Two-dimensional analogies to the deformation characteristics of a falling droplet and its collision

• Autorzy: Rafi Abid Hasan , Haque Mohammad Rejaul , Ahmed Dewan Hasan

Identyfikatory

DOI

10.24425/ame.2021.139649

• Języki publikacji: EN

Abstrakty

EN

The present study investigates the 2D numerical analogies to the changes of the droplet shapes during the freefall for a wide range of droplet sizes through the stagnation air. The freefall velocity, shape change due to frictional force during free-fall is studied for different considered cases. With the elapse of time, a droplet with a larger initial diameter is changing its original shape more compared to droplets with a smaller diameter. In addition, the spreading of the droplet during the freefall seems more rapid for the larger-diameter droplet. When a droplet with an initial diameter of 15 mm starts to fall with gravitational force, the diameter ratio is decreasing for droplets with higher density and surface tension while droplets having lower density and surface tension show a diameter ratio greater than one. The spreading and splashing of the droplet on a solid surface and liquid storage at the time of impact are much influenced by the freefall memories of the droplet during the freefall from a certain height. These freefall memories are influenced by the fluid properties, drag force, and the freefall height. However, these freefall memories eventually regulate the deformation of the droplet during the freefall.

Słowa kluczowe

EN

droplet; freefall; spreading; drag force

PL

kropelka; swobodny spadek; siła tarcia

• Wydawca: Komitet Budowy Maszyn PAN
• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2022
• Tom: LXIX, nr 1
• Strony: 21--43
• Opis fizyczny: Bibliogr. 64 poz., rys., tab.

Twórcy

autor

Rafi Abid Hasan

• Department of Mechanical and Production Engineering, Ahsanullah University of Science and Technology, Dhaka, Bangladesh

• https://orcid.org/0000-0002-5518-9088

autor

Haque Mohammad Rejaul

• Department of Mechanical and Production Engineering, Ahsanullah University of Science and Technology, Dhaka, Bangladesh

