...
Vertical
...
Flow
...
Flocculation
...
Design
...
Program
...
To
...
create
...
a
...
consistent
...
relation
...
between
...
vertical
...
and
...
horizontal
...
flow,
...
generic
...
notation
...
is
...
used.
...
J
...
represents
...
the
...
distance
...
to
...
turn.
...
The
...
flow
...
area,
...
which
...
is
...
the
...
cross
...
sectional
...
area
...
that
...
is
...
perpendicular
...
to
...
the
...
flow
...
of
...
the
...
water,
...
is
...
P*S.
Generic | Vertical | Horizontal |
Ρ | W | H |
S | S | S |
J | H | W |
This flocculator program determines the size, number, and spacing of the flocculator channels and baffles, based on the results of the Computational Fluid Dynamics (CFD) team. The tank is designed give an optimal energy dissipation rate to mix the alum (coagulating chemical) with the incoming water and to maximize the opportunity for flocs to form.
The program also outputs arrays of the location of each baffle in the tank; these arrays are used by the AutoCAD scripts to draw the baffles in place in the flocculator.
The programs used are Flocculator 3 (the design program) and floctank (the AutoCAD script). In the scheme of the whole plant, the flocculation tank is drawn after the sedimentation tank (so many of our variables are constrained by an already-drawn sedimentation tank).
In some scenarios, horizontal flow flocculation will be used.
Top View
Front View
Slopes
Flocculator Program Inputs and Outputs
Flocculation Tank Program Inputs
Flocculation Tank Program Outputs
Flocculation Tank AutoCAD Drawing Program
Flocculation Design Algorithm
Each section outlined below corresponds to its equivalent MathCAD code, identified by the same titles.
The first part mainly informs and establishes the equations and design ideas used in the actual drawing of the tank.
The second part determines the number, spacing, energy dissipation, and collision potential of the necessary baffles.
The third part determines the width, height, size, and the other parameters needed to draw the flocculation tank with the baffles inside it. This section is heavily relied upon by the MathCAD code in floctank that draws the plant.
The last part creates and outputs the matrix of baffle positions.
Computational Fluid Dynamics (CFD) Results and Functions
The research that went into this program was done by the CFD team. As such, many of the equations used have their basis in experimental findings; some of their work can be directly applied to the drawing of flocculation tanks, and some support the parameters used in this program. The minor loss coefficients calculated by the CFD team have been replaced with the value 2 because that more closely matches the measured loss coefficient from the Agalteca plant.
Linear interpolation is used to create functional relationships as a function of these J/S ratios. Then, an iterative code that determines the spacing of the floc baffles uses these relationships. Calculating the collision potential per baffle and the spacing that gives the target energy dissipation rate continue to use the parameters set by the research team.
Flocculator Functions
The critical balance in the flocculator is between ensuring that the alum and entering water are meeting the energy dissipation (ED) and collision potential (CP) goals, and not breaking up flocs that have formed.
Calculation of Flocculator Geometry
The height of water at the end of the flocculation tank is set by the user.
There are two baffle type options for vertical flocculators: plastic or rigid (i.e. concrete, brick, etc.). The baffles will have different thicknesses in either case.
The algorithm checks to see if the minimum channel width based on a baffle spacing equal to a human width is greater than the width of the plastic sheets. If not, a plastic baffle is chosen. If so, a concrete baffle is chosen.
Plastic Calculations
The width of the channel is set as the width of the plastic sheet.
