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ESCI SJR: 0.22 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimer: 2152-5102
ISSN En ligne: 2152-5110

# International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v38.i4.10
pages 291-311

## A Vortex Plate Theory of Hovering Animal Flight

Khaled M. S. Faqih
Information Systems Department, Al al-Bayt University, Jordan

### RÉSUMÉ

A mathematical model of vortex structure generated during animal hovering flight is adopted to determine the induced power requirement. The wake structure is modelled by a series of equispaced rigid rectangular vortex plates, positioned horizontally and moving vertically downwards with identical speeds; each plate is generated during powering of the functionally wing stroke. These plates are assumed to remain undistorted during their motion and act as rigid surfaces. The flow around the far wake is assumed to be identical to that of the flow about an infinite series of parallel vortex plates moving normal to themselves with constant speed. The vortex representation of the wake considered in the current theory allows a considerable loss of momentum to occur. This loss is approximated by Prandlt’s tip theory. The boundary conditions of this disjointed set of vortex plates determine their velocity potential which contribute to the calculation of the induced power requirement. The current theory is based on the assumption that the impulse associated with the vortex plate is adequate to support the animal’s weight for the duration of the wing stroke period. It is determined that the ratio of the initial vortex plate area Ai to wing swept area Ad is equal to the normal spacing parameter f; which can be related to the hovering parameter K by equating the impulse of the vortex sheet to the vortex plate impulse; K depends upon the animal’s morphology and the kinematics characteristic of the wing stroke. The classical model for induced power estimate is the actuator-disk model which renders the advantage of simplicity. This type of modelling does not precisely correspond to actual events that occur in animal flight. However, the current approach accords well with the nature of the wingbeat since it considers the unsteadiness in the wake as an important fluid dynamical characteristic. Induced power in hovering is calculated as the aerodynamic power required to generate the vortex wake system since this wake is primarily the main physical product of hovering action. Specific mean induced power to mean wing tip velocity ratio is determined by solely the normal spacing parameter f for a given wing stroke amplitude. The current theory gives much higher specific induced power estimate than anticipated by classical methods.

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