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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