Numerical Investigation of the Evolution of Vortex Instability in a 2-D Compressible Flow over a Cylinder

Abstract

This paper presents a computational fluid dynamics (CFD) study of 2-D flow over a cylinder at a Mach number of 0.3 and diameter based Reynolds numbers ranging between 50 and 1000. The flow simulation was marched in time from an impulsive start and reveals the evolution of vortex instability. After the cylinder has traveled between 100 and 1000 diameters, alternate vortex shedding begins, and a von Karman vortex street develops in the wake. Throughout the initial transient of the flow, the lift coefficient shows periodic oscillation with steady amplitude growth rates from machine precision until periodic vortex shedding is reached, and a distinct frequency shift is observed at the onset of vortex shedding at higher Reynolds numbers. The numerical algorithm is based on a finite volume description of the unsteady, compressible Navier Stokes equations. The inviscid subset of the equations is modeled according to the total variation diminishing (TVD) principle with the numerical viscosity control parameter set to zero. No turbulence modeling was implemented, since the flow is below the transition Reynolds number of 300,000. The accuracy of the scheme is second order in space and first order in time.