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).

Fluid-loaded elastic plate with mean flow: point forcing and three-dimensional effects

2001 ◽  
Vol 428 ◽  
pp. 305-331
Author(s):  
M. R. GREEN ◽  
D. G. CRIGHTON
Keyword(s):  
Elastic Plate ◽  
Critical Angle ◽  
Single Frequency ◽  
Absolute Instability ◽  
Frequency Range ◽  
Mean Flow ◽  
Curvature Effects ◽  
Flow Speeds ◽  
Neutral Mode ◽  
Asymptotic Forms

The unsteady behaviour of an infinitely long fluid-loaded elastic plate subject to a single-frequency line forcing in the presence of a uniform mean flow is known to exhibit a number of interesting phenomena. These include the onset of absolute instability for non-dimensional flow speeds U in excess of some critical speed Uc, and various interesting propagation effects when U < Uc. In the latter respect Crighton & Oswell (1991) have shown that over a particular frequency range there exists an anomalous neutral mode with group velocity directed towards the driver, in violation of the usual Lighthill outgoing radiation condition. Similar results have been found by Peake (1997) when transverse curvature effects are included. In this paper we seek to extend these results and consider the substantially harder problem of a fluid-loaded elastic plate with uniform mean flow which is subject to a point forcing, thereby resulting in a two-dimensional structural problem. A systematic method for determining the absolute instability threshold is developed, and it is shown that the flow is absolutely unstable for flow speeds U > Uc, where Uc is the one-dimensional value found by Crighton & Oswell. At flow speeds U < Uc the flow is marginally stable and convective growth is found to occur downstream of the driver, over a particular frequency range depending on the transverse Fourier wavenumber ky, within a wedge-shaped region. Outside this wedge-shaped region there is only neutral mode behaviour. Asymptotic forms are found for the dominant large-distance causal flexion response downstream of the driver inside and outside the wedge region, and the appropriate critical angle for the wedge region is identified. Within the convective instability wedge the flexion and critical angle take two different forms depending on whether the frequency ω is greater or less than U2/√5. In addition to this interesting behaviour, the flow also exhibits the usual anomalous neutral mode behaviour and, as with Peake's problem, we also find an extra stability (hoop) resulting in neutral mode behaviour over a small frequency range. Asymptotic forms are also found for the threshold frequencies which divide up the various regions of stability of the system (neutral, neutral anomalous, convectively unstable), as a function of ky, and are compared with the results of both Crighton & Oswell and Peake.

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.

ABSOLUTE INSTABILITY OR CHAOS? — A TRIBUTE TO DR. DAVID G. CRIGHTON

2002 ◽  
Vol 10 (04) ◽  
pp. 407-419
Author(s):  
SEAN F. WU
Keyword(s):  
Elastic Plate ◽  
Equilibrium Position ◽  
Flexural Vibration ◽  
Critical Value ◽  
Flow Speed ◽  
Multiple Equilibrium ◽  
Absolute Instability ◽  
Mean Flow ◽  
Structural Nonlinearities ◽  
The Mean

The stabilities of an elastic plate clamped on an infinite, rigid baffle subject to any time dependent force excitation in the presence of mean flow are examined. The mechanisms that can cause plate flexural vibrations to be absolute unstable when the mean flow speed exceeds a critical value are revealed. Results show that the instabilities of an elastic plate are mainly caused by an added stiffness due to acoustic radiation in mean flow, but controlled by the structural nonlinearities. This added stiffness is shown to be negative and increase quadratically with the mean flow speed. Hence, as the mean flow speed approaches a critical value, the added stiffness may null the overall stiffness of the plate, leading to an unstable condition. Note that without the inclusion of the structural nonlinearities, the plate has only one equilibrium position, namely, its undeformed flat position. Under this condition, the amplitude of plate flexural vibration would grow exponentially in time everywhere, known as absolute instability. With the inclusion of structural nonlinearities, the plate may possess multiple equilibrium positions. When the mean flow speed exceeds the critical values, the plate may be unstable and jump from one equilibrium position to another. Since this jumping is random, the plate flexural vibration may seem chaotic.

scholarly journals Finite disturbance effect on the stability of a laminar incompressible wake behind a flat plate

1970 ◽  
Vol 40 (2) ◽  
pp. 315-341 ◽  
Author(s):  
D. Ru-Sue Ko ◽  
T. Kubota ◽  
L. Lees
Keyword(s):  
Flat Plate ◽  
Finite Amplitude ◽  
Single Frequency ◽  
Shape Parameters ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Flow Parameters ◽  
Local Mean ◽  
The Mean ◽  
The Stability

