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为了探究微米级微小水滴撞击深水液池运动中空腔的成长过程与机理，采用自适应网格技术和流体体积方法对撞击速度为2.5–6.5 m/s的微小水滴撞击深水液池的运动进行数值模拟研究，考察不同撞击速度下水滴撞击深水液池后的水体混掺、毛细波传播、空腔变形规律以及气泡截留过程，并深入探究空腔运动的动力学机制.研究结果表明，不同撞击速度下，在忽略毛细波作用、空腔深度h∈（D，hmax）的前提下，空腔深度随时间的成长仍满足t∝h5/2的关系；液滴撞击产生的空腔形状有U形和半球形两种，前者一般向V形转变，后者空腔底部会变为圆柱形，产生细长射流，并有可能发生气泡截留现象；在撞击速度较低时，低压区首先在空腔侧壁与底部交界处产生，随后在靠近液面以及空腔底部靠近中心区域各产生一个较大的涡环；在撞击速度较高，产生细长射流时，涡环的生成被抑制，低压区首先在波浪底部与侧壁上交界处产生，随后空腔底部变为圆柱状，空腔侧壁首先坍塌形成气泡截留.As one of the most fundamental and iconic fluid motion, droplet impact exists widely in scientific technologies and natural environment, and the phenomenon has been studied both for fundamental mechanism and for industrial applications in aerospace engineering, inkjet printing, agricultural irrigation and hydraulic structure erosion. Therefore, it is of great significance to study such basic movements for understanding the interfacial deformation of gas and liquid flow and improving the applications of droplet impact movement in engineering. Droplet impacting on a deep liquid pool has been extensively investigated for droplets with millimeter diameter. In this article, focusing on the cavity formation mechanism during a Micron-sized waterdrop impact on a deep pool, we perform systematic numerical simulations with adaptive mesh refinement technique and volume of fluid method to study the impact of a 290 μm water droplet on a deep water pool at velocities in a range of 2.5-6.5 m/s. The free surface motion, geometric variation of the cavity, local pressure field and vorticity field at selected times are presented to identify the pool-drop water mixing, capillary wave propagation, cavity formation, vortex ring generation and bubble entrapment phenomenon, and the dynamic mechanism of cavity motion is further explored. It is found that under the premise of neglecting the surface tension effects on the cavity whose depth is in a range of h∈(D, hmax), where D is the radius of initial droplet and hmax is the maximum depth, the cavity growth time to reach its maximum depth still scales as t∝h5/2, where t is time, but in the end, the formation of the bottom of the cavity is driven by capillary waves. There are two types of the initial cavity shapes: one is U-shape and the other is hemispherical shape, the former one generally changes into V-shape, and in the latter case, the bottom of the cavity will gradually transform into cylindrical shape, resulting in a thin jet and possible bubble entrapment. Cavity collapse is closely related to capillary wave propagation. When the impact velocity is low (Fr=567.1, Re=1595, We=121.8), the low-pressure zone is initially generated at the junction between the cavity sidewall and the bottom, a large vortex ring is then generated near the free surface and the bottom of the cavity, respectively. Under high impact velocities (Fr=792.1, Re=1885, We=170.2), the thin jet is observed, the generation of the vortex ring is suppressed. The low-pressure zone is first generated at the junction between the wave bottom and the cavity sidewall, after the cavity becomes cylindrical, the cavity collapses before the capillary wave arrives at the bottom, causing a bubble entrapment.
