风沙流中沙粒的三维起跳初速度分布研究
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摘要
沙粒起跳初速度分布是对风沙流进行宏观理论预测时所必须的物理量,本学位论文针对风沙流中沙粒起跳初速度分布进行了研究。首先,通过PIV技术在风洞中对混合粒径沙粒的起跳和入射速度进行了实验测量,给出了考虑风速和沙粒粒径影响的沙粒起跳初速度概率密度分布函数；其次,建立了球形粒子三维(3D)随机粒-床碰撞理论模型,在此基础上分析了沙粒经粒-床碰撞过程后的起跳特征；然后,结合球形粒子3D随机粒-床碰撞模型给出了沙粒起跳初速度概率密度分布和旋转角速度概率密度分布的理论预测；最后,沿风场方向的不同位置,对风沙流进行观测,给出了风沙流中沙粒起跳初速度分布以及输沙率的沿程变化规律。主要工作如下：
1.在风洞中用粒子图像测速仪(PIV),通过改进粒子跟踪测速(PTV)算法,实现了天然混合沙丘沙形成的(粒径40-800μm)风沙流在距沙床床面0.5mm以上跃移沙粒的空间位置、运动速度和粒径的同步测量；研究了入射(起跳)沙粒水平速度、垂向速度、侧向速度和风向角的概率分布随风速、沙粒粒径以及高度的变化规律,并给出了跃移沙粒入射、起跳初速度密度分布随风速和粒径变化的经验公式。
2.根据经典碰撞理论,考虑了入射沙粒的速度及其方向,床面沙粒及其速度,以及沙粒间碰撞位置,同时考虑床面沙粒对被碰沙粒的作用,对粒-床碰撞这一极短时间内完成的力学过程进行建模,建立了一个3D随机粒-床碰撞理论模型,得到入射沙粒和被碰沙粒起跳后水平速度、垂向速度、侧向速度、滚旋角速度、侧旋角速度以及上旋角速度的解析表达,而且理论预测结果与实验结果吻合较好,这说明该模型是合理的。基于该模型进一步分析了粒-床碰撞后随机变量对沙粒起跳速度的影响,给出了沙粒的反弹、溅射特性,包括反弹速度、溅射速度与入射速度的比值,反弹角,溅射角以及入射沙粒的反弹概率。
3.基于3D随机粒-床碰撞模型,利用多维随机变量函数理论,给出了沙粒三维起跳初速度的概率密度分布函数,包括反弹、溅射沙粒的水平起跳初速度、垂向起跳初速度、侧向起跳初速度、滚旋角速度、侧旋角速度以及上旋角速度分布的概率密度函数；基于这些概率密度函数,预测了稳定风沙流中沙粒三维起跳初速度及起跳角速度概率密度分布,通过与实验结果的比较,证实了该研究方法的可靠性；最后分析了随机因素对沙粒起跳初速度概率密度分布的影响,发现风速和沙粒粒径不影响跃移沙粒起跳初速度概率密度分布形式,但影响其概率密度值。
4.开展了风沙流沿程变化规律的风洞实验研究。观测了风沙流中跃移沙粒起跳速度的沿程变化规律,结果表明：风沙流中沙粒起跳初速度在沿程方向存在明显差别,其均值和标准差均随着距沙床前缘距离的增大而先增大后减小概率分布的最大值出现的位置到沙床前缘的距离随着风速的增大而减小。通过集沙仪测量了水平输沙率沿程变化规律,认为水平输沙率在发展过程中先增大,再减小并最终达到饱和,其饱和长度和摩阻风速有关,随着摩阻风速的增大而减小；给出了不同摩阻风速条件下,可以真实反映风沙流中水平输沙率沿程变化规律的经验公式。
It is obvious that the probability distribution of lift-off velocities is the important parameter for the prediction of wind sand flux. The subject of investigated in this thesis focuses on the probability distribution of lift-off velocities of sand particles in windblown sand flows. Firstly experimental measurements were conducted in a wind tunnel with the Particle Image Velocimeter (PIV) which gave the probability distribution function (PDF) of the lift-off velocities of sand particles regarding wind velocities and sand diameters. Then a3D stochastic particle/bed collision model was established to analysis the dynamical characteristic of the particle/bed collision process in saltation layer. Further an empirical formula concerning the mass flux varying with height can be obtained through the measured data. Finally, a prediction of the PDF of lift-off velocities and angular velocities of sand particles was made combing with the3D stochastic model. The context includes the following sections:
1. Employing the PIV combing an improved algorithm of the Particles Tracing Velocimeter (PTV), this study realized synchronous measurements on the spatial positions, velocities and sizes of saltating sand particles in windblown sand flows on a size-mixed sand bed generated in a wind tunnel. The PDFs as well as their variations of the horizontal, vertical and lateral velocities of incident and lift-off sand particles were investigated considering the influence of wind velocities, particles sizes and heights. Empirical formulas describing the PDFs of incident and lift-off velocities in the saltating layer were put forward.
