A new analytical solution for self-similar compressible vortices is derived in this paper. Based on the previous incompressible formulation of intense vortices, we derived a theoretical model that includes density and temperature variations. The governing equations are simplified assuming strong vortex conditions. Part of the hydrodynamic problem (mass and momentum) is shown to be analogous to the incompressible kind and as such the velocity is obtained through a straightforward variable transformation. Since all the velocity components are bounded in the radial direction, the density and pressure are then determined by standard numerical integration without the usual stringent simplification for the radial velocity. While compressibility is shown not to affect the tangential velocity, it influences only the meridional flow (radial and axial velocities). The temperature, pressure, and density are found to decrease along the converging flow direction. The traditional homentropic flow hypothesis, often employed in vortex stability and optical studies, is shown to undervalue the density and greatly overestimate the temperature. Comparable to vorticity diffusion balance for the incompressible case, the incoming flow carries the required energy to offset the contributions of conduction, viscous dissipation, and material expansion, thus keeping the temperature steady. This model is general and can be used to obtain a compressible version for all classical previous incompressible analysis from the literature such as Rankine, Burgers, Taylor, and Sullivan vortices.
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e-mail: yasser.aboelkassem@mail.mcgill.ca
e-mail: vatistas@encs.concordia.ca
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August 2007
Technical Papers
New Model for Compressible Vortices
Yasser Aboelkassem,
Yasser Aboelkassem
Department of Mechanical Engineering,
e-mail: yasser.aboelkassem@mail.mcgill.ca
McGill University
, 817 Sherbrooke Street West, Montreal, Quebec, H3A-2K6, Canada
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Georgios H. Vatistas
Georgios H. Vatistas
Department of Mechanical and Industrial Engineering,
e-mail: vatistas@encs.concordia.ca
Concordia University
, Montreal, Quebec H3G 1M8, Canada
Search for other works by this author on:
Yasser Aboelkassem
Department of Mechanical Engineering,
McGill University
, 817 Sherbrooke Street West, Montreal, Quebec, H3A-2K6, Canadae-mail: yasser.aboelkassem@mail.mcgill.ca
Georgios H. Vatistas
Department of Mechanical and Industrial Engineering,
Concordia University
, Montreal, Quebec H3G 1M8, Canadae-mail: vatistas@encs.concordia.ca
J. Fluids Eng. Aug 2007, 129(8): 1073-1079 (7 pages)
Published Online: February 26, 2007
Article history
Received:
March 30, 2006
Revised:
February 26, 2007
Citation
Aboelkassem, Y., and Vatistas, G. H. (February 26, 2007). "New Model for Compressible Vortices." ASME. J. Fluids Eng. August 2007; 129(8): 1073–1079. https://doi.org/10.1115/1.2746897
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