First-principle description of acoustic radiation of shear flows

As a methodology complementary to acoustic analogy, the asymptotic approach to aeroacoustics seeks to predict aerodynamical noise on the basis of first principles by probing into the physical processes of acoustic radiation. The present paper highlights the principal ideas and recent developments of this approach, which have shed light on some of the fundamental issues in sound generation in shear flows. The theoretical work on sound wave emission by nonlinearly modulated wavepackets of supersonic and subsonic instability modes in free shear flows identifies the respective physical sources or emitters. A wavepacket of supersonic modes is itself an efficient emitter, radiating directly intensive sound in the form of a Mach wave beam, the frequencies of which are in the same band as those of the modes in the packet. By contrast, a wavepacket of subsonic modes radiates very weak sound directly. However, the nonlinear self-interaction of such a wavepacket generates a slowly modulated mean-flow distortion, which then emits sound waves with low frequencies and long wavelengths on the scale of the wavepacket envelope. In both cases, the acoustic waves emitted to the far field are explicitly expressed in terms of the amplitude function of the wavepacket. The asymptotic approach has also been applied to analyse generation of sound waves in wall-bounded shear flows on the triple-deck scale. Several subtleties have been found. The near-field approximation has to be worked out to a sufficiently higher order in order just to calculate the far-field sound at leading order. The back action of the radiated sound on the flow in the viscous sublayer and the main shear layer is accounted for by an impedance coefficient. This effect is of higher order in the subsonic regime, but becomes a leading order in the transonic and supersonic regimes. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.

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Acoustic Radiation from a Semi-Infinite Duct With a Subsonic Jet

International Journal of Aeroacoustics ◽

10.1260/1475472053730075 ◽

2005 ◽

Vol 4 (1-2) ◽

pp. 169-184 ◽

Cited By ~ 15

Author(s):

X. Zhang ◽

X.X. Chen ◽

C.L. Morfey

Keyword(s):

Euler Equations ◽

Acoustic Waves ◽

Numerical Solutions ◽

Acoustic Radiation ◽

Near Field ◽

Solution Process ◽

Far Field ◽

Acoustic Analogy ◽

Mean Flow ◽

Exhaust Duct

The radiation of high-order spinning modes from a semi-infinite exhaust duct is studied numerically. The issues involved have applications to noise radiation from the exhaust duct of an aircraft engine. The numerical method is based on solutions of linearised Euler equations (LEE) for propagation in the duct and near field, and the acoustic analogy for far field radiation. A 2.5D formulation of a linearised Euler equation model is employed to accommodate a single spinning mode propagating over an axisymmetric mean flow field. In the solution process, acoustic waves are admitted into the propagation area surrounding the exit of an axisymmetric duct and its immediate downstream area. The wave admission is realised through an absorbing non-reflecting boundary treatment, which admits incoming waves and damps spurious waves generated by the numerical solutions. The wave propagation is calculated through solutions of linearised Euler equations, using an optimised prefactored compact scheme for spatial discretisation. Far field directivity is estimated by solving the Ffowcs Williams-Hawkings equations. The far field prediction is compared with analytic solutions with good agreement.

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On generation of sound in wall-bounded shear flows: back action of sound and global acoustic coupling

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.416 ◽

2011 ◽

Vol 689 ◽

pp. 279-316 ◽

Cited By ~ 15

Author(s):

Xuesong Wu

Keyword(s):

