Suppression of Helmholtz resonance using inside acoustic liner

When a Helmholtz resonator is exposed to grazing flow, an unstable shear layer at the opening can cause the occurrence of acoustic resonance under appropriate conditions. In this paper, in order to suppress the flow-induced resonance, the effects of inside acoustic liners placed on the side wall or the bottom of a Helmholtz resonator are investigated. Based on the one-dimensional sound propagation theory, the time domain impedance model of a Helmholtz resonator with inside acoustic liner is derived, and then combined with a discrete vortex model the resonant behavior of the resonator under grazing flow is simulated. Besides, an experiment is conducted to validate the present model, showing significant reduction of the peak sound pressure level achieved by the use of the side-wall liners. And the simulation results match reasonably well with the experimental data. The present results reveal that the inside acoustic liner can not only absorb the resonant sound pressure, but also suppress the fluctuation motion of the shear layer over the opening of the resonator. In all, the impact of the acoustic liners is to dampen the instability of the flow-acoustic coupled system. This demonstrates that it is a convenient and effective method for suppressing Helmholtz resonance by using inside acoustic liner.     

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.     

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.     

Spectral analysis of the flow sound interaction at a bias flow liner

The interaction between the flow field and the sound field is responsible for the sound absorption at perforated acoustic liners with bias flow and has to be investigated contactlessly. Based on the optically measured flow velocity spectrum, an energy analysis was performed. As a result, the generation of broadband flow velocity fluctuations in the shear layer surrounding the bias flow caused by the flow sound interaction has been observed. In addition, the magnitude of this acoustically induced flow velocity oscillation exhibits a correlation with the acoustic dissipation coefficient of the bias flow liner. This supports the assumption that an energy transfer between the flow field and the sound field is responsible for the acoustic damping.     

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.     

Acoustic-excited vortex shedding and acoustic nonlinearity at a rectangular slit with bias flow

The acoustical response of a slit with a mean bias flow is numerically studied. By means of a potential flow model based on the discrete vortex method and a spanwise-averaged three-dimensional Green?s function, both unsteady vortical flow and slit impedance are obtained in a unified theoretical framework. The numerical simulation focuses on the acoustic-excited vortex structures of the slit flow while neglecting the viscous damping effect. Three representative flow features are demonstrated, which are the destabilized jet flow, the rolling up of vortex sheets and formation of vortex pairs, and the reversal flow with alternating vortex shedding on both sides of the slit. These features are corresponding to low, moderate, and high sound amplitude, respectively. The acoustic behavior of the slit can be divided into linear, transition, and nonlinear regimes. During its evolution through the three regimes, the resistance exhibits a constant value, a slight decrease, and a significant increase with the increasing sound amplitude. Correspondingly, the reactance first remains constant and then shows a modest decrease as the sound amplitude increases. The nonlinear effect also causes the gradual decrease of the mean bias velocity in company with the marked increase of the amplitude of the fluctuating velocity in the slit. The mean bias velocity decreases to about 80 percent of its linear value at the transition point where reversal flow begins to occur, and further decreases to only 10 percent in the highly nonlinear region. The slit impedance is also presented as a function of frequency and for different aspect ratios. And the effects of frequency and slit geometry are discussed.     

A note on the interaction of unsteady flow with an acoustic liner

The effects of a mean grazing flow on the energy exchanges involved in the interaction of a bias-flow acoustic liner with, respectively, incident sound and boundary layer turbulence are contrasted. The analysis of model problems which make use of a line vortex to simulate large scale, unsteady boundary layer structures indicates that, whereas acoustic waves may be effectively attenuated, dissipation caused by “jetting” in the apertures of the liner can result in a net transfer of energy from the mean flow to the turbulence in the boundary layer.     

Basic sound generation mechanisms in inviscid vortex interactions at low Mach number

The sound generation mechanisms during finite core vortex interactions at low Mach number are investigated in the present study. The theoretical deductions show clearly that the basic sound generation mechanisms are associated with the vortex core deformation and the vorticity centroid dynamics, independent of the vortex system. Such deductions are substantiated by numerical experiments with the interactions of two-dimensional vortices, vortex pairs and vortex rings. Detailed discussions on the similarities and differences between the sound generation processes of the two-dimensional and axisymmetric vortex systems are given. The relative importance of the two sound generation mechanisms in these vortex systems, their characteristics and interactions, which are hardly found in existing literature, are also examined. The present findings have also generalized and substantiated the previous results of the authors on the topic.     

ANALYSIS OF THE PERIODIC PRESSURE FLUCTUATIONS INDUCED BY FLOW OVER A CAVITY

Subsonic flows over Helmholtz resonators often cause strong periodic pressure fluctuations inside the resonators over a range of outer flow velocities. The flow-excitation mechanism is known to be governed by both the shedding of discrete vortices within the shear layer over the orifice and the acoustic response of the cavity. This self-sustained oscillation phenomenon is often analyzed by using a feedback loop model where the flow excitation and the acoustic response of the resonator are approximately modelled as a forward gain function and as a backward gain function respectively. In the present work, a similar approach was followed and a new forward gain function was derived based on the concept of “vortex sound” to model the flow excitation. The formulation combined this forward gain function with a backward gain function from previous work, within the framework of the feedback loop analysis. The approximate method allowed the frequency and the relative amplitude of the cavity pressure fluctuations to be predicted for a range of flow velocities. In addition, the extended Nyquist stability criterion was used to estimate the onset and the termination velocities of the first two modes of the shear layer flow oscillations. Experimental data were obtained using a rigid-walled cavity in a low-speed wind tunnel. The results showed that the model predictions were in reasonably good agreement with the experimental data.     

