Grid points influenced by a spacer

The second requirement treats grid points which are in the vicinity of a spacer, ie a grid point, z_K, which satisfies

$\begin{displaymath} (z_K-z_{\mbox{\protect\scriptsize sp}} < \Delta z_{\mbox{\p... ...criptsize sp}}) \wedge (z_K>z_{\mbox{\protect\scriptsize sp}}) \end{displaymath}$

(8.22)

6.7.2.3

If (8.22) is fulfilled we proceed as follows

The first grid point which is influenced by the spacer, z_S, is is placed on the location of the spacer, ie $z_S = z_{\mbox{\protect\scriptsize sp}}$ .

The next N grid points are distributed uniformly over the width, $\Delta z_{\mbox{\protect\scriptsize sp}}$ , ie

$\begin{displaymath}z_{i+S} = \frac{\Delta z_{\mbox{\protect\scriptsize sp}}}{N} ... ...\scriptsize sp}} \qquad {\mbox{for}} \quad i=\{1,2,\ldots,N\} \end{displaymath}$

where N and $\Delta z_{\mbox{\protect\scriptsize sp}}$ are user specified quantities.

In summary the grid is uniquely defined when the user has specified the following quantities

average steplength in the computational grid [m].
>: number of steplengths which follow a spacer [--].
>: width of a spacer pressure variation [m].

Note that in order to keep the truncation error associated with the pressure, p(z), reasonably low is advisable to choose $N \ge 5$ .

A typical computational grid is depicted in Figure 8.8.

$\begin{figure} % latex2html id marker 31162\rule{\textwidth}{0.2mm} \rule{0cm}... ... $h_{\mbox{\protect\scriptsize av}} = 0.1{\mbox{ m}}$\ and $N = 5$.}\end{figure}$

One could question the grid generation procedure since it only considers the variation of q' and not, for instance, the fact that the frictional pressure drop increases along the channel due to increased flow quality. The reason for not considering the pressure variation is that in practice the curvature of the pressure as a function of z is small when we compare to curves of $\mbox{$<\!{\alpha}\!>$}$ and $\mbox{$<\!{x}\!>$}$ . This means that it is absolutely no problem to control the truncation error in regard to the pressure.

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