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Lamella
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Design
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Program
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The
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lamella
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are
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the
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plate
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settlers
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place
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in
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the
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top
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section
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of
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the
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sedimentation
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tank
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that
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help
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floc
...
settle
...
out efficiently. 
Lamella Design Program Algorithm
The Lamella Design Program uses four constraints to determine design values, the critical velocity of 10 m/day, the upward velocity at the bottom of the tank, the minimum space between the lamella and the predetermined length of the sedimentation tank. All of these constraints come together to determine the length of the lamella. The minimum spacing between the lamella was determine via laboratory experiments, at spacing closer than 2 cm failure occured. The length of the sedimentation tank is set by the Sedimentation Program. The critical velocity is the rate at which a particle must fall to ensure that it settles out within the plate settlers. If the critical velocity is too large, flocs will not settle out, and will remain in the water sent through the distribution system. However, a small critical velocity comes at the expense of a large cross sectional tank area (so it is not practical to have an unnecessarily small critical velocity). The upward velocity at the bottom of the tank is important for sludge blanket formation, too high and the blanket will form too thin and will not capture particles, too slow and the blanket will either settle out instead of remaining suspended or the shear value in the blanket will be so high that flocs will get broken up in the blanket. Either of these issues would result in the sludge blanket being detrimental to the sedimentation process.
The program starts by determining the height needed for the launders above the lamella. This height needed for the launders is same as the depth of water needed above the lamella. This value is simply a function of leaving enough available headloss through the exit launder about the lamella to keep it properly submerged.
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To determine what the how long the lamella need to be, first the active length of the tank and the upward velocity under the lamella must be determined, but both of these values are dependent upon the length of the lamella. Therefore, an iterative loop of the following three equations was created to determine length of the lamella.
The active length of the tank is the total length of the sedimentation tank minus the inactive length of the sedimentation tank found below.
| Latex |
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efficiently. !lamella front view.png! !lamella front view close up.png! h2. Lamella Design Program Inputs and Outputs [Lamella Program Inputs|Lamella Design Program Inputs] [Lamella Program Outputs|Lamella Design Program Outputs] h2. Lamella Design Program Algorithm The Lamella Design Program uses four constraints to determine design values, the critical velocity of 10 m/day, the upward velocity at the bottom of the tank, the minimum space between the lamella and the predetermined length of the sedimentation tank. All of these constraints come together to determine the length of the lamella. The minimum spacing between the lamella was determine via laboratory experiments, at spacing closer than 2 cm failure occured. The length of the sedimentation tank is set by the [Sedimentation Program|Sedimentation Design program]. The critical velocity is the rate at which a particle must fall to ensure that it settles out within the plate settlers. If the critical velocity is too large, flocs will not settle out, and will remain in the water sent through the distribution system. However, a small critical velocity comes at the expense of a large cross sectional tank area (so it is not practical to have an unnecessarily small critical velocity). The upward velocity at the bottom of the tank is important for sludge blanket formation, too high and the blanket will form too thin and will not capture particles, too slow and the blanket will either settle out instead of remaining suspended or the shear value in the blanket will be so high that flocs will get broken up in the blanket. Either of these issues would result in the sludge blanket being detrimental to the sedimentation process. The program starts by determining the height needed for the launders above the lamella. This height needed for the launders is same as the depth of water needed above the lamella. This value is simply a function of leaving enough available headloss through the exit launder about the lamella to keep it properly submerged. {include:H.SedAbove} To determine what the how long the lamella need to be, first the active length of the tank and the upward velocity under the lamella must be determined, but both of these values are dependent upon the length of the lamella. Therefore, an iterative loop of the following three equations was created to determine length of the lamella. The active length of the tank is the total length of the sedimentation tank minus the inactive length of the sedimentation tank found below. {latex} \large $$ L.Inactive = L.SedPlate \cdot \cos (AN.SedPlate) + W.InletChannel + W.ExitChannel + 2 \cdot T.ChannelWall $$ {latex} \\ The upward velocity through the lamella: {latex} |
The upward velocity through the lamella:
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\large
$$
V.SedUpActiveBelow = {{Q.Sed} \over {W.Sed \cdot \left( {L.Sed - L.SedInactive} \right)}}
$$
{latex}
\\
Length of the Lamella:
{latex} |
Length of the Lamella:
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|---|
\large
$$
L.SedPlateEst = {{B.SedPlateMin \cdot \left( {{{V.SedUpActiveBelow} \over {V.SedCBod}} - 1} \right) + T.SedPlate} \over {\sin \left( {AN.SedPlate} \right) \cdot \cos \left( {AN.SedPlate} \right)}}
$$
|
The length found in the above loop is an estimated length, The actual lamella length is dependent on the length of the plastic sheeting material that available. Typically this sheeting length is either 8 or 12 feet.
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{latex} The length found in the above loop is an estimated length, The actual lamella length is dependent on the length of the plastic sheeting material that available. Typically this sheeting length is either 8 or 12 feet. {latex} \large $$ L.SedPlate = {{L.SedPlateSheet} \over {floor\left( {{{L.SedPlateSheet} \over {L.SedPlateEst}}} \right)}} $$ {latex} From this number the actual upward velocity |
From this number the actual upward velocity (V.SedUpActiveBelow)
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under
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the
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lamella
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and
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the
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actual
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space
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needed
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between
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the
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lamella
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are
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recalculated.
