On the emergence of secondary tones in airfoil noise

Abstract

© The Author(s), 2023. Published by Cambridge University Press.We present the results of direct numerical simulations of a NACA 0012 airfoil, with Mach number 0.3 and angle of attack of, examining the dynamics of the flow with increasing Reynolds numbers. Two-dimensional simulation results are obtained with chord-based Reynolds numbers in the range, 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. The development of the pressure fluctuations with time shows a transition from periodic to quasi-periodic attractor for, leading to the emergence of secondary tones in the wall and acoustic field pressure spectra, different from peaks related to the fundamental frequency and the respective harmonics; a second, incommensurate frequency appears, leading to several secondary tones with frequency, with and integers. Further increase of the Reynolds number leads to the emergence of a tertiary frequency, 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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