Modeling of air-jet-driven instruments: An unstable jet driven by pressure gradient
Seiji Adachi · The Journal of the Acoustical Society of America · 1999
A new model of the jet deflection is developed to understand the sound production of an organ flue pipe, which is representative of air-jet-driven instruments. This model provides a dynamical equation governing the displacement of a jet, which has the aerodynamical instability and is driven by the acoustic pressure gradient in the direction perpendicular to jet travel. Due to the instability, the growth factor of the deflection becomes exponential, as found in measurements of the jet movement such as hot-wire anemometry and flow visualization. The oscillation condition of an experimental E4 organ pipe is examined by considering the phase difference between the jet displacement at the labium and the acoustic pressure at the mouth. The sound is simulated by means of the physical modeling technique. The simulated pipe behavior is compared with that found in an actual pipe. Similarities and differences found in the transition between oscillation regimes are discussed.