用分形几何理论研究圆管糙率及其实用意义

在已有紊流阻力定律与试验研究基础上,分析了当量糙率KS在计算紊流沿程阻力损失中的重要作用,以及我国水利工程沿程阻力损失计算和工程应用现状。以圆管内壁糙率为例,用分形几何理论研究了圆管糙率的分形特征,给出了圆管糙率分数维的数学模型和算例。论证了圆管糙率分数维和当量糙率KS的关系,分别讨论了管道纵、横向糙率分数维的计算方法,提供了将前人所建立的紊流阻力定律与试验结果直接用于工程实际的途径。

Investigating the circle pipe's roughness with the fractal geometry theory and the practical application

The author analyzes the important effects of equivalent roughness K_S in calculating the friction losses of turbulent flow, based on the existing theoretical and experimental research achievements of resistance laws, as well as depicts the situation of calculating the friction losses and applicationin China''s hydraulic engineering. For the case of circle pipe''s roughness,the author researches on the fractal characteristics of roughness of pipe''s inner wall with the fractal geometry theory, and gives the mathematical model of the fractal dimension and numerical examples. The author also demonstrates the relationship between the fractal dimension and equivalent roughness K_S, the calculation methods of fractal dimension of pipe roughness in longitudinal and transverse are discussed respectively, then gives way to apply the turbulent resistance laws and research achievements provided by the former to engineering practice directly.