沙粒起动过程的非线性特性研究
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摘要
在风沙二相流中,颗粒在风场的作用下脱离床面起动的机理是重要的研究课题。颗粒脱离地表起动标志着地表风蚀的开始,风蚀是造成干旱半干旱沙漠地区土地退化的主要驱动力之一,起动风速又是影响风蚀的关键因素。因此,沙粒的起动风速一直受到研究者的高度关注
本学位论文的主要研究内容如下：
1.本文首先建立沙粒受力平衡方程,根据沙粒起动这一物理过程的突变特性,运用非线性科学中的突变理论建立了颗粒起动的尖点突变模型,通过理论推导验证了沙粒在受重力、拖曳力、升力及电场力时的起动可以用非线性尖点突变模型来刻画,并采用数值计算加以验证。本文在验证了尖点突变模型对沙粒起动建模可行性的基础上,主要讨论了电场力对沙粒起动的影响。计算结果也与实验及其他理论模型结果一致的,表明弱电场情况下电场力对沙粒起动的影响很小,在计算分析时可以忽略,强电场情况下,电场力对起动风速影响较大,故不能忽略。
2.实验观察到,风沙颗粒在风场作用下,起动之前,并非静止不动而是来回振动或摆动。而这种振动是由风场的脉动所引起的。但是由于以上都为实验观测结论,并没有理论模型加以支持。所以本文从沙粒的受力出发,建立了颗粒在风场作用下的微分动力学方程,并以正弦函数模拟风场脉动。首先,求解常微分方程的初值问题,得到无脉动时颗粒的临界起动风速,并且调整脉动强度,求解不同脉动强度对颗粒起动平均风速的影响。结果表明当风场的脉动强度越强,颗粒的临界起动平均风速就越小。其次,针对颗粒在风场作用下来回振动这一物理现象,本文通过建立非线性非自治系统模型并求解,对颗粒的周期运动,倍周期分岔,准周期运动,混沌等动力学特性进行了研究。并给出了激励参数不同时,床面颗粒不同的运动形态。
In the two-phase flow of sand blown, the mechanism of particles starting from the surface of bed under the effect of wind field is an important research subject. Particles starting from the earth's surface indicating the beginning of wind erosion, wind erosion is one of the main powers which causing the land degradation in arid and semiarid areas, while the threshold wind velocities of particles is a key factor which may influences wind erosion. Therefore, threshold wind velocities of particles has been pay high attention by researchers. The main contents of this thesis are as follows:
l.This thesis derived mechanical equilibrium equations of particles firstly, according to the mutation characteristics of process of particles starting from the surface of bed, using catastrophe theory in nonlinear science set Cusp Catastrophic Model on that process, through theoretical derivation verified that particles starting with effects of gravity、drag force、saffman force and electric field force can be described by Cusp Catastrophic Model and then verified this conclusion using numerical calculation. After verifying the feasibility of process of particles starting with Cusp Catastrophic Model, we mainly discussed the electric field force effect on that process. The calculated result is in accordance with experiment and other theory model results. It demonstrated that under the conditions of weak electric field, the electric field force has a low effect on process of particles starting, so it can be neglected when computational analysis. While under the conditions of strong electric field, electric field force has a high effect on threshold wind velocities, so it can not be neglected.
2. We observed that in the wind field effect before particles starting from the surface of bed,the particles is shaking instead of holding still. This kind of shaking is caused by fluctuating wind field. However, this conclusion is obtained from experimental observation and there is no theory model can support the conclusion. Therefore, we begin from force analysis of particles, established the differential dynamic equation of particles effected by the wind field and imitated the fluctuation as a sine function. Firstly, solving the initial boundary value of differential equation in order to get the threshold wind velocities of particles when there is no fluctuation, and then adjusting fluctuation intensity, getting the influence of different fluctuation intensity to get the threshold wind velocities of particles. The conclusion is that when the fluctuation intensity of wind field is stronger the of main value of threshold wind velocities will become slower. Secondly, aiming at the physical phenomenon that vibration of particles in fluctuating wind field, after setting the Nonlinear non-autonomous system model, we studied the dynamic characteristics of periodic vibration, period-doubling bifurcation, QPO, chaos and so on. And provided different movement form of particles on the bed under different incentive parameters.
