明渠植被水流流速分布解析解与阻力特性研究

发布时间：2018-06-16 02:20

本文选题：植被水流 + 流速解析解　；参考：《武汉大学》2016年博士论文

【摘要】：本文主要研究在植被存在情况下明渠水流的运动特性,即明渠植被水流的水动力学特性。研究的主要内容包括不同类型植被水流的流速分布解析解以及植被对水流的阻力特性。分别对柔性植被,双层刚性植被存在情况下的明渠恒定均匀流推导出纵向流速垂向分布的解析解模型。对非淹没刚性植被存在情况下,恒定非均匀流中的植被阻力特性进行研究,推导出植被拖曳力系数与雷诺数的变化关系。本文采用数学模型推导和实验室试验的相结合的方法对植被水流的水动力学特性进行了详细的研究,可以分为以下几个方面。柔性植被受到水流的作用会发生弯曲变形,本文针对这种情况研究并推导出柔性植被的弯曲特性以及在小弯曲情况下水流纵向流速的垂向分布解析解。将淹没柔性植被水流在垂向上分为植被层和自由水层分别来研究。首先,在植被层中对柔性植被应用悬臂梁理论推导出植被弯曲后各点的角度以及弯曲后的高度。然后,将植被阻力和雷诺应力的表达式代入水流控制方程中求解得到流速的解析解。其中,与刚性植被阻力不同,弯曲柔性植被在水流方向上的阻力为拖曳力与摩擦力的合力。当植被弯曲程度较小时,植被层中雷诺应力符合指数分布的形式,所以由此求解控制方程得到的流速解析解适用于植被发生小弯曲的情况。在自由水层中,为满足流速梯度在水面为零的条件,推导求解出流速分布的多项式表达式,与传统的对数流速表达式相比,该多项式表达式可以更好地符合实际情况。当水流流速较大或者植被柔性较高时,植被会发生大挠度的弯曲变形,在这种情况下,植被层中的雷诺应力不再符合指数分布形式,所以在植被小弯曲情况下得到的水流流速解析解在这里不适用。并且试验结果表明,植被弯曲程度较大时,其对水流的阻力会大幅减小,并与水流的流速近似为线性关系。基于这个现象,本文提出了新的植被阻力公式,并通过引入植被层和自由水层的卡门系数,求解得出植被发生大弯曲变形情况下,水流的纵向流速垂向分布的解析解。并且该模型能够很好地吻合试验所得的流速数据。在天然环境下,河道中的植被高度往往是不一样的,并且是高低交错排列的,在这种情况下,水流的流速特性更为复杂。本文以双层刚性植被为例,采用幂级数等方法求解水流控制方程,研究并得到双层刚性植被存在时,各层水流纵向流速的垂向分布解析解。与此同时,在实验室进行了双层植被水流的试验,并通过PIV粒子图像测速系统测量得到水流的流速特性,试验结果显示出流速在植被层下部近似恒定,而在植被层上部逐渐增大。通过与试验数据的对比,该流速解析解模型可以很好地预测双层植被水流的流速特性,同时本文给出了双层植被水流的剪切涡入侵深度的经验公式。上面所叙述的植被水流特性研究都是针对恒定均匀流情况,然而在实际河道中,水流往往是非均匀的。前人的研究成果已经得出在恒定均匀流情况下,拖曳力系数与雷诺数的关系,当采用前人所得到的拖曳力系数关系代入圣维南方程中求解恒定非均匀流的水面线时,计算结果与实际情况相差较大。说明在非均匀流情况下,植被的拖曳力系数不仅与雷诺数有关,还与水流的非均匀性有关。针对这种情况,本文研究并得出在恒定非均匀流情况下,植被拖曳力系数与雷诺数的关系是近似抛物线分布的,且抛物线的形状与水流的非均匀性和植被属性有关。同时,本文给出了在恒定非均匀流情况下,植被拖曳力系数的经验公式。在天然环境中,由于降雨的影响,河道中水面线也会发生变化。本文在上述恒定非均匀流的基础上加入降雨因素,继续研究在这些因素的综合影响下植被对水流的阻力特性。首先,在圣维南方程组中加入降雨项,推导出该情况下植被拖曳力系数的表达式。然后,通过实验室试验得到不同植被密度下、不同降雨强度下的水面线,并采用对数形式的水面线模型进行拟合,最终得到不同植被密度下、不同降雨强度时的拖曳力系数与雷诺数的关系。研究表明降雨对植被阻力特性有着较大的影响,并且随着降雨强度的增大,这种影响也在随之增大。在降雨强度很大的情况下,植被拖曳力系数随着雷诺数的增加而减小,呈现单调递减特性,这与没有降雨情况下的植被拖曳力系数特性完全不同。
[Abstract]:This paper mainly studies the motion characteristics of open channel flow under the presence of vegetation, that is the hydrodynamic characteristics of the vegetation flow of the open channel. The main contents of the study include the analytical solution of the flow velocity distribution of different types of vegetation flow and the resistance characteristics of the vegetation to the flow of water. The analytical solution model of vertical distribution of longitudinal velocity is derived. Under the presence of non submerged rigid vegetation, the characteristics of vegetation resistance in constant inhomogeneous flow are studied, and the relationship between the change of the drag coefficient of vegetation and the Reynolds number is derived. The hydrodynamic characteristics are studied in detail, which can be divided into the following aspects. The flexural deformation of the flexible vegetation will occur under the action of water flow. In this case, the bending characteristics of the flexible vegetation and the vertical distribution of the longitudinal flow velocity under the small bending condition are derived. Vertically, the vegetation layer and the free water layer are separately studied. First, the angle of each point and the height after the bending of the vegetation are derived from the cantilever beam theory in the vegetation layer. Then, the analytic solution of the velocity is obtained by replacing the expression of the vegetation resistance and Reynolds stress into the flow control equation. The resistance of the vegetative vegetation is different. The resistance of the flexural flexible vegetation in the direction of the flow is the resultant force of the drag force and the friction force. The Reynolds stress in the vegetation layer is in the form of exponential distribution when the degree of vegetation bending is small, so the analytical solution obtained by the solution of the control equation is suitable for the small bending of the vegetation. In order to satisfy the condition that the velocity gradient is zero on the surface of the water, the polynomial expression of the velocity distribution is derived. Compared with the traditional logarithmic velocity expression, the polynomial expression can better conform to the actual situation. When the flow velocity is larger or the vegetation flexibility is higher, the vegetation will bend the deflection of large deflection, in this case, The Reynolds