Fluid-structure System Research Articles

Piezoelectric Vibration Energy Harvesting From a Two-Dimensional Coupled Acoustic-Structure System With a Dynamic Magnifier

A class of piezoelectric energy harvester is presented to harness the vibration energy from coupled acoustic-structure systems such as those existing, for example, in aircraft acoustic cabin/flexible fuselage systems. Generic idealization of any of these systems involves the interaction between the dynamics of an acoustic cavity coupled with a flexible structure. Pressure oscillations inside the acoustic cavity induce vibration in the flexible structure and vice versa. Harnessing the associated vibration energy can be utilized to potentially power various vibration, noise, and health monitoring instrumentation. In this paper, the emphasis is placed on harnessing this energy using a special class of piezoelectric energy harvesters coupled with a dynamic magnifier in order to amplify its power output as compared to conventional harvesters. A finite element model (FEM) is developed to predict the performance of this class of harvesters in terms of the mechanical displacements of the flexible structure, the pressure inside the acoustic cavity, and the output electric voltage of the piezoelectric harvester. The FEM is formulated here to analyze a two-dimensional (2D) energy harvesting system which is composed of a rigid acoustic cavity coupled, at one end, with a vibrating base structure to which is attached the piezoelectric energy harvester. The developed FEM is exercised to predict the output electric power for broad interior pressure excitation frequencies. Numerical examples are presented to illustrate the behavior of the harvester and extract the conditions for maximum electric power output of the harvester. The obtained results demonstrate the feasibility of the dynamic magnifier concept as an effective means for enhancing the energy harvesting as compared to conventional harvesters. The presented model can be easily extended and applied to more complex fluid–structure systems such as aircraft and vehicle cabins.

Viscous flow past a collapsible channel as a model for self-excited oscillation of blood vessels

Motivated by collapse of blood vessels for both healthy and diseased situations under various circumstances in human body, we have performed computational studies on an incompressible viscous fluid past a rigid channel with part of its upper wall being replaced by a deformable beam. The Navier–Stokes equations governing the fluid flow are solved by a multi-block lattice Boltzmann method and the structural equation governing the elastic beam motion by a finite difference method. The mutual coupling of the fluid and solid is realized by the momentum exchange scheme. The present study focuses on the influences of the dimensionless parameters controlling the fluid–structure system on the collapse and self-excited oscillation of the beam and fluid dynamics downstream. The major conclusions obtained in this study are described as follows. The self-excited oscillation can be intrigued by application of an external pressure on the elastic portion of the channel and the part of the beam having the largest deformation tends to occur always towards the end portion of the deformable wall. The blood pressure and wall shear stress undergo significant variations near the portion of the greatest oscillation. The stretching motion has the most contribution to the total potential elastic energy of the oscillating beam.

Rational rates of uniform decay for strong solutions to a fluid-structure PDE system

In this work we investigate the uniform stability properties of solutions to a well-established partial differential equation (PDE) model for a fluid-structure interaction. The PDE system under consideration comprises a Stokes flow which evolves within a three-dimensional cavity; moreover, a Kirchhoff plate equation is invoked to describe the displacements along a (fixed) portion – say, Ω – of the cavity wall. Contact between the respective fluid and structure dynamics occurs on the boundary interface Ω. The main result in the paper is as follows: the solutions to the composite PDE system, corresponding to smooth initial data, decay at the rate of O(1/t). Our method of proof hinges upon the appropriate invocation of a relatively recent resolvent criterion for polynomial decays of C0-semigroups. While the characterization provided by said criterion originates in the context of operator theory and functional analysis, the work entailed here is wholly within the realm of PDE.

