Unsteady compressible flows in channel with varying walls

Abstract

This study deals with numerical solution of a 2D and 3D unsteady flows of a compressible viscous fluid in 2D and 3D 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, nearly closing the channel during oscillations. The channels shape is a simplified geometry of the glottal space in the human vocal tract. Goal is numerical simulation of flow in the channels which involves attributes of real flow causing acoustic perturbations. The system of Navier-Stokes equations closed with static pressure expression for ideal gas describes the unsteady laminar flow of compressible viscous fluid. The numerical solution is implemented using the finite volume method and the predictor-corrector MacCormack scheme with artificial viscosity using a grid of quadrilateral cells. The unsteady grid of quadrilateral cells is considered in the form of conservation laws using Arbitrary Lagrangian-Eulerian method. The application of developed method for numerical simulations of flow fields in the 2D and 3D channels, acquired from a developed program, are presented for inlet velocity u=4.12 m/s, inlet Reynolds number Re=4481 and the wall motion frequency 100 Hz.