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Interaction of a compliant wall with a turbulent channel flow is investigated experimentally by simultaneously measuring the time-resolved, three-dimensional (3D) flow field and the two-dimensional (2D) surface deformation. The optical set-up integrates tomographic particle image velocimetry to measure the flow with Mach–Zehnder interferometry to map the deformation. The Reynolds number is $Re_{\unicode[STIX]{x1D70F}}=2300$, and the Young’s modulus of the wall is 0.93 MPa, resulting in a ratio of shear speed to the centreline velocity ($U_{0}$) of 6.8. The wavenumber–frequency spectra of deformation show the surface motions consist of a non-advected low-frequency component and advected modes, some travelling downstream at approximately $U_{0}$ and others at ${\sim}0.72U_{0}$. The r.m.s. values of the advected and non-advected modes are $0.04~\unicode[STIX]{x03BC}\text{m}$$(0.004\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}})$ and $0.2~\unicode[STIX]{x03BC}\text{m}$ ($0.02\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$), respectively, much smaller than the wall unit ($\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$), hence they do not affect the flow. Trends in the wall dynamics are elucidated by correlating the deformation with flow variables, including the 3D pressure distribution calculated by spatially integrating the material acceleration. Predictions by the Chase [J. Acoust. Soc. Am., vol. 89 (6), pp. 2589–2596] linear model are also calculated and compared to the measured trends. The spatial deformation–pressure correlations peak at $y/h\approx 0.12$ ($h$ is half channel height), the elevation of Reynolds shear stress maximum in the log-layer. Streamwise lagging of the deformation behind the pressure is caused in part by phase lag of the pressure with decreasing distance from the wall, and in part by material damping. Positive deformations (bumps) caused by negative pressure fluctuations are preferentially associated with ejections involving spanwise vortices located downstream and quasi-streamwise vortices with spanwise offset. Results of conditional correlations are consistent with the presence of hairpin-like structures. The negative deformations (dimples) are preferentially associated with positive pressure fluctuations at the transition between an upstream sweep to a downstream ejection.

The flow-induced pressures generated by turbulent boundary layers cause vibration and, ultimately, sound. The convected nature of the pressures has led to considerable sophistication in the mathematical modeling of boundary-layer-induced vibration and sound. The work in this general area has been applied, and is of direct importance, to the prediction and reduction of cabin noise in aircraft fuselages and automobile interiors, the vibration of reentry vehicles, sound in sonar domes, and vibrations and sound generated in pipes and ducts. This chapter will develop various ways of describing the forcing function, discussing the nature of the cross-spectral and wave vector properties of surface pressures generated by turbulent flow over smooth or rough surfaces that relate to the production of sound and vibration.

Sound may be emitted whenever a relative motion exists in fluids or between a fluid and a surface. The common physical processes that are responsible for noise generation include turbulent fluid motions, vibration of structures, acoustics, and aerodynamics of wings and bodies. The parameters of various forms of interaction must be known in order to effect productive design changes for noise control. This chapter introduces the concepts of noise generation through flow and body–flow interactions. The dimensional analysis of sound generation is introduced along with the importance of geometrical similitude in modelling. The practical results of signal analysis are described including the fundamentals of correlation analysis, Fourier analysis, and simple filtering theory. The established means of quantifying acoustic variables is discussed and an illustration of nondimensionalization is given. The chapter ends with a refresher of the mathematical operations and definitions that occur throughout the rest of the book including coordinate systems, differential operators, integral theorems, and the Dirac delta function.

This chapter focuses on the flow-acoustics of axial flow machinery from helicopter blades to automotive cooling fans. This chapter will consider the special acoustic considerations brought about by the rotational motion of the blades relative to the acoustic medium; that multiple flow excitations may coexist, providing varied spectral quality in different frequency ranges; the modifications of blade forces owing to the interactions of blades in the rotor with each other and with other blade rows; and the frequency–wave number matching of the rotor with ingested disturbances on the one hand and with acoustical modes of enclosures on the other. The chapter starts with an examination of the fundamental characteristics of unsteady loads and of noise from rotating vanes, before discussing the important performance features of rotating machinery. Free-field rotor noise and self-noise of blades will be described, as well as examining turbulent and deterministic blade interaction sounds due to nonuniform inflow, and the fundamental acoustics of ducted rotors and centrifugal fans.

This chapter describes the theories and derives the equations that are the foundations of theoretical aero- hydroacoustics principally relating to subsonic flow and its excitation of elastic surfaces. The chapter will explore the common relationships of simple linear acoustic theory, emphasizing the fundamental qualities of single-pole and multipole source types. The general theory of fluid-induced noise generation, including theory of vortex-generated sound in low-speed (low Mach number) flow, is also derived with considerable attention given to the classification of source types and noise mechanisms as well as to the influences of solid boundaries of various types on radiated intensity.

