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In recent years, hydrophobic surface has attracted much attention for its potential applications in flow drag reduction. This article focuses on the drag reduction mechanism of hydrophobic surface by the multi-relaxation-time scheme and the Shan-Chen multiphase model of lattice Boltzmann method. At first, we validate our method through the multiphase cases of wall adhesion effect and the single-phase cases of flow around a square column, showing that the results from our method are in good consistence with those in previous literature. Then, we simulate and analyze the typical problem of flow around a square column with hydrophobic surface while Reynolds number is 100, in order to investigate the influences of contact angle and gas holdup of the inlet flow on drag coefficient and lift coefficient. The simulation results show that for a given contact angle, hydrophobic surface is capable of reducing drag when gas holdup of the inlet flow is in a certain range; otherwise, drag coefficient will increase. With an appropriate gas holdup of the inlet flow, both drag coefficient and lift coefficient will decrease as the contact angle becomes larger. Finally, we compare gas holdup contours and the corresponding streamline patterns under different drag coefficients. Analyses suggest that the increases of drag coefficient and lift coefficient are related to the gas mass shedding near the square column wall where the eddy forms. Increasing the gas holdup of the inflow is properly conducible to reducing the gas mass shedding and also both drag coefficient and lift coefficient greatly if contact angle is too large. However, if the near-wall gas holdup is saturated, it will aggravate the instability of gas holdup and change the near-wall gas holdup a little, which makes drag coefficient increase slightly. When gas holdup of the inlet flow is appropriate, the near-wall gas holdup becomes steadier with a larger contact angle. Through analysis we note that for hydrophobic surface, the key factor of drag reduction is to keep the near-wall gas layer stable, with which the effect of drag reduction becomes better as the contact angle becomes larger. However, the larger the contact angle, the more sensitive to the change of gas holdup both drag coefficient and lift coefficient are, so it is not recommended to adopt the hydrophobic surface with very large contact angle. With the analysis of the gas holdup near hydrophobic surface with different contact angles, in this article we put forward a new approach to the further exploration of the drag reduction mechanism of hydrophobic surface.
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Keywords:
- lattice Boltzmann method /
- hydrophobic surface /
- two-phase flow /
- drag reduction
[1] Yu Y S, Wei Q D 2005 J. Exp. Fluid Mech. 19 60 (in Chinese) [余永生, 魏庆鼎 2005 实验流体力学 19 60]
[2] Choi C H, Kim C J 2006 Phys. Rev. Lett. 96 066001
[3] Cao B Y, Chen M, Guo Z Y 2006 Phys. Rev. E 74 066311
[4] Ou J, Perot B, Rothstein J P 2004 Phys. Fluids 16 4635
[5] Tian J, Xu J F, Xue Q J 1997 J. Hydrodyn. 12 27 (in Chinese) [田军, 徐锦芬, 薛群基 1997 水动力研究与进展 12 27]
[6] Pan G, Hang Q G, Liu Z Y, Hu H B, Song B W 2011 J. Shanghai Jiaotong Univ. 45 1440 (in Chinese) [潘光, 黄桥高, 刘占一, 胡海豹, 宋保维 2011 上海交通大学学报 45 1440]
