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该文结合了Ott提出的修正连续性方程和Adami改进的动量方程, 对空气中的液滴碰撞问题进行了二维数值模拟. 为有效提高计算精度, 推导了适用于大密度差多相流的人工黏性和人工应力方程. 通过表面张力作用下方形液滴自然变化和空气中两液滴互溶的算例, 验证了算法的有效性; 对不同韦伯数 (8.8, 19.8)、不同碰撞参数 (0, 0.5)下的液滴碰撞过程进行了数值模拟, 并与VOF方法对比,取得了较为一致的结果; 进一步计算多个韦伯数、多个碰撞参数下的液滴碰撞, 得到了空气中二维液滴碰撞结果分布图,与实验结果相符合. 结果表明, 该算法对于求解涉及大密度差多相流的液滴碰撞破碎问题十分有效,而且该方法容易拓展到三维, 从而为进一步模拟火箭发动机的二次雾化过程奠定了基础.
[1] Park R W 1970 Ph. D. Dissertation (Madison: University of Wisconsin)
[2] Ashgriz N, Poo J Y 1990 J. Fluid Mech. 221 183
[3] Qian J, Law C K 1997 J. Fluid Mech. 331 59
[4] Willis K, Orme M 2003 Exp. Fluids 34 28
[5] Chen R H, Chen C T 2006 Exp. Fluids 41 453
[6] Chen R H 2007 Appl. Therm. Eng. 27 604
[7] Foote G B 1973 J. Comp. Phys. 11 507
[8] Mashayek F, Ashgriz N, Minkowycz W J, Shotorban B 2003 Int. J. Heat Mass Transfer 46 77
[9] Nobari M R, Jan Y J 1996 Phys. Fluids 8 29
[10] Poo J Y, Ashgriz N 1992 Proceeding of the 5th Annual Conference on Liquid Atomization and Spray System San Ramon, California, May 18–20, 1992 p110
[11] Sun Z H, Han R J 2008 Chin. Phys. B 17 3185
[12] Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫, 姚熊亮 2008 物理学报 57 339]
[13] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 3654]
[14] 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 物理学报 61 054701]
[15] Meleán Y, Sigalotti L D G 2005 Int. J. Heat Mass Transfer 48 4041
[16] Qiang H F, Chen F Z, Gao W R 2012 Eng. Mech. 29 21 (in Chinese) [强洪夫, 陈福振, 高巍然 2012 工程力学 29 21]
[17] Malavé A A 2012 AIP Adv. 2 042106
[18] Frank Ott, Erik Schnetter 2003 arXiv: physics/0303112v3 [physics.comp-ph]
[19] Adami S, Hu X Y, Adams N A 2010 J. Comp. Phys. 229 5011
[20] Monaghan J J 1994 J. Comp. Phys. 110 399
[21] Hu X Y, Adams N A 2007 J. Comp. Phys. 227 264
[22] Morris J P 2000 Int. J. Numer. Met. Fluids 33 333
[23] Monaghan J J 1992 Annu. Rev. Astro. Astrophys. 30 543
[24] Monaghan J J 2000 J. Comp. Phys. 159 290
[25] Gray J P, Monaghan J J, Swift R P 2001 Comput. Methods. Appl. Mech. Eng. 190 6641
[26] Morris J P, Fox P J, Zhu Y 1997 J. Comp. Phys. 136 214
-
[1] Park R W 1970 Ph. D. Dissertation (Madison: University of Wisconsin)
[2] Ashgriz N, Poo J Y 1990 J. Fluid Mech. 221 183
[3] Qian J, Law C K 1997 J. Fluid Mech. 331 59
[4] Willis K, Orme M 2003 Exp. Fluids 34 28
[5] Chen R H, Chen C T 2006 Exp. Fluids 41 453
[6] Chen R H 2007 Appl. Therm. Eng. 27 604
[7] Foote G B 1973 J. Comp. Phys. 11 507
[8] Mashayek F, Ashgriz N, Minkowycz W J, Shotorban B 2003 Int. J. Heat Mass Transfer 46 77
[9] Nobari M R, Jan Y J 1996 Phys. Fluids 8 29
[10] Poo J Y, Ashgriz N 1992 Proceeding of the 5th Annual Conference on Liquid Atomization and Spray System San Ramon, California, May 18–20, 1992 p110
[11] Sun Z H, Han R J 2008 Chin. Phys. B 17 3185
[12] Zhang A M, Yao X L 2008 Acta Phys. Sin. 57 339 (in Chinese) [张阿漫, 姚熊亮 2008 物理学报 57 339]
[13] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 3654]
[14] 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 物理学报 61 054701]
[15] Meleán Y, Sigalotti L D G 2005 Int. J. Heat Mass Transfer 48 4041
[16] Qiang H F, Chen F Z, Gao W R 2012 Eng. Mech. 29 21 (in Chinese) [强洪夫, 陈福振, 高巍然 2012 工程力学 29 21]
[17] Malavé A A 2012 AIP Adv. 2 042106
[18] Frank Ott, Erik Schnetter 2003 arXiv: physics/0303112v3 [physics.comp-ph]
[19] Adami S, Hu X Y, Adams N A 2010 J. Comp. Phys. 229 5011
[20] Monaghan J J 1994 J. Comp. Phys. 110 399
[21] Hu X Y, Adams N A 2007 J. Comp. Phys. 227 264
[22] Morris J P 2000 Int. J. Numer. Met. Fluids 33 333
[23] Monaghan J J 1992 Annu. Rev. Astro. Astrophys. 30 543
[24] Monaghan J J 2000 J. Comp. Phys. 159 290
[25] Gray J P, Monaghan J J, Swift R P 2001 Comput. Methods. Appl. Mech. Eng. 190 6641
[26] Morris J P, Fox P J, Zhu Y 1997 J. Comp. Phys. 136 214
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