液滴撞击倾斜壁面动力学过程研究
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摘要
带有自由表面的流动现象广泛存在于现实生活中,它与人类的生存和发展有着不可分割的联系。液滴与固体表面的撞击现象就是一种典型的自由表面流动问题。详细研究液滴撞击固体表面的动力学行为对研究这些自然现象和工业技术的发展起着至关重要的作用。
本文根据流体力学控制方程建立了液滴撞击壁面的理论模型,利用流体动力学商业软件FLUENT的VOF二维模型,对液滴撞击倾斜壁面的动力学过程进行了重点考察,将模拟结果与实验数据进行比较分析,验证其正确性。通过改变相关参数,分析了液滴在壁面的流动状态,详细的研究了壁面特性、撞击速度、撞击角及液滴物性对变形过程的影响。本文最后提出了关于两相流计算的VOF三维模型,对液滴撞击水平及倾斜壁面的各个方向的变形情况进行了更深入的研究分析。
结果表明；通过比较液滴撞击倾斜表面的模拟结果与实验数据,可以看出VOF数值模拟方法能够表现出液滴在撞击过程中的关键特征。当液滴撞击水平壁面时,液滴的流动是对称的,但是液滴撞击倾斜壁面时,液滴的流动是不对称的。对于液滴撞击水平表面,壁面湿润性的影响分别用静态接触角模型(SCA)和动态接触角模型(DCA)进行模拟,对比结果DCA模型更接近于实验观测值。对于液滴撞击倾斜壁面,壁面的可润湿性即壁面的接触角对液滴的流动状态有很大的影响。高润湿性表面仅仅表现出沉积铺展,低润湿性表面表现出明显的滑移现象；撞击速度越大,液滴铺展的长度越大；在相同的We数下,撞击角越小,液滴的铺展速度越快,最终铺展的程度越大；在相同的条件下,粘度大的液滴铺展速度慢,铺展的长度小。
The free surface flow problems are commonly found out in the real life,it has inextricably linked with human survival and development. Droplets of liquid impact onto solid surfaces is a typical phenomenon of the free surface flow problem, The dynamic behaviors of droplet impact onto solid surface plays an important role in the study of nature phenomenon and the development of industrial technology.
At first,this paper establishes the theoretical mode of the droplet deposition according fluid mechanical governing equation, VOF model in FLUENT of CFD software is applied to investigate the dynamic process of droplet impacting on inclined solid surface. In order to validated the model, simulated results are compared with experimental date. By altering concerned parameters, dynamics of droplet on solid surface are analyzed. Influence of parameters including feature of surface, impact velocity,impact angle and droplet properties on the deformation process is studied in detail. Next this article proposes three-dimensional VOF model based on 2D mathematical model, Then droplets impact onto horizontal and inclined surfaces were investigated by this model.
The results has shown that despite of error in simulated results, by compared with experimental data, VOF method could capture the key feature of droplet dynamics when impacting the solid surface. In the case of normal impact.the flow is symmetric, but it is asymmetric for the oblique impact. During the process of droplets impact onto flat surfaces, The influence of surface wetting characteristics was investigated by using static contact angle (SCA) and dynamic contact angle (DCA) models. It was found that the DCA model is closer to the experiment observed value. During the process of droplets impact onto inclined surfaces, The flow state is seriously influenced by the wettability of surface, the high wettability surface sediment only shows spreading, the low wettability surface shows not only, spreading but also slip phenomenon; The impact velocity is bigger, the spreading diameter of droplet is bigger; In the same We,the impact angle is smaller, the spreading speed ids faster,and the last spreading relative diameter is bigger; The liquid characteristic such as viscosity has significant influence to the droplet impact dynamics. The smaller of the liquid viscosity, the bigger of the maximum relative diameter of the droplets can be obtained, and the spreading speed is slower.
