8.11 Examples
261
shear force over the cylinder surface. Values obtained using results on all four
grids are shown in Fig. 8.18; the value obtained using Richardson extrapolation is also indicated. Second order convergence is obtained, as expected.
The discretization error on the finest grid was approximately 0.02%. The lift
coefficient converges in the same way; its extrapolated value is Cl = 0.0105.
The lift coefficient is thus about 530 times smaller than the drag coefficient.
Time
Grid 4 -
Grld 3 -----Grid 2
-1.5 I
I
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Time
Fig. 8.19. Variation of the coefficients of lift (above) and drag (below) on a cylinder
in a channel at Re = 100, as functions of time (results on the three finest grids are
shown); from Muzaferija et al. (1995)
When the Reynolds number is increased beyond a critical value (which
for a cylinder in infinite stream is about 40), the flow becomes unsteady
and vortices are shed from the cylinder. Flow at Re = 100 was investigated
by Muzaferija et al. (1995). A second-order three time-level implicit scheme
was used for time integration. Starting impulsively from rest, the flow goes
through a development stage and eventually becomes periodic. Due to vortex
shedding, both the drag and lift forces oscillate. In a symmetric configuration the lift coefficient would oscillate around zero; in this case, however, it