Julien Christophe

Computation of Wall-Pressure Spectra from Steady Flow Data for Noise Prediction

DOI: 10.2514/1.J050206 A method is proposed to calculate the trailing-edge broadband noise emitted from an airfoil, based on a steady Reynolds-averaged Navier–Stokes solution of the flowfield. For this purpose, the pressure spectrum on the airfoil surfacenearthetrailingedgeiscalculatedusingastatisticalmodelfromtheReynolds-averagedNavier–Stokesmean velocity and turbulence data in the airfoil boundary layer. The obtained wall-pressure spectrum is used to compute the radiated sound by means of an aeroacoustic analogy, namely, Amiet’s theory of airfoil sound. The statistical model for wall-pressure fluctuations is validated with two test cases from the literature, a boundary layer with an adverse pressure gradient, and a flat plate boundary layer without a pressure gradient. The influence of specific model assumptions is studied, such as the convection velocity of pressure-producing structures and the scale anisotropy of boundary-layer turbulence. Furthermore, the influence of the Reynolds-averaged Navier–Stokes simulation on the calculated spectra is investigated using three different turbulence models. The method is finally applied to the case of a Valeo controlled-diffusion airfoil placed in a jet wind tunnel in the anechoic facility of Ecole Centrale de Lyon. Reynolds-averaged Navier–Stokes solutions for this test case are computed with different turbulencemodels,thewall-pressurespectrumnearthetrailingedgeiscalculatedusingthestatisticalmodel,andthe radiated noise is computed with Amiet’s theory. All intermediate results of the method are compared with experimental data.

Trailing Edge Noise of a Controlled-Diffusion Airfoil at Moderate and High Angle of Attack

This paper proposes to study the flow and corresponding noise around a segment of an automotive blade (CD-airfoil) at design conditions, namely a 8 ◦ angle of attack, and a higher angle of attack of 15 ◦ for which there is experimental evidence that the flow regime has significantly changed. This study encompasses two aspects, the flow resolution around the profile using the commercial solver Fluent 6.3 and the noise propagation using Amiet’s theory based on the trailing edge wall-pressure spectrum or Curle’s analogy using the pressure distribution along the blade. All along, computational results are compared to experiments taken in the large anechoic chamber from Ecole Centrale de Lyon (ECL). For the 8 ◦ case, two mesh refinements in the spanwise direction and two boundary conditions in spanwise direction, periodic and symmetric, and combination of both are studied. It reveals that both improvement of mesh and use of periodic spanwise boundary condition, have an influence on the trailing edge spectrum, decreasing the low frequency content to approach experimental results. Furthermore, these numerical parameters help to predict correctly the spanwise coherence measured experimentally. On the contrary, this numerical configuration is not improving the mean and rms velocity profiles in the wake of the airfoil and can even have a negative effect on the energy spectrum of the wake velocity. Acoustic results show satisfactory agreement using Curle’s analogy especially in the low frequency range with experimentally measured noise, the sound radiated being under-predicted abobe 1 kHz. Amiet’s theory is over-predicting the sound radiated compared to experiments due to the over-prediction of the wall-spectrum at trailing edge. The first attempt to compute the flow around the same airfoil at 15 ◦ angle of attack reveals that, again, the wall-pressure spectrum is over-predicted at low frequencies. Furthermore, it appears that the computational domain in the spanwise direction is too restrited to capture correctly the low frequency content of the flow. The computation is then largely over-predicting the spanwise coherence at low frequencies.

Uncertainty Quantification for the Trailing-Edge Noise of a Controlled-Diffusion Airfoil

A study that examine uncertainties associated with the prediction of trailing-edge noise, through an uncertainty quantification (UQ) framework, using RANS computations or conventional LES computations, in order to determine their respective robustness and accuracy is presented. The uncertainty is introduced at the inlet boundary of the restricted computational domain. The physical variations in the experimental flow measurements are taken into account by selecting a 2.5% error bound on the streamwise velocity U and a 10% error bound on the crosswise velocity V around the deterministic numerical solution. This observation is a significant departure from RANS computations where the second recirculation zone beyond mid-chord never occurs for low aoa. This difference is related to the used RANS modelisation that is considering fully turbulent flows and therefore cannot correctly take into account the laminar and transition regions whereas LES calculations do.

