Unified Wall Function and Application for Steady Turbulent Pipe Flow with Uniform Wall Roughness

Abstract

A newly developed wall function for the velocity-profile of steady turbulent flow in various hydraulic regimes near rough walls was created. The wall function was then applied into two approaches to obtain the total flow energy loss (mechanical energy loss) of turbulent pipe flow. The energy loss values calculated through the above two approaches both predicted the experimental results well. The energy loss coefficient calculated through the second approach gave a more precise definition of the total flow characteristics than the Manning roughness coefficient as it was proved to be a function of the field statistics. It was furtherly found that this energy loss can be decomposed into the energy loss due to dissipation caused by molecular viscosity and the dissipation of turbulent kinetic energy, and that its density distribution falls mainly into the near-wall region.