VORTEX SINKS WITH AXIAL-FLOW - SOLUTION AND APPLICATIONS

In this paper we develop a new class of analytical solutions of the Na vier-Stokes equations and suggest ways to predict and control complex swirling flows. We consider vortex sinks on curved axisymmetric surfac es with an axial flow and obtain a five-parameter solution family that describes a large variety of flow patterns and models fluid motion in a cylindrical can, whirlpools, tornadoes, and cosmic swirling jets. T he singularity of these solutions on the flow axis is removed by match ing them with swirling jets. The resulting composite solutions describ e flows, consisting of up to seven separation regions (recirculatory ' 'bubbles'' and vortex rings), and model flows in the Ranque-Hilsch tub e, in the meniscus of electrosprays, in vortex breakdown, and in an in dustrial vortex burner. The analytical solutions allow a clear underst anding of how different control parameters affect the flow and guide s election of optimal parameter values for desired flow features. The ap proach permits extension to swirling flows with heat transfer and chem ical reaction, and have the potential of being significantly useful fo r further detailed investigation by direct or large-eddy numerical sim ulations as well as laboratory experimentation. (C) 1997 American Inst itute of Physics.