The number and spacing of floc spaces and floc baffles is calculated, as well as the CP, for the specific tank being drawn. Both the minimum and maximum number of floc spaces use the equation:
| Latex |
|---|
| Generic | Vertical | Horizontal | | Ρ | W | H | | S | S | S | | J | H | W | This flocculator program determines the size, number, and spacing of the flocculator channels and baffles, based on the results of the Computational Fluid Dynamics (CFD) team. The tank is designed give an optimal energy dissipation rate to mix the alum (coagulating chemical) with the incoming water and to maximize the opportunity for flocs to form. The program also outputs arrays of the location of each baffle in the tank; these arrays are used by the AutoCAD scripts to draw the baffles in place in the flocculator. The programs used are Flocculator 3 (the design program) and floctank (the autoCAD script). In the scheme of the whole plant, the flocculation tank is drawn after the sedimentation tank (so many of our variables are constrained by an already-drawn sedimentation tank). In some scenarios, [horizontal flow flocculation|Horizontal Flow Flocculation Design Program] will be used. h2. Top View !top view floc tank.PNG|width=1081,height=596! h2. Front View !side view floc tank.PNG|width=1166,height=425! h2. Slopes h2. Flocculator Program Inputs and Outputs [Flocculation Tank Program Inputs|Flocculation Tank Design Program Inputs] [Flocculation Tank Program Outputs|Flocculation Tank Design Program Outputs] [Flocculation Tank AutoCAD Drawing Program|AutoCAD Flocculation Tank Program] h2. Flocculation Design Algorithm Each section outlined below corresponds to its equivalent MathCAD code, identified by the same titles. The first part mainly informs and establishes the equations and design ideas used in the actual drawing of the tank. The second part determines the number, spacing, energy dissipation, and collision potential of the necessary baffles. The third part determines the width, height, size, and the other parameters needed to draw the flocculation tank with the baffles inside it. This section is heavily relied upon by the MathCAD code in floctank that draws the plant. The last part creates and outputs the matrix of baffle positions. \\ h2. Computational Fluid Dynamics (CFD) Results and Functions The research that went into this program was done by the CFD team. As such, many of the equations used have their basis in experimental findings; some of their work can be directly applied to the drawing of flocculation tanks, and some support the parameters used in this program. For example, a table of minor loss coefficients indicates that the minor loss coefficient is very large for small J/S values, where J/S values are the ratio of the length of flow in one baffle to baffle spacing. Linear interpolation is used to create functional relationships as a function of these J/S ratios. Then, an iterative code that determines the spacing of the floc baffles uses these relationships. Calculating the collision potential per baffle and the spacing that gives the target energy dissipation rate continue to use the parameters set by the research team. h2. Flocculator Functions The critical balance in the flocculator is between ensuring that the alum and entering water are meeting the energy dissipation (ED) and collision potential (CP) goals, and not breaking up flocs that have formed. h2. Calculation of Flocculator Geometry The height of water at the end of the flocculation tank is set by the user. There are two baffle type options for vertical flocculators: plastic or rigid (i.e. concrete, brick, etc.). The baffles will have different thicknesses in either case. The algorithm checks to see if the minimum channel width based on a baffle spacing equal to a human width is greater than the width of the plastic sheets. If not, a plastic baffle is chosen. If so, a concrete baffle is chosen. h4. Plastic Calculations The width of the channel is set as the width of the plastic sheet. The number and spacing of floc spaces and floc baffles is calculated, as well as the CP, for the specific tank being drawn. Both the minimum and maximum number of floc spaces use the equation: {latex} \large $$ N_{Spaces} = {{L + T} \over {S + T}} $$ {latex} \\ The |
The ceiling,
...
floor,
...
and
...
round
...
functions
...
are
...
used
...
to
...
force
...
this
...
number
...
to
...
be
...
even
...
(so
...
that
...
the
...
water
...
flows
...
from
...
port
...
to
...
port
...
in
...
all
...
channels
...
except
...
the
...
last).
...
When
...
trying
...
to
...
find
...
the
...
minimum
...
number
...
of
...
spaces
...
that
...
can
...
fit
...
in
...
a
...
channel,
...
the
...
value
...
is
...
rounded
...
up.
...
When
...
trying
...
to
...
find
...
the
...
maximum
...
number
...
of
...
spaces
...
that
...
can
...
fit
...
into
...
a
...
channel,
...
the
...
value
...
is
...
rounded
...
down.
...
Otherwise,
...
the
...
value
...
is
...
just
...
rounded.
...
When
...
calculating
...
both
...
the
...
min
...
and
...
the
...
max,
...
L
...
represents
...
the
...
length
...
of
...
the
...
sed
...
tank
...
