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Force-enhancing vortex equilibria for two parallel plates in uniform flow. (English) Zbl 1364.76023
Summary: 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 also contributes to a design problem for an efficient wind turbine with vertical blades. In order to obtain the point-vortex equilibria numerically, we make use of a linear algebraic algorithm combined with a stochastic process, called the Brownian ratchet scheme. The ratchet scheme allows us to capture a family of stationary point vortices in multiply connected domains with ease. As a result, we find that stationary point vortices exist around the two plates and they enhance the downward force and the counter-clockwise rotational force acting on the two plates.

MSC:
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
76D17 Viscous vortex flows
76B47 Vortex flows for incompressible inviscid fluids
76G25 General aerodynamics and subsonic flows
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