[7] Song B W, Ren F, Hu H B, Guo Y H 2014 Acta Phys. Sin. 63 054708(in Chinese) [宋保维, 任峰, 胡海豹, 郭云鹤 2014 63 054708]
[8] Wang B, Wang J D, Chen D R 2014 Acta Phys. Sin. 63 074702(in Chinese) [王宝, 汪家道, 陈大融 2014 63 074702]
[9] Hong W P 2010 Ph. D. Dissertation (Beijing: North China Electric Power University) (in Chinese) [洪文鹏 2010 博士学位论文 (北京:华北电力大学)]
[10] Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Vol. 1) (Beijing: Academic Press of China) p29 (in Chinese) [郭照立, 郑楚光 2009 格子Boltzmann方法的原理及应用(第1版) (北京:科技出版社)第29 页]
[11] Aidun C K, Clausen J R 2010 Annu. Rev. Fluid Mech. 42 439
[12] Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Vol. 1) (Beijing: Academic Press of China) p166 (in Chinese) [郭照立, 郑楚光 2009 格子Boltzmann方法的原理及应用 (第1版) (北京: 科技出版社) 第166页]
[13] Shan X, Chen H 1993 Phys. Rev. E 47 1815
[14] Lallemand P, Luo S L 2000 Phys. Rev. E 61 6546
[15] Mohamad A A 2011 Lattice Boltzmann Method Fundamentals and Engineering Applications with Computer Codes (London: Springer) pp101-105
[16] Sukop M C, Thorne D T 2006 Lattice Boltzmann Modeling An Introduction for Geoscientists and Engineers (Berlin: Springer) pp67-93
[17] Guo W B, Wang N C, Shi B C, Guo Z L 2003 Chin. Phys. 12 0067
[18] Wang G C, Shi B C, Deng B 2003 J. Basic Sci. Engineer. 11 335 (in Chinese) [王广超, 施保昌, 邓滨 2003 应用基础与工程科学学报 11 335]
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[1] Yu Y S, Wei Q D 2005 J. Exp. Fluid Mech. 19 60 (in Chinese) [余永生, 魏庆鼎 2005 实验流体力学 19 60]
[2] Choi C H, Kim C J 2006 Phys. Rev. Lett. 96 066001
[3] Cao B Y, Chen M, Guo Z Y 2006 Phys. Rev. E 74 066311
[4] Ou J, Perot B, Rothstein J P 2004 Phys. Fluids 16 4635
[5] Tian J, Xu J F, Xue Q J 1997 J. Hydrodyn. 12 27 (in Chinese) [田军, 徐锦芬, 薛群基 1997 水动力研究与进展 12 27]
[6] Pan G, Hang Q G, Liu Z Y, Hu H B, Song B W 2011 J. Shanghai Jiaotong Univ. 45 1440 (in Chinese) [潘光, 黄桥高, 刘占一, 胡海豹, 宋保维 2011 上海交通大学学报 45 1440]
[7] Song B W, Ren F, Hu H B, Guo Y H 2014 Acta Phys. Sin. 63 054708(in Chinese) [宋保维, 任峰, 胡海豹, 郭云鹤 2014 63 054708]
[8] Wang B, Wang J D, Chen D R 2014 Acta Phys. Sin. 63 074702(in Chinese) [王宝, 汪家道, 陈大融 2014 63 074702]
[9] Hong W P 2010 Ph. D. Dissertation (Beijing: North China Electric Power University) (in Chinese) [洪文鹏 2010 博士学位论文 (北京:华北电力大学)]
[10] Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Vol. 1) (Beijing: Academic Press of China) p29 (in Chinese) [郭照立, 郑楚光 2009 格子Boltzmann方法的原理及应用(第1版) (北京:科技出版社)第29 页]
[11] Aidun C K, Clausen J R 2010 Annu. Rev. Fluid Mech. 42 439
[12] Guo Z L, Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Vol. 1) (Beijing: Academic Press of China) p166 (in Chinese) [郭照立, 郑楚光 2009 格子Boltzmann方法的原理及应用 (第1版) (北京: 科技出版社) 第166页]
[13] Shan X, Chen H 1993 Phys. Rev. E 47 1815
[14] Lallemand P, Luo S L 2000 Phys. Rev. E 61 6546
[15] Mohamad A A 2011 Lattice Boltzmann Method Fundamentals and Engineering Applications with Computer Codes (London: Springer) pp101-105
[16] Sukop M C, Thorne D T 2006 Lattice Boltzmann Modeling An Introduction for Geoscientists and Engineers (Berlin: Springer) pp67-93
[17] Guo W B, Wang N C, Shi B C, Guo Z L 2003 Chin. Phys. 12 0067
[18] Wang G C, Shi B C, Deng B 2003 J. Basic Sci. Engineer. 11 335 (in Chinese) [王广超, 施保昌, 邓滨 2003 应用基础与工程科学学报 11 335]
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