Numerical Assessment of the Quasi-Steady Approximation in Glottal Air Flow

Abstract

Voice production involves air flow through the glottis and its interaction with the deformable vocal folds. The quasi-steady approximation involves modeling the complex unsteady flow through the glottis as a sequence of steady flows through rigid orifices, which is numerically less expensive. Theoretical and experimental assessments of the quasi-steady approximation have been attempted, but contradictions in previously reported results prompt further analysis. To investigate the validity of the quasi-steady approximation, a two-dimensional dynamic simulation of air flow through an idealized glottal orifice with moving walls was performed for different pressure gradients and oscillation frequencies. A series of steady flow simulations for configurations of the vocal folds and flow boundary conditions that instantaneously coincide with data from the dynamic simulations were performed. Dynamic and static simulations were performed using the COMSOL multiphysics® software. Both stationary and non-stationary geometries were created based on the M5 model with the orifice profile alternating between convergent and divergent included angles (−40° to 40°). The distance between the vocal cord tip and the centerline was established to maintain a constant vocal fold volume, thereby eliminating spurious monopole sources. The results include the fluid flow rate, the pressure drop across the glottis, the shear stress on the glottis walls, and the orifice coefficient. Comparison between these variables for both dynamic and static sets of data allowed the assessment of the accuracy of the quasi-steady approximation to predict the fluid flow in the glottis. The importance of time-dependent terms over short intervals during glottal opening and closure was scrutinized. The results may contribute to the general goal of creating flow models that are optimal for laryngeal orifice coefficient and sound pressure determination.