Parameter Formulation – Characterize Collision Potential
Introduction
The formulation of parameters
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
,
Unknown macro: {latex}
\large
$K_
Unknown macro: {baffle}
$
,
Unknown macro: {latex}
\large
$\Pi _
Unknown macro: {cell}
$
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.
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
:
Calculating a flow weighted average of
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
:
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
, where
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
,
Thus
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
:
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
where
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
:
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
, plug in
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
and simplify:
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
:
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
All parameters are calculated from summing over all nodes (finite element)
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
,
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
,
Unknown macro: {latex}
\large
$\theta \varepsilon ^
Unknown macro: {1/3}
$
, which can be calculated using the following UDF script:[parameters.c|^parameters.c]