6.5 Boundary layer separation

Boundary layers provide the main source of vorticity for turbulence as discussed in Sec. 6.4 . A boundary layer breaks away from the boundary when it reaches the end of the surface or by separation before reaching the end. Vorticity and turbulence are thereby swept into regions of fluid away from solid boundaries.

Flow around a cylinder illustrates boundary layer separation, vorticity and turbulence. The fluid flows at uniform velocity eqn upstream of the cylinder. It decelerates to stagnation, eqn, at point A on the surface (in the eqn-normal direction).

High pressure at A introduces a favourable pressure gradient eqn which increases the flow speed eqn around the cylinder towards B, developing a boundary layer in the process.

PICT\relax \special {t4ht=

The flow reaches a peak speed at B, then decelerates over the downstream side of the cylinder. The adverse pressure gradient eqn causes eqn to decrease. At some point C, the velocity gradient can reach eqn. Beyond C, the boundary layer can separate such that eqn along its profile, see point D.

Boundary layer separation in a cylinder depends on Reynolds number eqn, Eq. (2.68 ), using eqn and eqn. For eqn, there is no separation, with the flow exhibiting a pattern downstream that mirrors the upstream flow.6

For eqn, the boundary layer separates with its vorticity sustaining a pair of vortices attached to the rear of the cylinder.

PICT\relax \special {t4ht=

At eqn, vorticity is released downstream as vortices break off from the cylinder in a periodic manner known as the Kármán vortex street, shown above.

At eqn, the vorticity starts to become become chaotic, with turbulence beginning to appear in the vortices. At eqn, the entire wake region becomes turbulent.

The frequency of vortex shedding is characterised by another dimensionless number from Eq. (2.68 ), the Strouhal number eqn. For eqn, experiments show7 eqn, where eqn is the period at which the vortex pattern repeats.

6Sadatoshi Taneda, Experimental investigation of the wakes behind cylinders and plates at low Reynolds numbers, 1956.
7Vincenc Strouhal, Über eine besondere Art der Tonerregung, 1878 and Anatol Roshko, On the development of turbulent wakes from vortex streets, NACA Report 1191, 1954.

Notes on CFD: General Principles - 6.5 Boundary layer separation