Analytical and Computational Modelling of the Ranque-Hilsch Vortex Tube

The Ranque-Hilsch vortex tube (RHVT) is a simple mechanical device with no moving parts capable of separating a supply of compressed fluid into hot and cold streams through a process called temperature separation. The overall aim is to develop models which can be used to assess the temperature separation mechanisms in the RHVT, leading to a better overall understanding of the underlying physics. The introductory chapter contains a thermodynamic analysis and introduction to the flow physics, alongside three miniature literature reviews and critiques identifying research gaps. The body of the thesis contains three articles. The first article studies the flow of a perfect, inviscid gas through a duct, which rotates about an axis perpendicular to the direction of the duct. The analysis shows that gas flowing towards the center of rotation will cool while delivering energy to increase or maintain the angular momentum of the entire system. The study further generalizes the results to a duct with an arbitrarily varying cross-sectional area and arbitrary path through 3D space, yielding similar results. In the second article, a new technique for obtaining exact solutions to the Navier-Stokes equations is developed, and many new solutions are presented; most notably, a new solution describing a flow strongly resembling flow inside the RHVT. The third article contains three computational fluid dynamics studies of the RHVT; (1) testing the influence of different hydrodynamic boundary condition types and boundary condition locations on temperature separation, (2) examining the influence of four different turbulence models on temperature separation and energy transfer modes, and (3) examining the influence of the axisymmetric assumption using a novel method for computing the fluid injection angle. It was found that the assumptions made elsewhere in the literature are validated, although using mass-flow boundary conditions is preferred where possible, the choice of turbulence model strongly influences the temperature separation and the flow structure. The results herein indicate shear work transfer is the dominant energy transfer mechanism in the RHVT