Brian J. Tester

The propagation and attenuation of sound in lined ducts containing uniform or “plug” flow

This paper is concerned with a theoretical analysis of the inviscid, perturbed or acoustic field, at a particular frequency, in an infinite, two-dimensional duct of constant cross-section in which the fluid properties, other than the mean axial velocity, are constant; one duct wall has a uniform, locally reacting, frequency dependent wall impedance, the other wall is rigid. The perturbed duct field due to an infinite, uniform line source, or the two-dimensional Greens function, is formally derived for uniform or “plug” flow in the duct, and is expressed as an infinite sum of non-orthogonal modes. The optimization of modal, axial attenuation rates is examined in some detail. Under certain conditions it is found that not necessarily all the Greens function modes in “plug” flow decay away from the source: in a particular example it is shown that one mode is spatially amplified in the downstream direction and is a modified form of the well-known temporal instability of an incompressible vortex sheet adjacent to a single flexible wall.

Some aspects of “sound” attenuation in lined ducts containing inviscid mean flows with boundary layers

By an analytical study of the modal field in sheared flow it is shown that the pressure and normal particle displacement are constant through a boundary layer of arbitrary profile, in the limit as the boundary layer thickness tends to zero. Thus the physical effects of “thin” boundary layers on mode solutions are correctly included in the “plug” flow model. Approximate analytic solutions are obtained for the pressure and normal velocity variations through boundary layers to first order in a parameter proportional to boundary layer thickness and are used to interpret the behaviour of some exact mode solutions.

The optimization of modal sound attenuation in ducts, in the absence of mean flow

The optimization of modal, axial sound attenuation rates, in the sense defined by Cremer, is examined in detail for zero mean flow in the duct. Cremers result, for the lowest order mode pair in the absence of flow, is generalized so that the optimum impedance and attenuation rate can now be obtained for any mode pair in ducts of uniform rectangular, circular or annular cross-section. One qualification to Cremers result emerges in the derivation of the Greens function : at the optimum condition the mode pair degenerates into a single mode with the expected exponential attenuation rate but this is offset by an amplification rate which is directly proportional to the distance from the source. In spite of this effect the axial decay rate of the Greens function can reach a maximum for a wall impedance close to Cremers optimum value. Computed results for the attenuation compare favourably with available experimental values. The computation method produces slightly more accurate values of the optimum wall impedance for maximum attenuation of the “least damped mode” than those previously obtained by Cremer and by Morse. The theoretical approach developed is suitable for extension to attenuation (and attenuation optimization) studies in ducts carrying mean flow.

Relative importance of open rotor tone and broadband noise sources

A study is made of the noise levels and spectral characteristics of three contra-rotating propeller rigs: rig 140 tested in 1989, rig 145 build 1 tested in 2008, and rig 145 build 2 tested in 2010. We use tone deletion techniques, applied to the inflow microphone data, to show the relative importance of propeller broadband noise to propeller tones with increasing frequency and, in particular, that by the time we reach only moderate frequencies, the one third octave spectra become dominated by the broadband noise components. We also show that the broadband noise continues to be important as blade speed and rig thrust are varied and that these spectral characteristics are present on both modern and older contra-rotating propeller designs – even those with a profusion of tones and strong tone protusion. We also show how the tone and broadband noise levels have reduced with more recent, and aeroacoustically improved, blade designs

Spectral broadening of jet engine turbine tones

The process of turbulent scattering is studied for the generic experiment conducted by Candel et al.1 applying an analytic weak scattering model and CAA computations. For the analytic weak scattering model an approximate form of the Lilley equation is used. The source terms of this equation are in terms of the turbulence and the incident acoustic field. In the CAA simulations the wave equation proposed by Pierce for sound in fluids with unsteady inhomogeneous flow is integrated. The unsteady turbulent base-flow is modeled using a stochastic method to generate turbulence with locally varying turbulence features as provided by time-averaged RANS. To study the spectral broadening effect analytically and computationally, the experimental set-up of Candel is considered, which involves an omnidirectional sound source, located on the axis of a round jet. The analytical predictions show very good agreement with the general trends as measured by Candel for an observer position normal to the jet axis. The computations reveal a spectral shape, which is in good agreement with those found in the experiments.

