Explainable surrogate modeling for predicting temperature separation performance of the vortex tube

A vortex tube is a device that separates compressed air at ambient temperature into cold and hot air. Compared to other air conditioning devices, it has a more straightforward structure and does not require a separate power source, making it widely used in various industrial fields. Numerous studies have proposed a data-driven surrogate model to predict the temperature at an outlet. These data-driven models are a narrow model that is suitable for the specific device. Furthermore, due to the complex internal flow field within the vortex tube, no theoretical formula has been established to explain the temperature separation phenomenon. Therefore, this study aims to develop a general surrogate model for predicting the performance of the vortex tube using symbolic regression, a representative white-box machine learning model. A white-box machine learning model is one that allows users to understand how it was able to produce its output. Non-dimensionalization is applied to ensure unit consistency across the symbolic regression and to enhance the generalizability of the surrogate model. This study also introduces genetic programming permutation importance (GPPI), a variable selection method designed to prevent model overfitting. An intuitive surrogate model are created using the cold outlet orifice hold diameter, cold mass fraction, pressure ratio, nozzle area ratio, and tube aspect ratio from counter-flow vortex tube and it was verified with new experimental data. The existing black box model was suitable only for specific experiments, However, the proposed white-box model demonstrated suitability for new experimental data, achieving a maximum performance of R 2 = 0.8625.