Numerical Analysis of an Axisymmetric Jet Using a Streamline Coordinate System

Abstract

The complete equations which describe a viscous axisyrnmetric flow are formulated using a streamline coordinate system (φ, ψ), where ψ is the stream function. The independent variable φ is constant along the orthogonal trajectories of streamlines in a plane including a symmetric axis. The axisymmetric laminar jet leaving a Poiseuille tube into an inviscid outer fluid phase is solved numerically using parabolic differential equations which are simplified by a boundary-layer type analysis. The prediction of the velocity distributions and shape of the free surface profile, under the influence of both gravity and surface tension, is undertaken. The results obtained by the present method are found to agree very closely with experimental results. The behaviour of a laminar jet issuing from a convergent nozzle is also investigated by the same method.