A Avraham Hirschberg

Theoretical and experimental study of quasisteady‐flow separation within the glottis during phonation. Application to a modified two‐mass model

Most flow models used in numerical simulation of voiced sound production rely, for the sake of simplicity, upon a certain number of assumptions. While most of these assumptions constitute reasonable first approximations, others appear more doubtful. In particular, it is implicitly assumed that the air flow through the glottal channel separates from the walls at a fixed point. Since this assumption appears quite unrealistic, and considering that the position of the separation point is an important parameter in phonation models, in this paper a revised fluid mechanical description of the air flow through the glottis is proposed, in which the separation point is allowed to move. This theoretical model, as well as the assumptions made, are validated using steady- and unsteady-flow measurements combined with flow visualizations. In order to evaluate the effective impact of the revised theory, we then present an application to a simple mechanical model of the vocal cords derived from the classical two-mass model. As expected, implementation of a moving separation point appears to be of great importance for the modeling of glottal signals. It is further shown that the numerical model coupled with a more realistic description of the vocal cord collision can lead to signals surprisingly close to those observed in real speech by inverse filtering.

Self-sustained aero-acoustic pulsations in gas transport systems: Experimental study of the influence of closed side branches

Abstract A theoretical model is proposed for the aero-acoustic sources responsible for low-frequency self-sustained pulsations in pipes with closed side branches. The theory successfully explains the acoustic and hydrodynamic conditions for resonance in experiments with a single side branch. It also predicts the order of magnitude of the pulsation amplitude and the effect of losses due to friction and radiation. A high pulsation level, with acoustic velocities of the order of magnitude of the main flow, is observed in a double side branch set-up when the edges at the junctions are rounded. When in the double side branch set-up the rounded upstream edge of the second T-joint is replaced by a sharp edge, the pulsation amplitude is reduced by a factor of five. This effect, which can be explained with the theory of vortex sound, leads us to the design of spoilers. Various “spoilers” have been tested in scale model and full scale experiments. Some of these reduce the pulsation level by 40 dB.

Damping and reflection coefficient measurements for an open pipe at low Mach and low Helmholtz numbers

The propagation of plane acoustic waves in smooth pipes and their reflection at open pipe terminations have been studied experimentally. The accuracy of the measurements is determined by comparison of experimental data with results of linear theory for the propagation of acoustic waves in a pipe with a quiescent fluid. The damping and the reflection at an unflanged pipe termination are compared. In the presence of a fully developed turbulent mean flow the measurements of the damping confirm the results of Ronneberger & Ahrens (1977). In the high-frequency limit the quasi-laminar theory of Ronneberger (1975) predicts accurately the convective effects on the damping of acoustic waves. For low frequencies a simple theory combining the rigid-plate model of Ronneberger & Ahrens (1977) with the theoretical approach of Howe (1984) yields a fair prediction of the influence of turbulence on the shear stress. The finite response time of the turbulence near the wall to the acoustic perturbations has to be taken into account in order to explain the experimental data. The model yields a quasi-stationary limit of the damping which does not take into account the fundamental difference between the viscous and thermal dissipation observed for low frequencies. Measurements of the nonlinear behaviour of the reflection properties for unflanged pipe terminations with thin and thick walls in the absence of a mean flow confirm the theory of Disselhorst & van Wijngaarden (1980), for the low-frequency limit. It appears however that a two-dimensional theory such as proposed by Disselhorst & van Wijngaarden (1980) for the high-frequency limit underestimates the acoustical energy absorption by vortex shedding by a factor 2.5. The measured influence of wall thickness on the reflection properties of an open pipe end confirms the linear theory of Ando (1969). In the presence of a mean flow the end correction δ of an unflanged pipe end varies from the value at the high-Strouhal-number limit of δ/ a = 0.61, with a the pipe radius, which is close to the value in the absence of a mean flow given by Levine & Schwinger (1948) of δ/ a = 0.6133, to a value of δ/ a = 0.19 in the low-Strouhal-number limit which is close to the value predicted by Rienstra (1983) of δ/ a = 0.26. The pressure reflection coefficient is found to agree with the theoretical predictions by Munt (1977, 1990) and Cargill (1982 b ) in which a full Kutta condition is included. The accuracy of the theory is fascinating in view of the dramatic simplifications introduced in the theory. For a thick-walled pipe end and a pipe terminated by a horn the end correction behaviour is similar. It is surprising that the nonlinear behaviour at low frequencies and high acoustic amplitudes in the absence of mean flow does not influence the end correction significantly. The aero-acoustic behaviour of the pipe end is dramatially influenced by the presence of a horn. In the presence of a mean flow the horn is a source of sound for a critical range of the Strouhal number. The high accuracy of the experimental data suggests that acoustic measurements can be used for a systematic study of turbulence in unsteady flow and of unsteady flow separation.

Unsteady flow through in-vitro models of the glottis

The unsteady two-dimensional flow through fixed rigid in vitro models of the glottis is studied in some detail to validate a more accurate model based on the prediction of boundary-layer separation. The study is restricted to the flow phenomena occurring within the glottis and does not include effects of vocal-fold movement on the flow. Pressure measurements have been carried out for a transient flow through a rigid scale model of the glottis. The rigid model with a fixed geometry driven by an unsteady pressure is used in order to achieve a high accuracy in the specification of the geometry of the glottis. The experimental study is focused on flow phenomena as they might occur in the glottis, such as the asymmetry of the flow due to the Coanda effect and the transition to turbulent flow. It was found that both effects need a relatively long time to establish themselves and are therefore unlikely to occur during the production of normal voiced speech when the glottis closes completely during part of the oscillation cycle. It is shown that when the flow is still laminar and symmetric the prediction of the boundary-layer model and the measurement of the pressure drop from the throat of the glottis to the exit of the glottis agree within 40%. Results of the boundary-layer model are compared with a two-dimensional vortex-blob method for viscous flow. The difference between the results of the simpiflied boundary-layer model and the experimental results is explained by an additional pressure difference between the separation point and the far field within the jet downstream of the separation point. The influence of the movement of the vocal folds on our conclusions is still unclear.