An integral method is used to investigate the interaction between a two-dimensional, single frequency finite amplitude disturbance in a laminar, incompressible wake behind a flat plate at zero incidence. The mean flow is assumed to be a non-parallel flow characterized by a few shape parameters. Distribution of the fluctuation across the wake is obtained as functions of those mean flow parameters by solving the inviscid Rayleigh equation using the local mean flow. The variations of the fluctuation amplitude and of the shape parameters for the mean flow are then obtained by solving a set of ordinary differential equations derived from the momentum and energy integral equations. The interaction between the mean flow and the fluctuation through Reynolds stresses plays an important role in the present formulation, and the theoretical results show good agreement with the measurements of Sato & Kuriki (1961).

scholarly journals Large amplitude, short wave peristalsis and its implications for transport

2015 ◽  
Author(s):  
Lindsay D Waldrop ◽  
Laura A. Miller
Keyword(s):  
Fluid Flow ◽  
Large Amplitude ◽  
Compression Wave ◽  
Wave Speed ◽  
Flow Direction ◽  
Short Wave ◽  
Flow Speed ◽  
Biological Pumps ◽  
Flow Speeds ◽  
Flow Compression

Valveless, tubular pumps are widespread in the animal kingdom, but the mechanism by which these pumps generate fluid flow are often in dispute. Where the pumping mechanism of many organs was once described as peristalsis, other mechanisms, such as dynamic suction pumping, have been suggested as possible alternative mechanisms. Peristalsis is often evaluated using criteria established in a technical definition for mechanical pumps, but this definition is based on a small-amplitude, long-wave approximation which biological pumps often violate. In this study, we use a direct numerical simulation of large-amplitude, short-wave peristalsis to investigate the relationships between fluid flow, compression frequency, compression wave speed, and tube occlusion. We also explore how the flows produced differ from the criteria outlined in the technical definition of peristalsis. We find that many of the technical criteria are violated by our model: fluid flow speeds produced by peristalsis are greater than the speeds of the compression wave; fluid flow is pulsatile; and flow speed have a non-linear relationship with compression frequency when compression wave speed is held constant. We suggest that the technical definition is inappropriate for evaluating peristalsis as a pumping mechanism for biological pumps because they too frequently violate the assumptions inherent in these criteria. Instead, we recommend that a simpler, more inclusive definition be used for assessing peristalsis as a pumping mechanism based on the presence of non-stationary compression sites that propagate uni-directionally along a tube without the need for a structurally fixed flow direction.

scholarly journals An Efficient Scheme for Onboard Reduction of Moored χpod Data

2017 ◽  
Vol 34 (11) ◽  
pp. 2533-2546 ◽  
Author(s):  
Johannes Becherer ◽  
James N. Moum
Keyword(s):  
Heat Flux ◽  
Temperature Gradient ◽  
Fast Response ◽  
Flow Speed ◽  
Mean Flow ◽  
Temperature Variance ◽  
Efficient Scheme ◽  
Linear Accelerometer

AbstractA scheme for significantly reducing data sampled on turbulence devices (χpods) deployed on remote oceanographic moorings is proposed. Each χpod is equipped with a pitot-static tube, two fast-response thermistors, a three-axis linear accelerometer, and a compass. In preprocessing, voltage means, variances, and amplitude of the subrange (inertial-convective subrange of the turbulence) of the voltage spectrum representing the temperature gradient are computed. Postprocessing converts voltages to engineering units, in particular mean flow speed (and velocity), temperature, temperature gradient, and the rate of destruction of the temperature variance χ from which other turbulence quantities, such as heat flux, are derived. On 10-min averages, this scheme reduces the data by a factor of roughly 24 000 with a small (5%) low bias compared to complete estimates using inertial-convective subrange scaling of calibrated temperature gradient spectra.

Negative energy standing wave instability in the presence of flow

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
Michael S. Ruderman
Keyword(s):  
Standing Wave ◽  
Negative Energy ◽  
Flow Speed ◽  
Tangential Discontinuity ◽  
Positive Energy ◽  
Wave Instability ◽  
Long Wavelength ◽  
Backward Wave ◽  
Moving Plasma ◽  
The Difference

We study standing waves on the surface of a tangential discontinuity in an incompressible plasma. The plasma is moving with constant velocity at one side of the discontinuity, while it is at rest at the other side. The moving plasma is ideal and the plasma at rest is viscous. We only consider the long wavelength limit where the viscous Reynolds number is large. A standing wave is a superposition of a forward and a backward wave. When the flow speed is between the critical speed and the Kelvin–Helmholtz threshold the backward wave is a negative energy wave, while the forward wave is always a positive energy wave. We show that viscosity causes the standing wave to grow. Its increment is equal to the difference between the negative energy wave increment and the positive energy wave decrement.

