Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article

Degree

Doctor of Philosophy

Program

Mechanical and Materials Engineering

Supervisor

Straatman, Anthony G.

Abstract

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.

Summary for Lay Audience

The Ranque-Hilsch Vortex Tube (RHVT) is a device that behaves in an unexpected way: if a source of compressed air (such as an air hose used to pressurize tires at a gas station) is attached to the inlet of this tube, the air going through it will swirl and form a vortex. The air exits the tube from two openings: cold air from the center of the vortex exhausts through a small hole at one end, and hot air exhausts from a circular gap at the other end of the tube. This process is called temperature separation. Many researchers have proposed theories explaining why temperature separation happens, but there is no consensus yet. This thesis contains three articles which help predict the flow patterns and temperatures inside the RHVT, which are used to test the popular temperature separation theories.

In the first article, a different, simpler problem is studied: a source of compressed air is attached to one end of a small tube, while the opposite end of the tube rotates about an axis. The analysis reveals the air moving down the tube towards the axis cools along the way, and the energy lost from cooling contributes to spinning the tube faster about its axis of rotation.

In the second article, the mathematical equations that describe fluid motion are solved using a new technique, and in one case, the flow pattern is similar to the flow inside the RHVT.

Finally, the last article describes three studies using computer simulations to model the air flow inside the RHVT. It was found that simulation results matched experimental results well when the amount of air going into and out of the tube was fixed, and that 2D simulation results are accurate when the angle of the flow entering the tube is determined using the results of a 3D simulation. In this last work, evidence is found to support the hypothesis that the cooling happens inside the RHVT because of friction between layers of air spinning at different speeds.

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