2. Based on the classic collision theory, this study established a3D stochastic particle/bed collision model on the collision process between an incident particle and bed particles with respect to the incident velocity and angle, contact positions, creeping velocities as well as the counterforce acted on the incident particle from bed particles. With the model, the horizontal, vertical and lateral velocities, rolling and side-spinning angular velocities of the incident particle and bed particles were given in terms of analytical solutions. The model is proved plausible compared with experimental results which can reveal the characteristics of rebound and ejection of sand particles after collisions and the influence of above random variables to the sand particles'lift-off in quantity, including rebound velocities, the ratio of ejection velocities and incident velocities, rebound and ejection angles and the rebound probability of incident particles.
3. Based on the3D stochastic particle/bed collision model and the probability theory of multiple random variables, the PDFs of lift-off quantities of sand particles were presented including the horizontal, vertical and lateral components of rebound and ejected sand particles, rolling and top-and side-spinning angular velocities. With these PDFs, the PDFs of3D lift-off velocities and angular velocities can be obtained. The predicted results have good agreement with the experimental data which proved the reliability of the method used in this study. Eventually, the influence of above random variables to the PDF of lift-off velocities of sand particles in the saltating layer.
4. The variation law of windblown sand flux and lift-off velocities along with distance was investigated through wind-tunnel experiments. The changing law of the horizontal component of sand transport rate was revealed by sand traps, which demonstrates a trend of first increasing, then decreasing and finally reaching saturation. The measured saturation length was found decrease with the increasing friction wind speed which was expressed by an empirical formula. Further, an empirical relation between the horizontal sand transport rate and height was for the first time put forward to reflect the profile of windblown sand flows.
1.在风洞中用粒子图像测速仪(PIV),通过改进粒子跟踪测速(PTV)算法,实现了天然混合沙丘沙形成的(粒径40-800μm)风沙流在距沙床床面0.5mm以上跃移沙粒的空间位置、运动速度和粒径的同步测量；研究了入射(起跳)沙粒水平速度、垂向速度、侧向速度和风向角的概率分布随风速、沙粒粒径以及高度的变化规律,并给出了跃移沙粒入射、起跳初速度密度分布随风速和粒径变化的经验公式。
2.根据经典碰撞理论,考虑了入射沙粒的速度及其方向,床面沙粒及其速度,以及沙粒间碰撞位置,同时考虑床面沙粒对被碰沙粒的作用,对粒-床碰撞这一极短时间内完成的力学过程进行建模,建立了一个3D随机粒-床碰撞理论模型,得到入射沙粒和被碰沙粒起跳后水平速度、垂向速度、侧向速度、滚旋角速度、侧旋角速度以及上旋角速度的解析表达,而且理论预测结果与实验结果吻合较好,这说明该模型是合理的。基于该模型进一步分析了粒-床碰撞后随机变量对沙粒起跳速度的影响,给出了沙粒的反弹、溅射特性,包括反弹速度、溅射速度与入射速度的比值,反弹角,溅射角以及入射沙粒的反弹概率。
3.基于3D随机粒-床碰撞模型,利用多维随机变量函数理论,给出了沙粒三维起跳初速度的概率密度分布函数,包括反弹、溅射沙粒的水平起跳初速度、垂向起跳初速度、侧向起跳初速度、滚旋角速度、侧旋角速度以及上旋角速度分布的概率密度函数；基于这些概率密度函数,预测了稳定风沙流中沙粒三维起跳初速度及起跳角速度概率密度分布,通过与实验结果的比较,证实了该研究方法的可靠性；最后分析了随机因素对沙粒起跳初速度概率密度分布的影响,发现风速和沙粒粒径不影响跃移沙粒起跳初速度概率密度分布形式,但影响其概率密度值。
4.开展了风沙流沿程变化规律的风洞实验研究。观测了风沙流中跃移沙粒起跳速度的沿程变化规律,结果表明：风沙流中沙粒起跳初速度在沿程方向存在明显差别,其均值和标准差均随着距沙床前缘距离的增大而先增大后减小概率分布的最大值出现的位置到沙床前缘的距离随着风速的增大而减小。通过集沙仪测量了水平输沙率沿程变化规律,认为水平输沙率在发展过程中先增大,再减小并最终达到饱和,其饱和长度和摩阻风速有关,随着摩阻风速的增大而减小；给出了不同摩阻风速条件下,可以真实反映风沙流中水平输沙率沿程变化规律的经验公式。
