计算管内湍动流体摩擦因数的显式新方程  

A New Explicit Equation for Calculating the Friction Factor for the Turbulent Flow in Pipes

作　　者：王勇[1] 阮奇[1] 

机构地区：[1]福州大学化学化工学院,福州350002

出　　处：《中国工程科学》2006年第6期83-88,共6页Strategic Study of CAE

基　　金：福建省教育厅科技基金资助项目(JB03048)

摘　　要：管内湍动流体摩擦因数是雷诺数和相对粗糙度的二元非线性函数,由Colebrook隐式方程计算摩擦因数要用迭代的方法求解,很不方便。为了得到形式简单、精度高的计算摩擦因数的显式方程,提出了二元非线性多项式智能拟合法。该法将二元非线性多项式转化成多元线性多项式并建立线性最小二乘法标准矩阵,用遗传算法结合矩阵法对多项式的项数、项型式项指数及项系数进行搜索得到最优的拟合函数式。用该法拟合了Colebrook方程解的数据,得到一个计算管内湍动流体摩擦因数的显式新方程。在雷诺数3 000≤Re≤108、相对粗糙度0≤e/d≤0.05的范围内,该方程计算结果与Colebrook方程的平均偏差为0.5%,最大偏差不超过1.8%,与实验数据偏差为2.3%。新方程具有形式简单、精度高、适用范围广的优点,且便于简化成光滑管或阻力平方区等情况下的计算摩擦因数的方程。The friction factor for the turbulent flow in pipes is the binary nonlinear function of Reynolds number and relative roughness. Calculating friction factor by implicit Colebrook equation have to use iterative algorithm, which is discommodious. The intelligent fitting method for binary nonlinear polynomials was presented in order to obtain a high precise and simple form explicit equation for calculating the friction factor. The binary nonlinear polynomial was firstly transformed into multivariate linear polynomials, and the least squares standard matrix was established. Then the number, the form, the index and the coefficient of polynomials term were searched to obtain the optimum function by genetic algorithms combined with matrix method. Fitting the data calculated by Colebrook equation with the above method, a new explicit equation for calculating the friction factor for the turbulent flow in pipes was obtained. The new equation can reproduce the Colebrook equation with average deviation of 0.5 % and the maximum deviation of 1.8% in the range of Reynolds number being 3 000 ≤ Re ≤ 10^8 and relative roughness being 0 ≤ e/d ≤ 0.05, and it has an average deviation of 2.3 % to the experimental data. The new equation has the advantages such as simple form, high precise, wide range of application, and can be simplified to the equation for calculating the friction factor in the range of smooth pipe and the rough region easily.

关 键 词：湍动流动 摩擦因数 Colebrook隐式方程 遗传算法 智能拟合法 显式方程 

分 类 号：TQ022.1[化学工程] TQ021