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In-Depth Information
according to the Richter (
1973
)approach(see(
6
)) were considered by Lindner
(
1982
).
Based on test computations, Lindner (
1982
) found that
u
0,
n
/
u
0
increases with
increasing
a
x
/
d
but that for
a
x
/
d
40 the influence of the upstream cylinders is
negligible. Based on test computations, Lindner (
1982
) further concluded that
u
0,
n
/
u
0
is larger for a staggered setup than for a parallel setup and that
u
0,
n
/
u
0
decreases with increasing mean flow velocity
u
0
and decreasing slope
S
. Similarly,
for a constant volumetric element concentration, Lindner (
1982
) showed that the
disturbance of the flow is larger when the array is composed of cylinders with a
small diameter than the disturbance caused by an array of cylinders with a larger
diameter. It is also worth mentioning that Lindner (
1982
) validated his approach
based on a flume study in which only flow velocities were measured. Therefore,
the intention of the present study is to test the applicability of the Lindner (
1982
)
approach to estimate the drag coefficient based on experiments in which drag
forces were measured directly.
>
3 Experimental Setup
Experiments were carried out in a 32-m long, 0.6-m wide, and 0.4-m deep tilting
flume in the laboratory of the Leichtweiß-Institute for Hydraulic Engineering and
Water Resources, Technische Universit
at Braunschweig, Germany. In the experi-
ments, the discharge
Q
was controlled by a valve and measured by an inductive
flow meter. Water depth in the flume was adjusted by a tailgate located in a
distance of 25 m to the flume inlet. Ten piezometers installed along the flume
allowed for water level measurements. The water level measurements were used
to calculate water surface slope from linear regression and water depth
h
. The bed
roughness consisted of a rubber mat with 3-mm high pyramidal-shaped roughness
elements.
The experiments were carried out with both in-line (L) and staggered (S) cylinder
arrays and a density of 25 cylinders/m
2
(spacing between rows and between cylin-
ders in a row
a
x
/
a
y
¼
€
0.2/0.2 m). The plastic cylinders were 24.5-cm long and had a
diameter of
d
1 cm. In order to ensure fully developed flow conditions, the
cylinders were placed over a total length of 18.5 m starting at a distance of 6 m
from the flume inlet, i.e., approximately 45 cylinder rows were located upstream of
the test section. Figure
1
shows the investigated patterns in the 1.5-m long test
section which was located at a distance of 15.1 m to the flume inlet. For the staggered
pattern, some cylinders had to be placed close to the flume wall. To ensure a constant
density, the cylinder placed near the flume wall alternated from the right to left wall
(see Fig.
1
).
Drag forces exerted on the vegetation elements were measured simultaneously
with up to ten drag force sensors (DFS) described in Schoneboom et al. (
2008
). The
DFS were mounted in a box below the flume bottom in the test section. This setup
¼
