Flow-resonant sound interaction in a duct containing a plate,part I: Semi-circular leading edge

The interaction between flow and flow-induced acoustic resonances near rigid plates with semi-circular leading edges located in a hard-walled duct is described. These plates generate acoustic resonances over flow velocity ranges depending on thickness, chord and trailing edge geometry, together with rigidity, internal dimensions, length of the working section and shape of the terminations of the working section. A potential flow model for the plate with a smooth leading edge is developed, and the acoustic power generated by vortices growing and shedding from the trailing edge is calculated. The rate of growth of the vortices is determined by an instantaneous Kutta condition applied over part of the cycle. This technique simulates the influence of the sound field on vortex growth.     

Experimental examination of vortex-sound generation in an organ pipe: A proposal of jet vortex-layer formation model

Aero-dynamical models of sound generation in an organ pipe driven by a thin jet are investigated through an experimental examination of the vortex-sound theory. An important measurement requirement (acoustic cross-flow as an irrotational potential flow reciprocating sinusoidally) from the vortex-sound theory is carefully realized when the pipe is driven with low blowing pressures of about 60 Pa (jet velocities of about 10 m/s). Particle image velocimetry (PIV) is applied to measure the jet velocity and the acoustic cross-flow velocity over the mouth area at the same phase by quickly switching the jet drive and the loudspeaker-horn drive. The vorticity of the jet flow field and the associated acoustic generation term are evaluated from the measurement data. It is recognized that the model of the “jet vortex-layer formation” is more relevant to the sound production than the vortex-shedding model. The acoustic power is dominantly generated by the flow–acoustic interaction near the edge, where the acoustic cross-flow velocity takes larger magnitudes. The acoustic generation formula on the vortex sound cannot deny the conventional acoustical volume-flow model because of the in-phase relation satisfied between the acoustic pressure at the mouth and the acoustic volume flow into the pipe. The vortex layers formed along both sides of the jet act as the source of an accelerating force (through the “acceleration unbalance”) with periodically alternating direction to oscillate the jet flow and to reinforce the acoustic cross-flow at the pipe mouth.     

Aerodynamic sound generation of flapping wing

The unsteady flow and acoustic characteristics of the flapping wing are numerically investigated for a two-dimensional model of Bombus terrestris bumblebee at hovering and forward flight conditions. The Reynolds number Re, based on the maximum translational velocity of the wing and the chord length, is 8800 and the Mach number M is 0.0485. The computational results show that the flapping wing sound is generated by two different sound generation mechanisms. A primary dipole tone is generated at wing beat frequency by the transverse motion of the wing, while other higher frequency dipole tones are produced via vortex edge scattering during a tangential motion. It is also found that the primary tone is directional because of the torsional angle in wing motion. These features are only distinct for hovering, while in forward flight condition, the wing-vortex interaction becomes more prominent due to the free stream effect. Thereby, the sound pressure level spectrum is more broadband at higher frequencies and the frequency compositions become similar in all directions.     

VORTEX-SURFACE INTERACTION NOISE: A COMPENDIUM OF WORKED EXAMPLES

Students attending a graduate course on the Theory of Vortex Sound given recently at Boston University were required to investigate the low Mach number unsteady flow and the accompanying acoustic radiation for a selection of idealized flow-structure interactions. These included linear and non-linear parallel blade-vortex interactions for two-dimensional airfoils, and for finite span airfoils of variable chord; interactions between line vortices and surface projections from a plane wall; bluff-body interactions involving line and ring vortices impinging on circular cylindrical and spherical bodies, and vortex motion in the neighborhood of a wall aperture. In all cases, the effective source region was localized in either two or three dimensions, and could be regarded as acoustically compact, and the sound was calculated by routine numerical methods using the theory of compact Green functions. The results are collected together in this paper as a compendium of canonical solutions that provide qualitative and quantitative insight into the mechanisms responsible for sound production, and a database that can be used to validate predictions of more generally applicable numerical schemes.     

