This research concentrates on the swirl motion, and in particular the flow structure which develops under its action, in swirl burner/furnace systems. Although the Reynolds numbers for such systems are usually large and well into the turbulent regime, periodic oscillations and associated instabilities are still prevalent. The predominant coherent structure is the so-called precessing vortex core (PVC) which is a three-dimensional, time-dependent phenomenon. It is helical in shape, twisted against the flow, and precesses around the geometric centre of the system, in the sense of the flow. The aim of this work was to numerically model this instability in a 2MW industrial-size system, under isothermal conditions. A fully three-dimensional, time-dependent model was developed using the CFD (Computational Fluid Dynamics) software FLUENT. This study first presents an overview of publications on vortex breakdown, a similar phenomenon observed initially on delta wings, in order to highlight its significant features. A summary was also made of various recent studies, experimental and theoretical, carried out at Cardiff University, in the same equipment as used in the present work. This review allows a better understanding of the phenomenon and constitutes a basis for further validation of the mathematical model. Numerous flow pattern characteristics have- been predicted, which agree qualitatively with different published studies, such as crescent shaped regions of maximum axial and tangential velocities, off-centred reverse flow zone, and spiralling vortex core. Quantitatively, the agreement is good, in terms of range of velocities and frequency. However, the predicted flow pattern could. not be maintained in time and tended back to axisymmetry, possibly due to numerical diffusion. Grid refinement could not, however, be envisaged due to the practical limits of the available machines. Nevertheless, these results are encouraging and prove that mathematical modelling of these complex flows is a realistic objective.