Energy Production Characteristics of a Spring-Mounted Cantilevered-Free Flexible Plate in a Uniform Flow

2012 ◽  
Author(s):  
Richard M. Howell ◽  
Anthony D. Lucey
Keyword(s):  
Energy Harvesting ◽  
Flow Direction ◽  
Leading Edge ◽  
Flow Speed ◽  
Uniform Flow ◽  
Present System ◽  
Beam Model ◽  
Flexible Plate ◽  
Mean Flow ◽  
Energy Harvesting System

We study a new fundamental system that comprises a cantilevered thin flexible plate exactly aligned with the direction of a uniform flow in which the upstream end of the flexible plate is not fixed. Instead, it is attached to a spring-damper system that allows the entire system to oscillate perpendicularly to the flow direction as a result of the mounting’s dynamic interaction with the flow-induced oscillations of the flexible plate. This models an energy-harvesting system whereby the rate of energy extraction by the damper represents power generation from the kinetic-energy flux of the mean flow transferred via fluttering motions of the flexible plate to the motion of the mounting system. The two-dimensional modelling presented is an extension of the methods in [1,2] that mixed numerical simulation with eigenvalue analysis to study a fixed cantilevered flexible plate. The present system also includes a rigid inlet surface upstream of and fixed to the spring-mounted cantilever. Ideal flow is assumed wherein the rotationality of the boundary-layers is modelled by vortex elements on the solid-fluid interface and the imposition of the Kutta condition at the plate’s trailing edge. The Euler-Bernoulli beam model is used for the structural dynamics. Results presented first show how the replacement of the fixed leading edge with an interactively oscillating mounting modify the well-known linear-stability characteristics of a fluttering plate. The overall effect is that the critical flow speed for flutter onset is reduced and this is desirable for the present energy-harvesting application. This entails some subtle but important changes to the destabilisation mechanisms. The power generating potential of the fluid-structure interaction system is then illustrated. The present model of the dynamics of the plate-support interaction has been simplified so as to demonstrate proof-of-concept; thus, a discussion of the way forward to a more complete model is presented to close the paper.

Stability of slender inverted flags and rods in uniform steady flow

2016 ◽  
Vol 809 ◽  
pp. 873-894 ◽  
Author(s):  
John E. Sader ◽  
Cecilia Huertas-Cerdeira ◽  
Morteza Gharib
Keyword(s):  
Multiple Equilibria ◽  
Complex Dynamics ◽  
Flow Direction ◽  
Flow Speed ◽  
Uniform Flow ◽  
Biological Phenomena ◽  
Cantilever Length ◽  
The Stability ◽  
Elastic Sheets ◽  
Clamped Edge

Cantilevered elastic sheets and rods immersed in a steady uniform flow are known to undergo instabilities that give rise to complex dynamics, including limit cycle behaviour and chaotic motion. Recent work has examined their stability in an inverted configuration where the flow impinges on the free end of the cantilever with its clamped edge downstream: this is commonly referred to as an ‘inverted flag’. Theory has thus far accurately captured the stability of wide inverted flags only, i.e. where the dimension of the clamped edge exceeds the cantilever length; the latter is aligned in the flow direction. Here, we theoretically examine the stability of slender inverted flags and rods under steady uniform flow. In contrast to wide inverted flags, we show that slender inverted flags are never globally unstable. Instead, they exhibit bifurcation from a state that is globally stable to multiple equilibria of varying stability, as flow speed increases. This theory is compared with new and existing measurements on slender inverted flags and rods, where excellent agreement is observed. The findings of this study have significant implications to investigations of biological phenomena such as the motion of leaves and hairs, which can naturally exhibit a slender geometry with an inverted configuration.

