Flow in the Initial Region of Axisymmetric Turbulent Jets

Abstract

In the initial region of axisymmetric turbulent jets a core of uniform velocity is assumed to exist, bounded by an annular free shear layer. An empirical model for axial mean velocity is found from experimental measurements using a length scale which forces self-preservation in the central part of the free shear layer. This model is applied to the integral form of the momentum and energy equations, subject to the boundary layer simplifications, to obtain an approximate solution for the development of jets where the thickness of the mixing layer at the nozzle exit is assumed negligible. The differential form of momentum and continuity equations are also solved by a finite difference technique of DuFort-Frankel type using a typical boundary layer type of velocity profile at the exit of the nozzle. The results of this method are compared with those of the empirical velocity method, and the present and existing experimental results. Prandtl’s mixing length is shown to be a slightly nonlinear function of the axial distance and is used to define the eddy diffusivity for this region.