Flow-induced sound often involves more than direct dipole sound. It is common for flow-induced forces on bodies and structures to generate vibration, and this vibration in turn induces additional sound and may even modify the unsteady fluid forces. This chapter will develop the theory of flow-induced random vibrations of structures using the rectangular panel and the taut string as examples. The elements of noise and vibration control will follow directly as will many of the essential features of fluid loading of vibrating structures. In this chapter the general relationships that describe flow-induced vibration and structural radiation will be derived to express a response variable. Aeolian tone is also discussed in terms of the application of the results of this chapter to problems of flow-induced noise that involve vibration.

Phased arrays of pressure transducers have found broad application in both airborne and underwater acoustic technology. This chapter examines several examples of the responses of transducers, transducer arrays, and elastic structures to wave number-distributed turbulent boundary layer wall pressures and diffuse sound. The responses of planar surfaces in air with minimum fluid loading, fluid-loaded panels, and surfaces made of elastomeric materials are all discussed. This chapter also considers both rough and smooth wall boundary layers and incident acoustic fields as notionally occurring with an elastic panel in the wall of a reverberant chamber.

Whether or not a moving fluid is stable or unstable to some applied stimulation is associated largely with the spatial gradient and curvature of the mean velocity profile in the flow. This chapter describes the unstable characteristics of flow that are required to create fluid disturbances and relates those characteristics to the eventual breakdown into both regular and random vortex structures. Many of the analytical and experimental techniques that are used when the flow disturbances become irregular or turbulent are also introduced. This chapter will describe practical applications of the general theory of shear layer disturbances and develop the rules for predicting the occurrence of various types of vortex-induced tones in holes, cavities, and obstructed jets. The part played by ambient turbulence in the basic flow and the influence of the Reynolds number on the vortex structures will be discussed. Finally, some fundamental concepts in the similarity principles that govern noise from turbulent jets and some experimental approaches to validate those concepts will be introduced.

This chapter discusses the occurrence of cavitation and cavitation noise in hydrodynamics. Principles of bubble equilibrium and nonlinear dynamics will be applied to obtain rules describing the inception of frequently encountered types of cavitation. In this chapter single bubble will be used to derive general and practical scaling procedures for hydrodynamically induced cavitation noise in terms of physically measurable quantities. Less noisy types of bubble noise, such as noise emanating from the formation and splitting of bubbles which cause simple harmonic oscillations of bubble walls, will be described. Finally, splash noise and some of its practical consequences will be examined briefly.

In many engineering applications the noise and vibration produced by lifting surfaces dominate all other structural–acoustic sources. Lifting surfaces are not hydrodynamically and acoustically homogeneous and need not be acoustically compact. In noise-production in rotating machinery (fans, propellers, turbines, etc.), the relative velocity of the appropriate solid surface is the dominant variable. The general sound and vibration mechanisms that are common to all types of noncavitating lifting surfaces will be discussed in this chapter, including a discussion of aerodynamic noise theory that unifies all manners of flow–edge interactions by means of the idealized problem of turbulent flow past a half-plane. This chapter also provides a systematic development of the sound and vibration of wing and hydrofoil sections from the perspective of traditional aerodynamics of lifting surfaces and then for viscous-flow–edge interactions. This chapter provides the fundamentals for treating all the important types of single-phase flow-noise fans and rotors, and discusses the fluid-structure interactions of vibration and self-excitation.

In underwater acoustics, sound propagation may be influenced by the dynamics of suspended gas bubbles in the liquid. If the liquid flows past bodies, cavitation may occur if the static pressure in the fluid decreases below some critical value. Since an understanding of both propagation in bubbly fluids and cavitation requires some knowledge of the dynamics of bubbles; this chapter will examine the dynamics of bubbles; the linear perturbations of gas-filled bubbles by small amplitude pressures, the propagation through bubbly mixtures, the onset of nonlinear large-amplitude bubble motions, and implosive collapses that produce sound. The subject of nonlinear bubble dynamics as covered here is introductory to our coverage of hydrodynamic cavitation inception and noise in the next chapter. Accordingly, we emphasize the basic behavior of air bubbles in water and illustrate the various uses of the theory of single-bubble dynamics in estimating bubble motion and critical pressure for nonlinear growth. We will also show how a related linear modeling of the acoustics of bubble swarms is useful in describing the wave dispersion characteristics in water filled hydrodynamic test environments.

The sound radiated by flow across a circular cylinder, known also as the Aeolian tone, is one of the most fundamental of flow-acoustic phenomena. The aeroacoustic processes taking place in the Aeolian tone are one-dimensional examples of those which occur in almost all cases of flow-induced sound and vibration. Notably these processes are the generation of flow disturbances, the Reynolds number dependence of the related body forces, the spatial correlations of the forces, and the elements of dipole sound generation from nonvibrating bodies. This chapter will examine the Aeolian tone in detail, including in terms of flow variables and from flow over the surfaces of acoustically compact, rigid bodies from vortex–surface interactions, and will extend the specific results for the purpose of describing and scaling aerodynamic sound from acoustically similar air flow machinery. The chapter discusses the sounds emitted by cylinders held rigidly in the flow or allowed to vibrate slightly in relatively small displacements (with respect to radius of the cylinder). This chapter will describe the formulations to estimate oscillatory lift coefficients on the wake-forming bodies in terms of the strength and geometries of the shed vortex streets. Measured parameters, including shedding frequency, lift coefficients, and axial correlation-length scales, will also be reviewed. Influences on these parameters of upstream turbulence and cylinder vibration will be considered from an experimental basis.