Frequency response of a fixed–fixed pipe immersed in viscous fluids, conveying internal steady flow

Abstract Novel methods are desired to harvest and store power in harsh environments, like those found at the bottom of production wells, to power commercially available monitoring devices. These systems must not only be mechanically robust but also operationally resilient, capable of sufficient power output under the widely varying conditions expected over the service life of a well. Since energy harvesting systems are heavily dependent on natural frequency, this broad range of conditions and/or well configurations makes the design of a suitable energy harvester challenging. Although the American Petroleum Institute (API) has set standards on some of the system variables, other variables are less well defined and may be time dependent. A first step towards the design of an energy harvesting system, then, is to investigate the changes in the natural frequency of a well by varying those inputs possessing moderate to high uncertainty. An analytical model is formed using Euler–Bernoulli beam theory to model the coupled fluid-structural system found in a producing well. A hydrodynamic function is included in the formulation to model the effects of the viscous fluid filled annulus. Due to the form of the hydrodynamic function, the systems natural frequency is solved in the frequency domain using the spectral element method; a method for calculating the displacement response to an external force is also provided. A parametric study is performed to determine the effect various inputs have on a systems first natural frequency. The key inputs considered are the axial force in the production tube, the conveyed fluid velocity, and the hydrodynamic function, itself a function of the annulus fluid viscosity and geometry. The study׳s results are in-line with expectations based on previous publications investigating component wise analogous systems. The inclusion of an axial force shifts the natural frequency of the system and the conveyed fluid velocity at which divergence occurs. The added mass introduced by the real part of the hydrodynamic function causes a shift in natural frequency but not in the bifurcation point. Viscous effects generated by the imaginary part of the hydrodynamic function act to shift the natural frequency of the system and the bifurcation point (This publication approved by sponsor for release, LA-UR-14-27597)..

Smart load control on large-scale wind turbine blades due to extreme coherent gust with direction change

The control of a typical extreme load with varying velocity and direction, i.e., International Electro-technical Commission Extreme Coherent Gust with Direction Change (ECD) load, was investigated on an Upwind/National Renewable Energy Laboratory 5 MW reference wind turbine using a newly developed smart blade system. The control action was implemented through the local perturbation of the Deformable Trailing Edge Flap (DTEF) on the blade surface and thus flow-blade system. The investigations were separately conducted within four time zones, depending on the complex yaw or/and pitching functions of the turbine. It was found that, without DTEF control, the flapwise root moment and tip deflection of the blades experienced rather complicated fluctuations due to the ECD load, together with the influence of blade yaw and pitching. On the other hand, the smart rotor control was very effective to reduce both blade flapwise root moment and tip deflection up to 30% and even more. The good control performance lied in the altered nature of the flow-blade interactions by the local controllable DTEF perturbation to change the in-phased fluid-structure synchronization into anti-phased collision at dominant load frequencies, thus significantly enhancing the damping of fluid-structure system and impairing their correlations. Consequently, the ECD load on the rotor and even drive-chain components would be greatly suppressed.

Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations

We present analysis for the reduction of an inertial description of fluid-structure interactions subject to thermal fluctuations. We show how the viscous coupling between the immersed structures and the fluid can be simplified in the regime where this coupling becomes increasingly strong. Many descriptions in fluid mechanics and in the formulation of computational methods account for fluid-structure interactions through viscous drag terms to transfer momentum from the fluid to immersed structures. In the inertial regime, this coupling often introduces a prohibitively small time-scale into the temporal dynamics of the fluid-structure system. This is further exacerbated in the presence of thermal fluctuations. We discuss here a systematic reduction technique for the full inertial equations to obtain a simplified description where this coupling term is eliminated. This approach also accounts for the effective stochastic equations for the fluid-structure dynamics. The analysis is based on use of the Infinitesmal Generator of the SPDEs and a singular perturbation analysis of the Backward Kolomogorov PDEs. We also discuss the physical motivations and interpretation of the obtained reduced description of the fluid-structure system. Working paper currently under revision. Please report any comments or issues to tabak.gil@gmail.com.

Parameter study of sizing and placement of deformable trailing edge flap on blade fatigue load reduction

This paper presents a numerical study on the parametric effect of deformable trailing edge flap (DTEF) on the fatigue load of a large-scale wind turbine blade. Investigations were conducted within the operation regions II and III of the turbine, respectively. Results showed that, compared with the original collective pitch method, the control effectively reduced the fatigue load on blade and drive-chain components, and positively affected the generator power and pitch system as well. Furthermore, the performances were gradually improved with increasing DTEF spanwise location from the rotor center, spanwise and central chordwise length, and deflection angle range, except for the worse performance with increasing spanwise location to the blade tip within region II. It was found that the smart control altered the nature of the flow-blade interactions and changed the in-phased fluid-structure synchronization into anti-phased interaction at main load frequencies, thus significantly enhancing the damping of fluid-structure system and contributing to greatly attenuated fatigue load on both rotor and drive-chain components. These phenomena happened for all primary load frequencies within region III, due to less flow detachment under the effect of the pitching function, determining its superiority over region II in terms of the control performance.

