Simulation of unsteady compressible flow in a channel with vibrating walls - Influence of the frequency

Abstract This study deals with the 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 to the human vocal tract. The flow is described by the system of Navier–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 motion of the grid, the basic system of conservation laws is considered in the Arbitrary Lagrangian–Eulerian (ALE) form. The authors present the numerical simulations of flow fields in the channel, acquired from a program developed exclusively for this purpose. The numerical results for unsteady flows in the channel are presented for inlet Mach number M ∞  = 0.012, Reynolds number Re ∞  = 4.5 × 10 3 and the wall motion frequency 20 and 100 Hz.