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.

Extended Stokes series: laminar flow through a loosely coiled pipe

1978 ◽  
Vol 86 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Milton Van Dyke
Keyword(s):  
Laminar Flow ◽  
Flow Speed ◽  
Square Root ◽  
Mean Flow ◽  
Dean Number ◽  
Curvature Ratio ◽  
Wide Range ◽  
Square Root Singularity ◽  
Flow Through ◽  
The One

Dean's series for steady fully developed laminar flow through a toroidal pipe of small curvature ratio has been extended by computer to 24 terms. Analysis suggests that convergence is limited by a square-root singularity on the negative axis of the square of the Dean number. An Euler transformation and extraction of the leading and secondary singularities at infinity render the series accurate for all Dean numbers. For curvature ratios no greater than$\frac{1}{250} $, experimental measurements of the laminar friction factor agree with the theory over a wide range of Dean numbers. In particular, they confirm our conclusion that the friction in a loosely coiled pipe grows asymptotically as the one-quarter power of the Dean number based on mean flow speed. This contradicts a number of incomplete boundary-layer analyses in the literature, which predict a square-root variation.

Streamwise oscillations of a cylinder in a steady current. Part 1. Locked-on states of vortex formation and loading

2001 ◽  
Vol 427 ◽  
pp. 1-28 ◽  
Author(s):  
O. CETINER ◽  
D. ROCKWELL
Keyword(s):  
Oscillation Frequency ◽  
Vortex Formation ◽  
Uniform Flow ◽  
Transverse Force ◽  
Spectral Peak ◽  
Near Wake ◽  
Steady Current ◽  
Wide Range ◽  
Line Force ◽  
Oscillations Of A Cylinder

Streamwise oscillations of a circular cylinder in a steady uniform flow are investigated experimentally using a technique of high-image-density particle image velocimetry, in conjunction with instantaneous force measurements. This approach allows insight into the relationship between the loading and the patterns of vorticity and streamline topology in the near wake.In analogy with the classical locked-on state arising from transverse oscillations of a cylinder in uniform flow, it is possible to attain either locked-on or quasi-locked-on states due to streamwise oscillations. In these cases, however, the repetitive signature of the transverse force is not sinusoidal; rather, it is strongly modulated and the corresponding spectra can exhibit several sharply defined peaks. The predominant peak can vary over a remarkably wide range, extending from the subharmonic to the third harmonic of the cylinder oscillation frequency; for certain locked-on states of the transverse force signature, the spectral peak at the cylinder oscillation frequency is actually suppressed. Corresponding instantaneous traces and spectra of the in-line force simply show dominance of the spectral peak at the cylinder oscillation frequency. Further interpretation of the loading is provided in terms of Lissajous patterns of the transverse and in-line force coefficients.All of these features are related to the instantaneous patterns of vortex formation in the near wake. During a typical cycle of the cylinder oscillation, these patterns can be divided into two broad categories: Kármán-like shedding; and a nearly ‘frozen’ array of shed vortices. The order of occurrence of these basic patterns during an oscillation cycle dictates the instantaneous signatures and time-averaged spectra of the transverse force.

On the behaviour of a fluid-loaded cylindrical shell with mean flow

1997 ◽  
Vol 338 ◽  
pp. 387-410 ◽  
Author(s):  
N. PEAKE
Keyword(s):  
Flat Plate ◽  
Critical Radius ◽  
Radiation Condition ◽  
Negative Energy ◽  
Flow Speed ◽  
Single Frequency ◽  
Engineering Practice ◽  
Absolute Instability ◽  
Mean Flow ◽  
Flow Speeds

The unsteady behaviour of an infinitely long fluid-loaded elastic plate which is driven by a single-frequency point-force excitation in the presence of mean flow is known to exhibit a number of unexpected features, including absolute instability when the normalized flow speed, U, lies above some critical speed U0, and certain unusual propagation effects for U<U0. In the latter respect Crighton & Oswell (1991) have demonstrated most significantly that for a particular frequency range there exists an anomalous neutral (negative energy) mode which has group velocity pointing towards the driver, in violation of the usual radiation condition of outgoing waves at infinity. They show that the rate of working of the driver can be negative, due to the presence of other negative-energy waves, and can also become infinite at a critical frequency corresponding to a real modal coalescence. In this paper we attempt to extend these results by including, as is usually the case in a practical situation, plate curvature in the transverse direction, by considering a fluid-loaded cylinder with axial mean flow. In the limit of infinite normalized cylinder radius, a, Crighton & Oswell's results are regained, but for finite a very significant modifications are found. In particular, we demonstrate that the additional stiffness introduced by the curvature typically moves the absolute-instability boundary to a much higher flow speed than for the flat-plate case. Below this boundary we show that Crighton & Oswell's anomalous neutral mode can only occur for a>a1(U), but in practical situations it turns out that a1(U) is exceedingly large, and indeed seems much larger than radii of curvature achievable in engineering practice. Other negative-energy waves are seen to exist down to a smaller, but still very large, critical radius a2(U), while the existence of a real modal coalescence point, leading to a divergence in the driver admittance, occurs down to a slightly smaller critical radius a3(U). The transition through these various flow regimes as U and a vary is fully described by numerical investigation of the dispersion relation and by asymptotic analysis in the (realistic) limit of small U. The inclusion of plate dissipation is also considered, and, in common with Abrahams & Wickham (1994) for the flat plate, we show how the flow then becomes absolutely unstable at all flow speeds provided that a>a2(U).

