Figure 11: Computational 3D snapshots of droplet impact on a sphere; W e = 26.14, Re = 42.48, density ratio=328, contact angle=76◦, Bo = 0.0908.

평면 및 구형 표면의 액적 충돌을위한 고밀도 비율 격자-볼츠만 모델 적용

Duo Zhang1,2, K. Papadikis1∗, Sai Gu1
1Xi’an Jiaotong-Liverpool University, No. 111 Ren’ai Road, Suzhou Dushu Lake Higher Education
Town, Suzhou, China 215123.
2The University of Liverpool, Brownlow Hill, Liverpool, L69 7ZX, United Kingdom.
Tel: 0086-512-88161752
Email: Konstantinos.Papadikis@xjtlu.edu.cn
∗Corresponding author

현재 연구에서는 고밀도 비율을 견딜 수있는 3 차원 격자 Boltzmann 모델을 사용하여 액체 방울이 평면 및 구형 타겟에 충돌하는 것을 시뮬레이션합니다. Weber 및 Reynolds 수의 범위에 대해 운동 학적, 확산, 이완 및 평형 단계와 같이 평평한 표면에 대한 액적 충돌의 4 단계를 얻었습니다. 예측 된 최대 확산 계수는 문헌에 발표 된 실험 데이터와 잘 일치합니다. 액체 방울이 구형 타겟에 미치는 영향에 대해 타겟 표면에서 필름 두께의 시간적 변화를 조사합니다. 필름 역학의 세 가지 다른 시간적 위상, 즉 초기 낙하 변형 위상, 관성 지배 위상 및 점도 지배 위상이 재현되고 연구됩니다. 액적 레이놀즈 수와 목표 대 드롭 크기 비율이 필름 흐름 역학에 미치는 영향을 조사합니다.

고체 표면의 물방울 충돌은 땅에 떨어지는 빗방울, 잉크젯 인쇄, 뜨거운 표면의 스프레이 냉각, 스프레이 페인팅 및 코팅, 플라즈마 스프레이, 연소실의 연료 스프레이, 고정식 촉매 처리와 같은 일반적인 현상입니다. 베드 반응기 및 최근에는 미세 가공 및 미세 채널 [1]. 따라서 고체 표면에 영향을 미치는 물방울에 대한 연구는 연구원들의 큰 관심을 끌고 있습니다. Rein [2]은이 현상에 대한 포괄적 인 리뷰를 발표했습니다. Rioboo 등 [3]에 의해 체계적인 연구가 수행되었으며, 여기서 건식 벽에 대한 낙하 충격의 6 가지 가능한 결과, 즉 퇴적, 신속한 스플래시, 코로나 스플래시, 후퇴 이탈, 부분 반동 및 완전 반동이 밝혀졌습니다.

Keywords: Multiphase flow, Lattice Boltzmann, high-density-ratio, droplet impact, spread
factor, film thickness

Figure 2: Computational snapshots of the droplet impact on a flat surface; W e = 52, Re = 41, density ratio=240, contact angle=96◦ .
Figure 2: Computational snapshots of the droplet impact on a flat surface; W e = 52, Re = 41, density ratio=240, contact angle=96◦ .
Figure 6: Time evolution of the spread factor for Oh = 0.177.
Figure 6: Time evolution of the spread factor for Oh = 0.177.
Figure 11: Computational 3D snapshots of droplet impact on a sphere; W e = 26.14, Re = 42.48, density ratio=328, contact angle=76◦, Bo = 0.0908.
Figure 11: Computational 3D snapshots of droplet impact on a sphere; W e = 26.14, Re = 42.48, density ratio=328, contact angle=76◦, Bo = 0.0908.
Table 2: Summary of the simulation parameters for the cases of droplet impact onto a sphere.
Table 2: Summary of the simulation parameters for the cases of droplet impact onto a sphere.

References

References
[1] A.L.Yarin, Drop impact dynamics: Splashing, spreading, receding, bouncing. . . , Annu. Rev. Fluid Mech. 38(2006) 159-192.
[2] M.Rein, Phenomena of liquid drop impact on solid and liquid surface, Fluid. Dyn.
Res. 12(1993) 61-93.
[3] R.Rioboo, M.Marengo, C.Tropea, Time evolution of liquid drop impact onto solid,
dry surfaces, Exp. Fluids. 33(2002) 112-124.
[4] A.Asai, M.Shioya, S.Hirasawa, T.Okazaki, Impact of an ink drop on paper, J Imaging
Sci Techn. 37(1993) 205-207.
[5] B.L.Scheller, D.W.Bousfield, Newtonian drop impact with a solid surface, AIChE J.
41(1995) 1357-1367.
[6] S. Chandra and C. T. Avedesian, On the collision of a droplet with a solid surface,
Proc. R. Soc. London, Ser. A 432(1991) 13.
[7] M.Pasandideh-Fard, Y.M.Qiao, S.Chandra, J.Mostaghimi, Capillary effects during
droplet impact on a solid surface, Phys Fluids. 8(1996) 650-660.
[8] T.Mao, D.C.S.Kuhn, H.Tran, Spread and rebound of liquid droplets upon impact on
flat surfaces, AIChE J. 43(1997) 2169-2179.
[9] I.V.Roisman, R.Rioboo, C.Tropea, Normal impact of a liquid drop on a dry surface:
Model for spreading and receding, Proc. R. Soc. London, Ser. A 458(2002) 1411-1430.
[10] H.Dong, W.W.Carr, D.G.Bucknall, J.F.Morris, Temporally-resolved inkjet drop impaction on surfaces, AIChE J. 53(2007), 2606-2617.
[11] L.S.Hung, S.C.Yao, Experimental investigation of the impaction of water droplets
on cylindrical objects, Int. J. Multiphase Flow 25(1999) 1545-1559.

