Application of frequency-domain linearized Euler solutions to the prediction of aft fan tones and comparison with experimental measurements on model scale turbofan exhaust nozzles

Although it is widely accepted that aircraft noise needs to be further reduced, there is an equally important, on-going requirement to accurately predict the strengths of all the different aircraft noise sources, not only to ensure that a new aircraft is certifiable and can meet the ever more stringent local airport noise rules but also to prioritize and apply appropriate noise source reduction technologies at the design stage. As the bypass ratio of aircraft engines is increased - in order to reduce fuel consumption, emissions and jet mixing noise - the fan noise that radiates from the bypass exhaust nozzle is becoming one of the loudest engine sources, despite the large areas of acoustically absorptive treatment in the bypass duct. This paper addresses this 'aft fan' noise source, in particular the prediction of the propagation of fan noise through the bypass exhaust nozzle/jet exhaust flow and radiation out to the far-field observer. The proposed prediction method is equally applicable to fan tone and fan broadband noise (and also turbine and core noise) but here the method is validated with measured test data using simulated fan tones. The measured data had been previously acquired on two model scale turbofan engine exhausts with bypass and heated core flows typical of those found in a modern high bypass engine, but under static conditions (i.e. no flight simulation). The prediction method is based on frequency-domain solutions of the linearized Euler equations in conjunction with perfectly matched layer equations at the inlet and far-field boundaries using high-order finite differences. The discrete system of equations is inverted by the parallel sparse solver MUMPS. Far-field predictions are carried out by integrating Kirchhoff s formula in frequency domain. In addition to the acoustic modes excited and radiated, some nonacoustic waves within the cold stream-ambient shear layer are also captured by the computations at some flow and excitation frequencies. By extracting phase speed information from the near-field pressure solution, these non-acoustic waves are shown to be convective Kelvin-Helmholtz instability waves. Strouhal numbers computed along the shear layer, based on the local momentum thickness also confirm this in accordance with Michalke's instability criterion for incompressible round jets with a similar shear layer profile. Comparisons of the computed far-field results with the measured acoustic data reveal that, in general, the solver predicts the peak sound levels well when the farfield is dominated by the in-duct target mode (the target mode being the one specified to the in-duct mode generator). Calculations also show that the agreement can be considerably improved when the non-target modes are also included, despite their low in-duct levels. This is due to the fact that each duct mode has its own distinct directionality and a non-target low level mode may become dominant at angles where the higher-level target mode is directionally weak The overall agreement between the computations and experiment strongly suggests that, at least for the range of mean flows and acoustic conditions considered, the physical aeroacoustic radiation processes are fully captured through the frequency-domain solutions to the linearized Euler equations and hence this could form the basis of a reliable aircraft noise prediction method