This paper describes a reformulation of the Lighthill (1952) theory of aerodynamic sound. A revised approach to the subject is necessary in order to unify the various ad hoc procedures which have been developed for dealing with aerodynamic noise problems since the original appearance of Lighthill's work. First, Powell's (1961 a) concept of vortex sound is difficult to justify convincingly on the basis of Lighthill's acoustic analogy, although it is consistent with model problems which have been treated by the method of matched asymptotic expansions. Second, Candel (1972), Marble (1973) and Morfey (1973) have demonstrated the importance of entropy inhomogeneities, which generate sound when accelerated in a mean flow pressure gradient. This is arguably a more significant source of acoustic radiation in hot subsonic jets than pure jet noise. Third, the analysis of Ffowcs Williams & Howe (1975) of model problems involving the convection of an entropy ‘slug’ in an engine nozzle indicates that the whole question of excess jet noise may be intimately related to the convection of flow inhomogeneities through mean flow pressure gradients. Such problems are difficult to formulate precisely in terms of Lighthill's theory because of the presence of an extensive, non-acoustic, non-uniform mean flow. The convected-entropy source mechanism is actually absent from the alternative Phillips (1960) formulation of the aerodynamic sound problem.In this paper the form of the acoustic propagation operator is established for a non-uniform mean flow in the absence of vortical or entropy-gradient source terms. The natural thermodynamic variable for dealing with such problems is the stagnation enthalpy. This provides a basis for a new acoustic analogy, and it is deduced that the corresponding acoustic source terms are associated solely with regions of the flow where the vorticity vector and entropy-gradient vector are non-vanishing. The theory is illustrated by detailed applications to problems which, in the appropriate limit, justify Powell's theory of vortex sound, and to the important question of noise generation during the unsteady convection of flow inhomogeneities in ducts and past rigid bodies in free space. At low Mach numbers wave propagation is described by a convected wave equation, for which powerful analytical techniques, discussed in the appendix, are available and are exploited.Fluctuating heat sources are examined: a model problem is considered and provides a positive comparison with an alternative analysis undertaken elsewhere. The difficult question of the scattering of a plane sound wave by a cylindrical vortex filament is also discussed, the effect of dissipation at the vortex core being taken into account.Finally an approximate aerodynamic theory of the operation of musical instruments characterized by the flute is described. This involves an investigation of the properties of a vortex shedding mechanism which is coupled in a nonlinear manner to the acoustic oscillations within the instrument. The theory furnishes results which are consistent with the playing technique of the flautist and with simple acoustic measurements undertaken by the author.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112075002777

Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute

The primary objective of this investigation is to determine experimentally the sources of jet mixing noise. In the present study, four different approaches are used. It is reasonable to assume that the characteristics of the noise sources are imprinted on their radiation fields. Under this assumption, it becomes possible to analyse the characteristics of the far-field sound and then infer back to the characteristics of the sources. The first approach is to make use of the spectral and directional information measured by a single microphone in the far field. A detailed analysis of a large collection of far-field noise data has been carried out. The purpose is to identify special characteristics that can be linked directly to those of the sources. The second approach is to measure the coherence of the sound field using two microphones. The autocorrelations and cross-correlations of these measurements offer not only valuable information on the spatial structure of the noise field in the radial and polar angle directions, but also on the sources inside the jet. The third approach involves measuring the correlation between turbulence fluctuations inside a jet and the radiated noise in the far field. This is the most direct and unambiguous way of identifying the sources of jet noise. In the fourth approach, a mirror microphone is used to measure the noise source distribution along the lengths of high-speed jets. Features and trends observed in noise source strength distributions are expected to shed light on the source mechanisms. It will be shown that all four types of data indicate clearly the existence of two distinct noise sources in jets. One source of noise is the fine-scale turbulence and the other source is the large turbulence structures of the jet flow. Some of the salient features of the sound field associated with the two noise sources are reported in this paper.

https://www.math.fsu.edu/~tam/JFM%20vol.%20615,%20pp%20253-292.%202008.pdf

The sources of jet noise: experimental evidence

It is argued that because of the lack of intrinsic length and time scales in the core part of the jet flow, the radiated noise spectrum of a high-speed jet should exhibit similarity. A careful analysis of all the axisymmetric supersonic jet noise spectra in the data-bank of the Jet Noise Laboratory of the NASA Langley Research Center has been carried out. Two similarity spectra, one for the noise from the large turbulence structures/instability waves of the jet flow, the other for the noise from the fine-scale turbulence, are identified. The two similarity spectra appear to be universal spectra for axisymmetric jets. They fit all the measured data including those from subsonic jets. Experimental evidence are presented showing that regardless of whether a jet is supersonic or subsonic the noise characteristics and generation mechanisms are the same. There is large turbulence structures/instability waves noise from subsonic jets. This noise component can be seen prominently inside the cone of silence of the fine-scale turbulence noise near the jet axis. For imperfectly expanded supersonic jets, a shock cell structure is formed inside the jet plume. Measured spectra are provided to demonstrate that the presence of a shock cell structure has little effect on the radiated turbulent mixing noise. The shape of the noise spectrum as well as the noise intensity remain practically the same as those of a fully expanded jet. However, for jets undergoing strong screeching, there is broadband noise amplification for both turbulent mixing noise components. It is discovered through a pilot study of the noise spectrum of rectangular and elliptic supersonic jets that the turbulent mixing noise of these jets is also made up of the same two noise components found in axisymmetric jets. The spectrum of each individual noise component also fits the corresponding similarity spectrum of axisymmetric jets.