Self-induced sound generation by flow over perforated duct liners

An adverse “singing” phenomenon due to flow over perforated liners in a duct was studied experimentally. The liners consisted of honeycomb structures bonded to and sandwiched between two flat aluminum skins. The inner skin in contact with the flow had holes (perforations) with pitch distances either equal to or different from those of the honeycomb structures, forming, respectively, narrow-band or broadband liners. The shedding of vortices in the flow over these holes induced excitation of acoustic modes within the duct, and under the condition whereby the cut-on frequency of an excited mode coincided with, or was very near to, the shedding frequency a very strong tone corresponding to that particular modal cut-on frequency resulted. For narrow-band liners, the “singing” phenomenon could also be induced by cavity resonance. The shedding frequency increased with increase in flow velocities and thus higher order acoustic modes were excited consecutively in a similar manner. The Strouhal number calculated from the observed shedding frequency and the flow velocity was found to vary directly with the hole diameter of the perforate. The high signal to noise ratio during the peak of self-excitation presents a new method in the determination of the wall admittance under the flow conditions.     

A reduced-order deterministic model describing an intermittency route to combustion instability

Recently, there has been a growing interest in understanding and characterising intermittent burst oscillations that presage the onset of combustion instability. We construct a deterministic model to capture this intermittency route to instability in a bluff-body stabilised combustor by coupling the equations governing vortex shedding and the acoustic wave propagation in a confinement. A feedback mechanism is developed wherein the sound generated due to unsteady combustion affects the vortex shedding. This feedback leads to a variation in the time of impingement of the vortices with the bluff body causing the system to exhibit chaos, intermittency, and limit cycle oscillations. Experimental validation of the model is provided using various precursor measures that quantify the observed intermittent states.     

Analysis of liner performance using the NASA Langley Research Center Curved Duct Test Rig

The NASA Langley Research Center Curved Duct Test Rig (CDTR) is designed to test aircraft engine nacelle liner samples in an environment approximating that of the engine on a scale that approaches the full scale dimensions of the aft bypass duct. The modal content of the sound in the duct can be determined and the modal content of the sound incident on the liner test section can be controlled. The effect of flow speed, up to Mach 0.5 in the test section, can be investigated. The results reported in this paper come from a study to evaluate the effect of duct configuration on the acoustic performance of single degree of freedom (SDOF) perforate-over-honeycomb liners. Variations of duct configuration include: asymmetric (liner on one side and hard wall opposite) and symmetric (liner on both sides) wall treatment; inlet and exhaust orientation, in which the sound propagates either against or with the flow; and straight and curved (outlet is offset from the inlet by one duct width) flow path. The effect that duct configuration has on the overall acoustic performance is quantified. The redistribution of incident mode content is shown, in particular the mode scatter effect that liner symmetry has on symmetric and asymmetric incident mode shapes. The Curved Duct Test Rig is shown to be a valuable tool for the evaluation of acoustic liner concepts.     

圆孔声学非线性效应的数值模拟

本文发展了一种离散涡模型,模拟了在高声强声波作用下圆孔处发生的涡脱落过程。进而计算了圆孔中的声质点速度,并分析了孔中速度的畸变情况、最后给出了圆孔的非线性声阻和声抗的理论值。非线性声抗的理论预测是现有的研究圆孔声学非线性效应的准稳态模型没有满意解决的问题,因而所做的有关尝试是本文工作的特点之一。     

Sound generated by a vortex convected past an elastic sheet

We study the motion and sound generated when a line vortex is convected in a uniform low-Mach flow parallel to a thin elastic sheet. The linearized sheet motion is analyzed under conditions where the unforced sheet (in the absence of the line vortex) is stationary. The vortex passage above the sheet excites a resonance mode of motion, where the sheet oscillates at its least stable eigenmode. The sources of sound in the acoustic problem include the sheet velocity and fluid vorticity. It is shown that the release of trailing-edge vortices, resulting from the satisfaction of the Kutta condition, has two opposite effects on sound radiation: while trailing-edge vortices act to reduce the pressure fluctuations occurring owing to the direct interaction of the line vortex with the unperturbed sheet, they extend and amplify the acoustic signal produced by the motion of the sheet. The sheet motion radiates higher sound levels as the system approaches its critical conditions for instability, where the effect of resonance becomes more pronounced. It is argued that the present theory describes the essential mechanism by which sound is generated as a turbulent eddy is convected in a mean flow past a thin elastic airfoil.     