本文根据流体力学控制方程建立了液滴撞击壁面的理论模型,利用流体动力学商业软件FLUENT的VOF二维模型,对液滴撞击倾斜壁面的动力学过程进行了重点考察,将模拟结果与实验数据进行比较分析,验证其正确性。通过改变相关参数,分析了液滴在壁面的流动状态,详细的研究了壁面特性、撞击速度、撞击角及液滴物性对变形过程的影响。本文最后提出了关于两相流计算的VOF三维模型,对液滴撞击水平及倾斜壁面的各个方向的变形情况进行了更深入的研究分析。
结果表明；通过比较液滴撞击倾斜表面的模拟结果与实验数据,可以看出VOF数值模拟方法能够表现出液滴在撞击过程中的关键特征。当液滴撞击水平壁面时,液滴的流动是对称的,但是液滴撞击倾斜壁面时,液滴的流动是不对称的。对于液滴撞击水平表面,壁面湿润性的影响分别用静态接触角模型(SCA)和动态接触角模型(DCA)进行模拟,对比结果DCA模型更接近于实验观测值。对于液滴撞击倾斜壁面,壁面的可润湿性即壁面的接触角对液滴的流动状态有很大的影响。高润湿性表面仅仅表现出沉积铺展,低润湿性表面表现出明显的滑移现象；撞击速度越大,液滴铺展的长度越大；在相同的We数下,撞击角越小,液滴的铺展速度越快,最终铺展的程度越大；在相同的条件下,粘度大的液滴铺展速度慢,铺展的长度小。
The free surface flow problems are commonly found out in the real life,it has inextricably linked with human survival and development. Droplets of liquid impact onto solid surfaces is a typical phenomenon of the free surface flow problem, The dynamic behaviors of droplet impact onto solid surface plays an important role in the study of nature phenomenon and the development of industrial technology.
At first,this paper establishes the theoretical mode of the droplet deposition according fluid mechanical governing equation, VOF model in FLUENT of CFD software is applied to investigate the dynamic process of droplet impacting on inclined solid surface. In order to validated the model, simulated results are compared with experimental date. By altering concerned parameters, dynamics of droplet on solid surface are analyzed. Influence of parameters including feature of surface, impact velocity,impact angle and droplet properties on the deformation process is studied in detail. Next this article proposes three-dimensional VOF model based on 2D mathematical model, Then droplets impact onto horizontal and inclined surfaces were investigated by this model.
The results has shown that despite of error in simulated results, by compared with experimental data, VOF method could capture the key feature of droplet dynamics when impacting the solid surface. In the case of normal impact.the flow is symmetric, but it is asymmetric for the oblique impact. During the process of droplets impact onto flat surfaces, The influence of surface wetting characteristics was investigated by using static contact angle (SCA) and dynamic contact angle (DCA) models. It was found that the DCA model is closer to the experiment observed value. During the process of droplets impact onto inclined surfaces, The flow state is seriously influenced by the wettability of surface, the high wettability surface sediment only shows spreading, the low wettability surface shows not only, spreading but also slip phenomenon; The impact velocity is bigger, the spreading diameter of droplet is bigger; In the same We,the impact angle is smaller, the spreading speed ids faster,and the last spreading relative diameter is bigger; The liquid characteristic such as viscosity has significant influence to the droplet impact dynamics. The smaller of the liquid viscosity, the bigger of the maximum relative diameter of the droplets can be obtained, and the spreading speed is slower.
引文
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[2]陈大宏,李炜等.自由表面流动数值模拟方法的探讨.水动力学研究与进展,2001,16(2)：216-224.
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[10]Mao T, Kuhn DCS, Tran H. Spread and rebound of liquid droplets upon impact on flat surfaces. AIChE J 43:2169-2179.
[11]贾力,方肇洪,钱兴华.高等传热学.高等教育出版社,2003.
[12]张寅平等.固—液相变强化传热物理机制及影响因素分析.中国科学(E辑),2002,32(4).
[13]奥齐西克·M·N.热传导.北京：高等教育出版社,1983.
[14]WorthinGton A. On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc R Soc London 25:261-271.
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[16]Zhang X, Basaran OA Dynamic surface tension effects in impact of a drop with a solid surface. J Colloid Interface Sci 187:166-178.
[17]Chaidron, G., Soucemarianadin, A. and Attane, P., Study of the impact of drops onto solid surfaces, In proceedings of IS&T 15 international conference on digital printing technologies,1999:70-73.
[18]B. S. Kang, S. H. Lee, On the dynamic behavior of a liquid droplet impacting upon an inclined surface. Experiments in Fluids,2000,29:380-387.
