基于SPH方法的液滴撞击固壁过程的数值模拟研究
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摘要
自由表面流动问题在自然界中广泛存在,例如水利工程中的溃坝、自由表面溢流、明渠水流等,它无处不在影响着人类的生存和发展,因此自由表面流动的研究也具有十分重要的现实意义。液滴与固体壁面的碰撞是典型的自由表面流动问题。液滴与壁面碰撞后的扩散、回弹甚至破碎现象广泛地存在于化工制造、冶金技术等工业过程中,因此,研究液滴撞击固壁现象能更好地了解具有自由表面流动问题。
本文采用拉格朗日形式的无网格粒子法—光滑粒子流体动力学方法(SPH)对液滴撞击固壁问题进行数值模拟研究。研究了适用于广义流体动力学的SPH的基本方程及与其相关的数值技术,由拉格朗日形式下的流体基本方程推导出SPH形式下的流体基本方程。通过采用人工压缩率,把所有理论不可压缩流体模化为实际上是弱可压缩的;通过采用人工粘性来消除计算结果产生的非物理振荡。
采用SPH方法建立了二维液滴撞击固壁基本模型,对液滴撞击固壁后的动力学行为进行数值模拟,将数值模拟结果与物理实验结果进行对比分析;对撞击固壁后液滴内部流场、压强场、特征粒子的运动速度及位移情况进行分析研究;通过改变相关参数,如液滴的初始撞击速度、液滴的初始半径等,研究以上相关因素对液滴撞击固壁后铺展因素的影响;在此基础上,通过建立三维模型,来研究三维情况下液滴撞击固壁后的运动过程。
建立液滴撞击固壁后运动状态的理论模型,研究分析液滴铺展因素与接触角间的关系及液滴的撞击速度与接触角间的关系,从而得到液滴的铺展因素与液滴的撞击速度之间的关系,并把理论推导结果与数值模拟结果进行对比分析。
It exists extensively in nature for free surface flow, such as dam-break in hydraulic engineering, overflow in free surface and flow in open channels, which influences widely to the survival and development of mankind, so it’s of great significance to study free surface flow problem. A liquid droplet impacting on a solid surface is a classic free surface flow problem. The phenomenon of diffusion, rebound and broken of a droplet when it impacts on a solid surface exists extensively in chemical industry and metallurgical industry. It’s a good way to study free surface flow by studying the phenomenon of a droplet impacting on a solid surface.
The Smoothed Particle Hydrodynamics (SPH) method is applied in the numerical simulation of a droplet impacting on a solid surface which is a Lagrangian meshfree particle method. The SPH equations and the key technology which are suitable to generalized hydrokinetics are studied, and the SPH fluid equations are derived from Lagrangian fluid equations. Artificial Compression is applied to calculate the time derivative of stress considering incompressible fluid as compressible fluid. Artificial viscosity is applied to eliminate unphysical oscillation in results. The treatment method of boundary conditions including rigid boundary and free surface boundary is studied, and so do the search of free surface particles, the choice of time steps and the searching method among neighboring particles.
SPH method is applied to establish 2-Dimensional model to simulate a liquid droplet impacting on a solid surface. The comparison between the simulated results and experimental results is done, and the flow field, the pressure, the speed and displacement of the representative particles are all studied. The spreading factor is studied by changing the related parameters, such as initial velocity and initial radius of the droplet. Based on above analysis the 3-Dimensional model is established to study the motion of the droplet when it impacts on a solid surface.
The theoretical model of a droplet impacting on a solid surface is established to study the relationship between spreading factor and contact angel, the relationship between impacting velocity of the droplet and contact angel, so the relationship between spreading factor and impacting velocity of the droplet can be got, which can be compared with numerical simulated results.
