Marangoni流动对液滴撞击过热液池影响的数值模拟

doi:10.7523/j.ucas.2023.063

摘要/Abstract

摘要： 对液滴撞击过热液池的动态过程进行数值模拟，着重关注由液池表面不均匀温度引起的马兰戈尼效应(Marangoni effect)对液池内的流场和温度场演化过程的影响。当乙醇液滴落入过热油池后，液池表面温度随着液滴的靠近而迅速下降，从而在径向上产生很大的温度梯度。由此引发的沿径向向内的Marangoni力会与沿径向向外的蒸汽剪切应力相抗衡，进而在蒸汽层最薄的位置形成一个“热射流”结构。随着时间的推进，占据主导地位的Marangoni力逐渐将“热射流”向内推动，直至在液滴下方形成下沉羽流。此外，随着液池黏度的增加，液池内由表面蒸汽应力引起的流动将被抑制，进而导致界面附近的换热效率大幅下降。

关键词: 莱顿弗罗斯特, 马兰戈尼效应, 液滴撞击液池, 气-液相变

Abstract: We numerically investigate the dynamic behaviors of a droplet impacting onto the non-volatile superheated liquid pool, and focuse on the influence of the Marangoni effect resulted from the inhomogeneous temperature distribution at the surface of liquid pool. Particularly, the time evolution of the flow field and the temperature field inside the pool during and after the impacting are studied. We find that the pool surface, made of oil, is cooled quickly as the ethanol droplet approaches, and a large temperature gradient is produced along the radial direction. Correspondingly, the Marangoni force directs radially inwards to resist the radial outward vapor stress, and a “jet” like structure is formed at the position where the vapor layer becomes thinnest. As the time advances, the Marangoni force becomes dominant and the “jet” is pushed radially inwards until the rear of the droplet and form the downward plume flow. In addition, as the viscosity of the liquid pool increases, the flow induced by the vapor stress is suppressed which further reduce the heat exchange efficiency near the interface.

Key words: Leidenfrost, Marangoni effect, droplet impacting liquid pool, liquid-gas phase change

中图分类号:

O359.1

赵烁, 张杰, 倪明玖. Marangoni流动对液滴撞击过热液池影响的数值模拟[J]. 中国科学院大学学报, 2024, 41(3): 289-297.

ZHAO Shuo, ZHANG Jie, NI Mingjiu. Numerical simulation of Marangoni flow on droplet impingement on a superheated pool[J]. Journal of University of Chinese Academy of Sciences, 2024, 41(3): 289-297.

