Research on temperature performance prediction of vortex tubes based on artificial neural networks

This study constructs a hybrid neural network model by integrating the physical constraints of theBernoulli equation and Nikolaev's formula. The model is designed to explore and predict the variationpattern of the cold end temperature in a vortex tube. The input parameters include inlet pressure, inlettemperature, and cold mass fraction, with the cold end temperature as the output parameter. Thenetwork employs a multilayer feedforward model and the Levenberg-Marquardt learning algorithm,using a hyperbolic tangent function as the activation function. To evaluate the statistical validity of thedeveloped model, the coefficient of determination(R2)and root mean square error(RMSE)areutilized, along with an analysis of the model's uncertainty and robustness. The hybrid model achievesan R2of 0.9936 and an RMSE of 0.3392, demonstrating strong performance in terms of uncertaintyand robustness. These results indicate that the model accurately predicts the cold end temperaturevariation in the vortex tube. Furthermore, thefindings reveal an optimal pressure range(0.49 MPa to0.76 MPa)and cold mass fraction range(0.1 to 0.2)that minimize the cold end temperature.