Grid spacer pressure loss modeling

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Next: Subcooled boiling model Up: External Previous: Wall shear stress Contents Index

Grid spacer pressure loss modeling

The pressure loss of a spacer is like all other two-phase flow phenomena very complicated to model. The treatment of a spacer depends on whether the spacer is of wire-wrapped or grid spacer type. In the subsequent analysis we assume a grid type spacer. According to Lahey and Moody the total (integral) pressure loss due to a grid spacer, $\Delta p_{\mbox{\protect\scriptsize spacer}}$ , can be modeled by the empirical expression

$\begin{displaymath} \Delta p_{\mbox{\protect\scriptsize spacer}} = K_{\mbox{\pr... ...c{\rho_\ell - \rho_g}{\rho_g} \right]\mbox{$<\!{x}\!>$}\right) \end{displaymath}$

(6.77)

where $K_{\mbox{\protect\scriptsize SP}}$ [--] is the single-phase loss coefficient determined by experiment.

The typical pressure variation caused by the grid spacer is depicted in Figure 6.3. We have to approximate this pressure variation appropriately in order to solve the conservation equations which describe the hydraulics of the reactor core. We could, for instance, use the design approximation shown in the figure with a dashed attribute (-). However, since it is the differentiated version of the design approximation which enters the conservation equation in the form of a pressure loss per unit length, $P_{\mbox{\protect\scriptsize loc}}'$ , (see (6.57)) this design approximation is inconvenient in view of obtaining a numerical solution to the problem.

In order to avoid any discontinuities which may cause troubles with the numerical solution of the conservation equations we will employ a smoothed version of the design approximation shown in Figure 6.3 instead of using the design approximation directly. The derivative of this smoothed design approximation is shown in Figure 6.4.

$\begin{figure} % latex2html id marker 24323\rule{\textwidth}{0.2mm} \rule{0cm}... ...essure profile induced by a grid spacer and a design approximation.}\end{figure}$

The derivative of this smoothed design approximation, $P_{\mbox{\protect\scriptsize loc}}'$ , has the following functional form

$\begin{displaymath} P_{\mbox{\protect\scriptsize loc}}' = \left\{ \begin{array}... ... \le 4z_0 \\ 0 & {\mbox{ for }} z> 4z_0 \end{array} \right. \end{displaymath}$

(6.78)

where C is a constant [N/m].

The shape of the design approximation which is schematically illustrated in Figure 6.4 has the following properties

$P_{\mbox{\protect\scriptsize loc}}'$ is continuous.
$\frac{d}{dz}\left[P_{\mbox{\protect\scriptsize loc}}'\right]$ is continuous.

$\begin{figure} % latex2html id marker 24343\rule{\textwidth}{0.2mm} \rule{0cm}... ...hat it is the derivative of the pressure profile which is depicted.}\end{figure}$

The width of the pressure pulse, $\Delta z_{\mbox{\protect\scriptsize sp}}$ , is given by

$\begin{displaymath} \Delta z_{\mbox{\protect\scriptsize sp}} = 4z_0 \end{displaymath}$

(6.79)

The constant C in (6.88) is determined by

$\begin{displaymath} \Delta p_{\mbox{\protect\scriptsize spacer}} = \int\limits_... ...otect\scriptsize sp}}} P_{\mbox{\protect\scriptsize loc}}' dz \end{displaymath}$

(6.80)

Carrying out the integration reveals that the height of the pressure pulse, C, is governed by

$\begin{displaymath} C = \frac{ 4 \Delta p_{\mbox{\protect\scriptsize spacer}}}{3 \Delta z_{\mbox{\protect\scriptsize sp}}} \end{displaymath}$

(6.81)

Next: Subcooled boiling model Up: External Previous: Wall shear stress Contents Index

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