基于光滑粒子动力学方法的液滴冲击固壁面问题数值模拟

苏铁熊; 马理强; 刘谋斌; 常建忠

doi:10.7498/aps.62.064702

摘要

采用改进的光滑粒子动力学(SPH)方法对液滴冲击固壁面问题进行了数值模拟. 为了提高传统SPH方法的计算精度和数值稳定性, 在传统的SPH方法的基础上对粒子方法中的密度和核梯度进行了修正, 采用了考虑黎曼解法的SPH流体控制方程, 构造了一种新型的粒子间相互作用力(IIF)模型来模拟表面张力的影响. 应用改进的SPH方法对液滴冲击固壁面问题进行了数值模拟. 计算结果表明：新型的IIF 模型能够较好地模拟表面张力的影响, 改进的SPH方法能够精细地描述液滴与固壁面相互作用过程中液滴的内部压力场演变和自由面形态变化, 液滴的铺展因子随初始韦伯数的增大而增大, 数值模拟结果与实验得到的结果基本一致.

关键词:

Abstract

In this paper, we present a numerical simulation of a single liquid drop impacting onto solid surface with smoothed particle hydrodynamics (SPH). SPH is a Lagrangian, meshfree particle method, and it is attractive in dealing with free surfaces, moving interfaces and deformable boundaries. The SPH model includes an improved approximation scheme with corrections to kernel gradient and density to improve computational accuracy. Riemann solver is adopted to solve equations of fluid motion. An new inter-particle interaction force is used for modeling the surface tension effects, and the modified SPH method is used to investigate liquid drop impacting onto solid surfaces. It is demonstrated that the inter-particle interaction force can effectively simulate the effect of surface tension. It can well describe the dynamic process of morphology evolution and the pressure field evolution with accurate and stable results. The spread factor increases with the increase of the initial Weber number. The numerical results are in good agreement with the theoretical and experimental results in the literature.

Keywords:

作者及机构信息

1.
中北大学机电工程学院, 太原 030051;

2.
中国科学院力学研究所, 北京 100190

基金项目: 国家自然科学基金(批准号:50976108, 11172306) 资助的课题．

Authors and contacts

1.
School of Mechatronice Engineering, North University of China, Taiyuan 030051, China;

2.
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 50976108, 11172306).

参考文献

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[2]	Thoroddsen S T, Takehara K 2012 J. Fluid. Mech. 706 560
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[4]	Liu M B, Chang J Z 2011 Int. J. Comput. Meth. 8 637
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[9]	Eggers J, Fontelos M A, Josserand C, Zaleski S 2010 Phys. Fluids 22 301
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[11]	Ma L Q, Chang J Z, Liu H T, Liu M B 2012 Acta Phys. Sin. 61 054701 (in Chinese) [马理强, 常建忠, 刘汉涛, 刘谋斌 2012 61 054701]
[12]	Yang B H, Wang H, Zhu X, Ding Y D, Zhou J 2012 CIESC J. 10 3027 (in Chinese) [杨宝海, 王宏, 朱恂, 丁玉栋, 周劲 2012 化工学报 10 3027]
[13]	Sikalo S, Wilhelm H D, Roisman I V, Jakirlic S, Tropea C 2005 Phys. Fluids 17 062103
[14]	Liu M B, Liu G R, Zong Z, Lam K Y 2003 Comput. Fluids 32 305
[15]	Liu M B, Liu G R, Zong Z 2008 Int. J. Comput. Meth. 5 135
[16]	Liu M B, Liu G R 2010 Arxiv. Comput. Methods Engrg. 17 25
[17]	Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 26
[18]	Liu M B, Liu G R, Lam K Y 2003 Electron. Model. 25 113
[19]	Liu M B, Liu G R, Lam K Y 2003 J. Comput. Appl. Math. 155 263
[20]	Liu M B, Liu G R, Lam K Y, Zong Z 2003 Comput. Mech. 30 106
[21]	Liu M B, Shao J R 2012 Sci. China E 42 1
[22]	Monaghan J J 1992 Annu. Rev. Astron. Astr. 30 543
[23]	Jiang T, Ouyang J, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60 054701 (in Chinese) [蒋涛, 欧阳洁, 赵晓凯, 任金莲 2011 60 054701]
[24]	Zhang S, Morita K, Fukuda K, Shirakawa N 2007 Int. J. Numer. Meth. Fl. 55 225
[25]	Liu M B, Liu G R 2005 Comput. Mech. 35 332
[26]	Rioboo R, Marengo M, Tropea C 2002 Exp. Fluids 33 112