Broadband Scattering of the Turbulence-Interaction Noise of a Stationary Airfoil: Experimental Validation of a Semi-Analytical Model

A novel semi-analytical model based on Amiets theory is proposed to predict the scattered acoustic field related to turbulence-interaction noise. The simulated scattered acoustic field is compared to the corresponding measurements of a stationary airfoil in a turbulent stream for validation purposes. The paper is composed of three main parts, where improvements and extensions of this semi-analytical model are presented. In the first part of the paper, a new formulation taking an intermediate level of geometrical near-field correction into account is derived. The second part provides an implementation of a strip method accounting for spanwise varying incoming flow conditions. The acoustic free-field response of the airfoil is computed using the geometrical near-field formulation with the strip method. In the third part, an innovative Boundary Element Method (BEM) approach is proposed in order to compute the scattered acoustic field of the airfoil by an obstacle. Finally, the scattered acoustic field resulting from the presence of a flat screen is computed by the semi-analytical method combined with the new BEM approach. A good agreement is obtained comparing with the measurements performed in an anechoic room.

Prediction of Incoming Turbulent Noise Using a Combined Numerical / Semi-Empirical Method and Experimental Validation

The present paper investigates the case of a NACA0012 airfoil placed in a turbulent jet. The nozzle outlet diameter is equal to D = 0.041 m. The airfoil is placed at zero angle of incidence and with its leading edge located at 6D from the jet outlet. The chord of the airfoil is equal to D, and has a constant section over its span of 10D. The outlet velocity magnitude U0 is fixed to 13.2 m/s resulting in a Reynolds number based on the chord length of 36,000 and a Mach number of 0.04. The unsteady, three-dimensional incompressible flow around the airfoil is first computed with the LES module of the commercial solver FLUENT Rev. 6.2. The numerical flow results are compared with statistics on the velocity field (mean, RMS and spectra) obtained experimentally with hot wire anemometry on the same geometry and for the same operating conditions. This comparison reveals, as expected, that the mesh refinement influences the cut-off frequency resolution. Besides, an innovative procedure is proposed to compute from the same CFD computation, the noise radiated for the all frequency spectrum. The SYSNOISE Rev.5.6 solver, integrating Curle’s analogy, is used to predict the low frequency part of the noise spectrum, while Amiet’s theory is used to predict the high frequency range. The first one, limited to the computation of sound radiated by compact sources and then to the low frequency range, uses the unsteady pressure fluctuations on the airfoil stored during the CFD flow computation. The second one is a theory specially developed for airfoil sound radiation at high frequency and taking then into account, in an explicit way, non-compactness effects. The statistical flow data, needed by Amiet’s model, are fitted on the CFD data.

Numerical issues in the application of an amiet model for spanwise-varying incoming turbulence