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.

Critical-level behaviour and wave amplification of a gravity wave incident upon a shear layer

1975 ◽  
Vol 72 (4) ◽  
pp. 661-671 ◽  
Author(s):  
I. A. Eltayeb ◽  
J. F. McKenzie
Keyword(s):  
Shear Layer ◽  
Gravity Wave ◽  
Critical Level ◽  
Phase Speed ◽  
Flow Speed ◽  
Wave Incident ◽  
Mean Flow ◽  
Wave Amplification ◽  
The Mean ◽  
Streaming Motion

The properties of reflexion, refraction and absorption of a gravity wave incident upon a shear layer are investigated. It is shown that one must expect these properties to be very different depending upon the parameters (such as the Richardson number Ri, the wavelength normalized by the length scale of the shear and the ratio of the flow speed to the phase speed of the wave) characterizing the interaction of a gravity wave with a shear layer. In particular, it is shown that for all Richardson numbers there is a discontinuity in the net wave-action flux across the critical level, i.e. at a height where the flow speed matches the horizontal phase speed of the wave. When Ri > ¼, this is accompanied by absorption of part of the energy of the incident wave into the mean flow. In addition it is shown that the phenomenon of wave amplification (over-reflexion) can arise provided that the ultimate shear flow speed exceeds the horizontal phase speed of the wave and Ri is less than a certain critical value Ric ≃ 0·1129, in which case the reflected wave extracts energy from the streaming motion. It is also pointed out that wave amplification can lead to instability if the boundary conditions are altered in such a way that the system can behave like an ‘amplifier’.

Flow regimes associated with yawed rectangular cavities

2001 ◽  
Vol 105 (1045) ◽  
pp. 125-134 ◽  
Author(s):  
M. Czech ◽  
E. Savory ◽  
N. Toy ◽  
T. Mavrides
Keyword(s):  
Drag Coefficient ◽  
Shear Layer ◽  
Flow Direction ◽  
Feedback Mechanism ◽  
Cavity Flows ◽  
Mean Flow ◽  
Cavity Depth ◽  
Separated Shear Layer ◽  
Layer Flow ◽  
Low Speed Wind Tunnel

Abstract The present work is concerned with the aerodynamics of the turbulent boundary-layer flow over yawed rectangular cavities with the focus on the steady and unsteady pressures generated by the interaction. Cavities with a planform aspect ratio of 4-85 and streamwise length to depth ratios from 1 to 3 were studied experimentally in a low-speed wind tunnel. The results indicated three main types of cavity flows. The shear layer bridges the cavity for small angles between mean flow direction and minor cavity axis. The flow field remains almost two-dimensional with little change in drag coefficient. Strong instabilities, associated with a rise in drag coefficient, are found when the cavity is yawed to greater angles. An aerodynamic feedback mechanism depending on interactions between the separated shear layer and the cavity fluid is suggested as the mechanism responsible for the generated oscillations. The influence of the cavity depth is, hereby, found to be fundamental as it determines the degree to which interactions between the separated shear layer and the cavity base occur. As a result both the magnitude and the frequency of the instabilities are a function of the cavity depth. When rotating to higher angles a greater portion of the shear layer reattaches to the cavity base which leads to a loss of flow organisation and a significant increase in drag.

Computation of two-phase shear-layer flow using an Eulerian-Lagrangian analysis

1988 ◽  
Author(s):  
JAYANT SABNIS ◽  
SANG-KEUN CHOI ◽  
RICHARD BUGGELN ◽  
HOWARD GIBELING
Keyword(s):  
Shear Layer ◽  
Lagrangian Analysis ◽  
Two Phase ◽  
Layer Flow

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.

Sign in / Sign up

Export Citation Format

Share Document