NUMERICAL INVESTIGATION OF SHOCK-DROPLET INTERACTION WITH HIGH-MACH NUMBERS
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摘要:本文采用守恒清晰界面多相流数值方法模拟了超声速和高超声速环境下三维液滴的推进、变形和破碎演化过程.数值模拟结果与实验数据的一致性表明了本文所用数值方法和计算程序的准确性, 而网格无关性研究验证了采用的网格分辨率可以捕捉流场和界面的主要特征. 模拟结果验证了高韦伯数下液滴变形破碎过程所遵循的剪切诱导剥离(SIE)破碎机制, 其包含液滴的扁平化和剪切剥离两个主要特征. 而最近发现的SIE破碎机制下的循环破碎机制也在本文得到了验证, 即主液滴从球形液滴破碎为小液滴会经历多个循环重复的破碎阶段, 高韦伯数下液滴的破碎并非一次性剪切剥离的结果, 而是会发生逐层的剪切剥离和破碎. 本文还研究了马赫数对激波冲击液滴加速变形过程的影响. 结果表明, 高韦伯数下不同马赫数的液滴破碎过程具有高度一致性, 并遵循统一的SIE破碎机制.通过对液滴质心位移、速度、加速度和拽力系数的量化统计揭示其运动过程中的统一加速规律. 在激波的驱动下, 液滴并非以一个恒定的加速度做加速运动.在扁平化不明显的前期, 液滴以一个恒定的加速度做加速运动.随着液滴扁平化的发生, 迎风面积的增加导致拽力系数的增大, 进而导致液滴加速度的不断增大.Abstract:In order to reveal the evolution of droplet propulsion, deformation, and fragmentation in supersonic and hypersonic environment, a conservative sharp-interface multiphase method is used to simulate the shock-droplet interaction with high-Mach and extremely high-Mach numbers. The numerical results are in good agreement with the experimental results, which indicates the accuracy of the numerical method and the corresponding computer code. The grid independence study demonstrates that the grid resolution used in this paper can capture the main features of the flow field and interface. The numerical results verify the shear-induced entrainment (SIE) breaking mechanism followed by the droplet deformation and fragmentation under high-Weber number, including two main features, i.e. the flattening of droplets and the shearing of the sheet at the droplet equator. The recently discovered recurrent breakup mechanism under the SIE mechanism has also been verified in this paper. The initial spherical-droplet is deformed, and breaks into smaller sub-droplets via recurrent rupture stages. And the fragmentation of droplets for high-Weber number is indeed not the result of one single shearing process, but rather occurs recurrently. The effect of the Mach number on the shock-droplet interaction is also investigated here. Our results indicate that the droplet fragmentation process for different Mach numbers is highly analogous, following the general SIE mechanism. The time evolution of the dimensionless center-of-mass drift, velocity, acceleration, and drag coefficient reveal the unified acceleration tendency for droplet under shock impact. In addition, the droplet does not propel with a constant acceleration rate for the whole stage. Instead, when the flattening effect is absent in early stage, the droplet accelerates at a constant acceleration. As the flattening occurs, the increase of the upwind area leads to an increase in the drag coefficient, which in turn increases acceleration rate of the droplet movement.
