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Journal ArticleDOI

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

28 Oct 1975-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 71, Iss: 04, pp 625-673
TL;DR: In this article, a reformulation of the Lighthill (1952) theory of aerodynamic sound is described, and 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.
Abstract: 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.
Citations
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MonographDOI
TL;DR: In this paper, the analysis of noise and vibration signals is presented. But the authors focus on a case study of pipe flow noise and vibrations and use it as a diagnostic tool.
Abstract: Preface Acknowledgements Introductory comments 1. Mechanical vibrations: a review of some fundamentals 2. Sound waves: a review of some fundamentals 3. Interactions between sound waves and solid structures 4. Noise and vibration measurement and control procedures 5. The analysis of noise and vibration signals 6. Statistical energy analysis of noise and vibration 7. Pipe flow noise and vibration: a case study 8. Noise and vibration as a diagnostic tool 9. Worked examples Appendices Problems Answers to problems Index.

648 citations

Journal ArticleDOI
TL;DR: In this paper, a family of acoustic perturbation equations for the simulation of flow-induced acoustic fields in time and space is derived, which are excited by source terms determined from a simulation of the compressible or the incompressible flow problem.

584 citations

Journal ArticleDOI
M. S. Howe1
TL;DR: In this article, three different approaches to the subject are identified, consisting of theories based on Lighthill's acoustic analogy, the solution of special, linearized hydroacoustic problems, and ad hoc aerodynamic source models.

520 citations

Journal ArticleDOI
TL;DR: In this article, the authors analyzed the acoustic perturbations from a supercritical nozzle of finite length, in which the velocity increases linearly through the nozzle, for several inlet and discharge Mach number values and over a wide frequency range.

495 citations

Journal ArticleDOI
TL;DR: A critical review of computational techniques for flow-noise prediction and the underlying theories, in which the turbulent noise source field is computed and/or modeled separately from the far-field calculation, is provided.
Abstract: This article provides a critical review of computational techniques for flow-noise prediction and the underlying theories. Hybrid approaches, in which the turbulent noise source field is computed and/or modeled separately from the far-field calculation, are afforded particular attention. Numerical methods and modern flow simulation techniques are discussed in terms of their suitability and accuracy for flow-noise calculations. Other topics highlighted include some important formulation and computational issues in the application of aeroacoustic theories, generalized acoustic analogies with better accounts of flow-sound interaction, and recent computational investigations of noise-control strategies. The review ends with an analysis of major challenges and key areas for improvement in order to advance the state of the art of computational aeroacoustics.

399 citations


Cites background from "Contributions to the theory of aero..."

  • ...Alternative but still exact formulations [e.g., Howe (1975), Powell (1964); see also the recent book by Howe (2003)] emphasize the role of vorticity as sound sources....

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References
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Journal ArticleDOI
TL;DR: In this paper, a theory for estimating the sound radiated from a fluid flow, with rigid boundaries, which as a result of instability contains regular fluctuations or turbulence is initiated, based on the equations of motion of a gas.
Abstract: A theory is initiated, based on the equations of motion of a gas, for the purpose of estimating the sound radiated from a fluid flow, with rigid boundaries, which as a result of instability contains regular fluctuations or turbulence. The sound field is that which would be produced by a static distribution of acoustic quadrupoles whose instantaneous strength per unit volume is ρv i v j + p ij - a 2 0 ρ δ ij , where ρ is the density, v i the velocity vector, p ij the compressive stress tensor, and a 0 the velocity of sound outside the flow. This quadrupole strength density may be approximated in many cases as ρ 0 v i v j . The radiation field is deduced by means of retarded potential solutions. In it, the intensity depends crucially on the frequency as well as on the strength of the quadrupoles, and as a result increases in proportion to a high power, near the eighth, of a typical velocity U in the flow. Physically, the mechanism of conversion of energy from kinetic to acoustic is based on fluctuations in the flow of momentum across fixed surfaces, and it is explained in § 2 how this accounts both for the relative inefficiency of the process and for the increase of efficiency with U . It is shown in § 7 how the efficiency is also increased, particularly for the sound emitted forwards, in the case of fluctuations convected at a not negligible Mach number.

4,697 citations

Journal ArticleDOI

3,536 citations

Journal ArticleDOI
TL;DR: In this article, sound generation by turbulence and surfaces in arbitrary motion is discussed, and sound and multipole fields and governing equations are discussed. But sound generation is not discussed in this paper.
Abstract: Monograph on sound generation by turbulence and surfaces in arbitrary motion, discussing sound and multipole fields and governing equations

3,121 citations

Journal ArticleDOI
TL;DR: Elements of gasdynamics, Elements of gas dynamics, this paper, elements of gas dynamics, elements of gases, gas dynamism, and elements of dynamism.
Abstract: Elements of gasdynamics , Elements of gasdynamics , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

1,487 citations