Research on the prediction model of energy separation effect of vortex tube based on trajectory deflection characteristics and its numerical solution method

Abstract

In this paper, in order to establish the energy separation mechanism of the vortex tube, the hydrodynamic behavior of the compressible fluid in the asymmetric cavity space is investigated, and a numerical model of the trajectory deflection behavior is deduced and established; in order to form the optimal design method of the structural parameters of the vortex tube, the force situation of the fluid microelements entering different regions of the vortex chamber of the vortex tube is analyzed, and the trajectory deflection equations are corrected by combining with the expansion behavior of the fluid and the characterizing equations of vortex strength, transportability, and vortex initiation characteristics are given. The characterization equations of vortex strength, transportability and vortex initiation characteristics are given, and the numerical simulation of their influence parameters is carried out; in order to realize the prediction of the vortex tube performance of a given structure, the multifactor Pearson thermodynamic map is used to correlate and analyze the experimental data of vortex tubes reported publicly in the past years, and the polynomial regression equations are designed and established for the prediction of the vortex tube's energy separation effect and the confidence level and the degree of coincidence of the prediction results are examined. The confidence level and degree of agreement of the prediction results were examined. It is found that: the trajectory deflection motion of the compressible fluid in the asymmetric cavity space is the result of the combined effect of structural air pressure bias and the expansion behavior of the incident fluid; in order to improve the vortex strength in the vortex tube, the vortex initiation chamber space should be as small as possible; the increase of the diameters of the hot-end pipe and the cold-end pipe is conducive to the enhancement of vortex strength, but at the same time, it weakens the vortex transport in the heat pipe; the vortex initiation chamber size has a negative correlation with the hot-end temperature rise, and the inlet fluid pressure has a The negative correlation between the size of the vortex chamber and the temperature rise at the hot end, the positive correlation between the increase of inlet fluid pressure and the resulting temperature rise, and the strong correlation between the inlet fluid pressure and the friction coefficient on the effect of energy separation; the predictive equations for the effect of energy separation obtained by the fitting are in good agreement with the real situation.