Abstract
The aim of this study is to evaluate a three-equation turbulence model applied to pipe flow. Uncertainty is approximated by comparing with published direct numerical simulation results for fully-developed average pipe flow. The model is based on the Reynolds averaged Navier-Stokes equations. Boussinesq hypothesis is invoked for determining the Reynolds stresses. Three local length scales are solved, based on which the eddy viscosity is calculated. There are two parameters in the model; one accounts for surface roughness and the other is possibly attributed to the fluid. Error in the mean axial velocity and Reynolds stress is found to be negligible.
Highlights
The problem of turbulence dates back to the days of Claude-Louis Navier and George Gabriel Stokes, as well as others in the early nineteenth century
Along with direct numerical simulation (DNS) results of Wu and Moin [4], predicted mean velocity and Reynolds stress distributions are depicted in Figures 3 and 4, respectively for Reynolds number of 44,000
The agreement is excellent in all regions, including the laminar sub-layer and buffer and outer layers
Summary
The problem of turbulence dates back to the days of Claude-Louis Navier and George Gabriel Stokes, as well as others in the early nineteenth century. Direct numerical simulation (DNS) has emerged as an indispensible tool to tackle turbulence directly, albeit at relatively low Reynolds numbers. Several DNS studies on turbulent flow have been performed recently, including Eggels et al [2], Loulou et al [3], and Wu and Moin [4]. The latter has carried out DNS on a turbulent pipe flow at Reynolds number of 44,000, which is the largest among the three studies. Reynolds stresses, and turbulent intensities were presented and discussed, along with visualization of flow structure. Good agreement was attained with the Princeton Superpipe data on mean flow statistics and Lawn’s [5]
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