On the causal behaviour of flow over an elastic wall

1999 ◽  
Vol 396 ◽  
pp. 319-344 ◽  
Author(s):  
R. J. LINGWOOD ◽  
N. PEAKE
Keyword(s):  
Shear Layer ◽  
Finite Time ◽  
Radiation Condition ◽  
Flow Speed ◽  
Uniform Flow ◽  
Dispersion Function ◽  
Mean Flow ◽  
Wide Range ◽  
Line Force ◽  
Layer Flow

In this paper we consider the causal response of the inviscid shear-layer flow over an elastic surface to excitation by a time-harmonic line force. In the case of uniform flow, Brazier-Smith & Scott (1984) and Crighton & Oswell (1991) have analysed the long-time limit of the response. They find that the system is absolutely unstable for sufficiently high flow speeds, and that at lower speeds there exist certain anomalous neutral modes with group velocity directed towards the driver (in contradiction of the usual radiation condition of out-going disturbances). Our aim in this paper is to repeat their analysis for more realistic shear profiles, and in particular to determine whether or not the uniform-flow results can be regained in the limit in which the shear-layer thickness on a length scale based on the fluid loading, denoted ε, becomes small. For a simple broken-line linear shear profile we find that the results are qualitatively similar to those for uniform flow. However, for the more realistic Blasius profile very significant differences arise, essentially due to the presence of the critical layer. In particular, we find that as ε → 0 the minimum flow speed required for absolute instability is pushed to considerably higher values than was found for uniform flow, leading us to conclude that the uniform-flow problem is an unattainable singular limit of our more general problem. In contrast, we find that the uniform-flow anomalous modes (written as exp (ikx − iωt), say) do persist for non-zero shear over a wide range of ε, although now becoming non-neutral. Unlike the case of uniform flow, however, the k-loci of these modes can now change direction more than once as the imaginary part of ω is increased, and we describe the connection between this behaviour and local properties of the dispersion function. Finally, in order to investigate whether or not these anomalous modes might be realizable at a finite time after the driver is switched on, we evaluate the double Fourier inversion integrals for the unsteady flow numerically. We find that the anomalous mode is indeed present at finite time, once initial transients have propagated away, not only for impulsive start-up but also when the forcing amplitude is allowed to grow slowly from a small value at some initial instant. This behaviour has significant implications for the application of standard radiation conditions in wave problems with mean flow.

Optimal Energy Harvesting From Low-Frequency Bistate Force Loadings

2009 ◽  
Author(s):  
Jeff T. Scruggs ◽  
Sam Behrens
Keyword(s):  
Energy Harvesting ◽  
Low Frequency ◽  
Leading Edge ◽  
Optimal Time ◽  
Natural Period ◽  
Single Degree Of Freedom ◽  
Closed Form Solutions ◽  
Force Magnitude ◽  
Static Power ◽  
Energy Harvesting System

This paper considers techniques for harvesting energy from vibratory loadings that can be characterized by low-frequency alternations between a minimum and maximum force magnitude. In such cases, it is often impossible to tune the harvester to resonate in the frequency band of the excitation, due to constraints on the mass and transducer displacement. Here, we consider the case in which the harvester’s transient dynamics are characterized by a natural period which is orders of magnitude below the fundamental period of the disturbance, and which undergoes significant decay in between load alternations. In this case, the damped vibration of the harvester induced by each load alternation may be viewed as an isolated transient response. For such problems, we consider the optimization of generated power, through the use of an active power-electronic drive to explicitly regulate transducer current according to an optimized feedback law. The analysis accounts for both mechanical and electrical losses in the harvester, as well as dissipation in the electronics. It also accounts for the static power necessary to operate the control intelligence and gate the drive transistors. We show that the optimal feedback law is in general a time-varying linear controller. Further, we show that following the leading edge of each load alternation, there is an optimal time horizon over which to operate the electronic conversion system, beyond which the energy expended on static power exceeds the remaining energy recoverable from the dynamic response of the harvester. The analytical derivation of the controller is done generally, and is shown to simplify to easily-computable closed-form solutions in a number of simple cases. Analytical and simulation results are related to an experimental energy harvesting system involving a single degree-of-freedom electromagnetic transducer.