L.Sed
...
and
...
T
...
represents
...
the
...
thickness
...
of
...
a
...
baffle
...
T.FlocBaffle
...
.
...
To
...
get
...
the
...
maximum
...
number
...
of
...
floc
...
baffles,
...
S
...
is
...
taken
...
as
...
the
...
minimum
...
floc
...
baffle
...
spacing
...
S.FlocBaffleMin
...
.
...
However,
...
to
...
get
...
the
...
minimum
...
number
...
of
...
floc
...
baffles,
...
S
...
is
...
taken
...
as
| Latex |
|---|
} \large $$ {{J } \over {Pi_{JSMin} }} $$ {latex} \\ where _ |
where Pi.JSMin
...
is
...
a
...
parameter
...
describing
...
the
...
minimum
...
ratio
...
of
...
water
...
depth
...
to
...
baffle
...
spacing.
...
Rigid
...
Calculations
...
The
...
baffle
...
spacing
...
is
...
set
...
as
...
the
...
maximum
...
of
...
a
...
human
...
width
...
and
...
J/3
...
(the
...
optimal
...
value).
...
The
...
channel
...
width
...
can
...
then
...
be
...
directly
...
calculated
...
with
...
no
...
iteration.
...
Calculations
...
Applicable
...
to
...
Both
...
Baffle
...
Types
...
The
...
center-to-center
...
distance
...
between
...
baffles
...
includes
...
the
...
spacing
...
between
...
baffles
...
and
...
the
...
thickness
...
of
...
the
...
baffles,
...
for
...
each
...
channel.
...
This
...
is
...
an
...
array
...
with
...
an
...
element
...
for
...
each
...
channel,
...
as
...
each
...
channel
...
may
...
have
...
different
...
baffle
...
spacing.
| Latex |
|---|
} \large $$ B_{FlocBaffle} = S_{FlocBaffle} + T_{FlocBaffle} $$ {latex |
The residence time in the flocculator is determined as follows:
| Latex |
|---|
} \\ The residence time in the flocculator is determined as follows: {latex} \large $$ Ti_{Floc} = {{J_{FlocChannel} \cdot L_{FlocTank} \cdot P_{FlocChannel}} \over {Q_{Plant}}} $$ {latex} \\ The height of water at the beginning of the flocculator is based on the height of water at the end of the flocculator plus the headloss through the flocculator. The head loss is determined per baffle (and per channel, and in the whole flocculator) using the HL function in the [fluids functions program|Fluids Functions Design Program]. An additional 10 cm of freeboard space was added to the water level (HW) found at the beginning of the flocculator to determine the height of the flocculator walls. The head loss per baffle in each channel: {latex} |
The height of water at the beginning of the flocculator is based on the height of water at the end of the flocculator plus the headloss through the flocculator. The head loss is determined per baffle (and per channel, and in the whole flocculator) using the HL function in the fluids functions program. An additional freeboard space was added to the water level (HW) found at the beginning of the flocculator to determine the height of the flocculator walls.
The head loss per baffle in each channel:
| Latex |
|---|
\large
$$
HL_{FlocBaffle} = {{{Kp \cdot ({{J_{FlocChannel}} \over {S_{FlocBaffle}}}) \cdot Q_{Plant}^2 } \over {2 \cdot g \cdot (S_{FlocBaffle} \cdot P_{FlocChannel})^2 }}}
$$
|
Water flows between channels in the flocculator through ports cut in the concrete. The area of these ports is determined to ensure flocs will not be broken up.
