Numerical investigation of large bubble entrapment mechanism for micron droplet impact on deep pool

Pei Chuan-Kang; Wei Bing-Qian; Zuo Juan-Li; Yang Hong

doi:10.7498/aps.68.20190541

Abstract

Water droplet impacting into a deep liquid pool is one of the most well-known flow phenomena in fluid mechanics. As a ubiquitous natural aeration process, the coalescence of water droplets in lakes and ponds and the subsequent bubble entrapment are one of the most notable ways of gas-liquid exchange in nature, and it is of great significance for underwater sound transmission, aquatic ecosystems and chemical process. The shape of an oscillating droplet in impact under different surrounding medium and initial condition is a key factor for the subsequent cavity formation and bubble entrapment. In this study, the adaptive mesh refinement technique and volume of fluid (VOF) method are applied to the study of the water droplet impact phenomena. Five kinds of deformed micron water droplets with different aspect ratios and impact velocities of 4 m/s and 6 m/s are selected to investigate the influences of drop deformation and impact velocity on the bubble entrapment, capillary wave propagation, and vortex ring evolution. The results show that at low impact velocities (Fr = 75, We = 64.4, Re = 1160, V_i = 4 m/s), the shape of water droplet does not cause the cavity formation and bubble entrapment to change significantly. However, under higher impact velocity (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s), deformed droplet with an aspect ratio of 1.33 coalesces with the pool, and large bubble entrainment occurs. The large bubble entrapment is affected mainly by the vortex ring generated under the free surface at the neck between the droplet and the pool. The vortex ring penetrates more deeply before it pulls the free surface to generate a rolling jet at the upper interface of the cavity. The rolling jets then contact the center of the cavity and collapse to entrain a large bubble. At the end of the bubble entrapment phenomenon, the cyclone inside the cavity pushes the sidewall of the cavity continuously, and effectively increases the lateral volume of the bubble, which plays a vital role in the bubble entrainment process. In the initial stage of the impact, the flatter the shape of the droplet, the greater the curvature of the jet generated on the neck between the droplet and the pool, the greater the strength of the vortex ring generated under the free surface. However, the vortex ring formed by the oblate-shaped water droplet is generated too close to the free surface, and the early free surface pulling reduces the strength of the vortex ring, thus the vorticity maximum value decays relatively fast.

Keywords:

Authors and contacts

State Key Laboratory of Eco-hydraulics in Northwest Arid Region of China, Xi’an University of Technology, Xi’an 710048, China

Corresponding author: Wei Bing-Qian, weibingqian@xaut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11605136)