本文采用拉格朗日形式的无网格粒子法—光滑粒子流体动力学方法(SPH)对液滴撞击固壁问题进行数值模拟研究。研究了适用于广义流体动力学的SPH的基本方程及与其相关的数值技术,由拉格朗日形式下的流体基本方程推导出SPH形式下的流体基本方程。通过采用人工压缩率,把所有理论不可压缩流体模化为实际上是弱可压缩的;通过采用人工粘性来消除计算结果产生的非物理振荡。
采用SPH方法建立了二维液滴撞击固壁基本模型,对液滴撞击固壁后的动力学行为进行数值模拟,将数值模拟结果与物理实验结果进行对比分析;对撞击固壁后液滴内部流场、压强场、特征粒子的运动速度及位移情况进行分析研究;通过改变相关参数,如液滴的初始撞击速度、液滴的初始半径等,研究以上相关因素对液滴撞击固壁后铺展因素的影响;在此基础上,通过建立三维模型,来研究三维情况下液滴撞击固壁后的运动过程。
建立液滴撞击固壁后运动状态的理论模型,研究分析液滴铺展因素与接触角间的关系及液滴的撞击速度与接触角间的关系,从而得到液滴的铺展因素与液滴的撞击速度之间的关系,并把理论推导结果与数值模拟结果进行对比分析。
It exists extensively in nature for free surface flow, such as dam-break in hydraulic engineering, overflow in free surface and flow in open channels, which influences widely to the survival and development of mankind, so it’s of great significance to study free surface flow problem. A liquid droplet impacting on a solid surface is a classic free surface flow problem. The phenomenon of diffusion, rebound and broken of a droplet when it impacts on a solid surface exists extensively in chemical industry and metallurgical industry. It’s a good way to study free surface flow by studying the phenomenon of a droplet impacting on a solid surface.
The Smoothed Particle Hydrodynamics (SPH) method is applied in the numerical simulation of a droplet impacting on a solid surface which is a Lagrangian meshfree particle method. The SPH equations and the key technology which are suitable to generalized hydrokinetics are studied, and the SPH fluid equations are derived from Lagrangian fluid equations. Artificial Compression is applied to calculate the time derivative of stress considering incompressible fluid as compressible fluid. Artificial viscosity is applied to eliminate unphysical oscillation in results. The treatment method of boundary conditions including rigid boundary and free surface boundary is studied, and so do the search of free surface particles, the choice of time steps and the searching method among neighboring particles.
SPH method is applied to establish 2-Dimensional model to simulate a liquid droplet impacting on a solid surface. The comparison between the simulated results and experimental results is done, and the flow field, the pressure, the speed and displacement of the representative particles are all studied. The spreading factor is studied by changing the related parameters, such as initial velocity and initial radius of the droplet. Based on above analysis the 3-Dimensional model is established to study the motion of the droplet when it impacts on a solid surface.
The theoretical model of a droplet impacting on a solid surface is established to study the relationship between spreading factor and contact angel, the relationship between impacting velocity of the droplet and contact angel, so the relationship between spreading factor and impacting velocity of the droplet can be got, which can be compared with numerical simulated results.
引文
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[37]J. Bonet, S. Kulasegaram, M.X. Rodriguez-Paz, M. Profit. Variational formulation for the smooth particle hydrodynamic(SPH) simulation of fluid and solid problems[J], Computer Methods in Applied Mechanics and Engineering, 2004,193:1245-1256
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[2]洪方文,自由面附近运动物体流场的数值与试验研究:[博士学位论文],无锡:中国船舶科学研究中心,2001
[3]施明恒,单个液滴撞击表面时的流体动力学特性[J],力学学报,1985,17(5):419-425
[4] H.-Y. Kim, J.-H. Chun. The recoiling of liquid droplets upon collision with solid surfaces [J], Physics of Fluids, 2000, 13(3): 643-659
[5]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[J],力学与实践,1995,17(3):52-54
[6] Zhang Xiaoguang,Osman A.Basaran.Dynamic surface tension effects in impact of a drop with a solid surface[J], Journal of Colloid and Interface Science, 1997, 187(1): 166-178
[7]Hitoshi Fujimoto, Hiroaki Shiraishi, Natsuo Hatta. Evolution of liquid/solid contact area of a drop impacting on a solid surface[J], International Journal of Heat and Transfer, 2000,43:1673-1677