In order to reduce noise in a host of engineering applications, fluid flow directions must be changed, high-pressure flowing fluids must be vented, or throttled obstructions of one type or another must be interjected into a duct or pipe flow, since the flow at the boundary of the pipe or duct is a source of flow-induced vibration. Piping systems and ducts of varying lengths and terminations may have technical elements in common, although parameter differences make different noise-producing mechanisms dominant in each circumstance. This chapter will examine the various noise sources such as enclosed sources, internal or external excitation of the wall by turbulent wall flow, and acoustic coupling of wall vibration with the external acoustic medium. The roots of many empirically based prediction formulas used by industry will be described, and some of the engineering tools used to address them will be discussed. This chapter will use examples to illustrate applications for the description of sound transmission from pipes and ducts.

A methodology is presented to predict the frequency spectrum of fluctuating wall-pressures based on a steady Reynolds Averaged Navier Stokes (RANS) solution. The spectral modeling scheme solves a Poisson equation with a linear source term (LST) for the mean-velocity–turbulence interaction (MT) and non-linear source terms (NST) for the turbulence–turbulence interaction (TT). An anisotropic factor is used to account for the anisotropic features of the turbulence field. The prediction method was originally developed based on the equilibrium flow, i.e. turbulent flow with homogeneous and stationary characteristics, with the LST only. In this paper, the model is further applied to a non-equilibrium flow, i.e. flow over a backward facing step (BFS), to explore its predictability for the wall-pressure fluctuations. With the help of DNS results and experimental data for the BFSs, the model is investigated with the inclusion of NST. Prediction results demonstrate the impact of turbulence features of the wall shear layers to the predicted wall-pressure spectrum.

Expressions to describe the correlation length scales of turbulent inflow to an aerodynamic body are derived as functions of the classic integral length scale and anisotropy correction factors. These one-point parameters are significantly easier to determine experimentally than traditional correlation-scale measurement techniques, which involve multiple probes at multiple locations. As such correlation scales are necessary to properly estimate the aeroacoustic response of the body, such a technique could have substantial benefit in a wide variety of applications. The approach is applied to a recent experimental study examining the response of a stator downstream of a propeller that is itself ingesting broadband turbulence. Results suggest that the derived expressions not only accurately represent correlation length scales, but also enable the accurate prediction of the acoustic output of the stator.

To examine the aeroacoustic response of the downstream blade row of a rotor/stator pair, the turbulent flowfield between the two components must be accurately represented. To that end, a recent experimental study sought to examine this complex flowfield, establishing a causal relationship between the flowfield influences and their relative contributions to the total turbulence. Although these influences and their relative impact might depend on specific geometry, two will play a dominant role in almost every rotor/stator application: wake turbulence from the upstream blade row (the topic of Part 1) and turbulence ingested by the system and modified by the upstream blade row (the topic of Part 2). The extensive scope of decomposing these influences necessitates their discussion in separate publications. Part 1 begins with an overview as to the relevence and utility of separating these influences, providing motivation for the study. The paper then examines the contribution of the broadband and tonal contributions associated with wake turbulence. A model is proposed that infers broadband turbulence levels from a single, appropriately chosen length scale. This length scale is determined through reconstruction of the temporal mean wake profile shape utilizing the tonal component of the ensemble-averaged, measured wake spectra. Results show that simple models can be used effectively to isolate the wake turbulence contribution, forwarding the concept of a globally applicable theory for use in modeling efforts involving similar flowfields. Part 2 (the topic of this paper) examines turbulence ingested by the system and modified by the upstream upstream blade row. A theoretical model is adapted to predict the level of ingested turbulence suppression using easily quantified geometric arguments. With an appropriate choice of coordinate system, this model accurately predicts broadband suppression of ingested turbulence, showing that simple models can be used to isolate contributions and forwarding the concept of a globally applicable theory for extracting such information from other similar flowfields.

To examine the aeroacoustic response of the downstream blade row of a rotor/stator pair, the turbulent flowfield between the two components must be accurately represented. To that end, a recent experimental study sought to examine this complex flowfield, establishing a causal relationship between the flowfield influences and their relative contributions to the total turbulence. Although these influences and their relative impact might depend on specific geometry, two will play a dominant role in almost every rotor/stator application: wake turbulence from the upstream blade row (the topic of Part 1) and turbulence ingested by the system and modified by the upstream blade row (the topic of Part 2). The extensive scope of decomposing these influences necessitates their discussion in seperate publications. Part 1 begins with an overview as to the relevence and utility of separating these influences, providing motivation for the study. The paper then examines the contribution of the broadband and tonal contributions associated with wake turbulence. A model is proposed that infers broadband turbulence levels from a single, appropriately chosen length scale. This length scale is determined through reconstruction of the temporal mean wake profile shape utilizing the tonal component of the ensemble-averaged, measured wake spectra. Results show that simple models can be used effectively to isolate the wake turbulence contribution, forwarding the concept of a globally applicable theory for use in modeling efforts involving similar flowfields. Part 2 examines turbulence ingested by the system and modified by the upstream upstream blade row. A theoretical model is adapted to predict the level of ingested turbulence suppression using easily quantified geometric arguments. With an appropriate choice of coordinate system, this model accurately predicts broadband suppression of ingested turbulence, showing that simple models can be used to isolate contributions and forwarding the concept of a globally applicable theory for extracting such information from other similar flowfields.

