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.
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The English text was polished by Yunming Chen.
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Aboelkassem, Y., Vatistas, G. & Esmail, N. Viscous dissipation of Rankine vortex profile in zero meridional flow. ACTA MECH SINICA 21, 550–556 (2005). https://doi.org/10.1007/s10409-005-0073-3
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DOI: https://doi.org/10.1007/s10409-005-0073-3