Session F18: Fluid-Structure Interactions: General

Beam Flutter and Energy Harvesting in Internal Flow

Aeroelastic flutter, largely studied for causing engineering failures, has more recently been used as a means of extracting energy from the flow. Particularly, flutter of a cantilever or an elastically mounted plate in a converging-diverging flow passage has shown promise as an energy harvesting concept for internal flow applications. The instability onset is observed as a function of throat velocity, internal wall geometry, fluid and structure material properties. To enable these devices, our work explores features of the fluid-structure coupled dynamics as a function of relevant nondimensional parameters. The flutter boundary is examined through stability analysis of a reduced order model, and corroborated with numerical simulations at low Reynolds number. Experiments for an energy harvester design are qualitatively compared to results from analytical and numerical work, suggesting a robust limit cycle ensues due to a subcritical Hopf bifurcation.   

Analytical Solution for the Aeroelastic Response of a Two-Dimensional Elastic Plate in Axial Flow

The aeroelastic response of an elastic plate in an unsteady flow describes many engineering problems from bio-locomotion, deforming airfoils, to energy harvesting. However, the analysis is challenging because the shape of the plate is a priori unknown. This study presents an analytical model that can predict the two-way tightly coupled aeroelastic response of a two-dimensional elastic plate including the effects of plate curvature along the flow direction. The plate deforms due to the dynamic balance of wing inertia, elastic restoring force, and aerodynamic force. The coupled model utilizes the linearized Euler-Bernoulli beam theory for the structural model and thin airfoil theory as presented by Theodorsen, which assumes incompressible potential flow, for the aerodynamic model. The coupled equations of motion are solved via Galerkin's method, where closed form solutions for the plate deformation are obtained by deriving the unsteady aerodynamic pressure with respect to the plate normal functions, expressed in a Chebyshev polynomial expansion. Stability analysis is performed for a range of mass ratios obtaining the flutter velocities and corresponding frequencies and the results agree well with the results reported in the literature.   

Dynamic Response of an Energy Harvesting Device Under Realistic Flow Conditions

The need for reliable, cost-efficient, green energy alternatives has led to increased research in the area of energy harvesting. One approach to energy harvesting is to take advantage of self-sustaining flow-induced vibrations. Through the use of a piezoelectric flag, the mechanical strain from the flapping motion can be converted into electrical energy. While such devices show a lot of promise, the fluid-structure-electrical interactions are highly nonlinear and their response to off-design variations in flow conditions, such as those likely to be encountered upon deployment, is relatively unexplored. The purpose of the present work is to examine how a representative energy harvesting device performs in realistic atmospheric flow conditions involving wind gusts with spatial and temporal variations. A recently developed lattice-Boltzmann-immersed boundary-finite element model is used to perform fully-coupled 3D simulations of the fluid-structure system. For a range of unsteady flow conditions the resulting flow features and structural motion are examined and key behaviour modes are mapped out. The findings of this work will be particularly relevant for self-powered remote sensing networks, which often require deployment in unpredictable and varied environments.   

Flow-Induced Flutter of Multiple Inverted Flags for Improved Energy Harvesting

Multi-inverted flag configurations undergoing flow-induced flutter have been studied using a coupled fluid-structure interaction solver. Both tandem and side-by-side configurations are examined to better understand the dynamics and energy harvesting potential of these systems, and to identify configurations that enhance energy harvesting. Parametric sweeps over the separation distance demonstrate a rich variety of coupling modes and system dynamics. A number of operational regimes have been identified for this two-flag system and correlated to the vortex dynamics. Simulations indicate that the coupling between flags can be used to enhance overall energy harvesting potential.   

The effect of clamping angle on the inverted flag instability

Inverted flags are cantilevered elastic plates that, when subjected to a flow, are free to move at their leading edge while being clamped at their trailing edge. For a range of free-stream velocities, they are known to undergo a large-amplitude flapping motion. The effect of the clamping angle (or angle of attack of the undeformed plate) on the critical wind speed at which flapping is initiated is investigated. Three distinct behavioral regions can be observed in air. For small clamping angles, where the flow is initially attached, the critical wind speed decreases with angle. For clamping angles larger than 15 degrees, where the flow is always detached, the critical wind speed increases with angle. For clamping angles larger than 26 degrees no flapping occurs. The mechanisms underlying this behavior are explored.   