The present paper investigates the possible application of Amiet’s theory in spanwise varying conditions. This study encompasses two different aspects. Firstly, all the parameters of the turbulent flow upstream of the airfoil have to be known to rescale the theoretical turbulence spectrum used in the turbulence interaction theory. In that framework, a methodology to compute the turbulence length scale upstream of the airfoil has been developed through the use of Fourier transforms of the upwash velocity of the incoming flow. Secondly, Amiet’s theory has been developed for airfoil noise radiation in uniform flow. In case of spanwise varying conditions, a Segmentation Method is proposed to predict the radiated noise. This method consists in cutting the airfoil in segments having each its own upstream flow conditions and to sum up the resulting individual emitted noise to obtain the total radiated noise in the far-field. This direct method reveals that spurious effect due to radiation angle and finite size of segments can appear. A rescaling based on listener position and a new Inverse Segmentation Method using a combination of large span airfoils are proposed to solve both problems. This method has been tested for several flow parameters and has shown its potential to reproduce correctly the radiated noise. The methods proposed in this paper have been combined and used on the jet-airfoil interaction case, for which acoustic prediction using Amiet’s theory has shown a satisfactory agreement compared to experimental noise measurements. Noise pollution is encountered in various industrial applications : noise emitted by landing gear in transport industry; noise from wings and high-lift devices in aeronautics; noise due to windshield wipers, rear-view mirrors, engine cooling systems and mufflers in car industry. It also exists in other domains of applications, as wind turbines or fans. In most of the cases, the noise produced is spread among all the frequency spectrum leading sometimes to a significant participation of high frequencies to the overall sound produced. The definition itself of the limit between low and high frequencies is not straightforward but a common rule is to consider the non-compactness limit of the problem. In such situations of non-compactness, the influence of the higher frequencies is an important factor to take into account in the noise predictions and specific methods for these frequencies have to be developed. Among the methods available and widely used to predict the low frequency components are the hybrid methods (indirect methods) in which the computation of the flow is decoupled from the computation of the sound. The computational cost to obtain the acoustic field is highly reduced compared to direct methods, computing the flow and its sound field together, when high Reynolds number and low Mach number are considered, as in most of industrial applications of interest. These hybrid methods consist in two steps : a) firstly, near the noise source, the flow field is obtained from an unsteady computation ; b) secondly, the acoustic source radiation is computed in the far-field by the use of an analogy. 1–3 This methodology is based on the substitution of the real flow by equivalent sources, computed as a post-processing of the flow data.

Free and scattered acoustic field predictions of the broadband noise generated by a low-speed axial fan

Broadband noise generated by a low-speed industrial axial fan and its scattered field by a benchmark obstacle have been addressed. Amiets theory on turbulence-interaction noise has been extended in order to predict the acoustic response of a fan in its geometrical near-field. A segmentation technique has been applied for spanwise varying flow conditions. The improved model has been combined with boundary element method (BEM) for acoustic scattering. The validation of the broadband scattering technique has been performed through comparisons with an analytical model considering acoustic scattering from an infinite plate and with measurements of a low-speed axial fan operating nearby a flat scattering screen.

Effect of Inlet Distortions on Ducted Fan Noise

The paper presents an investigation of flow and noise produced by a generic ECS fan installed in a circular duct. A focus of the study is the evaluation of the effect of mean flow distortions and e ...

Influence of the noise prediction model on the aeroacoustic optimization of a contra-rotating fan

The results of the multidisciplinary optimization of a contra-rotating fan have been taken as the basis for the study of different features of a wake interaction noise model, which influence the prediction and hence drive the optimization procedure towards the goal of noise reduction. The source and propagation effects have been considered separately. First, the effect of modelling the source either with a parallel or with a skew gust formulation, based on Amiet’s theory, has been investigated. Then, the propagation formula has been modified to take into account the effect of the geometry of the blades on the retarded time of the emission.

Computation of the self-noise of a controlled-diffusion airfoil based on the acoustic analogy

The self-noise of a controlled-diffusion airfoil is computed with several numerical techniques based on the acoustic analogy and involving different degrees of approximation. The flow solution is obtained through an incompressible large eddy simulation. The acoustic field as described by Lighthill’s analogy is computed with a finite element method applied to the exact airfoil geometry, and this solution is compared with results based on a half-plane Green’s function. This problem behaves as a classical trailing-edge noise problem for a wide range of frequencies; however, other mechanisms of sound production become significant at high frequencies. The results highlight the relative strengths and weaknesses of quadrupole- and dipole-based formulations of the acoustic analogy based on incompressible Computational Fluid Dynamics (CFD) results when applied to wall-bounded turbulent flows.