stress in the vegetation layer is no longer in the form of exponential distribution, so the analytical solution of the flow velocity obtained under the small vegetation bending is not applicable here. And the experimental results show that the resistance of the flow to the flow will be greatly reduced when the degree of vegetation bending is large and the flow velocity is approximately linear. Based on this phenomenon, this paper A new formula of vegetation resistance is proposed. By introducing the Carmen coefficient of the vegetation layer and the free water layer, the analytical solution of vertical velocity distribution of the longitudinal velocity of the flow is obtained under the condition of large bending deformation of the vegetation, and the model can well accord with the flow velocity data obtained by the experiment. In natural environment, the height of vegetation in the river is often the same. In this case, the flow velocity characteristics are more complex. In this case, the flow velocity characteristics are more complex. In this paper, a two layer rigid vegetation is taken as an example to solve the flow control equation by means of power series and so on. The experiments of the double layer vegetation flow were carried out and the flow velocity characteristics were measured by the PIV particle image velocimetry system. The experimental results showed that the velocity of flow was approximately constant at the lower part of the vegetation layer and increased gradually in the upper part of the vegetation layer. By comparing with the experimental data, the flow velocity solution model could predict the flow of double layer vegetation well. At the same time, the empirical formula of the invasion depth of the shear vorticity of the two-layer vegetation flow is given. The study on the characteristics of the vegetation flow described above is aimed at the constant uniform flow. However, in the actual River, the flow is often inhomogeneous. The results of previous studies have already obtained the drag coefficient under the condition of constant uniform flow. The relationship between the Reynolds number and the drag force coefficient obtained by the predecessors is replaced by the Saint Venant equation to solve the water surface line of the constant nonuniform flow. The calculation results are quite different from the actual conditions. It shows that the drag coefficient of the vegetation is not only related to the Reynolds number, but also related to the inhomogeneity of the flow in the case of inhomogeneous flow. The relationship between the drag coefficient of the vegetation and the Reynolds number is approximately parabolic, and the shape of the parabola is related to the inhomogeneity of the flow and the vegetation properties. At the same time, this paper gives an empirical formula for the drag coefficient of the vegetation under the condition of constant inhomogeneous flow. In the environment, the water surface line in the river will also change because of the influence of rainfall. In this paper, we add rainfall factors on the basis of the constant non-uniform flow, and continue to study the resistance characteristics of the vegetation to the flow under the comprehensive influence of these factors. First, the rainfall item is added to the Saint Venant equation, and the drag coefficient of the vegetation is derived. Then, the water surface lines under different vegetation density and different rainfall intensity are obtained through laboratory experiments, and the logarithmic surface line model is used to fit the relationship between the drag force coefficient and the Reynolds number under different vegetation density and different rainfall intensity. The study shows that rainfall has a better characteristic of vegetation resistance than the Reynolds number. With the increase of rainfall intensity, the drag coefficient of vegetation decreases with the increase of Reynolds number, and presents a monotonous decreasing characteristic, which is completely different from the characteristics of the drag coefficient of the vegetation without rainfall.
【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TV133

【相似文献】