Direct numerical simulation of flow and acoustic fields around woodwind instruments with reed oscillations

To clarify the effects of tip opening and the waveform of reed displacement on the flow and acoustic fields around an actual woodwind instrument, the direct numerical simulation of flow and sound based on the compressible Navier-Stokes equations was performed. To simulate aeroacoustic fields radiated from a low Mach number flow, a higher order compact scheme with structural grids was utilized. Since shapes of reed instruments are very complicated and the reed is vibrating, VP methods were introduced to the compact scheme simulation. To reproduce the human blowing, the reed was placed in the pressure chamber. In actual instruments, the vibrations of the reed are determined by structural vibrations with the coupled phenomena of flow and structural field, however in this analysis, the reed vibrations give a sinusoidal wave or waveform measured by experiment as forced vibrations. In case of sinusoidal waveform, the tip opening was changed from 0.6 mm to 2.0 mm, where 0.6 mm equivalent to the tip opening of conventional actual instruments. At the narrowest tip opening of 0.6 mm, the fundamental and third harmonics were larger in comparison with the second harmonics. On the other hands the second harmonics became large when with the wider tip opening wider than above mentioned. When the tip opening was 2.0 mm, the magnitude of the second harmonics became approximately the same as that of the third harmonics. In case of the measured waveform, the third harmonics was clearly observed; it was larger than that of the sinusoidal waveform. It indicates that simulation realizes the intense radiation of the fundamental and odd harmonics which is characteristic of reed instruments. These results also indicate that the radiating sound from reed instruments depends on not only the waveform of the reed but also the displacement of the tip opening.