[8]陆军军,陈雪莉,曹显奎,等,液滴撞击平板的铺展特征[J],化学反应工程与工艺,2007,23(6):505-511
[9]李维仲,朱卫英,权生林,等,液滴撞击水平固体表面的可视化实验研究[J],热科学与技术,2008,7(2):155-160
[10]崔洁,陆军军,陈雪莉,等,液滴高速撞击固体板面过程的研究[J],化学反应工程与工艺,2008,24(5):390-394
[11]贺征,郜冶,顾璇,等,液滴与壁面碰撞模型[J],哈尔滨工程大学学报,2009,30(3):267-270
[12]M. Pasandideh-Fard, Y. M. Qiao, S. Chandra, J. Mostaghimi. Capillary effects during droplet impact on a solid surface[J], Physics of Fluids,1996,8(3):650-659
[13] Hitoshi Fujimoto, Yu Shiotani, Albert Y. Tong, Takayuki Hama, Hirohiko Takuda. Three-dimensional numerical analysis of the deformation behavior droplets impinging onto a solid substrate[J], International Journal of Multiphase Flow, 2007,33,317-332
[14]马利,陶伟明,郭乙木,等,SPH耦合有限元方法的水射流弹塑性碰撞模拟[J],浙江大学学报(工学版),2008,42(2):259-263
[15]沈胜强,李燕,郭亚丽,液滴撞击等温固体平壁的数值模拟[J],工程热物理学报,2009,30(12):2116-2118
[16]权生林,李爽,李维仲,等,用格子Boltzmann方法模拟液滴撞击固壁动力学行为[J],计算力学学报,2009,26(5):627-631
[17]张兆顺,崔桂香,流体力学(第二版),北京:清华大学出版社,2006:16~20
[18]Furzeland R M. A comparative study of numerical method for moving boundary problems. Journal of International mathematics Application, 1980, 20:411~429
[19]Harlow F H, Welch J E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids, 1965, 8(1):2182~2189
[20]Hirt C W , Nichols D B. Volume of fluid Method for the Dynamics of free boundaries. Journal of Computational Physics , 1981,39:201~225
[21]Osher S, Sethian J A. Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations. Journal of Computational Physics, 1988,79(l): 12~49
[22]Ashgriz N and Poo J Y. FLAIR: Flux Line-segment model for Advection and Interface Reconstruction. J Comput Phys, 1991, 39: 449~468
[23] Youngs D L.Numerical methods for fluid dynamics. Academic, New York,1982
[24]Ma T B, Wang C, Ning J G. Multi-material Eulerian formulations and hydro code for the simulation of explosions. CMES-Comp Model Eng Sci, 2008, 33(2): 155~178
[25]Youngs D L .Time-dependent multi-material flow with large fluid distortion. In: Morton K W, Baines M J, eds, Numerical Methods for Fluid Dynamics. New York: Academic Press, 1982: 273~285
[26]刘儒勋,舒其望,计算流体力学的若干新方法,北京:科学出版社,2003
[27]Boris J P, Book D L. Flux corrected transport. I SHASTA J Comput Phys.1973, 11:38~69
[28]Danping Peng, Barry Merriman, Stanley Osher. APDE-Based Fast Local Level Set Method. Journal of Computational Physics, 1999, 155(2):410~438
[29]Douglas Enright, Ronald Fedkiw. A Hybrid Particle Level Set Method for Improved Interface Capturing. Journal of Computational Physics, 2002, 183(l):83~116
[30]G.R.Liu, M.B.Liu[着],韩旭,杨刚,强洪夫[译],Smoothed Particle Hydrodynamics.长沙:湖南大学出版社,2005
[31]逄明华,王占奎,焦红伟,无网格法中SPH方法和有限元方法的对比分析[J],机械设计与制造,2008,2:32-34
[32]贝新源,岳宗五,三维SPH程序及其在斜高速碰撞问题的应用[J],计算物理,1997,14(2):155-166
[33]韩旭,杨刚,龙述尧,SPH方法在两相流问题中的典型应用[J],湖南大学学报(自然科学版),2007,34(1):28-32
[34]J.K. Chen, J.E. Beraun. A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems[J],Computer Methods in Applied Mechanics and Engineering, 2000,190:225-239
[35]Alexnader V. Potapov, Melany L. Hunt, Charles S. Campbell. Liquid-solid floes using smoothed particle hydrodynamics and the discrete element method[J], Powder Technology,2001,116:204-213
[36]汤文辉,毛益明,SPH数值模拟中固壁边界的一种处理方法[J],国防科技大学学报,2001,23(6):54-57
[37]J. Bonet, S. Kulasegaram, M.X. Rodriguez-Paz, M. Profit. Variational formulation for the smooth particle hydrodynamic(SPH) simulation of fluid and solid problems[J], Computer Methods in Applied Mechanics and Engineering, 2004,193:1245-1256
[38]Yasmin Melean, Leonardo Di G. Sigalotti, Anwar Hasmy. On the SPH tensile instability in forming viscous liquid drops[J], Computer Physics Communications, 2004,157:191-200
[39]徐志宏,汤文辉,罗永,SPH算法在高速侵彻问题中的应用[J],国防科技大学学报,2005,27(4):41-44
[40]张姝慧,汪继文,SPH法中初始时粒子配置的分析[J],计算机技术与发展,2007,17(6):36-38
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