h1. 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.
h5. Top View
!floc tank top view.PNG!
h5. Front View
!floctank front view.PNG!
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]
h3. 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.
{latex}
\large
$${W_{FlocChannel}} = {{2{Q_{Plant}}} \over {H{W_{FlocEnd}}}}{\left( {{{{K_{FlocBaffle180}}} \over {2P{i_{Epsilon}} \cdot H{W_{FlocEnd}} \cdot E{D_{FlocFinal}}}}} \right)^{1/3}}$$
{latex}
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.
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.
!EDFlocFunction.PNG!
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:
{latex}
\large
$$
CP.FlocBaffle\left[ {{{K.FlocBaffle180 \cdot \left( {Pi.Epsilon \cdot HW.FlocEnd} \right)^2 } \over 2}} \right]^{{1 \over 3}}
$$
{latex}
The baffle spacing for each baffle based on the continuous energy dissipation function graphed above was determined by the following equation.
{latex}
\large
$${S_{FlocBaffle}} = {{{Q_{Plant}}} \over {{W_{FlocChannel}}}}{\left( {{{{K_{FlocBaffle180}}} \over {2P{i_{Epsilon}} \cdot H{W_{FlocEnd}} \cdot E{D_{Floc}}}}} \right)^{1/3}}$$
{latex}
Graph of Baffle Spacing with Energy Dissipation
!FlocBaffleSpacing.PNG!
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.
!CumChannelLengthvsBaffle.PNG!
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.
!Cumultaive Baffles vs Channel Number.PNG!
TheA centerlinear tointerpolation centerwas distanceperformed betweenon baffles includesthe the thicknesscurve ofshown the bafflesabove. This fraction thicknessvalue is addedrounded up to determine the spacing calculated above.
The next step is to calculate integer number of channels needs for the flocculator.
The linear interpolation method was also used to determine the number of bafflesbaffles that should be in each spacing section. The channel, based on the curve of baffle number ofversus baffleschannel pernumber. spacingThe sectionfunction isforces foundthere to be an aeven rationumber of energy dissipation ratios forbaffles in each channel to ensure the entireproper sectionflow overpath. theThe energyequation dissipationused ratiocan forbe aseen singlebelow. baffle.
{latex}
\large
$${N_{FlocBaffleSection}} = ceil\left(
N.FlocChannelBaffles = 2 \cdot round\left[ {{{Pl{i_{FlocCP}}\mathop{\rm int}} erp\left( {nextChannel} \overright) - {lengthl{\mathop{\rm int}} erp\left( {E{D_{Floc}}}previousChannel} \right)P{i_{FlocBaffleCP}}}} \over 2}} \right)] - 1
$$
{latex}
The length ofIt is necessary to take the difference flocculatorof takennumber upof bybaffles thein the bafflesdesired ischannel determinedminus bythe summingprevious thechannel productto ofreturn the number of baffles in each section byfor just the spacingdesired forchannel eachand section.not
{latex}
\large
$${L_{FlocSections}} = \sum {{B_{FlocBaffle}}{N_{FlocBaffleSection}}} $$
{latex}
The the cumulative number of baffles.
The total number of channelsbaffles inis theN.FlocBaffles flocculatorand is determinedthe bysum takingof the estimatedvector length of the number flocculatorof neededbaffles toin fit all of theeach channel.
The spacing between baffles andis dividingset byto thebe lengtheven ofthroughout thea sedimentation tankchannel. Each ofKnowing the flocculatornumber channelsbaffles isin seteach tochannel beand samethe length of channel asthat the sedimentation tank. The resulting fractional number of channels is rounded up. baffles have to fit in, the spacing can be determined.
Spacing between baffles:
{latex}
\large
$${N_{FlocChannels}} = ceil\left( {{{{L_{FlocTankEst}}
S.FlocBaffle = {{L.Sed - N.FlocChannelBaffles \cdot T.FlocBaffles} \over {{L_{Sed}}}}} \right)N.FlocChannelBaffles + 1}}
$$
{latex}
The totalactual exactenergy lengthdissipation ofin theeach flocculatorchannel iscan recalculatedbe byfound multiplyinggiven the numberactual ofspacing channelsbetween byeach thebaffle length of one floc channelis know.
{latex}
\large
$${L_{FlocTank}} = {N_{FlocChannels}} \cdot {L_{Sed}}
ED.FlocChannel = {{K.FlocBaffle180} \over {2 \cdot HW.FlocEnd \cdot Pi.Epsilon}}\left[ {{{Q.Plant} \over {S.FlocBaffle \cdot W.FlocChannel}}} \right]^3
$$
{latex}
The residence time center to center distance between baffles includes the thickness of the flocculator baffles. This thickness is added to the spacing calculated with above.
The total, continuous length of the equationflocculator below. From the floc model created by Monroe Weber-Shirk, the ideal(L.FlocTank) is product of the length of one floc channel (L.Sed) times the number of floc channels needed.
The residence time was found to be around 20 minutes. in the flocculator is determined based on the following equations:
{latex}
\large
$${\theta _{Floc}}
Ti.Floc = {{H{W_{FlocEnd}}HW.FlocEnd \cdot {L_{.FlocTank}} \cdot {W_{.FlocChannel}}} \over {{Q_{.Plant}}}}
$$
{latex}
The height of water at the beginning of the flocculator channel is determined by adding the head loss through the flocculator to the water level at the end of 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|Fluids Functions Design 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.This The width of this port is doneset byto settingbe the port to have an energy dissipation rate no greater than that of the final section.
The width of this port is set to be the same as the baffle spacing in the final sectionsame 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:
{latex}
\large
$$
L.FlocBaffleLower = HW.FlocEnd - S.FlocBaffle \cdot Pi.FlocBaffle
$$
{latex}
The upper baffles are set to line up with the top of the tank rather than the waterlevel.
Length of Upper Baffles:
{latex}
\large
$$
L.FlocBaffleUpper = H.Floc - S.FlocBaffle \cdot Pi.FlocBaffle
$$
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.
| 