Time-domain characterization of the acoustic damping of a perforated liner with bias flow

Combustion instabilities are caused by the interaction of unsteady heat releases and acoustic waves. To mitigate combustion instabilities, perforated liners, typically subjected to a low Mach number bias flow (a cooling flow through perforated holes), are fitted along the bounding walls of a combustor. They dissipate the acoustic waves by generating vorticity at the rims of perforated apertures. To investigate the absorption of plane waves by a perforated liner with bias flow, a time-domain numerical model of a cylindrical lined duct is developed. The liners' damping mechanism is characterized by using a time-domain "compliance." The development of such time-domain compliance is based on simplified or unsimplified Rayleigh conductivity. Numerical simulations of two different configurations of lined duct systems are performed by combining a 1D acoustic wave model with the compliance model. Comparison is then made between the results from the present models, and those from the experiment and the frequency-domain model of previous investigation [Eldredge and Dowling, J. Fluid Mech. 485, 307-335(2003)]. Good agreement is observed. This confirms that the present model can be used to simulate the propagation and dissipation of acoustic plane waves in a lined duct in real-time.     

Modular system for studying tonal sound excitation in resonators with heat addition and mean flow

An educational experimental system has been developed for studying tonal sound generation in acoustic resonators. Tones are excited by either heat addition or vortex shedding in the presence of mean flow. The system construction is straightforward and inexpensive. Several test arrangements and experimental data are described in this paper. The experimental setups include a modified Rijke tube, a standing-wave thermoacoustic engine, a baffled tube with mean flow, and an acoustic energy harvester with a piezoelement. Simplified mathematical models for interpreting data are discussed, and references are provided to literature with more advanced analyses. The developed system can assist both graduate and undergraduate students in understanding acoustic instabilities via conducting and analyzing interesting experiments.     

Review of sound induced by vortex shedding from cylinders

Sound induced by periodic vortex shedding from cylinders has been studied more-or-less continuously since the first quantitative study by Strouhal in 1878. Measurements have shown that vortex shedding is a dipole source of sound. Theoretical models for aeroacoustic sound in a free space, mostly inspired by Lighthill's work, have been developed which can replicate the measurements once the vortex shedding force, coherence, and periodicity are experimentally measured. Vortex shedding from tubes in heat exchanger tube bundles can reach damaging intensities because the acoustic mode is bound by the lower speed of sound within the tube bank itself. However, the amplitude and occurrence of the resonance can only be approximately predicted at present.     

空腔非局域反应声衬传播特性研究

本文对声波在空腔非局域反应声衬管道内的传播进行了研究。特征方程通过声衬内和管道内两部分声场的耦合求解得到,并采用积分方法对特征方程积分求解,通过模态匹配的方法建立并求解了有限长管道非局域反应声衬的声辐射数值模型,展示了在管道消声主动控制方面的应用潜力。     

An aeroacoustically driven thermoacoustic heat pump

The mean flow of gas in a pipe past a cavity can excite the resonant acoustic modes of the cavity--much like blowing across the top of a bottle. The periodic shedding of vortices from the leading edge of the mouth of the cavity feeds energy into the acoustic modes which, in turn, affect the shedding of the next vortex. This so-called aeroacoustic whistle can excite very high amplitude acoustic standing waves within a cavity defined by coaxial side branches closed at their ends. The amplitude of these standing waves can easily be 20% of the ambient pressure at optimal gas flow rates and ambient pressures within the main pipe. A standing wave thermoacoustic heat pump is a device which utilizes the in-phase pressure and displacement oscillations to pump heat across a porous medium thereby establishing, or maintaining, a temperature gradient. Experimental results of a combined system of aeroacoustic sound source and a simple thermoacoustic stack will be presented.     

Flow visualization behind a streamwise oscillating cylinder and a stationary cylinder in tandem arrangement

Interference is investigated between a stationary cylinder wake and that of a downstream streamwise oscillating cylinder. Experiments were carried out in a water tunnel. A laser-induced fluorescence technique was used to visualize the flow structure behind two inline circular cylinders of identical diameterd. The downstream cylinder was forced to oscillate harmonically at the amplitude of 0.5d and the frequency ratiof _e f _s=1.8, wheref _e is the oscillation frequency of the downstream cylinder andf _s is the vortex shedding frequency from an isolated stationary cylinder. The investigation was conducted for the cylinder center-to-center spacingL/d=2.5 ∼ 4.5. Two flow regimes have been identified, i.e. the ‘single-cylinder shedding regime’ atL/d<-3.5 and the ‘two-cylinder shedding regime’ atL/d>3.5. At smallL/d, the upstream cylinder does not appear to shed vortices; vortices are symmetrically formed behind the downstream cylinder as a result of interactions between the shear layers separated from the upstream cylinder and the oscillation of the downstream cylinder. This is drastically different from that behind two stationary cylinders atL/d<-3.5, where vortices are shed alternately from the downstream cylinder only. AtL/d=4.5, both upstream and downstream cylinders shed vortices. This is true with or without the oscillation of the downstream cylinder. The flow structure is now totally different from that atL/d=3.5. The vortices are shed alternately from the upstream cylinder; a staggered spatial arrangement of vortices occurs behind the downstream cylinder.