本学位论文的主要研究内容如下：
1.本文首先建立沙粒受力平衡方程,根据沙粒起动这一物理过程的突变特性,运用非线性科学中的突变理论建立了颗粒起动的尖点突变模型,通过理论推导验证了沙粒在受重力、拖曳力、升力及电场力时的起动可以用非线性尖点突变模型来刻画,并采用数值计算加以验证。本文在验证了尖点突变模型对沙粒起动建模可行性的基础上,主要讨论了电场力对沙粒起动的影响。计算结果也与实验及其他理论模型结果一致的,表明弱电场情况下电场力对沙粒起动的影响很小,在计算分析时可以忽略,强电场情况下,电场力对起动风速影响较大,故不能忽略。
2.实验观察到,风沙颗粒在风场作用下,起动之前,并非静止不动而是来回振动或摆动。而这种振动是由风场的脉动所引起的。但是由于以上都为实验观测结论,并没有理论模型加以支持。所以本文从沙粒的受力出发,建立了颗粒在风场作用下的微分动力学方程,并以正弦函数模拟风场脉动。首先,求解常微分方程的初值问题,得到无脉动时颗粒的临界起动风速,并且调整脉动强度,求解不同脉动强度对颗粒起动平均风速的影响。结果表明当风场的脉动强度越强,颗粒的临界起动平均风速就越小。其次,针对颗粒在风场作用下来回振动这一物理现象,本文通过建立非线性非自治系统模型并求解,对颗粒的周期运动,倍周期分岔,准周期运动,混沌等动力学特性进行了研究。并给出了激励参数不同时,床面颗粒不同的运动形态。
In the two-phase flow of sand blown, the mechanism of particles starting from the surface of bed under the effect of wind field is an important research subject. Particles starting from the earth's surface indicating the beginning of wind erosion, wind erosion is one of the main powers which causing the land degradation in arid and semiarid areas, while the threshold wind velocities of particles is a key factor which may influences wind erosion. Therefore, threshold wind velocities of particles has been pay high attention by researchers. The main contents of this thesis are as follows:
l.This thesis derived mechanical equilibrium equations of particles firstly, according to the mutation characteristics of process of particles starting from the surface of bed, using catastrophe theory in nonlinear science set Cusp Catastrophic Model on that process, through theoretical derivation verified that particles starting with effects of gravity、drag force、saffman force and electric field force can be described by Cusp Catastrophic Model and then verified this conclusion using numerical calculation. After verifying the feasibility of process of particles starting with Cusp Catastrophic Model, we mainly discussed the electric field force effect on that process. The calculated result is in accordance with experiment and other theory model results. It demonstrated that under the conditions of weak electric field, the electric field force has a low effect on process of particles starting, so it can be neglected when computational analysis. While under the conditions of strong electric field, electric field force has a high effect on threshold wind velocities, so it can not be neglected.
2. We observed that in the wind field effect before particles starting from the surface of bed,the particles is shaking instead of holding still. This kind of shaking is caused by fluctuating wind field. However, this conclusion is obtained from experimental observation and there is no theory model can support the conclusion. Therefore, we begin from force analysis of particles, established the differential dynamic equation of particles effected by the wind field and imitated the fluctuation as a sine function. Firstly, solving the initial boundary value of differential equation in order to get the threshold wind velocities of particles when there is no fluctuation, and then adjusting fluctuation intensity, getting the influence of different fluctuation intensity to get the threshold wind velocities of particles. The conclusion is that when the fluctuation intensity of wind field is stronger the of main value of threshold wind velocities will become slower. Secondly, aiming at the physical phenomenon that vibration of particles in fluctuating wind field, after setting the Nonlinear non-autonomous system model, we studied the dynamic characteristics of periodic vibration, period-doubling bifurcation, QPO, chaos and so on. And provided different movement form of particles on the bed under different incentive parameters.
引文
[1]王涛,朱震达.中国沙漠化研究[J].中国生态农业学报,2001,9(2)：7-12.
[2]郑晓静,周又和.风沙运动中的若干关键力学问题[J].力学与实践,2003,25(2)：1-6.
