...
Gtheta
...
Computations
...
using
...
UDF
...
A
...
User
...
Defined
...
FLUENT
...
script
...
(
...
...
)
...
was
...
created
...
to
...
extract
...
the
...
G_theta
...
value
...
from
...
the
...
flocculator.
...
The
...
UDF
...
loops
...
through
...
all
...
of
...
the
...
individual
...
cells
...
of
...
the
...
converged
...
solution,
...
and
...
extracts
...
the
...
energy
...
dissipation^1/2
...
times
...
the
...
cell
...
area.
...
The
...
sum
...
of
...
this
...
quantity
...
for
...
all
...
cells
...
divided
...
by
...
flow
...
and
...
square
...
of
...
viscoisty
...
results
...
in
...
the
...
G_theta
...
value
...
of
...
the
...
entire
...
flocculator
...
as
...
shown
...
in
...
equation
...
1.
...
Gθ_baffle=1/Q*vis^(-1/2)*∑(ε^(1/2)*cell_area)
...
Eq.
...
1
...
The
...
above
...
formulation
...
has
...
been
...
determined
...
(with
...
Monroe's
...
help)
...
by
...
weighting
...
the
...
value
...
of
...
Gθ
...
by
...
volume.
The Gθ_baffle
...
values
...
weighted
...
by
...
the
...
area
...
or
...
number
...
of
...
cells
...
were
...
also
...
examined,
...
but
...
these
...
formulations
...
do
...
not
...
produce
...
sensible
...
results.
...
Below
...
is
...
the
...
G_theta
...
value
...
presented
...
for
...
flocculation
...
tanks
...
of
...
different
...
geometries:
...
Case |
|---|
...
Geometry |
|---|
...
(h-height,b-width,N-baffles) |
|---|
...
Gθ_Flocculator |
|---|
...
b=.1, |
...
h=1, |
...
N=1, |
...
Clearance |
...
height=.15 |
...
430 | |
b=.1, |
...
h=.3, |
...
N=5, |
...
sym |
...
bc | 1330 |
b=.1, |
...
h=.2, |
...
N=5 |
...
1060 |
Understanding the Gθ parameter
The Gθ value increases with increasing flocculation tank volume. Thus, when comparing different designs, each case should be normalized by the volume (or area for 2D geometries). This results in the following normalized values.
Case Geometry (h-height,b-width,N-baffles) |
|---|
...
Gθ_Flocculator/m^2 |
|---|
...
b=.1, |
...
h=1, |
...
N=1, |
...
Clearance |
...
height=.15 |
...
4,300 |
...
b=.1, |
...
h=.3, |
...
N=5, |
...
sym |
...
bc | 8,870 |
...
b=.1, |
...
h=.2, |
...
N=5 |
...
10,600 |
...
Comparison to Flocculation Tanks
Literature rates flocculators based on the Gθ value, as well as the G, epsilon value, and θ-value. For flocculators without recirculating solids, the recommended Gθ is 20,000-150,000
...
(Schulz,
...
C.
...
R.
...
and
...
D.
...
A.
...
Okun
...
(1984).
...
Surface
...
Water
...
Treatment
...
for
...
Communities
...
in
...
Developing
...
Countries
...
,
...
John
...
Wiley
...
&
...
Sons).
...
This
...
would
...
correspond
...
to
...
2-15
...
m^2
...
of
...
flocculator
...
area
...
based
...
on
...
the
...
weighted
...
Gθ-values
...
calculated.
...
This
...
seems
...
to
...
be
...
the
...
area
...
of
...
flocculators
...
currently
...
used
...
in
...
practice
...
in
...
Honduras.
...
Thus,
...
the
...
calculated
...
Gθ-values
...
seems
...
sensible.
...
Another
...
check
...
of
...
the
...
accuracy
...
of
...
the
...
results
...
can
...
be
...
seen
...
by
...
comparing
...
the
...
dissipation
...
rate
...
of
...
the
...
flocculation
...
tanks
...
to
...
values
...
recommended
...
by
...
Schulz
...
and
...
Okun
...
of
...
.4-10
...
mW/kg.
...
The
...
energy
...
dissipation
...
plotted
...
in
...
this
...
region
...
for
...
the
...
fh=3
...
case
...
results
...
in
...
the
...
plot
...
shown
...
below:
The regions in white are outside of this region, indicating that energy dissipation values above and below this recommended region exist in the flocculator.