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针对离散颗粒模型和欧拉-欧拉双流体模型在求解气粒两相流动问题中存在的不足，提出了一种新方法——SPH-FVM耦合方法，并应用于风沙运动过程的数值模拟计算. 新方法基于拟流体模型，采用光滑粒子流体动力学方法（SPH）对离散颗粒相进行求解，追踪单颗粒运动轨迹，采用有限体积法（FVM）求解连续气体相，捕捉流场特性，两相间通过曳力、压力梯度、体积分数等参量进行耦合，建立了两种不同坐标系下方法间的耦合框架. 对SPH 粒子所承载的物质属性进行了重定义，改造成了适用于离散颗粒相求解的光滑离散颗粒流体动力学模型（SDPH），阐述了SPH粒子与离散相中颗粒之间的关系，推导得到了拟流体SPH离散方程组. 模拟了风沙运动中沙粒跃移过程和自由来流风速作用下沙粒的运动过程以及沙丘在风力作用下缓慢向前蠕移的过程，分析了颗粒的运动轨迹，流场中沙粒水平速度分布规律以及气体速度场在沙粒反作用下的变化情况等，与实验结果相符合，结果表明该方法不仅精度较高，而且计算量较小，适于求解风沙运动问题乃至其他气粒两相流动问题.To overcome the drawback of discrete particle model (DPM) and Euler-Euler two-fluid model (TFM) in solving gas-solid two phase flow, a new method called SPH-FVM coupled method is presented, and then it is used to simulate aerolian sand transport problems. Based on a pseudo fluid model the smoothed particle hydrodynamics (SPH) is used to solve the discrete particle phase by tracing the movement of each individual particle, and the finite volume method (FVM) is used to discretize the continuum flow field on the stationary mesh by capturing fluid characteristics. Two phases are coupled through contributions due to the effects of drag, pressure gradient and volume fraction, and then the coupled framework of SPH-FVM is established. The properties of SPH are redesigned to be suited for the discrete phase named SDPH. The relationship between SPH particles and discrete particles is illustrated, and the SPH discrete equations of pseudo fluid are derived. Saltation processes of sands in aerolian sand transport, sand movement under free-air wind, and creeping processes of dune, are simulated; while the particle trajectories, the distribution characteristics of mean downwind velocity, and the changes of gas velocity under the sand reaction are analyzed. Through comparison with experiments, it is shown that the accuracy of the new method is high, and it can also reduce the computational cost. This indicates that the new method can be applied to aerolian sand transport even to other gas-solid multiphase flows.
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Keywords:
- smoothed particle hydrodynamics /
- finite volume method /
- coupled method /
- aerolian sand transport
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[1] Bagnold R A 1941 The Physics of Blown Sand and Desert Dunes (London: Methuen)
[2] White B R, Mounla H 1991 Acta Mech. Suppl. 1 145
[3] Greeley R, Blumberg D G, Williams S H 1996 Sedimentology 43 41
[4] Zou X Y, Wang Z L, Hao Q Z, Zhang C L, Liu Y Z, Dong G R 2001 Geomorphology 36 155
[5] Dong Z B, Liu X P, Wang X M, Li F, Zhao A G 2004 Earth Surface Processes and Landforms 29 343
[6] Kang L Q, Guo L J, Gu Z M, Liu D Y 2008 Geomorphology 97 438