Time-mean flow fields and turbulent flow characteristics obtained from solving the Reynolds averaged Navier-Stokes equations with a k‐ε turbulence model are used to predict the frequency spectrum of wall pressure fluctuations. The vertical turbulent velocity is represented by the turbulent kinetic energy contained in the local flow. An anisotropic distribution of the turbulent kinetic energy is implemented based on an equilibrium turbulent shear flow, which assumes flow with a zero streamwise pressure gradient. The spectral correlation model for predicting the wall pressure fluctuation is obtained through a Green’s function formulation and modeling of the streamwise and spanwise wave number spectra. Predictions for equilibrium flow agree well with measurements and demonstrate that when outer-flow and inner-flow activity contribute significantly, an overlap region exists in which the pressure spectrum scales as the inverse of frequency. Predictions of the surface pressure spectrum for flow over a backward-facing step are used to validate the current approach for a nonequilibrium flow.

This is the second of two papers that discuss an experimental investigation of the aeroacoustic response characteristics of a 10-bladed rotor to grid-generated turbulence. To characterize empirically the rotor response, both the ingested velocity field and resulting far-field sound were measured. In part 1, an empirical velocity characterization of the grid- generated turbulence field was presented. This characterization culminated in a semi-empirical model of the ingested small-scale turbulence field and a modal decomposition of the circumferentially varying mean velocity field in the rotor inlet plane. This detailed velocity model is now used to investigate the aeroacoustic response of a 10-bladed rotor ingesting the grid-generated turbulence field. In particular, the semi-empirical turbulence model is used, in conjunction with theoretical spectral analysis techniques, to predict the far-field sound generated by the 10-bladed rotor. These predictions are compared to corresponding measured data to assess the fidelity of the spectral analysis methods and the semi-empirical turbulence model

Results are presented of an experimental investigation into the aeroacoustic response characteristics of rotor turbulence ingestion. To fully characterize the rotor response, both the ingested velocity field and the resulting far-field sound were measured. The results are presented of a detailed velocity characterization, which was performed upstream of the rotor. The velocity measurements included an evaluation of the streamwise development of turbulence characteristics downstream of the grid, a high-resolution mapping of the spatial distribution of the mean velocity and rms turbulence fluctuations in the rotor inlet plane, and the development of a semi-empirical, functional representation of the three-dimensional wave number spectral density of the ingested turbulence

Ira Dyer’s work in structural acoustics is well known, but what I think is little known is his start in aeroacoustics followed by his early work in the response of structures to pressure fields of a kind that is typical of hydroacoustics. Lighthill’s seminal paper on aerodynamic noise in 1952 is generally regarded as the dawn of modern flow acoustics. Immediately after this, in 1953 and continuing into the early 1960s, Ira began his career by examining scaling laws for the sound and the structural vibration associated with jets and high speed flow over plate and shell structures. In this work he examined scaling laws for sound power, the importance of wave coincidence in fluid-structure interaction, and the effects of space-time decorrelation of excitation pressure fields. This paper will examine the conclusions of these early papers of Ira’s and trace their relevance through to modern times and across the combined fields of hydro-structural acoustics. Ira’s professional path led him away from these areas...

This paper summarizes an analytical model approach for calculating flow induced sound from either elastic or rigid surfaces with small roughness. The analytical approach used here provides a result for both the wave number-frequency spectrum of the structure’s excitation pressure and the structure’s response to that pressure and can be applied to many types of uneven surfaces, such as those on which are dispersed 2 or 3 dimensional deterministic or random geometric shape irregularities. This paper is focused on 3 dimensional distributed roughness elements. The shape of the unevenness protrudes into the boundary layer above it, acting as a flow spoiler and generating forces and wakes in the immediate region of the roughness element. It is assumed that these shapes are small and in the range of 10 to several hundred viscous scales. We will discuss the effects of surface elasticity on the ability of these sources to produce sound in regions both above the surface (on the flow side for both elastic and inelastic surfaces) and below the surface on the quiescent fluid side (in the case of elastic surfaces). A method for modeling forcing functions will also be presented in the context of the overall theory. The unevenness is presumed to be small enough, or of such a nature, as to not affect the basic elasticity of the surface. In the subject case of rough walls, analytical results will be compared with both aero-acoustics measurements made in multiple facilities and large eddy simulations. All research was made possible by a recent program sponsored by the U.S. Navy’s Office of Naval Research.

