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A unified colored-noise approximation (UCNA) method has been widely used to solve the simple one-dimensional problem, and this paper attempts to extend this method to multi-dimensional systems. Firstly, a Fokker-Planck equation is obtained by UCNA method based on the Langevin equation for particle motion, then a two-order moment trajectory model is established on this basis. The new model can be successfully used to predict the backward-facing step two-phase flow, and the simulation results agree well with the measurements. This study shows that the UCNA method is still effective in dealing with multi-dimensional two-phase turbulent systems.
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Keywords:
- unified colored-noise approximation /
- probability density function model /
- two-order moment model /
- numerical simulation
[1] Fang H P, Chen S Y 2004 Chin. Phys. 13 46
[2] Chen S, Shi B C, Liu Z H, He Z, Guo Z L, Zheng C G 2004 Chin. Phys. 13 1657
[3] Minier J P, Peirano E 2001 Phys. Rep. 352 1
[4] Li Z X, Xu J R, Yang Z H 2007 Chin. J. Comput. Phys. 23 413 (in Chinese) [李昭祥, 徐江荣, 杨忠华 2007 计算物理 23 413]
[5] Li Z X, Xu J R, Yang Z H 2010 Chin. J. Comput. Phys. 27 38 (in Chinese) [李昭祥, 徐江荣, 杨忠华 2010 计算物理 27 38]
[6] Jung P, Hanggi P 1987 Phys. Rev. A 35 4464
[7] Zhao Y, Xu W, Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵燕, 徐伟, 邹少存 2009 58 1396]
[8] Zhou B C, Xu W 2008 Acta Phys. Sin. 57 2035 (in Chinese) [周丙常, 徐伟 2008 57 2035]
[9] Cai H N, Zhou X J, Cao L 1998 J. Huazhong Univ. of Sci. & Tech. 26 54 (in Chinese) [蔡海宁, 周小计, 曹力 1998 华中理工大学学报 26 54]
[10] Risken H 1989 The Fokker-Planck Equation: Methods of solution and applications 2nd. (New York: Springer) pp133-162
[11] Tao W Q 2001 Numerical Heat Transfer (Second Edition) (Xi'an: Xi'an Jiaotong University Press) pp207-231 (in Chinese) [陶文铨编著2001 数值传热学(第2版)(西安: 西安交通大学出版社)第207–231页]
[12] Fessler J R, Eaton J K 1999 J. Fluid Mech. 394 97
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[1] Fang H P, Chen S Y 2004 Chin. Phys. 13 46
[2] Chen S, Shi B C, Liu Z H, He Z, Guo Z L, Zheng C G 2004 Chin. Phys. 13 1657
[3] Minier J P, Peirano E 2001 Phys. Rep. 352 1
[4] Li Z X, Xu J R, Yang Z H 2007 Chin. J. Comput. Phys. 23 413 (in Chinese) [李昭祥, 徐江荣, 杨忠华 2007 计算物理 23 413]
[5] Li Z X, Xu J R, Yang Z H 2010 Chin. J. Comput. Phys. 27 38 (in Chinese) [李昭祥, 徐江荣, 杨忠华 2010 计算物理 27 38]
[6] Jung P, Hanggi P 1987 Phys. Rev. A 35 4464
[7] Zhao Y, Xu W, Zou S C 2009 Acta Phys. Sin. 58 1396 (in Chinese) [赵燕, 徐伟, 邹少存 2009 58 1396]
[8] Zhou B C, Xu W 2008 Acta Phys. Sin. 57 2035 (in Chinese) [周丙常, 徐伟 2008 57 2035]
[9] Cai H N, Zhou X J, Cao L 1998 J. Huazhong Univ. of Sci. & Tech. 26 54 (in Chinese) [蔡海宁, 周小计, 曹力 1998 华中理工大学学报 26 54]
[10] Risken H 1989 The Fokker-Planck Equation: Methods of solution and applications 2nd. (New York: Springer) pp133-162
[11] Tao W Q 2001 Numerical Heat Transfer (Second Edition) (Xi'an: Xi'an Jiaotong University Press) pp207-231 (in Chinese) [陶文铨编著2001 数值传热学(第2版)(西安: 西安交通大学出版社)第207–231页]
[12] Fessler J R, Eaton J K 1999 J. Fluid Mech. 394 97
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