The displacement-thickness theory of trailing edge noise

The problem of estimating the sound generated by turbulent boundary layer flow over the edge of a rigid half-plane is re-examined. A theory is proposed which is strictly valid at low Strouhal numbers based on boundary layer width, wherein the flow inhomogeneities are specified in terms of the fluctuations in the boundary layer displacement thickness. This enables account to be taken of changes in the properties of the turbulence as it translates past the edge, which are shown to result in the appearance of an acoustic dipole whose axis is aligned with the mean flow, and which supplements the radiation field predicted by conventional methods [1,2]. Detailed comparison is made with acoustic and surface pressures which are calculated according to the evanescent wave theory of edge noise [3–5].     

High amplitude acoustic transmission through duct terminations: Theory

Recent experimental measurements have demonstrated that net acoustic energy dissipation can occur when sound waves interact with free shear layers, which are produced either by boundary layer separation in mean fluid flow at sharp edges, or by separation of the boundary layer in the acoustic flow at an edge in the absence of mean flow. This paper presents theoretical results which are offered in an attempt to explain these observations quantitatively. Comparison is made between the predicted and measured net energy loss which occurs upon transmission of high amplitude impulsive acoustic waves through various duct terminations, and also between calculated and measured reflection coefficients in the duct. The agreement is generally at least qualitatively good, and would appear to justify the physical assumptions on which the theoretical arguments are based.     

Experimental validation of numerical simulations for an acoustic liner in grazing flow: Self-noise and added drag

A coordinated experimental and numerical simulation effort is carried out to improve our understanding of the physics of acoustic liners in a grazing flow as well our computational aeroacoustics (CAA) method prediction capability. A numerical simulation code based on advanced CAA methods is developed. In a parallel effort, experiments are performed using the Grazing Flow Impedance Tube at the NASA Langley Research Center. In the experiment, a liner is installed in the upper wall of a rectangular flow duct with a 2 in. by 2.5 in. cross section. Spatial distribution of sound pressure levels and relative phases are measured on the wall opposite the liner in the presence of a Mach 0.3 grazing flow. The computer code is validated by comparing computed results with experimental measurements. Good agreements are found. The numerical simulation code is then used to investigate the physical properties of the acoustic liner. It is shown that an acoustic liner can produce self-noise in the presence of a grazing flow and that a feedback acoustic resonance mechanism is responsible for the generation of this liner self-noise. In addition, the same mechanism also creates additional liner drag. An estimate, based on numerical simulation data, indicates that for a resonant liner with a 10 percent open area ratio, the drag increase would be about 4 percent of the turbulent boundary layer drag over a flat wall.     

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.     

Acoustic propagation in partially choked converging-diverging ducts

A computer model based on the wave-envelope technique is used to study acoustic propagation in converging-diverging hard walled and lined circular ducts carrying near sonic mean flows. The influences of the liner admittance, boundary layer thickness, spinning mode number, and mean Mach number are considered. The numerical results indicate that the diverging portion of the duct can have a strong reflective effect for partially choked flows.     

The effect of turbulence damping on acoustic wave propagation in tubes

The attenuation of sound due to the interaction between a low Mach number turbulent boundary layer and acoustic waves can be significant at low frequencies or in narrow tubes. In a recent publication by the present authors the acoustics of charge air coolers for passenger cars has been identified as an interesting application where turbulence attenuation can be of importance. Favourable low-frequency damping has been observed that could be used for control of the in-duct sound that is created by the engine gas exchange process. Analytical frequency-dependent models for the eddy viscosity that controls the momentum and thermal boundary layers are available but are restricted to thin acoustic boundary layers. For cases with cross-sections of a few millimetres a model based on thin acoustic boundary layers will not be applicable in the frequency range of interest.In the present paper a frequency-dependent axis-symmetric numerical model for interaction between turbulence and acoustic waves is proposed. A finite element scheme is used to formulate the time harmonic linearized convective equations for conservation of mass, momentum and energy into one coupled system of equations. The turbulence is introduced with a linear model for the eddy viscosity that is added to the shear viscosity. The proposed model is validated by comparison with experimental data from the literature.     