参考文献

[1] Leidenfrost J G. On the fixation of water in diverse fire[J]. International Journal of Heat and Mass Transfer, 1966, 9(11): 1153-1166. DOI: 10.1016/0017-9310(66)90111-6.
[2] Kim J. Spray cooling heat transfer: the state of the art[J]. International Journal of Heat and Fluid Flow, 2007, 28(4): 753-767. DOI: 10.1016/j.ijheatfluidflow.2006.09.003.
[3] Moreira A L N, Moita A S, Panão M R. Advances and challenges in explaining fuel spray impingement: how much of single droplet impact research is useful?[J]. Progress in Energy and Combustion Science, 2010, 36(5): 554-580. DOI: 10.1016/j.pecs.2010.01.002.
[4] Biance A L, Clanet C, Quéré D. Leidenfrost drops[J]. Physics of Fluids, 2003, 15(6): 1632-1637. DOI: 10.1063/1.1572161.
[5] Quéré D. Leidenfrost dynamics[J]. Annual Review of Fluid Mechanics, 2013, 45: 197-215. DOI: 10.1146/annurev-fluid-011212-140709.
[6] Vakarelski I U, Marston J O, Chan D Y C, et al. Drag reduction by Leidenfrost vapor layers[J]. Physical Review Letters, 2011, 106(21): 214501. DOI: 10.1103/physrevlett.106.214501.
[7] Bouillant A, Mouterde T, Bourrianne P, et al. Leidenfrost wheels[J]. Nature Physics, 2018, 14(12): 1188-1192. DOI: 10.1038/s41567-018-0275-9.
[8] Tran T, Staat H J J, Prosperetti A, et al. Drop impact on superheated surfaces[J]. Physical Review Letters, 2012, 108(3): 036101. DOI: 10.1103/physrevlett.108.036101.
[9] Celestini F, Frisch T, Pomeau Y. Take off of small Leidenfrost droplets[J]. Physical Review Letters, 2012, 109(3): 034501. DOI: 10.1103/PhysRevLett.109.034501.
[10] Brunet P, Snoeijer J H. Star-drops formed by periodic excitation and on an air cushion:a short review[J]. The European Physical Journal Special Topics, 2011, 192(1): 207-226. DOI: 10.1140/epjst/e2011-01375-5.
[11] Ma X L, Burton J C. Self-organized oscillations of Leidenfrost drops[J]. Journal of Fluid Mechanics, 2018, 846: 263-291. DOI: 10.1017/jfm.2018.294.
[12] Bergen J E, Basso B C, Bostwick J B. Leidenfrost drop dynamics: exciting dormant modes[J]. Physical Review Fluids, 2019, 4(8): 083603. DOI: 10.1103/physrevfluids.4.083603.
[13] 胡子豪,任宁,俞熹.莱顿弗罗斯特水滴振荡模式的影响因素及机理探究[J].物理实验,2018,38(3):32-37. DOI:10.19655/j.cnki.1005-4642.2018.03.009.
[14] Linke H, Alemán B J, Melling L D, et al. Self-propelled Leidenfrost droplets[J]. Physical Review Letters, 2006, 96(15): 154502. DOI: 10.1103/physrevlett.96.154502.
[15] Cousins T R, Goldstein R E, Jaworski J W, et al. A ratchet trap for Leidenfrost drops[J]. Journal of Fluid Mechanics, 2012, 696: 215-227. DOI: 10.1017/jfm.2012.27.
[16] 庄峻杰. 高温锯齿表面形貌对Leidenfrost液滴运动影响的实验研究[D].北京：华北电力大学,2022. DOI:10.27140/d.cnki.ghbbu.2022.000379.
[17] Hashmi A, Xu Y H, Coder B, et al. Leidenfrost levitation: beyond droplets[J]. Scientific Reports, 2012, 2(1): 797. DOI: 10.1038/srep00797.
[18] Dupeux G, Baier T, Bacot V, et al. Self-propelling uneven Leidenfrost solids[J]. Physics of Fluids, 2013, 25(5): 051704. DOI: 10.1063/1.4807007.
[19] Maquet L, Sobac B, Darbois-Texier B, et al. Leidenfrost drops on a heated liquid pool[J]. Physical Review Fluids, 2016, 1(5): 053902. DOI: 10.1103/physrevfluids.1.053902.
[20] Mogilevskiy E. Levitation of a nonboiling droplet over hot liquid bath[J]. Physics of Fluids, 2020, 32(1): 012114. DOI: 10.1063/1.5131818.
[21] 王浩,徐进良.油面上相邻Leidenfrost液滴的相互作用及运动机制[J].物理学报,2023,72(5):226-237. DOI:10.7498/aps.72.20221822.
[22] Snoeijer J H, Brunet P, Eggers J. Maximum size of drops levitated by an air cushion[J]. Physical Review E, 2009, 79(3): 036307. DOI: 10.1103/physreve.79.036307.
