Modeling gasodynamic vortex cooling

We aim at studying gasodynamic vortex cooling in an analytically solvable, thermodynamically consistent model that can explain limitations on the cooling efficiency. To this end, we study a angular plus radial flow between two (co-axial) rotating permeable cylinders. Full account is taken of compressibility, viscosity and heat conductivity. For a weak inward radial flow the model qualitatively describes the vortex cooling effect|both in terms of temperature and of decrease of the stagnation enthalpy|seen in short uniflow vortex (Ranque) tubes. The cooling does not result from external work, and its efficiency is defined as the ratio of the lowest temperature reached adiabatically (for the given pressure gradient) to the actually reached lowest temperature. We show that for the vortex cooling the efficiency is strictly smaller than 1, but in another configuration with an outward radial flow, we found that the efficiency can be larger than 1. This is related to both the geometry and the finite heat conductivity.