Analysis of sound attenuation in a duct with a solid or porous splitter

The equivalent singularity method is developed for the analysis of sound propagation in a duct with a thin solid or point-reacting porous splitter of a finite streamwise length. The method consists in representing the splitter by a singular plane of pressure dipoles and mass sources, distributions of which are determined so that the boundary condition at the splitter surfaces is satisfied. The boundary condition is expressed in terms of two admittance parameters giving relations between pressures and normal displacements of fluid particles at the upper and lower surfaces of the splitter. Computed results are presented to illustrate the dependence of the sound power transmitted through the splitter section on the acoustic properties, length and location of the splitter and the flow Mach number. A principal cause of the sound attenuation due to a splitter is found to be the conversion of the acoustic energy into the wake vortex energy convected downstream. A solid splitter or a porous splitter of small admittance shows tuning effects—with a peak or multiple peaks in the attenuation spectrum. The tuning frequencies can be controlled by the splitter location.     

Sound generated by vortices in the presence of a porous half-cylinder mounted on a rigid plane

The sound generated by a single vortex and by two identical vortices in the presence of a half-cylinder made of porous material mounted on a rigid horizontal plane is studied theoretically using the acoustic analogy and the matched asymptotic expansion method. Both longitudinal and transverse dipoles are observed upon the introduction of the porous cylinder, but the former is considerably stronger than the latter in all the cases studied. Results suggest that the amplitudes of the dipoles and the overall acoustical energy radiated can be higher than that in the rigid cylinder case under some suitable combinations of flow parameters, especially when the flow resistance inside the porous material seen by the vortices is very small.     

Noise spectral power and non-equilibrium dynamics of vortices in the mixed state of Bi2Sr2CaCu2Oy

A model is proposed to explain the observed noise spectral power generated by the moving vortex lattice in Bi₂Sr₂CaCu₂O_y single crystals. The analysis is based on the observations that the noise generated is due to the vortex velocity rather than the thermodynamic phase of the material. The motion of vortices induces a gradual transition of the vortex lattice from the plastic flow to the uniform flow with increasing magnetic field. The influence of the disorder on the dynamics of vortices is such that a uniform distribution in the activation barrier width will exist. This distribution will affect the attempt frequency of the flux line hopping and consequently the spectral shape of the noise generated. The model provides physical basis to the fact that the observed 1/f-noise power corresponds to the smaller velocity of the vortex lattice, while the deviation from the 1/f-spectrum corresponds to the larger velocity region. The results of the simulation are compared to recent experimental measurements where good agreement has been achieved.     

Vortex sound due to a flexible boundary backed by a cavity in a low mach number mean flow

Low frequency sound radiated due to the unsteady motion of an inviscid vortex in the proximity of a flexible membrane backed by an airtight cavity on an otherwise rigid plane is investigated theoretically. Results show that both monopole and dipole are created but the latter is important only when the vortex is traversing over the membrane. The monopole results from the membrane vibration and the dipole from the transverse motion of the vortex. It is also found that these sound fields tend to counteract each other. The increase in the mean flow speed in general results in a stronger acoustic power radiation, but sound attenuation may be possible if the membrane-cavity system is weak compared with the mean flow momentum.     

A computational and experimental study of resonators in three dimensions

In a previous work by the present authors, a computational and experimental investigation of the acoustic properties of two-dimensional slit resonators was carried out. The present paper reports the results of a study extending the previous work to three dimensions. This investigation has two basic objectives. The first is to validate the computed results from direct numerical simulations of the flow and acoustic fields of slit resonators in three dimensions by comparing with experimental measurements in a normal incidence impedance tube. The second objective is to study the flow physics of resonant liners responsible for sound wave dissipation. Extensive comparisons are provided between computed and measured acoustic liner properties with both discrete frequency and broadband sound sources. Good agreements are found over a wide range of frequencies and sound pressure levels. Direct numerical simulation confirms the previous finding in two dimensions that vortex shedding is the dominant dissipation mechanism at high sound pressure intensity. However, it is observed that the behavior of the shed vortices in three dimensions is quite different from those of two dimensions. In three dimensions, the shed vortices tend to evolve into ring (circular in plan form) vortices, even though the slit resonator opening from which the vortices are shed has an aspect ratio of 2.5. Under the excitation of discrete frequency sound, the shed vortices align themselves into two regularly spaced vortex trains moving away from the resonator opening in opposite directions. This is different from the chaotic shedding of vortices found in two-dimensional simulations. The effect of slit aspect ratio at a fixed porosity is briefly studied. For the range of liners considered in this investigation, it is found that the absorption coefficient of a liner increases when the open area of the single slit is subdivided into multiple, smaller slits.     

