Structural acoustics with mean flow: Instability waves on force excited submerged elastic structures

2001 ◽  
Vol 109 (5) ◽  
pp. 2489-2489
Author(s):  
Sevag H. Arzoumanian
Keyword(s):  
Flow Instability ◽  
Structural Acoustics ◽  
Mean Flow ◽  
Elastic Structures ◽  
Instability Waves

scholarly journals Investigation of dominant traveling 10-day wave components using long-term MERRA-2 database

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Chunming Huang ◽  
Wei Li ◽  
Shaodong Zhang ◽  
Gang Chen ◽  
Kaiming Huang ◽  
...  
Keyword(s):  
Flow Instability ◽  
Transmission Condition ◽  
Wave Number ◽  
Mean Flow ◽  
Excited Wave ◽  
Propagating Waves ◽  
Zonal Wave Number ◽  
The Mean

AbstractThe eastward- and westward-traveling 10-day waves with zonal wavenumbers up to 6 from surface to the middle mesosphere during the recent 12 years from 2007 to 2018 are deduced from MERRA-2 data. On the basis of climatology study, the westward-propagating wave with zonal wave number 1 (W1) and eastward-propagating waves with zonal wave numbers 1 (E1) and 2 (E2) are identified as the dominant traveling ones. They are all active at mid- and high-latitudes above the troposphere and display notable month-to-month variations. The W1 and E2 waves are strong in the NH from December to March and in the SH from June to October, respectively, while the E1 wave is active in the SH from August to October and also in the NH from December to February. Further case study on E1 and E2 waves shows that their latitude–altitude structures are dependent on the transmission condition of the background atmosphere. The presence of these two waves in the stratosphere and mesosphere might have originated from the downward-propagating wave excited in the mesosphere by the mean flow instability, the upward-propagating wave from the troposphere, and/or in situ excited wave in the stratosphere. The two eastward waves can exert strong zonal forcing on the mean flow in the stratosphere and mesosphere in specific periods. Compared with E2 wave, the dramatic forcing from the E1 waves is located in the poleward regions.

Amplitude propagation in slowly varying trains of shear-flow instability waves

1986 ◽  
Vol 170 ◽  
pp. 21-51 ◽  
Author(s):  
J. M. Russell
Keyword(s):  
Variational Principles ◽  
Flow Instability ◽  
Near Field ◽  
Equations Of Motion ◽  
Wave Action ◽  
Small Disturbance ◽  
Instability Waves ◽  
Action Density ◽  
Spatial Coordinates ◽  
Shear Flow Instability

The analog of Whitham's law of conservation of wave action density is derived in the case of Rayleigh instability waves. The analysis allows for wave propagation in two space dimensions, non-unidirectionality of the background flow velocity profiles and weak horizontal nonuniformity and unsteadiness of those profiles. The small disturbance equations of motion in the Eulerian flow description are subject to a change of dependent variable in which the new variable represents the pressure-driven part of a disturbance material coordinate function as a function of the Cartesian spatial coordinates and time. Several variational principles expressing the physics of the small disturbance equations of motion are presented in terms of this new variable. A law of conservation of ‘bilinear wave action density’ is derived by a method intermediate between those of Jimenez and Whitham (1976) and Hayes (1970a). The distinction between the observed square amplitude of an amplified wavetrain and the wave action density is discussed. Three types of algebraic focusing are discussed, the first being the far-field ‘caustics’, the second being near-field ‘movable singularities’, and the third being a focusing mechanism due to Landahl (1972) which we here derive under somewhat weaker hypotheses.

Ribbed elastic structures under a mean flow

2005 ◽  
Vol 461 (2056) ◽  
pp. 913-931
Author(s):  
Paul D Metcalfe
Keyword(s):  
Band Structure ◽  
Transfer Matrix ◽  
Anderson Localization ◽  
Stop Band ◽  
Matrix Inversion ◽  
Mean Flow ◽  
Elastic Structures ◽  
Band Matrix ◽  
Disordered Structures ◽  
Static Fluid

The problem of a ribbed membrane or plate submerged in a fluid with mean flow is studied. We first derive a method which can be used to reduce this, and similar problems to a band matrix inversion. We then find the pass and stop band structure found in the case of static fluid persists when a mean flow is introduced, and we give an explanation in terms of the eigenvalues of the transfer matrix of the system. We then study disordered structures and observe the phenomenon of Anderson localization. In some parameter régimes the addition of disorder causes significant delocalization.