Dynamics of fluid flow over a circular flexible plate

AbstractThe dynamics of viscous fluid flow over a circular flexible plate are studied numerically by an immersed boundary–lattice Boltzmann method for the fluid flow and a finite-element method for the plate motion. When the plate is clamped at its centre and placed in a uniform flow, it deforms by the flow-induced forces exerted on its surface. A series of distinct deformation modes of the plate are found in terms of the azimuthal fold number from axial symmetry to multifold deformation patterns. The developing process of deformation modes is analysed and both steady and unsteady states of the fluid–structure system are identified. The drag reduction due to the plate deformation and the elastic potential energy of the flexible plate are investigated. Theoretical analysis is performed to elucidate the deformation characteristics. The results obtained in this study provide physical insight into the understanding of the mechanisms on the dynamics of the fluid–structure system.

On the dynamics of the fluid balancer

This paper is concerned with the dynamics of a so-called fluid balancer; a hula hoop ring-like structure containing a small amount of liquid which, during rotation, is spun out to form a thin liquid layer on the outermost inner surface of the ring. The liquid is able to counteract unbalanced mass in an elastically mounted rotor. The paper derives the equations of motion for the coupled fluid–structure system, with the fluid equations based on shallow water theory. An approximate analytical solution is obtained via the method of multiple scales. For a rotor with an unbalance mass, and without fluid, it is well known that the unbalance mass is in the direction of the rotor deflection at sub-critical rotation speeds, and opposite to the direction of the rotor deflection at super-critical rotation speeds (when seen from a rotating coordinate system, attached to the rotor). The perturbation analysis of the problem involving fluid shows that the mass center of the fluid layer is in the direction of the rotor deflection for any rotation speed. In this way a surface wave on the fluid layer can counterbalance an unbalanced mass.

On the validity of the independence principle applied to the vortex-induced vibrations of a flexible cylinder inclined at 60°

The vortex-induced vibrations (VIV) of a flexible cylinder inclined at 60° are investigated by means of direct numerical simulation, at a Reynolds number equal to 500, based on the cylinder diameter and inflow velocity. The cylinder has a circular cross-section and a length to diameter aspect ratio equal to 50; it is modeled as a tension-dominated structure which is free to oscillate in the in-line and cross-flow directions. The behavior of the coupled fluid–structure system is examined for two values of the tension. Particular attention is paid to the validity of the independence principle (IP) which states that the inclined and normal-incidence body cases are comparable if the inflow velocity normal component is used to scale the physical quantities.The flexible cylinder exhibits regular VIV for both values of the tension. In the high-tension configuration, where the in-line bending of the structure remains small, the IP is shown to be valid for the prediction of the cylinder responses and the fluid forces. In contrast, in the lower-tension configuration, the behavior of the fluid–structure system deviates from the IP. It is shown that this deviation is connected to the larger in-line bending of the structure which leads to considerably different profiles of the flow velocity locally perpendicular to the body in the inclined and normal cylinder cases. Since the system behavior appears to be mainly driven by this component of the flow, the profile modification induced by the larger in-line bending results in distinct responses: multi-frequency vibrations are observed in the inclined cylinder case whereas mono-frequency oscillations of larger amplitudes develop at normal incidence.

Vibro-acoustic analysis of laminated double glazing using the force identification method

This paper presents a procedure for identifying wave forms and excitation frequencies of some forces applied on a given complex fluid-structure coupled system by using only its vibro-acoustic response. The considered concept is called the Independent Component Analysis (ICA) which is based on the Blind Source Separation (BSS). In this work, the ICA method is exploited in order to determine the excitation force applied to a thin-film laminated double glazing system enclosing a thin fluid cavity and limited by an elastic joint. The dynamic response of the studied fluid-structure coupled system is determined by finite element discretization and minimization of the homogenized energy functional of the coupled problem. This response will serve as the input for the ICA algorithm in order to extract the applied excitation.

