Environmental Engineering Reference
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(a)
(b)
0.25
1
10
0.2
2
10
Re
=142
0.15
10
3
ω
z
0.1
10
4
0.05
0
5
10
-0.05
02468024
t
0
5
10
15
1
)
Frequency (t
(c)
(d)
1.4
1.2
1
10
1
Re
=256
0.8
2
10
ω
z
0.6
0.4
3
10
0.2
0
4
10
-0.2
0
2
4
6
8
10
12
14
0
5
1
0
15
t
1
)
Frequency (t
Fig. 6
Panels
a
,
c
show vorticity as a function of time for an array of eight magnets (see Fig.
5
b).
b
,
d
Power spectrum of the vorticity signal calculated by the Fast Fourier Transform. The first row
corresponds to
I
=
120mA (
Re
=
=
250mA (
Re
=
142) and the second row to
I
256)
alternatingmagnets we found experimentally and numerically that the transition from
steady to time-dependent flow occurs in the range 100
<
I
<
120 mA, correspond-
ing to 132
142. For a current of 120 mA, the flow develops a time-dependent
behavior characterized by the oscillatory motion of the vortices, as shown in Fig.
6
a
where the vorticity as a function of time at a certain point in the central flow region
shows a completely periodic behavior. Figure
6
b shows the corresponding power
spectrum obtained from the Fast Fourier Transform (FFT) of the vorticity signal
which yields a (dimensionless) characteristic frequency of
f
c
=
<
Re
<
.
3
72. If the applied
=
current increases to 250mA that corresponds to
Re
256, the amplitude of the vor-
ticity oscillation is not constant (see Fig.
6
c) and the characteristic frequency becomes
f
c
=
25. The power spectrum (see Fig.
6
d) also shows some harmonics and seems
to indicate the beginning of a distinct physical behavior than a purely periodic flow.
Figure
7
a, b show, respectively, the experimental flow visualization and
Lagrangian numerical trajectories at a given instant of the time-dependent flow pro-
duced by an array of eight magnets with alternating orientation and an applied current
of 200mA (
Re
6
.
212). We observe that the experimental visualization is reasonably
reproduced by the numerical simulation. At initial steps, the flow pattern presents a
symmetry with respect to the
y
axis (as observed in Fig.
5
a) but vortex interaction
=
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