Numerical study on a three-dimensional model of a flue organ pipe: relative phase between pipe and foot, and stability
Shiryu Ikoga, Tatsuki Onomata, R. Tabata, Shiro Iwagami, Taizo R. Kobayashi, Kin’ya Takahashi · 2022
To clarify the role of the foot of flue organ pipes, we numerically studied a three-dimensional model with changing foot geometry by compressible LES.The foot acts as a Helmholtz resonator and influences the acoustic oscillation in the pipe.We found that the relative phase of oscillations between the pipe and foot changes depending on the geometry of the foot, and the change of the relative phase can be explained by the theory of forced harmonic oscillators: the pipe works as a force driving the foot.When the resonance frequency of the foot, f f , is smaller than the frequency of acoustic oscillation, f a , antiphase synchronization between the pressure oscillation in the pipe and that in the foot is observed, while synchronization is observed when the f f is larger than f a .If f f is nearly equal to f a , the pressure oscillation in the foot is delayed by π/2 to that in the pipe, and the amplitude of the acoustic oscillation is smaller than in other cases.The weak instability observed in this case seems to be caused by nonlinear interaction between the pipe and foot via the jet oscillation.