8.4 Flow around a cylinder

Flow around a cylinder was used as an example of boundary layer separation in Sec. 6.5 . It showed an image of vortices shedding from the cylinder in a periodic manner, known as the Kármán vortex street.

The image comes from a CFD simulation in two dimensions, representative of a cylinder of infinite axial length, using the principal parameters: cylinder diameter eqn; freestream velocity eqn in the eqn-direction; and, fluid kinematic viscosity eqn . The corresponding Reynolds number eqn , which falls within the laminar flow regime.

The computational mesh used in the simulation is described in Sec. 8.3 . The centre height of the cells adjacent to the cylinder was eqn, corresponding to a calculated eqn.

The simulation used the transient solution algorithm in Sec. 5.19 , solving for momentum conservation for an incompressible fluid, with eqn and constant eqn. No energy equation was solved and no turbulence modelling was required since the flow was laminar.

The freestream boundary conditions from Sec. 4.16 were applied to eqn and eqn over the entire external boundary, with reference values eqn, eqn and eqn. The no-slip condition, eqn and eqn, was applied on the cylinder boundary.

The simulation ran for eqn with a time step eqn using recommended numerical schemes from Sec. 3.23 . Oscillations began in the wake of the cylinder at eqn, soon leading to shedding of vortices which reached a stable pattern at eqn.

The following figure, shaded by eqn, shows the slower-moving vortices as the darker structures which propagate downstream of the cylinder.

PICT\relax \special {t4ht=

The repeated vortex shedding causes oscillations in the force eqn of the fluid on the cylinder. The force is calculated as the sum of viscous and pressure forces acting on the cylinder patch faces (eqn), in kinematic units eqn (from kinematic eqn and eqn) by

 X X X f = Sf ☐☐☐ = Sf (pI ☐☐☐) = Sfp Sf ☐☐☐: f f f \relax \special {t4ht=
The dimensionless lift coefficient eqn is shown below, calculated from: the eqn-component of the force is eqn, where eqn is the unit vector in the eqn-direction; and, the projected frontal area eqn of the cylinder.

PICT\relax \special {t4ht=

The oscillation period eqn corresponds to a Strouhal number eqn, consistent with published data.1

1Christoffer Norberg, Flow around a circular cylinder: Aspects of fluctuating lift, 2001.

Notes on CFD: General Principles - 8.4 Flow around a cylinder