Mode detection with an optimised array in a model turbofan engine intake at varying shaft speeds

Modal measurement techniques in engine intakes have been used previously to analyse the generated fan noise. A proven method is to use a wall-mounted array of Kulite transducers and operate the (model) turbofan under constant shaft speeds. A drawback of this method is the large number of (expensive) microphones and acquisition channels needed to obtain complete m-mode spectra at high engine orders. Furthermore, to get a full scan of the m-mode spectra as a function of shaft speed, many measurements are required. The issue of the large number of microphones was addressed by using a sparse array instead of an equidistant array. An array optimisation technique, similar to a technique used for the design of phased microphone arrays for sound source localisation, was used to define such a sparse intake array. This array consists of 100 Kulites and is able to determine without aliasing the modal spectrum from m = -79 to m = -1-79, which is appropriate to determine the modal content up to 3 BPF of a modem turbofan. This array was tested in a Rolls-Royce model fan rig at Ansty as a part of the RESOUND project. A new digital data-acquisition system made it possible to simultaneously and continuously record the Kulite pressure data as the engine speed was varied continuously from idle to maximum speed or vice versa, with each acceleration/deceleration lasting for a period of 9 minutes. Time histories of the Kulites were processed giving power spectra of the engine orders, which revealed the rotor locked tonal components. For each rotor revolution, a Discrete Fourier Transform was applied and, after averaging over a number of revolutions, the m-mode spectra were determined. In this way, a full modal scan with respect to shaft speed in a very limited testing time was obtained. Paper presented at the 7th AIAA/CEAS Aeroacoustics Conference, 28-30 May 2001, Maastricht, The Netherlands.

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.

Validation of an analytical model for scattering by intake liner splices

Circumferential variations in the impedance of intake liners occur in aero-engine ducts due to the presence of hard strips or splices, which can cause a significant reduction in liner performance at certain conditions. New intake liner designs are currently aiming to minimise the number and width of splices, and while CAA or CFD methods can be used to model and predict the scattering effects, these are normally impractical for direct application to parametric or liner optimisation design studies, due to the significant CPU time required to solve this 3D problem at realistic frequencies. In the early 1990s at Rolls- Royce, Cargill developed an analytical model for the scattering by liner splices based on the Kirchhoff approximation. Now that robust, accurate CAA methods are becoming available, it is possible to conduct a theoretical validation of the Cargill model, which is the subject of this paper. The CAA code used, ACTRAN, is a commercially available finite element method, which assumes an irrotational mean flow and linear propagation. The ACTRAN and Cargill results agree well for no-flow case, except for some minor discrepancies in the back-scattered modes but these are of secondary importance compared to the forward scattered. A striking feature of these results is that the forward scattered modal sound power is almost equal for all spinning modes except for one or two modes adjacent to the rotor-alone modes. Results for flow Mach numbers up to 0.4 show that agreement between ACTRAN and Cargill is acceptable except again for the field dominated by the back- scattered field. In general, for engineering purposes, Cargills model agrees well with those obtained from the ACTRAN code, for relevant combinations of parameters. Cargills model has also helped to improve our understanding of the scattering process and provides a rapid method of evaluating splice scattering effects.

Influence of mean flow gradients on fan exhaust noise predictions

Aft fan noise is becoming a more dominant source as engine bypass ratio is increased n this paper an assessment of the effect of the mean flow gradients on fan exhaust noise propagation is carried out using both analytical models for simplified problems and numerical methods for realistic configurations. Fan exhaust noise can be significantly refracted by the mean flow gradients in the jet mixing layer, especially at high operating conditions (i.e. during take off). The refraction effect is predicted using either Lilley’s equation or the linearized Euler equations. For parallel base flows, an issue with these linear models is the presence of Kelvin-Helmholtz instabilities whose unlimited exponential growth is unphysical and problematic for computational methods. This problem is less critical for developing mixing layer for instance where the growth of the vorticity thickness reduces the growth of the instability waves [1]. Various techniques have been used for suppressing the instability; these include adding non-linear terms to saturate the growth of the instability [2], using frequency domain analysis [3], or removing the mean flow gradient terms [4]. It is the last approach, termed Gradient Term Suppression (GTS), which is investigated in the present work.

Acoustic energy flow in lined ducts containing uniform or “plug” flow

In connection with the method (used in simple insertion loss models) of relating, approximately, the perturbed duct field to the acoustic field radiated from the duct termination, expressions have been formulated for the energy flows associated with individual modes, according to certain definitions. It has been shown that the axial energy flow in a uniform flow duct can only be strictly equated with the radiated energy if the radiation is from an “inlet flow” termination, if the axial energy flow is calculated according to the energy flux defined by Cantrell and Hart and if the duct walls are non-absorptive. If the duct walls are absorptive the duct and radiated energy flows are approximately identical if the duct energy flow is primarily due to the existence of well “cut-on” modes.