基于SPH方法的风沙流中沙粒速度分布数值计算
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摘要
沙粒速度是沙粒传输理论研究中的重要参数,它可以反映风沙两相流运动中微观运动和宏观运动的信息。本文运用光滑粒子流体动力学(smoothed particle hydrodynamics,SPH)方法对风沙流动过程进行建模及数值计算,动态地显示跃移沙粒在整个风沙流过程中的运动状态,得到单个沙粒运动速度大小和方向的变化趋势,通过对单个沙粒的运动物理量进行统计分析,得到了沙粒群体运动行为的动力学特性。SPH方法的基本思想是将计算区域分解成独立的粒子,这些携带着自身质量,具有自身密度等物理特性的计算粒子可以随着控制方程运动,这点与自然界中沙粒的离散特点非常相符。本文针对SPH方法自身的关键因素进行了与风沙流特点相适应的改进和修正,使其在处理风沙流中两相物质的耦合时有它独到的优势。
The wind-blown sand movement is a kind of air-sand two-phase flow problem. Under the action of air flow,sand grains experience a lift-off when they are changed from static state to movement. The research on lift-off of sand is very important in physics of wind-blown sand,and the distribution of the lift-off speed and the lift-off angle are the main physical factors and play an important role in deciding the motion state of sand in air. There are three types of sand movement in air flow,such as creep,suspension and saltation. Among them,the saltation accounts for about 75% of the wind-blown sand movement types. Tomaster mechanism of saltation can help us understand the law of wind-blown sand movement,and it can be used to further improve the study on the physics of wind-blown sand. There are two main reasons for the lift-off of sand,i. e.,fluid starting driven directly by air flow and the impact starting caused by other sand grains. Speed distribution function of sand can reflect the information of the macro-scale movement and the micro-scale movement in wind-blown sand movement. To determine the speed distribution function of the sand can work out the various macro-scale statistical variables. The Smoothed Particle Hydrodynamics( SPH) method,a Lagrange Particle method,was applied in this paper to dissect the mathematical model of wind-blown sand movement. The air and sand phases are dissected to single particles. The status of dissected sand grains was consistent with their natural status,so the sand movement can be accurately described. It is very simple and accurate to deal with the collision role by setting smoothing length. SPH method was firstly applied in the numerical simulation of gas-solid two-phase flow in this paper. In this study,the numerical simulation of wind-blown sand movement near the ground surface was performed to observe the micro-scale motion of sand,and to reveal the interaction mechanism of air flow and sand.
The wind-blown sand movement is a kind of air-sand two-phase flow problem. Under the action of air flow,sand grains experience a lift-off when they are changed from static state to movement. The research on lift-off of sand is very important in physics of wind-blown sand,and the distribution of the lift-off speed and the lift-off angle are the main physical factors and play an important role in deciding the motion state of sand in air. There are three types of sand movement in air flow,such as creep,suspension and saltation. Among them,the saltation accounts for about 75% of the wind-blown sand movement types. Tomaster mechanism of saltation can help us understand the law of wind-blown sand movement,and it can be used to further improve the study on the physics of wind-blown sand. There are two main reasons for the lift-off of sand,i. e.,fluid starting driven directly by air flow and the impact starting caused by other sand grains. Speed distribution function of sand can reflect the information of the macro-scale movement and the micro-scale movement in wind-blown sand movement. To determine the speed distribution function of the sand can work out the various macro-scale statistical variables. The Smoothed Particle Hydrodynamics( SPH) method,a Lagrange Particle method,was applied in this paper to dissect the mathematical model of wind-blown sand movement. The air and sand phases are dissected to single particles. The status of dissected sand grains was consistent with their natural status,so the sand movement can be accurately described. It is very simple and accurate to deal with the collision role by setting smoothing length. SPH method was firstly applied in the numerical simulation of gas-solid two-phase flow in this paper. In this study,the numerical simulation of wind-blown sand movement near the ground surface was performed to observe the micro-scale motion of sand,and to reveal the interaction mechanism of air flow and sand.
引文
[1]倪晋仁,李振山.风沙两相流理论及其研究[M].北京:科学出版社,2006:27-40.[Ni Jinren,Li Zhenshan.The Theory and Research of Aeolian Sand Two Phase Flow[M].Beijing:Science Press,2006:27-40.]
[2]辛国伟,程建军,景文宏,等.来流廓线对风沙流场和风沙堆积影响的数值模拟:以挡沙墙为例[J].干旱区研究,2016,33(3):672-679.[Xin Guowei,Cheng Jianjun,Jing Wenhong,et al.Numerical simulation of the influence of incoming flow profile on sand flow field and aeolian sand deposition:A case study around sand retaining wall[J].Arid Zone Research,2016,33(3):672-679.]
