Comparative study of exergy and grey relational analyses for cascade and single counterflow Ranque-Hilsch vortex tubes

Abstract In this study, the exergy analysis and second law efficiency of two separate experimental vortex tubes, one single and the other cascade-connected, were calculated and evaluated independently. This experimental study was conducted for the first time in the literature to validate the hypothesis that a cascade-connected vortex tube would exhibit superior second-law efficiency and lower exergy losses compared to a single vortex tube. Air was used as the pressurized fluid in the vortex tubes of the experimental systems. Moreover, grey relational analysis was utilized to analyze complex multi-response systems. Based on the results, a comparison of the exergy analyses for the cascade counterflow vortex tube and the single counterflow vortex tube revealed that, at a pressure of 650 kPa, the cascade counterflow Ranque-Hilsch vortex tube (CRHVT) with five brass nozzles exhibited an exergy loss of 44.57 kJkg −1 . Additionally, the CRHVT with five brass nozzles achieved the highest second law efficiency among the two systems, approximately 71%, at the same pressure. The findings from the grey relational analysis further demonstrated that the cascade counterflow vortex tube with five brass nozzles exhibited the best system performance. At a pressure of 650 kPa, the second law efficiency of this configuration was approximately 10% higher than that of the single counterflow Ranque-Hilsch vortex tube (SRHVT) under identical experimental conditions.