Global modes and nonlinear simulations of inverted flag flapping

Inverted flag flapping, in which the flag is clamped at its trailing edge with respect to the oncoming flow, is capable of undergoing substantially larger-amplitude flapping than in the conventional configuration, where the flag is pinned or clamped at its leading edge. The associated increase in bending makes the inverted flag system a promising candidate for energy harvesting technologies that convert strain energy to electricity using, \emph{e.g.} piezoelectric materials. Because of this potential, recent studies have sought to investigate the response of the inverted flag system for a range of physical parameters. Of particular interest for this study, vortex shedding has been associated with large-amplitude flapping, and Sader \emph{et al.} (2016) showed that flapping possesses many features of a vortex-induced vibration (VIV) for a range of physical parameters. In this talk, we use a global mode analysis and nonlinear simulations to identify the mechanisms that initiate flapping. VIV is confirmed for a range of flow/flag parameters, and is shown to be initiated by an inherent instability in the deflected flag's equilibrium. Moreover, it is shown that non-VIV flapping is possible under a certain parameter space. This is yet to be observed experimentally.   

Periodic bubble formation and ejection for flow over paper

We study the motion of flow over flat paper attached at its leading edge to the floor of a wind tunnel. To allow freedom of angular motion, the leading edge is attached to a small diameter hypodermic tubing free to rotate in its support. Paper of width 8.5 in and density 0.075 g/sq cm was tested in lengths 12, 24, 32.5 in. Increasing the speed forms a steady bubble at the leading edge which at higher speed propagates down the sheet. We document the onset of bubble formation and the average frequency of bubble ejection. Another configuration is to tape the leading edge of the sheet directly to the tunnel floor. Initial results for a 12 in sheet reveal that the bubble forms half-way down the sheet before being ejected.   

Flow interaction with a flexible viscoelastic sheet

Many new engineered materials and almost all soft biological tissues are made up of heterogeneous multi-scale components with complex viscoelastic behavior. This implies that their macro constitutive relations cannot be modeled sufficiently with a typical integer-order viscoelastic relation and a more general mode is required. Here, we study the flow-induced vibration of a viscoelastic sheet where a generalized fractional constitutive model is employed to represent the relation between the bending stress and the temporal response of the structure. A new method is proposed for the calculation of the convolution integral inside the fractal model and its computational benefits will be discussed. Using a coupled fluid--structure interaction (FSI) methodology based on the immersed boundary technique, dynamic fluttering modes of the structure as a result of the fluid force will be presented and the role of fractal viscoelasticity on the dynamic of the structure will be shown. Finally, it will be argued how the stress relaxation modifies the flow-induced oscillatory responses of this benchmark problem.   

Fluid-structure-interaction of a flag in a channel flow.

The unsteady flow field and flapping dynamics of an inverted flag in water channel are investigated using time resolved particle image velocimetry (TR-PIV) measurements. The dynamically deformed profiles of the inverted flag are determined by a novel algorithm that combines morphological image processing and principle component analysis. Instantaneous flow field, phase averaged vorticity, time-mean flow field and turbulent kinematic energy are addressed for the flow. Four modes are discovered as the dimensionless bending stiffness decreases, i.e., the straight mode, the biased mode, the flapping mode and the deflected mode. Among all modes, the flapping mode is characterized by large flapping amplitude and the reverse von Kármán vortex street wake, which is potential to enhance heat transfer remarkably.   

Enhanced Small Scale Heat Transfer in Rectangular Channels using Autonomous, Aero-Elastically Fluttering Reeds

The limits of low Reynolds number forced convection heat transport within rectangular, mm-scale channels that model segments of air-cooled heat sinks are overcome by the deliberate formation of unsteady small-scale vortical motions that are induced by autonomous aero-elastic fluttering of cantilevered planar thin-film reeds. The coupled flow-structure interactions between the fluttering reeds and the embedding channel flow and the formation and evolution of the induced unsteady small-scale vortical motions are explored using video imaging and PIV. Concave/convex undulations of the reed's surface that are bounded by the channel's walls lead to the formation and advection of cells of vorticity concentration and ultimately to alternate shedding of spanwise CW and CCW vortices. These vortices scale with the channel height, and result in increased turbulent kinetic energy and enhanced dissipation that persist far downstream from the reed and are reminiscent of a turbulent flow at significantly higher Reynolds numbers (e.g., at \textit{Re}~$=$~800, TKE increases by 86{\%} ,40 channel widths downstream of reed tip). These small-scale motions lead to strong enhancement in heat transfer that increases with \textit{Re} (e.g., at \textit{Re}~$=$~1,000 and 14,000, \textit{Nu} increases by 36{\%} and 91{\%}, respectively). The utility of this approach is demonstrated in improving the thermal performance of low-Re heat sinks in air-cooled condensers of thermoelectric power plants.