Login | Register

Viscous Stability Analysis of Trailing Line Vortex

Title:

Viscous Stability Analysis of Trailing Line Vortex

Ebrahim nataj jelodar, Hamzeh (2013) Viscous Stability Analysis of Trailing Line Vortex. Masters thesis, Concordia University.

[thumbnail of Ebrahim_nataj_MASc_S2013.pdf]
Preview
Text (application/pdf)
Ebrahim_nataj_MASc_S2013.pdf - Accepted Version
Available under License Spectrum Terms of Access.
2MB

Abstract

This piece of work deals with the viscous stability of trailing line vortex. The perturbations are three dimensional and the viscous effects were encountered. The eigenvalue problem was solved by implementing a pseudo-spectral approach in MATLAB environment. The code was confirmed through comparing the results with those available in the literature, produced with Bachelor’s vortex model as base flow.
The code was afterwards used to investigate the stability of trailing line vortex where the azimuthal component of the base flow was the one of Vatistas’ vortex model. The stability of the linear modes (Kelvin’s waves) was investigated for axisymmetric and asymmetric disturbances. Results for the temporal viscous unstable modes were provided. The influence of swirl parameter and Reynolds number on the growth rate, phase speed and amplitude, of the perturbations were studied.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical and Industrial Engineering
Item Type:Thesis (Masters)
Authors:Ebrahim nataj jelodar, Hamzeh
Institution:Concordia University
Degree Name:M.A. Sc.
Program:Mechanical Engineering
Date:8 April 2013
Thesis Supervisor(s):Vatistas, G. H. and Abderrahmane, H. A.
Keywords:vortex model, Kelvin waves, stability analysis, pseudo-spectral method, trailing line vortex.
ID Code:977105
Deposited By: HAMZEH EBRAHIM NATAJ JELODA
Deposited On:07 Jun 2013 15:03
Last Modified:18 Jan 2018 17:43
Related URLs:

References:

[1]
Saffman P. G., Vortex Dynamics, New York, NY: Cambridge University Press, 1993.
[2]
Batchelor G., An Introduction to Fluid Dynamics, Cambridge University Press, 2000.
[3]
H. Schlichting, Aerodynamics of Airplanes, New York: McGraw-Hill, 1979.
[4]
Batchelor G.K. , Gill A.E., "Analysis of the stability of axisymmetric jets," J. Fluid Mech, vol. 14, no. 4, pp. 529-551, 1962.
[5]
Khorrami M. R., "A study of the temporal stability of multiple cell vortices," Progress Report, period ending 31 Oct. 1989 Old Dominion Univ., Norfolk, Virginia, 1989.
[6]
Gottlieb D., Orszag S.A., Numerical Analysis of Spectral Methods: Theory and Applications, Society for Industrial and Applied Mathematics, 1987.
[7]
Maxworthy T., " Wave motions on vortex cores," Journal of Fluid Mechanics, vol. 151, pp. 141-165, 1985.
[8]
Duck P. W., Foster M. R., "The inviscid stability of a trailing line vortex," Zeitschrift für Angewandte Mathematik und Physik (ZAMP), vol. 31, no. 4, pp. 524-532, 1980.
[9]
Lessen M., Paillet F., "The stability of a Trailing Line Vortex Part 2. Viscous Theory," J. of Fluid Mechanics, vol. 65, no. 4, pp. 769-779, 1974.
[10]
Pedley T., "On the instability of viscous flow in a rapidly rotating pipe," Journal of Fluid Mechanics, vol. 35, no. 01, pp. 97--115, 1969.
[11]
Maslowe S., "Instability of rigidly rotating flows to non-axisymmetric disturbances," Journal of Fluid Mechanics, vol. 64, no. 02, pp. 307--318, 1974.
[12]
MAO X., Sherwin S., "Continuous spectra of the Batchelor vortex," Journal of Fluid Mechanics, vol. 681, pp. 1-23, 2011.
[13]
Cottet G.H., Koumoutsakos P.D., Vortex Methods: Theory and Practice, Cambridge University Press, 2000.
[14]
Helmholtz H., "LXIII. On Integrals of the hydrodynamical equations, which express vortex-motion," Philosophical Magazine Series 4, vol. 33, no. 226, pp. 485-512, 1867.
[15]
Donnelly R., "Quantized vortices and turbulence in helium II," Annual review of fluid mechanics, vol. 25, no. 1, pp. 325-371, 1993.
[16]
Hasimoto H., "Elementary Aspects of Vortex motion," in IUTAM Symposium on Fundamental Aspects of Vortex Motion, Tokyo, Japan, 1988.
[17]
Kozel V., Experimental and Theoritical Studies on Concentrated Columnar Vortices, Montreal,, Quebec: Mechanical Engineering, Concordia University, 1991.
[18]
Vatistas G. H., "New model for intense self-similar vortices," Journal of Propulsion and and Power, vol. 14, no. 4, pp. 462-469, 1998.
[19]
Thomson W., "XXIV. Vibrations of a columnar vortex," Philosophical Magazine Series 5, vol. 10, no. 61, pp. 155-168, 01 September 1880.
[20]
Mogens V. Melander, Hussain F., "Core dynamics on a vortex column," Fluid Dynamics Research, vol. 13, no. 1, pp. 1-37, 1994.
[21]
Maxworthy T., "Waves on vortex cores," in IUTAM Symposium on Fundamental Aspects of Vortex Motion, Tokyo, Japan, 1988.
[22]
Duraisamy K., Studies in Tip Vortex, Formation, Evolution and Control, Maryland: University of Maryland, 2005.
[23]
Leibovich S., "Vortex stability and breakdown; survey and extension," AIAA, vol. 22, pp. 1192-1206, 1984.
[24]
Leibovich S., K. Stewartson, "A sufficient condition for the instability of columnar vortices," Journal of Fluid Mechanics, vol. 126, pp. 335-356, 1983.
[25]
Fabre D., Jacquin L., "Viscous instabilities in trailing vortices," Journal of Fluid Mechanics, vol. 500, p. 239–262, 2004.
[26]
Vatistas G. H., Kozel V., "A simpler model for concentrated vortices," Experiments in Fluids, vol. 11, no. 1, pp. 73-76, 1991.
[27]
Bagai A., Leishman J. G., "Flow visualization of compressible vortex structures using density gradient techniques," Experiments in Fluids, vol. 15, pp. 431-442, 1993.
[28]
Brix S., Neuwerth G., Jacob D., "The inlet-vortex system of jet engines operating near the ground," in 18th applied aerodynamics conference, Denver, 2000.
[29]
Nguyen T., An Investigation of Vortex Breakdown from the Point of View of Hydrodynamic Stability, University of California, Berkeley, 1980.
102
[30]
Rossow V. J., "Lift-generated vortex wakes of subsonic transport aircraft," Progress in Aerospace Sciences, vol. 35, no. 6, p. 507–660, August 1999.
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Research related to the current document (at the CORE website)
- Research related to the current document (at the CORE website)
Back to top Back to top