Geoscience Reference
In-Depth Information
shows the location of the vertical measuring planes and the images dimensions
relatively to the cylinder.
4.4 Results and Discussion
The dimensions of the horseshoe vortex were estimated based on the vorticity
maps, as shown in Fig.
36
, being the vortex equivalent diameter
D
v
determined
by
D
V
¼
a
p
. This procedure was applied to the greatest instantaneous vortex
observed in each test and to the equivalent vortex, which is characterized by the
separated flow region that shows a circulation pattern with nonzero vorticity and
resulting from the time-averaged vortical instantaneous structures registred in that
flow region.
The time-averaged vorticity map and streamlines obtained before the beginning
of the scour hole are shown in Fig.
37
. Figure
38
shows instantaneous vorticity
maps in two vertical positions of the measuring plane.
The time-averaged vorticity map shows the presence of an equivalent horseshoe
vortex. It is observed that the vortex location, relatively to the cylinder, depends on
the boundary layer thickness (details in Nogueira et al.
2008
). With an increasing
thickness of the boundary layer, the longitudinal dispersion of the vortex location
also increases (cf. Baker
1980
). However, the instantaneous vortexes are apparently
independent of the thickness of the boundary layer (Fig.
38
).
The time-averaged velocity components
u
and
w
obtained at the upper part of the
scour hole are presented in Fig.
39
, in the symmetry axis, and in Fig.
40
, in a plane
30
from the symmetry axis (see also Fig.
35
), where
u
p
is the longitudinal direction
0.4
700
600
500
400
300
200
100
0
0.35
a
0.3
b
0.25
0.2
0.15
0.1
−
100
−
200
−
300
π
ab
A
V
=
0.05
4
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
x/D
(
−
)
Fig. 36 Determination of the dimensions of the horseshoe vortex
