Adaptive Neuro-Fuzzy Inference System Models to Predict the Energy Separation Procedure in Vortex Tube Using Desirability Function

The vortex tube is one of the widely used cooling systems in the industry. Investigating the effect of all input variables on the outlet cold temperature difference in laboratory state is time-consuming and costly. To this purpose, in the current study, attempts were made to model and predict the effect of all input variables on the outlet cold temperature difference of air and inlet air using adaptive neuro-fuzzy inference system (ANFIS) method. The ANFIS method was designed with three structures of fuzzy inference systems called subtractive clustering (SC) algorithm, fuzzy c-means (FCM), and grid partition (GP) with four types of input membership functions including trimf, gaussmf, gbellmf, and pimf. For model training and testing, 326 laboratory data were used. The developed models were compared using statistical parameters of correlation coefficient, mean absolute relative deviation, standard deviation, and root mean square error (RMSD) together with general desirability function. The results showed that GP algorithm with input pimf membership function with the greatest value of correlation coefficient (0.9975) and lowest value of RMSD for test data (0.4199) and general desirability function value of 0.71 is the best method to predict outlet cold temperature difference. Using the above-mentioned method, the most optimum state of vortex tube performance for industrial applications was found to be the use of 3 or 6 nozzels, at the pressure range of 0.55 to 0.6MPa and the nozzle angle of 20 to30 degrees, and for laboratory applications was obtained to be the use of 6 nozzles, at the pressure range of 0.55 to 0.6MPa, and the nozzle angle of 25 to 35 degrees.