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图 2二维切割网格下的守恒离散示意图
Figure 2.Two-dimensional schematic of the conservative discretization in a cut cell
图 4不同网格分辨率下的无量纲质心位移和速度演化
Figure 4.Evolution of the dimensionless center-of-mass drift and velocity for various grid resolutions
图 5表面张力和黏性力对激波冲击液滴数值纹影图的影响
Figure 5.Effects of capillary and viscous forces on Numerical schlieren images for shock-droplet simulations
图 6表面张力和黏性力对液滴无量纲质心位移、速度和加速度演化的影响
Figure 6.Effects of capillary and viscous forces on evolution of the dimensionless center-of-mass drift and velocity and acceleration for shock-droplet simulations
图 7数值模拟结果(上)和实验可视化(下)侧视图对比
Figure 7.Comparison of numerical results (upper) and experimental visualizations (lower) for side view
图 8数值模拟结果(上)和实验可视化(下)前侧30°视图对比
Figure 8.Comparison of numerical results (upper) and experimental visualizations (lower) for 30° front side view
图 9Ms= 3的激波冲击下流场的早期数值纹影图
Figure 9.Numerical schlieren images for Mach 3 simulations at early stage
图 13Ms= 11下激波冲击液滴破碎的光线追踪渲染(前侧45°视图). 第一次到第三次破碎分别使用箭头、红色虚线和蓝色虚线来标识
Figure 13.Ray-traced rendering of shock-droplet breakup for Mach 11 simulation (45° front side view). The first to third breakup are identified by arrows, red dotted lines and blue dotted lines, respectively
图 14不同马赫数下的液滴界面演化过程
Figure 14.Evolution of the droplet interface for various Mach air shocks
图 15不同马赫数下无量纲流向直径和无量纲横向直径的演化
Figure 15.The evolution of the dimensionless cross-stream and the dimensionless streamwise diameter at various Mach air shocks
图 16不同马赫数下的无量纲质心位移、速度、加速度以及拽力系数演化
Figure 16.The evolution of the dimensionless center-of-mass drift and velocity and acceleration and drag coefficient at various Mach air shocks
图 17直接对液滴质心位移求导得出的无量纲速度和加速度演化
Figure 17.The evolution of the dimensionless velocity and acceleration derived directly from the dimensionless center-of-mass drift
表 1不同激波马赫数下的激波后流动状态
Table 1.Flow conditions behind various Mach air shocks
Ms We Oh pg/MPa ug/m·s−1 ρg/(kg·m−3) 3 12773 0.00198 1.033 758.9 4.628 6 835450 0.00198 4.183 1660.2 6.322 11 3196139 0.00198 14.10 3105.1 6.914 
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[1] Waldman GD, Reinecke WG, Glenn DC. Raindrop breakup in the shock layer of a high-speed vehicle.AIAA Journal, 1972, 10(9): 1200-1204doi:10.2514/3.50350 [2] Hinze JO. Critical speeds and sizes of liquid globules.Applied Scientific Research Section A:Mechanics Heat Chemical Engineering Mathematical Methods, 1949, 1(4): 273-288 [3] Hanson AR, Domich EG, Adams HS. Shock tube investigation of the breakup of drops by air blasts.Physics of Fluids, 1963, 6(8): 1070-1080doi:10.1063/1.1706864 [4] Ranger AA, Nicholls JA. Aerodynamic shattering of liquid drops.AIAA Journal, 1969, 7(2): 285doi:10.2514/3.5087 [5] Patel PD, Theofanous TG. Hydrodynamic fragmentation of drops.Journal of Fluid Mechanics, 1981, 103: 207-223 [6] Pilch M, Erdman CA. Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid-drop.International Journal of Multiphase Flow, 1987, 13(6): 741-757doi:10.1016/0301-9322(87)90063-2 [7] 易翔宇. 激波诱导高速气流中液滴的变形与破碎实验研究. [博士论文]. 合肥: 中国科学技术大学, 2017Yi Xiangyu. Experimental study of the deformation and breakup of a liquid drop in shock induced gas flow. [PhD Thesis]. Hefei: University of Science and Technology of China, 2017 (in Chinese)) [8] Theofanous TG. Aerobreakup of newtonian and viscoelastic liquids.Annual Review of Fluid Mechanics, 2011, 43: 661-690doi:10.1146/annurev-fluid-122109-160638 [9] Theofanous TG, Li GJ. On the physics of aerobreakup.Physics of Fluids, 2008, 20(5): 052103 [10] Chen H. Two-dimensional simulation of stripping breakup of a water droplet.AIAA Journal, 2008, 46(5): 1135-1143doi:10.2514/1.31286 [11] Kaiser JWJ, Winter JM, Adami S, et al. Investigation of interface deformation dynamics during high-Weber number cylindrical droplet breakup.International Journal of Multiphase Flow, 2020, 132: 103409 [12] Chang CH, Deng XL, Theofanous TG. Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method.Journal of Computational Physics, 2013, 242: 946-990doi:10.1016/j.jcp.2013.01.014 [13] Han J, Tryggvason G. Secondary breakup of axisymmetric liquid drops. II. Impulsive acceleration.Physics of Fluids, 2001, 13(6): 1554-1565 [14] Meng JC, Colonius T. Numerical simulation of the aerobreakup of a water droplet.Journal of Fluid Mechanics, 2018, 835: 1108-1135doi:10.1017/jfm.2017.804 [15] Klein AL, Bouwhuis W, Visser CW, et al. Drop shaping by laser-pulse impact.Physical Review Applied, 2015, 3(4): 044018doi:10.1103/PhysRevApplied.3.044018 [16] Dorschner B, Biasiori-Poulanges L, Schmidmayer K, et al. On the formation and recurrent shedding of ligaments in droplet aerobreakup.Journal of Fluid Mechanics, 2020, 904(A20): 2020699 [17] Sharma S, Singh AP, Rao SS, et al. Shock induced aerobreakup of a droplet.Journal of Fluid Mechanics, 2021, 929(A27): 2021860 [18] Wang ZG, Hopfes T, Giglmaier M, et al. Effect of Mach number on droplet aerobreakup in shear stripping regime.Experiments in Fluids, 2020, 61(9): 193 [19] Wang ZG, Hopfes T, Giglmaier M, et al. Experimental investigation of shock-induced tandem droplet breakup.Physics of Fluids, 2021, 33(1): 012113 [20] Leung J, Menon SK. Design and test of a shock tube facility to investigate droplet aerobreakup//AIAA Propulsion and Energy Forum, 2020 [21] Nykteri G, Gavaises M. Droplet aerobreakup under the shear-induced entrainment regime using a multiscale two-fluid approach.Physical Review Fluids, 2021, 6(8): 084304 [22] Garcia-Magarino A, Sor S, Velazquez A. New droplet aero-breakup mechanism associated to unsteady flow loading.Experimental Thermal and Fluid Science, 2021, 121: 110290 [23] 陆守香, 秦友花. 激波诱导的液滴变形和破碎. 高压物理学报, 2000(02): 151-154doi:10.3969/j.issn.1000-5773.2000.02.012Lu Shouxiang, Qin Youhua. Deformation and breakup of droplets behind shock wave.Chinese Journal of High Pressure Physics, 2000(02): 151-154(in Chinese)doi:10.3969/j.issn.1000-5773.2000.02.012 [24] 耿继辉, 叶经方, 王健等. 激波诱导液滴变形和破碎现象实验研究. 工程热物理学报, 2003(05): 797-800doi:10.3321/j.issn:0253-231X.2003.05.023Geng Jihui, Ye Jingfang, Wang Jian, et al. Experimental investigation on phenomena of shock wave-induced droplet deformation and breakup.Journal of Engineering Thermophysics, 2003(05): 797-800 (in Chinese)doi:10.3321/j.issn:0253-231X.2003.05.023 [25] 楼建锋, 洪滔, 朱建士. 液滴在气体介质中剪切破碎的数值模拟研究. 计算力学学报, 2011, 28(02): 210-213doi:10.7511/jslx201102010Lou Jianfeng, Hong Tao, Zhu Jianshi. Numerical study on shearing breakup of liquid droplet in gas medium.Chinese Journal of Computational Mechanics, 2011, 28(02): 210-213 (in Chinese)doi:10.7511/jslx201102010 [26] 杨威, 贾明, 孙凯等. 液滴变形-袋式-多模式破碎转换研究. 工程热物理学报, 2017, 38(02): 416-420Yang Wei, Jia Meng, Sun Kai, et al. Investigation on transitions of deformation-bag-multimode breakup for liquid droplets.Journal of Engineering Thermophysics, 2017, 38(02): 416-420 (in Chinese) [27] Yang W, Jia M, Che ZZ, et al. Transitions of deformation to bag breakup and bag to bag-stamen breakup for droplets subjected to a continuous gas flow.International Journal of Heat and Mass Transfer, 2017, 111: 884-894doi:10.1016/j.ijheatmasstransfer.2017.04.012 [28] Zhu WL, Zhao NB, Jia XB, et al. Effect of airflow pressure on the droplet breakup in the shear breakup regime.Physics of Fluids, 2021, 33(5): 053309 [29] 施红辉, 师顺, 刘晨等. 超声速条件下亚毫米液滴的变形破碎模态. 航空动力学报, 2020, 35(10): 2017-2027doi:10.13224/j.cnki.jasp.2020.10.001Shi Honghui, Shi Shun, Liu Chen, et al. Deformation and fracture patterns of sub-millimeter droplets under supersonic conditions.Journal of Aerospace Power, 2020, 35(10): 2017-2027 (in Chinese)doi:10.13224/j.cnki.jasp.2020.10.001 [30] Shen Y, Ren Y, Ding H. A 3D conservative sharp interface method for simulation of compressible two-phase flows.Journal of Computational Physics, 2020, 403: 109107doi:10.1016/j.jcp.2019.109107 [31] 沈毅. 守恒型尖锐界面方法及激波诱导的含泡液滴演化动力学. [博士论文]. 