Physics and mathematics model of vortex tube working process

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

Similarities and differences between working processes of Ranque effect and Hartmann–Sprenger tube

The physical and mathematical models of the processes occurring in the vortex tubes (Ranque effect) and Hartmann–Sprenger tube. The physical models most closely corresponding to the physical processes in these devices have been identified. The similarities and differences between the effects arising during the operation of vortex tubes and the Hartmann–Sprenger tube are found. The proof of the influence of viscosity on the Ranque effect and the interaction of gases in the Hartmann–Sprenger tube is given. Regularities of changes in total pressure and total temperature in a vortex tube and a Hartmann–Sprenger tube are given. The factors influencing the energy exchange in the vortex tube and the Hartmann–Sprenger tube are determined. The influence of the exchange of work and heat on the Ranque effect and the Hartmann–Sprenger tube is revealed. The mechanism of energy transfer between gas layers in a vortex tube and in a dead-end Hartmann– Sprenger cavity is found