Linearized Theory of Three-Dimensional Jet Mixing With and Without Walls

Abstract

The laminar jet mixing of an incompressible and viscous fluid issuing from a nozzle of rectangular cross section into a uniform stream has been studied theoretically. When the jet velocity deviates slightly from that of free stream, exact solutions have been obtained. Three different cases have been discussed. First is the three-dimensional jet in an infinite domain of uniform stream. Second is the three-dimensional jet in a finite domain of uniform flow bounded by parallel walls, and third is the three-dimensional jet with adjoining parallel walls and axial pressure gradient. The following main results are obtained: (a) The rate of decrease of maximum velocity in the jet decreases as the aspect ratio of the nozzle increases for a given jet velocity. (b) The spread of the jet is different along different directions and the cross section of the jet tends to be circular far downstream from the nozzle. (c) The adjoining walls would increase the velocity in the jet, and (d) favorable axial pressure gradient increases the velocity in the jet. Numerical results for various cases are presented.