The energy dissipation rate through the ports is set to be same as around the baffles; the dimensions of the port are calculated to be the same as that of the baffles.
| Latex |
|---|
{latex} \\ Water flows between channels in the flocculator through ports cut in the concrete. The area of these ports is determined to ensure flocs will not be broken up. \\ The energy dissipation rate through the ports is set to be same as around the baffles; the dimensions of the port are calculated to be the same as that of the baffles. {latex} \large $$ W_{FlocPortEst} = S_{FlocBaffle} $$ {latex} \\ The width of these ports is set to include the thickness of the concrete lip needed to hold the baffle in place. {latex} |
The width of these ports is set to include the thickness of the concrete lip needed to hold the baffle in place.
| Latex |
|---|
\large
$$
W_{FlocPort} = W_{FlocPortEst} - S_{FlocChannel}
$$
{latex}
\\
h2. Position Calculations for Each Baffle
The length of the lower floc baffles is determined based on the height of water at the end of the floc tank and the water as it goes around each turn. The baffles are oriented to go |
Position Calculations for Each Baffle
The length of the lower floc baffles is determined based on the height of water at the end of the floc tank and the water as it goes around each turn. The baffles are oriented to go up-down-up-down
...
so
...
that
...
the
...
flow
...
of
...
water
...
is
...
smooth
...
through
...
the
...
tank.
...
This
...
order,
...
however,
...
is
...
reversed
...
in
...
the
...
last
...
channel,
...
since
...
there
...
is
...
an
...
even
...
number
...
of
...
baffles
...
and
...
the
...
water
...
must
...
flow
...
under
...
the
...
last
...
baffle
...
and
...
up
...
to
...
the
...
exit
...
port
...
that
...
leads
...
to
...
the
...
sed
...
tank.
...
Length
...
of
...
Lower
...
Baffle:
| Latex |
|---|
} \large $$ L_{FlocBaffleLower} = J_{FlocChannel} - S_{FlocBaffle} \cdot Pi_{FlocBaffle} $$ {latex} |
The
...
upper
...
baffles
...
are
...
set
...
to
...
line
...
up
...
with
...
the
...
top
...
of
...
the
...
tank
...
rather
...
than
...
the
...
water
...
level.
...
Length
...
of
...
Upper
...
Baffles:
| Latex |
|---|
} \large $$ L_{FlocBaffleUpper} = H_{Floc} - S_{FlocBaffle} \cdot Pi_{FlocBaffle} $$ {latex} \\$$ |
The
...
last
...
channel
...
in
...
the
...
flocculator
...
must
...
be
...
treated
...
differently
...
than
...
the
...
other
...
channels
...
since
...
there
...
are
...
more
...
constraints.
...
The
...
inlet
...
channel
...
to
...
the
...
sed
...
tank
...
connects
...
to
...
the
...
outlet
...
of
...
the
...
floc
...
tank
...
by
...
an
...
exit
...
port.
...
This
...
already
...
has
...
a
...
size
...
and
...
location
...
by
...
the
...
time
...
the
...
floc
...
tank
...
is
...
drawn
...
and
...
designed.
...
Additionally,
...
as
...
described
...
above,
...
there
...
are
...
an
...
even
...
number
...
of
...
baffles
...
in
...
this
...
last
...
channel,
...
and
...
there
...
obviously
...
cannot
...
be
...
any
...
baffles
...
drawn
...
in
...
the
...
way
...
of
...
the
...
exit
...
port.
...
Therefore
...
the
...
program
...
that
...
places
...
the
...
baffles
...
for
...
the
...
last
...
channel
...
first
...
considers
...
the
...
baffle
...
spacing.
...
If
...
the
...
spacing
...
for
...
the
...
baffles
...
is
...
smaller
...
than
...
the
...
width
...
of
...
the
...
exit
...
port,
...
there
...
will
...
either
...
be
...
one
...
or
...
two
...
baffles
...
that
...
fall
...
within
...
the
...
exit
...
port
...
space.
...
| Wiki Markup |
|---|
{float:left|border=2px solid black}
[!baffle in exit port.PNG|width=450px!|AutoCAD Channel Program]
Baffle in the Way of the Exit Port
{float} |
...
If
...
there
...
is
...
one
...
baffle
...
in
...
the
...
way,
...
the
...
program
...
spaces the
...
baffles
...
by shifting
...
them
...
down
...
the
...
channel
...
and
...
leaving
...
only
...
the
...
exit
...
port
...
width
...
at
...
the
...
end.
...
