Flows in convergent channel: comparison of numerical results of different mathematical models

Abstract

This study deals with numerical solution of 2D unsteady flow of compressible and incompressible viscous fluid in convergent channel for low inlet airflow velocity. Three mathematical models based on system of Navier-Stokes equations for laminar flow are presented and numerical results of the models in the channel are compared. 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 numerical solution is implemented using the finite volume method and the predictor-corrector MacCormack scheme with Jameson 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 numerical results, acquired from a developed program, are presented for inlet velocity \(\hat{u}_{\infty }=4.12\) ms\(^{-1}\) and Reynolds number Re\(_{\infty } = 4 \times 10^3\) and the wall motion frequency 100 Hz.