The role of nonlinear critical layers in boundary layer transition

1995 ◽  
Vol 352 (1700) ◽  
pp. 425-442 ◽  
Keyword(s):  
Asymptotic Methods ◽  
Nonlinear Effects ◽  
Boundary Layer Transition ◽  
Critical Layer ◽  
Mean Flow ◽  
Layer Transition ◽  
Instability Waves ◽  
Laminar Boundary Layers ◽  
Instability Modes ◽  
Critical Layers

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear spatially growing instability waves evolve downstream in nominally two-dimensional laminar boundary layers. The first nonlinear reaction takes place locally within a so-called ‘critical layer’, with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves - which may or may not be accompanied by an associated plane wave. The amplitudes of these waves, which are completely determined by nonlinear effects within the critical layer, satisfy either a single integro-differential equation or a pair of integro-differential equations with quadratic to quartic-type nonlinearities. The physical implications of these equations are discussed.

Sound generated by instability wave/shock-cell interaction in supersonic jets

2007 ◽  
Vol 587 ◽  
pp. 173-215 ◽  
Author(s):  
PRASUN K. RAY ◽  
SANJIVA K. LELE
Keyword(s):  
Cell Structure ◽  
Cell Interaction ◽  
Linear Instability ◽  
Supersonic Jets ◽  
Instability Wave ◽  
Destructive Interference ◽  
Source Terms ◽  
Mean Flow ◽  
Shock Cell ◽  
Instability Waves

Broadband shock-associated noise is an important component of the overall noise generated by modern airplanes. In this study, sound generated by the weakly nonlinear interaction between linear instability waves and the shock-cell structure in supersonic jets is investigated numerically in order to gain insight into the broadband shock-noise problem. The model formulation decomposes the overall flow into a mean flow, linear instability waves, the shock-cell structure and shock-noise. The mean flow is obtained by solving RANSequations with a k-ε model. Locally parallel stability equations are solved for the shock structure, and linear parabolized stability equations are solved for the instability waves. Then, source terms representing the instability wave/shock-cell interaction are assembled and the inhomogeneous linearized Euler equations are solved for the shock-noise.Three cases are considered, a cold under-expanded Mj = 1.22 jet, a hot under-expanded Mj = 1.22 jet, and a cold over-expanded Mj = 1.36 jet.Shock-noise computations are used to identify and understand significant trends in peak sound amplitudes and radiation angles. The peak sound radiation angles are explained well with the Mach wave model of Tam & Tanna J. Sound Vib. Vol. 81, 1982, p. 337). The observed reduction of peak sound amplitudes with frequency correlates well with the corresponding reduction of instability wave growth with frequency. However, in order to account for variation of sound amplitude for different azimuthal modes, the radial structure of the instability waves must be considered in additionto streamwise growth. The effect of heating on the Mj = 1.22 jet is shown to enhance the sound radiated due to the axisymmetric instability waves while the other modesare relatively unaffected. Solutions to a Lilley–Goldstein equation show that soundgenerated by ‘thermodynamic’ source terms is small relative to sound from ‘momentum’ sources though heating does increase the relative importance of the thermodynamic source. Furthermore, heating preferentially amplifies sound associated with the axisymmetric modes owing to constructive interference between sound from the momentumand thermodynamic sources. However, higher modes show destructive interference between these two sources and are relatively unaffected by heating.

Tip Leakage Behavior and Large Coherent Perturbation Analysis of an Axial-radial Combined Compressor with Outlet Distortion

2021 ◽  
Author(s):  
Li Fu ◽  
Ce Yang ◽  
Chenxing Hu ◽  
Xin Shi
Keyword(s):  
Transient Flow ◽  
Flow Instability ◽  
Complex Structure ◽  
Potential Effect ◽  
Structure Design ◽  
Mean Flow ◽  
Tip Leakage Flow ◽  
Compact Structure ◽  
Tip Leakage ◽  
Flow Unsteadiness

Abstract Increasing performance requirements and compact structure design promote the generation of axial-radial combined compressors. However, its complex structure and asymmetrical outlet boundary cause difficulty to get an in-depth comprehension of the flow unsteadiness associated with spike-stall. In this work, unsteady full-annular simulations of an axial-radial combined compressor coupled with performance experiment validations were carried out. Based on the overall understanding of outlet distortion on each component, the general feature of tip leakage flow with asymmetrical outlet boundary was extracted. The temporal and spatial development of large coherent perturbations was revealed by the decomposition and reconstruction of the transient flow data with the DMD approach. The results demonstrate that the outlet distortion can propagate reversely to the compressor inlet and the degree of distortion decreases gradually, which leads to the highest possibility for radial rotor to suffer from flow unsteadiness. In the circumferential location with distortion affected, the leakage momentum of the adjacent blade LE is enhanced by the secondary leakage, inducing the expansion of TLV and causing flow instability. Besides organized perturbation structures related to mean flow and BPF, two large low-frequency stall perturbations approximately one-third and three-fourth RF was captured by the DMD method, which is caused by volute potential effect and stator/rotor interference, respectively. The former occurs in the radial rotor and decays during its propagation, while the latter always exists owing to the multiple rotor/stator or stator/rotor interference in the axial-radial combined compressor.

