IMPACT OF A PLANAR SHOCK ONTO SIDE-BY-SIDE DROPLETS: A 3D NUMERICAL STUDY

Wu Runlong; Li Zhujun; Ding Hang

doi:10.6052/0459-1879-22-358

Volume 54 Issue 11

Nov. 2022

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2022 > 54(11): 2958-2969

Wu Runlong, Li Zhujun, Ding Hang. Impact of a planar shock onto side-by-side droplets: A 3D numerical study. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 2958-2969 doi: 10.6052/0459-1879-22-358

Citation:

Wu Runlong, Li Zhujun, Ding Hang. Impact of a planar shock onto side-by-side droplets: A 3D numerical study. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 2958-2969 doi: 10.6052/0459-1879-22-358

Citation:

PDF( 3280 KB)

IMPACT OF A PLANAR SHOCK ONTO SIDE-BY-SIDE DROPLETS: A 3D NUMERICAL STUDY

doi: 10.6052/0459-1879-22-358

Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China

Received Date: 2022-08-05
Accepted Date: 2022-09-30

Available Online: 2022-10-01

Publish Date: 2022-11-18

Abstract

Abstract

In this paper we investigate the evolution dynamics of side-by-side droplets after being impacted by a planar shock by using a three-dimensional conservative sharp interface method. Our research mainly focuses on the development of wave structures after the shock impact and the asymmetric interface evolution of single droplet induced by the coupling between the side-by-side droplets. Firstly, we analyze the development of the wave system including those inside and outside the channel between the side-by-side droplets. We find that at the early stage of impact, the intersection of reflected shock waves accounts for the formation of new reflected shock waves and Mach rods. This is quite different from the curved wave front formed by the reflected shock wave on the other side of the droplet transversely opposite to the channel. The difference of the flow field on the two sides of the droplet is responsible for the asymmetric interface evolution of the droplet in the middle stage of the droplet-shock interaction. Secondly, we investigate the interface morphology and its evolution in the middle stage of shock impact, especially when the incident shock wave moves to the downstream of and is far away from the droplets, and report the occurrence of new flow phenomena at the downstream outlet of the channel, such as interface coalescence caused by airflow expansion and subsequent interface fragmentation owing to airflow blockage. Finally, the effect of the gap between the side-by-side droplets on the droplet interaction is studied. We find that the gap size has a significant effect on the occurrence of pressure peaks in the channel. Specifically, a smaller gap not only brings higher pressure peak, but also makes the peak appear at an earlier time.
- shock,
- droplets,
- compressible multiphase flows,
- conservative sharp interface method,
- interface deformation

FullText(HTML)

References(39)