This paper, in 2 parts, presents a unified analytical model of flow induced sound from elastic or rigid surfaces with geometric irregularities of small arbitrary shapes. The cases in point are general and include surfaces on which are dispersed geometric shape irregularities which may be randomized (distributed roughness, say) or which may be geometric and regular. In either case, the shape protrudes into the boundary layer above it, acting as a flow spoiler and generating forces and wakes in the immediate region of the roughness element. It is assumed that these shapes are small and in the range of 10 to several hundred viscous scales. Regular patterns of 2dimensional geometries are also generally accommodated by the work presented here and might also include ridges and gaps in surfaces which also spoil the flow; these cases will not be discussed, but the general analysis presented here does include such surfaces implicitly. We will discuss the effects of service elasticity on the sources of sound that might be produced both above the surface (on the flow side for both elastic and inelastic surfaces) below the surface on the quiescent fluid side (in the case of elastic surfaces). A method for modeling forcing functions will be presented in the context of overall theory, but this paper deals specifically with the case of fully-rough turbulent boundary layers of 3-dimensional roughness when they are on either rigid surfaces or elastic surfaces.

This paper is the second part of a general analytical description of flow-induced sound from elastic or rigid surfaces with geometric irregularities of small arbitrary shapes. This part deals with the construction of the relevant forcing mechanism and the use of measured data in wind tunnels. The cases in point are general and include surfaces on which are dispersed geometric shape irregularities which may be randomized (distributed roughness, say) or which may be geometric and regular. In either case, the shape protrudes into the boundary layer above it, acting as a flow spoiler and generating forces and wakes in the immediate region of the roughness element. It is assumed that these shapes are small and in the range of 10 to several hundred viscous scales. Regular patterns of 2dimensional geometries are also generally accommodated by the work presented here and might also include ridges and gaps in surfaces which also spoil the flow; these cases will not be discussed, but the general analysis presented here does include such surfaces implicitly. This paper deals specifically with the case of fully-rough turbulent boundary layers of 3dimensional roughness when they are on either rigid surfaces or elastic surfaces. Since these are contiguous with the flowing fluid medium on one side of the plate, they include sources with either random or spatially organized geometric patterns of irregularities. An approach will therefore also be given for those cases in which the roughness elements are of random sizes. Analytical results will be compared with aero-acoustics measurements made in multiple facilities and large eddy simulations, both of which were made in a recent program sponsored by the U.S. Navy's Office of Naval research.

Data analysis techniques were previously developed for rotating machinery that predicted the far-field radiation, inferred inflow characteristics, and defined the near-field/far-field acoustic Green's function based on measurements of the pressure near field (Minniti, R. J., Blake, W. K., and Mueller, T. J., Inferring Propeller Inflow and Radiation from Near-Field Response, Part 1: Analytic Development, AIAA Journal, Vol. 39, No. 6, 2000, pp. 1030-1036). The techniques are applied to a free-running propeller in subsonic flow. As a first case, the propeller ingesting large-scale, mean-flow distortions as would be present downstream of stators or inlet guide vanes was considered. This simplified case allowed qualitative analysis in the time domain and complimenting quantitative analysis in the frequency domain. In addition, the case acted as a calibrating configuration to map the frequency response of the individual blades to the incoming flow by varying the number of distortions present and the rotational speed of the propeller. Based on the results of the first case, the analysis was extended to the propeller ingesting grid-generated turbulence. Because of the complex nature of the flow, all analysis was completed in the frequency domain. By the use of the techniques in Inferring Propeller Inflow and Radiation from Near-Field Response, Part 1: Analytic Development, an estimate of the blade summation gain was used to complete the direct solution of the aeroacoustic problem and predict the acoustic far field from a measurement of the ingested flow. Additionally, the inflow character was inferred from the near-field measurements.

The inverse aeroacoustic problem associated with a flat-plate airfoil in unsteady compressible flow is formulated in terms of a Fredholm integral equation of the first kind. The feasibility of determining the unsteady pressure along the airfoil surface from the radiated acoustic signal is demonstrated. It is shown that the Hadamard conditions of existence and uniqueness of the inverse solution can be satisfied. The third Hadamard condition for the continuous dependence of the solution on the input acoustic data shows the problem to be ill-posed. The singular value decomposition method with regularization is used to treat the associated ill-conditioned algebraic problem. Discretization and collocation techniques are used to represent the unsteady pressure on the airfoil. Both methods give very accurate reconstructions when "perfect" input data are used. The collocation method requires only a small amount of input data either from the far field or the near field, thus making it more suitable for applications.

This report documents the use of the acoustic beamforming technique to pinpoint and measure noise levels from heavy truck traffic. The system uses an elliptical array of more than 70 microphones and data acquisition software to measure noise levels from a variety of noise sources on large trucks—including the engine, tires, mufflers, and exhaust pipes. The results validate the feasibility of beamforming technology, offer new insight into the distribution of truck noise sources, and provide valuable input to the design and testing of quieter pavements and noise barrier systems. This report will be of interest to anyone concerned with understanding and mitigating highway noise levels.

