Analytical investigation on energy separation in Ranque-Hilsch vortex tube

A vortex tube is a simple device with no moving parts that has the inherent capability of separating the high pressure inlet stream into two low pressure outlet streams. One of the outlet streams is the peripheral stream that has higher temperature than the inlet while the other outlet stream is the inner or core stream that has temperature lower than the inlet. Various theories have been put forwarded by many investigators to explain the mechanism of this temperature separation in vortex tube. This article deals with the analytical approach to calculate the amount of heat transfer between the core and the peripheral streams. In the process, we have established an empirical relationship between the length of the vortex tube and the surface that divides the cold and the hot flows, proceeding in the opposite directions through the tube. We have also derived the dependence of heat transfer on the length of the vortex tube keeping the diameter of the vortex tube constant. The necessary boundary conditions needed for the analysis are obtained from CFD analysis.