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PSS
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Dynamics
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Model
Introduction
The current theory of plate settlers predicts the failure for a specific sedimentation tank and plate settler spacing based on a failure mechanism called floc roll-up.
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The
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floc
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roll-up
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theory
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looks
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at
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the
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ongoing
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force
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dynamics
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acting
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on
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the
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single
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floc
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particle.
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The
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theory
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states
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that
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a
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floc
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hitting
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the
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bottom
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plate
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will
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experience
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two
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opposing
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velocities
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-
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a
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fluid
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velocity
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at
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its
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edge
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and
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a
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settling
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velocity
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due
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to
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the
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gravity force.
The velocity experienced at the edge of the particle is given by the following expression:
| Latex |
|---|
force. \\ \\ !ss.png|align=center! \\ \\ The velocity experienced at the edge of the particle is given by the following expression: \\ {latex} \large $$ {{ V_{ParticleEdge} }} = {{ 2 V_{\alpha} \left(1 - \left(\frac{R - d_{Particle}}{R} \right)^2 \right) }} $$ {latex} \\ |
Thus,
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if
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the
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velocity
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experienced
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at
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the
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particle's
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edge
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is
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greater
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than
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the
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settling
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velocity,
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then
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the
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floc
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will
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roll
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up
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and
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exit
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the
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sedimentation
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tank
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without
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being
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captured.
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Ultimately,
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the
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effluent
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turbidity
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increases.
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Conversely,
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if
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the
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floc's
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settling
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velocity
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is
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greater
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than
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the
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upflow
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velocity,
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the
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floc
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will
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roll
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down
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and
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end
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up
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being
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trapped
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in
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the
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floc
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blanket.
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The
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roll-up
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theory
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is
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based
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on
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the
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following
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assumptions:
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- The
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- velocity
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- profile
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- at
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- the
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- edge
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- of
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- the
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- particle
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- is
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- linearized.
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- Flocs
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- are
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- following
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- straight
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- lines.
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- Flocs
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- are
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- spheres.
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- There
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- is
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- no
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- floc
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- breakup
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- or
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- collision.
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- The
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- presence
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- of
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- flocs
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- do
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- not
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- affect
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- the
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- velocity
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- profile.
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- The
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- entrance
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- region
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- of
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- a
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- plate
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- settler
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- (where
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- the
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- velocity
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- profile
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- is
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- not
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- fully-developed)
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- is
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- ignored.
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The
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current
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theory
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predicts
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failure
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by
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the
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mean
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of
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a
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dimensionless
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| Latex |
|---|
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\huge $$\Pi$$ |
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which
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is
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explained
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on
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this
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page:
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.
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When
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this
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ratio
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is
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less
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than
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one,
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then
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the
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effluent
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turbidity
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should
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be
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above
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0.25
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NTU.
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This
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means
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that
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the
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spacing
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for
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a
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given
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flow
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rate
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is
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going
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to
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be
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above
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the
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maximum
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allowed
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turbidity.
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Our
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first
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experimental
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results
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showed
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that
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this
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ratio
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is
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able
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to
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predict
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effluent
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turbidity
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that
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will
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be
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above
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0.25
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NTU
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but
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it
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is
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unable
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to
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predict
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the
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magnitude
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of
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failure.
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Therefore,
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the
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PSS
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team
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concluded
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that
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a
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numerical
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simulation
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taking
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more
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phenomenon
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into
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account
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is
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needed
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in
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order
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to
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be
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able
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to
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better
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understand
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the
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failure
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mechanisms
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and
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be
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able
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to
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assess
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the
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effluent
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turbidity.
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How
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does
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the
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code
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work?
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The
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code
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works
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on
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a
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Velocity-Verlet
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algorithm
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which
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computes
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all
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particles
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paths
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based
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on
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their
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experienced
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local
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velocities.
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The
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code
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takes
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particles
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sizes,
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the
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tube
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(or
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plate)
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geometry,
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and
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the
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up
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flow
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velocity
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as
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an
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input.
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The
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figure
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below
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summarizes
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the
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steps
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taken
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by
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the
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algorithm:
The output of the program is the number of particles that were not captured and their respective paths.
Further Developments
The team plans to adjust some of the parameters in order to be able to compare (at least roughly) the results and predictions of the numerical model with the experiments.
Further steps include implementing more interactions than floc roll up (e.g. floc break-up, floc recombination and how flocs influence the local velocity profile. Hence, the plate settler performance).