Prediction of the aerodynamic noise of an airfoil via the hybrid methods of aeroacoustics

Abstract

The accurate prediction of the trailing-edge noise and the determination of its sources are essential to reduce fans and propellers noise. This noise component is due to the scattering of the turbulent boundary layer into acoustic waves by the trailing edge. In this paper, the noise emanating from a CD (Controlled-Diffusion) airfoil is simulated and computed via the hybrid methods of aeroacoustics. In these methods, the aerodynamic and acoustic fields are computed separately. The flow data are obtained using the in-house LES solver SFELES. ACTRAN acoustic solver has been used to solve the acoustics and to provide the near and far fields propagation via Lighthill’s analogy. Curle’s analogy is applied as well in its integral compact formulation which takes the presence of walls into account. Curle’s formulation is applied proposing an approach where the volume and surface integrals have been implemented in SFELES to be calculated simultaneously with the flow in order to avoid the storage of noise sources which requires a huge space. In Lighthill’s analogy, sources and near field maps show that the turbulent boundary layer and wake are the more efficient sources and the center of radiation is the trailing edge. The comparison of the numerical results with the experimental measurements, performed by Moreau and Roger and Moreau et al. , shows an overall excellent agreement confirming the capability of SFELES (LES sources) combined with ACTRAN (Lighthill’s analogy) to predict correctly the noise generated by turbulent flows around airfoils. The acoustic spectrum presents an overprediction up to 5 dB at the frequencies 300 Hz and 550 Hz and an underprediction about 5 dB at the frequencies 1100 Hz and 1750 Hz. The sound pressure level (SPL) obtained using the proposed approach of Curle’s analogy matches very well the experimental results. Thus, Curle’s analogy can be used to obtain a fast, approximated and acceptable results about the noise radiation of airfoils avoiding the storage of noise sources which requires a huge space and time.

Keywords

Hybrid methods of aeroacoustics trailing edge noise CFD aeroacoustics lighthill’s analogy curle’s integral formulation

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References

Snyder

. A parallel finite-element/spectral LES algorithm for complex two dimensional geometries. PhD Thesis, von Karman Institute for Fluid Dynamics, Belgium USA: Utah State University, 2002.

Actran aeroacoustic solutions:free-field-technologies, Belgium, user’s manual, 2014.

Curle

. The influence of solid boundaries upon aerodynamic sound. Proc Roy Soc Lond Math Phys Sci 1955; 231(1187): 505–514.

Moreau

Roger

. Effect of airfoil aerodynamic loading on trailing-edge noise sources. AIAA J 2005; 43(1): 41–52.

Moreau

Neal

Foss

. Hot-wire measurements around a controlled diffusion airfoil in an open-jet anechoic wind tunnel. J Fluid Eng 2006; 128: 699–706.

Lighthill

, On sound generated aerodynamically: I. General theory, Proc Roy Soc Lond Series A, 1952, 211,564–587.

Mohring

. A well posed acoustic analogy based on a moving acoustic medium, Aeroacoustic workshop, Aeroacoustic workshop. Dresden, 1999.

Amiet

. Acoustic radiation from an airfoil in a turbulent stream. J Sound Vib 1975; 41(4): 407–420.

Kucukcoskun

Christophe

Schram

, et al. An extension of Amiet’s theory for spanwise-varying incident turbulence and broadband noise scattering using a boundary element method. In: 16th AIAA/CEAS aeroacoustics conference, 2010.

10.

Amiet

. High frequency thin-airfoil theory for subsonic flow. AIAA J 1976; 14(8): 1076–1082.

11.

Amiet

. Noise due to turbulent flow past a trailing edge. J Sound Vib 1976; 47(3): 387–393.

12.

Roger

Moreau

. Back-scattering correction and further extensions of Amiet’s trailing-edge noise model. Part 1: theory. J Sound Vib 2005; 286: 477–506.

13.

Ffowcs Williams

Hall

. Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane. J Fluid Mech 1970; 40: 657–670.

14.

Wang

Moreau

Roger

. LES prediction of wall-pressure fluctuations and noise of a low-speed airfoil. Int J Aeroacoustics 2009; 8(3): 177–198.

15.

Matouk

Christophe

Degrez

. Aerodynamics and aeroacoustics study of the flow around an automotive fan airfoil. Int J Aeroacoustics 2015; 14: 1049–1070.

16.

Smagorinsky

. General circulation experiments with the primitive equations part I: the basic experiment. Mon Weather Rev 1963; 91: 99–164.

17.

Nicoud

Ducros

. Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow, Turbul Combust 1999: 183–200.

18.

Ghorbaniasl

Agnihotri

Lacor

. A self-adjusting flow dependent formulation for the classical Smagorinsky model coefficient. Phys Fluids 2013; 25: 1–26.

19.

EnSight User Manual for Version 10.0 . Computational Engineering International, Inc.

20.

Matouk

. Calculation of aerodynamic noise of wing airfoils by hybrid methods. PhD Thesis. Belguim: Université Libre de Bruxelles, 2016.

21.

Caro

Detandt

Manera

, et al. Validation of a new hybrid CAA strategy and application to the noise generated by a flap in a simplied HVAC duct. In: 15th AIAA/CEAS aeroacoustics conference and exhibit. Miami, FL, 11–13 May 2009.

22.

Wang

Moin

. Computation of trailing-edge flow and noise using large-eddy simulation. AIAA J 2000; 38(12): 2201–2209.

23.

Astley

Coyette

. Conditioning of infinite element schemes for wave problems. Commun Numer Methods Eng 2001; 17: 31–41.

24.

Astley

Coyette

. The performance of spheroidal infinite elements. Int J Numer Methods Eng 2001; 52: 1379–1396.

25.

Astley

. Computational acoustics of noise propagation in fluids - finite and boundary element methods. Springer, ch. Infinite elements 2008: 197–230.

26.

Caro

Ploumhans

Gallez

. Implementation of Lighthill’s acoustic analogy in a finite/infinite elements framework. AIAA, 2004, p. 2891.

27.

Burnett

Holford

. An ellipsoidal acoustic infinite element. Comput Methods Appl Mech Eng 1998; 164: 49–76.

28.

Wilcox

. A generalization of theorems of Rellich and Atkinson. Proc Am Math Soc 1956: 271–276.

29.

Astley

, Infinite elements, Institute of sound and vibration research. Highfield, Southampton, SO17 1BJ, United Kingdom.: University of Southampton.

30.

Christophe

. Application of hybrid methods to high frequency aeroacoustics. PhD Thesis. Université Libre de Bruxelles, 2011.

31.

LMS International Leuven, Belgium . Virtual.Lab 9a, User’s Manual. 2009; 52: 114.