A piecewise linear mean flow model for studying stability in a lined channel

Acoustic liners are used to reduce sound emission by turbofan engines. Under grazing flow they may sustain hydrodynamic instabilities and these are studied using a stability analysis, based on a simplified model: the liner is a mass–spring–damper system, the base channel flow is piecewise linear, and the inviscid, incompressible Rayleigh equation is used. The model is an extension to the channel case of a boundary layer model by Rienstra and Darau. The piecewise linear profile introduces a finite boundary layer thickness which ensures well-posedness, allowing an initial value problem to be conducted to investigate absolute stability. For typical values in aeronautics the flow above the liner is unstable. Absolute instability is obtained for somewhat extreme values of the mean flow (tiny boundary layer thickness), and under realistic conditions the flow is convectively unstable. The effect of finite channel height is investigated in both cases. In particular, for large boundary layer thicknesses associated with convective instability the channel height has little effect on the unstable mode. Favorable outcomes and failures of the model are shown by comparison to a published experimental work.     

DNS of compressible turbulent boundary layer around a sharp cone

Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20° cone angle (or 10° half-cone angle) is performed by using the mixed seventh-order up-wind biased finite difference scheme and sixth-order central difference scheme. The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch. The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer. Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow. The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations. The turbulent energy equation in the cylindrical coordinate is given and turbulent energy budget is studied. The computed results show that the effect of circumferential curvature on turbulence characteristics is not obvious.     

The prediction of broadband noise from wind turbines

This paper describes a broadband noise prediction scheme for wind turbines. The source mechanisms included in the method are unsteady lift noise, unsteady thickness noise, trailing edge noise and the noise from separated flow. Special methods have been developed to model the inflow turbulence from the atmospheric boundary layer and acoustic radiation to the geometric near field of the rotor. Predictions are compared with measurements on 20 m and 80 m diameter wind turbines. The results show that the turbulence length scale in the atmospheric boundary layer is too large to give the measured noise levels. Very good agreement is obtained between predictions and measurements if the turbulence length scale is taken to be equal to the blade chord.     

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.     

On the simulation of trailing edge noise with a hybrid LES/APE method

A hybrid method is applied to predict trailing edge noise based on a large eddy simulation (LES) of the compressible flow problem and acoustic perturbation equations (APE) for the time-dependent simulation of the acoustic field. The acoustic simulation in general considers the mean flow convection and refraction effects such that the computational domain of the flow simulation has to comprise only the significant acoustic source region. Using a modified rescaling method for the prediction of the unsteady turbulent inflow boundary layer, the LES just resolves the flow field in the immediate vicinity of the trailing edge. The linearized APE completely prevent the unbounded growth of hydrodynamic instabilities in critical mean flows.     

On the use of spires for generating inflow conditions with energetic coherent structures in large eddy simulation

While it has long been a practice to place spires near the inlet of a wind tunnel to quickly develop a turbulent boundary layer with similarities to an atmospheric boundary layer, this has not been the case for creating turbulent boundary layer inflow in large eddy simulations (LESs) of turbulent flows. We carry out LES with the curvilinear immersed boundary method to simulate the flow in a wind tunnel with a series of spires in order to investigate the feasibility of numerically developing inflow conditions from a precursory spire LES and assessing the similarities of the turbulence statistics to those of an atmospheric boundary layer. The simulated mean velocity field demonstrates that a turbulent boundary layer with height equal to the spire height develops very quickly, within five spire heights downstream. The major attribute of using spires for precursory simulations is the spatially evolving coherent structures that form downstream of the spires offering a range of length scales at both the vertical and streamwise directions allowing multiple turbulent inflow conditions to be extracted from a single simulation. While the distribution of length scales far from the spires resembles an atmospheric boundary layer, some turbulence statistics have some significant differences.     

Convection and correlation of coherent structure in turbulent boundary layer using tomographic particle image velocimetry

The present experimental work focuses on a new model for space–time correlation and the scale-dependencies of convection velocity and sweep velocity in turbulent boundary layer over a flat wall. A turbulent boundary layer flow at Reθ= 2460 is measured by tomographic particle image velocimetry(tomographic PIV). It is demonstrated that arch, cane,and hairpin vortices are dominant in the logarithmic layer. Hairpins and hairpin packets are responsible for the elongated low-momentum zones observed in the instantaneous flow field. The conditionally-averaged coherent structures systemically illustrate the key roles of hairpin vortice in the turbulence dynamic events, such as ejection and sweep events and energy transport. The space–time correlations of instantaneous streamwise fluctuation velocity are calculated and confirm the new elliptic model for the space–time correlation instead of Taylor hypothesis. The convection velocities derived from the space–time correlation and conditionally-averaged method both suggest the scaling with the local mean velocity in the logarithmic layer. Convection velocity result based on Fourier decomposition(FD) shows stronger scale- dependency in the spanwise direction than in streamwise direction. Compared with FD, the proper orthogonal decomposition(POD) has a distinct distribution of convection velocity for the large- and small-scales which are separated in light of their contributions of turbulent kinetic energy.     

