Simulation of edge tone generation

The edge tone generation was also simulated using the four different models introduced above.

Figure 9.5 depicts the movement of the air jet oscillating around the edge of the upper lip. On the left hand side of the figure, att = 4.6 ms the jet is moving from the left to the right. In the middle picture, att = 5.0 msthe jet has nearly reached its rightmost position, whereas in the right hand side, att = 5.4 msits already moving back, from right to left, hitting the edge with its centerline. The typical vortex generation process in this flow configuration is also clearly followable in Figure 9.5.

Since the edge tone acts as a dipole sound source the spectra of pressure forces acting on the upper lip contain the same tonal components as the edge tone. The amplitudes of pressure force components are not directly comparable to microphone edge tone measurements reported by Außerlechneret al.[19], as the propagation from the edge to the microphone position is sup-posedly strongly dependent on the frequency. Also the pressure force spectra are expected to have higher noise baseline since they contain the forces of vortices shedding from the upper lip

1The fit was unsuccessful in they= 5 mmcase for the data of Vaik & Paál.

9.4. RESULTS AND DISCUSSION 121

Figure 9.6.Spectra of pressure forces acting on the upper lip.

Mode frequencies [Hz]

Mode Measured Vaik & Paál 2D laminar 2D LES 3D laminar 3D LES

I. 1 060 1 100 1 150 1 125 1 050 1 025

II. 2 610 2 940 2 675 2 750 2 675 2 675

III. 4 465 4 600 N/A 4 575 N/A 4 300

Table 9.3.Comparison of measured and simulated frequencies of edge tone modes

and other unsteady pressure fluctuations, which are attenuated by the acoustic propagation to a great extent. Nevertheless, the frequencies of the tonal components observed in the pressure force spectra should be comparable and in good agreement with the tonal components of the radiated sound of the edge tone.

The pressure

force spectra pressure force spectra were calculated as follows. The forces acting on the upper lip were

evaluated every 10^thtime step leading tof_s= 200 kHzsampling rate. Since the Reynolds number is of order10³, the pressure forces are dominant over viscous forces. Only thexcomponent of the forces were taken into account. The forces were normalized by dividing them by thez-size of the model, therefore the resulting normalized forces are interpreted asN/m. An FFT window size of8 000points were chosen, which corresponds to a time window ofT_win = 0.04s and a frequency resolution of∆f = 25 Hz. Spectra of successive time windows were evaluated using Hann window function and85%overlapping between the time windows. Finally, the amplitudes of the spectra were averaged with 27 and 11 averages—resulting from the above method—in the 2D and 3D cases, respectively. The resulting spectra are displayed in Figure 9.6.

As it spectrum

comparison is seen in Figure 9.6, the predicted edge tone components are close in frequency in all

cases. The exact values of the calculated frequencies are listed in Table 9.3. In case of 2D models, there is an artifact in the spectra in the low frequency range, around125 Hz. These components are also found in the spectra reported by Vaik & Paál [140]. The artifact components are not present in the 3D model and the low frequency fluctuations have remarkably smaller amplitudes in the 3D cases. Also the baseline of the spectra is much lower in the 3D cases despite the lower number of spectral averages. This is due to the fact that the evaluation of pressure forces is done by integration over the surface of the upper lip, hence it inherently contains averaging in the

z direction. It can also be seen that in case of the 3D LES model, the second and third modes become remarkably stronger than in other cases.

The third edge tone mode tonal

com-ponents

could not be clearly detected in the laminar simulations. The fre-quencies of the modes attained from the simulations are in good agreement with the measure-ments reported in [19]. As it is seen, the 2D models slightly overestimate the mode frequencies, whereas the 3D models provide a better match with the measurements. The prediction of mode frequencies using the 3D models are also better than the ones obtained by Vaik & Paál [140], espe-cially for the second mode, where the deviation between the measured and the simulated mode frequency is reduced from13%to less than3%.

