Modelling vortex-induced fluid–structure interaction

Abstract

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flowoscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid-structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion.Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid-structure interaction models entails -formulating generalized equations of motion, as a superset of the flow-oscillator models; and -developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier-Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flowoscillator models.

The onset of vortex-induced vibrations of a flexible cylinder at large inclination angle

“…The fundamentals of VIV have been well documented for a cylinder whose axis in quiescient fluid is perpendicular to the oncoming flow (normal incidence case), the body being either rigid and elastically-mounted (King et al 1973;Bearman 1984Bearman , 2011Naudascher 1987;Mittal & Tezduyar 1992;Hover et al 1998;Okajima et al 2002;Sarpkaya 2004;Williamson & Govardhan 2004;Klamo et al 2006;Leontini et al 2006;Benaroya & Gabbai 2008;Lucor & Triantafyllou 2008;Dahl et al 2010;Navrose & Mittal 2013;Cagney & Balabani 2014;Konstantinidis 2014) or flexible (Trim et al 2005;Chaplin et al 2005;Lie & Kaasen 2006;Lucor et al 2006;Huera-Huarte & Bearman 2009, 2014; Vandiver et al 2009;Modarres-Sadeghi et al 2011;Bourguet et al 2011aBourguet et al ,b, 2012Bourguet et al , 2013a. VIV naturally appear both in the cross-flow direction and in the in-line direction, i.e.…”

Reduced-order modeling of fluid–structure interaction and vortex-induced vibration systems using an extension of Jourdain׳s principle

“…These ad hoc methods are outside of the scope of this work that is focused on first principles models, specifically, using variational principles. Reviews of the empirical models can be found in [2], [6] and [7].…”

Flow-Oscillating Structure Interactions and the Applications to Propulsion and Energy Harvest

“…Another study showed the monofrequencyas well as multi-frequency vortex-induced vibration of a tensioned beam immersed in a linear shear flowand free to move in both the in-line and cross-flow directions, using direct numerical simulation (Bourguet, Lucor, & Triantafyllou, 2012). A reduced-order analytical model of nonlinear fluid-structure interactions was alsodeveloped by using the Hamilton's principle and Navier-Stokes equations (Benaroy & Gabbaia, 2008;Gabbaia & Benaroy, 2008). A similar study built a general low-order fluid-structure interaction model capable of evaluating themulti-mode interactions in vortex-induced vibration of flexible curved/straight structures (Srini, 2010).…”

“…General reduced-order, analytical models of nonlinear flow-oscillator interactions were developed by usingHamilton's variational formulation coupling Navier-Stokes equations (Benaroy & Gabbaia, 2008;Gabbaia & Benaroy, 2008). Many wake-body models are shown to be recoverable from the more general model derived byexplicit assumptions.…”