Limits of temperature separation in a vortex tube

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Abstract
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: (Th-To)/T0or=T0(1-X)( gamma -1/ gamma ), where gamma =1.4 for air, and X=(p0-pc)/p0 is the normalized pressure drop between the inlet (p0) 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.