Geoscience Reference
In-Depth Information
term is Stokes drag. Retaining only this term, the smaller turbulent scale measur-
able for a given velocity increment is:
1
18
d
ð
s
1
Þ
Dr
¼
Du
(3)
v
ðwÞ
where
S
is the specific gravity of the seeding grains,
v
(
w
)
is the kinematic viscosity
of the fluid, and
Du
is the velocity increment. To measure water flows, the diameter
of seeding particles ranges normally from 5 to 50
m
m and are denser than the fluid.
Assuming
s
1.65, the smallest turbulent scale associated to a velocity
increment of 0.1 susceptible to be measured with seeding particles of 50
m
m
would be 2.3
1
¼
10
5
m. For current laboratory flumes this value would be well
within the dissipative range and would not be a cause of significant errors.
The size of the measuring volume is important when discussing the quality of
turbulent flow measurements. The dimensions of the measuring volume in the
directions normal and parallel to the probe axis are:
4
F
l
p
D
L
cos
4
F
l
p
D
L
sin
d
x
¼
and
d
y
¼
(4)
ð
y
=
2
Þ
ð
y
=
2
Þ
respectively, where
F
is the focal distance and
D
L
is the diameter of the beam just
before the lens. Control volumes too large may smooth out small turbulent scales,
since particles with symmetric velocities belonging to the same eddy simultaneously
present in the measurement volume may disturb burst detection. One other adverse
effect of a large control volume is the generation of noise. If d
y
encompasses strong
spatial gradients, particles with different velocities will cross the control volume and
will be interpreted as turbulence even if the flow is laminar. Naturally, if the flow is
turbulent, this type of noise will also be present but will be very difficult to detect as it
may not be uncorrelated. A typical system with
F
30
, l
¼
0.40 m, y
¼
¼
632.8
nm, and
D
L
¼
0.0012 m. The lateral
size of the control volume, of the order of magnitude of 1 mm, would be a cause of
some noise introduced in the turbulent signal.
The major favorable features of the LDA technique can be summarized as
follows:
0.001 m will exhibit d
x
¼
0.0003 m and d
y
¼
1. LDA is relatively low intrusive technique; given that the focal distances are
large, no material pieces of instrumentation are required near the flow under
measurement.
2. When measuring river and channel flows, sampling frequencies are generally
high (it is easy to obtain 300 Hz), given that the flow is normally seeded with
natural sediment tracers; the time discrertization of the velocity series is among
the highest achievable in channel flows.
3. The spatial discretization of the velocity signal is good, relatively to acoustic
Doppler techniques and other point-wise or profiling acoustic techniques; in
fact, the measuring volumes of the latter are often one order of magnitude larger
than that of the LDA.
