A model for velocity and eddy diffusivity distributions in fully turbulent pipe flow

TLDR: In this paper, a model for the eddy diffusivity and mean velocity distributions in fully developed turbulent isothermal smooth pipe flow (4 x lo3 < Re < 5 x 10').

Abstract: A model was developed for the eddy diffusivity and mean velocity distributions in fully developed turbulent isothermal smooth pipe flow (4 x lo3 < Re < 5 x 10'). Reichardt's tworegion eddy diffusivity models were modified so as to fulfill the requirements that the eddy diffusivity be represented by a smooth, continuous curve, and vanish with the third power of the distance from the wall; the continuity equation be satisfied; and the ratio of the bulk velocity to centerline velocity agree with experimental data. The descripition is in excellent agreement with Laufer's experimental mean velocity data and, in general, provides a method of accurately predicting the mean velocity distribution. n turbulent flow, the instantaneous flow properties I are normally expressed as the sum of a time-averaged component and a fluctuating component. In an effort to provide engineering solutions to problems involving turbulent processes, which are difficult to describe on a mechanistic basis, the eddy diffusivity concept has been widely used to provide models for the fluctuating motion'". Unfortunately, the eddy diffusivity of momentum, a major parameter in most models, has not been well described in a manner consistent with the boundary conditions and available experimental data'a'. An objective of this work is, therefore, to generate an expression for the eddy diffusivity which will be compatible with both the boundary conditions and experimental data. A second concurrent objective is the development of a consistent expression for the mean velocity distribution. The approach used involves the iterative solution of mutually dependent expressions for the velocity distribution and eddy diffusivity in response to experimental and analytical constraints, in order to develop the most consistent over-all picture. Although an incompressible constant property fluid in fully-developed pipe flow is assumed in the model, such assumptions are often made in initial, idealized analyses of practical systems.