任意带角断面通道紊流摩擦阻力的理论解

Theoretical Analysis of Turbulent Flow Frictional Resistance Inside Ducts of Arbitrary Angular Cross Sections

对带角断面通道紊流,用水力直径作为当量直径来计算壁平均摩擦系数将带来偏差。偏差多大,目前学术界只对一些具体断面做过试验,无通用公式。本文将带角断面的角区看做是无角断面的附加,分析并计算角区层流区的大小,定量的确定水力直径做为当量直径的偏差大小,从而导出了任意带角断面通道紊流摩擦系数的计算公式。该公式为通用公式,适用于断面带任意多个角,角度任意大小,即适用于任意带角断面,且形式简单,计算结果附合物理机理和试验结论。

It is recognized that for turbulent flow inside a duct of angular cross section, delation will take place if the flow diameter is used as the equivalent diameter to calculate the mean friction coefficient of the duct wall. It remains still a question of defining the extent of such deviation as no common formula is available now and only few cross sections have been tested. This paper presents an approach which takes the angle area of the angular cross section as an addition to the angle-less circular cross section, calculates and studies the size of laminal flow area of the angle area, quantifies the amount of deviation of using flow diameter as the equivalent diameter and finally obtains the formula for calculating the turbulent flow friction coefficients of the ducts of arbitrary angular cross sections. The formula such derived has the common-use nature and so is applicable to cross sections with arbitrary number of angles and arbitrary forms of angles, i. e. arbitrary angular cross sections. Experience shows it is easy to use and the result obtained by using this formula has a good agreement with physical mechanism and test measurements.