FullText HTML : translate this paragraph

References

[1]	Yarin A L 2006 Annu. Rev. Fluid Mech. 38 159 Google Scholar
[2]	Prosperetti A, Oğuz H N 1993 Annu. Rev. Fluid Mech. 25 577 Google Scholar
[3]	Jayaratne O W, Mason B J 1964 Proc. R. Soc. London Ser. A-Math. Phys. Eng. Sci. 280 545 Google Scholar
[4]	Michon G J, Josserand C, Séon T 2017 Phys. Rev. Fluids 2 023601 Google Scholar
[5]	董琪琪, 胡海豹, 陈少强, 何强, 鲍路瑶 2018 物理学报 67 054702 Google Scholar Dong Q Q, Hu H B, Chen S Q, He Q, Bao L Y 2018 Acta Phys. Sin. 67 054702 Google Scholar
[6]	黄虎, 洪宁, 梁宏, 施保昌, 柴振华 2016 物理学报 65 084702 Google Scholar Huang H, Hong N, Liang H, Shi B C, Chai Z H 2016 Acta Phys. Sin. 65 084702 Google Scholar
[7]	Wang A B, Kuan C C, Tsai P H 2013 Phys. Fluids 25 101702 Google Scholar
[8]	Blanchette F, Bigioni T P 2009 J. Fluid Mech. 620 333 Google Scholar
[9]	Worthington A M 1908 A Study of Splashes (London: Longmans, Green) pp129–132
[10]	Thoroddsen S T, Takehara K, Nguyen H D, Etoh T G 2018 J. Fluid Mech. 848 R3 Google Scholar
[11]	Deka H, Ray B, Biswas G, Dalal A, Tsai P H, Wang A B 2017 Phys. Fluids 29 09210
[12]	Bouwhuis W, Hendrix M H, van der Meer D, Snoeijer J H 2015 J. Fluid Mech. 771 503 Google Scholar
[13]	Pumphrey H C, Elmore P A 1990 J. Fluid Mech. 220 539 Google Scholar
[14]	Oğuz H N, Prosperetti A 1990 J. Fluid Mech. 219 143 Google Scholar
[15]	Oğuz H N, Prosperetti A 1989 J. Fluid Mech. 203 149 Google Scholar
[16]	Oğuz H N, Prosperetti A 1991 J. Fluid Mech. 228 417
[17]	Prosperetti A 1988 J. Acoust. Soc. Am. 84 1042 Google Scholar
[18]	Deng Q, Anilkumar A V, Wang T G 2007 J. Fluid Mech. 578 119 Google Scholar
[19]	Chen S, Guo L 2014 Chem. Eng. Sci. 109 1 Google Scholar
[20]	Volkov R S, Kuznetsov G V, Strizhak P A 2015 Int. J. Heat Mass Transf. 85 1 Google Scholar
[21]	Strizhak P A 2013 J. Eng. Phys. Thermophys. 86 895 Google Scholar
[22]	Thokchom A K, Gupta A, Jaijus P J, Singh A 2014 Int. J. Heat Mass Transf. 68 67 Google Scholar
[23]	Varaksin A Y 2013 High Temp. 51 377 Google Scholar
[24]	Volkov R S, Vysokomornaya O V, Kuznestov G V, Strizhak P A 2013 J. Eng. Phys. Thermophys. 86 1413 Google Scholar
[25]	Wang C Y, Zhang C B, Huang X Y, Liu X D, Chen Y P 2016 Chin. Phys. B 25 108202 Google Scholar
[26]	丁思源, 王瑞祥, 徐荣吉, 张一灏, 蔡骥驰 2016 化工学报 67 2495 Ding C Y, Wang R X, Xu R J, Zhang Y H, Cai J C 2016 CIESC Journal 67 2495
[27]	Roman B, Bico J 2010 J. Phys.Condes. Matter 22 493101 Google Scholar
[28]	裴传康, 魏炳乾 2018 物理学报 67 224703 Google Scholar Pei C K, Wei B Q 2018 Acta Phys. Sin. 67 224703 Google Scholar
[29]	Popinet S 2003 J. Comput. Phys. 190 572 Google Scholar
[30]	Popinet S 2009 J. Comput. Phys. 228 5838 Google Scholar
[31]	Thoraval M J, Li Y, Thoroddsen S T 2016 Phys. Rev. E 93 033128

Cited By

图 1 各工况下水滴几何形态

Figure 1. Water droplet geometry in different cases.

DownLoad: Full-Size Img PowerPoint

图 2 计算区域简图

Figure 2. Schematic diagram of the computational domain.

DownLoad: Full-Size Img PowerPoint

图 3 实验摄得自由液面随时间运动过程^[31]

Figure 3. Experimental image of free surface movement at selected times^[31].

DownLoad: Full-Size Img PowerPoint

图 4 数值模拟自由液面随时间运动过程

Figure 4. Numerical simulation of the free surface movement at selected times.

DownLoad: Full-Size Img PowerPoint

图 5 不同工况下自由液面随时间的运动过程(Fr = 75, We = 64.4, Re = 1160, V_i = 4 m/s)　(a) AR = 1.16; (b) AR = 1.00; (c) AR = 0.84

Figure 5. Free surface profiles with simulated at selected times (Fr = 75, We = 64.4, Re = 1160, V_i = 4 m/s): (a) AR = 1.16; (b) AR = 1.00; (c) AR = 0.84.

