The application of a mathematical model for the simulation of thermal separation in a Ranque-Hilsch vortex tube is presented in this paper. The modelling of turbulence for compressible, swirling flows used in the simulation is discussed. The work has been carried out in order to provide an understanding of the physical behaviors of the flow, pressure, temperature in a vortex tube. A staggered finite volume approach with the standard kappa-epsilon turbulence model and an algebraic stress model (ASM) is used to carry out all the computations. To investigate the effects of numerical diffusion on the predicted results, the second-order upwind (SOU) and the QUICK numerical schemes are used and compared with the first-order upwind and the hybrid schemes. The computations show that the differences of results obtained from using the various schemes are marginal. In addition, results predicted by both turbulence models generally are in good agreement with measurements but the ASM performs better agreement between the numerical results and experimental data. The computations with selective source terms of the energy equation suppressed show that the diffusive transport of mean kinetic energy has a substantial influence on the maximum temperature separation occurring near the inlet region. In the downstream region far from the inlet, expansion effects and the stress generation with its gradient transport are also significant. (c) 2006 Elsevier Ltd. All rights reserved.