2012
DOI: 10.1098/rspa.2011.0617
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Force-enhancing vortex equilibria for two parallel plates in uniform flow

Abstract: A two-dimensional potential flow in an unbounded domain with two parallel plates is considered. We examine whether two free point vortices can be trapped near the two plates in the presence of a uniform flow and observe whether these stationary point vortices enhance the force on the plates. The present study is an extension of previously published work in which a free point vortex over a single plate is investigated. The flow problem is motivated by an airfoil design problem for the double wings. Moreover, it… Show more

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Cited by 8 publications
(7 citation statements)
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“…This lift enhancing effect makes the lift larger than that predicted by the Wagner model. This conclusion is especially useful for steady flow problems with an attached vortex, since, according to previous studies by Saffman & Sheffield (1977), and Sakajo (2012), an attached vortex may greatly enhance lift. The present conclusion, when applied to steady flow, means that a stationary clockwise vortex is always lift enhancing.…”
Section: Additional Vortex Force and Additional Vortex Force Mapmentioning
confidence: 68%
See 1 more Smart Citation
“…This lift enhancing effect makes the lift larger than that predicted by the Wagner model. This conclusion is especially useful for steady flow problems with an attached vortex, since, according to previous studies by Saffman & Sheffield (1977), and Sakajo (2012), an attached vortex may greatly enhance lift. The present conclusion, when applied to steady flow, means that a stationary clockwise vortex is always lift enhancing.…”
Section: Additional Vortex Force and Additional Vortex Force Mapmentioning
confidence: 68%
“…As pointed out by Xia & Mohseni (2013), early investigations for these problems to understand the basic physical flight mechanisms mainly used experimental studies to attribute the lift enhancing mechanism to the attached LEV. The LEV may be stably attached to the wing as a result of three-dimensional effects (Birch & Dickinson 2001;Birch et al 2004) or satisfaction of a self-equilibrium condition (Saffman & Sheffield 1977;Sakajo 2012); thus a steady lift model based on attached LEV should yield useful results for these cases.…”
mentioning
confidence: 99%
“…They can be used, for example, in fluid dynamics to study a wide class of two-dimensional ideal irrotational flows via a new calculus involving the prime function recently expounded by one of the authors [31]. Of particular interest could be the configurations of stationary vortices [35][36][37], which have been shown to enhance the lift on an aerofoil. An intriguing application is to periodic arrays of slits, aerofoils or blades relevant in aviation and turbomachinery applications.…”
Section: Discussionmentioning
confidence: 99%
“…Following this, section 3 will detail the numerical method used to solve the equations. This algorithm generalizes that of Sakajo (2012) to domains of arbitrary connectivity, the main theoretical difference here being that a more general complex potential must now be considered. In section 4 this algorithm will be used to compute equilibria consiting of a single point vortex near three plates arranged in a Kapser Wing configuration.…”
Section: Introductionmentioning
confidence: 99%