Response of a fluid‐loaded infinite plate subject to a line force excitation in mean flow

1994 ◽  
Vol 95 (5) ◽  
pp. 2918-2918
Author(s):  
Jinshuo Zhu ◽  
Sean F. Wu
Keyword(s):  
Infinite Plate ◽  
Mean Flow ◽  
Line Force ◽  
Force Excitation

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.

Scattering and distortion of the unsteady motion on transversely sheared mean flows

1979 ◽  
Vol 91 (4) ◽  
pp. 601-632 ◽  
Author(s):  
M. E. Goldstein
Keyword(s):  
Boundary Condition ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Low Frequency ◽  
Unsteady Motion ◽  
Transverse Component ◽  
Mean Flow ◽  
Hydrodynamic Motion ◽  
Inhomogeneous Wave Equation ◽  
Derivatives Of

It is shown that the pressure and velocity fluctuations of the unsteady motion on a transversely sheared mean flow can be expressed entirely in terms of the derivatives of two potential functions. One of these is a convected quantity (i.e. it is frozen in the flow) that can be specified as a boundary condition and is related to a transverse component of the upstream velocity field. The other can be determined by solving an inhomogeneous wave equation whose source term is also a convected quantity that can be specified as a boundary condition in any given problem. The latter is related to the curl of the upstream vorticity field. The results are used to obtain an explicit representation of the three-dimensional gust-like or hydrodynamic motion on a transversely sheared mean flow. It is thereby shown that this motion is ‘driven’ entirely by the two convected quantities alluded to above.The general theory is used to study the interaction of an unsteady flow with a scmi-infinite plate embedded in a shear layer. The acoustic field produced by this interaction is calculated in the limits of low and high frequency. The results are compared with experimental one-third octave sound pressure level radiation patterns. The agreement is found to be excellent, especially in the low frequency range, where the mean-flow and convective effects are shown to have a strong influence on the directivity of the sound.

The influence of vortex shedding on the generation of sound by convected turbulence

1976 ◽  
Vol 76 (4) ◽  
pp. 711-740 ◽  
Author(s):  
M. S. Howe
Keyword(s):  
Vortex Shedding ◽  
Infinite Plate ◽  
Vortex Sheet ◽  
Realistic Model ◽  
Diffraction Field ◽  
Mean Flow ◽  
Turbulent Eddy ◽  
Trailing Edge ◽  
Kutta Condition ◽  
Mathematical Problems

This paper discusses the theory of the generation of sound which occurs when a frozen turbulent eddy is convected in a mean flow past an airfoil or a semi-infinite plate, with and without the application of a Kutta condition and with and without the presence of a mean vortex sheet in the wake. A sequence of two-dimensional mathematical problems involving a prototype eddy in the form of a line vortex is examined, it being argued that this constitutes the simplest realistic model. Important effects of convection are deduced which hitherto have not been revealed by analyses which assume quadrupole sources to be at rest relative to the plate or airfoil. It is concluded that, to the order of approximation to which the sound from convected turbulence near a scattering body is usually estimated, the imposition of a Kutta condition at the trailing edge leads to a complete cancellation of the sound generated when frozen turbulence convects past a semi-infinite plate, and to the cancellation of the diffraction field produced by the trailing edge in the case of an airfoil of compact chord.

Fluid Structure Interaction With Mean Flow: Over-Scattering and Unstable Resonance Growth

2010 ◽  
Author(s):  
Sevag Arzoumanian ◽  
Nigel Peake
Keyword(s):  
Convective Instability ◽  
Plate Theory ◽  
Computational Study ◽  
Infinite Plate ◽  
Negative Energy ◽  
Linear Instability ◽  
Mean Flow ◽  
Scattering Coefficients ◽  
Resonance Frequencies ◽  
Long Time

It is known theoretically [1–3] that infinitely long fluid loaded plates in mean flow exhibit a range of unusual phenomena in the ‘long time’ limit. These include convective instability, absolute instability and negative energy waves which are destabilized by dissipation. However, structures are necessarily of finite length and may have discontinuities. Moreover, linear instability waves can only grow over a limited number of cycles before non-linear effects become dominant. We have undertaken an analytical and computational study to investigate the response of finite, discontinuous plates to ascertain if these unusual effects might be realized in practice. Analytically, we take a “wave scattering” [2,4] — as opposed to a “modal superposition” [5] — view of the fluttering plate problem. First, we solve for the scattering coefficients of localized plate discontinuities and identify a range of parameter space, well outside the convective instability regime, where over-scattering or amplified reflection/transmission occurs. These are scattering processes that draw energy from the mean flow into the plate. Next, we use the Wiener-Hopf technique to solve for the scattering coefficients from the leading and trailing edges of a baffled plate. Finally, we construct the response of a finite, baffled plate by a superposition of infinite plate propagating waves continuously scattering off the plate ends and solve for the unstable resonance frequencies and temporal growth rates for long plates. We present a comparison between our computational results and the infinite plate theory. In particular, the resonance response of a moderately sized plate is shown to be in excellent agreement with our long plate analytical predictions.

Eddy forcing of the mean flow in the Southern Ocean

2001 ◽  
Vol 106 (C2) ◽  
pp. 2713-2722 ◽  
Author(s):  
Chris W. Hughes
Keyword(s):  
Southern Ocean ◽  
Mean Flow ◽  
The Mean
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