Manikis, Fani (2015) New Solutions for Two-Cell Vortices. Masters thesis, Concordia University.
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Abstract
Two celled incompressible vortices are known from the work of Sullivan (1959). This dissertation first extends the previously derived wider latitude, incompressible, steady two-cell vortex of Vatistas (1998) to account for the effects of time as it decays. Then, it is also broadened to simulate steady vortices where the density variation is included.
Based on the conservation of mass and momentum equations, a new method to analytically characterize two-cell decaying vortices is presented. The study shows that the core radius increases linearly with time, while the maximum velocity reduces hyperbolically. In comparison to Lamb (1932) - Oseen (1912) one-cell vortex, the dominant tangential velocity in the two-celled type is shown to decline considerably faster. Both effects are attributed to the increased viscous dissipation. Based on theoretical grounds, it is argued that the cause of the previously discovered vortex strength reduction in wing tip vortices with an externally imposed central jet is due to the switch of the one cell tip vortex into a two-cell, and not due to the added turbulence caused by the jet.
Because Sullivan’s vortex assumes an unbounded radial velocity in the radial direction, its extension to compressible kind, taking into account the convective heat transfer in the energy equation, is not possible without some very drastic simplifications concerning the problem. In this dissertation an alternate approach to the problem is offered where the previous weakness is absent. The earlier contribution of Vatistas (1998) vis-à-vis incompressible two-cell vortices is now generalized to account for density variation. The conservation equations of mass, momentum and energy are abridged assuming intense vortex conditions. The system of equations, describing the thermal side of the problem is brought into a closure via the inclusion of the equation of state for a calorically perfect gas. The temperature, density and pressure are then calculated using straightforward, readily available, numerical integration software.
It is found that along the converging flow direction, the temperature first decreases (in the outer cell), increases within the inner cell, and then flattens close to the vortex center. The cause of this effect is identified to be due to the interplay of dilation-contraction and mechanical dissipation in the infinitesimal fluid element. Density and pressure near the axis, where the whirl is cold, are shown to be under sub ambient conditions, i.e. the gas density is thinner and the pressure is under vacuum conditions. All these properties depend strongly on the vortex Mach number.
| Divisions: | Concordia University > School of Graduate Studies |
|---|---|
| Item Type: | Thesis (Masters) |
| Authors: | Manikis, Fani |
| Institution: | Concordia University |
| Degree Name: | M.A. Sc. |
| Program: | Mechanical Engineering |
| Date: | 26 August 2015 |
| Thesis Supervisor(s): | Vatistas, Georgios H. |
| Keywords: | vortex model, two-cell vortices, compressible vortices, decaying vortices |
| ID Code: | 980336 |
| Deposited By: | FANI MANIKI |
| Deposited On: | 03 Nov 2015 15:31 |
| Last Modified: | 18 Jan 2018 17:51 |
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