I.
Theoretical Transitions Between Flow Patterns
A
cylinder with a diameter D is placed in a flow with a velocity U
in the direction of the x-axis, as shown on figure 1 below :
Figure 1 :
Flow past the cylinder
The
Reynolds number Re = UD/n characterizes the flow pattern past the cylinder, and the following transitions have
been experimentally observed
(e.g. see figure 2) :
- For
Re lower than 4, the flow past the cylinder remains uniform with
both an
upstream/downstream
symmetry and a
right-hand/left-hand one. This flow pattern is called
a creeping flow.
- From
Re = 4 to a critical Reynolds
number approximatively equal to 40, vortices appear in
the immediate wake of
the cylinder, yet they stay closely attached to it. This area is called the
recirculation zone, since the two vortices rotate in
opposite senses, and the x-axis symmetry
is the only one to
remain. Furthermore, the size of the
vortices increases with the Reynolds number.
- For
Reynolds numbers
lower than 200, the flow
downstream the cylinder becomes unsteady, even though all the imposed
conditions are being held steady. Two rows of vortices appear on
either sides of the wake : all those on one side rotates
in the same sense, whereas all those on the opposite side
rotate in the opposite sense. It can be noticed that the flow
remains bi-dimensional.This new pattern turns out to be periodic, and
the period can be calculated by
determining the length of time between the formation of
two vortices. This
period increases with the Reynolds number, and according to the
dependency of the Strouhal number on this adimensional
variable.
- For
Reynolds number greater than 200, the flow looses its
bi-dimensional characteristics, and for Re = 400, vortices themselves
become turbulent from their very point of generation.
- For
higher values of Reynolds number, vortices loose their
regular shape and their coherency, therefore
visualization is difficult.
Figure 2 :
Streaklines in the wake behind a cylinder for different Reynolds
numbers.
Figure
3 : Vortices in the wake behind the
cylinder (click on picture to animate)