If
...
there
...
are
...
two
...
baffles,
...
the
...
program
...
must
...
delete
...
two
...
baffles,
...
to
...
keep
...
the
...
even
...
number,
...
and
...
since
...
the
...
spacing
...
in
...
the
...
last
...
channel
...
must
...
be
...
greater
...
than
...
the
...
spacing
...
in
...
any
...
other
...
channel,
...
it
...
then
...
spaces the
...
remaining
...
baffles
...
evenly.
...
The
...
placement
...
of
...
the
...
baffles
...
in
...
the
...
flocculator
...
is
...
determined
...
by
...
algorithms
...
that
...
create
...
a
...
matrix
...
of
...
baffle
...
displacements
...
from
...
the
...
end
...
of
...
the
...
flocculator
...
(see
...
this drawing program for step-by-step
...
details
...
of
...
how
...
the
...
lamina,
...
baffles,
...
slots,
...
and
...
other
...
tank
...
details
...
are
...
drawn).
...
Drain Design
Port Sizing
When baffles are made from ferrocement, ports need to be cut out of the bottom of the lower baffles so that water is not trapped between them when the flocculator is being drained through a valve at one end of the tank. The ports must be on alternating sides of the lower baffles so that water does not move linearly (bypassing the mixing process) through the flocculator during normal operation.
As long as the port area is no larger than the valve area, the port area limits the flocculator drain time. For this reason, the port area is set to be equal to the area of the valve used to drain the flocculator. The area of the ports, and therefore the diameter of the valve, is calculated based on a drain time set in the expert inputs. The time required to drain a tank is:
| Latex |
|---|
Design h3. Port Sizing When baffles are made from ferrocement, ports need to be cut out of the bottom of the lower baffles so that water is not trapped between them when the flocculator is being drained through a valve at one end of the tank. The ports must be on alternating sides of the lower baffles so that water does not move linearly (bypassing the mixing process) through the flocculator during normal operation. As long as the port area is no larger than the valve area, the port area limits the flocculator drain time. For this reason, the port area is set to be equal to the area of the valve used to drain the flocculator. The area of the ports, and therefore the diameter of the valve, is calculated based on a drain time specified by the user. The time required to drain a tank is: {latex} \large $$ t = {{\sqrt {h_0 } - \sqrt h } \over {{{A_{or} } \over {2A_{res} }}\sqrt {{{2g} \over {K_{minor} }}} }} $$ {latex} |
where
...
h
...
o is
...
the
...
initial
...
water
...
height
...
in
...
the
...
tank,
...
h
...
is
...
the
...
water
...
height
...
at
...
time
...
t,
...
A
...
or is
...
the
...
area
...
of
...
the
...
orifice
...
through
...
which
...
the
...
water
...
drains
...
(in
...
this
...
case
...
the
...
port
...
or
...
valve
...
area),
...
A
...
res is
...
the
...
plan
...
area of the reservoir or tank (i.e. the space between two lower baffles), and Kminor is the minor loss coefficient associated with the flow.
The flocculator can be separated into two parts. The first part is the horizontal portion above the top lower baffles where the water drains as a single tank; the highest lower baffle was used for this calculation, resulting in a slight overestimate of the total drain time. The second part is the portion below the top of the lower baffles where these baffles form small "tanks" within the flocculator. For the upper portion, the area of the orifice is the area of the valve,
| Latex |
|---|
of the reservoir or tank, and K{~}minor~ is the minor loss coefficient associated with the flow. Using the above equation, the flocculator can be separated into two parts. The first part is the horizontal portion above the top lower baffles where the water drains as a single tank; the highest lower baffle was used for this calculation, resulting in a slight overestimate of the total drain time. The second part is the portion below the top of the lower baffles where these baffles form small "tanks" within the flocculator. For the upper portion, the area of the orifice is the area of the valve, {latex} \large $$ ({{\pi D_{valve}^2 } \over 4}) $$ {latex} |
and
...
the
...
minor
...
loss
...
coefficient
...
is
...
that
...
associated
...
with
...
the
...
chosen
...
valve.
...