Effects of Shield Gas Flow on Meltpool Variability and Signature in Scanned Laser Melting

2020 ◽  
Author(s):  
David C. Deisenroth ◽  
Jorge Neira ◽  
Jordan Weaver ◽  
Ho Yeung
Keyword(s):  
Additive Manufacturing ◽  
Aspect Ratio ◽  
Flow Velocity ◽  
Process Monitoring ◽  
Gas Flow ◽  
Laser Energy ◽  
Flow Speed ◽  
Powder Bed ◽  
Flow Speeds ◽  
Gas Flow Velocity

Abstract In laser powder bed fusion metal additive manufacturing, insufficient shield gas flow allows accumulation of condensate and ejecta above the build plane and in the beam path. These process byproducts are associated with beam obstruction, attenuation, and thermal lensing, which then lead to lack of fusion and other defects. Furthermore, lack of gas flow can allow excessive amounts of ejecta to redeposit onto the build surface or powder bed, causing further part defects. The current investigation was a preliminary study on how gas flow velocity and direction affect laser delivery to a bare substrate of Nickel Alloy 625 (IN625) in the National Institute of Standards and Technology (NIST) Additive Manufacturing Metrology Testbed (AMMT). Melt tracks were formed under several gas flow speeds, gas flow directions, and energy densities. The tracks were then cross-sectioned and measured. The melt track aspect ratio and aspect ratio coefficient of variation (CV) were reported as a function of gas flow speed and direction. It was found that a mean gas flow velocity of 6.7 m/s from a nozzle 6.35 mm in diameter was sufficient to reduce meltpool aspect ratio CV to less than 15 %. Real-time inline hotspot area and its CV were evaluated as a process monitoring signature for identifying poor laser delivery due to inadequate gas flow. It was found that inline hotspot size could be used to distinguish between conduction mode and transition mode processes, but became diminishingly sensitive as applied laser energy density increased toward keyhole mode. Increased hotspot size CV (associated with inadequate gas flow) was associated with an increased meltpool aspect ratio CV. Finally, it was found that use of the inline hotspot CV showed a bias toward higher CV values when the laser was scanned nominally toward the gas flow, which indicates that this bias must be considered in order to use hotspot area CV as a process monitoring signature. This study concludes that gas flow speed and direction have important ramifications for both laser delivery and process monitoring.

scholarly journals Experimental Study on the Effects of a Vertical Jet Impinging on Soft Bottom Sediments

2020 ◽  
Vol 12 (9) ◽  
pp. 3775 ◽  
Author(s):  
Wei Fan ◽  
Weicheng Bao ◽  
Yong Cai ◽  
Canbo Xiao ◽  
Zhujun Zhang ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Side Effects ◽  
Field Experiments ◽  
Sediment Resuspension ◽  
Ecological Engineering ◽  
Phosphorus Release ◽  
Flow Speed ◽  
Critical Conditions ◽  
Water Tank ◽  
Flow Speeds

Artificial downwelling, which is an ecological engineering method, potentially alleviates bottom hypoxia by bringing oxygen-rich surface water down below the pycnocline. However, the downward flow is likely to disturb sediments (or induce sediment resuspension) when reaching the bottom and then have unwanted side effects on the local ecosystem. To evaluate this, our paper presents a theoretical model and experimental data for the sediment resuspension caused by artificial downwelling. The theoretical model considers the critical conditions for sediment resuspension and the scour volume with the downwelling flow disturbing sediment. Experiments with altered downwelling flow speeds, discharge positions relative to the bottom, and particle sizes of sediment were conducted in a water tank, and the results were consistent with our theoretical model. The results show that the critical Froude number (hereinafter Fr) for sediment resuspension is 0.5. The prevention of sediment resuspension requires the downwelling flow speed and the discharge position to be adjusted so that Fr < 0.5; otherwise a portion of sediment is released into the water and its volume can be predicted by the derived formulation based on the Shields theory. Furthermore, sediment resuspension has side effects, such as a water turbidity increase and phosphorus release, the magnitudes of which are discussed with respect to engineering parameters. Further study will focus on field experiments of artificial downwelling and its environmental impacts.

Sign in / Sign up

Export Citation Format

Share Document