THEORETICAL AND NUMERICAL INVESTIGATIONS OF FREQUENCY ANALYSIS OF TWO CIRCULAR CYLINDERS OSCILLATING IN A INCOMPRESSIBLE VISCOUS FLUID

A potential flow is presented in this paper for the analysis of the fluid-structure interaction systems including, but not limited to, the idealized human head. The model considers a cerebro-spinal fluid (CSF) medium interacting with two solid domain. The fluid field is governed by the linearized Navier–Stokes equation. A potential technique is used to obtain a general solution for a problem. The method consists in solving analytically partial differential equations obtained from the linearized Navier–Stokes equation. From the solution, modal shapes and stokes cells are shown. In the analysis, the elastic skull model and the rigid skull model are presented. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effects of the fluid thickness is also investigated.

Coupling Analysis of Liquid Sloshing and Structural Vibration Using General Software

In this paper, a convenient modal analysis method for the linear coupled vibration of a container that is partially filled with a fluid is introduced. This problem is important for various reasons, such as stability analysis. The fluid-structure interactions in an elastic tank with an incompressible liquid are assumed to produce small vibrations. Reduced symmetric finite element equations of the system are acquired according to the component mode synthesis method. Considering that the liquid satisfies the same governing equation as steady heat conduction, general programs can be used to calculate the mass matrix and stiffness matrix of the coupled system. Then, modal analysis of the liquid container using general software, e.g., MSC Nastran, that ensures accuracy and stableness in the process, is applied to demonstrate that this method can determine the modal frequency in a fluid-structure coupled system.

Hybrid parallel strategy for the simulation of fast transient accidental situations at reactor scale

This contribution is dedicated to the latest methodological developments implemented in the fast transient dynamics software EUROPLEXUS (EPX) to simulate the mechanical response of fully coupled fluid–structure systems to accidental situations to be considered at reactor scale, among which the Loss of Coolant Accident, the Core Disruptive Accident and the Hydrogen Explosion.Time integration is explicit and the search for reference solutions within the safety framework prevents any simplification and approximations in the coupled algorithm: for instance, all kinematic constraints are dealt with using Lagrange Multipliers, yielding a complex flow chart when non-permanent constraints such as unilateral contact or immersed fluid–structure boundaries are considered. The parallel acceleration of the solution process is then achieved through a hybrid approach, based on a weighted domain decomposition for distributed memory computing and the use of the KAAPI library for self-balanced shared memory processing inside subdomains.

Experimental investigation on VIV-galloping interaction of a rectangular 3:2 cylinder

The interaction between galloping and vortex-induced vibration was experimentally investigated for an infinitely long rectangular cylinder with a side ratio of 3:2, free to vibrate in the transverse mode in smooth flow. This geometry showed strong proclivity to instability and large oscillations occurred also at high Scruton numbers, in a range of flow speeds where no excitation was expected according to the classical theory. A high value of the ratio of the quasi-steady galloping critical wind speed to Karman-vortex resonance velocity is necessary to avoid such a combined instability. Measurements of transverse displacements, velocity fluctuations in the wake of the oscillating body and pressures on its surface highlighted nonlinear features of the fluid-structure coupled system, such as superharmonic resonances and hysteresis. In particular, for low values of the Scruton number, non-negligible excitation was observed at low reduced wind speed due to secondary resonance.

A numerical solution to fluid-structure interaction of membrane structures under wind action

A numerical simultaneous solution involving a linear elastic model was applied to study the fluid-structure interaction (FSI) of membrane structures under wind actions, i.e., formulating the fluid-structure system with a single equation system and solving it simultaneously. The linear elastic model was applied to managing the data transfer at the fluid and structure interface. The monolithic equation of the FSI system was formulated by means of variational forms of equations for the fluid, structure and linear elastic model, and was solved by the Newton-Raphson method. Computation procedures of the proposed simultaneous solution are presented. It was applied to computation of flow around an elastic cylinder and a typical FSI problem to verify the validity and accuracy of the method. Then fluid-structure interaction analyses of a saddle membrane structure under wind actions for three typical cases were performed with the method. Wind pressure, wind-induced responses, displacement power spectra, aerodynamic damping and added mass of the membrane structure were computed and analyzed.

