...
Data
...
Acquisition
...
The
...
Flocculator
...
Residual
...
Turbidity
...
Analyzer
...
(FReTA)
...
allows
...
us
...
to
...
gather
...
data
...
and
...
investigate
...
a
...
number
...
of
...
different
...
factors
...
affecting
...
flocculator
...
performance,
...
including
...
shear
...
(G),
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residence
...
time
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(θ),
...
alum
...
dose,
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and
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influent
...
turbidity.
...
The
...
shear
...
rate
...
in
...
the
...
flocculator
...
can
...
be
...
controlled in ProCoDA Software by either holding constant or varying the plant flow rate as desired. A given flow rate will define a particular shear rate in the flocculator. The shear rates in the tube flocculator can be calculated from flow rates and other characteristics of the setup using the following equations:
The following equations and methods were developed to describe shear in FReTA by Ian Tse in his thesis: Fluid shear influences on hydraulic flocculation systems characterized using a newly developed method for quantitative analysis of flocculation performance
Based on dimensional analysis, the velocity gradient G can be expressed as a function of the average energy dissipation rate (ε) and kinematic viscosity of the fluid (ν):
| Latex |
|---|
in [Process Controller] by either holding constant or varying the plant flow rate as desired. A given flow rate will define a particular shear rate in the flocculator. The shear rates in the tube flocculator can be calculated from flow rates and other characteristics of the setup using the following equations: _The following equations and methods were developed to describe shear in FReTA by Ian Tse in his thesis:_ _[_Fluid shear influences on hydraulic flocculation systems characterized using a newly developed method for quantitative analysis of flocculation performance_|Tube Floc Data Acquisition^Ian Tse MS Thesis.doc]_ _Based on dimensional analysis, the velocity gradient G can be expressed as a function of the average energy dissipation rate (ε) and kinematic viscosity of the fluid (ν):_ {latex} \large $$ G = \sqrt {{\varepsilon \over \nu }} $$ {latex} _ |
(1.3)
...
Using
...
conservation
...
of
...
energy,
...
ε
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can
...
be
...
expressed
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as
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kinetic
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energy
...
loss
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over
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a
...
period
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of
...
time:
| Latex |
|---|
} \large $$ \varepsilon = {{gh_L } \over \theta } $$ {latex} _ |
(1.4)
...
where:
...
g
...
is
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gravitational
...
acceleration,
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hL
...
is
...
head
...
loss
...
and
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θ
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is
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average
...
hydraulic
...
residence
...
time.
...
The
...
head
...
loss
...
through
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a
...
straight
...
tube
...
can,
...
in
...
turn,
...
be
...
defined
...
as
...
(Robertson
...
et
...
al,
...
1993):
| Latex |
|---|
} \large $$ h_L = f_s {L \over d}{{U^2 } \over {2g}} $$ {latex} _ |
(1.5)
...
where:
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L
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is
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the
...
length
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of
...
the
...
flocculator
...
and
...
fs
...
is
...
the
...
friction
...
factor
...
in
...
a
...
straight
...
tube.
...
For
...
laminar
...
flow,
...
the
...
friction
...
factor
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fs
...
=
...
64/Red,
...
and
...
Red
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is
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the
...
Reynolds
...
number
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as
...
defined
...
as:
| Latex |
|---|
} \large $$ {\mathop{\rm Re}\nolimits} _d = {{Ud} \over \nu } $$ {latex} _ |
(1.6)
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where:
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U
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is
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the
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average
...
axial
...
velocity
...
and
...
d
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is
...
the
...
tube
...
inner
...
diameter.
...
The
...
formulation
...
for
...
G
...
derived
...
by
...
Gregory
...
(1981)
...
(see
...
Equation
...
1.2)
...
can
...
also
...
be
...
derived
...
from
...
algebraic
...
rearrangement
...
of
...
Equations
...
1.3-1.6.
...
A
...
correlation
...
factor
...
(Mishra
...
&
...
Gupta
...
1979)
...
can
...
be
...
applied
...
to
...
Equation
...
1.7
...
to
...
replace
...
fs
...
with
...
fc
...
and
...
correct
...
for
...
the
...
differences
...
in
...
head
...
loss
...
between
...
straight
...
and
...
curved
...
tubes.
| Latex |
|---|
} \large $$ {{f_c } \over {f_s }} = 1 + 0.033\log \left( {De} \right)^4 $$ {latex} _ |
(1.7)
...
where:
...
