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Modeling gasodynamic vortex cooling

A. E. Allahverdyan1 and S. Fauve2

  • 1Yerevan Physics Institute, 2 Alikhanian Brothers Street, 375036 Yerevan, Armenia
  • 2Laboratoire de Physique Statistique, École Normale Supérieure, PSL Research University; UPMC, Sorbonne Universités; Université Paris Diderot, Sorbonne Paris-Cité; and CNRS, 24 Rue Lhomond, 75005 Paris, France

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Phys. Rev. Fluids 2, 084102 – Published 23 August, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.084102

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 an angular plus radial flow between two (coaxial) 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, in terms of both temperature and the 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 lowest temperature actually reached. We show that for the vortex cooling the efficiency is strictly smaller than 1, but in another configuration with an outward radial flow, we find that the efficiency can be larger than 1. This is related to both the geometry and the finite heat conductivity.

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Phys. Rev. Fluids 2, 084102– Published 23 August, 2017
  • Received 1 March 2017

©2017 American Physical Society

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