Nonlinear evolution of a pair of oblique instability waves in a supersonic boundary layer

1995 ◽  
Vol 282 ◽  
pp. 339-371 ◽  
Author(s):  
S. J. Leib ◽  
Sang Soo Lee
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Nonlinear Evolution ◽  
Supersonic Boundary Layer ◽  
Inviscid Limit ◽  
Instability Wave ◽  
Neutral Stability ◽  
Mean Flow ◽  
Number Range ◽  
Instability Waves

We study the nonlinear evolution of a pair of oblique instability waves in a supersonic boundary layer over a flat plate in the nonlinear non-equilibrium viscous critical layer regime. The instability wave amplitude is governed by the same integro-differential equation as that derived by Goldstein & Choi (1989) in the inviscid limit and by Wu, Lee & Cowley (1993) with viscous effects included, but the coefficient appearing in this equation depends on the mean flow and linear neutral stability solution of the supersonic boundary layer. This coefficient is evaluated numerically for the Mach number range over which the (inviscid) first mode is the dominant instability. Numerical solutions to the amplitude equation using these values of the coefficient are obtained. It is found that, for insulated and cooled wall conditions and angles corresponding to the most rapidly growing waves, the amplitude ends in a singularity at a finite downstream position over the entire Mach number range regardless of the size of the viscous parameter. The explosive growth of the instability waves provides a mechanism by which the boundary layer can break down. A new feature of the compressible problem is the nonlinear generation of a spanwise-dependent mean distortion of the temperature along with that of the velocity found in the incompressible case.

scholarly journals An investigation into inflection-point instability in the entrance region of a pulsating pipe flow

2017 ◽  
Vol 473 (2197) ◽  
pp. 20160590 ◽  
Author(s):  
J. J. Miau ◽  
R. H. Wang ◽  
T. W. Jian ◽  
Y. T. Hsu
Keyword(s):  
Pipe Flow ◽  
Inflection Point ◽  
Flow Instability ◽  
Mixing Layer ◽  
Phase Region ◽  
Entrance Region ◽  
Mean Flow ◽  
Layer Model ◽  
Flow Disturbance ◽  
Stokes Layer

This paper investigates the inflection-point instability that governs the flow disturbance initiated in the entrance region of a pulsating pipe flow. Under such a flow condition, the flow instability grows within a certain phase region in a pulsating cycle, during which the inflection point in the unsteady mean flow lifts away from the viscous effect-dominated region known as the Stokes layer. The characteristic frequency of the instability is found to be in agreement with that predicted by the mixing-layer model. In comparison with those cases not falling in this category, it is further verified that the flow phenomenon will take place only if the inflection point lifts away sufficiently from the Stokes layer.

On the non-separable baroclinic parallel flow instability problem

1970 ◽  
Vol 40 (2) ◽  
pp. 273-306 ◽  
Author(s):  
Michael E. McIntyre
Keyword(s):  
Flow Instability ◽  
Baroclinic Instability ◽  
Short Wave ◽  
Perturbation Series ◽  
Rate Of Change ◽  
Horizontal Shear ◽  
Mean Flow ◽  
Wave Regime ◽  
Parallel Flows ◽  
The Mean

Perturbation series are developed and mathematically justified, using a straightforward perturbation formalism (that is more widely applicable than those given in standard textbooks), for the case of the two-dimensional inviscid Orr-Sommerfeld-like eigenvalue problem describing quasi-geostrophic wave instabilities of parallel flows in rotating stratified fluids.The results are first used to examine the instability properties of the perturbed Eady problem, in which the zonal velocity profile has the formu=z+ μu1(y,z) where, formally, μ [Lt ] 1. The connexion between baroclinic instability theories with and without short wave cutoffs is clarified. In particular, it is established rigorously that there is instability at short wavelengths in all cases for which such instability would be expected from the ‘critical layer’ argument of Bretherton. (Therefore the apparently conflicting results obtained earlier by Pedlosky are in error.)For the class of profiles of formu=z+ μu1(y) it is then shown from an examination of theO(μ) eigenfunction correction why, under certain conditions, growing baroclinic waves will always produce a counter-gradient horizontal eddy flux of zonal momentum tending to reinforce the horizontal shear of such profiles. Finally, by computing a sufficient number of the higher corrections, this first-order result is shown to remain true, and its relationship to the actual rate of change of the mean flow is also displayed, for a particular jet-like form of profile withfinitehorizontal shear. The latter detailed results may help to explain at least one interesting feature of the mean flow found in a recent numerical solution for the wave régime in a heated rotating annulus.

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