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

Abstract

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.

On the viscous-inviscid interaction of the flow passing through the glottis

“…The Reynolds number of glottal flow is of the order of 1,000 [5], implying that a thin boundary layer is formed near the surface of the vocal folds. When the boundary layer is thin enough, it behaves like a discontinuity plane of the velocity field, i.e., the vortex sheet.…”

“…Flow through the glottis can be assumed to be incompressible, since the flow velocity is sufficiently lower than the sound velocity [5]. The flow is also assumed to be one-dimensional for the sake of mathematical convenience, although this is slightly less accurate than a two-dimensional model.…”

“…On the other hand, a constitutive approach has been taken in the simulation of phonation based on the boundary-layer approximation [5][6][7][8]. The theory implies that the bulk of the flow, i.e., the core flow, can be assumed to be inviscid and irrotational.…”

“…To understand the physical mechanism of voice production, the dynamic behavior of flow passing through the glottis has been studied extensively incorporating the basic idea of flow separation and free jet formation [1][2][3][4][5][6]. The Reynolds number of glottal flow is of the order of 1,000 [5], implying that a thin boundary layer is formed near the surface of the vocal folds.…”

A water hammer analysis of pressure and flow in the voice production system

“…The flow picture through glottis and supraglottal tract used in the now classic two-mass model of Ishizaka and Flanagan [12] is the result of a considerable number of assumptions that, since then, have been thoroughly revisited and reconsidered. Much effort has been devoted in particular to correct the glottal flow model, which needs to capture flow separation and turbulent dissipation of the jet that is formed at the glottal exit [13,14]. On the other hand, the vocal tract is satisfactorily described in terms of linear acoustical properties.…”