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Keywords:
- water droplet /
- deep water pool /
- cavity movement
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[17] Dai J F, Fan X P, Meng B, Liu J F 2015 Acta Phys. Sin. 64 094704 (in Chinese) [戴剑锋, 樊学萍, 蒙波, 刘骥飞 2015 物理学报 64 094704]
[18] Huang H, Hong N, Liang H, Shi B C, Chai Z H 2016 Acta Phys. Sin. 65 084702 (in Chinese) [黄虎, 洪宁, 梁宏, 施保昌, 柴振华 2016 物理学报 65 084702]
[19] Zhao H, Brunsvold A, Munkejord S T 2011 Exp. Fluids 50 621
[20] Popinet S 2003 J. Comput. Phys. 190 572
[21] Popinet S 2009 J. Comput. Phys. 228 5838
[22] Agbaglah G, Delaux S, Fuster D, Hoepffner J, Josserand C, Popinet S, Ray P, Scardovelli R, Zaleski S 2011 C. R. Mec. 339 194
[23] Morton D, Rudman M, Jong-Leng L 2000 Phys. Fluids 12 747
[24] Ray B, Biswas G, Sharma A 2015 J. Fluid Mech. 768 492
[25] Berberović E, van Hinsberg N P, Jakirli S, Roisman I V, Tropea C 2009 Phys. Rev. E 79 036306
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[1] Yarin A L 2006 Annu. Rev. Fluid Mech. 38 159
[2] Jomaa S, Barry D A, Brovelli A, Sander G C, Parlange J Y, Heng B C P, Tromp-van Meerveld H J 2010 J. Hydrol. 395 117
[3] Ferreira A G, Larock B E, Singer M J 1985 Soil Sci. Soc. Am. J. 49 1502
[4] Takagaki N, Kurose R, Baba Y, Nakajima Y, Komori S 2014 Int. J. Multiph. Flow 65 1
[5] Worthington A M 1908 A Study of Splashes (London: Longmans, Green) pp129-132
[6] Chapman D S, Critchlow P R 1967 J. Fluid Mech. 29 177
[7] Dooley B S, Warncke A E, Gharib M, Tryggvason G 1997 Exp. Fluids 22 369
[8] Liow J 2001 J. Fluid Mech. 427 73
[9] Michon G J, Josserand C, Séon T 2017 Phys. Rev. Fluids 2 023601
[10] Zhbankova S L, Kolpakov A V 1990 Fluid Dyn. 25 470
[11] Hirt C W, Nichols B D 1981 J. Comput. Phys. 39 201
[12] Osher S, Sethian J A 1988 J. Comput. Phys. 79 12
[13] Sussman M, Puckett E G 2000 J. Comput. Phys. 162 301
[14] Yue P, Zhou C, Feng J J 2006 Phys. Fluids 18 102102
[15] Ray B, Biswas G, Sharma A 2010 J. Fluid Mech. 655 72
[16] Castillo-Orozco E, Davanlou A, Choudhury P K, Kumar R 2015 Phys. Rev. E 92 053022
[17] Dai J F, Fan X P, Meng B, Liu J F 2015 Acta Phys. Sin. 64 094704 (in Chinese) [戴剑锋, 樊学萍, 蒙波, 刘骥飞 2015 物理学报 64 094704]
[18] Huang H, Hong N, Liang H, Shi B C, Chai Z H 2016 Acta Phys. Sin. 65 084702 (in Chinese) [黄虎, 洪宁, 梁宏, 施保昌, 柴振华 2016 物理学报 65 084702]
[19] Zhao H, Brunsvold A, Munkejord S T 2011 Exp. Fluids 50 621
[20] Popinet S 2003 J. Comput. Phys. 190 572
[21] Popinet S 2009 J. Comput. Phys. 228 5838
[22] Agbaglah G, Delaux S, Fuster D, Hoepffner J, Josserand C, Popinet S, Ray P, Scardovelli R, Zaleski S 2011 C. R. Mec. 339 194
[23] Morton D, Rudman M, Jong-Leng L 2000 Phys. Fluids 12 747
[24] Ray B, Biswas G, Sharma A 2015 J. Fluid Mech. 768 492
[25] Berberović E, van Hinsberg N P, Jakirli S, Roisman I V, Tropea C 2009 Phys. Rev. E 79 036306
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