...
Horizontal
...
Flow
...
Flocculation
...
Design
...
Program
...
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
...
and
...
the
...
specification
...
of
...
horizontal
...
flow.
...
Horizontal
...
flow
...
is
...
used
...
for
...
very
...
high
...
flow
...
rates
...
to
...
avoid
...
building
...
the
...
plants
...
even
...
taller,
...
instead
...
making
...
them
...
wider.
...
Horizontal
...
flocculators
...
are
...
also
...
easier
...
to
...
drain
...
than
...
vertical
...
flocculators
...
made
...
of
...
cement
...
baffles
...
because
...
individual
...
drains
...
are
...
not
...
needed
...
for
...
every
...
lower
...
baffle
...
as
...
they
...
are
...
in
...
the
...
vertical
...
flocculator.
...
The
...
tank
...
is
...
designed
...
given
...
an
...
optimal
...
energy
...
dissipation
...
rate
...
to maximize the opportunity for flocs to form and to produce flocs that are small enough that they can be transported to the sedimentation tank without breaking.
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). The design program from horizontal flow is integrated into the same program used to design vertical flow flocculators and an algorithm is used to select between the two designs.
Generic | Vertical | Horizontal |
Ρ | W | H |
S | S | S |
J | H | W |
To create a consistent relation between vertical and horizontal flow, generic notation is used. J represents the flow travel distance between flow direction changes. The flow area, which is the cross sectional area that is perpendicular to the flow of the water, is P*S.
Top View
Flocculation Design Algorithm
Each section outlined below corresponds to its equivalent MathCAD code, identified by the same titles.
To view the first part that informs and establishes the equations and design ideas used in the actual drawing of the tank refer to the Vertical Flow Flocculation Design Program page as these equations and ideas are the same.
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.
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.
Calculating the number of baffle spaces that gives the target ED and CP is done with a non-iterative code (as opposed to the vertical code which is iterative sometimes). The optimal J/S value of 3 found from the CFD calculations can be used for horizontal flocculators since the flocculator can be made as wide as necessary (whereas in vertical flocculation, J was constrained by the height of the sedimentation tank), so iteration is not needed. The space between two baffles is determined using the following code:
| Latex |
|---|
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|https://confluence.cornell.edu/display/AGUACLARA/AutoCAD+Flocculation+Tank+Program]). 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). The design program from horizontal flow is integrated into the same program used to design vertical flow flocculators and an [algorithm|Choosing Horizontal or Vertical] is used to select between the two designs. | Generic | Vertical | Horizontal | | Ρ | W | H | | S | S | S | | J | H | W | 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. h2. Top View !Horizontal Top Dimensions.PNG|width=1081,height=596! h2. Flocculation Design Algorithm Each section outlined below corresponds to its equivalent MathCAD code, identified by the same titles. To view the first part that informs and establishes the equations and design ideas used in the actual drawing of the tank refer to the [Vertical Flow Flocculation Design Program] page as these equations and ideas are the same. 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. 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. Calculating the number of baffle spaces that gives the target ED and CP is done with a non-iterative code (as opposed to the vertical code which is iterative sometimes). The optimal J/S value of 3 found from the CFD calculations can be used for horizontal flocculators since the flocculator can be made as wide as necessary (whereas in vertical flocculation, J was constrained by the height of the sedimentation tank), so iteration is not needed. The space between two baffles is determined using the following code: {latex} \large $$ S = \mathop {\left( {{{\mathop Q\nolimits_{Plant} } \over {\mathop P\nolimits_{FlocChannel} }}} \right)}\nolimits^{{3 \over 4}} \mathop {\left( {{1 \over {\mathop {Pi}\nolimits_{JS} }}} \right)}\nolimits^{{1 \over 4}} \mathop {\left( {{{\mathop K\nolimits_P \mathop \alpha \nolimits_\varepsilon } \over {2ED}}} \right)}\nolimits^{{1 \over 4}} $$ {latex} \\ The number of spaces per channel is determined by a |
The number of spaces per channel is determined by a non-iterative
...
code
...
also
...
since
...
the
...
length
...
of
...
the
...
channels
...
are
...
fixed
...
to
...
be
...
the
...
length
...
of
...
the
...
sedimentation
...
tank.