References

[1]	Taylor GI. The shape and acceleration of a drop in a high-speed air stream. The Scientific Papers of GI Taylor, 1963, 3: 457-464
[2]	Harper EY, Grube GW, Chang ID. On the breakup of accelerating liquid drops. Journal of Fluid Mechanics, 1972, 52(3): 565-591
[3]	Hinze JO. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE Journal, 1955, 1(3): 289-295 doi: 10.1002/aic.690010303
[4]	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, 14(2): 151-154 (Lu Shouxiang, Qin Youhua. Deformation and breakup of droplets behind shock wave. Chinese Journal of High Pressure Physics, 2000, 14(2): 151-154 (in Chinese)
[5]	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: 741-757 doi: 10.1016/0301-9322(87)90063-2
[6]	Guildenbecher D, Lopez-Rivera C, Sojka P. Secondary atomization. Experiments in Fluids, 2009, 46(3): 371-402 doi: 10.1007/s00348-008-0593-2
[7]	Gelfand BE. Droplet breakup phenomena in flows with velocity lag. Progress in Energy and Combustion Science, 1996, 22(3): 201-265 doi: 10.1016/S0360-1285(96)00005-6
[8]	Wierzba A. Deformation and breakup of liquid drops in a gas stream at nearly critical weber numbers. Experiments in Fluids, 1990, 9(1): 59-64
[9]	Dai Z, Faeth GM. Temporal properties of secondary drop breakup in the multimode breakup regime. International Journal of Multiphase Flow, 2001, 27(2): 217-236 doi: 10.1016/S0301-9322(00)00015-X
[10]	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(2): 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(2): 416-420 (in Chinese)
[11]	Hanson AR, Domich EG, Adams HS. Shock tube investigation of the breakup of drops by air blasts. Physics of Fluids, 1963, 6: 1070-1080 doi: 10.1063/1.1706864
[12]	Nicholls JA, Ranger AA. Aerodynamic shattering of liquid drops. AIAA Journal, 1969, 7(2): 285-290 doi: 10.2514/3.5087
[13]	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(2): 210-213 (Lou Jianfeng, Hong Tao, Zhu Jianshi. Numerical study on shearing breakup of liquid droplets in gas medium. Chinese Journal of Computational Mechanics, 2011, 28(2): 210-213 (in Chinese)
[14]	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
[15]	Simpkins PG, Bales EL. Water-drop response to sudden accelerations. Journal of Fluid Mechanics, 1972, 55(4): 629-639 doi: 10.1017/S0022112072002058
[16]	Joseph DD, Belanger J, Beavers GS. Breakup of a liquid drop suddenly exposed to a high-speed airstream. International Journal of Multiphase Flow, 1999, 25(6): 1263-1303
[17]	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, 24(5): 797-800 (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, 24(5): 797-800 (in Chinese)
[18]	Theofanous TG, Li GJ, Dinh TN. Aerobreakup in rarefied supersonic gas flows. Journal of Fluids Engineering, 2004, 126(4): 516-527 doi: 10.1115/1.1777234
[19]	Liu Z, Reitz RD. An analysis of the distortion and breakup mechanisms of high speed liquid drops. International Journal of Multiphase Flow, 1997, 23(4): 631-650 doi: 10.1016/S0301-9322(96)00086-9
[20]	Theofanous TG, Li GJ. On the physics of aerobreakup. Physics of Fluids, 2008, 20(5): 52-103
[21]	Sembian S, Liverts M, Tillmark N, et al. Plane shock wave interaction with a cylindrical water column. Physics of Fluids, 2016, 28(5): 56-102
[22]	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
[23]	Liu N, Wang ZG, Sun MB, et al. Numerical simulation of liquid droplet breakup in supersonic flows. Acta Astronautica, 2018, 145: 116-130 doi: 10.1016/j.actaastro.2018.01.010
[24]	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
[25]	Yoshida T, Wierzba A, Takayama K. Breakup and interaction of two droplets columns in a shock wave induced high-speed air flow. Transactions of the Japan Society of Mechanical Engineers, 1989, 55(514): 1607-1612 doi: 10.1299/kikaib.55.1607
[26]	Igra D, Takayama K. Experimental investigation of two cylindrical water columns subjected to planar shock wave loading. Journal of Fluids Engineering, 2003, 125(2): 325-331 doi: 10.1115/1.1538628
[27]	Chen H, Liang SM. Flow visualization of shock/water column interactions. Shock Waves, 2008, 17(5): 309-321 doi: 10.1007/s00193-007-0115-9
[28]	Nourgaliev RR, Din TN, Theofanous TG. Adaptive characteristics-based matching for compressible multifluid dynamics. Journal of Computational Physics, 2006, 213: 500-529 doi: 10.1016/j.jcp.2005.08.028
[29]	Chang CH, Deng X, 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
[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]	Osher S, Sethian JA. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 1988, 79: 12-49 doi: 10.1016/0021-9991(88)90002-2
[32]	林健宇. 切割网格方法及激波与气泡相互作用研究. [博士论文]. 合肥: 中国科学技术大学, 2016 Lin Jianyu. Development of cut-cell method and dynamics of shock-bubble interactions. [PhD Thesis]. Hefei: University of Science and Technology of China, 2016 (in Chinese)
[33]	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)
[34]	Liou MS. A sequel to AUSM, part ii: AUSM⁺-up for all speeds. Journal of Computational Physics, 2006, 214(1): 137-170 doi: 10.1016/j.jcp.2005.09.020
[35]	Osher S, Fedkiw R. Level Set Methods and Dynamic Implicit Surfaces. New York: Springer, 2003: 17-90
[36]	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
[37]	Russo G, Smereka P. A remark on computing distance functions. Journal of Computational Physics, 2000, 163(1): 51-67 doi: 10.1006/jcph.2000.6553
[38]	Min C. On reinitializing level set functions. Journal of Computational Physics, 2010, 229(8): 2764-2772 doi: 10.1016/j.jcp.2009.12.032
[39]	Theofanous TG, Mitkin VV, Ng CL, et al. The physics of aerobreakup ii. viscous liquids. Physics of Fluids, 2012, 24(2): 22-104