# Simulation and Instability Investigation of the Flow around a Cylinder between Two Parallel Walls

## TL;DR

This study uses CFD to analyze flow around a cylinder between parallel walls at Re=40 and 100, investigating vortex formation and flow instability mechanisms with energy gradient theory.

## Contribution

It applies energy gradient theory to elucidate flow instability and vortex street formation in confined cylinder flows, providing new insights into turbulence transition mechanisms.

## Key findings

- Flow instability originates from shear layer interactions and absolute instability.
- Attached rear eddies do not influence flow instability in steady conditions.
- Energy gradient theory effectively explains flow stability and vortex formation.

## Abstract

The two-dimensional flows around a cylinder between two parallel walls at Re=40 and Re=100 are simulated with computational fluid dynamics (CFD). The governing equations are Navier-Stokes equations. They are discretized with finite volume method (FVM) and the solution is iterated with PISO Algorithm. Then, the calculating results are compared with the numerical results in literature, and good agreements are obtained. After that, the mechanism of the formation of Karman vortex street is investigated and the instability of the entire flow field is analyzed with the energy gradient theory. It is found that the two eddies attached at the rear of the cylinder have no effect on the flow instability for steady flow, i.e., they don't contribute to the formation of Karman vortex street. The formation of Karman vortex street originates from the combinations of the interaction of two shear layers at two lateral sides of the cylinder and the absolute instability in the cylinder wake. For the flow with Karman vortex street, the initial instability occurs at the region inner a vortex downstream of the wake and the center of a vortex firstly loses its stability inner a vortex. For pressure driven flow, it is confirmed that the inflection point on the time-averaged velocity profile leads to the instability. It is concluded that the energy gradient theory is potentially applicable to study the flow stability and to reveal the mechanism of turbulent transition.

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Source: https://tomesphere.com/paper/1902.02460