Geoscience Reference
In-Depth Information
4 Results and Discussion
Figure
2
shows the measured time-averaged drag forces exerted by individual
cylinders for the staggered (full symbols) and in-line (open symbols) arrangement
as a function of the cylinder Reynolds number
Re
d
. The figure reveals a large
variability of the measured drag forces for both arrangements with deviations from
the spatial mean between
19% for
the staggered setup, respectively. The coefficient of variation
c
v
(or normalized
random error, defined as the standard deviation of the drag force measurements
divided by the spatially averaged drag force; Bendat and Piersol
2000
) indicated
that
c
v
was largest for the lowest velocities and became reasonably constant for the
largest flow velocities (see Table
1
). The analysis of the corresponding drag
coefficients showed that
C
D
i
deviated between
28% and
þ
27% for the in-line and
23% and
þ
30% and
þ
28% and
18% and
þ
22% from the mean value for the in-line arrangement and staggered arrangement,
respectively. The variability of the drag forces and
C
D
i
-values showed that the
spatially averaged drag force and drag coefficient
C
D
for a cylinder array cannot be
estimated unambiguously from drag force measurements with a single cylinder. A
similar result has been reported by Schoneboom et al. (
2010
) for drag forces of
flexible artificial vegetation elements within vegetation arrays.
Figure
3
shows the spatially averaged drag forces
<
F
D
>
and drag coefficients
C
D
as a function of the cylinder Reynolds number. Despite the observed spatial
variability of drag forces in Fig.
2
, the spatially averaged drag force
F
D
>
followed a squared relationship with mean flow velocity for the in-line and stag-
gered setup (
F
D
<
1.14
u
0
2
and
F
D
1.42
u
0
2
, respectively, with
R
2
1). Further-
more, Fig.
3
and the proportionality factors 1.14 and 1.42 showed that
<
was
consistently larger for the staggered than for the in-line pattern. This was also
F
D
>
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2000
4000
6000
8000
Re
Fig. 2 Spatial variability of drag forces
F
D
for setup 20L (
open symbols
) and 20S (
full symbols
)