[19]H. Fujimoto, T. Ogino, et al, Collision of a droplet with a hemispherical static droplet on a solid, International Journal of Multiphase Flow,2001,7:1227-1245.
[20]E. F. Crafton, W. Z. Black, Heat transfer and evaporation rates of small liquid droplets on heated horizontal surfaces, International Journal of Heat and Mass Transfer,47: 1187-1200.
[21]Sikalo, S., Tropea, C., Ganic, E. N.,2005a. Dynamic wetting angle of a spreading droplet. Experimental Thermal and Fluid Science 29,795-802.
[22]Sikalo, S., Tropea, C., Ganic, E. N.,2005b. Impact of droplets onto inclined surfaces. Journal of Colloid and Interface Science 286,661-669.
[23]Sikalo, S., Marengo, M., Tropea, C., Ganic, E. N.,2005c. Analysis of impact of droplets on horizontal surfaces. Experimental Thermal and Fluid Science 25,503-510.
[24]Sikalo, S., Tropea, C., Ganic, E. N., Phenomena of droplet-surface interactions, Experimental Thermal and Fluid Science 31 (2006) 97-110
[25]施明恒.单个液滴碰击表面时的流体动力学特性.力学学报.1985(05)：419-425.
[26]毛靖儒,施红辉,俞茂铮等.液滴撞击固体表面时的流体动力特性实验研究.力学与实践,1995,17(3)：52-54.
[27]李维仲,朱卫英等,液滴撞击水平固体表面的可视化实验研究。热科学与技术。2008,7(2)：155-160
[28]陆军军、刘海峰等,液滴撞击平板的铺展特性。化学反应工程及工艺。2007,23(6)：506-510
[29]Harlow F H, Welch J E, Shannon J P, et al. The MAC method, a computing technique for solving viscous, incompressible, transient fluid problems involving free surface. Report LA-3425, Los Alamos Scientific Laboratory,1965.
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[31]Hirt C W and Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comp. Physics,1981,39:201-225.
[32]Prashant R. Gunjal.Vivek V. Ranade,Raghunath V. Chaudhari. Dynamics of Drop Impact on Solid Surface Experiments and VOF Simulations. AIChE J 51:59-78.
[33]Sikalo, S., Wilhelm, H. D., Roisman, I.V., Jakirlic, S., Tropea, C.,2005d.. Dynamic contact angle of spreading droplets:experiments and simulations. Physics of Fluids 17, 062103,1-13.
[34]林志勇、彭晓峰,震荡液滴内部流态,工程热物理学报,28(2007)2：289-291.
[35]李燕,沈胜强.液滴撞击等温固体平壁的数值模拟.工程热物理学报,2009/2010年,第30/30卷.
[36]Bussmann, M., Mostaghimi, J., Chandra, S., On a three-dimensional volume tracking model of drop impact. Phys. Fluids (1999) 11,1406-1417.
[37]Brackbill, J.U., Kothe, D.B., Zemach, C.,. A continuum method for modeling surface tension. J. Comput. Phys. (1992) 100,335-354.
[38]Pasandideh-Fard M, Chandra S, Mostaghimi J. A Three-Dimensional Model of Droplet Impact and Solidification. Int. J. Heat and Mass Transfer,2002,45:2229-2242.
[39]Bussmann, M. Afkhami S., Drop Impact Simulation with a Velocity-Dependent Contact Angle. Chemical Engineering Science,2007,62 (24):7214-7224
[40]Hitoshi Fujimoto,Yu Shiotani, Albert Y. Tong et al. Three-dimensional numerical analysis of the deformation behavior of droplets impinging onto a solid substrate. International Journal of Multiphase Flow,2007,33:317-332.
[41]H. Fujimoto, T. Ogino, et al, Collision of a droplet with a hemispherical static droplet on a solid, International Journal of Multiphase Flow,27(2001)7:1227-1245.
[42]林建忠,阮晓东,陈邦国.流体力学.北京：清华大学出版社,2005.
[43]李丽,均匀液滴喷射微制造的理论模型与数值模拟[硕士学位论文],西安：西北工业大学,2006
[44]刘儒勋,王志锋,数值模拟方法和运动界面追踪。合肥：中国科学技术大学出版社,2001
[45]Youngs, D. L. Time-Dependent Multi-Material Flow with Large Fluid Distortion. Numerical Methods for Dynamics, K. W. Morton and M. J. Baines, eds.1982.
