STUDY OF FLUID-STRUCTURE-ACOUSTIC
INTERACTIONS DURING THE PRODUCTION OF
CONSONANTS

Raphaël Chottin, Alaa Yazbek, Annemie van Hirtum, Xavier Pelorson

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Raphaël Chottin, Alaa Yazbek, Annemie van Hirtum, Xavier Pelorson. STUDY OF FLUID-STRUCTURE-ACOUSTIC INTERACTIONS DURING THE PRODUCTION OF CONSONANTS. Proc. 31st International Congress on Sound and Vibration (ICSV31), 2025, Incheon, South Korea. hal-05173509

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# STUDY OF FLUID-STRUCTURE-ACOUSTIC INTERACTIONS DURING THE PRODUCTION OF CONSONANTS

Raphaël Chottin, Alaa Yazbek, Annemie Van Hirtum, Xavier Pelorson

University of Grenoble Alpes, CNRS, Grenoble INP, LEGI, 38000 Grenoble, France

email: xavier.pelorson@legi.cnrs.fr

This paper presents an experimental study aimed at exploring the aeroacoustic interactions between human vocal folds and the vocal tract. This is achieved by reproducing fluid-structure-acoustic interactions in a controlled environment. The experimental setup is based on the use of either an acoustic source or a silicone replica of the vocal folds. These are placed upstream of constrictions of variable shapes and sections. The objective is therefore to reproduce and quantify the physical phenomena occurring during the production of voiced and unvoiced consonants.

The measured parameters are, in addition to the volume flow rate and the supply pressure, the pressure distribution downstream of the vocal folds and the radiated acoustic pressure field. Particular attention is paid to the factors influencing the vibration, maintenance and offset of vocal folds self-oscillations and the acoustic consequences. Typical results are presented and the relationship between size and geometry of constrictions is quantitatively evaluated.

Keywords: voice, aeroacoustics, fluid-structure interaction

## 1. Introduction

The fluid-structure-acoustic interactions in the production of consonants have been extensively studied using mechanical replicas, notably through the pioneering work of Shadle [1] and more recent research [2]. Moreover, numerous studies have explored the effects of various vocal fold replicas (rigid, flexible, forced, self-oscillating, etc.) on airflow [3, 4]. However, few studies have focused on voiced consonants, which combine vocal fold replicas, vocal tract constrictions, and obstacles mimicking teeth. This work represents a first step towards simulating a more complete vocal tract in a controlled environment. The present contribution proposes an experimental approach aimed at studying the influence of obstacles combined with a constriction on acoustic generation, in the presence of a rigid vocal fold replica in forced oscillation.

Section 2 describes the experimental setup, as well as two theoretical models used to compare with the experimental data. Section 3 presents the pressure and acoustic measurements obtained with and without the vocal fold replica. Finally, Section 4 summarizes the results, discusses their implications, and suggests directions for future work.
# 2. Methodology

## 2.1 Description of the Setup

In order to study fluid-structure-acoustic interactions in a controlled environment, an experimental setup mimicking the dynamics of a vocal tract was established. The vocal tract replica (Fig. 1(a)) consists of connected tubes with a total length L and an internal diameter of $D_0 = 2.5$ cm, divided into three main sections:

* A "source" section mimicking the vocal folds, with a length of $L_s = 5$ cm, consisting of a rigid replica of vocal folds undergoing forced oscillations at 5 or 15 Hz.

* A "constriction" section of length $L_c = 1$ cm, featuring a constriction defined in Fig. 2(a). A circular constriction with $D_{BC} = 1$ cm and an elliptical constriction with height $h = 2.24$ cm and width $w = 0.45$ cm are used, such that the area of the constriction is $A_c = 0.79 \text{ cm}^2$. The hydraulic diameters are $D = 1$ cm for the circular constriction and $D = 0.67$ cm for the elliptical constriction. Notably, the area ratio $A_0/A_c$ between the cross-sectional area of the tube without, $A_0$, and with the constriction, $A_c$, is 6.25.

* An "obstacle" section of length $L_0$, designed to simulate the presence of teeth, consisting of an obstacle model as defined in Fig. 2(b).

<figure><img src="image_3.png" /><figcaption>Figure 1: left: pressure measurement setup. Right: Microphone positions inside the anechoic chamber.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 2: Constrictions and obstacles geometry.</figcaption></figure>

The replica is fed by a volumetric air flow $\Phi$, measured by a flowmeter (TSI 4054; ±0.1 L/min) upstream of the device. The replica is attached via a nozzle to an aero-acoustic conditioning chamber, the interior walls of which are covered with acoustic foam and grids to condition the flow. The wall pressure inside the replica is measured at six positions $x_n$ in addition to the specific one at the constriction, using pressure taps. These measurements are taken by ENDEVCO 8510-B 500 pressure sensors and
Kulite XCS-093-035BARG sensors powered at 10 V by an EA3005S power supply. The sensors were pre-calibrated with an accuracy of ±5 Pa.

