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Displacement thickness evaluation for semi-empirical airfoil trailing-edge noise prediction model

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Abstract

This study proposes a criterion for evaluating the turbulent boundary layer displacement thickness when predicting airfoil trailing-edge noise with semi-empirical methods. The boundary layer integral parameter is usually employed as the typical turbulence length-scale in the classic NASA-BPM semi-empirical airfoil self-noise prediction model and its variations. Although the semi-empirical noise prediction methods have been, in theory, superseded by more complex and demanding simplified-theoretical methods, they arguably remain the most suitable methods for noise investigation during the preliminary design phase of airfoils and wind turbine blades. The purpose of the criterion discussed is to limit the adverse impact of the uncertainty associated with the scaling parameter into the overall intrinsic quality of the semi-empirical noise prediction method. The criterion may be then employed, along with computational efficiency, to sort out methods for the task of feeding the popular BPM noise prediction model and its variations. As an illustration of the application of the proposed criterion, the performance of CFD-RANS and XFoil codes are examined and compared with experimental data from turbulent, incompressible flow available from the literature in the range \(5.0 \times 10^{5} < \text{Re}_{\text{C}} < 1.5\, \times 10^{6}\).

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Notes

  1. δ* is also affected by the freestream turbulence level, which determines transition, but the concern here is with airfoil self-noise only.

  2. Average of 36 min per point in a four processor 3 GHz machine.

Abbreviations

A :

Empirical spectral shape based on the Strouhal number (dB)

C :

Airfoil chord (m)

\(\bar{D}_{\text{h}}\) :

Directivity function, high-frequency noise ()

f :

Frequency (Hz)

K 1 :

SPL level experimental correction factor (dB)

L :

Span of the airfoil (m)

M :

Mach number ()

OASPL:

Overall sound pressure level (dB)

ReC :

Reynolds number, based on airfoil chord ()

r e :

Effective observer distance (m)

SPL1/3 :

Sound pressure level for a 1/3 octave band (dB)

SPLp, 1/3 :

Sound pressure level for a 1/3 octave band, at pressure side (dB)

St:

Strouhal number, fδ*/U ()

Stp, St1 :

Strouhal number, peak frequency ()

TU:

Turbulence intensity (% of U)

U :

Local mean velocity (m/s)

U ∞ :

Uniform flow velocity (m/s)

Y + :

Wall coordinate, dimensionless distance to wall ()

α :

Angle of attack (°)

δ * :

Boundary layer displacement thickness (m)

\(\delta^{*}_{p}\) :

Boundary layer displacement thickness, pressure side (m)

k - ω :

Turbulence model based on the turbulent kinetic energy and energy dissipation rate transport equations for mathematical closure

γ - Reθ :

Transition model based on the intermittency factor and momentum thickness Reynolds number

AOA:

Angle of attack

BEM:

Blade-element momentum theory

BL:

Boundary layer

BPM:

Brooks, Pope, Marcolini, NASA semi-empirical noise prediction model

CAA:

Computational aero-acoustic (noise prediction models)

CFD:

Computational fluid mechanics

HAWT:

Horizontal axis wind turbine

IAG:

Institut für Aerodynamik und Gasdynamik, Stuttgart

LE:

Leading-edge

NREL:

National Renewable Energy Laboratory, USA

POLI-USP:

Polytechnic School of the University of Sao Paulo

RANS:

Reynolds-averaged Navier–Stokes equations

R&D:

Research and development

SE:

Semi-empirical (noise prediction models)

SST:

Shear stress transport

ST:

Simplified-theoretical (noise prediction models)

TBL:

Turbulent boundary layer

TBL-FP:

Turbulent boundary layer over a flat plate model

TE:

Trailing-edge

TU-Berlin:

Technische Universität Berlin

WT:

Wind turbine

WTN:

Wind turbine noise

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Authors and Affiliations

  1. Department of Mechanical Engineering, Polytechnic School, Sao Paulo State University (USP), Av. Prof. Luciano Gualberto, 530, Cidade Universitária, SP, 05508-010, Brazil

    Joseph Y. Saab Jr. & Marcos de Mattos Pimenta

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  1. Joseph Y. Saab Jr.
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  2. Marcos de Mattos Pimenta
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Correspondence to Joseph Y. Saab Jr..

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Technical Editor: Fernando Alves Rochinha.

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Saab, J.Y., de Mattos Pimenta, M. Displacement thickness evaluation for semi-empirical airfoil trailing-edge noise prediction model. J Braz. Soc. Mech. Sci. Eng. 38, 385–394 (2016). https://doi.org/10.1007/s40430-015-0341-5

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