Limits of temperature separation in a vortex tube

The heating and cooling in a vortex tube is attributed to conversion of kinetic energy into heat and to the reverse process. A two-component model yields the upper limit for the temperature increase on the hot side: (T h -To)/T 0 or=T 0 (1-X) ( gamma -1 / gamma ), where gamma =1.4 for air, and X=(p 0 -p c )/p 0 is the normalized pressure drop between the inlet (p 0 ) and the cold exhaust port (Pc) Extensive experimental data for a vortex tube of 18 mm inner diameter with working fluid air all fall between these limits. The model predicts that the inlet velocity reaches the speed of sound for X=0.7. No values X>0.7 could be obtained in these experiments, indicating that the flow always remain subsonic.