Rie Sugimoto

A numerical integration scheme for special finite elements for the Helmholtz equation

The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite elements for the solution of the Helmholtz equation for very short waves is presented. A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration abscissae and weights are made available. The results are compared with those obtained using large numbers of Gauss-Legendre integration points for a range of testing wave problems. The results demonstrate that the method gives correct results, which gives confidence in the procedures, and show that large savings in computation time can be achieved.

Prediction of Forward Fan Noise Propagation and Radiation from Intakes

This paper presents a prediction method for fan tone noise propagation and radiation, and a study on the modal power distribution required to accurately model fan broadband noise. The results from the predictions are validated against rig measurements. In the prediction method for fan tone noise propagation and radiation, the source can be described as multimodal at subsonic tip speeds, and composed of a multimodal content and a high pressure amplitude rotor-locked content at supersonic tip speeds. In-duct sound pressure level (SPL) measurements from mode detection have been used to calibrate the predictions

Validation and Application of a Hybrid Prediction Scheme for Bypass Duct Noise

A prediction scheme for noise propagation and radiation from aeroengine bypass ducts is validated against measured data and applied to a generic bypass duct to study the efiects of bypass duct geometry on modal scattering. The objective has been to develop a relatively simple scheme which can predict the efiects of bypass duct geometry and acoustic treatment at acceptable computational cost. To achieve this, the in-duct and radiation problems are uncoupled and separate methods applied to each. Two difierent radiation models are implemented and compared. The approach is validated by a comparison of predicted and measured data for the NASA ANCF (Active Noise Control Fan) ∞ow test rig. A well deflned interference tone is used as a source. The rig is of simple geometry but incorporates the efiects of mean ∞ow and refraction through the bypass shear layer. Numerical predictions for aft radiated noise are shown to be in a good agreement with measured data, and both radiation models are self-consistent except at small angles from the aft axis. This persists at higher frequencies for which measured data are not available. The model is also used to study in-duct geometry efiects on modal scattering and attenuation in a generic lined bypass ducts. I. Introduction The prediction of aft radiated fan noise from turbofan aero-engines is challenging for conventional numerical schemes, more so than for the corresponding intake problem. The major complicating factor is the presence of a shear layer between the bypass stream and the external ∞ow. This precludes the straightforward use of frequency-domain flnite and inflnite element (FE/IE) analysis, 1 an approach which has proven efiective for intake problems. 2 This approach, and others based on the solution of a convected wave equation for the acoustic potential, cannot readily be applied to exhaust problems due to the presence of irrotational mean ∞ow. 3,4 High order schemes based on the numerical solution of the Linearised Euler Equations (LEE) in the time domain have however been applied both to intake and exhaust problems . 5,6 The intrinsic instability of the shear layer gives rise however to unstable transient solutions in the linearised Euler solution for exhaust ∞ows which must be removed or flltered from the numerical solution. 7{9 Agarwal et al. 10 have demonstrated that this instability can be suppressed if the governing equations are solved by a direct solver in the frequency domain. Parabolic approximations, 11 have also been applied to both intake and exhaust problems, 12,13 but do not deal well with propagation at high mode angles. In all of the above numerical schemes, the discrete solution is terminated by a non-re∞ecting condition which must be imposed at a flnite boundary. This must be placed close to the near fleld if the overall problem size is to be contained within acceptable limits. This constraint is particularly demanding in cases where a full three-dimensional numerical model is required. In the current paper, a hybrid modal/numerical/analytic prediction scheme for the noise propagation and radiation from aeroengine bypass ducts is presented, validated against ∞ow data and applied to a generic lined bypass duct. The objective of the current approach has been to develop a scheme which can predict the efiects of bypass duct geometry and acoustic treatment at acceptable computational cost. To achieve this, the in-duct and radiation problems are uncoupled and treated separately. The in-duct problem is treated by a Finite Element (FE) scheme. The radiation problem is treated using two approximate methods. An outline of the method was presented at the 11th AIAA/CEAS Aeroacoustics conference 14 and numerical predictions

Acoustic Effects of Liner Damage on Zero-Splice Turbofan Intake Liners: Computational Study

Traditional installations of turbofan intake liners include acoustically “hard” axial splices between liner segments for ease of fabrication and assembly. The splices scatter energy from strong rotor-locked tones into adjacent azimuthal orders for which the liner is less effective, thereby degrading the liner performance. The significance of this “splice effect” has led to the adoption of “zero-splice” liners in recent turbofan nacelles. However, damage can occur to such liners in service, and the extent to which local liner repairs reduce the effectiveness of the zero-splice design then becomes an issue. In the current paper, the acoustic effect of damage and repair in a zero-splice liner is simulated numerically. The effects of the extent and the location of a hard patch, representing the liner damage and repair, on the overall performance of the liner are predicted. A close agreement is demonstrated with results from an asymptotic analytical model valid for small patch widths. An approximate method is ...