De
...
is
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the
...
nondimensional
...
Dean
...
Number
...
and
...
characterizes
...
the
...
effect
...
of
...
curvature
...
on
...
fluid
...
flow:
| Latex |
|---|
} \large $$ De = \sqrt {{r \over {R_c }}} {\mathop{\rm Re}\nolimits} _d $$ {latex} _ |
(1.8)
...
where:
...
r
...
is
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the
...
inner
...
radius
...
of
...
the
...
tube,
...
Rc
...
is
...
the
...
radius
...
of
...
curvature.
...
The
...
average
...
head
...
loss
...
measured
...
as
...
the
...
pressure
...
drop
...
across
...
the
...
tube
...
flocculator
...
was
...
within
...
2%
...
of
...
the
...
head
...
loss
...
calculated
...
using
...
Equations
...
1.5
...
and
...
1.7
...
(Figure
...
1.4).
...
The
...
figure
...
eight
...
coil
...
configuration
...
used
...
in
...
this
...
research
...
was
...
different
...
from
...
the
...
flow
...
regime
...
modeled
...
by
...
Mishra
...
and
...
Gupta.
...
The
...
fact
...
that
...
our
...
data
...
agrees
...
with
...
their
...
model
...
suggests
...
that
...
the
...
change
...
in
...
direction
...
of
...
the
...
coil
...
had
...
only
...
a
...
small
...
effect
...
on
...
total
...
head
...
loss.
...
The
...
following
...
G
...
value
...
obtained
...
from
...
combining
...
Equations
...
1.3-1.8
...
was
...
used
...
to
...
design
...
the
...
experimental
...
runs.
| Latex |
|---|
} \large $$ G_c = G_s \left( {1 + 0.033\log \left( {De} \right)^4 } \right)^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}} $$ {latex} _ |
(1.9)
...
We
...
can
...
also
...
study
...
the
...
effect
...
of
...
increasing
...
the
...
residence
...
time
...
in
...
the
...
flocculator
...
and
...
holding
...
shear
...
constant
...
by
...
increasing
...
the
...
length
...
of
...
the
...
flocculator
...
while
...
holding
...
the
...
flow
...
rate
...
constant;
...
this
...
will
...
increase
...
the
...
amount
...
of
...
time
...
water
...
spends
...
in
...
the
...
flocculator
...
without
...
changing
...
the
...
shear
...
rate.
...
Currently,
...
setup
...
can
...
easily
...
be
...
modified
...
to
...
handle
...
three
...
different
...
flocculator
...
lengths,
...
27.96
...
m,
...
55.92
...
m,
...
and
...
83.88
...
m.
...
ProCoDA Software can also be used to vary alum dosage, and set the desired influent turbidity for the raw water. This allows us complete control over what enters the flocculator, how long it spends in the flocculator, and how quickly it moves through the flocculator.
When running an experiment on FReTA, we allow 1.5-2 flocculator residence times to pass before collecting data. This ensures that the alum has the necessary time to react with the clay particles in order to produce a steady state distribution of flocs at the end of the flocculator.
After this loading time, ProCoDA Software begins the actual data collection. The pumps ramp down gradually, and a ball valve is used to seal off the settling column (see Apparatus Setup) from the rest of the flocculator over a period of 6 seconds. The reason for this gradual shut down is to prevent turbulence that could disrupt flocs in the settling column. ProCoDA Software then records the residual turbidity every second for half an hour (1800 s) at which point the valves open to begin backwashing for a new run.
The settling velocities corresponding to the time range we are studying are calculated by dividing the distance between the valve and the effluent turbiditmeter in the settling column (16 cm) by the time since settling began. Thus, the remaining turbidity after 10 s of settling would correspond to all particles with a settling velocity of greater than 1.6 cm/s. We are not interested in recording data after half an hour because this corresponds to extremely low settling velocities (>0.0889 mm/s). Additionally, we define residual turbidity as the turbidity with settling velocity less than 0.12 mm/s. This is the capture velocity of the plate settlers, so any particles with lower setting velocities will exit with the effluent.