An Investigation of Confined Vortex Flow Phenomena

Abstract

The swirling, incompressible flow within a short vortex chamber of aspect ratio 1/9, defined by the ratio of chamber height to chamber diameter, has been investigated analytically. The theoretical analysis consists of the adaptation of Wormley’s analytical technique and the extension of the method to include the apparent viscosity factor. The Runge-Kutta method is used to solve numerically the set of differential equations. The analytical results are compared with those of the experimental investigations conducted by Savino and Keshock. The analytical results prove that the values of apparent viscosity seriously affect the velocity profiles within the vortex chamber. The results also show that the apparent viscosity varies from 7000μ at the vortex chamber periphery to 4500μ at the orifice exit plane, where μ is the operating fluid viscosity. An empirical expression for the apparent viscosity is found in the form μa = K1 νδn + K2 , where n, K1 , and K2 are constants and νδ is the tangential velocity. The constants n, K1 , and K2 are found to be −1/3, 0.01, and 0.0005, respectively, for this investigation.