DownLoad: Full-Size Img PowerPoint

图 6 不同工况下自由液面随时间的运动过程 (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s)　(a) AR = 1.33; (b) AR = 1.16; (c) AR = 1.00; (d) AR = 0.84; (e) AR = 0.67

Figure 6. Free surface profiles simulated at selected times (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s): (a) AR = 1.33; (b) AR = 1.16; (c) AR = 1.00; (d) AR = 0.84; (e) AR = 0.67.

DownLoad: Full-Size Img PowerPoint

图 7 不同时间节点下长椭圆形变水滴撞击液池涡量场和压力场等值线图(Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s, AR = 1.33)

Figure 7. Vorticity and pressure contours of a prolate water droplet impacting into a water pool at selected times (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s, AR = 1.33).

DownLoad: Full-Size Img PowerPoint

图 8 不同时间节点下长椭圆形变水滴撞击液池速度矢量场 (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s, AR = 1.33)

Figure 8. Velocity field of a prolate water droplet impacting into a water pool at selected times (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s, AR = 1.33).

DownLoad: Full-Size Img PowerPoint

图 9 自由表面下涡环的最大涡量随时间变化 (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s)

Figure 9. Vorticity maximum of the vortex ring generated under the free surface with time under different cases (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s).

DownLoad: Full-Size Img PowerPoint

图 10 自由表面下涡环的最大涡量位置随时间变化(Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s)

Figure 10. Vorticity maximum location of the vortex ring generated under the free surface with time under different cases (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s).

DownLoad: Full-Size Img PowerPoint

图 11 自由表面下涡环的最大涡量横向位置随时间变化 (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s)

Figure 11. Lateral position of the vorticity maximum in the vortex ring generated under the free surface with time under different cases (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s).

DownLoad: Full-Size Img PowerPoint

图 12 自由表面下涡环的最大涡量垂向位置随时间变化(Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s)

Figure 12. Vertical position of the vorticity maximum in the vortex ring generated under the free surface with time under different cases (Fr = 112.5, We = 145, Re = 1740, V_i = 6 m/s).