[7] Wang P, Sun H Q, Shao J L, Qin C S, Li X Z 2012 Acta Phys. Sin. 61 234703 (in Chinese) [王裴, 孙海权, 邵建立, 秦承森, 李欣竹 2012 物理学报 61 234703]
[8] Liu H T, Tong Z H, An K, Ma L Q 2009 Acta Phys. Sin. 58 6369 (in Chinese)[刘汉涛, 仝志辉, 安康, 马理强 2009 物理学报 58 6369]
[9] Tong Z H 2010 Acta Phys. Sin. 59 1884 (in Chinese)[仝志辉 2010 物理学报 59 1884]
[10] Zhou J, Cai L, Zhou F Q 2008 Chin. Phys. B 17 1535
[11] Gao Z K, Jin N D 2009 Chin. Phys. B 18 5249
[12] Xie H Q, Zeng Z, Zhang L Q, Liang G Y, Hiroshi M, Yoshiyuki K 2012 Chin. Phys. B 21 124703
[13] Wu B Z, Xu Y S, Liu Y, Huang G X 2005 Chin. Phys. 14 2046
[14] Han Z Z, Liu Z M 2012 Chin. Phys. B 21 084701
[15] Tian J P, Yao K L 2002 Chin. Phys. 11 0358
[16] Kang L Q, Guo L J 2006 Powder Technology 162 111
[17] Kang L Q, Liu D Y 2010 Geomorphology 115 156
[18] Kang L Q 2012 Geomorphology 139-140 536
[19] Yang J C, Zhang Y, Liu D Y, Wei X L 2010 Sci. Sin. Phys. Mech. & Astron 40 904 (in Chinese) [杨杰程, 张宇, 刘大有, 魏小林 2010 中国科学: 物理学力学天文学 40 904]
[20] Li Z Q, Wang Y, Wang L 2011 Acta Aero. Sin. 29 784 (in Chinese) [李志强, 王元, 王丽 2011 空气动力学学报 29 784]
[21] Lu L Y, Gu Z L, Luo X L, Lei K B 2008 Acta Phys. Sin. 57 6939 (in Chinese) [鲁录义, 顾兆林, 罗昔联, 雷康斌 2008 物理学报 57 6939]
[22] Wei W, Lu L Y, Gu Z L 2012 Acta Phys. Sin. 61 158301 (in Chinese) [危卫, 鲁录义, 顾兆林 2012 物理学报 61 158301]
[23] Gu Z M, Guo L J 2004 J. Eng. Therm. 25 79 (in Chinese) [顾正萌, 郭烈锦 2004 工程热物理学报 25 79]
[24] Zhou F, Qi H Y, You C F 2004 J. Tsinghua Univ.(Sci. & Tech.) 44 1079 (in Chinese) [周芳, 祁海鹰, 由长福 2004 清华大学学报: (自然科学版) 44 1079]
[25] Wu S Z, Ren C Y 2012 J. Lanzhou Univ.(Sci. & Tech.) 48 104 (in Chinese) [武生智, 任春勇 2012 兰州大学学报: (自然科学版) 48 104]
[26] Zhou X S, Wang Y, Li Z Q 2014 J. Xi'an Jiaotong Univ. 48 201 (in Chinese) [周晓斯, 王元, 李志强 2014 西安交通大学学报 48 201]
[27] Lucy L B 1977 Astron. J. 82 1013
[28] Gingold R A, Monaghan J J 1977 Mon. Not. R. Astron. Soc. 181 375
[29] Monaghan J J 2005 Rep. Prog. Phys. 68 1703
[30] Qiang H F, Liu K, Chen F Z 2012 Acta Phys. Sin. 61 204701
[31] Lu B, Maimtimin G, Jin A F, Xu Y J 2013 Acta Mech. Sin. 45 177 (in Chinese)[逯博, 买买提·艾尼, 金阿芳, 徐玉娟 2013 力学学报 45 177]
[32] Lun C K K, Savage S B, Jeffrey D J 1984 J. Fluid Mech. 140 223
[33] Gidaspow D, Bezburuah R, Ding J 1992 Fluidization?, Proceedings of the 7th Engineering Foundation Conference on Fluidization, Brisbance, Australia, 1992 75
[34] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Meshfree Particle Method (Singapore: World Scientific) 132
[35] Gidaspow D 1994 Multiphase Flow and Fluidization (Boston: Academic Press) p89
[36] Chen J K, Beraun J E, Carney T C 1999 Int. J. Numer. Meth. Eng. 46 231
[37] Qiang H F, Wang K P, Gao W R 2008 ICCES Special Symposium on meshless methods, Suzhou, October 13-17, 2008, 1
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