h1. Parameter Formulation -- Characterize Collision Potential
(under construction...)
h3. Introduction
The formulation of parameters{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex},
{latex}
\large
$K_{baffle} $
{latex}
,
{latex}
\large
$\Pi _{cell} $
{latex}
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.
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
:
Calculating a flow weighted average of
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
:
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
, where
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
,
Thus
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
:
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}\\
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}\\
where
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
:
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
, plug in
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
and simplify:
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
:
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
\\
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
All parameters are calculated from summing over all nodes (finite element)
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
,
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
,
{latex}
\large
$\theta \varepsilon ^{1/3} $
{latex}
, which can be calculated using the following UDF script:[parameters.c|^parameters.c] | 