DownLoad: Full-Size Img PowerPoint

[1]	Yarin A L 2006 Annu. Rev. Fluid Mech. 38 159 Google Scholar
[2]	Prosperetti A, Oğuz H N 1993 Annu. Rev. Fluid Mech. 25 577 Google Scholar
[3]	Jayaratne O W, Mason B J 1964 Proc. R. Soc. London Ser. A-Math. Phys. Eng. Sci. 280 545 Google Scholar
[4]	Michon G J, Josserand C, Séon T 2017 Phys. Rev. Fluids 2 023601 Google Scholar
[5]	董琪琪, 胡海豹, 陈少强, 何强, 鲍路瑶 2018 物理学报 67 054702 Google Scholar Dong Q Q, Hu H B, Chen S Q, He Q, Bao L Y 2018 Acta Phys. Sin. 67 054702 Google Scholar
[6]	黄虎, 洪宁, 梁宏, 施保昌, 柴振华 2016 物理学报 65 084702 Google Scholar Huang H, Hong N, Liang H, Shi B C, Chai Z H 2016 Acta Phys. Sin. 65 084702 Google Scholar
[7]	Wang A B, Kuan C C, Tsai P H 2013 Phys. Fluids 25 101702 Google Scholar
[8]	Blanchette F, Bigioni T P 2009 J. Fluid Mech. 620 333 Google Scholar
[9]	Worthington A M 1908 A Study of Splashes (London: Longmans, Green) pp129–132
[10]	Thoroddsen S T, Takehara K, Nguyen H D, Etoh T G 2018 J. Fluid Mech. 848 R3 Google Scholar
[11]	Deka H, Ray B, Biswas G, Dalal A, Tsai P H, Wang A B 2017 Phys. Fluids 29 09210
[12]	Bouwhuis W, Hendrix M H, van der Meer D, Snoeijer J H 2015 J. Fluid Mech. 771 503 Google Scholar
[13]	Pumphrey H C, Elmore P A 1990 J. Fluid Mech. 220 539 Google Scholar
[14]	Oğuz H N, Prosperetti A 1990 J. Fluid Mech. 219 143 Google Scholar
[15]	Oğuz H N, Prosperetti A 1989 J. Fluid Mech. 203 149 Google Scholar
[16]	Oğuz H N, Prosperetti A 1991 J. Fluid Mech. 228 417
[17]	Prosperetti A 1988 J. Acoust. Soc. Am. 84 1042 Google Scholar
[18]	Deng Q, Anilkumar A V, Wang T G 2007 J. Fluid Mech. 578 119 Google Scholar
[19]	Chen S, Guo L 2014 Chem. Eng. Sci. 109 1 Google Scholar
[20]	Volkov R S, Kuznetsov G V, Strizhak P A 2015 Int. J. Heat Mass Transf. 85 1 Google Scholar
[21]	Strizhak P A 2013 J. Eng. Phys. Thermophys. 86 895 Google Scholar
[22]	Thokchom A K, Gupta A, Jaijus P J, Singh A 2014 Int. J. Heat Mass Transf. 68 67 Google Scholar
[23]	Varaksin A Y 2013 High Temp. 51 377 Google Scholar
[24]	Volkov R S, Vysokomornaya O V, Kuznestov G V, Strizhak P A 2013 J. Eng. Phys. Thermophys. 86 1413 Google Scholar
[25]	Wang C Y, Zhang C B, Huang X Y, Liu X D, Chen Y P 2016 Chin. Phys. B 25 108202 Google Scholar
[26]	丁思源, 王瑞祥, 徐荣吉, 张一灏, 蔡骥驰 2016 化工学报 67 2495 Ding C Y, Wang R X, Xu R J, Zhang Y H, Cai J C 2016 CIESC Journal 67 2495
[27]	Roman B, Bico J 2010 J. Phys.Condes. Matter 22 493101 Google Scholar
[28]	裴传康, 魏炳乾 2018 物理学报 67 224703 Google Scholar Pei C K, Wei B Q 2018 Acta Phys. Sin. 67 224703 Google Scholar
[29]	Popinet S 2003 J. Comput. Phys. 190 572 Google Scholar
[30]	Popinet S 2009 J. Comput. Phys. 228 5838 Google Scholar
[31]	Thoraval M J, Li Y, Thoroddsen S T 2016 Phys. Rev. E 93 033128

