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
Unable to render embedded object: File (top view floc vert.bmp) not found.
Front View
Unable to render embedded object: File (front view floc vert.bmp) not found.
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.
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.
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:
Unknown macro: {latex}
=
$$
\large
$$
N_
L + T} \over {S + T$$
The ceiling, floor, and round functions are used to force this number to be even (so that the water flows from port to port in all channels except the last). When trying to find the minimum number of spaces that can fit in a channel, the value is rounded up. When trying to find the maximum number of spaces that can fit into a channel, the value is rounded down. Otherwise, the value is just rounded.
When calculating both the min and the max, L represents the length of the sed tank L.Sed and T represents the thickness of a baffle T.FlocBaffle. To get the maximum number of floc baffles, S is taken as the minimum floc baffle spacing S.FlocBaffleMin. However, to get the minimum number of floc baffles, S is taken as
Unknown macro: {latex}
\large
$$
{{J } \over {Pi_
Unknown macro: {JSMin}
}}
$$
where Pi.JSMin is a parameter describing the minimum ratio of water depth to baffle spacing.
Rigid Calculations
The baffle spacing is set as the maximum of a human width and J/3 (the optimal value). The channel width can then be directly calculated with no iteration.
Calculations Applicable to Both Baffle Types
The center-to-center distance between baffles includes the spacing between baffles and the thickness of the baffles, for each channel. This is an array with an element for each channel, as each channel may have different baffle spacing.
Unknown macro: {latex}
\large
$$
B_
Unknown macro: {FlocBaffle}
= S_
+ T_
Unknown macro: {FlocBaffle}
$$
The residence time in the flocculator is determined as follows:
Unknown macro: {latex}
\large
$$
Ti_
Unknown macro: {Floc}
= {{J_
Unknown macro: {FlocChannel}
\cdot L_
Unknown macro: {FlocTank}
\cdot P_{FlocChannel}} \over {Q_
Unknown macro: {Plant}
}}
$$
The height of water at the beginning of the flocculator is based on the height of water at the end of the flocculator plus the headloss through the flocculator. The head loss is determined per baffle (and per channel, and in the whole flocculator) using the HL function in the fluids functions program. An additional 10 cm of freeboard space was added to the water level (HW) found at the beginning of the flocculator to determine the height of the flocculator walls.
The head loss per baffle in each channel:
Unknown macro: {latex}
\large
$$
HL_
Unknown macro: {FlocBaffle}
= {Kp \cdot ({{J_{FlocChannel \over {S_
}}) \cdot Q_
Unknown macro: {Plant}
^2 } \over {2 \cdot g \cdot (S_
Unknown macro: {FlocBaffle}
\cdot P_
Unknown macro: {FlocChannel}
)^2 }}}
$$
Water flows between channels in the flocculator through ports cut in the concrete. The area of these ports is determined to ensure flocs will not be broken up.
The energy dissipation rate through the ports is set to be same as around the baffles; the dimensions of the port are calculated to be the same as that of the baffles.
Unknown macro: {latex}
\large
$$
W_
Unknown macro: {FlocPortEst}
= S_
Unknown macro: {FlocBaffle}
$$
The width of these ports is set to include the thickness of the concrete lip needed to hold the baffle in place.
Unknown macro: {latex}
\large
$$
W_
Unknown macro: {FlocPort}
= W_
Unknown macro: {FlocPortEst}
- S_
Unknown macro: {FlocChannel}
$$
Position Calculations for Each Baffle
The length of the lower floc baffles is determined based on the height of water at the end of the floc tank and the water as it goes around each turn. The baffles are oriented to go up-down-up-down so that the flow of water is smooth through the tank. This order, however, is reversed in the last channel, since there is an even number of baffles and the water must flow under the last baffle and up to the exit port that leads to the sed tank.
Length of Lower Baffle:
Unknown macro: {latex}
\large
$$
L_
Unknown macro: {FlocBaffleLower}
= J_
Unknown macro: {FlocChannel}
- S_
Unknown macro: {FlocBaffle}
\cdot Pi_
$$
The upper baffles are set to line up with the top of the tank rather than the water level.
Length of Upper Baffles:
Unknown macro: {latex}
\large
$$
L_
Unknown macro: {FlocBaffleUpper}
= H_
Unknown macro: {Floc}
- S_
Unknown macro: {FlocBaffle}
\cdot Pi_
$$
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.
Unknown macro: {float}
Baffle in the Way of the Exit Port
If there is one baffle in the way, the program respaces the baffles, 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 respaces 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 specified by the user. The time required to drain a tank is:
Unknown macro: {latex}
\large
$$
t = {{\sqrt
Unknown macro: {h_0 }
- \sqrt h } \over {{{A_
Unknown macro: {or}
} \over {2A_
Unknown macro: {res}
}}\sqrt {{
Unknown macro: {2g}
\over {K_
Unknown macro: {minor}
}}} }}
$$
where ho is the initial water height in the tank, h is the water height at time t, Aor is the area of the orifice through which the water drains (in this case the port or valve area), Ares is the plan area of the reservoir or tank, and Kminor is the minor loss coefficient associated with the flow.
Using the above equation, the flocculator can be separated into two parts. The first part is the horizontal portion above the top lower baffles where the water drains as a single tank; the highest lower baffle was used for this calculation, resulting in a slight overestimate of the total drain time. The second part is the portion below the top of the lower baffles where these baffles form small "tanks" within the flocculator. For the upper portion, the area of the orifice is the area of the valve,
Unknown macro: {latex}
\large
$$
({{\pi D_
Unknown macro: {valve}
^2 } \over 4})
$$
and the minor loss coefficient is that associated with the chosen valve.
The flow through the tank is calculated as follows:
Unknown macro: {latex}
\large
$$
Q = {{\pi D^2 } \over 4}\sqrt {{
Unknown macro: {2g(h_1 - h_2 )}
\over {K_
Unknown macro: {minor}
}}}
$$
where h1 (the height inside the tank) is greater than h2 (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 the two channels with the most "tanks" in them.
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.
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.
Unable to render embedded object: File (coupling.bmp) not found.
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.
Unable to render embedded object: File (gate valve.bmp) not found.