显式Colebrook-White摩阻系数方程
New Explicit Reformulation of the Colebrook-White Equation
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- 引用格式:
-
苑伟民.显式Colebrook-White摩阻系数方程[J].天然气与石油,2013,31(1):0.doi:
.New Explicit Reformulation of the Colebrook-White Equation[J].Natural Gas and Oil,2013,31(1):0.doi:
- DOI:
- 作者:
- 苑伟民
- 作者单位:
- 中国石化天然气分公司广西液化天然气工程项目部
- 关键词:
- 摩阻系数；Colebrook-White方程；隐式方程；数值方法；迭代方程；显式方程
Friction factor； Colebrook-White equation； Implicit formula； Numerical method； Iterative formula； Explicit formula
- 摘要:
- Colebrook-White方程为计算流体摩阻系数f的隐式方程，使用迭代算法计算耗时长，不方便。为了解决这一问题，采用多个数学软件求解。在使用MATLAB、Mathematica、Maple等数学软件直接求解Colebrook-White方程时，方程的一部分被表示为LambertW函数、Wright Omega函数或ProductLog函数的形式，得到的结果无法直接应用于工程计算，实际应用意义不大。为此，研究数值算法，提出新的迭代方程，推导出了新的适用于所有雷诺数的显式Colebrook-White方程。应用该方程对多个已有的显式Colebrook-White方程进行计算精度和计算时间的对比分析，新方程具有计算时间短、精度高、计算简便的优点。
Colebrook-White equation is commonly used for fluid friction factor calculation and it is an implicit equation of friction factor f and a great deal of time and effort is needed to apply it in actual calculation. Applied is such mathematical software in order to solve this equation as MATLAB， Mathematica and Maple. However， results obtained by the equation can not be applied in engineering calculation. Studied is numerical method， proposed is a new iteration formula， and a new explicit Colebrook-White formula is derived from it and the new one is suitable to all Reynolds numbers. Comparative analysis shows that the new formula has such advantages as short calculation time， high accuracy and easy application.
