Aerodynamic excitation and sound production of blown-closed free reeds without acoustic coupling: the example of the accordion reed.

The accordion reed is an example of a blown-closed free reed. Unlike most oscillating valves in wind musical instruments, self-sustained oscillations occur without acoustic coupling. Flow visualizations and measurements in water show that the flow can be supposed incompressible and potential. A model is developed and the solution is calculated in the time domain. The excitation force is found to be associated with the inertial load of the unsteady flow through the reed gaps. Inertial effect leads to velocity fluctuations in the reed opening and then to an unsteady Bernoulli force. A pressure component generated by the local reciprocal air movement around the reed is added to the modeled aerodynamic excitation pressure. Since the model is two-dimensional, only qualitative comparisons with air flow measurements are possible. The agreement between the simulated pressure waveforms and measured pressure in the very near-field of the reed is reasonable. In addition, an aeroacoustic model using the permeable Ffowcs Williams-Hawkings integral method is presented. The integral expressions of the far-field acoustic pressure are also computed in the time domain. In agreement with experimental data, the sound is found to be dominated by the dipolar source associated by the strong momentum fluctuations of the flow through the reed gaps.