Transport of magnetic vortices by surface acoustic waves

In a thin film of superconducting Y Ba₂Cu₃O₇ the impact of surface acoustic waves (SAWs) traveling on the piezoelectric substrate is investigated. A pronounced interaction between the ultrasonic waves and the vortex system in the type II superconductor is observed. The occurrence of a SAW-induced dc voltage perpendicular to the sound path is interpreted as dragging of vortices by the piezoacoustic SAW, which acts as a conveyor for the flux quanta. The antisymmetry of this voltage with respect to the magnetic field directly evidences the induced, directed flux motion. This dynamic manipulation of vortices can be seen as an important step towards flux-based electronic devices.     

Chaotic capture of vortices by a moving body. I. The single point vortex case

The study of the dynamical properties of vortex systems is an important and topical research area, and is becoming of ever increasing usefulness to a variety of physical applications. In this paper, we present a study of a model of a rotational singularity which obeys a logarithmic potential interacting with a bluff body in a uniform inviscid laminar flow, e.g., a line vortex interacting with a cylinder in three dimensions or a point vortex with a circular boundary in two dimensions. We show that this system is Hamiltonian and simple enough to be solved analytically for the stagnation points and separatrices of the flow, and a bifurcation diagram for the relevant parameters and classification of the various types of motion is given. We also show that, by introducing a periodic perturbation to the body, chaotic motion of the vortex can be readily generated, and we present analytic criteria for the generation of chaos using the Poincare-Melnikov-Arnold method. This leads to an important dynamical effect for the model, i.e., that the possibility exists for the vortex to be chaotically captured around the body for periods of time which are extremely sensitive to initial conditions. The basic mechanism for this capture is due to the chaotic dynamics and is similar to that of other chaotic scattering phenomena. We show numerically that cases exist where the vortex can be captured around an elliptic point external to (and possibly far from) the body, and the existence of other very complicated motions are also demonstrated. Finally, generalizations of the problem of the vortex-body interaction are indicated, and some possible applications are postulated such as the interaction of line vortices with aircraft wings.     

Analytical and numerical study of acoustic intensity field in irregularly shaped room

The modal expansion method has been used to formulate expressions for real and imaginary parts of the complex sound intensity inside enclosures. Based on theoretical results, the computer program has been developed to simulate the acoustic intensity vector field inside the irregular room whose shape resembles the capital letter L. Calculation results have shown that a low-frequency distribution of the acoustic intensity is strongly influenced by the modal localization and the characteristic objects in the active intensity field are energy vortices and saddle points positioned irregularly inside the room. It was found that for small sound damping the vortex centers lie exactly on the lines corresponding to zeros of the eigenfunction for a dominant mode. An increase in a sound attenuation results in the change of vortex positions and can cause the formation of new vortices. Finally, an influence of the wall impedance on the quantitative relation between the acoustic and reactive intensities was studied and it was concluded that for very small sound damping the behavior of the sound intensity is basically only oscillatory.     

Irregular scattering of acoustic rays by vortices

The scattering of high-frequency sound wave, under geometrical acoustic approximation, by three stationary vortices in two dimensions is investigated. For a sufficiently high Mach number of the vortex flow, the scattering of sound rays becomes irregular, displaying a new example of chaotic scattering for a time-reversal breaking system. The fractal dimension, as well as the unstable and stable manifolds of the scattering dynamics, is presented.     