It is obvious that the probability distribution of lift-off velocities is the important parameter for the prediction of wind sand flux. The subject of investigated in this thesis focuses on the probability distribution of lift-off velocities of sand particles in windblown sand flows. Firstly experimental measurements were conducted in a wind tunnel with the Particle Image Velocimeter (PIV) which gave the probability distribution function (PDF) of the lift-off velocities of sand particles regarding wind velocities and sand diameters. Then a3D stochastic particle/bed collision model was established to analysis the dynamical characteristic of the particle/bed collision process in saltation layer. Further an empirical formula concerning the mass flux varying with height can be obtained through the measured data. Finally, a prediction of the PDF of lift-off velocities and angular velocities of sand particles was made combing with the3D stochastic model. The context includes the following sections:
1. Employing the PIV combing an improved algorithm of the Particles Tracing Velocimeter (PTV), this study realized synchronous measurements on the spatial positions, velocities and sizes of saltating sand particles in windblown sand flows on a size-mixed sand bed generated in a wind tunnel. The PDFs as well as their variations of the horizontal, vertical and lateral velocities of incident and lift-off sand particles were investigated considering the influence of wind velocities, particles sizes and heights. Empirical formulas describing the PDFs of incident and lift-off velocities in the saltating layer were put forward.
2. Based on the classic collision theory, this study established a3D stochastic particle/bed collision model on the collision process between an incident particle and bed particles with respect to the incident velocity and angle, contact positions, creeping velocities as well as the counterforce acted on the incident particle from bed particles. With the model, the horizontal, vertical and lateral velocities, rolling and side-spinning angular velocities of the incident particle and bed particles were given in terms of analytical solutions. The model is proved plausible compared with experimental results which can reveal the characteristics of rebound and ejection of sand particles after collisions and the influence of above random variables to the sand particles'lift-off in quantity, including rebound velocities, the ratio of ejection velocities and incident velocities, rebound and ejection angles and the rebound probability of incident particles.
3. Based on the3D stochastic particle/bed collision model and the probability theory of multiple random variables, the PDFs of lift-off quantities of sand particles were presented including the horizontal, vertical and lateral components of rebound and ejected sand particles, rolling and top-and side-spinning angular velocities. With these PDFs, the PDFs of3D lift-off velocities and angular velocities can be obtained. The predicted results have good agreement with the experimental data which proved the reliability of the method used in this study. Eventually, the influence of above random variables to the PDF of lift-off velocities of sand particles in the saltating layer.
4. The variation law of windblown sand flux and lift-off velocities along with distance was investigated through wind-tunnel experiments. The changing law of the horizontal component of sand transport rate was revealed by sand traps, which demonstrates a trend of first increasing, then decreasing and finally reaching saturation. The measured saturation length was found decrease with the increasing friction wind speed which was expressed by an empirical formula. Further, an empirical relation between the horizontal sand transport rate and height was for the first time put forward to reflect the profile of windblown sand flows.
引文
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