Geoscience Reference
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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 )
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