管道内流动阻力系数的尼古拉兹公式迭代计算收敛区间研究

Research on the Convergence of Iterative Calculation of Flow Resistance Coefficient in Energy Transportation Pipeline

计算管道内流动阻力系数的尼古拉兹公式是以隐函数形式给出的,不能利用此公式直接计算出阻力系数,必须采用迭代算法。但是关于"迭代初值应如何选取才能保证迭代是收敛的"这一问题,迄今为止没有明确结论。为解决此问题,以"数值分析"理论中关于迭代收敛的定义为依据,分析了迭代函数的单调性,并利用连续函数的拉格朗日中值定理,证明了当迭代初值选取在普通能源输送管道阻力系数的范围内时,迭代总是收敛的。给出了收敛区间。此项研究结果为尼古拉兹公式的应用提供了完备的理论依据。

The Nikuradse formula which was used to calculate flow resistance coefficient in pipeline was given in the forms of implicit function, the flow resistance coefficient could not directly be calculated by means of this formula and might adopt the iterative algorithm. But so far there has been no clear conclusion about how to choose the initial value of iteration in order to guarantee the convergence of the iteration. In order to solve this problem, according to the definition of the convergence of the iteration in the numerical analysis theory, analyzes the iterative function monotonieity, and makes use of Lagrange mean value theorem on continuous function, proves that when the iterative initial value is selected in the range of resistance coefficient of ordinary energy transportation pipeline the iteration is always convergent. The convergence interval is given. The results of this research provide Nikuradse formula application with complete theory basis.