Optimal Energy Harvesting From Low-Frequency Bistate Force Loadings

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
J. T. Scruggs ◽  
S. Behrens
Keyword(s):  
Energy Harvesting ◽  
Low Frequency ◽  
Leading Edge ◽  
Optimal Time ◽  
Natural Period ◽  
Single Degree Of Freedom ◽  
Closed Form Solutions ◽  
Force Magnitude ◽  
Static Power ◽  
Energy Harvesting System

This paper considers techniques for harvesting energy from vibratory loadings that can be characterized by low-frequency alternations between a minimum and maximum force magnitude. In such cases, it may be impossible to tune the harvester to resonate in the frequency band of the excitation due to constraints on the mass and transducer displacement. Here, we consider the case in which the harvester’s transient dynamics are characterized by a natural period, which is orders of magnitude below the fundamental period of the disturbance and which undergoes significant decay in between load alternations. In this case, the damped vibration of the harvester induced by each load alternation may be viewed as an isolated transient response. For such problems, we consider the optimization of generated power through the use of an active power-electronic drive to explicitly regulate transducer current according to an optimized feedback law. The analysis accounts for both mechanical and electrical losses in the harvester, as well as dissipation in the electronics. It also accounts for the static power necessary to operate the control intelligence and gate the drive transistors. We show that the optimal feedback law is, in general, a time-varying linear controller. Further, we show that following the leading edge of each load alternation, there is an optimal time horizon over which to operate the electronic conversion system beyond which the energy expended on static power exceeds the remaining energy recoverable from the dynamic response of the harvester. The analytical derivation of the controller is done generally and is shown to simplify to easily computable closed-form solutions in a number of simple cases. Analytical and simulation results are related to an experimental energy harvesting system involving a single degree-of-freedom electromagnetic transducer.

The Measurements of Mean Flow Angles Between an Automotive Fan and Stator

2002 ◽  
Author(s):  
Gregory A. Kopp ◽  
Robert J. Martinuzzi
Keyword(s):  
Flow Direction ◽  
Leading Edge ◽  
Laser Doppler Velocimeter ◽  
Hot Wire ◽  
Mean Flow ◽  
Mean Velocity ◽  
Flow Angle ◽  
Automotive Engine ◽  
Engine Cooling ◽  
The Mean

Measurements of the mean velocity vector were conducted to determine the exit angle from an automotive engine cooling fan module. The measurements were made at 15 locations along a radius between the hub and the band. The radius investigated was located in a plane roughly half-way between the blade trailing edge and stator leading edge. A two-component laser Doppler velocimeter and a four-wire hot-wire probe were used to measure the flow fields. It was found that the results obtained from hot-wire anemometry will have significant bias errors when used to measure the velocity vectors between the fan and the stator unless phase-averaged data are obtained with the probe re-oriented by phase. The differences between the techniques occur because the distribution of instantaneous swirl angles is bi-modal. Further, the mean flow angle is close to a local minimum in the probability density function of the swirl angle. This will act to increase errors in measurement devices whose accuracy depends on flow direction (the quantity being measured) such as five-hole probes which are used in industry.

scholarly journals Boundary-layer receptivity for a parabolic leading edge

1996 ◽  
Vol 310 ◽  
pp. 243-267 ◽  
Author(s):  
P. W. Hammerton ◽  
E. J. Kerschen
Keyword(s):  
Boundary Layer ◽  
Acoustic Waves ◽  
Free Stream ◽  
Asymptotic Methods ◽  
Leading Edge ◽  
Flow Speed ◽  
The Body ◽  
Large Reynolds Number ◽  
Mean Flow ◽  
Nose Radius

The effect of the nose radius of a body on boundary-layer receptivity is analysed for the case of a symmetric mean flow past a body with a parabolic leading edge. Asymptotic methods based on large Reynolds number are used, supplemented by numerical results. The Mach number is assumed small, and acoustic free-stream disturbances are considered. The case of free-stream acoustic waves, propagating obliquely to the symmetric mean flow is considered. The body nose radius, rn, enters the theory through a Strouhal number, S = ωrn/U, where ω is the frequency of the acoustic wave and U is the mean flow speed. The finite nose radius dramatically reduces the receptivity level compared to that for a flat plate, the amplitude of the instability waves in the boundary layer being decreased by an order of magnitude when S = 0.3. Oblique acoustic waves produce much higher receptivity levels than acoustic waves propagating parallel to the body chord.