[3]Zheng X J. Mechanics of Wind-blown Sand Movement [M].German:Springer,2009.
[4]Dooley E E. Environmental health perspectives [J].2002,110:A77.
[5]吴正等.风沙地貌与治沙工程学[M].北京：科学出版社,2003.
[6]王涛,赵哈林,肖红浪.中国沙漠化研究的进展[J].中国沙漠,1999,19(4)：299-311.
[7]王涛,陈广庭.中国北方沙城暴现状及对策[J].中国沙漠,2001,9(2)：7-12.
[8]刘贤万.实验风沙物理学与风沙工程学[M].北京：科技出版社,1995.
[9]Shao Y P. Physics and modeling of wind erosion [M]. Boston:Kluwer Academic publishers, 2000.
[10]Bagnold R A. The physics of blown sand and desert dune [M]. London:Methuen,1941.
[11]董飞,刘大有,贺大良.风沙运动的研究进展和发展趋势[J].力学进展,1995,25(3)：368-391.
[12]Cornish V. On Desert sand-dunes bordering the Nile Delta [J]. The Geographical Journal, 1990,15(1):1-30.
[13]Cornish, V. On kumatology[J]. The Geographical Journal,1989,13(6):624-628.
[14]戚隆溪,王柏鼓.士壤侵蚀的流体力学机制(Ⅱ)—风蚀[J].力学进展,1996,26(1)：41-55.
[15]Chepil W S. Dynamics of wind erosion:Ⅰ. Nature of movement of soil by wind [J]. Soil Science.1945,60(4):305-320.
[16]Zingg A W. Wind tunnel studies of the movement of sedimentary material [J]. Iowa City, 5th Hydraulic Conference Proceedings Bulletin.1953,34:111-135.
[17]Iversen J D, Pollack J B, Greeley R, and White B R.1976. Saltation threshold on Mars:the effect of interparticle force, surface roughness, and low atmospheric density. Icarus,29: 111-119.
[18]White B R. Soil transport by winds on mars [J]. Journal of Geophysical Research,1979, 84(B9):4643-4651.
[19]Owen P R. Saltation of uniform grains in air [J]. Journal of Fluid Mechanics,1964,20(2): 225-242.
[20]Ungar J, Haff P K. Steady state saltation in air [J]. Sedimentology,1987,34(2):289-299.
[21]何丽红,郑晓静,武建军.跃移沙粒起跳垂直速度分布函数的统计分析[J].兰州大学学报,2004,40(2)：31-35.
[22]Huang N, Zheng X J, Zhou, Y H. Simulation of wind-blown sand movement and probability density function of liftoff velocities of sand particles [J]. Journal of Geophysical Research,2006,111:D20201.
[23]Anderson R S, Haff P K. Simulation of eolian saltation [J]. Science,1988, 241(4867):820-823.
[24]Anderson R S, Haff P K. Wind modification and bed response during saltation of sand in air [J]. Acta Mechanica (Suppl.).1991,1:21-51.
[25]黄宁.沙粒带电及风沙电场对风沙跃移运动影响的研究[博士论文].兰州大学,2002.
[26]董治宝.风沙起动形式与起动假说[J].干旱气象,2005,23(2)：64-69.
[27]Bisal F, Nielsen K C. Movement of soil particles in saltation[J]. Canadian Journal of Soil Science,1962,42:81-86.
[28]Lyles L, Krauss K. Threshold velocities and initial particle motion as influenced by air turbulence[J]. Transaction of the American Society of Agricutural Engineers,1971,14: 563-566.
[29]Chepil W S. Equilibrium of soil grains at the threshold of movement by wind [C]. Proceedings of Soil Science Society of America,1959,23:422-428.
[30]陈予恕,唐云.非线性动力学中的现代分析方法[M].北京：科学出版社,2000.
[31]张伟,胡海岩.非线性动力学理论应用的新进展[M].北京：科学出版社,2009.
[32]凌复华.突变理论及其应用[M].上海：上海交通大学出版社,1987.
[33]武际可,苏先樾.弹性系统的稳定性[M].北京：科学出版社,1994.
[34]董治宝,李振山.风成沙粒度特征对其风蚀可蚀性的影响[J].土壤侵蚀与水土保持学报,1998,4(4)：1-5.
