On the mixing of axi-symmetric ducted jets

Abstract

Because of practical application to jet pumps, ejectors, furnaces and similar devices, the turbulent discharge of a round jet into a coaxial duct and the mixing patterns in the various regions into which the flow may be divided, are of considerable interest. In this paper the mixing of an incompressible jet with a similar fluid in a cylindrical tube is considered up to the plane which marks the disappearance of potential flow. Under the assumption of similarity of velocity profile and with neglect of the wall boundary layer and nozzle wake, the continuity and momentum equations, in integral form, are solved for the velocities and mixing region radii at any given section. Prandtl's momentum transfer hypothesis may be used to determine the dependence of these on distance downstream. By examining the various flow regimes in detail this analysis is formally able to cover ratios of primary to secondary flow velocities of from one to infinity and, similarly, all ratios of duct to nozzle diameters, thereby extending earlier investigations. It also corrects work on similar basis in which inappropriate linearisations were made. The ‘exact’ results constitute a basis from which extension to include additional effects may be made.