This work was aimed at gaining understanding of the physical behaviours of the flow and temperature separation process in a vortex tube. To investigate the cold mass fraction’s effect on the temperature separation, the numerical calculation was carried out using an algebraic Reynolds stress model (ASM) and the standard k-ε model. The modelling of turbulence of com-pressible, complex flows used in the simulation is discussed. Emphasis is given to the derivation of the ASM for 2D axisymmet-rical flows, particularly to the model constants in the algebraic Reynolds stress equations. The TEFESS code, based on a staggered Finite Volume approach with the standard k-ε model and first-order numerical schemes, was used to carry out all the computations. The predicted results for strongly swirling turbulent compressible flow in a vortex tube suggested that the use of the ASM leads to better agreement between the numerical results and experimental data, while the k-ε model cannot capture the stabilizing effect of the swirl. This work was aimed at gaining understanding of the physical behaviors of the flow and temperature separation process in a vortex tube. The numerical calculation was carried out using an algebraic Reynolds stress model (ASM) and the standard k-ε model. The modeling of turbulence of com-pressible, complex flows used in the simulation is discussed. Emphasis is given to the derivation of the ASM for 2D axisymmet-rical flows, particularly to the model constants in the algebraic The TEFESS code, based on a staggered Finite Volume approach with the standard k-ε model and first-order numerical schemes, was used to carry out all the computations. The predicted results for strongly swirling turbulent compressible flow in a vortex tube suggested that the use of the ASM leads to better agreement between the numerical results and experimental data, while the k-ε model can not capture the stabilizing effect of the swirl.