/pdf/on-the-two-components-of-turbulent-mixing-noise-from-1wfas8tvbo.pdf

On the Two Components of Turbulent Mixing Noise from Supersonic Jets

It is known that turhulent mixing noise from high-speed jets consists of two components. They are the noise from large turbulent structures in the form of Mach wave radiation and the less directional fine-scale turbulence noise. The Mach wave radiation dominates in the downstream direction. The fine-scale turbulence noise dominates in the sideline and upstream directions. A semiempirical theory is developed for the prediction of the spectrum, intensity, and directivity of the fine-scale turhulence noise. The prediction method is self-contained. The turbulence information is supplied by the k-e turhulence model. The theory contains three empirical constants beyond those of the k-e model. These constants are determined by best fit of the calculated noise spectra to experimental measurements. Extensive comparisons between calculated and measured noise spectra over a wide range of directions of radiation,jet velocities, and temperatures have heen carried out. Excellent agreements are found. It is believed that the present theory offers significant improvements over current empirical or semiempirical jet noise prediction methods in use. There is no first principle jet noise theory at the present time.

Jet Mixing Noise from Fine-Scale Turbulence

We study the velocity fields of unforced, high Reynolds number, subsonic jets, issuing from round nozzles with turbulent boundary layers. The objective of the study is to educe wavepackets in such flows and to explore their relationship with the radiated sound. The velocity field is measured using a hot-wire anemometer and a stereoscopic, time-resolved PIV system. The field can be decomposed into frequency and azimuthal Fourier modes. The low-angle sound radiation is measured synchronously with a microphone ring array. Consistent with previous observations, the azimuthal wavenumber spectra of the velocity and acoustic pressure fields are distinct. The velocity spectrum of the initial mixing layer exhibits a peak at azimuthal wavenumbers ranging from 4 to 11, and the peak is found to scale with the local momentum thickness of the mixing layer. The acoustic pressure field is, on the other hand, predominantly axisymmetric, suggesting an increased relative acoustic efficiency of the axisymmetric mode of the velocity field, a characteristic that can be shown theoretically to be caused by the radial compactness of the sound source. This is confirmed by significant correlations, as high as 10 %, between the axisymmetric modes of the velocity and acoustic pressure fields, these values being significantly higher than those reported for two-point flow–acoustic correlations in subsonic jets. The axisymmetric and first helical modes of the velocity field are then compared with solutions of linear parabolized stability equations (PSE) to ascertain if these modes correspond to linear wavepackets. For all but the lowest frequencies close agreement is obtained for the spatial amplification, up to the end of the potential core. The radial shapes of the linear PSE solutions also agree with the experimental results over the same region. The results suggests that, despite the broadband character of the turbulence, the evolution of Strouhal numbers 0.3 ≤ St ≤ 0.9 and azimuthal modes 0 and 1 can be modelled as linear wavepackets, and these are associated with the sound radiated to low polar angles.

/pdf/wavepackets-in-the-velocity-field-of-turbulent-jets-4vs492oc7y.pdf

Wavepackets in the velocity field of turbulent jets

A harmonic point source of sound was placed within the potential core of an air jet and the distortion of its sound field by the jet flow was measured. An axial intensity minimum was observed that increases with increasing velocity, frequency, or temperature. The investigation indicates that the cleft in the heart‐shaded directivity pattern of subsonic jet noise can be attributed mainly to refraction.

Refraction of Sound from a Point Source Placed in an Air Jet

: The heart-shaped pattern of subsonic jet noise normally peaks somewhere between 15 degrees and 45 degrees from the axis, depending on conditions, falling off sharply as the axis is approached. Conflicting explanations of this directivity pattern appear in the literature. The present investigation suggests that the deep cleft in the pattern can be attributed mainly to refraction of the sound out of the jet by the velocity and temperature fields. The evidence lies in measurements made of the sound field of a harmonic 'point' source placed within a 3/4 in. dia. air jet. The source is the orifice of a tube about 1/16 in. i.d. driven through a conical coupling by a horn-type loudspeaker driver; this radiates sound essentially omnidirectionally up to about 15,000 cps. The experiment established the formation of an axial intensity minimum, which appears to be mainly due to refraction. The depth of the refraction valley increases with jet velocity, jet temperature, and sound frequency; a depth corresponding to an intensity reduction of the order of 35 dB is attained at M = 0.9 for 3000 cps. (Author)

/pdf/refraction-of-sound-by-jet-flow-or-jet-temperature-39oamr40jv.pdf

H. S. Ribner

Papers

Refraction of Sound from a Point Source Placed in an Air Jet

Refraction of sound by jet flow or jet temperature