Journal of
Mechanical Engineering Research

  • Abbreviation: J. Mech. Eng. Res.
  • Language: English
  • ISSN: 2141-2383
  • DOI: 10.5897/JMER
  • Start Year: 2009
  • Published Articles: 118

Full Length Research Paper

Mathematical formalism of an internal air flow through a vortex tube machine of Hilsch-Ranque type: An analytical representation for velocity field

J. Venetis
  • J. Venetis
  • School of Civil Engineering National Technical University (NTU) Athens, Greece
  • Google Scholar
E. Sideridis
  • E. Sideridis
  • School of Applied Mathematics and Physical Sciences National Technical University (NTU) Athens, Greece
  • Google Scholar


  •  Accepted: 06 March 2013
  •  Published: 31 March 2013

Abstract

 

In this paper, we will attempt to derive an analytical representation of velocity field for the concept of an internal air flow inside a vortex tube machine of Hilsch-Ranque type. The basic assumption here is that the flux field is assumed to be steady and incompressible.Τhe vector which denotes instantaneous velocity, for the description of the flux field viaLagrangian stand point, will be expressed in a cylindrical coordinate system with orthonormal basis in the center line of the cross section of this vortex tube. We also assume here, that the aforementioned flux field varies only in radial direction, hence velocity vector is actually an one-dimensional damped circular helix trajectory with variable pitch.

 

Key words: Vortex tube, homographic function, vortex lines, helix trajectory.