Turbulent boundary layer flows over rough surfaces are known to produce elevated far-field acoustic sound levels. The nature by which surface irregularities alter the near-field surface pressures and subsequently affect the sound generation to the scattering of high wavenumber convective pressures to low wavenumber acoustic pressures, which is typically interpreted as a dipole-like source. The focus of the current investigation is the experimental interrogation of both near- and far-field pressures due to the flow over roughened surfaces in order to identify the source mechanisms and to validate physical models of roughness sound. For rough surfaces composed of large geometrical elements (defined by large Reynolds numbers based on roughness height and friction velocity), such as hemispheres and cubes, the measured near-field surfaces pressures indicate that the local interstitial flows become important in determining the sound radiation characteristics. In order to describe the aeroacoustic source region, scaling laws are developed for surface pressures at locations around the roughness elements for various roughness configurations and flow speeds. Relationships between surface pressures amongst the rough surface elements and far-field pressures measured at several directional aspects were examined to identify roughness sound source mechanisms. Measurements of a dipole directivity pattern and dipole efficiency factors obtained when normalizing radiated sound by surface pressures offer support to the scattering theories for roughness sound. Using existing pressure scattering models as a basis, an empirical model for roughness sound is generated.

The region downstream of a ducted rotor has been experimentally investigated in terms of its wake characteristics and the duct wall pressure fluctuations. The motivation for the measurements was to document and understand the sources of structural excitation that would lead to shell vibration. The wake measurements indicated a swirling hydrodynamic flow field that decayed rapidly in the streamwise direction. The interior duct wall pressure similarly indicated strong decay in the fluctuation levels in the streamwise direction. The spectral features of the wall pressure at various speeds and axial positions were described, and found to be influenced by the relative interactions of the blade rate harmonics and the duct cut-on modes. A circumferential modal analysis was used to describe the specific features of the hydrodynamic and acoustic pressure components. I. Introduction HE prediction of sound generated by turbomachines operating within a cylindrical duct represents one of the canonical aeroacoustic problems. A significant source of radiated sound can be structure-borne when the duct material is elastic. Direct mechanical forces as well as fluid pressure at the wall can lead to excitation of the structure. The unsteady surface pressure can be characterized in terms of both acoustic pressure and the convected, or hydrodynamic, pressure fluctuations. Prediction of the shell motion and sound radiated through the duct walls can only be made if an adequate space-time (alternatively, wavenumber-frequency) description of the wall pressure is known 1 . T

A new formulation for predicting the noise generated by a ducted rotor interacting with a casing boundary layer has been developed. The method accounts for the streamwiseelongated turbulent structures that have been recently observed in ∞at-plate boundary layers. These structures have been measured to have streamwise lengths on the order of 20‐, which is long enough to cause unsteady lift that is correlated between rotor blades. An analytical relation between the rotor unsteady lift and the two-point correlation of upwash velocity provides a link between the elongated turbulent structures and the sound radiated by the ducted rotor. A simple model for the true two-point correlation function in the duct boundary layer allows for the unsteady lift to be estimated. The predicted unsteady lift spectrum matches an experimentally determined spectrum within … §4 dB up to about flve times the blade passing frequency.

An airfoil subjected to turbulence in the approach stream radiates sound due to the unsteady lift. Prediction of the spectral density of the unsteady lift requires knowledge of the magnitude and correlation length of the chord normal, or upwash, component of velocity. Additionally, a lift function must be specified based on the geometry of the airfoil. The present research experimentally investigated the sound radiated from a thin airfoil placed in a single stream shear layer. The results indicated a substantial level of agreement between the measured and modeled sound spectra with deviations at low frequencies due to anisotropic turbulence. The high frequency magnitudes were found to match the predictions well only if a thickness correction was applied to the unsteady lift function.

The objective of this study was to experimentally investigate the broadband trailing edge noise generated by a sharp trailing edge geometry and an asymmetric blunt edge. The flow field in the vicinity of the sharp trailing edge was found to be equivalent to that of a flat plate turbulent boundary layer. The interaction of the two boundary layers with the edge was responsible for broadband noise generation. The blunt trailing edge geometry exhibited additional complexity, with turbulent boundary layer separation and sound generated by vortex shedding. The measurement program included hot-wire anemometry, unsteady surface pressure, and radiated sound utilizing two microphone arrays. The boundary layer parameters and wall pressure spectra were used to compute the radiated sound from existing scattering theory. These calculations agreed very well with the array data, with differences typically within 2dB over the frequency range considered valid for the theory.Copyright © 2008 by ASME

Sound generation in low Mach number turbomachines is typically dominated by unsteady fluid forces on rigid surfaces. As a result, the radiated sound is closely related to the unsteady flow field. The present study focused on the self noise that is generated by a ducted rotor separate from the effect of noise due to inflow turbulence. The flow rate through the rotor was independently varied in order change the mean lift on the blades. Measurements of the flow field around a ducted rotor were found to provide insight to the various mechanisms of sound that are present at different mean loading conditions. At lower flow rates the blades were partially stalled, resulting in significantly increased noise levels. The measurements included rotor wake measurements using hot-wire anemometry and far field sound. A simple model to predict the radiated self noise based on the hot-wire measurements is presented.Copyright © 2008 by ASME