Acoustic Field ◽

Acoustic Radiation ◽

Leading Order ◽

Mean Flow ◽

S Wave ◽

Acoustic Coupling ◽

Hydrodynamic Motion ◽

Roughness Elements ◽

Supersonic Regime ◽

Back Action

AbstractIn two previous papers (Wu, J. Fluid Mech., vol. 453, 2002, p. 289, and Wu & Hogg, J. Fluid Mech., vol. 550, 2006, p. 307), a formal asymptotic procedure was developed to calculate the sound radiated by unsteady boundary-layer flows that are described by the triple-deck theory. That approach requires lengthy calculations, and so is now improved to construct a simpler composite theory, which retains the capacity of systematically identifying and approximating the relevant sources, but also naturally includes the effect of mean-flow refraction and more importantly the back action of the emitted sound on the source itself. The combined effect of refraction and back action is represented by an ‘impedance coefficient’, and the present analysis yields an analytical expression for this parameter, which was usually introduced on a semi-empirical basis. The expression indicates that for Mach number $M= O(1)$, the mean-flow refraction and back action of the sound have a leading-order effect on the acoustic field within the shallow angles to the streamwise directions. A parametric study suggests that the back effect of sound is actually appreciable in a sizeable portion of the acoustic field for $M\gt 0. 5$, becomes more pronounced, and eventually influences the entire acoustic field in the transonic limit. In the supersonic regime, the acoustic field is characterized by distinctive Mach-wave beams, which exert a leading-order influence on the source. The analysis also indicates that acoustic radiation in the subsonic and supersonic regimes is fundamentally different. In the subsonic regime, the sound is produced by small-wavenumber components of the hydrodynamic motion, and can be characterized by acoustic multipoles, whereas in the supersonic regime, broadband finite-wavenumber components of the hydrodynamic motion contribute and the concept of a multipolar source becomes untenable. The global acoustic feedback loop is investigated using a model consisting of two well-separated roughness elements, in which the sound wave emitted due to the scattering of a Tollmien–Schlichting (T–S) wave by the downstream roughness propagates upstream and impinges on the upstream roughness to regenerate the T–S wave. Numerical calculations suggest that at high Reynolds numbers and for moderate roughness heights, the long-range acoustic coupling may lead to global instability, which is characterized by self-sustained oscillations at discrete frequencies. The dominant peak frequency may jump from one value to another as the Reynolds number or the distance between the roughness elements is varied gradually.

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Shock Propagation and MPT Noise From a Transonic Rotor in Nonuniform Flow

Journal of Turbomachinery ◽

10.1115/1.4006497 ◽

2012 ◽

Vol 135 (1) ◽

Cited By ~ 4

Author(s):

Jeffrey J. Defoe ◽

Zoltán S. Spakovszky

Keyword(s):

High Speed ◽

Acoustic Energy ◽

Shock Propagation ◽

Far Field ◽

Nonuniform Flow ◽

Mean Flow ◽

Flow Distortion ◽

Inlet Distortion ◽

Circumferential Extent ◽

Transonic Rotor

One of the major challenges in high-speed fan stages used in compact, embedded propulsion systems is inlet distortion noise. A body-force-based approach for the prediction of multiple-pure-tone (MPT) noise was previously introduced and validated. In this paper, it is employed with the objective of quantifying the effects of nonuniform flow on the generation and propagation of MPT noise. First-of-their-kind back-to-back coupled aero-acoustic computations were carried out using the new approach for conventional and serpentine inlets. Both inlets delivered flow to the same NASA/GE R4 fan rotor at equal corrected mass flow rates. Although the source strength at the fan is increased by 38 dB in sound power level due to the nonuniform inflow, far-field noise for the serpentine inlet duct is increased on average by only 3.1 dBA overall sound pressure level in the forward arc. This is due to the redistribution of acoustic energy to frequencies below 11 times the shaft frequency and the apparent cut-off of tones at higher frequencies including blade-passing tones. The circumferential extent of the inlet swirl distortion at the fan was found to be two blade pitches, or 1/11th of the circumference, suggesting a relationship between the circumferential extent of the inlet distortion and the apparent cut-off frequency perceived in the far field. A first-principles-based model of the generation of shock waves from a transonic rotor in nonuniform flow showed that the effects of nonuniform flow on acoustic wave propagation, which cannot be captured by the simplified model, are more dominant than those of inlet flow distortion on source noise. It demonstrated that nonlinear, coupled aerodynamic and aero-acoustic computations, such as those presented in this paper, are necessary to assess the propagation through nonuniform mean flow. A parametric study of serpentine inlet designs is underway to quantify these propagation effects.

