A weak-scattering model for turbine-tone haystacking outside the cone of silence

We consider the scattering of sound by turbulence in a jet shear layer. The turbulent, time-varying inhomogeneities in the flow scatter tonal sound fields in such a way as to give spectral broadening, which decreases the level of the incident tone, but increases the broadband level around the frequency of the tone. The scattering process is modelled for observers outside the cone of silence of the jet, using high-frequency asymptotic methods and a weak-scattering assumption. An analytical model for the far-field power spectral density of the scattered field is derived, and the result is compared to experimental data. The model correctly predicts the behaviour of the scattered field as a function of jet velocity and tone frequency<br/

A weak scattering model for tone haystacking

The scattering of sound by turbulence in a jet shear layer is considered. Spectral broadening or 'haystacking' is the process whereby the turbulent, time-varying inhomogeneities in the flow scatter tonal sound fields, which decreasesthe level of the incident tone, but increases the broadband level around the frequency of the tone. The scattering process is modelled analytically, using high-frequency asymptotic methods and a weak-scattering assumption. Analytical models for the far-field spectral density of the scattered field are derived for two cases: (1) any polar angle including inside the cone of silence; (2) polar angles outside the cone of silence. At polar angles outside the cone of silence, the predictions from the two models are very similar, but using the second model it is considerably simpler to evaluate the far-field spectral density. Simulation results are compared to experimental data, albeit only at a polar angle of 90º. The model correctly predicts the behaviour of the scattered field as a function of jet velocity and tone frequency. Also simulations at other polar angles and a parametric study are presented. These simulations indicate how the 'haystacking' is predicted to vary as a function of the polar angle, and also as a function of the characteristic length, time and convection velocity scales of the turbulence contained in the jet shear layer

Modal scattering at an impedance transition in a lined flow duct

An explicit Wiener-Hopf solution is derived to describe the scattering of duct modes at a hard-soft wall impedance transition in a circular duct with uniform mean flow. Specifically, we have a circular duct r = 1,-8 &lt;x &lt;8 with mean flow Mach number M &gt; 0 and a hard wall along x &lt;0 and a wall of impedance Z along x &gt; 0. A minimum edge condition at x = 0 requires a continuous wall streamline r = 1 + h(x, t ), no more singular than h = O(x1/2) for x ¿ 0. A mode, incident from x &lt;0, scatters at x = 0 into a series of reflected modes and a series of transmitted modes. Of particular interest is the role of a possible instability along the lined wall in combination with the edge singularity. If one of the "upstream" running modes is to be interpreted as a downstream-running instability, we have an extra degree of freedom in the Wiener-Hopf analysis that can be resolved by application of some form of Kutta condition at x = 0, for example a more stringent edge condition where h = O(x3/2) at the downstream side. The question of the instability requires an investigation of the modes in the complex frequency plane and therefore depends on the chosen impedance model, since Z = Z(¿) is essentially frequency dependent. The usual causality condition by Briggs and Bers appears to be not applicable here because it requires a temporal growth rate bounded for all real axial wave numbers. The alternative Crighton-Leppington criterion, however, is applicable and confirms that the suspected mode is usually unstable. In general, the effect of this Kutta condition is significant, but it is particularly large for the plane wave at low frequencies and should therefore be easily measurable. For ¿ ¿ 0, the modulus tends to |R001| ¿ (1 + M)/(1 - M) without and to 1 with Kutta condition, while the end correction tends to8without and to a finite value with Kutta condition. This is exactly the same behaviour as found for reflection at a pipe exit with flow, irrespective if this is uniform or jet flow

A review of engine noise source diagnostic methods for static engine tests, with phased array and polar correlation techniques

This paper reviews the state of the art of engine noise source evaluation using microphone arrays and identifies issues that are currently not well understood. It is found that most methods currently assume a model of uncorrelated point sources. However it will be shown that this is not a necessary assumption and images of the complete source CSD can be obtained, but that the effect of source convection cannot be readily obtained from the source image. It is also shown how source images can be improved by frequency averaging across the far field CSD matrix. This approaches reduces aliasing and improves the source image especially at high frequencies

Solving the Lilley equation with quadrupole and dipole jet noise sources

The literature contains various methods for solving the Lilley equation with different types of quadrupole and dipole sources to represent the mixing noise radiated into the far-field by isothermal and heated jets. These include two basic numerical solution methods, the ‘direct’ and the ‘adjoint’, and a number of asymptotic, analytic solutions. The direct and adjoint equations are reviewed and it is shown that their solutions are not only related through the adjoint property: the radial ODE for the adjoint displacement Green's function is the same as that governing the direct displacement Green's function because this particular Green's function obeys classical reciprocity with respect to its radial dependence. Further, by comparing the two numerical solution methods within the context of the parallel flow assumption of the Lilley equation, it is shown that the numerical effort for the two methods is equivalent. The numerical solutions are compared with analytic low frequency ‘thin shear layer’ solutions and WKB solutions, both outside and inside the cone of silence. It is concluded that the former should be used with caution at all angles, while the WKB has some limitations inside the cone of silence. Although numerical solutions can be obtained with little computational effort and are the preferred route for jet mixing noise predictions, the analytic solutions still offer important physical insights as well as verification of numeric result