Theoretical analysis of the compressible flow in Ranque–Hilsch vortex tube

The Ranque–Hilsch vortex tube is a widely adopted fluidic thermal separation device. Existing theoretical models lack the integrity needed to consistently predict the characteristics of vortex tube swirl flow. The present study introduces an integrated theoretical model specifically designed for the vortex tube swirl flow field. Accuracy of the model is validated through reliable computational predictions from previous research, demonstrating its capability to calculate fluid properties under maximum thermal separation conditions. The empirical correlations and energy equation are assigned for enabling the model to calculate the change in fluid properties by the thermal separation and internal friction. However, a significant limitation of the model is its inability to account for variations in cold exit mass fractions. While the model can accurately predict most fluid properties, it shows a deviation of 16%–26% when calculating temperature at the central axis, highlighting some inherent limitations. The exergy analysis comprehends the utility of the newly developed model in optimizing vortex tube design tailored to specific applications with an overall efficiency of 47%. Furthermore, the model is tested for predicting flow properties in vortex tubes for synthesizing hydrogen-enriched slush-liquefied natural gas. The current study acknowledges limitations of the model in calculating the multi-phase flow of a real gas like methane. This prompts considerations for future enhancements of the theoretical model to incorporate the cold mass fraction effects and phase-change phenomenon of real gases.