Viscous dissipation of Rankine vortex profile in zero meridional flow |
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Authors: | Yasser Aboelkassem Georgios H. Vatistas Nabil Esmail |
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Affiliation: | (1) Department of Mechanical and Industrial Engineering, Concordia University, Montreal, Quebec, H3G 1M8, Canada |
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Abstract: | An analytical solution is given for a time-decay Rankine vortex profile due to viscous effects. The vortex filament is assumed to be isolated, strong, concentrated and having zero-meridional flow (i.e. radial and axial velocities are equal to zero). Zero-meridional renders the governing equations for an unsteady, incompressible and axisymmetric vortex in a simple form. Based on the tangential momentum equation, the spatial-temporal distributions of the swirl velocity are given in terms of Fourier-Bessel series by using separation of variables technique. A general formula is derived by total differentiation of the swirl velocity with respect to time, depicting the viscous dissipation for Oseen and Taylor-like vortex profiles. This analysis is validated by comparison with previous experimental data. The English text was polished by Yunming Chen. |
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Keywords: | Rankine vortex Dissipation Fourier series Monopolar Zero-Meridional |
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