Numerical Simulation of 3D PTT Droplet Impact Onto Solid Surface With an Improved Smoothed Particle Hydrodynamics Method

XU Xiao-yang; PENG Yan; DENG Fang-an

doi:10.3879/j.issn.1000-0887.2015.06.006

Volume 36 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2015 > 36(6): 616-627

XU Xiao-yang, PENG Yan, DENG Fang-an. Numerical Simulation of 3D PTT Droplet Impact Onto Solid Surface With an Improved Smoothed Particle Hydrodynamics Method[J]. Applied Mathematics and Mechanics, 2015, 36(6): 616-627. doi: 10.3879/j.issn.1000-0887.2015.06.006

Citation:

PDF( 15324 KB)

Numerical Simulation of 3D PTT Droplet Impact Onto Solid Surface With an Improved Smoothed Particle Hydrodynamics Method

doi: 10.3879/j.issn.1000-0887.2015.06.006

School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong, Shanxi 723000, P.R.China

Funds: The National Natural Science Foundation of China(11305097)

Received Date: 2014-11-13
Rev Recd Date: 2015-03-03
Publish Date: 2015-06-15

Abstract

Abstract

Based on an improved smoothed particle hydrodynamics (SPH) method, the spreading deformation of 3D PTT droplets impacting onto solid surface was numerically simulated. In order to prevent the fluid particles from crossing the suface, an improved treatment technique for the suface boundary was proposed, which can drastically reduce the consumed CPU time for 3D numerical simulation. Furthermore, an artificial stress term was added to the momentum equation to remove the socalled tensile instability. The dynamic processes of 3D PTT droplets impacting onto solid surface were numerically simulated with the improved SPH method. The different flowing features between the Newtonian and PTT fluid droplets during impacting were discussed. The effects of the elongational parameter on the collision behavior were analyzed in detail. The simulation results demonstrate that the improved SPH method can effectively describe the rheological characteristics of 3D PTT droplets impacting onto solid surface.
- smoothed particle hydrodynamics,
- 3D,
- Phan-Thien-Tanner,
- viscoelastic,
- droplet,
- solid surface

FullText(HTML)

References(24)

References

[1]	Tran T, Staat J J, Prosperetti A, Sun C, Lohse D. Drop impact on superheated surfaces[J]. Physical Review Letters,2012,108(3): 036101.
[2]	谢驰宇, 张建影, 王沫然. 液滴在固体平表面上均匀蒸发过程的格子Boltzmann模拟[J]. 应用数学和力学, 2014,35(3): 247-253.(XIE Chi-yu, ZHANG Jian-ying, WANG Mo-ran. Lattice Boltzmann simulation of droplet evaporation on flat solid surface[J]. Applied Mathematics and Mechanics,2014,35(3): 247-253.(in Chinese))
[3]	夏盛勇, 胡春波. 三氧化二铝液滴对心碰撞直接数值模拟[J]. 应用数学和力学, 2014,35(4): 377-388.(XIA Sheng-yong, HU Chun-bo. Direct numerical simulation of head-on binary collision of aluminum oxide droplets[J]. Applied Mathematics and Mechanics,2014,35(4): 377-388.(in Chinese))
[4]	Tomé M F, Mangiavacchi N, Cuminato J A, Castelo A, McKee S. A finite difference technique for simulating unsteady viscoelastic free surface flows[J]. Journal of Non-Newtonian Fluid Mechanics,2002,106(2/3): 61-106.
[5]	Oishi C M, Martins F P, Tomé M F, Alves M A. Numerical simulation of drop impact and jet buckling problems using the extended pom-pom model[J]. Journal of Non-Newtonian Fluid Mechanics,2012,169(1): 91-103.
[6]	Figueiredo R A, Cuminato J A, Oishi C M. Estudo numérico do impacto da gota 3D: influência dos parametros do modelo viscoelástico Giesekus(in Brazil)[C]//Congresso de Matemática Aplicada e Computacional(CMAC),2013: 73-76.
[7]	Lucy L B. A numerical approach to the testing of the fission hypothesis[J]. Astronomical Journal,1977,83(1): 1013-1024.
[8]	Gingold R A, Monaghan J J. Smoothed particle hydrodynamics theory and application to non-spherical stars[J]. Monthly Notices of the Royal Astronomical Society,1977,181(1): 375-389.
[9]	Liu G R, Liu M B. Smoothed Particle Hydrodynamics: A Meshfree Particle Method [M]. Singapore: World Scientific, 2003.
[10]	Monaghan J J. Simulating free surface flows with SPH[J]. Journal of Computational Physics,1994,110(2): 399-406.
[11]	Le Touzé D, Colagrossi A, Colicchio G, Greco M. A critical investigation of smoothed particle hydrodynamics applied to problems with free-surface[J]. International Journal for Numerical Methods in Fluids,2013,73(7): 660-691.
[12]	Cummins S J, Rudman M. An SPH projection method[J]. Journal of Computational Physics,1999,152(2): 584-607.
[13]	XU Xiao-yang, OUYANG Jie, JIANG Tao, LI Qiang. Numerical analysis of the impact of two droplets with a liquid film using an incompressible SPH method[J]. Journal of Engineering Mathematics,2014,85(1): 35-53.
[14]	Monaghan J J, Kocharyan A. SPH simulation of multi-phase flow[J]. Computer Physics Communications,1995,87(1/2): 225-235.
[15]	ZHOU Guang-zheng, GE Wei, LI Bo, LI Xi-peng, WANG Peng, WANG Jun-wu, LI Jing-hai. SPH simulation of selective withdrawal from microcavity[J]. Microfluidics and Nanofluidics,2013,15(4): 481-490.
[16]	Fang J N, Owens R G, Tacher L, Parriaux A. A numerical study of the SPH method for simulating transient viscoelastic free surface flows[J]. Journal of Non-Newtonian Fluid Mechanics,2006,139(1/2): 68-84.
[17]	Rafiee A, Manzari M T, Hosseini M. An incompressible SPH method for simulation of unsteady viscoelastic free-surface flows[J]. International Journal of Non-Linear Mechanics,2007,42(10): 1210-1223.
[18]	杨波, 欧阳洁, 蒋涛, 许晓阳. PTT黏弹性流体的光滑粒子动力学方法模拟[J]. 力学学报, 2011,43(4): 667-673.(YANG Bo, OUYANG Jie, JIANG Tao, XU Xiao-yang. Numerical simulation of the viscoelastic flows for PTT model by the SPH method[J]. Chinese Journal of Theoretical and Applied Mechanics,2011,43(4): 667-673.(in Chinese))
[19]	Phan-Thien N, Tanner R T. A new constitutive equation derived from network theory[J]. Journal of Non-Newtonian Fluid Mechanics,1977,2(4): 353-365.
[20]	Monaghan J J. Smoothed particle hydrodynamics and its diverse applications[J]. Annual Review of Fluid Mechanics,2012,44(1): 323-346.
[21]	Swegle J W, Hicks D L, Attaway S W. Smoothed particle hydrodynamics stability analysis[J]. Journal of Computational Physics,1995,116(1): 123-134.
[22]	Monaghan J J. SPH without a tensile instability[J]. Journal of Computational Physics,2000,159(2): 290-311.
[23]	Gray J P, Monaghan J J, Swift R P. SPH elastic dynamics[J]. Computer Methods in Applied Mechanics and Engineering,2001,190(49/50): 6641-6662.
[24]	Morris J P, Fox P J, Zhu Y. Modeling low Reynolds number incompressible flows using SPH[J]. Journal of Computational Physics,1997,136(1): 214-226.