[35]王协康,敖汝庄,等.泥沙起动条件机理的非线性研究[J].长江科学院报,1999,16(4)：39-5.
[36]岳高伟,黄宁,郑晓静.沙粒形状的不规则性及静电力对起动风速的影响[J].中国沙漠,2003,23(6)：621-626.
[37]武建军,孙焕青.沙粒起动风速的影响因素研究[J].中国沙漠,2010,30(4).
[38]Schmidt D S, Schmidt R A, Dent J D. Electrostatic force on saltating sand [J]. Journal of Geophysical Research,1998,103:8997-9001.
[39]彭晓庆,王萍.正弦风场变化下的非平稳跃移风沙流模拟[J].中国沙漠,2011,31(3).
[40]武建军.磁悬浮—轨道耦合控制系统的动力稳定性研究[博士论文].兰州大学,2000.
[41]卢启韶,彭林平等.常微分方程与动力系统[M].北京：北京航天航空大学出版社,2009.
[42]罗冠炜.两自由度碰撞振动系统的Hopf分岔与混沌研究[博士论文].西南交通大学,1998.
[43]Nayfeh A H, Mook D T. Nonlinear oscillations[M]. New York:John Wiley,1979.
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[45]Zhou Youhe, Gao Yuanwen, Zheng Xiaojing. Stability analyses on dynamic control for a moving body levitated magnetically over elastic guideways [J]. Acta Mechanica solida sinica,12,3(1999):239-247.
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[48]盛小伟,洛志远,蔡庆东.颗粒材料上运动物体所受摩擦力的数值模拟[J].计算物理,2009,26(3).
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[51]郑晓静,武建军,周又和.周期变系数常微分方程动力系统稳定性分析的Lyapunov指数判据[J].兰州大学学报,35,2(1999)：17-20.
[52]Phillips M. A force balance model for particle entrainment into a fluid system [J]. Journal of Applied Physics,1980,13:221-233.
[53]董治宝,罗万银.风沙床面起动临界受力平衡模型对比分析[J].中国沙漠,2007,27(3)：356-361.
[54]Zheng X J, Huang N, Zhou Y. The effect of electrostatic force on the evolution of sand saltation cloud [J]. The European Physical Journal E,2006,19(4):129-138.
[55]闫民,孙保平,等.风沙运动的散体动力学模型及其动力学过程[J],中国水土保持科学,2005,3(1)：82-87.
[56]孙其诚,王光谦.模拟风沙运动的离散颗粒动力学模型[J],泥沙研究,2001,4：12-18.
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[58]武建军,孙焕青,何丽红.沙粒起动风速的影响因素研究[J].中国沙漠,2010,30(4)：743-748.
[59]王志强.风沙运动过程的非线性特性研究[硕士论文].兰州大学,2010.
[2]郑晓静,周又和.风沙运动中的若干关键力学问题[J].力学与实践,2003,25(2)：1-6.
[3]Zheng X J. Mechanics of Wind-blown Sand Movement [M].German:Springer,2009.
[4]Dooley E E. Environmental health perspectives [J].2002,110:A77.
[5]吴正等.风沙地貌与治沙工程学[M].北京：科学出版社,2003.
[6]王涛,赵哈林,肖红浪.中国沙漠化研究的进展[J].中国沙漠,1999,19(4)：299-311.
[7]王涛,陈广庭.中国北方沙城暴现状及对策[J].中国沙漠,2001,9(2)：7-12.
[8]刘贤万.实验风沙物理学与风沙工程学[M].北京：科技出版社,1995.
[9]Shao Y P. Physics and modeling of wind erosion [M]. Boston:Kluwer Academic publishers, 2000.
[10]Bagnold R A. The physics of blown sand and desert dune [M]. London:Methuen,1941.
[11]董飞,刘大有,贺大良.风沙运动的研究进展和发展趋势[J].力学进展,1995,25(3)：368-391.
[12]Cornish V. On Desert sand-dunes bordering the Nile Delta [J]. The Geographical Journal, 1990,15(1):1-30.
[13]Cornish, V. On kumatology[J]. The Geographical Journal,1989,13(6):624-628.
