*** This version of Confluence is for testing only and contains a copy of content from June 29th 2026. No changes will be preserved. ***
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Gtheta
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Computations
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using
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UDF
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Methodology
A
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User
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Defined
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FLUENT
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script
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(
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...
)
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was
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created
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to
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extract
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the
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G_theta
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value
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from
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the
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flocculator.
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The
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UDF
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loops
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through
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all
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of
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the
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individual
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cells
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of
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the
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converged
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solution,
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and
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extracts
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the
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energy
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dissipation^1/2
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times
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the
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cell
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area.
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The
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sum
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of
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this
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quantity
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for
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all
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cells
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divided
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by
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flow
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and
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square
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of
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viscoisty
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results
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in
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the
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G_theta
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value
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of
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the
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entire
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flocculator
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as
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shown
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in
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equation
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1.
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Gθ_baffle=1/Q*vis^(-1/2)*∑(ε^(1/2)*cell_area)
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Eq.
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1
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The
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above
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formulation
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has
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been
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determined
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(with
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Monroe's
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help)
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by
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weighting
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the
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value
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of
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Gθ
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by
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volume.
The Gθ_baffle
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values
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weighted
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by
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the
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area
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or
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number
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of
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cells
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were
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also
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examined,
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but
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these
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formulations
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do
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not
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produce
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sensible
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results.
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Gθ Computation
Below is the Gθ values for flocculation tanks of different geometries:
Case Geometry (h-height,b-width,N-baffles) |
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Gθ_Flocculator |
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b=.1, |
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h=1, |
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N=1, |
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Clearance |
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height=.15 |
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430 | |
b=.1, |
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h=.3, |
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N=5, |
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sym |
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bc | 1330 |
b=.1, |
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h=.2, |
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N=5 |
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1060 |
Normalizing the Gθ parameter
The Gθ value increases with increasing flocculation tank volume. Thus, when comparing different designs, each case should be normalized by the volume (or area for 2D geometries). This results in the following normalized values.
Case Geometry (h-height,b-width,N-baffles) |
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Gθ_Flocculator/m^2 |
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b=.1, |
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h=1, |
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N=1, |
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Clearance |
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height=.15 |
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4,300 |
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b=.1, |
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h=.3, |
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N=5, |
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sym |
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bc | 8,870 |
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b=.1, |
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h=.2, |
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N=5 |
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10,600 |
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Comparison to Flocculation Tanks
Literature rates flocculators based on the Gθ value, as well as the G, epsilon value, and θ-value. For flocculators without recirculating solids, the recommended Gθ is 20,000-150,000
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(Schulz,
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C.
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R.
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and
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D.
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A.
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Okun
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(1984).
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Surface
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Water
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Treatment
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for
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Communities
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in
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Developing
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Countries
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,
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John
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Wiley
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&
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Sons).
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This
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would
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correspond
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to
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2-15
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m^2
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of
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flocculator
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area
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based
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on
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the
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weighted
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Gθ-values
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calculated.
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This
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seems
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to
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be
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the
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area
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of
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flocculators
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currently
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used
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in
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practice
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in
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Honduras.
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Thus,
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the
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calculated
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Gθ-values
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seems
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sensible.
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Another
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check
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of
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the
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accuracy
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of
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the
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results
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can
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be
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seen
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by
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comparing
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the
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dissipation
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rate
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of
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the
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flocculation
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tanks
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to
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values
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recommended
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by
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Schulz
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and
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Okun
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of
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.4-10
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mW/kg.
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The
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energy
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dissipation
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plotted
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in
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this
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region
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for
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the
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fh=3
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case
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results
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in
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the
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plot
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shown
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below
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:
Figure 1: Energy Dissipation Rate in the range of .4-10 mW/kg for fh/w=3, Re=10,000
The regions in white are outside of this region, indicating that energy dissipation values above and below this recommended region exist in the flocculator.