Environmental Engineering Reference
In-Depth Information
ʔ
where
U
q
is the velocity component in the direction
q
and
q
is the spatial step in
the
q
-direction. The Courant number can be interpreted as the ratio of the distance
traveled by a particle during a time step
t
and the size of a volume element. To
guarantee time convergence the Courant number must be less than 1.
ʔ
3 Results
Numerical simulations were carried out for two cases: a pulse and a periodic flow
with
S
02. For the pulsing flow we have chosen a channel width of 2 cm, a layer
depth of 2 cm and a maximal flow rate
Q
0
=
=
0
.
10
−
5
. On the other hand, for the
periodic forcing flow we have chosen a channel width of 4 cm, a layer depth of 2 cm
and the same maximal flow rate
Q
0
2
×
10
−
5
. In order to have
S
=
2
×
=
0
.
02 the
forcing period must be T
=
80 s. In both cases the Reynolds number is
Re
=
1
,
000.
3.1 The Pulse
A pulse was applied for 4 s in the following manner (see Fig.
2
): during 0.5 s the
flow rate grows from zero to the maximal value
Q
0
=
10
−
5
. After, the flow rate
remains constant for 3 s. Finally Q decreases from
Q
0
to zero during 0.5 s.
In Fig.
3
we plot the velocity field in the symmetry plane (y
2
×
=
0) and the vorticity
distribution in a region in front of the channel at t
20 s. Figure
3
a, b, c show how the
spanwise vortex detaches from the bottom as it moves. At t
=
=
10 s (Fig.
3
a) the span-
wise vortex is already present, its center is located at (x, z)
=
(7 cm, 0.5 cm), whereas
at t
(13cm,1.2cm)(Fig.
3
c). To see
the shape of the spanwise vortex we include Fig.
3
d, in which dipole's isovorticity
surfaces are shown. The top of the surface with value
=
20 s the vortex has moved to position (x, z)
=
s was removed in
order to see the inner surface corresponding to the spanwise vortex (value
|
ˉ
|=
0
.
5
/
s
in blue). We can observe that the spanwise vortex has a horseshoe shape and that it
ˉ
x
=−
1
/
Fig. 2
Pulse applied to
generate the flow through the
channel
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