Boundary layer effects on sound in a circular duct

Boundary layer effects on an acoustic field in a unidirectional flow with transverse shear are studied. The acoustic pressure variation in the direction normal to that of the flow is governed in the boundary layer by a second order differential equation. The problem in the boundary layer is reduced from a two point boundary value problem to a one point boundary value problem by transforming the governing equation into the Riccati equation. The Riccati equation is easily integrated with standard numerical procedures. The integration process yields the effective admittance of the wall-boundary layer combination. The acoustic field in the uniform flow is then determined for this effective admittance. Further complications imposed by the boundary layer are thus eliminated. The simplicity of the technique allows calculation of the propagation and decay constants in a circular duct over a wide range of parameters and duct modes.     

Reduction of fan noise by annulus boundary layer removal

Much of the noise produced by a fan is due to varying forces caused by the unsteady flow field through which it passes. In the absence of inlet guide vanes, support struts and other mechanical obstructions, the flow irregularities are caused by large scale intake turbulence and temporal and spatial variations in the annulus boundary layer. In many cases the most effective source is the annulus boundary layer, as this interacts with the blade tip which is the fastest part of the blade and is therefore the most effective noise source. This noise can be reduced if the annulus boundary layer is smoothly bled away from the rotor so that the blade tip sees a thin, uniform boundary layer. A one metre diameter ventilation fan has been run in a duct with and without a boundary layer bleed system and a reduction of far field sound power of approximately 5 dB has been obtained for a bleed of 5 % of the main flow with some far field tone reductions of more than 15 dB. Measurements of far field directivities, in-duct acoustic modes and aerodynamic distortions have confirmed the suggested explanation for this phenomenon. The tests have shown that great care must be taken in the design of a bleed system so that residual boundary layer distortions are not in the correct wavelength range to produce propagating acoustic waves at important blade passing harmonic frequencies. If such distortions are present, the far field noise can increase instead of decrease.     

The effect of an aircraft’s boundary layer on propeller noise

This study concerns the influence of the boundary layer at an aircraft??s fuselage, simulated by an infinite hard cylinder, on propeller noise in the acoustic far field. Also studied is the effect of the boundary layer on noise as a function of the thickness and profile of the mean velocity of the boundary layer, the Mach number of the incident flow, and the rotation speed of the propeller. It is shown that the boundary layer at the fuselage can substantially modify propeller noise in the far field and should therefore be taken into account in calculating community noise.     

网格湍流对剪切层中预混火焰结构的影响

本文研究网格湍流对射流剪切层以及建立在其中的预混火焰的影响。利用热线风速仪测量射流的速度场,发现网格湍流使剪切层内湍流强度明显降低,抑制了低频速度脉动,同时增加了湍动能在小尺度脉动上的分配,使湍流更趋于各向同性,这表明网格湍流抑制了剪切层内的大涡和拟序结构。用细丝热电偶测量了火焰温度,结果显示网格湍流使火焰前峰的低频大幅摆动减少,小尺度皱褶增加,火焰区平均温度更高,说明网格湍流有利于剪切层中预混火焰的强化和稳定。     

Analysis of the turbulent boundary layer in the vicinity of a self-excited cylindrical Helmholtz resonator

This study investigates the changes in the structure of a turbulent boundary layer downstream of a flow-excited Helmholtz resonator. To this end, a fully developed turbulent boundary layer over a resonator mounted flush with a flat plate was simulated by implementing a large eddy simulation (LES). To assist in understanding the effect of the resonator on the flow structure, a sensitivity study was undertaken by changing the main geometrical parameters of the resonator. The results demonstrated that when the boundary layer thickness equals the orifice length, the cross-stream component of velocity fluctuations penetrates the boundary layer, resulting in a reduction of the turbulence intensity by up to 12%. Therefore, it is concluded that a Helmholtz resonator has the potential to reduce the instabilities within the boundary layer. These investigations also assist in identifying the optimal parameters to delay turbulence events within the grazing flow using Helmholtz resonators.     

Measurements of energy exchange between acoustic fields and non-uniform steady flow fields

This paper describes an experimental investigation of interactions between acoustic waves and a non-uniform steady flow field. Data have been obtained for a resonance tube having a vent at the center in the lateral boundary, an average flow being introduced at the ends. Experiments have been done for both circular and slot vents, over ranges of both frequency and Mach number. According to the one- dimensional linear stability analysis, the interactions between the longitudinal acoustic field and the mean flow in the vicinity of the vent cause a net transfer of acoustic energy from the average flow to the acoustic field. This result has been verified by the experiments reported here. The gain of energy measured is less than that deduced from a one-dimensional analysis.