On wavenumber spectra for sound within subsonic jets

This paper clarifies the nature of sound spectra within subsonic jets. Three problems, of increasing complexity, are presented. Firstly, a point source is placed in a two-dimensional plug flow and the sound field is obtained analytically. Secondly, a point source is embedded in a diverging axisymmetric jet and the sound field is obtained by solving the linearised Euler equations. Finally, an analysis of the acoustic waves propagating through a turbulent jet obtained by direct numerical simulation is presented. In each problem, the pressure or density field are analysed in the frequency-wavenumber domain. It is found that acoustic waves can be classified into three main frequency-dependent groups. A physical justification is provided for this classification. The main conclusion is that, at low Strouhal numbers, acoustic waves satisfy the d'Alembertian dispersion relation.Comment: 20 pages, 9 figure

Prediction of noise from serrated trailing edges

A new analytical model is developed for the prediction of noise from serrated trailing edges. The model generalizes Amiet’s trailing-edge noise theory to sawtooth trailing edges, resulting in a complicated partial differential equation. The equation is then solved by means of a Fourier expansion technique combined with an iterative procedure. The solution is validated through comparison with the finite element method for a variety of serrations at different Mach numbers. The results obtained using the new model predict noise reduction of up to 10 dB at 90$^{\circ }$ above the trailing edge, which is more realistic than predictions based on Howe’s model and also more consistent with experimental observations. A thorough analytical and numerical analysis of the physical mechanism is carried out and suggests that the noise reduction due to serration originates primarily from interference effects near the trailing edge. A closer inspection of the proposed mathematical model has led to the development of two criteria for the effectiveness of the trailing-edge serrations, consistent but more general than those proposed by Howe. While experimental investigations often focus on noise reduction at 90$^{\circ }$ above the trailing edge, the new analytical model shows that the destructive interference scattering effects due to the serrations cause significant noise reduction at large polar angles, near the leading edge. It has also been observed that serrations can significantly change the directivity characteristics of the aerofoil at high frequencies and even lead to noise increase at high Mach numbers.The first author (BL) wishes to gratefully acknowledge the financial support co-funded by the Cambridge Commonwealth European and International Trust and China Scholarship Council. The second author (MA) would like to acknowledge the financial support of the Royal Academy of Engineering. The third author (SS) wishes to gratefully acknowledge the support of the Royal Commission for the exhibition of 1851.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2016.13

The radiating part of circular sources

An analysis is developed linking the form of the sound field from a circular source to the radial structure of the source, without recourse to far-field or other approximations. It is found that the information radiated into the field is limited, with the limit fixed by the wavenumber of source multiplied by the source radius (Helmholtz number). The acoustic field is found in terms of the elementary fields generated by a set of line sources whose form is given by Chebyshev polynomials of the second kind, and whose amplitude is found to be given by weighted integrals of the radial source term. The analysis is developed for tonal sources, such as rotors, and, for Helmholtz number less than two, for random disk sources. In this case, the analysis yields the cross-spectrum between two points in the acoustic field. The analysis is applied to the problems of tonal radiation, random source radiation as a model problem for jet noise, and to noise cancellation, as in active control of noise from rotors. It is found that the approach gives an accurate model for the radiation problem and explicitly identifies those parts of a source which radiate.Comment: Submitted to Journal of the Acoustical Society of Americ

Geometric algebra and an acoustic space time for propagation in non-uniform flow

This study aims to make use of two concepts in the field of aeroacoustics; an analogy with relativity, and Geometric Algebra. The analogy with relativity has been investigated in physics and cosmology, but less has been done to use this work in the field of aeroacoustics. Despite being successfully applied to a variety of fields, Geometric Algebra has yet to be applied to acoustics. Our aim is to apply these concepts first to a simple problem in aeroacoustics, sound propagation in uniform flow, and the more general problem of acoustic propagation in non-uniform flows. By using Geometric Algebra we are able to provide a simple geometric interpretation to a transformation commonly used to solve for sound fields in uniform flow. We are then able to extend this concept to an acoustic spacetime applicable to irrotational, barotropic background flows. This geometrical framework is used to naturally derive the requirements that must be satisfied by the background flow in order for us to be able to solve for sound propagation in the non-uniform flow using the simple wave equation. We show that this is not possible in the most general situation, and provide an explicit expression that must be satisfied for the transformation to exist. We show that this requirement is automatically satisfied if the background flow is incompressible or uniform, and for both these cases derive an explicit transformation. In addition to a new physical interpretation for the transformation, we show that unlike previous investigations, our work is applicable to any frequency