Modelling inertial effects in periodic fluid–structure systems with an homogenisation approach: Application to seismic analysis of tube bundles

Fluid–structure interaction (FSI) is of major importance when describing the dynamic behaviour of nuclear pressure vessels, since the presence of confined fluid strongly influences the response of structures when subjected to external loadings, such as a seismic loading. Accounting for FSI when performing the seismic analysis of nuclear reactors or steam generators can be done through the description of inertial effects, which are predominant in the low frequency domain. Finite element techniques are now of common use in design office to model coupled (quiescent) fluid–structure systems, using standard non-symmetric (u,p) or symmetric (u,p,φ) coupled formulations. When considering complex systems such as a tube bundle in steam generators, producing a finite element model which includes tubes, fluid and structures is a tedious task which is out of reach in many practical applications. A homogenisation method has been proposed which allows FSI modelling of tube bundles: it has been successfully applied to a complex structure. In the aforementioned developments, focus was put on the mathematical and numerical aspects of the method, leaving out some questions regarding the physical interpretation of the calculations. In the present paper, a new insight on the homogenisation approach is exposed with the objective of proposing a formulation of the method based on physical considerations, leading to a correction of the homogenised problem. Enhancement of the method is discussed from an engineering standpoint: it allows for a wider range of applications in the nuclear industry.

Stability of a flexible insert in one wall of an inviscid channel flow

A hybrid of computational and theoretical methods is extended and used to investigate the instabilities of a flexible surface inserted into one wall of an otherwise rigid channel conveying an inviscid flow. The computational aspects of the modelling combine finite-difference and boundary-element methods for structural and fluid elements respectively. The resulting equations are coupled in state-space form to yield an eigenvalue problem for the fluid–structure system. In tandem, the governing equations are solved to yield an analytical solution applicable to inserts of infinite length as an approximation for modes of deformation that are very much shorter than the overall length of the insert. A comprehensive investigation of different types of inserts – elastic plate, damped flexible plate, tensioned membrane and spring-backed flexible plate – is conducted and the effect of the proximity of the upper channel wall on stability characteristics is quantified. Results show that the presence of the upper-channel wall does not significantly modify the solution morphology that characterises the corresponding open-flow configuration, i.e. in the absence of the rigid upper channel wall. However, decreasing the channel height is shown to have a very significant effect on instability-onset flow speeds and flutter frequencies, both of which are reduced. The channel height above which channel-confinement effects are negligible is shown to be of the order of the wavelength of the critical mode at instability onset. For spring-backed flexible plates the wavelength of the critical mode is much shorter than the insert length and we show very good agreement between the predictions of the analytical and the state-space solutions developed in this paper. The small discrepancies that do exist are shown to be caused by an amplitude modulation of the critical mode on an insert of finite length that is unaccounted for in the travelling-wave assumption of the analytical model. Overall, the key contribution of this paper is the quantification of the stability bounds of a fundamental fluid–structure interaction (FSI) system which has hitherto remained largely unexplored.

On well-posedness and small data global existence for an interface damped free boundary fluid–structure model

We address a fluid–structure system which consists of the incompressible Navier–Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. Given sufficiently small initial data, we prove the global-in-time existence of solutions by establishing a key energy inequality which in addition provides exponential decay of solutions.

Hydroelastic response of a floating runway to cnoidal waves

The hydroelastic response of mat-type Very Large Floating Structures (VLFSs) to severe sea conditions, such as tsunamis and hurricanes, must be assessed for safety and survivability. An efficient and robust nonlinear hydroelastic model is required to predict accurately the motion of and the dynamic loads on a VLFS due to such large waves. We develop a nonlinear theory to predict the hydroelastic response of a VLFS in the presence of cnoidal waves and compare the predictions with the linear theory that is also developed here. This hydroelastic problem is formulated by directly coupling the structure with the fluid, by use of the Level I Green-Naghdi theory for the fluid motion and the Kirchhoff thin plate theory for the runway. The coupled fluid structure system, together with the appropriate jump conditions are solved in two-dimensions by the finite-difference method. The numerical model is used to study the nonlinear response of a VLFS to storm waves which are modeled by use of the cnoidal-wave theory. Parametric studies show that the nonlinearity of the waves is very important in accurately predicting the dynamic bending moment and wave run-up on a VLFS in high seas.