[3]俞祥祥,李生宇,王海峰,等.沙漠公路防护林不同林带位置的风沙流结构[J].干旱区研究,2017,34(3):707-715.[Yu Xiangxiang,Li Shengyu,Wang Haifeng,et al.Aeolian-sand flow structure at different locations along desert highway shelterbelt[J].Arid Zone Research,2017,34(3):707-715.]
[4]Bagnold R A.The Physics of Blown Sand and Desert Dunes[M].London:Methuen&Co.Ltd,1941.
[5]Liu G R,Liu M B.Smoothed Particle Hydrodynamics:A Meshfree Particle Method[M].Singapore:World Scientific,2003:25-34.
[6]石传奇,安翼,杨家修.滑坡涌浪的三维SPH方法模拟及其工程应用[J].中国科学:物理学力学天文学,2015,45(10):1-9.[Shi Chuanqi,An Yi,Yang Jiaxiu.A SPH based numerical method of landslide induced impulse wave and its application on Huangtian Landslide event[J].Scientia Sinica:Physica,Mechanica&Astronomica,2015,45(10):1-9.]
[7]Zheng Xiaojing.Mechanics of Wind-blown Sand Movement[M].New York:Verlag Berlin Heidelberg,2009:22-25.
[8]金阿芳,买买提明·艾尼,胡国玉,等.基于SPH方法的沙粒起跳风速的研究[J].工程力学,2014,31(9):14-20,27.[Jin Afang,Maimtimin Geni,Hu Guoyu,et al.Study on threshold fluid wind velocity for sand particle take-off using the SPH method[J].Engineering Mechanices,2014,31(9):14-20,27.]
[9]顾兆林.风扬粉尘:近地层湍流与气固两相流[M].北京:科学出版社,2010:153-155.[Gu Zhaolin.Surface Layer Turbulence and the Gas-solid Two Phase Flow[M].Beijing:Science Press,2010:153-155.]
[10]吴正.风沙地貌与治沙工程学[M].北京:科学出版社,2003:21-30.[Wu Zheng.Geomorphology of Wind-drift Sands and Their Controlled Engineering[M].Beijing:Science Press,2003:21-30.]
[11]Srensen M.An analytic model of wind-blown sand transport[J].Acta Mechanica,1991,1(Suppl.):67-81.
[12]Kang Liqiang,Guo Liejin,Liu Dayou.Reconstructing the vertical distribution of the aeolian saltation mass flux based on the probability distribution of lift-off velocity[J].Geomorphology,2008,96:1-15.
[13]杨杰程,张宇,刘大有,等.三维风沙运动的CFD-DEM数值模拟[J].中国科学:物理学力学天文学,2010,40(7):904-915.[Yang Jiecheng,Zhang Yu,Liu Dayou,et al.The CFD-DEM numerical simulation for 3D motion of wind-blown sand[J].Scientia Sinica:Physica,Mechanica&Stronomica,2010,40(7):904-915.]
[14]杨斌,张伟,张洋,等.非定常风沙流中风速脉动对沙粒相瞬时浓度影响的实验研究[J].实验流体力学,2013,27(3):47-50.[Yang Bin,Zhang Wei,Zhang Yang,et al.Experiment study of the wind fluctuation’s effect on the sand concentration in unsteady wind-sand flow[J].Journal of Experiments in Fluid Mechanics,2013,27(3):47-50.]
[15]Shi F,Huang N.Measurement and simulation of sand saltation movement under fluctuating wind in a natural field environment[J].Physica A,2012,391:474-484.
[16]Philip Nalpanis,Hunt J C R,Barrett C F.Saltating particles over flat beds[J].Fluid Mech,1993(251):661-685.
[17]邳华伟,冯广龙.塔里木盆地西北部3种典型下垫面风沙活动特征[J].干旱区研究,2016,33(2):441-448.[Pi Huawei,Feng Guanglong.Characteristics of wind-blown sand over three typical underlying surfaces in the Northwest Tarim Basin[J].Arid Zone Research,2016,33(2):441-448.]
[18]赵国丹,亢力强,邹学勇,等.稳态风沙流中沙粒体积浓度的模型分析[J].中国沙漠,2015,35(5):1 113-1 119.[Zhao Guodan,Kang Liqiang,Zou Xueyong,et al.A model of particle volume concentration in steady windblown sand movement[J].Journal of Desert Research,2015,35(5):1 113-1 116.]
[19]何艺峰,王志强,富宝锋,等.混合沙跃移运动数值模拟[J].干旱区资源与环境,2014,28(1):49-54.[He Yifeng,Wang Zhiqiang,Fu Baofeng,et al.Numerical simulation of mixed sand saltation[J].Journal of Arid Land Resources and Eviroment,2014,28(1):49-54.]
[2]辛国伟,程建军,景文宏,等.来流廓线对风沙流场和风沙堆积影响的数值模拟:以挡沙墙为例[J].干旱区研究,2016,33(3):672-679.[Xin Guowei,Cheng Jianjun,Jing Wenhong,et al.Numerical simulation of the influence of incoming flow profile on sand flow field and aeolian sand deposition:A case study around sand retaining wall[J].Arid Zone Research,2016,33(3):672-679.]