A square screen of 30 cm on each side is placed at the exit of the replica as shown in Fig. 1(b), and the acoustic radiation is measured by two Brüel & Kjær 4192 microphones, labeled M1 and M2, connected to a Brüel & Kjær 5935L amplifier located in front of the replica exit, at 108 cm, and to the left of the tube at 94 cm, as well as two Neumann KM 184mt microphones, labeled M3 and M4, powered by a Phantom Hex RPB486. The tube output with the screen is positioned inside an anechoic chamber (volume 7.45 m³ [5]) that also houses the microphones.

All signals from the pressure sensors, microphones, and the output signal from the amplifier are recorded (sampling frequency 22050 Hz) using a National Instruments BCN-2090A acquisition card.

## 2.2 Pressure and flow theoretical models

The models used are a "boundary layer" model referred to here as bl, and a "viscous" model referred to as vi. Both models are derived from [6]. The first model accounts for the boundary layer near the walls. The pressure variation in the constriction $P_c$, relative to the jet pressure $P_j$ and the upstream pressure $P_0$, is estimated based on the hydraulic diameter D and the area $A_c$ of the tube at the constriction, and the jet area $A_j$,

$$ \frac{\Delta P_c}{P_0} = \frac{P_0 - P_j}{P_0} \left(1 - \frac{A_j}{A_c}\right) \qquad (1) $$

with

$$ \frac{A_j}{A_c} = \left(1 - 2\frac{\delta_1}{D}\right)^2 \qquad (2) $$

where the boundary layer displacement thickness, $\delta_1$ is approximated by the value corresponding to a flat plate of length $L_c$ associated with a Blasius velocity profile:

$$ \delta_1 = 1.7 $$

where the Reynolds number $Re = \frac{Du_{ref}}{\nu}$ is defined using the hydraulic diameter D, the kinematic viscosity of the fluid $\nu$, and a reference velocity $u_{ref} = \sqrt{\frac{2P_0}{\rho}}$, with $\rho$ representing the air density. The second model aims to account for the viscous effects of the fluid. It is derived from the Navier-Stokes equation, approximated using the conservation of volumetric flow rate $d\Phi/dx = 0$ as :

$$ -\frac{\Phi^2 dA}{A^3 dx} + \frac{1}{\rho} \frac{dP}{dx} = \nu \left( \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} \right) \qquad (3) $$

where $u(x,y,z)$ is the flow velocity. Integration of the equation (3) gives the following pressure distribution $P(x,t)$:

$$ P(x,t) = P_0 + \frac{1}{2} \rho \Phi^2 \left( \frac{1}{A^2(x_0)} - \frac{1}{A^2(x,t)} \right) + \mu \Phi \int_{x_0}^{x} \frac{dx}{\beta(x,t)} \qquad (4) $$

with $A(x,t)$ being the cross-sectional area of the tube, $\Phi$ the volumetric flow rate, $\mu$ the dynamic viscosity coefficient of air, and $\beta(x,t)$ a geometric term depending on the shape of the constriction section, $\frac{A^2}{8\pi}$ for a circle and $\frac{w^2A^3}{\pi^2w^4+16A^2}$ for an ellipse.
# 3. Results

## 3.1 Without Vocal folds replica

Initially, the setup was tested for the four obstacle positions without a vocal source: no obstacle, low obstacle, high obstacle, and double obstacle as shown in Fig. 2(b). The air flow rate is set to approximately twenty values between 50 and 250 L/min, corresponding to Reynolds numbers Re ranging from $3.5 \times 10^3$ to $19 \times 10^3$.

### 3.1.1 Validation of Pressure and Flow Without Obstacle

First, the values of the ratio between the pressure $P_1$ at the center of each constriction and the pressure $P_0$ located upstream (measured at the pressure tap $x_6$) as a function of the Reynolds number in the constriction were calculated and compared with two models (Fig. 3(a)), along with the flow rate $\Phi$ (Fig. 3(b)). The results show a strong agreement between the boundary layer model (bl) and the measurements taken at the circular constriction, with a difference of less than 10% across the entire range of Re. It is noteworthy that the boundary layer model predicts increasingly negative pressures $P_1$ with Re, which matches the measurements. In contrast, the viscous model (vi) predicts $P_1 = 0$ for all evaluated values of Re. For the elliptical constriction, both models show poor correspondence with the measurements, with differences exceeding 10% for all Re values. However, the boundary layer model results in the smallest error for low Re values, while the viscous model provides the smallest error for high Re values. In general, the boundary layer model (resp. viscous model) underestimates (resp. overestimates) the pressure loss. Again, note that the boundary layer model predicts negative pressures $P_1$, which matches the measurements, whereas the viscous model predicts positive or zero pressures. Nevertheless, the viscous model predicts that $P_1$ becomes independent of Re for sufficiently high values of Re ($Re \gtrsim 7000$), whereas the boundary layer model does not capture this trend.

