Numerical Study on Acoustic Oscillations of 2D and 3D Flue Organ Pipe Like Instruments with Compressible LES

Acoustic oscillations of flue instruments are investigated numerically using compressible Large Eddy Simulation (LES). Investigating 2D and 3D models of flue instruments, we reproduce acoustic oscillations excited in the resonators as well as an important characteristic feature of flue instruments - the relation between the acoustic frequency and the jet velocity described by the semi-empirical theory developed by Cremer & Ising, Coltman and Fletcher et al. based on experimental results. Both 2D and 3D models exhibit almost the same oscillation frequency for a given jet velocity, but the acoustic oscillation as well as the jet motion is more stable in the 3D model than in the 2D model, due to less stability in 3D fluid of the rolled up eddies created by the collision of the jet with the edge, which largely disturb the jet motion and acoustic field in the 2D model. We also investigate the ratio of the amplitude of the acoustic flow through the mouth opening to the jet velocity, comparing with the experimental results and semi-empirical theory given by Hirschberg et al..