[14]戚隆溪,王柏鼓.士壤侵蚀的流体力学机制(Ⅱ)—风蚀[J].力学进展,1996,26(1)：41-55.
[15]Chepil W S. Dynamics of wind erosion:Ⅰ. Nature of movement of soil by wind [J]. Soil Science.1945,60(4):305-320.
[16]Zingg A W. Wind tunnel studies of the movement of sedimentary material [J]. Iowa City, 5th Hydraulic Conference Proceedings Bulletin.1953,34:111-135.
[17]Iversen J D, Pollack J B, Greeley R, and White B R.1976. Saltation threshold on Mars:the effect of interparticle force, surface roughness, and low atmospheric density. Icarus,29: 111-119.
[18]White B R. Soil transport by winds on mars [J]. Journal of Geophysical Research,1979, 84(B9):4643-4651.
[19]Owen P R. Saltation of uniform grains in air [J]. Journal of Fluid Mechanics,1964,20(2): 225-242.
[20]Ungar J, Haff P K. Steady state saltation in air [J]. Sedimentology,1987,34(2):289-299.
[21]何丽红,郑晓静,武建军.跃移沙粒起跳垂直速度分布函数的统计分析[J].兰州大学学报,2004,40(2)：31-35.
[22]Huang N, Zheng X J, Zhou, Y H. Simulation of wind-blown sand movement and probability density function of liftoff velocities of sand particles [J]. Journal of Geophysical Research,2006,111:D20201.
[23]Anderson R S, Haff P K. Simulation of eolian saltation [J]. Science,1988, 241(4867):820-823.
[24]Anderson R S, Haff P K. Wind modification and bed response during saltation of sand in air [J]. Acta Mechanica (Suppl.).1991,1:21-51.
[25]黄宁.沙粒带电及风沙电场对风沙跃移运动影响的研究[博士论文].兰州大学,2002.
[26]董治宝.风沙起动形式与起动假说[J].干旱气象,2005,23(2)：64-69.
[27]Bisal F, Nielsen K C. Movement of soil particles in saltation[J]. Canadian Journal of Soil Science,1962,42:81-86.
[28]Lyles L, Krauss K. Threshold velocities and initial particle motion as influenced by air turbulence[J]. Transaction of the American Society of Agricutural Engineers,1971,14: 563-566.
[29]Chepil W S. Equilibrium of soil grains at the threshold of movement by wind [C]. Proceedings of Soil Science Society of America,1959,23:422-428.
[30]陈予恕,唐云.非线性动力学中的现代分析方法[M].北京：科学出版社,2000.
[31]张伟,胡海岩.非线性动力学理论应用的新进展[M].北京：科学出版社,2009.
[32]凌复华.突变理论及其应用[M].上海：上海交通大学出版社,1987.
[33]武际可,苏先樾.弹性系统的稳定性[M].北京：科学出版社,1994.
[34]董治宝,李振山.风成沙粒度特征对其风蚀可蚀性的影响[J].土壤侵蚀与水土保持学报,1998,4(4)：1-5.
[35]王协康,敖汝庄,等.泥沙起动条件机理的非线性研究[J].长江科学院报,1999,16(4)：39-5.
[36]岳高伟,黄宁,郑晓静.沙粒形状的不规则性及静电力对起动风速的影响[J].中国沙漠,2003,23(6)：621-626.
[37]武建军,孙焕青.沙粒起动风速的影响因素研究[J].中国沙漠,2010,30(4).
[38]Schmidt D S, Schmidt R A, Dent J D. Electrostatic force on saltating sand [J]. Journal of Geophysical Research,1998,103:8997-9001.
[39]彭晓庆,王萍.正弦风场变化下的非平稳跃移风沙流模拟[J].中国沙漠,2011,31(3).
[40]武建军.磁悬浮—轨道耦合控制系统的动力稳定性研究[博士论文].兰州大学,2000.
[41]卢启韶,彭林平等.常微分方程与动力系统[M].北京：北京航天航空大学出版社,2009.
[42]罗冠炜.两自由度碰撞振动系统的Hopf分岔与混沌研究[博士论文].西南交通大学,1998.
[43]Nayfeh A H, Mook D T. Nonlinear oscillations[M]. New York:John Wiley,1979.
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