Energy Dissipation Flocculation Design Program
This flocculator program determines the size of the flocculator channels and number and spacing of baffles based on an energy dissipation rate determined for each 180 degree turn around a baffle. This 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. The programs used are Flocculator 3 (the design program) and floctank (the autoCAD script).
Top View
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Front View
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Flocculator Program Inputs and Outputs
Flocculation Tank Program Inputs
Flocculation Tank Program Outputs
Flocculation Tank AutoCAD Drawing Program
Flocculation Design Algorithm
The first step in the flocculator program is to assume that the headloss of the water traveling from the end of the flocculator to the sedimentation tank is negligible, with this assumption it was determined that the height of the water at the end of the flocculator is the same and water height in the sedimentation tank. The largest baffle spacing was set to be one half of the height of water at the end of the flocculator.
The width of the flocculator channels are calaculated to give the final spacing of the flocculator section a set energy dissipation rate. The equation used can be seen below. w floc channel is still used but the equation doesn't seem to look like that anymore. but it does default to 45 as the min
Unknown macro: {latex}
\large
$${W_{FlocChannel}} = {{2{Q_
Unknown macro: {Plant}
}} \over {H{W_{FlocEnd}}}}{\left( {{{{K_
Unknown macro: {FlocBaffle180}
}} \over {2P{i_{Epsilon}} \cdot H{W_{FlocEnd}} \cdot E{D_
Unknown macro: {FlocFinal}
}}}} \right)^{1/3}}$$
If this calulated width is smaller than 45 cm then the width of the flocculator channel will default to 45 cm. This minimum value was set to ensure that a person can fit into the channel for construction purposes.
Initial calculations for the flocculator assume a continuously changing baffle spacing and energy dissipation rate.
i would like to delete the vast majority of this, including pictures :
the flocculator is set to have max and min energy dissipation rate, and at certain fraction of the number of baffles in the flocculator the energy dissipation changes off of the min and then changes linearly until reaching the fraction at which the max energy dissipation begins.
a sample graph of this relationship between energy dissipation and baffle number can be seen below.
Unable to render embedded object: File (EDFlocFunction.PNG) not found.
The minimum number of baffles required in the flocculator is determined using the ratio of the collision potential of single baffle divided by the collision potential set for the entire flocculator. Collision potential for the entire flocculator is set in the Expert Client Inputs file to be 110 m 2/3 .
Collision potential for a single baffle
also, cp floc baffles does not exist in the code anymore
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\large
$$
CP.FlocBaffle\left[ {{{K.FlocBaffle180 \cdot \left(
Unknown macro: {Pi.Epsilon cdot HW.FlocEnd}
\right)2 } \over 2}} \right]1 \over 3
$$
The baffle spacing for each baffle based on the continuous energy dissipation function graphed above was determined by the following equation. and s floc baffle eq has been changed
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\large
$${S_{FlocBaffle}} = {{{Q_
Unknown macro: {Plant}
}} \over W_{FlocChannel}}{\left( {{{{K_
Unknown macro: {FlocBaffle180}
}} \over {2P{i_{Epsilon}} \cdot H{W_{FlocEnd}} \cdot E{D_
Unknown macro: {Floc}
}}}} \right)^{1/3}}$$
Graph of Baffle Spacing with Energy Dissipation
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To determine the number of channels first the total length of channel needed to fit all baffles was determined by summing the spacings needed by all baffles. A graph of this cumulative channel length is graphed versus the cumulative baffle below.
Unable to render embedded object: File (CumChannelLengthvsBaffle.PNG) not found.
Next the Cumulative Channel Length is divided by the Length of one channel and rounded up to determine the number of channels needed.
A graph of the channel number versus the baffle number can be found below.
Unable to render embedded object: File (Cumultaive Baffles vs Channel Number.PNG) not found.
A linear interpolation was performed on the the curve shown above. This fraction value is rounded up to determine the integer number of channels needs for the flocculator.
The linear interpolation method was also used to determine the number baffles that should be in each channel, based on the curve of baffle number versus channel number. The function forces there to be an even number of baffles in each channel to ensure the proper flow path. The equation used can be seen below. this n floc channel baffles is totally changed, DNE at all
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\large
$$
N.FlocChannelBaffles = 2 \cdot round\left[ {l{\mathop{\rm int erp\left(
Unknown macro: {nextChannel}
\right) - l{\mathop{\rm int}} erp\left(
Unknown macro: {previousChannel}
\right)} \over 2}} \right] - 1
$$
It is necessary to take the difference of number of baffles in the desired channel minus the previous channel to return the number baffles for just the desired channel and not the cumulative number of baffles.
The total number of baffles is N.FlocBaffles and is the sum of the vector of the number of baffles in each channel.
The spacing between baffles is set to be even throughout a channel. Knowing the number baffles in each channel and the length of channel that the baffles have to fit in, the spacing can be determined.
Spacing between baffles:
this s floc baffle seems to be different in the current code. and should be named something different here b/c right now it has the same name as the sflocbaffle above
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$$
S.FlocBaffle = L.Sed - N.FlocChannelBaffles \cdot T.FlocBaffles} \over {N.FlocChannelBaffles + 1
$$
The actual energy dissipation in each channel can be found given the actual spacing between each baffle is known.
this equation is known as ED(Q,H,S,W) in the current code
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$$
ED.FlocChannel = K.FlocBaffle180} \over {2 \cdot HW.FlocEnd \cdot Pi.Epsilon\left[ {{
Unknown macro: {Q.Plant}
\over
Unknown macro: {S.FlocBaffle cdot W.FlocChannel}
}} \right]^3
$$
The center to center distance between baffles includes the thickness of the baffles. This thickness is added to the spacing calculated above.
The total, continuous length of the flocculator (L.FlocTank) is product of the length of one floc channel (L.Sed) times the number of floc channels needed.
The residence time in the flocculator is determined based on the following equations:
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$$
Ti.Floc = HW.FlocEnd \cdot L.FlocTank \cdot W.FlocChannel} \over {Q.Plant
$$
The height of water at the beginning of the flocculator is based on the height of water at the end of the flocculator, which is the same as in the sedimentation tank, plus the headloss through the flocculator. The head loss is determined per baffle using the hl.erect function in the fluids function program.An additional 10 cm of freeboard space was added to the water level found at the beginning of the flocculator to determine the height of the flocculator walls.
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 width of this port is set to be the same as the baffle spacing in the final section minus a the thickness of the concrete lip needed to hold the baffle in place (S.FlocBaffle). It should be noted that this lip needs to be taken into account when determining baffle spacing for smaller plant when this length loss becomes significant. The height of the port is determined by the dividing the total port area, by the set width.
The length of the floc baffles is determined based on the height of water at the end of the floc tank and the height water needed for the turn.
Length of Lower Baffle:
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$$
L.FlocBaffleLower = HW.FlocEnd - S.FlocBaffle \cdot Pi.FlocBaffle
$$
The upper baffles are set to line up with the top of the tank rather than the waterlevel.
Length of Upper Baffles:
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$$
L.FlocBaffleUpper = H.Floc - S.FlocBaffle \cdot Pi.FlocBaffle
$$
The placement of the baffles in the flocculator is determined by an algorithm that creates a matrix of baffle displacements from the end of the flocculator. Water flows back and forth with flow direction alternating in each successive channel.