[1]	Zhang Ya-Jing, Li Fan, Lei Zhao-Kang, Wang Ming-Hao, Wang Cheng-Hui, Mo Run-Yang. Size quantification of non-spherical bubbles by ultrasound. Acta Physica Sinica, 2023, 72(3): 034301. doi: 10.7498/aps.72.20222074
[2]	Fang Long, Chen Guo-Ding. Temperature charateristics of droplet impacting on static hot pool. Acta Physica Sinica, 2019, 68(23): 234702. doi: 10.7498/aps.68.20190809
[3]	Yang Hai-Jun, Wu Feng, Fang Hai-Ping, Hu Jun, Hou Zheng-Chi. Mechanism of soil environmental regulation by aerated drip irrigation. Acta Physica Sinica, 2019, 68(1): 019201. doi: 10.7498/aps.68.20181357
[4]	Dong Qi-Qi, Hu Hai-Bao, Chen Shao-Qiang, He Qiang, Bao Lu-Yao. Molecular dynamics simulation of freezing process of water droplets impinging on cold surface. Acta Physica Sinica, 2018, 67(5): 054702. doi: 10.7498/aps.67.20172174
[5]	Pei Chuan-Kang, Wei Bing-Qian. Numerical investigation of cavity formation mechanism for micron-waterdrop impact on deep pool. Acta Physica Sinica, 2018, 67(22): 224703. doi: 10.7498/aps.67.20181422
[6]	Wang Hao-Ruo, Zhang Chong, Zhang Hong-Chao, Shen Zhong-Hua, Ni Xiao-Wu, Lu Jian. Spatiotemporal distributions of plasma and optical field during the interaction between ultra-short laser pulses and water nanodroplets. Acta Physica Sinica, 2017, 66(12): 127801. doi: 10.7498/aps.66.127801
[7]	Zheng Jian, Zhang Duo, Jiang Bang-Hai, Lu Fang-Yun. Formation mechanism of water jets induced by the interaction between bubble and free surface. Acta Physica Sinica, 2017, 66(4): 044702. doi: 10.7498/aps.66.044702
[8]	Sun Chuan-Qin, Huang Hai-Shen, Bi Qing-Ling, Lü Yong-Jun. Wetting kinetics of water droplets on the metallic glass. Acta Physica Sinica, 2017, 66(17): 176101. doi: 10.7498/aps.66.176101
[9]	Hu Hai-Bao, He Qiang, Yu Si-Xiao, Zhang Zhao-Zhu, Song Dong. Freezing behavior of droplet impacting on cold surfaces. Acta Physica Sinica, 2016, 65(10): 104703. doi: 10.7498/aps.65.104703
[10]	Zhang Kai, Lu Yong-Jun, Wang Feng-Hui. Motion of the nanodrops driven by energy gradient on surfaces with different microstructures. Acta Physica Sinica, 2015, 64(6): 064703. doi: 10.7498/aps.64.064703
[11]	Li Da-Shu, Qiu Xing-Qi, Zheng Zhi-Wei. Numerical analysis on air entrapment during droplet impacting on a wetted surface. Acta Physica Sinica, 2015, 64(22): 224704. doi: 10.7498/aps.64.224704
[12]	Wang Yong, Lin Shu-Yu, Mo Run-Yang, Zhang Xiao-Li. Vibration of the bubble in bubbly liquids. Acta Physica Sinica, 2013, 62(13): 134304. doi: 10.7498/aps.62.134304
[13]	Ni Bao-Yu, Li Shuai, Zhang A-Man. Jet splitting after bubble breakup at the free surface. Acta Physica Sinica, 2013, 62(12): 124704. doi: 10.7498/aps.62.124704
[14]	Shi Jian, Zhou Lin, Yang Long-Ying. Influence of sea spray droplets on drag coefficient in high wind speed. Acta Physica Sinica, 2013, 62(3): 039201. doi: 10.7498/aps.62.039201
[15]	Wang Cheng-Hui, Cheng Jian-Chun. Forced oscillations of gaseous bubbles in microtubules. Acta Physica Sinica, 2012, 61(19): 194303. doi: 10.7498/aps.61.194303
[16]	Zhang A-Man, Wang Chao, Wang Shi-Ping, Cheng Xiao-Da. Experimental study of interaction between bubble and free surface. Acta Physica Sinica, 2012, 61(8): 084701. doi: 10.7498/aps.61.084701
[17]	Shen Zhuang-Zhi, Lin Shu-Yu. Chaotic characteristics of gas bubble motion in acoustic field. Acta Physica Sinica, 2011, 60(10): 104302. doi: 10.7498/aps.60.104302
[18]	Jiang Fang-Ming, Liao Quan, Zeng Jian-Bang, Li Long-Jian. Simulation of bubble growth process in pool boilingusing lattice Boltzmann method. Acta Physica Sinica, 2011, 60(6): 066401. doi: 10.7498/aps.60.066401
[19]	Zhang A-Man, Yao Xiong_Liang, Li Jia. The dynamics of bubbles. Acta Physica Sinica, 2008, 57(3): 1672-1682. doi: 10.7498/aps.57.1672
[20]	Zhang A-Man, Yao Xiong-Liang. The law of the bubble motion near the wall. Acta Physica Sinica, 2008, 57(3): 1662-1671. doi: 10.7498/aps.57.1662

Catalog

Vol. 68, Issue 20 - 2019-10-20

Metrics

Abstract views: 6924
PDF Downloads: 77
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板