9.5 Concluding remarks

Simulations of the air jet and edge tone generation in the foot model of a labial organ pipe were reported in this chapter. Two- and three-dimensional models were created, extending the scope of recent simulations by Vaik & Paál [140]. The quality of the computational models were as-sessed by means of comparison against measurement results of Außerlecheret al.[18, 19]. Good agreement of measurements and simulations was found both in the “Jet” and “Edge” cases.

It

findings has been shown that 3D models give better fit to the measured jet velocity profiles, whereas 2D models overestimate the width of the air jet to a significant extent. The models successfully capture other characteristic properties of the flow field, such as thevena contractaeffect at the jet exit. In case of edge tone simulations very good agreement of the measured and simulated tonal components have been found. The 3D models give excellent agreement with measured mode frequencies, yet 2D models give a slight overestimation. From the results presented here, it can be assessed that by taking 3D effects of the flow field into account the quality of air jet and edge tone CFD simulations can be significantly increased, and better match to measurement results can be attained at a cost of increased computational effort.

As it possible

im-provements

was seen, the pressure forces obtained from CFD simulations can only be compared to edge tone sound measurements in an indirect manner. This difficulty could be overcome by applying an aeroacoustic propagation model to simulate the acoustic pressure field near the pipe mouth. This would enable a more detailed evaluation of edge tone simulations. In order to get a realistic sound generation model of an organ pipe, the “Edge” model presented here has to be extended by acoustic feedback from the pipe resonator. Incorporating the latter extensions into the model are among the future plans of the author.

Chapter 10

Conclusions and outlook

This final chapter briefly summarizes the results of the research presented in the thesis. Novel results contributing to pipe organ research are listed briefly in Section 10.1. Thesis statements are given in Section 10.2. Possibilities of further research on the topics addressed in this thesis are discussed finally in Section 10.3.

10.1 Contributions

The dissertation presented the following new results.

• A novel scaling method for chimney pipes was introduced in Chapter 5. The proposed technique relies on the one-dimensional acoustic model of the pipe and incorporates an iterative and a global optimization routine for determining the geometry of the resonator.

The process offers sound design by the amplification / suppression of the targeted har-monic partials in the steady state sound. The applicability of the proposed technique was validated by means of measurements and listening tests performed on chimney pipes built with optimized resonators.

• A measurement campaign performed on labial organ pipes with tuning slots revealed pre-viously unknown properties of the pipe sound. Reproducible measurements on experimen-tal pipes were reported in Chapter 6, and the impact of each scaling parameter of the tuning slot on the character of the pipe sound was documented. It was proven by measurements and listening experiments that current design rules of tuning slots are suboptimal and do not lead to the best achievable sound characteristics. It was also shown that in order to fully exploit the capabilities of the tuning slot, the length above the slot should be proportional to the length of the pipe length instead of the diameter.

• For the accurate characterization of the acoustic behavior of labial pipes with a tuning slot, Chapter 7 introduced a hybrid technique incorporating 1D waveguide elements and 3D finite element simulation results. It was shown that the proposed approach gives reliable prediction of the eigenfrequency-structure of the pipe and overcomes the limitations of previous analytical models.

• The numerical characterization of the radiation impedance of an open conical pipe end was given in Chapter 8. By post-processing the computational results, the resulting bi-variate impedance function was incorporated into the one-dimensional acoustic model. It was proven that the resulting hybrid model improves the accuracy of the prediction of the eigenfrequencies in case of tapering pipe ends.

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• A low frequency acoustic model of the shallot was introduced in Chapter 8. The model was validated by means of comparison with results of transfer function measurements.

• Three-dimensional flow simulations of the edge tone configuration in an organ pipe foot model were presented in Chapter 9. It was shown that by extending the simulation into three dimensions a remarkable improvement on the predicted properties of the flow field is attained. This statement was validated by comparison to measurements and 2D simulation results found in the corresponding literature.