F. Farassat

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

Extension of Kirchhoff's formula to radiation from moving surfaces

Kirchhoffs formula for radiation from a closed surface has been used recently for prediction of the noise of high speed rotors and propellers. Because the closed surface on which the boundary data are prescribed in these cases is in motion, an extension of Kirchhoffs formula to this condition is required. In this paper such a formula, obtained originally by Morgans for the interior problem, is derived for regions exterior to surfaces moving at speeds below the wave propagation speed, by making use of some results of generalized function theory. It is shown that the usual Kirchhoff formula is a special case of the main result of the paper. The general result applieds to a deformable surface. However, the special form it assumes for a rigid surface in motion is also noted. Some possible areas of application of the formula to problems of current interest in aeroacoustics are discussed.

Modeling aerodynamically generated sound of helicopter rotors

Abstract A great deal of progress has been made in the modeling of aerodynamically generated sound of rotors over the past decade. Although the modeling effort has focused on helicopter main rotors, the theory is generally valid for a wide range of rotor configurations. The Ffowcs Williams–Hawkings (FW–H) equation has been the foundation for much of the development. The monopole and dipole source terms of the FW–H equation account for the thickness and loading noise, respectively. Blade–vortex-interaction noise and broadband noise are important types of loading noise, hence much research has been directed toward the accurate modeling of these noise mechanisms. Both subsonic and supersonic quadrupole noise formulations have been developed for the prediction of high-speed impulsive noise. In an effort to eliminate the need to compute the quadrupole contribution, the FW–H equation has also been utilized on permeable surfaces surrounding all physical noise sources. Comparisons of the Kirchhoff formulation for moving surfaces with the FW–H equation have shown that the Kirchhoff formulation for moving surfaces can give erroneous results for aeroacoustic problems. Finally, significant progress has been made incorporating the rotor noise models into full vehicle noise prediction tools.

Acoustic analogy and alternative theories for jet noise prediction

Several methods for the prediction of jet noise are described. All but one of the noise prediction schemes are based on Lighthills or Lilleys acoustic analogy, whereas the other is the jet noise generation model recently proposed by Tam and Auriault. In all of the approaches, some assumptions must be made concerning the statistical properties of the turbulent sources. In each case the characteristic scales of the turbulence are obtained from a solution of the Reynolds-averaged Navier-Stokes equation using a kappa-sigma turbulence model. It is shown that, for the same level of empiricism, Tam and Auriaults model yields better agreement with experimental noise measurements than the acoustic analogy. It is then shown that this result is not because of some fundamental flaw in the acoustic analogy approach, but instead is associated with the assumptions made in the approximation of the turbulent source statistics. If consistent assumptions are made, both the acoustic analogy and Tam and Auriaults model yield identical noise predictions. In conclusion, a proposal is presented for an acoustic analogy that provides a clearer identification of the equivalent source mechanisms, as is a discussion of noise prediction issues that remain to be resolved.

The Uses and Abuses of the Acoustic Analogy in Helicopter Rotor Noise Prediction

This paper is theoretical in nature and addresses applications of the acoustic analogy in helicopter rotor noise prediction. It is argued that in many instances the acoustic analogy has not been used with care in rotor noise studies. By this it is meant that approximate or inappropriate formulations have been used. By considering various mechanisms of noise generation, such abuses are identified and the remedy is suggested. The mechanisms discussed are thickness, loading, quadrupole, and blade-vortex interaction noise. The quadrupole term of the Ffowcs Williams-Hawkings equation is written in a new form which separates the contributions of regions of high gradients such as shock surfaces. It is shown by order of magnitude studies that such regions are capable of producing noise with the same directivity as the thickness noise. The inclusion of this part of quadrupole sources in current acoustic codes is quite practical. Some of the difficulties with the use of loading noise formulations of the first author in predictions of blade-vortex interaction noise are discussed. It appears that there is a need for development of new theoretical results based on the acoustic analogy in this area. Because of the impulsive character of the blade surface pressure, a time scale of integration different from that used in loading and thickness computations must be used in a computer code for prediction of blade-vortex interaction noise.

ADVANCED TURBOPROP NOISE PREDICTION BASED ON RECENT THEORETICAL RESULTS

Abstract This paper is about the development of a high speed propeller noise prediction code at Langley Research Center. The code utilizes two recent acoustic formulations in the time domain for subsonic and supersonic sources. The selection of appropriate formulation is automatic in the code. The structure and capabilities of the code are discussed. Grid size study for accuracy and speed of execution on a computer is also presented. The code is tested against an earlier Langley code. Considerable increase in accuracy and speed of execution are observed. Some examples of noise prediction of a high speed propeller for which acoustic test data are available are given. A brisk derivation of formulations used is given in Appendix 1.

Broadband trailing edge noise predictions in the time domain

Abstract A recently developed analytic result in acoustics, “Formulation 1B,” is used to compute broadband trailing edge noise from an unsteady surface pressure distribution on a thin airfoil in the time domain. This formulation is a new solution of the Ffowcs Williams–Hawkings equation with the loading source term, and has been shown in previous research to provide time domain predictions of broadband noise that are in excellent agreement with experimental results. Furthermore, this formulation lends itself readily to rotating reference frames and statistical analysis of broadband trailing edge noise. In the present work, Formulation 1B is used to calculate the farfield noise radiated from the trailing edge of a NACA 0012 airfoil in a low Mach number flow, using both analytical and experimental data on the airfoil surface. The acoustic predictions are compared with analytical results and experimental measurements that are available in the literature. Good agreement between predictions and measurements is obtained.

Computation of Engine Noise Propagation and Scattering off An Aircraft

The purpose of this paper is to demonstrate the feasibility of computing the fan inlet noise field around a real twin-engine aircraft, which includes the radiation of the main spinning modes from the engine as well as the reflection and scattering by the fuselage and the wing. This first-cut large-scale computation is based on time domain and frequency domain approaches that employ spectral element methods for spatial discretization. The numerical algorithms are designed to exploit high-performance computers such as the IBM SP4. Although the simulations could not match the exact conditions of the only available experimental data set, they are able to predict the trends of the measured noise field fairly well.

Aircraft Engine Noise Scattering by Fuselage and Wings: A Computational Approach

The paper presents a time-domain method for computation of sound radiation from aircraft engine sources to the far field. The effects of non-uniform flow around the aircraft and scattering of sound by fuselage and wings are accounted for in the formulation. The approach is based on the discretization of the inviscid flow equations through a collocation form of the discontinuous Galerkin spectral element method. An isoparametric representation of the underlying geometry is used in order to take full advantage of the spectral accuracy of the method. Large-scale computations are made possible by a parallel implementation based on message passing. Results obtained for radiation from an axisymmetric nacelle alone are compared with those obtained when the same nacelle is installed in a generic configuration, with and without a wing.

Open Rotor Noise Prediction Methods at NASA Langley- A Technology Review

Open rotors are once again under consideration for propulsion of the future airliners because of their high efficiency. The noise generated by these propulsion systems must meet the stringent noise standards of today to reduce community impact. In this paper we review the open rotor noise prediction methods available at NASA Langley. We discuss three codes called ASSPIN (Advanced Subsonic-Supersonic Propeller Induced Noise), FW - H pds (Ffowcs Williams-Hawkings with penetrable data surface) and the FSC (Fast Scattering Code). The first two codes are in the time domain and the third code is a frequency domain code. The capabilities of these codes and the input data requirements as well as the output data are presented. Plans for further improvements of these codes are discussed. In particular, a method based on equivalent sources is outlined to get rid of spurious signals in the FW - Hpds code.