LAUSR

Abstract This review will focus on perfect gas models developed to predict the performances of counterflow vortex tubes. It includes empirical and thermodynamics models, models of heat exchangers, models based on a pressure gradient, models based on the momentum transfer with particles spinning inward and models based on unsteady phenomena like the vortex breakdown. A detailed comparison of these models shows that most of them solve the same set of equations but lead to different explanations regarding the flow and heat transfer phenomena within Ranque-Hilsch tubes. The energy balance links the hot and cold flow temperatures for a given cold mass fraction as long as kinetic energy is included in the analysis. Secondly, almost all models consider the radial momentum balance, which reduces to a simple expression linking the pressure gradient and the tangential velocity. Usually, a given velocity profile (forced vortex or Rankine vortex) closes this set of equations. The form of the velocity profile may be dependent on the magnitude of the radial flow. None of the analytical models analyzed in this paper could predict all the geometrical parameters of a vortex tube. Empirical knowledge is still required. However, the pressure difference between the inlet and the cold outlet is a major component. It is related to the pressure drop of the cold air downstream of the vortex tube. To predict the main vortex tube dimensions (diameter and length), the most promising avenue is linked to the occurrence and the good localization of the vortex breakdown inside the tube. This review ends with some future views to improve the predictions of the existing models and the knowledge of the temperature separation phenomenon within vortex tubes.