Two-demensional (2D) models of a flue organ pipe are studied with compressible fluid simulation, specifically compressible Large Eddy Simulation, focusing on the influence of the geometry of the flue and the foot on the jet motion and acoustic oscillation in the pipe. When the foot geometry is fixed, the models having a flue with chamfers show good performances in stabilizing the acoustic oscillation in the steady state. Furthermore, we find that the foot chamber works as a Helmholtz resonator. If the frequency of the acoustic oscillation in the pipe is higher than the resonance frequency of the Helmholtz resonator by almost the full-width at half-maximum, anti-phase synchronization between the acoustic oscillation in the pipe and that in the foot chamber occurs. In this case, the acoustic oscillation in the pipe grows rapidly in the attack transient and is stabilized in the steady state.

The geometry of flue and foot influences the stability of jet oscillation, which products aerodynamic sound as the sound source of “air-jet instruments. Thus, we numerically study the influence of mouth-flue-foot geometry on the stability of jet oscillation with compressible LES. We introduce a 2D flue organ pipe model terminated with a closed end. We investigate the influence of the length of the flue, the existence of chamfers at the flue exit and the volume of the foot. As a result, eliminating the chamfer makes the jet oscillation unstable, while adding the chamfer stabilizes the jet oscillation and sound generation. A long flue makes the jet motion stable and robust, so that it spends a long time to reach a stable oscillation and cannot response quickly to the change of the air supply. Thus a relatively short flue with the chamfers is suitable for a performance. This result qualitatively agrees with the experimental result reported by Segoufin et al.. We also found that the existence of foot stabilizes the sound oscillation in the pipe: the pressure oscillation in the foot synchronizes with that in the pipe with a phase delay, but eliminating the foot rather makes the sound oscillation unstable.