Modeling gasodynamic vortex cooling

TL;DR

This paper develops an analytical model of gasodynamic vortex cooling in rotating cylinders, revealing efficiency limitations and conditions under which cooling efficiency can exceed unity due to flow and heat transfer effects.

Contribution

It introduces a thermodynamically consistent, analytical model for vortex cooling that accounts for compressibility, viscosity, and heat conductivity, explaining efficiency limits and potential for super-efficient cooling.

Findings

Efficiency is always less than 1 in inward flow configurations.

Outward radial flow can achieve efficiency greater than 1.

Model qualitatively matches observed vortex cooling effects.

Abstract

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.