Numerical study of mechanics of phonation

Abstract

Human phonation is a highly complex process that involves three-way interactions between fluid dynamics of the glottal flow, acoustic waves in the vocal tract, and structural mechanics of the vocal folds. Due to its complex nature, the underlying phonation mechanism is yet to be fully understood. Available clinical measurements are often insufficient in diagnosing the pathology of voice disorders and the severity of them. Since in vivo measurements of glottal flows are difficult due to the space limitations of the larynx, numerical simulations and experiments using scaled-up models are often used to study the behaviors of vocal folds, glottal flows, and sound generation/propagation. There have been a variety of numerical studies on the coupled system. However, so far, there are limited studies that aim at a quantitative description of the overall process using a fully-coupled aeroelastic-aeroacoustic approach. To accomplish this, two major challenges must be overcome: 1. Appropriate models should be employed to resolve the coupled system that requires both fluid-structure interaction and aeroacoustics. A suitable FSI scheme is needed to identify the interface accurately to capture the wave motion of the vocal fold surface, i.e., mucosal waves, especially at the glottal gap which can be very small when the glottis is closing. The aeroacoustic model should be able to resolve both fluid dynamics and acoustics. 2. It is difficult to quantify the acoustic and energy efficiency in the phonation process since the contributions of each part in the aeroacoustic sources and the energy budget are not directly measurable and their relationships remain unclear. Therefore, an effective tool is desired to provide a unified quantification of each contribution and reveal the physical significance and the underlying mechanism of phonation. To address the above issues, first, a coupled fluid-structure-acoustic finite element algorithm is developed based on the immersed finite element method (IFEM). The algorithm is enhanced in several aspects to overcome the numerical difficulties mentioned in regards to accurate modeling of fluid-structure-acoustics. A slightly-compressible fluid model is developed to capture the nonlinear coupling of aeroacoustics. Spalart-Allmaras turbulence model is implemented to resolve subgrid-scale vortices in the glottal jets. Non-reflecting boundary conditions using the Perfectly Matched Layers (PML) are strategically applied to eliminate the spurious reflection of acoustic waves that would otherwise appear on non-treated numerical boundaries. A sharp FSI interface algorithm is developed and employed to accommodate the vocal fold surface waves. Additionally, A grid study in both temporal and spatial resolution is done to study their impact on the solution. To characterize the aeroacoustic source strengths and phonatory flow, a control volume framework is developed to quantify the contributions of each part of the aeroacoustic sources as well as the energy budget in terms of volume integrals in the larynx region. Using the control volume approach, the significance of all the quantities present in the aeroacoustic sources and mechanical energy balance equations can be directly compared to each other. This control volume analysis is performed on-the-fly in the numerical simulation of the coupled system. This research can help us understand the intrinsic physics of the complex behavior behind human phonation, which may in the future help develop novel diagnostic measurements of voice disorder.