Quasi-stationary model of air flow in the reed channel of single-reed woodwind instruments
Avraham Hirschberg, van de Rwa Robert Laar, JP Marrou-Maurieres, A. P. J. Wijnands, H. J. Dane, SG Kruijswijk, Ajm Adrian Houtsma · TU/e Research Portal · 1990
A quasi-stationary model of the flow in the reed aperture of single-reed woodwind instruments such as the clarinet and the reed-organ pipe has been developed. The model is based on a numerical study of the flow through a two-dimensional channel (Borda tube). It includes the effect of flow separation and friction. The resulting expression for the hydrodynamic force on the reed contains a nonlinear dependence on the reed channel aperture. This dependence partially explains the observed correlation between blowing pressure and playing frequency. The strong increase of frequency with blowing pressure observed at high pressures, however, is mainly due to the beating of the reed against the lay. Flow separation may either occur locally at the entrance of the channel or occur along the entire channel length. The transition from one type of behaviour to the other leads to hysteresis in the force on the reed. This hysteresis may be of fundamental importance for understanding reed operation in the absence of acoustical feedback and hence the onset of oscillation.