• https://orcid.org/0000-0003-3105-0927

autor

Ahmed Dewan Hasan

• https://orcid.org/0000-0002-7024-249X

Bibliografia

• [1] X. Cao, Y. Ye, Q. Tang, E. Chen, Z. Jiang, J. Pan, and T. Guo. Numerical analysis of droplets from multinozzle inkjet printing. The Journal of Physical Chemistry Letters, 11(19):8442–8450, 2020. doi: 10.1021/acs.jpclett.0c02250.
• [2] H. Wijshoff. Drop dynamics in the inkjet printing process. Current Opinion in Colloid & Interface Science, 36:20–27, 2018. doi: 10.1016/j.cocis.2017.11.004.
• [3] W. Zhou, D. Loney, A.G. Fedorov, F.L. Degertekin, and D.W. Rosen. Shape evolution of droplet impingement dynamics in ink-jet manufacturing. Proceedings for the 2011 International Solid Freeform Fabrication Symposium, pages 309–325, Austin, USA, 2011. doi: 10.26153/tsw/15297.
• [4] L. Mouzai and M. Bouhadef. Water drop erosivity: Effects on soil splash. Journal of Hydraulic Research, 41(1):61–68, 2003. doi: 10.1080/00221680309499929.
• [5] M. Hajigholizadeh, A.M. Melesse, and H.R. Fuentes. Raindrop-induced erosion and sediment transport modelling in shallow waters: A review. Journal of Soil and Water Science, 1(1):15–25, 2018. doi: 10.36959/624/427.
• [6] P.C. Ekern. Raindrop impact as the force initiating soil erosion. Soil Science Society of America Journal, 15(C):7–10, 1951. doi: 10.2136/sssaj1951.036159950015000C0002x.
• [7] R. Andrade, O. Skurtys, and F. Osorio. Drop impact behavior on food using spray coating: Fundamentals and applications. Food Research International, 54(1):397–405, 2013. doi: 10.1016/j.foodres.2013.07.042.
• [8] M. Toivakka. Numerical investigation of droplet impact spreading in spray coating of paper. Proceedings of the 2003 Spring Advanced Coating Fundamentals Symposium, Atlanta, USA, 2003.
• [9] A. Prasad and H. Henein. Droplet cooling in atomization sprays. Journal of Materials Science, 43(17):5930–5941, 2008. doi: 10.1007/s10853-008-2860-2.
• [10] W. Jia and H.-H. Qiu. Experimental investigation of droplet dynamics and heat transfer in spray cooling. Experimental Thermal and Fluid Science, 27(7):829–838, 2003. doi: 10.1016/S0894-1777(03)00015-3.
• [11] G. Duursma, K. Sefiane, and A. Kennedy. Experimental studies of nanofluid droplets in spray cooling. Heat Transfer Engineering, 30(13):1108–1120, 2009. doi: 10.1080/01457630902922467.
• [12] W.-C. Qin, B.-J. Qiu, X.-Y. Xue, C. Chen, Z.-F. Xu, and Q.-Q. Zhou. Droplet deposition and control effect of insecticides sprayed with an unmanned aerial vehicle against plant hoppers. Crop Protection, 85:79–88, 2016. doi: 10.1016/j.cropro.2016.03.018.
• [13] S. Chen, Y. Lan, Z. Zhou, F. Ouyang, G. Wang, X. Huang, X. Deng, and S. Cheng. Effect of droplet size parameters on droplet deposition and drift of aerial spraying by using plant protection UAV. Agronomy, 10(2):195, 2020. doi: 10.3390/agronomy10020195.
• [14] D.T. Sheppard. Spray Characteristics of Fire Sprinklers. Ph.D. Thesis, Northwestern University, Evanston, USA, June 2002.
• [15] H. Liu, C.Wang, I.M. De Cachinho Cordeiro, A.C.Y. Yuen, Q. Chen, Q.N. Chan, S. Kook, and G.H. Yeoh. Critical assessment on operating water droplet sizes for fire sprinkler and water mist systems. Journal of Building Engineering, 28:100999, 2020. doi: 10.1016/j.jobe.2019.100999.
• [16] D.C. Blanchard. The behavior of water drops at terminal velocity in air. Eos, Transactions American Geophysical Union, 31(6):836–842, 1950. doi: 10.1029/TR031i006p00836.
• [17] H.R. Pruppacher and K.V. Beard. A wind tunnel investigation of the internal circulation and shape of water drops falling at terminal velocity in air. Quarterly Journal of the Royal Meteorological Society, 96(408):247–256, 1970. doi: 10.1002/qj.49709640807.
• [18] H.R. Pruppacher and R.L. Pitter. A semi-empirical determination of the shape of cloud and rain drops. Journal of the Atmospheric Sciences, 28(1):86–94, 1971. doi: 10.1175/1520-0469(1971)0280086:ASEDOT>2.0.CO;2.
• [19] K.V. Beard and C. Chuang. A new model for the equilibrium shape of raindrops. Journal of the Atmospheric Sciences, 44(11):1509–1524, Jun. 1987. doi: 10.1175/1520-0469(1987)0441509:ANMFTE>2.0.CO;2.
• [20] É.Reyssat, F. Chevy, A.L. Biance, L. Petitjean, and D. Quéré. Shape and instability of free-falling liquid globules. Europhysics Letters, 80(3):34005, 2007. doi: 10.1209/0295-5075/80/34005.