...
Unlike
...
in
...
vertical
...
flow
...
flocculation,
...
channels
...
will
...
always
...
have
...
an
...
odd
...
number
...
of
...
spaces
...
to
...
ensure
...
that
...
water
...
flows
...
into
...
successive
...
channels
...
and
...
eventually
...
into
...
the
...
sedimentation
...
tank.
...
See
...
Calculation
...
of
...
Flocculator
...
Geometry
...
for
...
this
...
equation.
Calculation of Flocculator Geometry
The depth of water at the end of the flocculation tank is set by the user. The different options are described in the algorithm that chooses between horizontal and vertical. If the floc tank is shallower than the sed tank, the floc tank is elevated so that the water levels match.
The number and spacing of floc spaces and floc baffles is calculated, as well as the Collision Potential, for the specific tank being drawn. The number of floc spaces is determined using the following function which forces the number of spaces to be an odd integer:
| Latex |
|---|
h2. Calculation of Flocculator Geometry The height of water at the end of the flocculation tank is set by the user. The different options are described in the [algorithm|Choosing Horizontal or Vertical] that chooses between horizontal and vertical. If the floc tank is shallower than the sed tank, the floc tank is elevated so that the water levels match. The number and spacing of floc spaces and floc baffles is calculated, as well as the Collision Potential, for the specific tank being drawn. The number of floc spaces is determined using the following function which forces the number of spaces to be an odd integer: {latex} \large $$ {N_{FlocSpacesF}}(L,{\rm{T}},S) = Floor({{L + {\rm{T}}} \over {S + {\rm{T}}}} + 1,2) - 1 $$ {latex} \\ When calculating the |
When calculating the spacing,
...
L
...
represents
...
the
...
length
...
of
...
the
...
sed
...
tank
...
L.Sed
...
and
...
T
...
represents
...
the
...
thickness
...
of
...
a
...
baffle
...
T.FlocBaffle
...
.
...
The
...
minimum
...
baffle
...
spacing
...
is
...
45
...
cm,
...
which
...
is
...
the
...
width
...
that
...
a
...
human
...
could
...
walk
...
through
...
if
...
needed
...
for
...
maintenance.
...
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.
...
Since
...
the
...
horizontal
...
design
...
is
...
untapered,
...
each
...
channel
...
should
...
have
...
the
...
same
...
baffle
...
spacing,
...
but
...
the
...
code
...
was
...
kept
...
as
...
similar
...
to
...
the
...
vertical
...
code
...
as
...
possible.
...
The
...
exception
...
is
...
the
...
last
...
channel,
...
which
...
might
...
have
...
corrected
...
spacing
...
to
...
make
...
up
...
for
...
the
...
wide
...
entrance
...
into
...
the
...
inlet
...
channel.
| Latex |
|---|
} \large $$ B_{FlocBaffle} = S_{FlocBaffle} + T_{FlocBaffle} $$ {latex} \\ The total number of channels is found by dividing the total target collision potential by the collision potential per space and rounding that value up according to how many spaces are in a channel. The residence time in the flocculator is determined as follows: {latex} |
The total number of channels is found by dividing the total target collision potential by the collision potential per space and rounding that value up according to how many spaces are in a channel.
The residence time in the flocculator is determined as follows:
| Latex |
|---|
\large
$$
Ti_{Floc} = {{HW_{FlocEnd} \cdot L_{FlocTank} \cdot
{{\rm P}_{FlocChannel}}} \over {Q_{Plant}}}
$$
{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) based on the minor loss coefficient for flow around a baffle. 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:
| 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} \large $$ HL_{FlocBaffle} = {{{Kp \cdot ({{J_{FlocChannel}} \over {S_{FlocBaffle}}}) \cdot Q_{Plant}^2 } \over {2 \cdot g \cdot (S_{FlocBaffle} \cdot P_{FlocChannel})^2 }}} $$ {latex} \\ Water flows between channels in the flocculator. There are no ports as there were for the vertical flocculator because they were only necessary to maintain the vertical flow pattern. The width is the same as the baffle spacing in the previous channel and the height is the height of the floc tank. \\ h2. Position Calculations for Each Baffle The length of the lower floc baffles and upper floc baffles that was seen in vertical flow is now the length of the left and right baffles (both are on the same height level). These baffles are set to line up with the top of the tank rather than the water level. The baffles are oriented to switch from one side of the tank channel's wall to other ("east" to "west") so that the flow of water is smooth back and forth through the tank. The baffles must be staggered in opposite directions in each channel so that the baffles at the end will form the necessary channel connecting the larger floc channels. Length of "Lower" Baffle = Length of "Upper" Baffle: {latex} |
Water flows between channels in the flocculator. There are no ports as there were for the vertical flocculator because they were only necessary to maintain the vertical flow pattern. The width is the same as the baffle spacing in the previous channel and the height is the height of the floc tank.
