Numerical studies of aeroacoustic aspects of wind instruments

The characteristics of the dynamic flow in single-reed mouthpiece systems, as well as the influence of low Mach number mean flows on parameters associated with the acoustic radiation from wind instruments and generic waveguides are investigated in this thesis. In the first case, a numerical technique based on the lattice Boltzmann method coupled to a finite difference scheme is developed in order to investigate the fluid-structure interaction within the mouthpiece-reed system due to an unsteady low Mach number viscous flow. Results obtained for a stationary simulation with a static reed agree very well with those predicted by the literature based on the quasi-stationary approximation. However, simulations carried out for a dynamic regime with an oscillating reed show that the phenomenon associated with flow detachment and reattachment diverges considerably from the theoretical assumptions. The influence of low Mach number mean flows on the acoustic transmission properties of wind instruments and generic waveguides is also investigated by means of an axisymmetric lattice Boltzmann scheme. The results obtained from an unflanged pipe model agree very well with those provided by the available theories and experimental data. The effect of different horn types attached to the open end of a pipe is also investigated in detail. When compared to an unflanged pipe, horns act to significantly increase the gain of the reflection coefficient magnitude (|R| > 1) in the same critical regions observed in the unflanged pipe. Conversely, horns act to drastically decrease the end correction in the low-frequency limit. The results suggest that the magnitude of the reflection coefficient is independent of the horn geometry at low Strouhal numbers, whereas the end correction is highly dependent. When the simulations are conducted with the same parameters found during clarinet playing (catenoidal horn and very low Mach numbers), it is observed that the effect of the mean flow becomes negligible in terms of the reflection coefficient magnitude but can be significant on the estimation of the end correction and, consequently, on the calculation of the instrument's fundamental frequency.