Shock waves in trombones

Based on physical models of musical instruments and of the human voice, a new generation of sound synthesizers is born: virtual instruments. The models used for wind instruments are simple feedback loops in which a nonlinear sound source drives a linear filter representing the pipe of the instrument. While very rewarding musical sounds have been obtained with these models, it has become obvious that some essential phenomena escape such a description. In particular the brightness of the sound generated by trombones is expected to be due to the essential nonlinearity of the wave propagation in the pipe. At fortissimo levels this leads to shock wave formation observed in our experiments both from pressure measurements and flow visualization. A modest modification of the physical model could already take this phenomenon into account. The key idea is that the nonlinear effect is essential for the transfer of sound from the source toward the listener, but can be ignored in a model of the generation of the pipe ...

An in vitro setup to test the relevance and the accuracy of low-order vocal folds models.

An experimental setup and human vocal folds replica able to produce self-sustained oscillations are presented. The aim of the setup is to assess the relevance and the accuracy of theoretical vocal folds models. The applied reduced mechanical models are a variation of the classical two-mass model, and a simplification inspired on the delayed mass model for which the coupling between the masses is expressed as a fixed time delay. The airflow is described as a laminar flow with flow separation. The influence of a downstream resonator is taken into account. The oscillation pressure threshold and fundamental frequency are predicted by applying a stability analysis to the mechanical models. The measured frequency response of the mechanical replica together with the initial (rest) area allows us to determine the model parameters (spring stiffness, damping, geometry, masses). Validation of theoretical model predictions to experimental data shows the relevance of low-order models in gaining a qualitative understanding of phonation. However, quantitative discrepancies remain large due to an inaccurate estimation of the model parameters and the crudeness in either flow or mechanical model description. As an illustration it is shown that significant improvements can be made by accounting for viscous flow effects.

Self-sustained oscillations in a closed side branch system

Self-sustained oscillations of the flow in a closed side branch system due to a coupling of vortex shedding with acoustical resonances are considered. The configuration consists of two closed side branches of same length placed opposite to each other along a main pipe. This is called a cross-junction. Numerical simulations, based on the Euler equations for two-dimensional inviscid and compressible flows, are performed. As the radiation into the main pipe is negligible at the resonance frequency, this acoustically closed system is a good test-case of such Euler numerical calculations. The numerical results are compared to acoustical measurements and flow visualization obtained in a previous study. Depending on the flow conditions, the predicted pulsation amplitudes are about 30–40% higher than the measured amplitudes. This is partially due to the absence of visco-thermal dissipation in the numerical model but also to the effect of wall vibrations in experiments. A simple analytical model is proposed for the prediction of the pulsation amplitudes. This model is based on Nelsons representation of the shear layer as a row of discrete vortices convected at constant velocity from the upstream edge towards the downstream edge. When the downstream edge is sharp, this results in a spurious interaction between the singularity of the vortices and of the edge flow. This artefact is partially compensated by suppressing the singularity of the acoustical flow at the edge, or when a junction with rounded edges, as found in engineering practice, is considered. In spite of its crudeness, the analytical model provides a fair prediction (within 30%) which makes it useful for engineering applications.

Quasisteady aero-acoustic response of orifices

The low frequency response of orifices (slit, circular diaphragm, and perforated plate) in the presence of mean flow is well predicted by a quasisteady theory. A refinement is brought to the theory by considering a Mach number dependent vena contracta coefficient. The measurements of the vena contracta coefficient of a slit agree well with the simple analytical expression existing in the case of the Borda tube orifice. The measured scattering matrix coefficients do not depend strongly on the geometry of the element. If the frequency is increased the moduli remain relatively unaffected while the arguments exhibit a complex behavior which depends on the geometry. From these considerations an anechoic termination efficient at high mass flow is designed.

Influence of collision on the flow through in-vitro rigid models of the vocal folds

Measurements of pressure in oscillating rigid replicas of vocal folds are presented. The pressure upstream of the replica is used as input to various theoretical approximations to predict the pressure within the glottis. As the vocal folds collide the classical quasisteady boundary layer theory fails. It appears however that for physiologically reasonable shapes of the replicas, viscous effects are more important than the influence of the flow unsteadiness due to the wall movement. A simple model based on a quasisteady Bernoulli equation corrected for viscous effect, combined with a simple boundary layer separation model does globally predict the observed pressure behavior.

Flow Induced Pulsations in Gas Transport Systems: Analysis of the Influence of Closed Side Branches

A theoretical analysis is presented of the low frequency aero-acoustic behavior of closed side branches along a gas transport pipe. The theory predicts the hydrodynamic conditions for moderate and strong pulsations. A model is proposed which predicts the order of magnitude of the power generated by the aero-acoustic source. The theoretical analysis leads to the design of spoilers which reduce the pulsation level by 30 to 40 dB. The results obtained by theoretical analysis and model experiments (Reynolds number 10-6) have been confirmed in full scale tests (Reynolds number 10-8).