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Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet

Journal of Fluid Mechanics ◽

10.1017/s0022112009990577 ◽

2009 ◽

Vol 637 ◽

pp. 173-211 ◽

Cited By ~ 28

Author(s):

XUESONG WU ◽

PATRICK HUERRE

Keyword(s):

Acoustic Field ◽

Low Frequency ◽

Base Flow ◽

Matched Asymptotic Expansion ◽

Sound Waves ◽

Mean Flow ◽

Flow Distortion ◽

Experimental Conditions ◽

Modulation Equation ◽

Instability Modes

A possible fundamental physical mechanism by which instability modes generate sound waves in subsonic jets is presented in the present paper. It involves a wavepacket of a pair of helical instability modes with nearly the same frequencies but opposite azimuthal wavenumbers. As the wavepacket undergoes simultaneous spatial–temporal development in a circular jet, the mutual interaction between the helical modes generates a strong three-dimensional, slowly modulating ‘mean-flow distortion’. It is demonstrated that this ‘mean field’ radiates sound waves to the far field. The emitted sound is of very low frequency, with characteristic time and length scales being comparable with those of the envelope of the wavepacket, which acts as a non-compact source. A matched-asymptotic-expansion approach is used to determine, in a self-consistent manner, the acoustic field in terms of the envelope of the wavepacket and a transfer factor characterizing the refraction effect of the background base flow. For realistic jet spreading rates, the nonlinear development of the wavepacket is found to be influenced simultaneously by non-parallelism and non-equilibrium effects, and so a composite modulation equation including both effects is constructed in order to describe the entire growth–attenuation–decay cycle. Parametric studies pertaining to relevant experimental conditions indicate that the acoustic field is characterized by a single-lobed directivity pattern beamed at an angle about 45°–60° to the jet axis and a broadband spectrum centred at a Strouhal number St ≈ 0.07–0.2. As the nonlinear effect increases, the radiation becomes more efficient and the noise spectrum broadens, but the gross features of the acoustic field remain robust, and are broadly in agreement with experimental observations.

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Shock Propagation and MPT Noise From a Transonic Rotor in Non-Uniform Flow

Volume 7: Turbomachinery, Parts A, B, and C ◽

10.1115/gt2011-45645 ◽

2011 ◽

Author(s):

J. J. Defoe ◽

Z. S. Spakovszky

Keyword(s):

Power Level ◽

Uniform Flow ◽

Acoustic Energy ◽

Shock Propagation ◽

Far Field ◽

Mean Flow ◽

Flow Distortion ◽

Inlet Distortion ◽

Circumferential Extent ◽

Transonic Rotor

One of the major challenges in hig4h-speed fan stages used in compact, embedded propulsion systems is inlet distortion noise. A body-force-based approach for the prediction of multiple-pure-tone (MPT) noise was previously introduced and validated. In this paper, it is employed with the objective of quantifying the effects of non-uniform flow on the generation and propagation of MPT noise. First-of-their-kind back-to-back coupled aero-acoustic computations were carried out using the new approach for conventional and serpentine inlets. Both inlets delivered flow to the same NASA/GE R4 fan rotor at equal corrected mass flow rates. Although the source strength at the fan is increased by 45 dB in sound power level due to the non-uniform inflow, far-field noise for the serpentine inlet duct is increased on average by only 3.1 dBA overall sound pressure level in the forward arc. This is due to the redistribution of acoustic energy to frequencies below 11 times the shaft frequency and the apparent cut-off of tones at higher frequencies including blade-passing tones. The circumferential extent of the inlet swirl distortion at the fan was found to be 2 blade pitches, or 1/11th of the circumference, suggesting a relationship between the circumferential extent of the inlet distortion and the apparent cut-off frequency perceived in the far field. A first-principles-based model of the generation of shock waves from a transonic rotor in non-uniform flow showed that the effects of non-uniform flow on acoustic wave propagation, which cannot be captured by the simplified model, are more dominant than those of inlet flow distortion on source noise. It demonstrated that non-linear, coupled aerodynamic and aero-acoustic computations, such as those presented in this paper, are necessary to assess the propagation through non-uniform mean flow. A parametric study of serpentine inlet designs is underway to quantify these propagation effects.