施引文献

[1]	Tuan T 2012 Phys. Rev. Lett. 108 036101
[2]	Thoroddsen S T, Takehara K 2012 J. Fluid. Mech. 706 560
[3]	Zhang M K, Chen S, Shang Z 2012 Acta Phys. Sin. 61 034701 (in Chinese) [张明焜, 陈硕, 尚智 2012 61 034701]
[4]	Liu M B, Chang J Z 2011 Int. J. Comput. Meth. 8 637
[5]	Worthington A M 1876 Proc. R. Soc. Lond. 25 261
[6]	Roisman I V, Opfer L, Tropea C, Raessi M, Mostaghimi J, Chandra S 2008 Colloids Surfaces A 322 183
[7]	Qiang H F, Liu K, Chen F Z 2012 Acta Phys. Sin. 61 204701 (in Chinese) [强洪夫, 刘开, 陈福振 2012 61 204701]
[8]	Bussmann M, Chandra S, Mostaghimi J 2000 Phys. Fluids 12 3121
[9]	Eggers J, Fontelos M A, Josserand C, Zaleski S 2010 Phys. Fluids 22 301
[10]	Ellis A S, Smith F T, White A H 2011 Q. J. Mech. Appl. Math. 64 107
[11]	Ma L Q, Chang J Z, Liu H T, Liu M B 2012 Acta Phys. Sin. 61 054701 (in Chinese) [马理强, 常建忠, 刘汉涛, 刘谋斌 2012 61 054701]
[12]	Yang B H, Wang H, Zhu X, Ding Y D, Zhou J 2012 CIESC J. 10 3027 (in Chinese) [杨宝海, 王宏, 朱恂, 丁玉栋, 周劲 2012 化工学报 10 3027]
[13]	Sikalo S, Wilhelm H D, Roisman I V, Jakirlic S, Tropea C 2005 Phys. Fluids 17 062103
[14]	Liu M B, Liu G R, Zong Z, Lam K Y 2003 Comput. Fluids 32 305
[15]	Liu M B, Liu G R, Zong Z 2008 Int. J. Comput. Meth. 5 135
[16]	Liu M B, Liu G R 2010 Arxiv. Comput. Methods Engrg. 17 25
[17]	Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 26
[18]	Liu M B, Liu G R, Lam K Y 2003 Electron. Model. 25 113
[19]	Liu M B, Liu G R, Lam K Y 2003 J. Comput. Appl. Math. 155 263
[20]	Liu M B, Liu G R, Lam K Y, Zong Z 2003 Comput. Mech. 30 106
[21]	Liu M B, Shao J R 2012 Sci. China E 42 1
[22]	Monaghan J J 1992 Annu. Rev. Astron. Astr. 30 543
[23]	Jiang T, Ouyang J, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60 054701 (in Chinese) [蒋涛, 欧阳洁, 赵晓凯, 任金莲 2011 60 054701]
[24]	Zhang S, Morita K, Fukuda K, Shirakawa N 2007 Int. J. Numer. Meth. Fl. 55 225
[25]	Liu M B, Liu G R 2005 Comput. Mech. 35 332
[26]	Rioboo R, Marengo M, Tropea C 2002 Exp. Fluids 33 112

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