The flow rate is also compared with the model and shows excellent agreement with both models (boundary layer and viscous) for both constrictions (circular and elliptical). However, it can be noted that the viscous model provides a better approximation of the measured flow rate for the circular constriction, while the boundary layer model better predicts the measured flow rates for the elliptical constriction.

<figure><img src="image_5.png" /><figcaption>Figure 3: Measured values (e - symbol) and theoretical values, boundary layer model (bl - solid line) and viscosity model (vi - dashed line) as a function of the Reynolds number Re for the circular constriction (noted cl) and elliptical constriction (noted el) for a no-obstacle configuration: (left) Pressure ratio $P_1/P_0$; (right) Volumetric flow rate $\Phi$.</figcaption></figure>
### 3.1.2 Acoustic measurements of the obstacles influence

An example of acoustic spectra up to 10 kHz (in dB SPL), measured for a tube with an elliptical constriction, for each of the four obstacle positions (see Fig. 2(b)), is presented in Fig. 4 for three flow rates (50, 150, and 250 L/min), corresponding to Reynolds numbers $Re$ of $3.5 \times 10^3$ (low), $11 \times 10^3$ (medium), and $19 \times 10^3$ (high), respectively.

<figure><img src="image_6.png" /><figcaption>Figure 4: Frequency spectra of microphone M1 as a function of the flow rate in L/min without oscillation of vocal cord replicas for an elliptical constriction. (a) : no obstacle, obstacle positioned (b) : at the top (c) : at the bottom (d) : at both top and bottom.</figcaption></figure>

The frequency spectrum for the no-obstacle experiment (Fig. 4(a)) shows a very low acoustical pressure level (below ≈ 10 dB SPL) generated by the flow for all frequencies. However, for the two highest flow rates, associated with $Re > 10^4$, the spectrum exhibits several frequency peaks around 700, 1800, and 4100 Hz. These frequencies arise due to flow instabilities and their interaction with the elliptical constriction, notably due to vortex generation.

When a single obstacle is placed near the tube exit (low or high configuration), increasing the flow rate causes an increase in the frequency content (above 10 dB SPL), especially in the mid-frequency range between 500 and 2000 Hz, as well as at higher frequencies, from 3 kHz to 5 kHz. An increase in noise is observed around the frequency peaks observed without an obstacle, indicating that the noise is generated during the interaction between the structures in the flow and the obstacle.

When two obstacles are present near the tube exit (double configuration), increasing the flow rate causes an increase in the frequency content across the entire spectrum, with a broad increase in noise above 20 dB SPL. However, the noise remains concentrated in the frequency bands observed in the presence of a single obstacle.

The increase in mid-frequency does not match human data when producing sibilant fricatives (e.g., /s/ in "soup"), whose spectral peaks generally occur around 6-7 kHz [7]. However, it is closer to the typical spectra associated with voiceless postalveolar fricatives (e.g., /ʃ/ in "shoe"). This may be
explained by the dimensions of the mechanical replica being larger than those of a human vocal tract. However, for a flow rate of 250 L/min, the double obstacle generates more aero-acoustic noise between 6 kHz and 9 kHz, approaching values observed in humans.

A measurement providing information on the directivity of the aero-acoustic radiation as a function of the obstacle for a flow rate of 250 L/min is shown in Fig. 5. This measurement suggests that the greatest directivity effects occur for the double obstacle. Indeed, around 8 kHz, an increase in the acoustic level can be observed on microphones M2 and M4 but is not observed on microphone M3 placed below the tube exit.

<figure><img src="image_7.png" /><figcaption>Figure 5: Frequency spectrum of the sound recorded at different locations. From left to right: in front of the tube exit, below the exit and above the exit.</figcaption></figure>

## 3.2 With Vocal Folds replica

The setup is tested with a replica of rigid vocal folds, for which the oscillation frequency is imposed (see Section 2.1). Acoustic measurements are made to study the influence of the obstacle's position: no obstacle, low obstacle, high obstacle, and double obstacle, as shown in Fig. 2(b). Acoustic spectra up to 10 kHz (in dB SPL) are considered.

