Unsteady, viscous, circular flow Part 3. Application to the Ranque-Hilsch vortex tube

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Abstract
A new explanation of the vortex tube is presented. The proposed model leads to an equivalent unsteady-flow analysis for the development of the flow in the vortex tube. Using this analysis, radial distributions of velocity and temperature can now be calculated at successive axial positions in the tube. Many characteristics of these calculated profiles are found to be in qualitative agreement with corresponding experimental profiles. The qualitative similarity in the development of the calculated and experimental sets profiles with axial position is considered especially significant.A theory of vortex-tube performance based upon an idealized three-dimensional flow pattern for the vortex tube is derived. Some experiments relating the idealized vortex tube analysed to previous vortex-tube measurements are described. The performance curves obtained from the theory resemble those measured. An important additional effect predicted by the theory is that both the hot and the cold temperature differences should increase as the effective height of the inlet nozzle increases, and this result has been substantiated by experiment.