C.R. Lowis

Multi-mode sound transmission in ducts with flow

Abstract Exhaust mufflers, large exhaust stacks, and turbofan engines are common examples of ducted noise. The most useful measure of the sound produced by these noise sources is the sound power transmitted along the duct. When airflow is present, sound power flow can no longer be uniquely determined from the usual measurements of acoustic pressure and particle velocity. One approach to sound power determination from in-duct pressure measurement, and the one discussed in this paper, is to predict the relationship between the sound power and pressure based upon an assumed mode amplitude distribution. This paper investigates the relationship between acoustic pressure and power for a family of idealized source distributions of arbitrary temporal and spatial order. Incoherent monopole and dipole sources uniformly distributed over a duct cross-section can be obtained as special cases. This paper covers the sensitivity of the pressure–power relationship to source multipole order, frequency and, in particular, flow speed. It is shown that the introduction of flow in a hard-walled duct can have a substantial effect on the behavior of the pressure–power relationship for certain source distributions. Preliminary experimental results in a no-flow facility are presented in order to verify some of the main results.

A Focused Beamformer Technique for Separating Rotor and Stator-Based Broadband Sources

This paper presents an in-duct technique for measuring the relative contributions to the fan broadband noise generated in an aeroengine duct due to the rotor and stator. The basis of the technique is a focused beamformer whose point of focus rotates at the shaft rotational frequency. Rotating the beam causes the noise due to stationary sources to be suppressed. In the same way, the noise due to rotating sources is suppressed when the beam is stationary. The feasibility of the technique is demonstrated by simulations of the noise due to rotor and stator sources in a hard-walled infinite duct. It is shown, using a wallmounted array consisting of 3 rings of 50 microphones, that the suppression of stationary sources by the rotating beam is approximately 10dB, when the source separation distance is greater than the axial beamwidth of the beamformer. When the sources are closer than a beamwidth, the technique is still able to separate the sources, with a rejection of around 6dB, by virtue of the mismatch between rotational speeds of the beam and the sources. The resolution of the beamformer is also investigated. It is shown that because the beamformer formulation relies on a modal decomposition, the beamwidth has a very strong dependence on the number of propagating modes in the duct, and only a weak dependence on the array geometry. The axial beamwidth is shown to be equal to a Doppler-shifted wavelength.

Inversion Technique for Determining the Strength of Rotating Broadband Sources in Ducts

Aeroengine broadband fan noise is a major contributor to the community noise exposure from aircraft. Currently there are no measurement techniques that allow the localisation and quantification of rotor-based broadband noise sources. This paper presents an inversion technique for estimating the broadband acoustic source strength distribution over a ducted rotor using pressure measurements made at the duct wall. It is shown that the rotation of acoustic sources in a duct prevents the use of standard acoustic inversion techniques. The technique presented here makes use of a new Green function that takes into account the effect of source rotation. The new Green function is used together with a modal decomposition technique to remove the effect of source rotation, thereby allowing an estimation of the rotor-based source strengths in the rotating reference frame. It is shown that the pressure measured at the sensors after application of this technique is identical to that measured by sensors rotating at the same speed as the rotor. Results from numerical simulations are presented to investigate the resolution limits of the inversion technique. The azimuthal resolution limit, namely the ability of the measurement technique to discriminate between sources on adjacent blades, is shown to improve as the speed of rotation increases. To improve the robustness of the inversion technique a simplifying assumption is made whereby the sources on different blades are assumed to be identical. It is also shown that the accuracy and robustness of the inversion procedure improve as the axial separation between the rotor and sensors decreases. Simulations demonstrate that for a 26-bladed fan, rotating at Mt = 0.5, the aerodynamic source strengths can be estimated with acceptable robustness and approximately 1dB accuracy, when measurements are made 0.1 acoustic wavelengths from the rotor.

An in-duct beamformer for the estimation of far-field directivity

This paper presents a measurement technique for estimating the far-field directivity of the sound radiated from a duct using measurements of pressure made inside the duct. The technique is restricted to broadband, multi-mode sound fields whose directivity patterns are axi-symmetric, and whose modes are mutually uncorrelated. The technique uses a transfer function to relate the output from an in-duct axial beamformer to measurements of the far-field polar directivity. A transfer function for a hollow cylindrical duct with no flow is derived, and investigated in detail. The transfer function is shown to be insensitive to the mode-amplitude distribution inside the duct, and hence a predicted transfer function can be used to predict the directivity in practice where the noise source distribution is unknown. It is suggested that the proposed technique will be especially useful for fan rig experiements, where direct measurement of directivity, for example by use of an anechoic chamber, is impossible. The technique is validated using a no-flow experiment.

An in-situ Phase Calibration technique for In-Duct Axial Microphone Arrays

In-duct microphone arrays are used in experimental test facilities to understand the generation of noise by aeroengine componants such as fan-blades. A typical microphone array used to perform modal analysis, for example, is a linear array of wall-mounted microphones. Accurate results can only be obtained if the microphone array is well calibrated for both magnitude and phase. As in-situ calibration is often impossible the microphones must therefore be calibrated outside of the duct. This is unsatisfactory as changes in the phase response that result from mounting the microphones in the duct wall after calibration, where they are exposed to ow and temperature e ects, and the e ects of the microphone mounting are not accounted for. This paper presents a method to calibrate the microphones in-situ using properties of the broadband noise generated, for example, by rotating fan blades. The technique allows the relative phase di erence between individual microphones to be determined. The technqiue is validated using experimental data obtained from a laboratory scale noow rig.