[3]俞祥祥,李生宇,王海峰,等.沙漠公路防护林不同林带位置的风沙流结构[J].干旱区研究,2017,34(3):707-715.[Yu Xiangxiang,Li Shengyu,Wang Haifeng,et al.Aeolian-sand flow structure at different locations along desert highway shelterbelt[J].Arid Zone Research,2017,34(3):707-715.]
[4]Bagnold R A.The Physics of Blown Sand and Desert Dunes[M].London:Methuen&Co.Ltd,1941.
[5]Liu G R,Liu M B.Smoothed Particle Hydrodynamics:A Meshfree Particle Method[M].Singapore:World Scientific,2003:25-34.
[6]石传奇,安翼,杨家修.滑坡涌浪的三维SPH方法模拟及其工程应用[J].中国科学:物理学力学天文学,2015,45(10):1-9.[Shi Chuanqi,An Yi,Yang Jiaxiu.A SPH based numerical method of landslide induced impulse wave and its application on Huangtian Landslide event[J].Scientia Sinica:Physica,Mechanica&Astronomica,2015,45(10):1-9.]
[7]Zheng Xiaojing.Mechanics of Wind-blown Sand Movement[M].New York:Verlag Berlin Heidelberg,2009:22-25.
[8]金阿芳,买买提明·艾尼,胡国玉,等.基于SPH方法的沙粒起跳风速的研究[J].工程力学,2014,31(9):14-20,27.[Jin Afang,Maimtimin Geni,Hu Guoyu,et al.Study on threshold fluid wind velocity for sand particle take-off using the SPH method[J].Engineering Mechanices,2014,31(9):14-20,27.]
[9]顾兆林.风扬粉尘:近地层湍流与气固两相流[M].北京:科学出版社,2010:153-155.[Gu Zhaolin.Surface Layer Turbulence and the Gas-solid Two Phase Flow[M].Beijing:Science Press,2010:153-155.]
[10]吴正.风沙地貌与治沙工程学[M].北京:科学出版社,2003:21-30.[Wu Zheng.Geomorphology of Wind-drift Sands and Their Controlled Engineering[M].Beijing:Science Press,2003:21-30.]
[11]Srensen M.An analytic model of wind-blown sand transport[J].Acta Mechanica,1991,1(Suppl.):67-81.
[12]Kang Liqiang,Guo Liejin,Liu Dayou.Reconstructing the vertical distribution of the aeolian saltation mass flux based on the probability distribution of lift-off velocity[J].Geomorphology,2008,96:1-15.
[13]杨杰程,张宇,刘大有,等.三维风沙运动的CFD-DEM数值模拟[J].中国科学:物理学力学天文学,2010,40(7):904-915.[Yang Jiecheng,Zhang Yu,Liu Dayou,et al.The CFD-DEM numerical simulation for 3D motion of wind-blown sand[J].Scientia Sinica:Physica,Mechanica&Stronomica,2010,40(7):904-915.]
[14]杨斌,张伟,张洋,等.非定常风沙流中风速脉动对沙粒相瞬时浓度影响的实验研究[J].实验流体力学,2013,27(3):47-50.[Yang Bin,Zhang Wei,Zhang Yang,et al.Experiment study of the wind fluctuation’s effect on the sand concentration in unsteady wind-sand flow[J].Journal of Experiments in Fluid Mechanics,2013,27(3):47-50.]
[15]Shi F,Huang N.Measurement and simulation of sand saltation movement under fluctuating wind in a natural field environment[J].Physica A,2012,391:474-484.
[16]Philip Nalpanis,Hunt J C R,Barrett C F.Saltating particles over flat beds[J].Fluid Mech,1993(251):661-685.
[17]邳华伟,冯广龙.塔里木盆地西北部3种典型下垫面风沙活动特征[J].干旱区研究,2016,33(2):441-448.[Pi Huawei,Feng Guanglong.Characteristics of wind-blown sand over three typical underlying surfaces in the Northwest Tarim Basin[J].Arid Zone Research,2016,33(2):441-448.]
[18]赵国丹,亢力强,邹学勇,等.稳态风沙流中沙粒体积浓度的模型分析[J].中国沙漠,2015,35(5):1 113-1 119.[Zhao Guodan,Kang Liqiang,Zou Xueyong,et al.A model of particle volume concentration in steady windblown sand movement[J].Journal of Desert Research,2015,35(5):1 113-1 116.]
[19]何艺峰,王志强,富宝锋,等.混合沙跃移运动数值模拟[J].干旱区资源与环境,2014,28(1):49-54.[He Yifeng,Wang Zhiqiang,Fu Baofeng,et al.Numerical simulation of mixed sand saltation[J].Journal of Arid Land Resources and Eviroment,2014,28(1):49-54.]