考虑雷诺数和形状影响的坝岸根石水平水流拖曳力系数修正

对于水利工程坝岸散抛根石冲揭失稳,水流作用下根石的拖曳力是重要的力学分析参数。该文基于黄河坝岸散抛根石的形状参数特征,利用水槽试验量测球体及不同形状块体受水流作用的水平拖曳力,研究雷诺数、物体形状指标与拖曳力相关关系及变化规律,明确影响因素,率定双因素影响下块体的拖曳力系数函数。结果表明,水下球体或近似球状物体的拖曳力系数,基本不受水流及物体形态影响,拖曳力系数趋于0.40～0.56;有棱角块体的水流拖曳力系数,块体雷诺数小于3×104的影响区域,系数函数呈双曲线趋势变化;块体雷诺数大于3×104的影响区域,迎水面宽高比不大于侧立面长高比,拖曳力系数趋于0.80～0.90,迎水面宽高比大于侧立面长高比,拖曳力系数趋于1.00～1.10。进一步通过试验修正了水流作用下不同形态物体的水平拖曳力系数,提出了块体雷诺数、形状参数双因素影响下物体水平拖曳力系数函数,得到了以不同物体来流方向投影响面积为基准的水平拖曳计算公式,经拟合公式的合理性分析与验证,拖曳力系数拟合优度达到0.90以上,平均相对误差为8.7%;修正后拖曳力平均相对误差仅为7.5%,公式计算效果良好,更准确地反映散抛根石的水下受力特征,为分析水下抛石受水流冲击离散形态提供理论依据。

Modification of horizontal drag force coefficient of bam bank root stone considering influence of Reynolds number and shape

Abstract: Scattered root stone loss under the action of water flow is one of main reasons causing bank instability. Drag force is an important parameter for understanding the related mechanisms. In this paper, we investigated the effects of shape and Reynolds number on the drag force coefficient of root stone under the action of water flow. Scattered root stones on Yellow River bank had the width-height ratio of 1.01-2.55, the length-height ratio of 1.29-3.40, and unit weight of 17.70-26.20 kN/m3. Based on these investigated results, samples of different shapes (block and ball) and sizes were prepared. A set of force measurement system was developed for determining velocity and pressure signals simultaneously, which could measure horizontal drag force under the action of water flow on balls and different sizes of blocks by controlling water flow of sloping flume. Based on the analysis on the relationship between Reynolds number, shape and drag force, drag coefficient function of block was calibrated. Results showed that the drag force coefficients of underwater balls or balls were not influenced by the flow and shape. Their drag force coefficients were 0.40-0.56. However, the drag force coefficient of blocks was affected by the water flow and object shape. When the Reynolds number of block was less than 3×104, the drag force coefficient changed in hyperbolic shape.When the Reynolds number of block was greater than 3×104, if the width-height ratio of upstream face was less than or equaled to the length-height ratio of upstream of side elevation, the drag coefficients tended to be constant values of 0.80-0.90, or if the width-height ratio of upstream face was more than the length-height ratio of upstream of side elevation, the drag coefficients tended to be constant values of 1.00-1.10. Considering the interaction effects of the Reynolds number and block shape, the horizontal drag force coefficient formula of block stone could be obtained under 7 combination conditions. Based on the measured data, the drag coefficients under different application conditions were fitted by least square method. The formulas of drag force coefficients of block stone were presented under the influence of Reynolds number and shape parameters. And then the horizontal drag force calculation formula was suggested with the projected area of different objects in the flow direction. It could more accurately reflect the force characteristics of the underwater root stone. The goodness of fit of drag force coefficient reached above 0.90, and the mean of relative error was 8.7%. After correction the mean of relative error of drag force was only 7.5%. Compared to the regular method considering the drag coefficient as a constant of 0.45 (the mean relative error of drag force), the corrected method had a higher accuracy, indicating that the modification in this study is reasonable and the formula established is useful for block root stones. The research results make up for inadequacy of theoretical basis for drag force analysis of underwater root stones in the process of revetment engineering stability calculation. These results can be applied to planning and designing revetment projects in water conservancy projects.