Numerical study of body shape and wing flexibility in fluid structure interaction
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Numerical study of body shape and wing flexibility in fluid structure interaction Bogdan Nita1 · Peter Nolan1 · Ashwin Vaidya1
Received: 25 October 2015 / Revised: 29 January 2016 / Accepted: 1 March 2016 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016
Abstract In this paper, we numerically investigate the impact of body shape and wing orientation upon the flow induced drag forces experienced by a body in its steady state. The current study focuses on simple toy models but derives its motivations from previous reported work on wind-induced drag on birds in flight most of which are experimental in nature. Our numerical results show that body shape/eccentricites, wing length and orientation are all important in determining the forces experienced by a body in a flow. Their geometries and specific features are key to determining the optimal mode of locomotion which is determined by looking at the relationship between drag force, bending behavior versus flow and geometric parameters. Keywords
Fluid-structure interaction · Flexibility · Vogel exponent
Mathematics Subject Classification
76Bxx · 76Zxx
1 Introduction In this paper, we study the equilibrium (re)configuration of deformable fibers in a twodimensional flow. Practical applications of such a study are plentiful. Some common problems of interest to the scientific community include the physics of snoring where soft-palate in the pharynx oscillates due to air flow (Huang et al. 1995). Another widely studied problem is the dynamics of cilia which line much of the human body and whose motion helps propel bodily fluids (Pedersen and Rosenbaum 2008). The breakdown of the ciliary mechanism is the cause of several human pathologies and constitutes an important medical question.
Communicated by Jorge X. Velasco.
B 1
Ashwin Vaidya [email protected] Complex Fluids Laboratory, Department of Mathematical Sciences, Montclair State University, Montclair, NJ 07043, USA
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B. Nita et al.
Fluid structure problems are also essential to our understanding of the mechanics of flying and swimming (Childress 1981; Tennekes 1996). The investigation of the positioning and orientation of wings, their length and equilibrium configurations, flapping modes, can all assist in optimal flight design. In the context of plant biology, the work of Vogel (Vogel 1984, 1989) has lead to considerable attention to the interaction of plants and trees with winds (Harder et al. 2004; Luhar and Nepf 2011). Their flexibility and bending prowess can serve as an important indicator of their health. The current problem is also of interest from a fundamental fluid mechanics perspective. The terminal state, including velocity and orientation, of a rigid body in a fluid flow is a well studied problem for over a century and continues to be explored (see for instance, Camassa et al. 2010; Fields et al. 1997; Galdi et al. 2001; Galdi 2002; Kirchoff 1869; Leal 1980; Tanabe et al. 1994; Willmarth et al. 1967). The classical problem of the terminal orientation of a body i
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