Parameter Formulation – Characterize Collision Potential
Introduction
The formulation of parameters
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,
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,
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and are described below, for characterizing flocculation potential using numerical solutions from CFD simulations. Note that this is a work in progress, so the notation of variables and interpretation of equations still need to be further clarified.
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:
Calculating a flow weighted average of
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:
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\sum\limits_
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, where
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\large$${\theta _{fe}} = {{{\forall _
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,
Thus
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${K_{baffle}}$
:
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$${\varepsilon _{fe}} = g{h_l \over \theta _{fe}}$$
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$$
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= {K_{baffle}}{V^2 \over {2g}}$$
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$$
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= {\varepsilon _{fe{\theta _
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$${K_{baffle}} =
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2g} \over {{V^2}$$
where
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$${\theta _{fe}} = {{{\forall _
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$${K_{baffle}} =
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{{\varepsilon _{fe{\theta _
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$${K_{baffle}} = {2 \over {Q
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$${K_{baffle}} = {2 \over {bw
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where
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$$Q = Vbw$$
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${\Pi _{cell}}$
:
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$${\varepsilon {cell}} = {K{baffle{V^3}} \over {2{\Pi _{cell}}b}}$$
, plug in
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${K_{baffle}}$
and simplify:
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$${\Pi {cell}} = {1 \over b^2}w{{{{\left( {\sum\limits
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$G\theta $
:
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$$G{\theta _{baffle}} =
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\sum\limits_
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G_{fe{\theta {fe}}{Q
}} $$
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$${\theta _{fe}} = {{{\forall _
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$$G{\theta _{baffle}} =
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$${G_{fe}} \propto \sqrt {{{{\varepsilon _
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$$G{\theta _{baffle}} =
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{\sqrt {{{{\varepsilon _
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$$G{\theta {baffle}} = {1 \over {Q\sqrt \nu }}\sum\limits
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All parameters are calculated from summing over all nodes (finite element)
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,
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,
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$$\sum \forall _{fe{\varepsilon _
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, which can be calculated using the following UDF script:performance.c.