Validation of the Modified k − ε Turbulence Model for Conical Vortex Tubes Accounting for Compressibility Effects

The problem of numerical simulation of Ranque-Hilsch energy separation in a vortex tube is considered in the paper. The standard (Formula presented.) turbulence model is modified to incorporate the fluid compressibility effect. In particular, the regular heat flows due to momentum exchange and turbulent thermal conductivity are complemented by the additional heat flow due to fluid compressibility. The new closure constant (Formula presented.) is introduced to the model for the first time for balancing heat flows. Careful calibration of the model suggested the recommended value (Formula presented.) which provides the best turbulence model accuracy in terms of the integral characteristics of the conical vortex tubes. The given value of (Formula presented.) is interpreted as a deviation of the gas compression from the adiabatic process with a polytropic index of (Formula presented.) It is demonstrated that turbulent thermal conductivity is dominant in the standard (Formula presented.) turbulence model, while heat flow due to fluid compressibility dominates in the modified model. Such redistribution of heat flows is considered to be the main reason for the improvement of the energy separation effect prediction when comparing the modified and standard turbulence models. Nevertheless, the universality of the modified turbulence model is still not guaranteed.