The acoustic spectra for a vibration of the vocal cords forced at 5 Hz and 15 Hz are presented in Fig. 6, in the left and right columns, respectively. As in the case without an acoustic source, a harmonic peak around 4100 Hz can be observed. However, the peaks observed at lower frequencies are masked by the appearance of a low-frequency component between 0 and 1000 Hz, which may indicate disturbance due to the interaction between the imposed oscillation and the generated vortices.

Many other harmonic peaks appear between 2000 and 7500 Hz, suggesting a nonlinear interaction between the flow affected by the vocal cord replicas and the rest of the setup. It should be noted that these effects are not observed for the lowest volumetric flow rate of 50 L/min, ruling out the possibility of sound originating from the motor powering the vocal cord replicas.

Once again, the high and low obstacles provide similar results due to their comparable dimensions. The spectrum of the double obstacle is also very close to the case without vocal cords for a flow rate of 250 L/min, with a broad low-to-mid frequency component between 100 and 2000 Hz and a higher frequency range between 3000 and 8000 Hz. However, for a lower flow rate of 150 L/min, the high-frequency component appears to attenuate more than without the replicas.

The oscillation frequency of the replicas does not seem to have a major effect on the acoustic field. It is possible that a higher oscillation frequency, closer to human vocal cords (between 100 and 200 Hz), would have a greater impact on the flow, and that the frequencies used here may be too low. To observe results, it would therefore be advisable to use a higher excitation frequency or employ deformable models whose vibration frequencies are closer to those observed in humans.
<figure><img src="image_8.png" /><figcaption>Figure 6 – Frequency spectra of microphone M1 as a function of flow rate in L/min with oscillations of vocal cord replicas at 5 Hz (left) and 15 Hz (right) for an elliptical constriction (a). Without obstacle and with an obstacle placed (b). at the top (b). at the bottom (d). at both top and bottom.</figcaption></figure>

4. Conclusion

Experiments were conducted to reproduce fluid-structure-acoustic interactions in a controlled environment. For this, a rigid tube was used, integrating two types of constrictions (circular or elliptical) placed downstream of a rigid replica of vocal cords under forced oscillations. Three obstacle configurations, mimicking teeth, were also tested downstream of the constriction: one obstacle at the top of the flow, one at the bottom, and a combination of both (bottom first, then top).

Pressure measurements within the conduit were compared to two models: one based on boundary layer theory and the other accounting for the viscous effects of the fluid. A good agreement with the boundary layer model was observed for the circular constriction (<10% discrepancy), while the elliptical
constriction showed a significant deviation (>10%), indicating a notable divergence from the model's predictions.

Acoustic measurements taken in an anechoic chamber at various positions revealed a significant impact of the three obstacle configurations around 4.1 kHz. Furthermore, the configuration combining both obstacles showed a marked influence on high frequencies (6-10 kHz). Preliminary measurements of directivity suggest that the most significant effects also occur with this double configuration, notably with a high-frequency component absent on the microphone located below the tube containing a cylindrical constriction.

Finally, experiments conducted with the rigid vocal cord replicas under forced oscillations revealed a significant influence on the number of harmonic frequency peaks when no obstacle was present. However, this effect appears to be largely attenuated once an obstacle is added. Furthermore, no influence of the excitation frequency of the replicas (5 and 15 Hz) was observed.

These preliminary results suggest exploring higher excitation frequencies or using deformable vocal cord replicas to better replicate human physiological conditions.

## Acknowledgements

This project was funded by the CNRS through the 80|Prime (InteracSon) project and by the National Research Agency (Full3DTalkingHead, ANR-20-CE23-0008-03).

## REFERENCES

1. Shadle C. H. The acoustics of fricative consonants, PhD thesis, *Massachusetts Institute of Technology* (1985)

2. Van Hirtum A., Pelorson X., Estienne O., Experimental validation of flow models for a rigid vocal tract replica *Journal of Acoustical Society of America*, 130, 2128–2138 (2011)

3. Ruty N., Pelorson X., Bailly L., Van Hirtum A., Hirschberg A. Modélisation théorique et validation expérimentale des interactions fluide/structure dans le larynx. Applications aux pathologies de la voix. *18ème Congrès Français de Mécanique* (2007)

4. Misun V, Svancara P, Vasek M., Experimental Analysis of the Characteristics of Artificial Vocal Folds, *Journal of Voice*, 25, 308-318 (2011)

5. Van Hirtum A., Fujiso Y. Insulation room for aero-acoustic experiments at moderate Reynolds and low Mach numbers, *Applied Acoustics*, 73, 72-77 (2012)

6. Van Hirtum A. Analytical modeling of constricted channel flow, *Mechanics Research Communications*, 83, 53-57 (2017)

7. Jongman A., Wayland R., Wong S., Acoustic characteristics of English fricatives, *Journal of Acoustical Society of America*, 108, 1252-1263 (2000)