The interaction between a steady jet flow and a supersonic blade tip

1993 ◽  
Vol 248 ◽  
pp. 543-566 ◽  
Author(s):  
N. Peake
Keyword(s):  
Flow Direction ◽  
Leading Edge ◽  
Delta Function ◽  
Tip Vortex ◽  
Sound Waves ◽  
Mean Flow ◽  
Side Edge ◽  
Counter Rotation ◽  
Blade Tip ◽  
High Level

The potentially high level of noise generated by modern counter-rotation propellers has attracted considerable interest and concern, and one of the most potent mechanisms involved is the unsteady interaction between the tip vortex shed from the tips of the forward blade row and the rear row. In this paper a model problem is considered, in which the tip vortex is represented by a jet of constant axial velocity, which is convected at right angles to itself by a uniform supersonic mean flow, and which is cut by a rigid airfoil with its chord aligned along the mean flow direction. Ffowcs Williams & Guo have previously considered this problem for an infinite-span airfoil and a circular jet; in this paper we extend their analysis to include the effects of the presence of the second-row blade tip on the interaction, by considering a semi-infinite-span airfoil. As a first attempt, the case of a highly compact jet, represented by a delta-function upwash on the airfoil, is considered, and both the total lift on the airfoil and the radiation are investigated. The presence of the airfoil corner and side edge is seen to cause the lift to decay in time from its infinite-span value towards zero, due to a spanwise motion round the side edge; whilst the radiation is shown to be composed of two Signals, the first received directly from the interaction between the jet and the leading edge, and the second resulting from the diffraction of sound waves emanating from the leading edge by the side edge. The effect of choosing a more diffuse upwash distribution is then considered, in which case it becomes clear that the first signal has a considerably larger amplitude, and shorter duration, than the second, diffracted signal.

Examination of the flow near the leading edge of attached cavitation. Part 2. Incipient breakdown of two-dimensional and axisymmetric cavities

1998 ◽  
Vol 376 ◽  
pp. 91-113 ◽  
Author(s):  
A. TASSIN LEGER ◽  
L. P. BERNAL ◽  
S. L. CECCIO
Keyword(s):  
Flow Direction ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Mean Flow ◽  
Local Flow ◽  
Particle Imaging ◽  
Axisymmetric Cavities ◽  
Test Objects

Local and global three-dimensionality of cavity interfaces near detachment was examined. Cavities forming on hydrophilic test objects at higher Reynolds numbers (Re>105) exhibited a local flow structure in the cavity interface called ‘divots’. Divots resulted from a local breakdown of the two-dimensional laminar boundary separation. Divots did not form on hydrophobic test objects. Instead, at higher Reynolds numbers (Re>105), the cavity at detachment was composed of a series of wedge shaped structures. Flows with strong adverse pressure gradients upstream of cavity detachment exhibited only local three-dimensionality near one cavity detachment. Flows with weak adverse pressure gradients upstream of cavity detachment were more susceptible to breakdown into global three-dimensionality. This was the case for cavitation on the hydrofoils. Holographic particle imaging velocimetry (HPIV) was used to examine the spanwise and streamwise variation of the flow upstream of the cavity detachment. Three-dimensionality of the cavity detachment was associated with strong variations of the flow upstream of the cavity in the direction perpendicular to the mean flow direction.

scholarly journals Energy Harvesting Performance of Plate Wing from Discrete Gust Excitation

Aerospace ◽  
2019 ◽  
Vol 6 (3) ◽  
pp. 37 ◽  
Author(s):  
Yun Cheng ◽  
Daochun Li ◽  
Jinwu Xiang ◽  
Andrea Da Ronch
Keyword(s):  
Energy Harvesting ◽  
Plate Theory ◽  
Leading Edge ◽  
Load Resistance ◽  
Flow Speed ◽  
Small Scale ◽  
Lattice Method ◽  
Aeroelastic Response ◽  
Linear State ◽  
Ceramic Transducer

Energy harvesting from aeroelastic response tends to have a wide application prospect, especially for small-scale unmanned aerial vehicles. Gusts encountered in flight can be treated as a potential source for sustainable energy supply. The plate model is more likely to describe a low aspect ratio, thin plate wing structure. In this paper, the Von Kármán plate theory and 3D doublet lattice method, coupled with a piezoelectric equation, are used to build a linear state-space equation. Under the load of “one-minus-cosine” discrete gust, the effects of flow speed and gust amplitude, thickness of piezoelectric ceramic transducer (PZTs) layers, and mounted load resistance are investigated. Results reveal that the PZTs layers on the wing root of the leading edge can obtain the highest electrical parameters. The flow velocity, thickness of the PZTs layers and load resistance are used to optimize energy harvesting data.

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