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The
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equation
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for
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V.SedUpActiveBelow
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is
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the
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same
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was
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used
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above.
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The
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perpendicular,
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center
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to
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center,
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space
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between
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lamella:
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} \large $$ B.SedPlate = {{L.SedPlate \cdot \sin \left( {AN.SedPlate} \right) \cdot \cos \left( {AN.SedPlate} \right) - T.SedPlate} \over {{{V.SedUpActiveBelow} \over {V.SedCBod}} - 1}} $$ {latex} |
Perpendicular
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open
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space
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between
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lamella
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(does
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not
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include
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material
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thickness):
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|
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The
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horizontal
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distance
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between
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lamella;
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this
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accounts
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for
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the
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angle
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of
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the
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lamella
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in
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the
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tank:
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} \large $$ B.SedPlateHorizontal = {{B.SedPlate} \over {\sin \left( {AN.SedPlate} \right)}} $$ {latex} |
Using
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the
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available
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active
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length
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in
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the
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sedimentation
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tank
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and
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the
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known
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length
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of
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the
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lamella,
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the
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number
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of
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lamella
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that
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can
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fit
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in
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the
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tank
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can
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be
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calculated
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as
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follows.
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The
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Number
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of
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Lamella:
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} \large $$ N.SedPlates = ceil\left( {{{L.SedActiveMax} \over {B.SedPlateHorizontal}}} \right) $$ {latex} |
The
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vertical
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height
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taken
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up
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by
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the
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lamella
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is
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simply
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a
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function
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of
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the
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lamella
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length
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and
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angle.
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} \large $$ H.SedPlate = L.SedPlate \cdot \cos \left( {AN.SedPlate} \right) $$ {latex} |
The
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thickness
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of
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the
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lamella
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contributes
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a
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small
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but
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significant
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dead
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zone
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to
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the
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tank.
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Now
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that
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the
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exact
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number
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of
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lamella
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has
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been
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calculated,
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more
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accurate
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values
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of
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active
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tank
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length,
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upward
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velocity,
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and
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critical
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velocity
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can
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be
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found.
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Calculations
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for
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these
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values
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are
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shown
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below.
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Active
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Length
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of
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the
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Tank:
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|---|---|---|---|---|
|
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The
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Actual
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Upward
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Velocity
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at
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the
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Bottom
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of
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the
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Tank:
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|---|---|---|---|---|
|
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The
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Critical
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Velocity
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Up
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through
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the
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Lamella:
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|---|---|---|---|---|
|
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The
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height
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of
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the
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water
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in
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the
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sedimentation
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tank
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can
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now
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be
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determined.
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The
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inletchannel
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and
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the
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lamella
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and
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launders
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coexist
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in
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the
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same
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top
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portion
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the
...
tank.
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Therefore
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the
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water
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height
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is
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the
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maximum
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of
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these
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two
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pieces
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plus
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space
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needed
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for
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the
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elements
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in
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the
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bottom
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of
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the
...
tank,
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which
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include
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the
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inlet
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manifold
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and
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drain.
| Latex |
|---|
}
\large
$$
HW.Sed = \max \left( {\left( {Z.SedSlopes + H.SedFrameWall + H.SedBetween + 2 \cdot outerdiameter(ND.SedPlateFrame) + H.SedPlate + H.SedAbove} \right),\left( {H.SedManifoldPort + H.SedBetween + T.ChannelWall + H.InletChannel} \right)} \right)
$$
|
where
For tanks where there are more than one bay per tank, a wall is constructed to separate bays. This wall has height that comes up to the top of ledge that supports the lamella frame. This was done so that the wall can lend support to the center section of the lamella. The equation used is as follows.
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{latex}
where
!Sed tank Water height.PNG!
For tanks where there are more than one bay per tank, a wall is constructed to separate bays. This wall has height that comes up to the top of ledge that supports the lamella frame. This was done so that the wall can lend support to the center section of the lamella. The equation used is as follows.
{latex}
\large
$$
H.SedBayDivider = Z.SedSlopes + H.SedFrameWall
$$
|
The inlet manifold is formed by laying concrete plates next to each other. The width of each slope plate is defined by the user. If the length of the sedimentation tank is not equally divided by the width of the plate, there is a leftover space that needs to be filled by a fraction of a plate. This is used for construction purposes. More details of about the inlet manifold can be found on the inlet manifold design page. It should be noted that this calculation could not be done in the inlet manifold program because the size of the inlet channel was needed, and the inlet channel is not defined until after the inlet manifold program.
| Latex |
|---|
{latex} The inlet manifold is formed by laying concrete plates next to each other. The width of each slope plate is defined by the user. If the length of the sedimentation tank is not equally divided by the width of the plate, there is a leftover space that needs to be filled by a fraction of a plate. This is used for construction purposes. More details of about the inlet manifold can be found on the [inlet manifold design page|Sedimentation Inlet Slopes Design Program]. It should be noted that this calculation could not be done in the inlet manifold program because the size of the inlet channel was needed, and the inlet channel is not defined until after the inlet manifold program. {latex} \large $$ {\rm{W}}_{{\rm{SedSlopePlateRemaining}}} = L_{Sed} - N_{SedPorts} \cdot W_{SedSlopePlate} $$ {latex} |