[46]Fluent Inc. Fluent 6.0 User's Guide. Fluent Inc,2003
[47]王志东。VOF方法中自由液面重构的方法研究。水动力学研究与进展：A辑。2003,18(1)：52-56
[48]赵大勇,李维仲,VOF方法中儿种界面重构技术的比较。热科学与技术。2003,2(4)：318-323
[49]Brackbill, J. U., D. B. Kothe, C. Zemach. A Continuum Method for Modeling Surface Tension. J. Comput. Phys.,1992,100:355-365.
[50]陶文铨。数值传热学2版。西安：西安交通大学出版社,2001.
[51]S.V.帕坦卡著。郭宽良译.传热和流体流动的数值方法.合肥：安徽科学技术出版,1984
[52]李人宪.有限体积法基础.北京：国防工业出版社,2005.
[53]莫里森(S. R. Morrison)表面化学物.赵璧英等译.北京：北京大学出版社.1984.
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[57]Chandra, S., and C. T. Avedisian, On the Collision of a Droplet with a Solid Surface. Proc. Roy. SOC. (London),1991,432,13
[2]陈大宏,李炜等.自由表面流动数值模拟方法的探讨.水动力学研究与进展,2001,16(2)：216-224.
[3]陶文铨.数值传热学.西安：西安交通大学出版社,2001.
[4]田立平.含有相变问题的数字化处理.工业加热,1996.
[5]杨世铭,陶文铨.传热学.北京：高等教育出版社,1998.
[6]王补宣.工程传质传热学(上).北京：科学出版社,2002.
[7]王补宣.工程传质传热学(下).北京：科学出版社,2002.
[8]Chandra S, Averdisian C T. On the collision of a droplet with a solid surface. Proc. Roy. Soc. London A,1991,432:13-14.
[9]Pasandideh-Fard, M, Qiao, Y. M., Chandra, S. and Mostaghimi, J, Capillary effects during droplet impact on a solid surface, Phys. Fluids,1996,8 (3).
[10]Mao T, Kuhn DCS, Tran H. Spread and rebound of liquid droplets upon impact on flat surfaces. AIChE J 43:2169-2179.
[11]贾力,方肇洪,钱兴华.高等传热学.高等教育出版社,2003.
[12]张寅平等.固—液相变强化传热物理机制及影响因素分析.中国科学(E辑),2002,32(4).
[13]奥齐西克·M·N.热传导.北京：高等教育出版社,1983.
[14]WorthinGton A. On the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc R Soc London 25:261-271.
[15]WorthinGton A. A second paper on the forms assumed by drops of liquids falling vertically on a horizontal plate. Proc R Soc London 25:498-503.
[16]Zhang X, Basaran OA Dynamic surface tension effects in impact of a drop with a solid surface. J Colloid Interface Sci 187:166-178.
[17]Chaidron, G., Soucemarianadin, A. and Attane, P., Study of the impact of drops onto solid surfaces, In proceedings of IS&T 15 international conference on digital printing technologies,1999:70-73.
[18]B. S. Kang, S. H. Lee, On the dynamic behavior of a liquid droplet impacting upon an inclined surface. Experiments in Fluids,2000,29:380-387.
[19]H. Fujimoto, T. Ogino, et al, Collision of a droplet with a hemispherical static droplet on a solid, International Journal of Multiphase Flow,2001,7:1227-1245.
[20]E. F. Crafton, W. Z. Black, Heat transfer and evaporation rates of small liquid droplets on heated horizontal surfaces, International Journal of Heat and Mass Transfer,47: 1187-1200.
[21]Sikalo, S., Tropea, C., Ganic, E. N.,2005a. Dynamic wetting angle of a spreading droplet. Experimental Thermal and Fluid Science 29,795-802.
[22]Sikalo, S., Tropea, C., Ganic, E. N.,2005b. Impact of droplets onto inclined surfaces. Journal of Colloid and Interface Science 286,661-669.
[23]Sikalo, S., Marengo, M., Tropea, C., Ganic, E. N.,2005c. Analysis of impact of droplets on horizontal surfaces. Experimental Thermal and Fluid Science 25,503-510.
