Semi-empirical turbulence model for numerical simulation of swirled compressible flows observed in Ranque–Hilsch vortex tube

• Modified energy conservation equation for RANS numerical models is proposed.
• The equation considers turbulent heat exchange caused by fluid compressibility.
• Numerical simulation of energy separation effect in a vortex tube was conducted.
• The improved agreement with experimental data was found.
• The proposed numerical model is recommended for the simulation of compressible flows.

This paper presents a three-dimensional numerical model of swirled compressible flow in the Ranque–Hilsch vortex tube. We proposed the modification of the energy conservation equation used in Reynolds Averaged Navier–Stokes (RANS) numerical simulations. While the additional turbulent heat transfer mechanism caused by gas compressibility is taken into account in the proposed equation, it is not applied in standard RANS models. The data were obtained both by standard and proposed energy conservation equations using the k − ε turbulence model. The application of the proposed energy conservation equation was shown to increase the accuracy of static and total temperature distribution prediction. The objective of this paper is the demonstration of the applicability of the new numerical model based on the proposed energy conservation equation after the calibration of empirical coefficients.