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Next: Core flow numerics Up: Core flow modeling Previous: Subcooled boiling model Contents Index

Review of the model

In this section we summarize the mathematical problem which we have to solve in order to obtain the 1-D steady-state flow field in the reactor core.

The mathematical problem consists of the following system of equations in the four dependent variables $(p,\mbox{$<\!{\alpha}\!>$},\mbox{$<\!{x}\!>$},\mbox{$<\!{h}\!>$})$ (see (6.57), (6.73), (6.97), (6.93) and (6.58))

$\begin{displaymath} -\frac{dp}{dz} - \tau_w \frac{P_f}{A_c} -g( (1-\mbox{$<\!{\... ...ac{\mbox{$<\!{x}\!>$}^2}{\rho_g\mbox{$<\!{\alpha}\!>$}}\right] \end{displaymath}$

(6.89)

$\begin{displaymath} \mbox{$<\!{\alpha}\!>$}= f_2(\mbox{$<\!{x}\!>$},\rho_\ell,\rho_g,\mbox{$<\!{G}\!>$}) \end{displaymath}$

(6.90)

$\begin{displaymath} \mbox{$<\!{x}\!>$}= f_4(\mbox{$<\!{h}\!>$},h_f,h_{fg},h_{\ell,d}) \end{displaymath}$

(6.91)

$\begin{displaymath} \mbox{$<\!{G}\!>$} \frac{d}{dz}\left[ \mbox{$<\!{h}\!>$} \right] \simeq \frac{q'}{A_c} \end{displaymath}$

(6.92)

ie we have a system which consists of two ODEs^6.15 and two algebraic equations.

In addition we have the following functions (see (6.88), (6.80) and (6.93))

$\begin{displaymath} P_{\mbox{\protect\scriptsize loc}}' = f_0(z_0,K_{sp},\mbox{$<\!{G}\!>$},\rho_\ell,\rho_g,\mbox{$<\!{x}\!>$}) \end{displaymath}$

(6.93)

$\begin{displaymath} \tau_w = f_1(p,\mbox{$<\!{G}\!>$},\rho_\ell,\rho_g,\mbox{$<\!{x}\!>$}) \end{displaymath}$

(6.94)

and

$\begin{displaymath} h_{\ell,d} = f_3(h_f,q_w'',D_H,C_{p,\ell},k_\ell,\mbox{$<\!{G}\!>$}) \end{displaymath}$

(6.95)

To effect closure of the system of equations (6.100)-(6.103) we need firstly the equations of state discussed in section 6.7.1 (these will not be repeated here) and secondly appropriate boundary conditions

$\begin{eqnarray*} p(0) &=& p_0\\ \mbox{$<\!{\alpha(0)}\!>$} &=& 0\\ \mbox{$<\!{x(0)}\!>$} &=& 0\\ \mbox{$<\!{h(0)}\!>$} &=& h_{\ell,0} \end{eqnarray*}$

$\textstyle \parbox{1.50cm}{\begin{eqnarray} \end{eqnarray}}$

Furthermore we have tacitly assumed that the total mass flux $\mbox{$<\!{G}\!>$}$ is specified, ie

$\begin{displaymath} \mbox{$<\!{G}\!>$} = G_0 \end{displaymath}$

(6.96)

Note that the first three equations (6.100)-(6.102) are coupled through the pressure dependent fluid properties. The fourth equation (6.103) can be solved independently of the three other equations.

Next: Core flow numerics Up: Core flow modeling Previous: Subcooled boiling model Contents Index

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