Physics and mathematics model of vortex tube working process

Abstract

Based on the physical model of the Ranque effect, proposed earlier, a simplified mathematical model of the working process
of a vortex tube is compiled taking into account the exchange of work and heat during the interaction of peripheral and axial gas flows. The effect of viscosity and angular velocity gradient on the transfer of kinetic energy from the axis to the periphery is shown. The difference in thermodynamic temperatures when heat is supplied from the periphery to the axis is taken into account, which leads to a decrease in the cooling efficiency of the axial gas flow. Energy exchange is based on the assumption that the peripheral gas layers are compressed by the axial flow. The axial flow work is determined by the pressure difference between the valve and the outlet of the diaphragm.