Numerical simulations of fluid-structure interactions in single-reed mouthpieces

Abstract

Most single-reed woodwind instrument models rely on a quasistationary approximation to describe the relationship between the volume flow and the pressure difference across the reed channel. Semiempirical models based on the quasistationary approximation are very useful in explaining the fundamental characteristics of this family of instruments such as self-sustained oscillations and threshold of blowing pressure. However, they fail at explaining more complex phenomena associated with the fluid-structure interaction during dynamic flow regimes, such as the transient and steady-state behavior of the system as a function of the mouthpiece geometry. Previous studies have discussed the accuracy of the quasistationary approximation but the amount of literature on the subject is sparse, mainly due to the difficulties involved in the measurement of dynamic flows in channels with an oscillating reed. In this paper, a numerical technique based on the lattice Boltzmann method and a finite difference scheme is proposed in order to investigate the characteristics of fully coupled fluid-structure interaction in single-reed mouthpieces with different channel configurations. Results obtained for a stationary simulation with a static reed agree very well with those predicted by the literature based on the quasistationary 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. Furthermore, in the case of long reed channels, the results obtained for the vena contracta factor are in significant disagreement with those predicted by theory. For short channels, the assumption of constant vena contracta was found to be valid for only 40% of the duty cycle.

The effect of blowing pressure, lip force and tonguing on transients: A study using a clarinet-playing machine

“…The clarinet is a suitable instrument on which to study transients. Its steady state acoustical behaviour has been well studied experimentally (e.g., Wilson and Beavers, 1974;Bak and Dolmer, 1987;Idogawa et al, 1993;Mayer, 2003;Dalmont et al, 2003;Dalmont and Frapp e, 2007;Ganzengel et al, 2007;Almeida et al, 2013) and theoretically (e.g., Gilbert et al, 1989;Grand et al, 1997;Kergomard et al, 2000;Dalmont et al, 2003Dalmont et al, , 2005Atig et al, 2004;Facchinetti et al, 2003;Ollivier et al, 2004Ollivier et al, , 2005Dalmont and Frapp e, 2007;da Silva et al, 2007).…”

Time‐resolved strain and deformation measurement on the vibrating saxophone reed

“…To optimize the design of mouthpieces based on physical insight and parameter‐driven design, the system's mechanics first needs to be measured and understood. Attempts have been made to model reed dynamics, [ 10–13 ] but important input data are still lacking.…”

“…Strain in the direction perpendicular to the reed has not been investigated. In modelling reed dynamics, strain in this direction has not yet been considered, [ 10,13,22 ] while it might be an important aspect of reed behaviour.…”

CFD Simulation of Air Flow Behaviour at Different Flow Rates in a Turkish Woodwind Instrument (Turkish Treble Recorder)

“…McIntyre et al (1983) emerge as the pioneer of the first simulation studies on sound generation in wind instruments [27]. Recently, international studies in this field using advanced computers and numerical method-based engineering simulations contribute to this research area [28]- [35]. These literatures also provide a good understanding of numerical solutions of the compressible Navier-Stokes equations in various aspects of sound production in recorder like musical instruments.…”