Prediction of in-duct and near-field noise for a fan rig intake

Aircraft noise is composed of contributions from various source mechanisms. Fan noise propagates through engine intake and bypass ducts and is radiated to the far field. Fan noise is one of major contributors to aircraft noise at take-off and landing. The capability of accurately predicting the propagation, attenuation and radiation of fan noise is crucial for acoustic design of the intake and liners, and consequently for realising quieter aircraft. In this study, numerical and analytical models are applied to predicting the fan noise propagation through and radiation from a fan rig intake. Predictions are compared to test data. The predictions are based on those obtained by using Computational AeroAcoustic code ACTRAN/TM which is a linear analysis code and solves the convected Helmholtz equation. The code has been widely used for predicting this type of problems but the degree of agreement between its solutions and measured data depends on individual cases. There are many factors contributing to the accuracy of prediction models and also issues regarding measurements. Although it is not practical to incorporate all aspects in a prediction model, complementing a computational model with some physics such as non-linear effects evaluated separately by using analytical model can provide improvements. This report deals with such a combined approach. The focus is on predicting the in-duct and near-field noise.

A computational study of the effects of liner damage on zero-splice turbofan intake liners

Traditional installations of turbofan intake liners have acoustically ‘hard’ axial splices between liner segments for ease of fabrication and assembly. The splices scatter energy from the rotor-locked tones into adjacent azimuthal orders for which the liner is less eective, thereby degrading the liner performance. The signicance of this ‘splice eect’ has led to the adoption of ‘zero-splice’ liners in many current turbofan engines. However, damage can occur to such liners in service. The extent to which local impedance changes due to liner repairs reduce the eectiveness of the zero-splice design then becomes an issue when determining how much damage is acceptable before noise certication levels are compromised. In the current paper, the acoustic eect of damage in a zero-splice liner is simulated by using a computational model. The eects of the extent and the location of the damage on the overall performance of the liner is assessed. The computed results are also compared to an asymptotic analytical model. Finally, a methodology is described to model non-linear propagation eects in an approximate way within the linear predictions.

Fan noise propagation within curved bypass ducts with 3D features

This paper focuses on aft radiated fan noise propagating through the bypass duct: the effect of duct geometry on noise propagation is examined. The acoustic benefits of a novel highly curved bypass geometry are compared with those of a typical modern turbofan engine bypass geometry. Both 2D and 3D finite element models are used to examine the effect of duct geometry and other features on noise propagation, including modal scattering within the duct. An analytic radiation model is also used to examine the effect of these features on sound directivity patterns in the far-field.

Integrating CFD source predictions with time-domain CAA for intake fan noise prediction

A method is proposed for integrating a source prediction obtained from a Computational Fluid Dynamics (CFD) model for the fan stage of a turbofan engine with a Computational Aero-Acoustics (CAA) propagation code to predict tonal noise radiation in the far field. The Reynolds-Averaged Navier–Stokes equations are used to model the generation of the tones. Their propagation through the intake is simulated by applying the Discontinuous Galerkin Method to solve the linearized Euler equations in the time domain. The CFD and the CAA solutions are matched in a region where both solutions overlap and where non-linear effects, important close to the fan, can be considered to be less significant. An equivalent modal source on a notional source plane behind the fan is used to duplicate the sound field in this matching region and is then to drive a fully three-dimensional CAA radiation model for a near-field acoustic solution. The far-field sound pressure is obtained by applying the Ffowcs Williams-Hawkings formulation on a porous surface within the CAA domain. The accuracy and efficiency of this approach are investigated and results obtained are compared to measured data from a fan rig.

Folded cavity liners for turbofan engine intakes

Reducing aircraft noise is crucial to the growth of air transport and quality of people’s lives. Fan noise propagates through engine intake and bypass ducts and is radiated to the far eld. It is a major contributor to aircraft noise at take-o and landing. Acoustic liners are installed on the internal walls in the engine ducts to attenuate the fan noise. They are typically single or double degree of freedom liners, and their acoustic performance is strongly dependent on the cell depth. Typical cell depths are selected to attenuate noise in the frequency range which is critical to community noise. Increasing the attenuation at low frequencies requires deeper cells, which is often prohibited by mechanical design constraints. A potential remedy would be to fold the cells to t in a shallow space. In this study, the design and performance of folded cavity liners for turbofan engine intakes are investigated. A nite element model was developed for predicting acoustic impedance of such liners. The numerical model was used for parametric studies and validated against test data. The acoustic performance of folded cavity liners when installed in the nacelle of a rig intake was predicted by using a nite/innite element analysis with the predicted acoustic impedance of a folded cavity liner and compared to the noise reduction by an optimised community noise liner. It is demonstrated that folded cavity liners work as a combination of a deep and shallow liners corresponding to the centreline length and the hight to the fold. The performance can be tuned and optimised to be eective over wide frequency range by selecting the geometry and properties of resistive layers, i.e., facing and septum sheets. Folded cavity liners have a great potential to provide a solution for reducing both mid-high frequency community noise as well as low-frequency noise.

A numerical study on multimode sound propagation in lined ducts and radiation to the far field

In previous articles, the authors developed a hybrid scheme for analysing bypass duct noise, in which a numerical analysis using finite element method for in‐duct propagation and an analytic radiation code with fully represented effects of bypass shear layer are coupled. Such procedure permits detailed study on the interaction between duct configurations, such as geometry and acoustic liner impedances, and modal propagation and attenuation, and also the effects on the radiation pattern, within practical timescale and at modest computational cost. The scheme has been applied to realistic aero‐engine bypass ducts and has been integrated with an optimisation programme. The numerical results obtained so far have revealed that for ducts with acoustic liners highly attenuated modes are not necessarily those with high mode angles, which is contrary to general anticipation. The aim of the study in the current paper is to understand the physics behind this phenomenon and its effect on the radiation to the far fiel...