Numerical solutions of unsteady flows with low inlet Mach numbers

摘要

This study deals with a numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The channel is a simplified model of the glottal space in the human vocal tract and the flow can represent a model of airflow coming from the trachea, through the glottal region with periodically vibrating vocal folds, and to the human vocal tract. The flow is described by a system of Navicr-Stokes equations for laminar flows. The numerical solution is implemented using the finite volume method (FVM) and the predictor-corrector MacCormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. Due to the unsteadiness of the grid (motion of the grid), the basic system of conservation laws is considered in a changed form using the Arbitrary Lagrangian-Eulerian (ALE) method. The numerical solution has been carried out for a symmetric and a non-symmetric flow field in two computational domains. The numerical results for unsteady flows in the channel are presented for inlet Mach number M_∞ = 0.012, Reynolds number Re = 5 × 10~3 and wall motion frequency 100Hz. The authors present the numerical solution and simulations of flow fields in the channel, acquired from a program that has been developed exclusively for this purpose. The reason for using a numerical simulation was the lack of data from experimental results of flows through the glottal region, and the capability of such simulation to model the problem.