EI、Scopus 收录
中文核心期刊
Song Jiaxi, Pan Shucheng. Numerical investigation of shock-droplet interaction with high-Mach numbers. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2419-2434. DOI: 10.6052/0459-1879-22-191
Citation: Song Jiaxi, Pan Shucheng. Numerical investigation of shock-droplet interaction with high-Mach numbers. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(9): 2419-2434. DOI: 10.6052/0459-1879-22-191

NUMERICAL INVESTIGATION OF SHOCK-DROPLET INTERACTION WITH HIGH-MACH NUMBERS

  • Received Date: May 03, 2022
  • Accepted Date: July 08, 2022
  • Available Online: July 09, 2022
  • 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.
  • [1]
    Waldman GD, Reinecke WG, Glenn DC. Raindrop breakup in the shock layer of a high-speed vehicle. AIAA Journal, 1972, 10(9): 1200-1204 doi: 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): 1070-1080 doi: 10.1063/1.1706864
    [4]
    Ranger AA, Nicholls JA. Aerodynamic shattering of liquid drops. AIAA Journal, 1969, 7(2): 285 doi: 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): 741-757 doi: 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, 2017

    Yi 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: 661-690 doi: 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): 1135-1143 doi: 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: 946-990 doi: 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: 1108-1135 doi: 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): 044018 doi: 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): 151-154 doi: 10.3969/j.issn.1000-5773.2000.02.012

    Lu 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): 797-800 doi: 10.3321/j.issn:0253-231X.2003.05.023

    Geng 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): 210-213 doi: 10.7511/jslx201102010

    Lou 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): 416-420

    Yang 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: 884-894 doi: 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): 2017-2027 doi: 10.13224/j.cnki.jasp.2020.10.001

    Shi 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: 109107 doi: 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, 2020

    Shen 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): 89-100 doi: 10.11883/bzycj-2020-0051

    Shen 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): 1962-1970 doi: 10.13224/j.cnki.jasp.2019.09.013

    Shi 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): 2575-2580

    Chu 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): 1246-1256

    Cui 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): 553-578 doi: 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: 131-152 doi: 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: 870-895 doi: 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: 110021 doi: 10.1016/j.jcp.2020.110021
    [40]
    Jiang GS, Shu CW. Efficient Implementation of Weighted ENO Schemes. Journal of Computational Physics, 1996, 126(1): 202-228 doi: 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): 399-414 doi: 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): 12-49 doi: 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): 146-159 doi: 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): 457-492 doi: 10.1006/jcph.1999.6236
    [46]
    Harten A. Adaptive multiresolution schemes for shock computations. Journal of Computational Physics, 1994, 115(2): 319-338 doi: 10.1006/jcph.1994.1199
    [47]
    Popinet S. Numerical models of surface tension. Annual Review of Fluid Mechanics, 2018, 50: 49-75 doi: 10.1146/annurev-fluid-122316-045034
    [48]
    Ranjan D, Oakley J, Bonazza R. Shock-bubble interactions. Annual Review of Fluid Mechanics, 2011, 43(1): 117-140 doi: 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): 056102 doi: 10.1063/1.4948274
    [50]
    Igra D, Takayama K. Numerical simulation of shock wave interaction with a water column. Shock Waves, 2001, 11(3): 219-228 doi: 10.1007/PL00004077
  • Related Articles

    [1]Zhuo Yue, Luo Kai, Shang Jiahao, Yu Qinghao, Wang Qiu, Wang Yejun, Liang Jinhu, Zhao Wei. EXPERIMENTAL STUDY ON THE CHARACTERIZATION OF TRANSVERSE JET INTERACTION IN HYPERSONIC RAREFIED FLOW[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(5): 1053-1062. DOI: 10.6052/0459-1879-22-599
    [2]Nie Shaojun, Wang Yunpeng, Xue Xiaopeng, Jiang Zonglin. RESEARCH ON RUPTURE CHARACTERISTICS OF STEEL DIAPHRAGM BETWEEN HIGH AND LOW PRESURE SECTION IN SHOCK TUNNEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(6): 1747-1757. DOI: 10.6052/0459-1879-20-341
    [3]Wang Yunpeng, Yang Ruixin, Nie Shaojun, Jiang Zonglin. DEEP-LEARNING-BASED INTELLIGENT FORCE MEASUREMENT SYSTEM USING IN A SHOCK TUNNEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1304-1313. DOI: 10.6052/0459-1879-20-190
    [4]Jiang Zonglin, Li Jinping, Hu Zongmin, Liu Yunfeng, Yu Hongru. SHOCK TUNNEL THEORY AND METHODS FOR DUPLICATING HYPERSONIC FLIGHT CONDITIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1283-1291. DOI: 10.6052/0459-1879-18-238
    [5]Wang Yunpeng, Liu Yunfeng, Yuan Chaokai, Luo Changtong, Wang Chun, Hu Zongmin, Han Guilai, Zhao Wei, Jiang Zonglin. STUDY ON FORCE MEASUREMENT IN LONG-TEST DURATION SHOCK TUNNEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 545-556. DOI: 10.6052/0459-1879-15-295
    [6]Meng Baoqing, Han Guilai, Jiang Zonglin. THEORETICAL INVESTIGATION ON AERODYNAMIC FORCE MEASUREMENT INTERFERED BY STRUCTURAL VIBRATIONS IN LARGE SHOCK TUNNEL[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1): 102-110. DOI: 10.6052/0459-1879-15-152
    [7]Jiang Zonglin, Li Jinping, Zhao Wei, Liu Yunfeng, Yu Hongru. INVESTIGATING INTO TECHNIQUES FOR EXTENDING THE TEST-DURATION OF DETONATION-DRIVEN SHOCK TUNNELS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(5): 824-831. DOI: 10.6052/0459-1879-12-160
    [8]Hongru Yu. Development study of detonation driving techniques for a shock tunnel[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(6): 978-983. DOI: 10.6052/0459-1879-2011-6-lxxb2011-331
    [9]Jinping Li, Heng Feng, Zonglin Jiang. Test gas contamination induced by the interaction of shock/boundary layer in shock tunnels[J]. Chinese Journal of Theoretical and Applied Mechanics, 2008, 40(3): 289-296. DOI: 10.6052/0459-1879-2008-3-2007-110
    [10]OXV-HYDROGEN COMBUSTION AND DETONATION DRIVEN SHOCK TUBE[J]. Chinese Journal of Theoretical and Applied Mechanics, 1999, 31(4): 389-397. DOI: 10.6052/0459-1879-1999-4-1995-046

Catalog

    Article Metrics

    Article views (1148) PDF downloads (257) Cited by()
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return