Numerical Simulation of Unsteady Compressible Flow in Convergent Channel: Pressure Spectral Analysis

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 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 Mac-Cormack 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 numerical results of unsteady flows in the channel are presented for inlet Mach number $M_{\infty }=0.012$, Reynolds number ${\text{Re}}_{\infty }=\mathrm{4481,}$ and the wall motion frequency 100 Hz.