[12] Y.Hardalupas, A.M.K.P.Taylor, J.H.Wilkins, Experimental investigation of submillimeter droplet impingement onto spherical surfaces, Int. J. Heat Fluid Flow 20 (1999)
477-485.
[13] S.Bakshi, L.V.Roisman, C.Tropea, Investigations on the impact of a drop onto a
small spherical target, Phys Fluids. 19(2007) 032102.
[14] S.Mukherjee, Numerical simulation of wall impinging drops, Ph.D.thesis, School of
Mechanical Engineering, Purdue University 2006.
[15] G.Trapaga, J.Szekely, Mathematical Modeling of the Isothermal Impingement of
Liquid Droplets in Spraying Processes, Metall. Trans. B. 22(1991) 901-914.
[16] M.Bussmann, S.Afkhami, Drop impact simulation with a velocity-dependent contact
angle, Chem. Eng. Sci. 62(2007) 7214-7224.
[17] A.Gupta, R.Kumar, Droplet impingement and breakup on a dry surface, Comput.
Fluids. 39(2010) 1696-1703.
[18] A.Gupta, R.Kumar, Two-dimensional lattice Boltzmann model for droplet impingement and breakup in ow density ratio liquids, Comm. Comp. Phys. 10(2011) 767-784.
[19] Y.Y.Yan, Y.Q.Zu, A lattice Boltzmann method for incompressible two-phase flows
on partial wetting surface with large density ratio, J. Comput. Phys. 227(2007) 763-
775.
[20] T.Inamuro, T.Ogata, S.Tajima, N.Konishi, A lattice Boltzmann method for incompressible two-phase flows with large density differences, J. Comput. Phys. 198(2004)
628-644.
[21] A.J.Briant, P.Papatzacos, J.M.Yeomans, Lattice Boltzmann simulations of contact
line motion in a liquid-gas system, Philos. Trans. Roy. Soc. Lond. A. 360(2002) 485-
495.

[22] A.Fakhari, M.H.Rahimian, Phase-field modeling by the method of lattice Boltzmann
equations, Phys. Rev. E. 81(2010) 036707.
[23] M.R.Swift, E.Orlandini, W.R.Osborn, J.M.Yeomans, Lattice Boltzmann simulations
of liquid-gas and binary fluid systems, Phys. Rev. E. 54(1996) 5041-5052.
[24] S.Q.Shen, F.F.Bi, Y.L.Guo, Simulation of droplets impact on curved surfaces with
lattice Boltzmann method, Int. J. Heat Mass Tranf. 55(2012) 6938-6943.
[25] X.Shan, H.Chen, Simulation of nonideal gases and liquid-gas phase transitions by
the lattice Boltzmann equation, Phys. Rev. E. 49(1994) 2941-2948.
[26] P.Yuan, L.Schaefer, Equations of state in a lattice Boltzmann model, Phys Fluids.
18(2006) 042101.
[27] D.H.Rothman, J.M.Keller, Immiscible cellular-automation fluids, J. Statist. Phys.
52(1988) 1119-1129.
[28] X.He, S.Chen, R.Zhang, A lattice Boltzmann scheme for incompressible multiphase
flow and its application in simulation of Rayleigh-Taylor instability, J. Comput. Phys.
152(1999) 642-663.
[29] T.Reis, T.N.Phillips, Lattice Boltzmann model for simulating immiscible two-phase
flows, J. Phys. A: Math. Theor. 40(2007) 4033-4053.
[30] S.Leclaire, M.Reggio, J.-Y.Trepanier, Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model. 36(2012) 2237-2252.
[31] S.Leclaire, P.Nicolas, M.Reggio, J.-Y.Trepanier, Enhanced equilibrium distribution
functions for simulationg immiscible multiphase flows with variable density ratios in
a class of lattice Boltzmann models. 57(2013) 159-168.
[32] H.B.Huang, H.W.Zheng, X.Y.Lu, C.Shu, An evaluation of a 3D free-energy-based
lattice Boltzmann model for multiphase flows with large density ratio, Int. J. Numer.
Meth. Fluids. 63(2009) 1193-1207.

[33] T.Lee, C.L.Lin, A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio, J. Comput. Phys.
206(2005) 16-47.
[34] H.W.Zheng, C.Shu, Y.T.Chew, A lattice Boltzmann model for multiphase flows with
large density ratio, J. Comput. Phys. 218(2006) 353-371.
[35] D.A.Perumal, A.K.Dass,Application of lattice Boltzmann method for incompressibe
viscous flows, Applied Mathematical Modelling. 37(2013) 4075-4092.