Vortex dynamics models in flow control problems

Abstract

In this paper we review the state of the art in the field of control of vortex dynamics. We focus on problems governed by two-dimensional incompressible Euler equations in domains both with and without boundaries. Following a comprehensive review of earlier approaches, we discuss how methods of modern control and optimization theory can be employed to solve control problems for vortex system. In addition, we also address the companion problem of the state estimation for vortex systems. While most of the discussion concerns point vortex systems, in the second part of the paper we also introduce a novel approach to the control of Euler flows involving finite-area vorticity distributions. The paper concludes with what, in the author's opinion, represent promising new research directions.

Low-order modeling of wind farm aerodynamics using leaky Rankine bodies

“…28 More recently, another potential flow model known as the F€ oppl point vortex system has been used to study vortex dynamics and control for solid bodies. 29,30 An underlying assumption of both the F€ oppl system and free-streamline theory is that a non-zero drag on a body in potential flow requires that a wake region be modeled explicitly; this is a feature of the LRB model. More precisely, it can be shown that there exists a finite force required to hold a source or a sink in place within a uniform flow.…”

How do singularities move in potential flow?

“…Applications include chaotic advection [4], integrable systems [5][6][7], control of fluid flows [8,9], biological locomotion and models of vortex shedding and wakes [10][11][12][13][14][15] as well as geophysical applications [16,17]. Related problems arise in superfluids [18] and in dislocation theory [19], but we limit ourselves here to potential flow.…”

Extremely simple pressure regulator – computation studies

“…[7]. It is probably associated with the Ringleb's idea [8] of trapped vortex -several times seemingly disproved (e.g., [9]) and yet later resuscitated, e.g., in the form of vortex trapped in a cornice-shaped cavity on the top surface of an airfoil, known as the "Kasper vortex" [10], a subject of current research efforts [11,12].…”