The
...
flow
...
through
...
the
...
tank
...
is
...
calculated
...
as
...
follows:
| Latex |
|---|
} \large $$ Q = {{\pi D^2 } \over 4}\sqrt {{{2g(h_1 - h_2 )} \over {K_{minor} }}} $$ {latex} |
where
...
h
...
1 (the
...
height
...
inside
...
the
...
tank)
...
is
...
greater
...
than
...
h
...
2 (the
...
height
...
outside
...
the
...
tank).
...
If
...
the
...
water
...
height
...
outside
...
the
...
tank
...
is
...
higher
...
than
...
that
...
inside
...
the
...
tank,
...
the
...
flow
...
is
...
assigned
...
a
...
value
...
of
...
zero.
...
This
...
equation
...
is
...
easily
...
applied
...
to
...
the
...
upper
...
portion
...
of
...
the
...
tank,
...
but
...
must
...
be
...
applied
...
individually
...
to
...
the
...
spaces
...
between
...
the
...
lower
...
baffles.
...
Using
...
this
...
equation,
...
a
...
function
...
calculates
...
the
...
flow
...
rate
...
through
...
each
...
port
...
for
...
a
...
time
...
step.
...
The
...
flow
...
rate
...
is
...
based
...
on
...
the
...
difference
...
in
...
water
...
height
...
between
...
successive
...
"tanks"
...
and
...
the
...
size
...
time
...
step
...
is
...
determined
...
using
...
known
...
flocculator
...
parameters.
...
The
...
resulting
...
height
...
due
...
to
...
the
...
flow
...
into
...
and
...
out
...
of
...
each
...
of
...
the
...
"tanks"
...
is
...
computed.
...
This
...
process
...
is
...
repeated
...
until
...
the
...
water
...
height
...
in
...
each
...
of
...
the
...
"tanks"
...
is
...
below
...
1mm.
...
The
...
cumulative
...
time
...
is
...
then
...
returned
...
from
...
the
...
function
...
as
...
the
...
total
...
time
...
required
...
to
...
drain
...
the
...
flocculator.
...
Since
...
there
...
is
...
a
...
valve
...
in
...
every
...
other
...
channel,
...
the
...
maximum
...
number
...
of
...
channels
...
being
...
drained
...
by
...
any
...
given
...
valve
...
is
...
two.
...
Therefore,
...
the
...
time
...
it
...
takes
...
to
...
drain
...
the
...
flocculator
...
can
...
be
...
approximated
...
by
...
the
...
time
...
it
...
takes
...
to
...
drain two channels. For a flocculator with two channels, there will be a valve in both channels. In this case, the port size is based on the time to drain a single channel.
A function to determine the valve diameter iterates from the smallest possible diameter to the largest diameter, calculating the respective drain times using the time function. The valve diameter function returns the smallest diameter that allows the flocculator to drain within the time defined by the user. The iteration stops once a time no greater than the desired time.
The nominal valve diameter returned is used to calculate the cross-sectional area of the port, since it is equal to the port area. The square root of this area is the length of the side of the square port. The length of the baffle slot is added as well for ease of construction.
Male Adapters
The calculated nominal diameter is that of the slip side of the adapter and is used to calculate its corresponding inner and outer diameters. The outer diameter of the slip side is also the inner diameter of the threaded side. The outer diameter of the threaded side is used as the inner diameter of the valve which fits it.
Drain Slopes
Since the center of the valve is aligned with the floor of the flocculator, slopes are required in the floor of the tank. The slopes have a width equal to the diameter of the valve and a depth equal to half the diameter (placing the center of the valve at-grade) with a slope of 30 degrees. If the distance the slope extends into the channel is longer than the spacing between baffles, the slope would extend through a baffle. To correct this problem, the distance the slope extends into the channel will be set to a distance of 5 cm from the nearest baffle.
Gate Valves
Gate valves are placed at the base of every other channel in the flocculator at-grade to allow for draining. Additionally, the design requires a drain in the first and last channel of the flocculator, so if there is an even number of channels, the first two channels (the ones closest to the entrance tank) will each have a valve.
