Geoscience Reference
In-Depth Information
from the well known relationship between
C
D
and the cylinder Reynolds-number
Re
d
for an isolated emergent cylinder in an infinite wide flow (e.g., Nakayama
1999
;
Schlichting and Gersten
2006
).
Although this relationship is valid only for a single isolated cylinder, it has also
been used to estimate the drag coefficient for cylinders within a multicylinder array
(e.g., DVWK
1991
; Rowinski and Kubrak
2002
; Baptist et al.
2007
; Huthoff et al.
2007
). However, the flow in a multicylinder array is influenced by the decay and
spread characteristics of wakes forming at upstream cylinders (e.g., Petryk
1969
;Li
and Shen
1973
; Lindner
1982
; Wilkerson
2007
). Studies carried out by e.g., Petryk
(
1969
), Li and Shen (
1973
), Lindner (
1982
), Nepf (
1999
) and Poggi et al. (
2004
)
showed that, in general, lower drag coefficients can be expected for a cylinder
within a multicylinder array than for a single isolated cylinder. On the other hand,
Kothyari et al. (
2009
) reported, based on drag force measurements of a single
cylinder within a multicylinder array, larger drag coefficients than the ones
expected for an isolated cylinder while Dunn et al. (
1996
) and Stone and Shen
(
2002
) reported similar
C
D
-values for cylinders in multicylinder arrays and for an
isolated cylinder. These contradicting results can partly be explained by differences
in the definition of hydraulic variables (e.g., Statzner et al.
2006
), the experimental
setup (array density and cylinder Reynolds number), and the fact that drag forces
were not directly measured in some of the studies. Especially the latter fact is of
major importance, as the adequate determination of the drag coefficient must be
based on the approach velocity on an individual cylinder.
Therefore, the objective of the present study was to test the computational
approach presented by Lindner (
1982
) for the determination of the drag coefficient
of cylinders in multicylinder arrays by comparing measured and computed drag
forces and drag coefficients, taking into account the wake flow structure.
2 Background
The drag force
F
D
exerted by a single isolated cylinder can be estimated from:
C
D
A
p
u
c
2
F
D
¼
0
:
5
r
(1)
where
r ¼
fluid density,
C
D
¼
plant projected area, and
u
c
¼
characteristic mean flow velocity of the undisturbed flow. For emergent cylindrical
rigid elements,
A
p
corresponds to the product of water depth
h
and diameter
d
.
The drag coefficient
C
D
depends on the separation characteristics of the cylinder
boundary layer and is a function of the cylinder Reynolds number
Re
d
¼
drag coefficient,
A
P
¼
u
c
d
/
n
,
where
denotes the fluid kinematic velocity (e.g., Nakayama
1999
). Within the
so-called subcritical flow regime (
Re
d
n
10
5
), the flow around a cylinder is
laminar (e.g., Schlichting and Gersten
2006
). The subcritical flow regime is rele-
vant for most practical applications, and for
Re
d
<
4
800, the drag coefficient can be
