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Introduction

In this chapter we present the model of the flow, ie the hydraulics, of the core. The flow in a BWR-core is complicated by a number of special phenomena of which some are not encountered in boiling two-phase flows elsewhere. The first complication is that the flow is distributed between an active flow which flows through the fuel assemblies and a so-called bypass flow which flows in the cross section between the fuel assemblies ([18, p. 280] and [41, p. 2-16]). Typically the bypass flow amounts to approximately 10 percent of the total core flow, ie it represents a non-negligible part of the core flow. We will, however, due to time constraints be forced to neglect the bypass flow, ie assume all flow through the core to pass through the fuel assemblies. The next phenomenon which requires special attention is the influence of the grid spacers. The approximately seven grid spacers serve as mechanical stabilizers which ensure that the bow of the fuel pins is kept at a minimum and fluid-mechanical oscillations are prevented. The spacers disturb the flow field in a complicated way--they enhance transverse mixing and perhaps most importantly induce a pressure loss of considerable size. A special phenomenon which occurs in a nuclear reactor is that some of the heat (approximately 3 percent [11]) is added in a volumetric manner by absorption of energy associated with nuclear radiation (both n- and $\gamma$-radiation). However, since the used flow model is of relatively simple form we cannot incorporate the volumetric source terms in a satisfactory way. In order to do so we would have to treat the flow at least by a drift-flux model (see [33]) with constitutive relations for the mass transfer rate, $\mbox{$\dot{m}$}_{g\ell}'$, (see, for instance, (6.27)) and apply a subcooled boiling model based upon heat transfer between the two phases instead of a simple profile fit.

The flow model to be utilized is based on a so-called mixture formulation of the time and cross-section averaged conservation equations. Before discussing the flow model we have to introduce some general description notation and quantities relevant to boiling two-phase flow.

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