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On the emergence of secondary tones in airfoil noise

Published online by Cambridge University Press:  27 June 2023

Alex Sano Open the ORCID record for Alex Sano [Opens in a new window] ,
André V.G. Cavalieri Open the ORCID record for André V.G. Cavalieri [Opens in a new window] ,
André F.C. da Silva Open the ORCID record for André F.C. da Silva [Opens in a new window]  and
William R. Wolf Open the ORCID record for William R. Wolf [Opens in a new window]
Alex Sano*
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP 12228-900, Brazil
André V.G. Cavalieri
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP 12228-900, Brazil
André F.C. da Silva
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP 12228-900, Brazil
William R. Wolf
Affiliation:
Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, Campinas, SP 12228-900, Brazil
*
†Email address for correspondence: [email protected]
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Abstract

We present the results of direct numerical simulations of a NACA 0012 airfoil, with Mach number 0.3 and angle of attack of $3^\circ$, examining the dynamics of the flow with increasing Reynolds numbers. Two-dimensional simulation results are obtained with chord-based Reynolds numbers in the range $3.2 \times 10^3 \leq Re \leq 2.70 \times 10^4$, where each simulation uses the last time step of the previous one as a starting point, to capture the evolution of dynamics as a function of $Re$. The development of the pressure fluctuations with time shows a transition from periodic to quasi-periodic attractor for $2.38 \times 10^4 \leq Re \leq 2.42 \times 10^4$, leading to the emergence of secondary tones in the wall and acoustic field pressure spectra, different from peaks related to the fundamental frequency $f_1$ and the respective harmonics; a second, incommensurate frequency $f_2$ appears, leading to several secondary tones with frequency $af_1 + bf_2$, with $a$ and $b$ integers. Further increase of the Reynolds number leads to the emergence of a tertiary frequency, $f_3$, indicating a route to chaos of the Ruelle–Takens–Newhouse type. Such a mechanism is related to the ladder-type characteristic structure of the tones, indicating that dynamic systems theory is an important tool for understanding airfoil tonal noise.

JFM classification

Acoustics: Aeroacoustics Nonlinear Dynamical Systems: Bifurcation Nonlinear Dynamical Systems: Chaos
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 966 , 10 July 2023 , A8
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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