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Next: Steam separator assembly, Up: Primary coolant circulation loop Previous: Core flow path, Contents Index

Riser flow path, $\fbox{2}$

Since the riser consists of a single pipe the flow is modeled as circular pipe flow.

Assuming adiabatic flow in the riser the conservation of energy and momentum state (see (6.57) with $P_{\mbox{\protect\scriptsize loc}} = 0$ and (6.58) on p. )

$\begin{displaymath} \mbox{$<\!{h}\!>$}= \mbox{$<\!{h}\!>$}_{{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 1}}},e} \end{displaymath}$

(5.2)

$\begin{displaymath} - \frac{dp}{dz} = \tau_w \frac{P_{f,{\framebox[1.5ex]{\rais... ...{\mbox{$<\!{x}\!>$}^2}{\rho_g \mbox{$<\!{\alpha}\!>$}} \right] \end{displaymath}$

(5.3)

where $\mbox{$<\!{h}\!>$}_{{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 1}}},e}$ is the mixture enthalpy at the exit of the core [J/kg] and the subscript f denotes saturated liquid. Notice we make the reasonable assumption of saturated conditions in the riser. This assumption is fulfilled in all cases relevant to power production.

The riser mass flux, $\mbox{$<\!{G}\!>$}_{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 2}}}$ [kg/( ${\mbox{m}}^2\cdot$ s)], is given by the continuity equation

$\begin{displaymath} \mbox{$<\!{G}\!>$}_{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt]... ...framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 2}}}}} \end{displaymath}$

(5.4)

where $\mbox{$\dot{m}$}_i$ [kg/s] is the total recirculation mass flow rate and $A_{c,{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 2}}}}$ [ ${\mbox{m}}^2$ ] is the flow cross-sectional area of the riser flow path.

As stated previously we assume that the riser flow is adiabatic. The reason for this assumption is illuminated in the subsequent.

The schematic of the BWR internals (cf Figure 5.1) reveals that we in flow paths $\framebox{1}$ and $\framebox{2}$ mostly have saturated conditions and with subcooled fluid in flow path $\framebox{5}$ , which is situated next to the former, a heat flux into the recirculation flow in path $\framebox{5}$ through the core shroud and riser walls is established. If one calculates this heat flux by utilizing, for instance, the Dittus-Boelter turbulent heat transfer correlation for constant wall temperature with a driving temperature potential in the order of 15 ${}^\circ\mbox{C}$ the resulting temperature rise of the recirculation flow is very low (in the order of $10^{-3}\mbox{${}^\circ\mbox{C}$}$ for a typical recirculation mass flow rate of approximately 6000 kg/s) and thus negligible.

The boundary conditions in regard to the momentum equation for the riser (see (5.3)) are now to be treated. We will assume negligible quality change across the expansion from flow path $\framebox{1}$ to $\framebox{2}$ , ie

$\begin{displaymath} \mbox{$<\!{x}\!>$}_{{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt... ...ramebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 1}}},e} \end{displaymath}$

(5.5)

where the subscripts i and e denotes inlet and exit conditions respectively.

In order to estimate the void fraction in the riser accurately we calculate a inlet void fraction, $\mbox{$<\!{\alpha}\!>$}_{{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 2}}},i}$ [--], based on the new mass flux, $\mbox{$<\!{G_{{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 2}}}}}\!>$}$ , ie (cf (6.101) p. )

$\begin{displaymath} \mbox{$<\!{\alpha}\!>$}_{{\framebox[1.5ex]{\raisebox{-2.2pt... ...\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 2}}}) \end{displaymath}$

(5.6)

Next: Steam separator assembly, Up: Primary coolant circulation loop Previous: Core flow path, Contents Index

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