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.
Skip Nav Destination
e-mail: yasser.aboelkassem@mail.mcgill.ca
e-mail: vatistas@encs.concordia.ca
Article navigation
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
Search for other works by this author on:
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
Download citation file:
Get Email Alerts
Cited By
Entrance Lengths for Fully Developed Laminar Flow in Eccentric Annulus
J. Fluids Eng (May 2025)
Switching Events of Wakes Shed From Two Short Flapping Side-by-Side Cylinders
J. Fluids Eng (May 2025)
Related Articles
Approximation of Transient 1D Conduction in a Finite Domain Using Parametric Fractional Derivatives
J. Heat Transfer (July,2011)
Sub-Continuum Simulations of Heat Conduction in Silicon-on-Insulator Transistors
J. Heat Transfer (February,2001)
Thermal Analysis of the Transient Temperatures Arising at the Contact Spots of Two Sliding Surfaces
J. Tribol (October,2005)
Heat Transfer Enhancement for Finned-Tube Heat Exchangers With Winglets
J. Heat Transfer (February,2005)
Related Proceedings Papers
Related Chapters
Pulsating Supercavities: Occurrence and Behavior
Proceedings of the 10th International Symposium on Cavitation (CAV2018)
Cavitating Structures at Inception in Turbulent Shear Flow
Proceedings of the 10th International Symposium on Cavitation (CAV2018)
Energy Balance for a Swimming Pool
Electromagnetic Waves and Heat Transfer: Sensitivites to Governing Variables in Everyday Life