This paper describes the development of a new method for measuring pass-by sound from trucks and other vehicles using 2-dimensional arrays. The approach provides 2-dimensional quantitative maps “images” of the cross-range and elevation distribution in the vehicle side view. The method is an application and extension of an array technology that was originally used for the characterization of static aeroacoustic sources in wind tunnels. The focus of this work is on identifying and rank-ordering the important contributing sources of passby noise. This development includes two phases: developmental testing at a test track site, and road-side testing at two California State highway sites. The acquisition post-processing allows the “observer” to track the vehicle cross-range in order to create a time sequence of source maps that may be interpreted as both level relationships and directivity patterns. The processing applies both range and approximate Doppler adjustments to spectra as a function of time during pass-by or, equivalently, to vehicle position relative to the array’s center. An image demodulation scheme is shown to clarify the images. The initial phase of this work occurred at a test track using known “cooperative” truck sources. This experience permitted the verification of the method and the definition of a final measurement approach that was viable at a highway site. Subjects were all trucks that varied in model, vehicle speed, tread, and the presence of a trailer. The array beamformer’s ability to localize and the measurement system’s ability to track were validated using both stationary and moving sources. Following validation at the test track site, the instrumentation was transferred to two California highway sites. There, acoustic calibration was used to align the array with the road track and to provide a spatial reference for mapping the “images”. Both light and heavy vehicles at these sites were “uncooperative” with arrivals and speeds randomly determined by traffic flow. This work was funded by the California Department of Transportation.Copyright © 2008 by ASME

A formulation is developed to predict the vibration response of a finite length, submerged plate due to a line drive. The formulation starts by describing the fluid in terms of elliptic cylinder coordinates, which allows the fluid loading term to be expressed in terms of Mathieu functions. By moving the fluid loading term to the right-hand side of the equation, it is considered to be a force. The operator that remains on the left-hand side is the same as that of the in vacuo plate: a fourth-order, constant coefficient, ordinary differential equation. Therefore, the problem appears to be an inhomogeneous ordinary differential equation. The solution that results has the same form as that of the in vacuo plate: the sum of a forced solution, and four homogeneous solutions, each of which is multiplied by an arbitrary constant. These constants are then chosen to satisfy the structural boundary conditions on the two ends of the plate. Results for the finite plate are compared to the infinite plate in both the wave number and spatial domains. The theoretical predictions of the plate velocity response are also compared to results from finite element analysis and show reasonable agreement over a large frequency range.

Steady mean flow fields and turbulent flow characteristics obtained from solving the Reynolds Averaged Navier Stokes (RANS) equations with a k-ε isotropic turbulence model are used to predict the frequency spectrum of wall-pressure fluctuations for flow past a backward facing step. The linear source term (LST) of the governing fluctuating-pressure equation is used in deriving the final double integration formula for the fluctuating wall pressure. The integrand of the solution formula includes the mean-flow velocity gradient, modeled turbulence normal fluctuation, Green’s function and the spectral model for the interplane correlation. An anisotropic distribution of the turbulent kinetic energy is implemented using a function named anisotropic factor. This function represents a ratio of the turbulent normal Reynolds stress to the turbulent kinetic energy and is developed based on an equilibrium turbulent flow or flows with zero streamwise pressure gradient. The spectral correlation model for predicting the wall-pressure fluctuations is obtained through modeling of the streamwise and spanwise wavenumber spectra. The nonlinear source term (NST) in the original fluctuating-pressure equation is considered following the conclusion of Kim’s direct numerical simulation (DNS) study of channel flow. Predictions of frequency spectra for the reattachment flow past a backward facing step (BFS) are investigated to verify the validity of the current modeling. Detailed turbulence features and wall-pressure spectra for the flow in the reattachment region of the BFS are predicted and discussed. DNS and experimental data for BFSs are used to develop and validate these calculations. The prediction results based on different modeling characteristics and flow physics agree with the observed turbulence field.

Steady turbulent flow fields obtained from solving the Reynolds Averaged Navier Stokes (RANS) equations with an isotropic model are used to predict the frequency spectrum of wall pressure fluctuations. The fluctuating turbulent velocity normal to the wall is represented by the turbulent kinetic energy contained in the local flow. An anisotropic distribution of the turbulent kinetic energy is implemented based on a turbulent boundary layer over a flat plate. The spectral correlation model for predicting the wall pressure fluctuations is obtained through a Green’s function formulation and modeling of the streamwise and spanwise wavenumber spectra. Predictions for a zero-pressure-gradient flow agree welll with measurements and reveal an overlap region of an inverse of the frequency, which has been proved as a resultant of the velocity profile in the logarithmic region. Spectrum predictions for flow over a backward facing step are used to demonstrate the robustness of the current approach for a non-zero-pressure-gradient flow with a flow recirculation and a reattachment region.