[24]Sikalo, S., Tropea, C., Ganic, E. N., Phenomena of droplet-surface interactions, Experimental Thermal and Fluid Science 31 (2006) 97-110
[25]施明恒.单个液滴碰击表面时的流体动力学特性.力学学报.1985(05)：419-425.
[26]毛靖儒,施红辉,俞茂铮等.液滴撞击固体表面时的流体动力特性实验研究.力学与实践,1995,17(3)：52-54.
[27]李维仲,朱卫英等,液滴撞击水平固体表面的可视化实验研究。热科学与技术。2008,7(2)：155-160
[28]陆军军、刘海峰等,液滴撞击平板的铺展特性。化学反应工程及工艺。2007,23(6)：506-510
[29]Harlow F H, Welch J E, Shannon J P, et al. The MAC method, a computing technique for solving viscous, incompressible, transient fluid problems involving free surface. Report LA-3425, Los Alamos Scientific Laboratory,1965.
[30]Harlow F H, Welch J E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physcis of Fluids,1965,8:2182-2186.
[31]Hirt C W and Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comp. Physics,1981,39:201-225.
[32]Prashant R. Gunjal.Vivek V. Ranade,Raghunath V. Chaudhari. Dynamics of Drop Impact on Solid Surface Experiments and VOF Simulations. AIChE J 51:59-78.
[33]Sikalo, S., Wilhelm, H. D., Roisman, I.V., Jakirlic, S., Tropea, C.,2005d.. Dynamic contact angle of spreading droplets:experiments and simulations. Physics of Fluids 17, 062103,1-13.
[34]林志勇、彭晓峰,震荡液滴内部流态,工程热物理学报,28(2007)2：289-291.
[35]李燕,沈胜强.液滴撞击等温固体平壁的数值模拟.工程热物理学报,2009/2010年,第30/30卷.
[36]Bussmann, M., Mostaghimi, J., Chandra, S., On a three-dimensional volume tracking model of drop impact. Phys. Fluids (1999) 11,1406-1417.
[37]Brackbill, J.U., Kothe, D.B., Zemach, C.,. A continuum method for modeling surface tension. J. Comput. Phys. (1992) 100,335-354.
[38]Pasandideh-Fard M, Chandra S, Mostaghimi J. A Three-Dimensional Model of Droplet Impact and Solidification. Int. J. Heat and Mass Transfer,2002,45:2229-2242.
[39]Bussmann, M. Afkhami S., Drop Impact Simulation with a Velocity-Dependent Contact Angle. Chemical Engineering Science,2007,62 (24):7214-7224
[40]Hitoshi Fujimoto,Yu Shiotani, Albert Y. Tong et al. Three-dimensional numerical analysis of the deformation behavior of droplets impinging onto a solid substrate. International Journal of Multiphase Flow,2007,33:317-332.
[41]H. Fujimoto, T. Ogino, et al, Collision of a droplet with a hemispherical static droplet on a solid, International Journal of Multiphase Flow,27(2001)7:1227-1245.
[42]林建忠,阮晓东,陈邦国.流体力学.北京：清华大学出版社,2005.
[43]李丽,均匀液滴喷射微制造的理论模型与数值模拟[硕士学位论文],西安：西北工业大学,2006
[44]刘儒勋,王志锋,数值模拟方法和运动界面追踪。合肥：中国科学技术大学出版社,2001
[45]Youngs, D. L. Time-Dependent Multi-Material Flow with Large Fluid Distortion. Numerical Methods for Dynamics, K. W. Morton and M. J. Baines, eds.1982.
[46]Fluent Inc. Fluent 6.0 User's Guide. Fluent Inc,2003
[47]王志东。VOF方法中自由液面重构的方法研究。水动力学研究与进展：A辑。2003,18(1)：52-56
[48]赵大勇,李维仲,VOF方法中儿种界面重构技术的比较。热科学与技术。2003,2(4)：318-323
[49]Brackbill, J. U., D. B. Kothe, C. Zemach. A Continuum Method for Modeling Surface Tension. J. Comput. Phys.,1992,100:355-365.
[50]陶文铨。数值传热学2版。西安：西安交通大学出版社,2001.
[51]S.V.帕坦卡著。郭宽良译.传热和流体流动的数值方法.合肥：安徽科学技术出版,1984
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