Three-dimensional effects in low Reynolds number flow around confined cylinders

Abstract

An experimental and numerical study is carried out to investigate three-dimensional effects in the flow of Newtonian fluids around confined cylinders, for Reynolds numbers below 40 and aspect ratios between 1 and 16. Experiments rely on flow visualizations and detailed velocity measurements by PIV, while predictions were carried out using a finite volume method. Velocity peaks near the side walls were found to occur at all Reynolds numbers and for AR > 3. At low Reynolds numbers these velocity peaks are due to the excessive braking role of the side wall, which forces a local fluid acceleration for mass conservation that the very small diffusive spanwise-streamwise momentum flux x (xz) is unable to smooth out. This disappears when the aspect ratio is reduced and by implication the xz stress increases strongly. Inertia counteracts the role of this diffusive momentum flux so much that at AR = 1 there are still velocity peaks when Re = 40. When inertia is strong there is flow separation in the wake of the cylinder, but this separated flow region is open. The fluid particles near the side wall, but not too near, are better able to sustain the adverse streamwise pressure gradient and recover better the pressure as they flow across the cylinder. Consequently, the separated flow region is shorter and the pressure is higher in that region leading to a secondary spiraling spanwise flow from the side wall to the centre plane. The fluid exits the recirculation region at the centre plane and enters it at the velocity peak region near the wall, which is being fed by fluid coming from the neighbour region located to the inner side of the duct. This has a positive feedback enhancing the velocity peaks. At the wall itself friction extracts so much energy from the fluid particles that these are less able to sustain the adverse streamwise pressure gradient and the separated flow length increases significantly.