A comparison of the silent base flow and vortex sound analogy sources in high speed subsonic jets

Definitions of the sound sources obtained by re-arranging the Navier-Stokes equations are dependent on two choices: the base flow on the one hand, the dependent variables on the other hand. This paper chooses a silent base dlow for the former, and compares two different options for the latter. The first option, analogous to that chosen by Lighthill, uses density, momentum and modified pressure as the dependent variables. The second options, proposed by Doak, uses total enthalpy, velocity and entropy and is related to vortex sound theory. The resulting silent base flow sources are computed and compared for two simulated high speed subsonic jets obtained by direct numerical simulation. It is shown that, despite having different expressions, both formulations identify the same noise generation mechanism. In particular, the divergence of the source terms are in close agreement

Reprint of: Flow filtering and the physical sources of aerodynamic sound

The physical sources of sound are expressed in terms of the non-radiating part of the flow. The non-radiating part of the flow can be obtained from convolution filtering, as we demonstrate numerically by using an axi-symmetric jet satisfying the Navier-Stokes equations. Based on the frequency spectrum of the source, we show that the sound sources exhibit more physical behaviour than sound sources based on acoustic analogies. To validate the sources of sound, one needs to let them radiate within the non-radiating flow field. However, our results suggest that the traditional Euler operator linearized about the time-averaged part of the flow should be sufficient to compute the sound field. © 2010 Published by Elsevier Ltd

A quasi-potential flow formulation for the prediction of the effect of the circulation on the acoustic shielding from a lifting body by means of a finite element method

This paper presents a new simplified approach for the prediction of the acoustic shielding from liftingbodies by means of a finite element method. It extends a method already validated for aerodynamicapplications to Aeroacoustics on the basis of the small perturbation expansion. A numerical modelto represent the effect of the circulation developed by a slender body on the noise radiation inan unbounded domain is provided. A quasi-potential flow formulation is adopted by introducing asimplified shear layer model: a frozen wake with finite thickness and extent. The effect of the sounddiffraction in the wake region is accounted for by applying the continuity of pressure across thewake line in the aeroacoustic field. An incompressible steady mean flow is considered and the Kuttacondition is applied to overcome the singularity at the trailing edge. The circulation in the meanflow is predicted by reducing the potential solution to a single-valued problem. The non- uniformbase flow is superimposed on the wave propagation and the linear aeroacoustic problem is solvedby means of the full acoustic potential equation. The finite element method is applied both to thesolution of the base flow and to the acoustic radiation. The acoustic field scattered by a 2D airfoilfrom a line source in presence of a non-uniform base flow is predicted as a numerical example of theproposed model. The circulation modifies the extent of the acoustic shielding by altering the wavepropagation around the slender body, the wave diffraction at the trailing edge and the refraction inthe shear layer

On computing the physical sources of jet noise

We derive a closed system of equations that relates the acoustically radiating flow variables to the sources of sound for homentropic flows. We use radiating density, momentum density and modified pressure as the dependent variables which leads to simple source terms for the momentum equations. The source terms involve the non-radiating parts of the density and momentum density fields. These non-radiating components are obtained by removing the radiating wavenumbers in the Fourier domain. We demonstrate the usefulness of this new technique on an axi-symmetric jet solution of the Navier-Stokes equations, obtained by direct numerical simulation (DNS). The dominant source term is proportional to the square of the non-radiating part of the axial momentum density. We compare the sound sources to that obtained by an acoustic analogy and find that they have more realistic physical properties. Their frequency content and amplitudes are consistent with. We validate the sources by computing the radiating sound field and comparing it to the DNS solution. © 2010 by S. Sinayoko, A. Agarwal