Scattering and absorption of sound at flow duct expansions

The scattering of plane acoustic waves at area expansions in flow ducts is analysed using the vortex sheet model where the flow at the expansion is modelled as a jet, with a vortex sheet emanating from the edge. Of particular interest is the influence of the flow field on acoustic scattering and absorption.First, it is demonstrated that the stability properties of the shear layer can be simulated by modifying the edge condition within the vortex sheet model. To this end the accuracy for the region where the shear layer is changing from unstable to stable is improved by introducing a gradually relaxed Kutta edge condition with empirically derived coefficients. For low Strouhal numbers the vortex sheet model applies and for higher Strouhal numbers the two models converge.Second, it is demonstrated that the acoustic transmission through the jet expansion region can be determined by neglecting the scattering there. Incorporating this assumption, the vortex sheet model reproduces well the experimental results on transmission and absorption for an area expansion. This result supports the assumption that the main part of the scattering occurs at the area expansion at least for the low-frequency range. Furthermore, the influence of the flow field is particularly strong for small Strouhal numbers.     

EXPERIMENTAL STUDY OF NOISE PRODUCED BY STEADY FLOW THROUGH A SIMULATED VASCULAR STENOSIS

An in vitro experiment is carried out in order to study the acoustic effects of a vascular constriction (stenosis) in people and provide correlations between these effects and parameters relevant to the hydrodynamic and acoustic processes. For this purpose, we measure the sound produced when water flows through an elastic tube which is either unobstructed or contains a rigid axisymmetric constriction. The sound is measured at the outside of a large annular container filled with water and bounded at the inside by the coaxial elastic tube. The analysis of the acoustic fields shows that a stenosis has two basic acoustic effects. These are a general increase in the sound level and the production of a number of additional distinct peaks (new frequency components) in the acoustic power spectrum. The frequencies of these peaks are close to the characteristic frequencies of vortex formation in the disturbed flow region behind a stenosis and the resonance frequencies of vibration of the post-stenotic segment of the tube. Another important result is that the stenosis generated acoustic power is approximately proportional to the fourth power of the stenosis severity and the same power of the flow Reynolds number.     

磁通运动的电压噪声频谱分析和动力学相变

用Langevin分子动力学方法模拟磁通运动的纵向电压噪声谱随磁场和电流的变化.计算结果表明，外加磁场增大到磁通运动动力学相变场F_P，电压噪声 谱中低频宽带噪声减小而出现洛伦兹形高频窄带噪声.外加磁场增大到熔化场F_m附近，高频窄带噪声 峰值增高 ，峰值对应频率增大.在外加电流增强到磁通弹性运动区域，高频窄带噪声频谱呈现搓衣板 形式.搓衣板高频窄带噪声产生于磁通平移速度的周期性调制，它表明层状超导体中运动的 磁通格子存在有平移序的BG相. 关键词： 第Ⅱ类超导体 电压噪声 动力学模拟     

The sound of a suddenly tensioned membrane

The sound produced by suddenly tugging one end of an elastic sheet is investigated. The elastic equations of motion are solved within the membrane in the limit where fluid loading may be neglected. It is found that if the membrane is paper a tension wave travels supersonically through the sheet. There is no motion ahead of this wave but behind it the tensioned sheet supports a transverse vibration. We find that a membrane excited in this way is silent except at the tugged end and at the tension front. The far field density perturbation has the characteristic features of a two-dimensional sound field produced by a stationary line source at the tugged end and a supersonically moving line source at the tension front. When the tension is impulsively applied there is a sonic boom that travels in an unattenuated beam on the Mach wedge, the relevant Mach number being the ratio of the speed of the tension wave to the speed of sound in the surrounding fluid, but the sound field is always of order $\text{r}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$, where r is the distance of the observer from the source, when the tension is applied over a small but non-zero interval. Fluid loading has a dampening effect on the sheet which is not easy to handle analytically but has an obvious physical interpretation. This model problem is thought to bear on the question of how much noise is made by the vibration of the paper web in a rotary printing machine, where the web tension is often changed abruptly by irregularities in the reel surfaces. The parameters that control the noise output are identified, and the dependence of the sound field on these variables is determined.     