• [21] R. Clift, J.R. Grace, and M.E. Weber. Bubbles, Drops and Particles. Academic Press, 1978.
• [22] S.-C. Yao and V.E. Schrock. Heat and mass transfer from freely falling drops. Journal of Heat Transfer, 98(1):120–126, 1976. doi: 10.1115/1.3450453.
• [23] T.J. Horton, T.R. Fritsch, and R.C. Kintner. Experimental determination of circulation velocities inside drops. The Canadian Journal of Chemical Engineering, 43(3):143–146, 1965. doi: 10.1002/cjce.5450430309.
• [24] R.H. Magarvey and B.W. Taylor. Free fall breakup of large drops. Journal of Applied Physics, 27(10):1129–1135, 1956. doi: 10.1063/1.1722216.
• [25] M.N. Chowdhury, F.Y. Testik, M.C. Hornack, and A.A. Khan. Free fall of water drops in laboratory rainfall simulations. Atmospheric Research, 168:158–168, 2016. doi: 10.1016/j.atmosres.2015.08.024.
• [26] M. Abdelouahab and R. Gatignol. Study of falling water drop in stagnant air. European Journal of Mechanics - B/Fluids, 60:82–89, 2016. doi: 10.1016/j.euromechflu.2016.07.007.
• [27] J.H. van Boxel. Numerical model for the fall speed of raindrops in a rainfall simulator. I.C.E Special Report, 1998/1, 77–85,
• [28] A.K. Kamra and D.V Ahire. Wind-tunnel studies of the shape of charged and uncharged water drops in the absence or presence of an electric field. Atmospheric Research, 23(2):117–134, 1989. doi: 10.1016/0169-8095(89)90003-3.
• [29] M. Thurai and V.N. Bringi. Drop axis ratios from a 2D video disdrometer. Journal of Atmospheric and Oceanic Technology, 22(7):966–978, 2005. doi: 10.1175/JTECH1767.1.
• [30] C. Josserand and S.T. Thoroddsen. Drop impact on a solid surface. Annual Review of Fluid Mechanics, 48:365–391, 2016. doi: 10.1146/annurev-fluid-122414-034401.
• [31] J. Eggers, M.A. Fontelos, C. Josserand, and S. Zaleski. Drop dynamics after impact on a solid wall: Theory and simulations. Physics of Fluids, 22(6):062101, 2010. doi: 10.1063/1.3432498.
• [32] S. Chandra and C.T. Avedisian. On the collision of a droplet with a solid surface. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 432(1884):13–41, 1991. doi: 10.1098/rspa.1991.0002.
• [33] O.G. Engel. Waterdrop collisions with solid surfaces. Journal of Research of the National Bureau of Standards, 54(5):281–298, 1955. doi: 10.6028/jres.054.033.
• [34] I.V. Roisman, R. Rioboo, and C. Tropea. Normal impact of a liquid drop on a dry surface: model for spreading and receding. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 458(2022):1411–1430, 2002. doi: 10.1098/rspa.2001.0923.
• [35] Y. Renardy, S. Popinet, L. Duchemin, M. Renardy, S. Zaleski, C. Josserand, M.A. Drumright-Carke, D. Richard, C. Clanet, and D. Quéré. Pyramidal and toroidal water drops after impact on a solid surface. Journal of Fluid Mechanics, 484:69–83, 2003. doi: 10.1017/S0022112003004142.
• [36] D. Bartolo, F. Bouamrirene, É. Verneuil, A. Buguin, P. Silberzan, and S. Moulinet. Bouncing or sticky droplets: Impalement transitions on superhydrophobic micropatterned surfaces. Europhysics Letters, 74(2):299–305, 2006. doi: 10.1209/epl/i2005-10522-3.
• [37] D. Bartolo, C. Josserand, and D. Bonn. Singular jets and bubbles in drop impact. Physical Review Letters, 96:124501, 2006. doi: 10.1103/PhysRevLett.96.124501.
• [38] C. Clanet, C. Béguin, D. Richard, and D. Quéré. Maximal deformation of an impacting drop. Journal of Fluid Mechanics, 517:199–208, 2004. doi: 10.1017/S0022112004000904.
• [39] L.H.J. Wachters, L. Smulders, J.R. Vermeulen, and H.C. Kleiweg. The heat transfer from a hot wall to impinging mist droplets in the spheroidal state. Chemical Engineering Science, 21(12):1047–1056, 1966. doi: 10.1016/0009-2509(66)85042-X.
• [40] C.O. Pedersen. An experimental study of the dynamic behavior and heat transfer characteristics of water droplets impinging upon a heated surface. International Journal of Heat and Mass Transfer, 13(2):369–381, 1970. doi: 10.1016/0017-9310(70)90113-4.
• [41] M.A. Styricovich, Y.V. Baryshev, G.V. Tsiklauri and M E. Grigorieva. The mechanism of heat and mass transfer between a water drop and a heated surface. Proceedings of the Sixth International Heat Transfer Conference, Vol. 1, pages 239-243, Toronto, Canada, August 7-11, 1978.
• [42] P. Savic and G.T. Boult. The fluid flow associated with the impact of liquid drops with solid surfaces. Proceedings of Heat Transfer Fluid Mechanics Institution, 43-84, 1957.
