含沙波明渠水流摩阻流速模型研究

A shear velocity model for open channel flow with bed forms

当河流中存在沙波时,工程上常采用爱因斯坦的水力半径切割法求解河床阻力,该方法中将水力半径划分为平整床面对应的水力半径R'b和沙波存在时额外增加的水力半径Rb″。不同学者在利用对数公式求解平整床面摩阻流速时,床面粗糙度ks的取值不同,本文利用348组实测平整床面数据对ks进行率定,率定结果表明ks可用中值粒径d50代替。由于紊流对数流速公式只适用于紊流粗糙区,为求解紊流过渡区内流速,爱因斯坦在公式中加入修正系数χ,本文通过分析经典的尼古拉兹管流试验数据得到了χ的统一表达式。此外,由于Rb″是由床面不平整而产生的,通过分析实测数据,找出了静平整床面以及动平整床面所处的区域,并且求出其表达式,解决了爱因斯坦原始文献中求解Rb″时不能剔除动平整床面的难题,最后,在实测数据的基础之上,得到了Rb″的统一表达式。通过与935组实验数据和40组野外实测数据比较,发现本文摩阻流速模型的计算值与实测摩阻流速值吻合度较好。

Einstein＇s method, namely, the bed hydraulic radius is the sum of two hydraulic radii correspond- ing to grain resistance R′b and bed form resistance R″b , was usually used in engineering for open channel flow with bed forms. A wide range of ks values have been suggested by different researchers when they use the logarithmic equation to calculate R″b. 348 data sets of plane bed data were used for verifying the grain roughness ks, the results showed that the error is minimum when ks = ds0 ; Einstein introduced a correction factorX into the logarithmic velocity equation to obtain the velocity in the transitional regimes, by analyzing Nikuradse＇s pipe flow data, consequently a uniform formula was developed to compute the correction factorX. The bed form resistance related to R″b , resulting from resistance to flow due to the bed configuration. By analyzing the measured data, the area of movable and stationary fiat bed were distinguished to solve the problem that the Einstein＇s method could not solve. An empirical equation for the bed form resistance related radius Rb″ has been developed by analyzing the measured data. Finally, the model for calculating shear velocity was tested against a wide range of measured data and compared with original Einstein model; the results showed that present model got a lower error. Furthermore, the present model was more acceptable physically because R＂b was zero for upper and lower plane bed regimes compared with the original Einstein model.