基于诊断函数的薄层流对数律研究

Logarithmic law of shallow water flow by using diagnostic function

薄层流是一种特殊形态的明渠流,其特点是水深浅薄。为探讨薄层流流速分布是否满足对数律,该研究利用高分辨率粒子图像测速(Particle Image Velocimetry,PIV)技术,分析8组薄层流(水深0.49~1.1 cm,雷诺数835~2877)及1组深水明渠紊流(对照)床面至水面的流速分布、紊动强度及雷诺应力。并基于诊断函数,研究薄层流流速是否满足对数律、对数区的范围及卡门常数变化规律。结果表明,薄层流的无量纲流速从过渡区开始偏离深水明渠水流中的理论曲线;薄层流的流向紊动强度大于深水明渠紊流,但垂向紊动强度小于深水明渠紊流,随着水深的增加,两者的紊动强度逐渐重合;雷诺应力的特征表明,随着水深的增加,受黏性力影响的范围越来越小。薄层流诊断函数曲线的特征说明薄层流中不存在严格意义的对数区,但当水深极浅时(水深≤0.53 cm),流速基本满足对数律,且卡门常数在0.2~0.3范围内。当水深和雷诺数增加,薄层流诊断函数曲线出现波动而不再近似水平。为方便实际计算,若允许诊断函数有一定的倾斜,对数区在极大值与极小值之间的范围,薄层流的卡门常数随着雷诺数的增加而增加。此外,薄层流对数区的范围并非稳定,随着雷诺数的增加,对数区影响的范围变大。该研究可为薄层流的理论研究和流速计算提供参考。

Shallow water flow is a special type of open channel flow,where the fluid behaves with a free surface in a canal.The flow depth of shallow water flow is extremely thin,and even reaches several millimeters.At present,there is no obvious evidence that the logarithmic theory is suitable for shallow water flow,even though it is widely used to describe velocity profile for open channel flow.The reason is that the viscous and inertia force exert no significant influences on shallow water flow,due to extremely thin flow depth.It is necessary to clarify the presence of the region without influenced by viscous and inertia force.The present study aims to analyze the velocity characteristics of shallow water flow,thereby to verify logarithmic law using diagnostic function.The Particle Image Velocimetry(PIV)with high resolution(64 pixels/mm)was also used to measure flow fields.Eight conditions of shallow water flow were surveyed(flow depth ranged from 0.49 to 1.1 cm and Reynolds number ranged from 835 to 2877),and a deep-water open channel flow was considered as control group.The statistical parameters were measured,including the velocity distribution from flume bed to free surface,streamwise and wall-normal turbulent intensity.Logarithmic theory was also explored,such as the diagnostic function,Karman constant,and scope of log-law region.Results showed that:1)From the transition region,dimensionless streamwise velocity of shallow water flow deviated from the logarithmic law,which was used in deep-water open channel flow.The streamwise turbulent intensity of shallow water flow was larger than that of deep-water open channel turbulent flow,while the wall-normal turbulent intensity was smaller than that.The turbulent intensity of two flows gradually overlapped with increasing flow depth.The characteristics of Reynolds stress showed that the region influenced by viscous force became smaller as the flow depth increased.2)There weren’t strict horizontal lines in the diagnostic function curves,implying that there was no strict log-law region in shallow water flow.However,an approximate line was obtained in the diagnostic function curves for the extremely shallow depth(flow depth not less than 0.53 cm),when the dimensionless flow depth was larger than 10,indicating the logarithmic law was basically suitable for this region.Simultaneously,the Karman constant was at the range of 0.2 and 0.3.There was a region without influenced by viscous force and inertia force away from flume bed,due to the weakness of inertia force.In the flow depth larger than 0.53 cm,the diagnostic function curves became fluctuate due to the inertia force,particularly in the regions with dimensionless flow depth larger than 10.An upward trend occurred near the free surface,where firstly decreased and then increased to the maximum,finally decreased to the minimum.3)The log-law region appeared in the scope between the maximum and minimum for the actual application of shallow water flow,although there was no strict log-law region for a certain tilt of diagnostic function.The extreme value of Karman constant increased with the increasing Reynolds number,indicating no stable Karman constant for shallow water flow.In addition,the scope of log-law region was not stable.As the Reynolds number increased,the scope of log-law region would be expanded.This present study can be benefit to further understand the characteristics of shallow water flow,thereby for the theoretical investigation of shallow water flow using particle image velocimetry.