The use of correlation techniques provides a vital tool in understanding and characterizing mechanisms of flow induced sound and vibration. This chapter outlines the basic mathematical relations used in the derivation of such techniques, introducing fundamental quantities such as the cross-correlation function and coherence function. These techniques are then applied to specific aeroacoustic examples, establishing the causal relationship between measured sound and its source. These examples include the measurement of trailing edge noise by suppression of background acoustic contamination, correlation measurements between surface pressure and far field radiated acoustic pressure fields, and the characterization of a turbulent flow field using the integrated surface pressure response of a rotating propeller.

The decade of the 1950s provided us with the beginnings of sub-disciplines of acoustics that we now call aeroacoustics and hydroacoustics. In the beginning, the attention was placed on mechanisms relevant to the aeronautical engineering and the early rocket and space vehicle communities. Accordingly, much published work at the time dealt with jet noise and structural fatigue resulting from that noise and from turbulent boundary layer excitation. In 1956, Murray Strasberg and Hugh Fitzpatrick published a seminal paper, “Hydrodynamic Sources of Sound”, 1st Hydrodynamics Symposium. This paper put the aerodynamic noise theory of Lighthill (1952) in the context of Navy application and defined relevant source types. A. Prosperetti will discuss Murray's legacy regarding bubble noise and cavitation discussed in that paper. I will discuss the other interest of Murray: i.e., flow induced vibration and sound. Although he published little on this subject the impact that he had on others who did was important. Accordingly, Murray had continuing impact on the developing knowledgebase of flow-induced sound and vibration, and we will use the area of TBL noise as an example of how concepts in flow noise and vibration have evolved under Murray's career span.

This investigation examined the unsteady response of a stator located downstream of a propeller ingesting broadband turbulence. This response is governed by the turbulent flowfield downstream of the propeller. The analysis of the flowfield is organized in a manner which reflects the causal relationship between influences on the flowfield and the evolution of the flowfield itself. Mathematical models for the contribution of propeller wakes and modification of ingested turbulence are presented and analyzed. Results suggest that this complex flowfield may be fully and accurately represented using simple mathematical models supported by baseline empirical information. Nomenclature

This paper discusses an experimental investigation of the aeroacoustic response characteristics of a ten-bladed rotor to grid-generated turbulence that was performed at Notre Dame. In order to empirically characterize the rotor response, both the ingested velocity field and resulting far-field sound were measured. The detailed velocity characterization included: a high-resolution mapping of the spatial distribution of the mean velocity and RMS turbulence fluctuations in the rotor plane; an evaluation of the streamwise development of “nearly isotropic” conditions at the rotor inlet plane; and the development of a semi-empirical, functional representation of the 3D wave number spectral density of the ingested turbulence. This turbulence model was used, in conjunction with theoretical speckal analysis techniques, to predict the sound pressure levels in the far-field. These predictions were compared to conesponding measured data to assess the fidelity of the spectral analysis methods and the semi-empirical turbulence model. The measured ten-bladed acoustic response was also compared to the corresponding response of a four-bladcd rotor ingesting the same grid-generated turbulence field, to demonstrate the effect of blade spacing on rotor turbulence ingestion noise.

The propeller turbulence ingestion problem has been the subject of prior experimental work at the University of Notre Dame. These prior tests focused on the aeroacoustic response of a four-bladed propeller to grid-generate d turbulence. A new project has recently begun, in which the aeroacoustic response characteristics of a ten-bladed propeller ingesting turbulence will be investigated. The initial phase of this project is to characterize the spectral content of the turbulent inflow. Turbulence characterization is being performed in three stages. In the first stage, single degreeof-freedom statistical parameters are measured, such as the autocorrelation and temporal autospectrum of the axial turbulence component, from which estimates of the nominal turbulence intensity and integral scale can by derived. The next task is to determine the spectral content in both the temporal frequency and tangential wave number domains. These data are derived from a series of two-point velocity correlation measurements made along arcs in the tangential direction of the propeller plane. The final turbulence characterization task is to extend the spectral analysis to include the radial wave number domain. The subject of this paper is the data collected during the first two stages of the turbulence characterization. These data demonstrate the expected roll-off characteristics at higher frequencies and wave numbers. In addition to the expected turbulence behavior, a surprising degree of cross-stream spatial structure is demonstrated by the tangential distribution of streamwise velocity.

The elliptical array described in the previous paper (Part 1) was deployed road‐side at a test track for measuring the sound emitted from trucks during passby. Measurements were made on various truck models in various operating states with and without trailers. Extensive spherical‐source calibrations confirmed the array's beamforming at both on‐normal and steering angles (to 45°); they also disclosed the magnitudes of ground reflection paths for localized sources at different elevations. In all cases, the array output was computationally inverted to produce two‐dimensional spatial maps of source levels in the side profile of the truck. In the cases of stationary trucks, the source maps were correlated with simultaneously‐obtained intensity maps. Comparisons verified that the array‐based source maps for the trucks ranked sound sources of disparate levels in the same order as did the sound power levels deduced from the sound intensity data. Acoustic source maps obtained during truck passbys were then used to provide time‐histories and spatial distributions of sources and source paths from the engine, muffler, tires, and certain body components. This project is funded by the National Cooperative Highway Research Program of the Transportation Research Board of the National Academies, USA.