The influence of glottal cross-section shape on theoretical flow models

Abstract

Physical and mathematical phonation models commonly rely on a quasi-one-dimensional flow model. The assumption of quasi-one-dimensional flow through a glottis with fixed length is analyzed for different cross-section shapes: Circle, rectangle, ellipse, and circular segment. A simplified flow model is formulated which accounts for kinetic losses, viscosity, and cross-section shape. It is seen that the cross-section shape cannot be neglected since it alters boundary layer development and hence the viscous contribution to the pressure drop across the glottis. The commonly applied quasi-one-dimensional flow model is shown to be inaccurate, indicating the potential benefit of taking into account the cross-section shape.

Influence of glottal cross-section shape on phonation onset

“…It was shown that varying the cross-section shape alters the pressure distribution within a glottal constriction significantly, 20% up to 100% when comparing to the quasione-dimensional flow solution. 23 This amounts to the same order of magnitude as well-studied flow events such as the position of flow separation. 14,15,24 Therefore, applying a flow model for which the viscous contribution depends on the cross-section shape potentially affects the outcome of physical or mathematical models of phonation such as the phonation onset pressure threshold Pon.…”

“…The pressure distribution Pðx; tÞ for x 0 x x s is obtained by integration of (1) 22,23 and results in a quadratic equation of volume flow rate U as follows:…”

“…with upstream pressure P u , downstream pressure P d , dynamic viscosity of air l ¼ 1:8 Â 10 À5 Pa s, b is introduced to express the viscous contribution to the pressure drop and depends on the cross-section shape as given in Table I. 23 For each cross section shape, b is obtained from the analytical solution-using separation of variables-of a classical Dirichlet problem representing the reduced streamwise momentum equation describing viscous channel flow. 22 In addition, the volume flow rate U is estimated as…”