• [43] S.E. Hinkle. Water drop kinetic energy and momentum measurement considerations. Applied Engineering in Agriculture, 5(3):386–391, 1989. doi: 10.13031/2013.26532.
• [44] C.D. Stow and R.D. Stainer. The physical products of a splashing water drop. Journal of Meteorological Society of Japan, 55(5):518–532, 1977.
• [45] Z. Levin and P.V. Hobbs. Splashing of water drops on solid and wetted surfaces, Hydrodynamics and charge separation. Philosophical Transactions of the Royal Society A Mathematical, Physical and Engineering Sciences, 269(1200):555–585, 1971. doi: 10.1098/rsta.1971.0052.
• [46] C.D. Stow, M.G. Hadfield. An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 37(1755):419–441, 1981. doi: 10.1098/rspa.1981.0002.
• [47] C. Mundo, M. Sommerfeld, and C. Tropea. Droplet-wall collisions: Experimental studies of the deformation and breakup process. I nternational Journal of Multiphase Flow, 21(2):151–173, 1995. doi: 10.1016/0301-9322(94)00069-V.
• [48] M. Bussmann, S. Chandra, and J. Mostaghimi. Modeling the splash of a droplet impacting a solid surface. Physics of Fluids, 12(12):3121–3132, 2000. doi: 10.1063/1.1321258.
• [49] L. Xu, W.W. Zhang, and S.R. Nagel. Drop splashing on a dry smooth surface. Physical Review Letters, 94(18):184505, 2005. doi: 10.1103/PhysRevLett.94.184505.
• [50] B.T. Helenbrook and C.F. Edwards. Quasi-steady deformation and drag of uncontaminated liquid drops. International Journal of Multiphase Flow, 28(10):1631–1657, 2002. doi: 10.1016/S0301-9322(02)00073-3.
• [51] J.Q. Feng. A deformable liquid drop falling through a quiescent gas at terminal velocity. Journal of Fluid Mechanics, 658:438–462, 2010. doi: 10.1017/S0022112010001825.
• [52] J.Q. Feng and K.V. Beard. Raindrop shape determined by computing steady axisymmetric solutions for Navier-Stokes equations. Atmospheric Research, 101(1–2):480–491, 2011. doi: 10.1016/j.atmosres.2011.04.012.
• [53] J. Han and G. Tryggvason. Secondary breakup of axisymmetric liquid drops. I. Acceleration by a constant body force. Physics of Fluids, 11(12):3650–3667, 1999. doi: 10.1063/1.870229.
• [54] J. Han and G. Tryggvason. Secondary breakup of a axisymmetric liquid drops. II. Impulsive acceleration. Physics of Fluids, 13(6):1554–1565, 2001. doi: 10.1063/1.1370389.
• [55] P. Khare and V. Yang. Breakup of non-Newtonian liquid droplets. 44th AIAA Fluid Dynamics Conference, Atlanta, USA, 16-20 June 2014. doi: 10.2514/6.2014-2919.
• [56] M. Sussman and E.G. Puckett. A Coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows. Journal of Computational Physics, 162(2):301–337, 2000. doi: 10.1006/jcph.2000.6537.
• [57] R. Scardovelli and S. Zaleski. Direct numerical simulation of free-surface and interfacial flow. Annual Review of Fluid Mechanics, 31:567–603, 1999. doi: 10.1146/annurev.fluid.31.1.567.
• [58] S. Shin and D. Juric. Simulation of droplet impact on a solid surface using the level contour reconstruction method. Journal of Mechanical Science and Technology, 23:2434–2443, 2009. doi: 10.1007/s12206-009-0621-z.
• [59] M. García Pérez and E. Vakkilainen. A comparison of turbulence models and two and three dimensional meshes for unsteady CFD ash deposition tools. Fuel, 237:806–811, 2019. doi: 10.1016/j.fuel.2018.10.066.
• [60] M. Mezhericher, A. Levy, and I. Borde. Modeling of droplet drying in spray chambers using 2D and 3D computational fluid dynamics. Drying Technology, 27(3):359–370, 2009. doi: 10.1080/07373930802682940.
• [61] S. Afkhami and M. Bussmann. Height functions for applying contact angles to 2D VOF simulations. International Journal for Numerical Methods in Fluids, 57(4):453-472, 2008. doi: 10.1002/fld.1651.
• [62] J. Zheng, J. Wang, Y. Yu, and T. Chen. Hydrodynamics of droplet impingement on a thin horizontal wire. Mathematical Problems in Engineering, 2018:9818494, 2018. doi: 10.1155/2018/9818494.
• [63] J. Thalackottore Jose and J.F. Dunne. Numerical simulation of single-droplet dynamics, vaporization, and heat transfer from impingement onto static and vibrating surfaces. Fluids, 5(4):188, 2020. doi: 10.3390/fluids5040188.
• [64] H. Liu. Science and Engineering of Droplets: Fundamentals and Applications. Noyes Publications, USA, 1999.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).