Fluid dynamics of a flow excited resonance,Part II: Flow acoustic interaction

This is the second of two companion papers in which the physics and detailed fluid dynamics of a flow excited resonance are examined. The approach is rather different from those previously used, in which stability theory has been applied to small wavelike disturbances in a linearly unstable shear layer, with an equivalent source driving the sound field which provides the feedback. In the approach used here, the physics of the flow acoustic interaction is explained in terms of the detailed momentum and energy exchanges occurring inside the fluid. Gross properties of the flow and resonance are described in terms of the parameters necessary to determine the behaviour of the feedback system. In this second paper it is shown that two relatively distinct momentum balances can be considered in the resonator neck region. One can be identified with the vortically induced pressure and velocity fluctuations and the other with the reciprocating potential flow. The fluctuating Coriolis force caused by the interaction of the potential and vortical flows is shown to be the only term in the linearized momentum equation which is not directly balanced by a fluctuating pressure gradient. This force provides the mechanism for the exchange of the mean energies associated with the mean and fluctuating momenta, respectively. A source and sink of energy are identified in which mean energy associated with fluctuating momentum is extracted from and returned to the mean flow, respectively. The imbalance between the source and sink is responsible for both the radiated acoustic power and the power carried away by the vortices as they convect downstream. This radiated acoustic power and vortically convected power, and the source and sink powers, are all of the same order of magnitude. With the vortex shedding and reciprocating potential flow “phase locked” the amplitude of the steady state oscillations is determined by the condition that the net power produced in the resonator neck (the source power less the sink power) is equal to the sum of the radiated acoustic power and that carried by the vortices.     

Direct simulations of trailing-edge noise generation from two-dimensional airfoils at low Reynolds numbers

The aeroacoustic sound generated from the flow around two NACA four-digit airfoils is investigated numerically, at relatively low Reynolds numbers that do not prompt boundary-layer transition. By using high-order finite-difference schemes to discretize compressible Navier–Stokes equations, the sound scattered on airfoil surface is directly resolved as an unsteady pressure fluctuation. As the wavelength of an emitted noise is shortened compared to the airfoil chord, the diffraction effect on non-compact chord length appears more noticeable, developing multiple lobes in directivity. The instability mechanism that produces sound sources, or unsteady vortical motions, is quantitatively examined, also by using a linear stability theory. While the evidence of boundary-layer instability waves is captured in the present result, the most amplified frequency in the boundary shear layer does not necessarily agree with the primary frequency of a trailing-edge noise, when wake instability is dominant in laminar flow. This contradicts the observation of other trailing-edge noise studies at higher Reynolds numbers. However, via acoustic disturbances, the boundary-layer instability may become more significant, through the resonance with the wake instability, excited by increasing a base-flow Mach number. Evidence suggests that this would correspond to the onset of an acoustic feedback loop. The wake-flow frequencies derived by an absolute-instability analysis are compared with the frequencies realized in flow simulations, to clarify the effect of an acoustic feedback mechanism, at a low Reynolds number.     

Self-consistent turbulence in the two-dimensional nonlinear Schrödinger equation with a repulsive potential

The dynamics of dark solitons (vortices) with the same topological charge (vorticity) in the two-dimensional nonlinear Schr?dinger (NLS) equation in a defocusing medium is studied. The dynamics differ from those in incompressible media due to the possibility of energy and angular momentum radiation. The problem of the breakup of a multicharged dark soliton, which is a local decrease of the wave function intensity, into a number of chaotically moving vortices with single charge, is studied both analytically and numerically. After an initial period of intensive wave radiation, there emerges a nonuniform, steady turbulent self-organized motion of these vortices which is restricted in space by the size of the potential well of the initial multicharged dark soliton. Separate orbits of finite widths arise in this turbulent motion. That is, the statistical probability to observe a vortex in a given point has maxima near certain points (orbit positions). In spite of the fact that numerical calculations were performed in a finite region, the turbulent distributions of the vortices do not depend on the size of the container when its radius is larger than the size of the potential well of the primary multicharged dark soliton. The steady turbulent distribution of vortices on these orbits can be obtained as the extremal of the Lyapunov functional of the NLS equation, and obeys some simple rules. The first is the absence of Cherenkov resonance with linear (sound) waves. The second is the condition of a potential energy maximum in the region of vortex motion. These conditions give an approximately equidistant disposition of orbits of the same number of vortices on each orbit, which corresponds to a constant rotating velocity. The magnitude of this velocity is mainly determined by the sound velocity. An integral estimation of the self-consistent rotation of the vortex zone is given.