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Effects of trailing edge bluntness on airfoil tonal noise at low Reynolds numbers

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Abstract

The aim of this study is to analyze the effects of trailing edge bluntness on airfoil tonal noise generation and propagation at low Reynolds numbers. Several simulations are conducted for a NACA0012 airfoil at four different free-stream Mach numbers, \(M_{\infty }\) = 0.2–0.5. The angle of incidence is set equal to 3°, and the Reynolds number based on the airfoil chord is \(Re_{c}\) = 5,000. The effects of compressibility on sound generation and propagation are analyzed along with the effects of scattering by blunt trailing edges with four different radii of curvature. Sound generation by vortex shedding is computed by a hybrid method and an accurate two-dimensional direct calculation, and results are compared. The hybrid approach uses direct calculation for near-field source computations and the Ffowcs Williams–Hawkings equation as the acoustic analogy formulation. Numerical results show that the airfoil emits an intense “narrow-band” tone and that a thicker trailing edge emits higher noise levels than a thinner one since the magnitude of quadrupole sources is larger for the thicker configuration. Moreover, the spatial distribution of quadrupole sources shows that the peak quadrupole values are closer to the surface when the trailing edge is thicker, which, again, increases the scattered far-field noise.

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Abbreviations

\(c_{\infty }\) :

Free-stream speed of sound

\(c\) :

Airfoil chord

\(E\) :

Total energy

\(f\) :

FW-H surface

\(F_i\) :

Dipole source

\(G\) :

Green’s function

\(g_{ij}\) :

Covariant metric tensors

\(g^{ij}\) :

Contravariant metric tensors

\(H\) :

Heaviside function

\(H_0^{(2)}\) :

Hankel function of the second kind and order zero

\(i\) :

Imaginary unit

\(M_{\infty }\) :

Free-stream Mach number

\(q_{j}\) :

Heat flux

\(p\) :

Pressure

\(Pr\) :

Prandtl number

\(Q\) :

Monopole source

\(Re_{c}\) :

Reynolds number based on airfoil chord \(c\)

\(t\) :

Time

\(T\) :

Temperature

\(T_{ij}\) :

Quadrupole source (Lighthill stress tensor)

\(u_i\) :

Fluid velocity

\(u^i\) :

Contravariant velocity components

\(U_i\) :

Mean flow velocity

\(\mathbf {x}\) :

Observer position

\(\mathbf {y}\) :

Source position

\(\gamma\) :

Ratio of specific heats

\(\delta _{ij}\) :

Kronecker delta

\(\rho\) :

Density

\(\tau _{ij}\) :

Viscous stress tensor

\(\omega\) :

Angular frequency

\(\kappa\) :

Thermal conductivity

\({\mu }\) :

Dynamic viscosity coefficient

\(\nu\) :

Kinematic viscosity coefficient

\({}^{\prime}\) :

Perturbation value

\(\hat{\cdot }\) :

Fourier-transformed quantity

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Acknowledgments

The authors acknowledge the financial support received from Fundação de Amparo à Pesquisa do Estado de São Paulo, FAPESP, under Grant Nos. 2014/10166-6, 2013/03413-4 and 2013/07375-0, the financial support received from Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, under Grant No. 470695/2013-7 and the financial support received from Pró-Reitoria de Pós-Graduação da Universidade Estadual de Campinas, PRP-UNICAMP, under FAEPEX Grant No. 259/2014. The authors also thank to Centro Nacional de Processamento de Alto Desempenho em São Paulo, CENAPAD-SP, for providing the computer resources for the numerical simulations under project 551. The authors also acknowledge Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, CAPES, and FAPESP for providing a MSc. scholarship to the first author.

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  1. Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, Rua Mendeleyev, 200, Campinas, SP, CEP 13083-860, Brazil

    Walter Arias Ramírez & William Roberto Wolf

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  1. Walter Arias Ramírez
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  2. William Roberto Wolf
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Correspondence to Walter Arias Ramírez.

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Technical Editor: Francisco Ricardo Cunha.

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Arias Ramírez, W., Wolf, W.R. Effects of trailing edge bluntness on airfoil tonal noise at low Reynolds numbers. J Braz. Soc. Mech. Sci. Eng. 38, 2369–2380 (2016). https://doi.org/10.1007/s40430-015-0308-6

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