Position Calculations for Each Baffle
The length of the lower floc baffles and upper floc baffles that was seen in vertical flow is now the length of the left and right baffles (both are on the same height level). These baffles are set to line up with the top of the tank rather than the water level. The baffles are oriented to switch from one side of the tank channel's wall to other ("east" to "west") so that the flow of water is smooth back and forth through the tank. The baffles must be staggered in opposite directions in each channel so that the baffles at the end will form the necessary channel connecting the larger floc channels.
Length of "Lower" Baffle = Length of "Upper" Baffle:
| Latex |
|---|
\large
$$
L_{FlocBaffleLower} = J_{FlocChannel} - S_{FlocBaffle}
$$
$$
L_{FlocBaffleUpper} = J_{FlocChannel} - S_{FlocBaffle}
$$
{latex}
|
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
...
...
...
for
...
step-by-step
...
details
...
of
...
how
...
the
...
lamina,
...
baffles,
...
and
...
other
...
tank
...
details
...
are
...
drawn).
...
All
...
baffles
...
are
...
also
...
placed
...
at
...
the
...
bottom
...
of
...
the
...
tank,
...
which
...
is
...
represented
...
in
...
a
...
Z-matrix
...
for
...
the
...
baffles.
Drain Design
Port Sizing
The time it takes to drain the flocculator can be approximated by:
| Latex |
|---|
\\large $$ D = {\sqrt {{\sqrt {h_0 }} \over {{{\pi t} \over {8A_{res} }}\sqrt {{{2g} \over {K_{minor} }}} }}} $$ |
where D is the nominal valve diameter, ho is the initial water height in the flocculator, Ares is the plan area the entire tank, and Kminor is the minor loss coefficient associated with the valve and subsequent expansion. Since there is a valve in every other channel, the maximum number of channels being drained by any given valve is two. Applying this equation to two channels gives the calculated value for the idealized size of the valve, which is then rounded up to the next available nominal diameter. For a flocculator that has only two channels, each of the channels will have a valve in it. In this case, the above equation will be applied to a single channel only.
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.
| Wiki Markup |
|---|
h2. Drain Design h3. Port Sizing 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: {latex} \large $$ D = {\sqrt {{\sqrt {h_0 }} \over {{{\pi t} \over {8A_{res} }}\sqrt {{{2g} \over {K_{minor} }}} }}} $$ {latex} where D is the nominal valve diameter, h{~}o~ is the initial water height in the flocculator, A{~}res~ is the plan area of two channels in the flocculator, and K{~}minor~ is the minor loss coefficient associated with the valve. 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. h3. Couplings The nominal valve diameter is the inner diameter of the slip side of the adapter, and is used to calculate the outer diameter of the slip side. The nominal diameter is also the outer diameter on the threaded side which will be used as the inner diameter for the valve that fits it. \\ {float:left|border=2px solid black} [!sw iso horiz coupling.bmppng|width=1000px600px!|AutoCAD Channel Program] SlopeAdapters for inDraining Floorthe of Flocculator {float} |
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.
| Wiki Markup |
|---|
\\ h3. 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. \\ {float:left|border=2px solid black} [!horiz floc slopes side by side.PNG|width=1000px!|AutoCAD Channel Program] Slope in Floor of Flocculator {float} |
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.
| Wiki Markup |
|---|
of Flocculator {float} \\ h3. 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. \\ {float:left|border=2px solid black} [!sw iso horiz valves.bmppng|width=1000px!|AutoCAD Channel Program] SlopeValves for inDraining Floor ofthe Flocculator {float} \\ \\ \\ \\ |