[23] Adda-Bedia M, Kumar S, Lechenault F, et al. Inverse Leidenfrost effect: levitating drops on liquid nitrogen[J]. Langmuir, 2016, 32(17): 4179-4188. DOI: 10.1021/acs.langmuir.6b00574.
[24] Janssens S D, Koizumi S, Fried E. Behavior of self-propelled acetone droplets in a Leidenfrost state on liquid substrates[J]. Physics of Fluids, 2017, 29(3): 032103. DOI: 10.1063/1.4977442.
[25] Matsumoto R, Hasegawa K. Self-propelled Leidenfrost droplets on a heated glycerol pool[J]. Scientific Reports, 2021, 11: 3954. DOI: 10.1038/s41598-021-83517-1.
[26] Gauthier A, Diddens C, Proville R, et al. Self-propulsion of inverse Leidenfrost drops on a cryogenic bath[J]. Proceedings of the National Academy of Sciences of the United States of America, 2019, 116(4): 1174-1179. DOI: 10.1073/pnas.1812288116.
[27] Van Limbeek M A J, Sobac B, Rednikov A, et al. Asymptotic theory for a Leidenfrost drop on a liquid pool[J]. Journal of Fluid Mechanics, 2019, 863: 1157-1189. DOI: 10.1017/jfm.2018.1025.
[28] Sobac B, Maquet L, Duchesne A, et al. Self-induced flows enhance the levitation of Leidenfrost drops on liquid baths[J]. Physical Review Fluids, 2020, 5(6): 062701. DOI: 10.1103/physrevfluids.5.062701.
[29] Brackbill J U, Kothe D B, Zemach C. A continuum method for modeling surface tension[J]. Journal of Computational Physics, 1992, 100(2): 335-354. DOI: 10.1016/0021-9991(92)90240-Y.
[30] Zhao S, Zhang J, Ni M J. Boiling and evaporation model for liquid-gas flows: a sharp and conservative method based on the geometrical VOF approach[J]. Journal of Computational Physics, 2022, 452: 110908. DOI: 10.1016/j.jcp.2021.110908.
[31] Popinet S. An accurate adaptive solver for surface-tension-driven interfacial flows[J]. Journal of Computational Physics, 2009, 228(16): 5838-5866. DOI: 10.1016/j.jcp.2009.04.042.
[32] Bell J B, Colella P, Glaz H M. A second-order projection method for the incompressible Navier-Stokes equations[J]. Journal of Computational Physics, 1989, 85(2): 257-283. DOI: 10.1016/0021-9991(89)90151-4.
[33] Weymouth G D, Yue D K P. Conservative volume-of-fluid method for free-surface simulations on Cartesian-grids[J]. Journal of Computational Physics, 2010, 229(8): 2853-2865. DOI: 10.1016/j.jcp.2009.12.018.
[34] Cummins S J, Francois M M, Kothe D B. Estimating curvature from volume fractions[J]. Computers & Structures, 2005, 83(6-7): 425-434. DOI: 10.1016/j.compstruc.2004.08.017.
[35] Francois M M, Cummins S J, Dendy E D, et al. A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework[J]. Journal of Computational Physics, 2006, 213(1): 141-173. DOI: 10.1016/j.jcp.2005.08.004.
[36] Popinet S. Numerical models of surface tension[J]. Annual Review of Fluid Mechanics, 2018, 50: 49-75. DOI: 10.1146/annurev-fluid-122316-045034.
[37] Seric I, Afkhami S, Kondic L. Direct numerical simulation of variable surface tension flows using a volume-of-fluid method[J]. Journal of Computational Physics, 2018, 352: 615-636. DOI: 10.1016/j.jcp.2017.10.008.
[38] Tripathi M K, Sahu K C. Motion of an air bubble under the action of thermocapillary and buoyancy forces[J]. Computers & Fluids, 2018, 177: 58-68. DOI: 10.1016/j.compfluid.2018.10.003.
[39] Johansen H, Colella P. A Cartesian grid embedded boundary method for Poisson’s equation on irregular domains[J]. Journal of Computational Physics, 1998, 147(1): 60-85. DOI: 10.1006/jcph.1998.5965.