Purpose

The purpose of this paper is the numerical investigation of the friction laws for incompressible flow in undulated channels, with emphasis on the applicability of the hydraulic diameter concept. A focal point of the study is the derivation of correlations to increase the accuracy of the hydraulic diameter approach.

Design/methodology/approach

Calculations are performed for laminar and turbulent flow, for Reynolds number ranges between 10–2,000 and 5,000–100,000. For turbulent flow, the shear stress transport (SST) model is used. A simple, sawtooth-like undulation shape is considered, where the channel geometry can be described by means of three length parameters. Letting each to take three values, totally 27 geometries are analyzed.

Findings

It is observed that the hydraulic diameter concept applied via analytical or empirical expressions to obtain friction coefficients does not lead to accurate results. For laminar flow, the maximum deviations of analytical values from predicted are about 70%, while 20% deviation is observed on average. For turbulent flow, deviations of Blasius correlation from predicted ones are smaller, but still remarkable with about 20% for maximum deviation and about 10% on average.

Originality/value

Applicability of the hydraulic diameter concept to undulated channels was not computationally explored. A further original ingredient of the work is the derivation of correlations that lead to improved accuracy in calculating the friction coefficient using hydraulic diameter. For laminar flow, the maximum and average deviations of present correlations from numerical predictions are below 5% and 2%, respectively. For turbulent flow, these numbers turn out to be approximately 12% for the maximum deviation and about 2% for the average.

中文翻译：

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波纹状通道内层流和湍流摩擦定律的数值研究

目的

本文的目的是对波动通道中不可压缩流动的摩擦定律进行数值研究，重点是水力直径概念的适用性。研究的重点是相关性的推导，以提高液压直径方法的准确性。

设计/方法/方法

对于层流和湍流进行计算，雷诺数范围在10–2,000到5,000–100,000之间。对于湍流，使用剪切应力传输（SST）模型。考虑一种简单的锯齿状起伏形状，其中通道的几何形状可以通过三个长度参数来描述。让每个取三个值，总共分析了27个几何。

发现

可以看出，通过解析或经验表达式应用水力直径概念以获得摩擦系数并不能得出准确的结果。对于层流，分析值与预测值的最大偏差约为70％，而平均观察到的偏差为20％。对于湍流，Blasius相关性与预测值之间的偏差较小，但仍然很明显，最大偏差约为20％，平均约为10％。

创意/价值

水力直径概念在起伏通道中的适用性尚未在计算上进行探讨。这项工作的另一个原始要素是相关性的推导，这导致使用水力直径计算摩擦系数时提高了精度。对于层流，当前相关性与数值预测的最大偏差和平均偏差分别低于5％和2％。对于湍流，这些数字最大偏差约为12％，平均偏差约为2％。