技术研究. 物理学报, 2016, 65(6): 064204. doi: 10.7498/aps.65.064204
[12]	吴里银, 王振国, 李清廉, 李春. 超声速气流中液体横向射流的非定常特性与振荡边界模型. 物理学报, 2016, 65(9): 094701. doi: 10.7498/aps.65.094701
[13]	彭志勇, 王向军, 卢进. 近高超声速高温蓝宝石窗口下中波红外成像退化分析仿真与性能测试实验. 物理学报, 2013, 62(23): 230702. doi: 10.7498/aps.62.230702
[14]	张强, 陈鑫, 何立明, 荣康. 矩形喷口欠膨胀超声速射流对撞的实验研究. 物理学报, 2013, 62(8): 084706. doi: 10.7498/aps.62.084706
[15]	刘诚, 潘兴臣, 朱健强. 基于光栅分光法的相干衍射成像. 物理学报, 2013, 62(18): 184204. doi: 10.7498/aps.62.184204
[16]	王淑莹, 章海军, 张冬仙. 基于微球透镜的任选区高分辨光学显微成像新方法研究. 物理学报, 2013, 62(3): 034207. doi: 10.7498/aps.62.034207
[17]	周光照, 王玉丹, 任玉琦, 陈灿, 叶琳琳, 肖体乔. 相干X射线衍射成像三维重建的数字模拟研究. 物理学报, 2012, 61(1): 018701. doi: 10.7498/aps.61.018701
[18]	周光照, 佟亚军, 陈灿, 任玉琦, 王玉丹, 肖体乔. 相干X射线衍射成像的数字模拟研究. 物理学报, 2011, 60(2): 028701. doi: 10.7498/aps.60.028701
[19]	蓝可, 贺贤土, 赖东显, 李双贵. 柱输运管中扩散超声速辐射波的能流. 物理学报, 2006, 55(7): 3789-3795. doi: 10.7498/aps.55.3789
[20]	袁行球, 李辉, 赵太泽, 俞国扬, 郭文康, 须平. 超声速等离子体射流的数值模拟. 物理学报, 2004, 53(8): 2638-2643. doi: 10.7498/aps.53.2638

计量

文章访问数: 7495
PDF下载量: 123
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板