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Scattering of acoustic waves by a vortex

Journal of Fluid Mechanics ◽

10.1017/s0022112099004371 ◽

1999 ◽

Vol 386 ◽

pp. 305-328 ◽

Cited By ~ 38

Author(s):

RUPERT FORD ◽

STEFAN G. LLEWELLYN SMITH

Keyword(s):

Mach Number ◽

Acoustic Waves ◽

Scattering Amplitude ◽

Polar Angle ◽

Scattered Wave ◽

Two Dimensions ◽

Far Field ◽

Leading Order ◽

Axisymmetric Vortex ◽

Wave Region

We investigate the scattering of a plane acoustic wave by an axisymmetric vortex in two dimensions. We consider vortices with localized vorticity, arbitrary circulation and small Mach number. The wavelength of the acoustic waves is assumed to be much longer than the scale of the vortex. This enables us to define two asymptotic regions: an inner, vortical region, and an outer, wave region. The solution is then developed in the two regions using matched asymptotic expansions, with the Mach number as the expansion parameter. The leading-order scattered wave field consists of two components. One component arises from the interaction in the vortical region, and takes the form of a dipolar wave. The other component arises from the interaction in the wave region. For an incident wave with wavenumber k propagating in the positive X-direction, a steepest descents analysis shows that, in the far-field limit, the leading-order scattered field takes the form i(π−θ)eikX+½cosθcot(½θ) (2π/kR)1/2ei(kR−π/4), where θ is the usual polar angle. This expression is not valid in a parabolic region centred on the positive X-axis, where kRθ2=O(1). A different asymptotic solution is appropriate in this region. The two solutions match onto each other to give a leading-order scattering amplitude that is finite and single-valued everywhere, and that vanishes along the X-axis. The next term in the expansion in Mach number has a non-zero far-field response along the X-axis.

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Theoretical investigation of alteration and radiation of large-scale structures due to jet impingement

International Journal of Aeroacoustics ◽

10.1177/1475472x18812810 ◽

2018 ◽

Vol 18 (2-3) ◽

pp. 231-257

Author(s):

SAE Miller ◽

Alexander N Carr

Keyword(s):

Acoustic Waves ◽

Large Scale ◽

Acoustic Radiation ◽

Jet Impingement ◽

Far Field ◽

Spectral Broadening ◽

Aircraft Carrier ◽

Instability Waves ◽

Large Scale Structures ◽

Scale Structures

Jet flows impinge on launch pad structures and aircraft carrier deck blast deflectors. Turbulent structures are deformed and acoustic radiation is reflected by the deflector. The coupling of reflected acoustic waves with the instability waves of the jet turbulence increases their amplitude and causes a feedback loop. Resultant far-field acoustic radiation is amplified. This amplification results in additional tones with significant spectral broadening occurring at frequencies corresponding to the constructive interference. We present a simple prediction methodology in the form of an acoustic analogy. The analogy accounts for reflected acoustic waves through a tailored Green’s function and models the large-scale structures as spatially and temporarily growing and decaying instability waves. The predictions are compared with two experimental datasets. Predictions compare favorably with measured frequencies and spectral broadening in the far-field.

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Acoustic radiation patterns of the silo music phenomenon

EPJ Web of Conferences ◽

10.1051/epjconf/202124903018 ◽

2021 ◽

Vol 249 ◽

pp. 03018

Author(s):

J.R. Hernández-Juárez ◽

D.A. Serrano ◽

A. López-Villa ◽

A. Medina

Keyword(s):

Acoustic Waves ◽

Line Source ◽

Sound Pressure ◽

Acoustic Radiation ◽

Pressure Level ◽

Discharge Process ◽

Far Field ◽

Continuous Line ◽

Acoustic Source ◽

Beam Patterns

In this work, we apply the theory of radiation and reception of acoustic waves in the analysis of the acoustic contributions of the silo music phenomenon. The length portion of the silo where the silo music phenomenon occurs is considered a continuous line source. The continuous line source modeled as a simple acoustic source permits the analysis of the acoustic far field, interpreting the polar graphics of the beam patterns of the acoustic contributions. We propose to apply this technique in the silo design to diminish adverse acoustic effects during the discharge process of granular materials. Additionally, we present calculations of the sound pressure level of the silo music phenomenon.

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