A numerical simulation of a single-reed instrument with a pressure chamber is conducted to examine the interaction among the flow, reed oscillation, and acoustic propagation. The flow and acoustic fields are predicted using the three-dimensional compressible Navier–Stokes equations, whereas the one-dimensional dynamic beam equation is solved for reed oscillation. The deforming geometry in the aeroacoustic field is expressed by the volume penalization method as an immersed boundary technique. The results showed that the waveforms of the tip opening and far-field acoustic spectra agreed well with those measured experimentally. The three-dimensional flow configuration near the tip opening was visualized, and the measurement of the instantaneous volume flow rate at the tip opening revealed that 30%–40% of the total flow rate passed through the side opening. The spectral tendencies of the time derivatives of the flow rate for different tip openings were consistent with that of the far-field sound, indicating that the slope of the flow rate waveform significantly affects the generated sound's harmonics.
The evaluation of temporal and spatial fluctuations of energy using compressible fluid analysis is proposed as an effective method to clarify the fundamental mechanism of the self-sustained oscilla-tions in a actual recorder. The main factors of the self-sustained oscillations are investigated in more detail by evaluating not only the steady state of the sound where the flow field and the sound field are completely coupled, but also the characteristics at the attack transient of the sound before the coupling is established. By analyzing the large energy fluctuations that occur just below the edge of the labium in the attack transient, it was shown that this phenomenon may be one of the main causes of the self-sustained oscillations. And the characteristics of the energy fluctuations and sound power generation during the steady state of the sound are discussed. It was also focused on the energy variations in another region that is near the exit of the windway.
The sound of a single-reed instrument is produced by the interactions among flow, reed oscillation, and acoustic resonance in the resonator. To investigate the effects of lip stiffness on the reed oscillation and acoustic propagation in the single-reed instrument, we conduct a flow simulation coupled with a dynamic beam analysis. The flow and acoustic fields are simulated by solving the three-dimensionalNavier–Stokes equations, while the geometry of the instrument is expressed by the volume penalization method in the computational grids. The lip force on the reed is modeled as a function proportional to the distance between the lip position and reed surface, and the coefficient of lip stiffness was changed in the simulation. The mouthpiece of the instrument was set in the pressure chamber. The results showed that the self-sustained oscillation of reed started by adjusting the initial pressure condition of the chamber without the lip force, and amplitudes of the reed displacement decreased until a stable condition by adding the lip force. The lip stiffness was found to affect the amplitude of reed displacement, indicating the necessity of controlling the lip force to obtain stable oscillation.
To clarify the effects of the windway geometry on the aeroacoustic feedback in the jet fluctuations in recorders, direct aeroacoustic simulations were performed along with experiments. The simulations were based on the compressible Navier-Stokes equations to predict the fluid-acoustic interactions. The volume penalization method was used to reproduce the flow and acoustic fields around the complex shape of the recorders. Two recorders with straight and arch-shaped windway were explored. The occurrence of mode change was observed at the higher velocity for an arch-shaped windway model compared with the straight windway model. The modified formulation of the negative displacement model (N.H.Fletcher et al., 1976, J. Acoust.) was proposed based on the predicted jet fluctuations, where the jet fluctuations were divided into hydrodynamic and acoustic components. The ratio of the hydrodynamic component to the acoustic component near the windway exit was lower in the arch-shaped windway model than that in the straight windway model, whereas the amplification factor of the jet fluctuations was larger in the arch-shaped windway model. The relevance of these results and the mode change along the jet velocity is to be discussed.
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