Formulation for volume flowrate induced by vortex rings, through circular orifice of arbitrary section profile

Abstract

A new theoretical formulation that relates the volume flowrate to the vorticity distribution for the circular orifice of an arbitrary section profile is presented. The formulation is based on axisymmetric potential theory involving Green's function of Stokes' streamfunction. The results showed that the volume flowrate through the orifice opening can be separated into potential and vortical portions, and the kernel of the vortical portion is the homogeneous streamfunction of the orifice. The formulation for the thin circular orifice was verified by comparing analytical solutions. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4791776]