合肥: 中国科学技术大学, 2020Shen Yi. Conservative sharp interface method and shock-induced dynamics of droplet containing a bubble. [PhD Thesis]. Hefei: University of Science and Technology of China, 2020 (in Chinese)) [32] 申帅, 李建玲, 刘金宏等. 高韦伯数条件下黏性对液滴变形过程的影响. 爆炸与冲击, 2020, 40(12): 89-100doi:10.11883/bzycj-2020-0051Shen Shuai, Li Jianling, Liu Jinhong et al. Viscous effect on the droplet deformation process under high Weber number conditions.Explosion and Shock Waves, 2020, 40(12): 89-100 (in Chinese)doi:10.11883/bzycj-2020-0051 [33] 施红辉, 刘晨, 熊红平等. 激波冲击下液滴变形破碎的黏性特征. 航空动力学报, 2019, 34(09): 1962-1970doi:10.13224/j.cnki.jasp.2019.09.013Shi Honghui, Liu Chen, Xiong Hongping, et al. Viscosity characteristics of droplet deformation and breakup under shock wave.Journal of Aerospace Power, 2019, 34(09): 1962-1970 (in Chinese)doi:10.13224/j.cnki.jasp.2019.09.013 [34] 褚贵东, 钱丽娟, 丛红钏等. 非牛顿流体液滴袋状破碎的数值模拟研究. 工程热物理学报, 2021, 42(10): 2575-2580Chu Guidong, Qian Lijuan, Cong Hongchuan, et al. Numerical Simulation on Bag Breakup for Non-Newtonian Liquid Droplet.Journal of Engineering Thermophysics, 2021, 42(10): 2575-2580 (in Chinese) [35] 崔竹轩, 丁举春, 司廷. 反射激波作用下三维凹气柱界面演化的数值研究. 力学学报, 2021, 53(05): 1246-1256Cui Zhuxuan, Ding Jujun, Si Ting, et al. Numerical study on the evolution of three-dimensonal concave cylindrical interface accelerated by reflected shock.Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(05): 1246-1256 (in Chinese) [36] Hu XY, Khoo BC, Adams NA, et al. A conservative interface method for compressible flows.Journal of Computational Physics, 2006, 219(2): 553-578doi:10.1016/j.jcp.2006.04.001 [37] Han LH, Hu XY, Adams NA. Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure.Journal of Computational Physics, 2014, 262: 131-152doi:10.1016/j.jcp.2013.12.061 [38] Pan S, Han L, Hu X, et al. A conservative interface-interaction method for compressible multi-material flows.Journal of Computational Physics, 2018, 371: 870-895doi:10.1016/j.jcp.2018.02.007 [39] Long T, Cai J, Pan S. An accelerated conservative sharp-interface method for multiphase flows simulations.Journal of Computational Physics, 2021, 429: 110021doi:10.1016/j.jcp.2020.110021 [40] Jiang GS, Shu CW. Efficient Implementation of Weighted ENO Schemes.Journal of Computational Physics, 1996, 126(1): 202-228doi:10.1006/jcph.1996.0130 [41] Shu CW, Osher S. Efficient implementation of essentially non-oscillatory shock-capturing schemes.Journal of Computational Physics, 1989, 77(2): 439-471 [42] Meng JC, Colonius T. Numerical simulations of the early stages of high-speed droplet breakup.Shock Waves, 2015, 25(4): 399-414doi:10.1007/s00193-014-0546-z [43] Osher S, Sethian JA. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations.Journal of Computational Physics, 1988, 79(1): 12-49doi:10.1016/0021-9991(88)90002-2 [44] Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow.Journal of Computational physics, 1994, 114(1): 146-159doi:10.1006/jcph.1994.1155 [45] Fedkiw RP, Aslam T, Merriman B, et al. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method).Journal of Computational Physics, 1999, 152(2): 457-492doi:10.1006/jcph.1999.6236 [46] Harten A. Adaptive multiresolution schemes for shock computations.Journal of Computational Physics, 1994, 115(2): 319-338doi:10.1006/jcph.1994.1199 [47] Popinet S. Numerical models of surface tension.Annual Review of Fluid Mechanics, 2018, 50: 49-75doi:10.1146/annurev-fluid-122316-045034 [48] Ranjan D, Oakley J, Bonazza R. Shock-bubble interactions.Annual Review of Fluid Mechanics, 2011, 43(1): 117-140doi:10.1146/annurev-fluid-122109-160744 [49] Sembian S, Liverts M, Tillmark N, et al. Plane shock wave interaction with a cylindrical water column.Physics of Fluids, 2016, 28(5): 056102doi:10.1063/1.4948274 [50] Igra D, Takayama K. Numerical simulation of shock wave interaction with a water column.Shock Waves, 2001, 11(3): 219-228doi:10.1007/PL00004077 -
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