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On the emergence of secondary tones in airfoil noise
Published online by Cambridge University Press: 27 June 2023
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.
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- © The Author(s), 2023. Published by Cambridge University Press
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