Geoscience Reference
In-Depth Information
1
1.2
0.9
1
0.8
0.7
0.8
0.6
0.5
0.6
0.4
0.4
0.3
0.2
0.2
0.1
0
0
0
2000
4000
6000
8000
Re
Fig. 3 Spatial averaged drag forces (
diamonds
) and drag coefficients (
squares
) dependent on
stem-Reynolds number
Re
d
for the staggered (
filled symbols
) and in-line arrangement (
open
symbols
)
reflected by the spatially averaged drag coefficients which were larger for the
staggered than for the in-line arrangement (Fig.
3
). A similar behavior has been
reported by Li and Shen (
1973
) and Lindner (
1982
) for cylinder arrays and by
Schoneboom et al. (
2010
) for flexible vegetation elements.
Figure
3
further indicated that the observed drag coefficients
C
D
were approximately
constant for the two investigated arrangements. The mean
C
D
-values corresponded, for
the range of cylinder Reynolds numbers varying between 2,000
Re
d
7,000, to
C
D
¼
1.07 for the in-line and staggered setup, respectively. The
difference to the expected drag coefficient for a single isolated emergent cylinder in
an undisturbed flow for the same cylinder Reynolds-numbers of
C
D
¼
0.87 and
C
D
¼
1.0 indicated the
importance of the flow structure within cylinder arrays.
As aforementioned, the flow structure in a multicylinder array can be taken into
account applying the Lindner (
1982
) approach. In the following application of this
approach, the additional drag caused by surface waves around the cylinder
D
C
D
was
neglected as the experiments were carried out with just submerged flow conditions.
Furthermore, according to the recommendation of Lindner (
1982
), the computa-
tions were based on the approach velocity on the 20th cylinder
u
0,20
because the
number of approximately 45 upstream cylinders exceeded this threshold. In fact,
test computations showed that the approach velocity did not change significantly
following the 20th cylinder confirming the conclusion of Lindner (
1982
).
The calculated drag coefficients are presented in Table
1
and showed that the
drag coefficients for the in-line arrangement were underestimated by approximately
16% for the in-line setup and overestimated by 5% for the staggered setup. Given
the large number of underlying assumptions, these deviations can be considered
