4. METHODS
The global solution, comprising such information as node-averaged fluxes and face-averaged partial currents, can be used to construct local high-order interpolates providing accurate approximations of group fluxes and power density inside homogenised nodes. In more detail, the flux distribution inside a homogeneous node is assumed to be separable in the x-y plane and in the axial (z) direction. An analytical solution is used for the axial shape while a non separable biquartic polynomial with 21 coefficients (the terms x3y3, x3y4, x4y3 and x4y4 are missing) is constructed as an approximation for the radial flux shape in the node. Finally, the resulting power distribution in the homogenised node is modulated by an array of rod power factors featuring the actual heterogeneous structure of the node and computed from a library of input reference values on the basis of local burnup, coolant density and burnup-weighted coolant density.
The thermal-hydraulic model used for the subchannel analysis of an individual fuel rod bundle (an upgraded version of the COBRA-3C code, called COBRA-EN), is based on three partial differential equations that describe the conservation of mass, energy and momentum for the water liquid/vapor mixture and the interaction of the two-phase coolant with the system structures. Optionally, a fourth equation can be added which tracks the vapor mass separately and which, along with the correlations for vapor generation and slip ratio, replaces the subcooled quality and quality/void fraction correlations, needed by the homogeneous model.
In each coolant channel, the one-dimensional (z) fluid dynamics equations in the vertical direction as well as the one-dimensional (r) equation in the horizontal direction that models the heat transfer in solid structures are approximated by finite differences. The resulting equations for hydrodynamic phenomena form a system of coupled nonlinear equations that are solved by the an upflow scheme (allowed when no reverse flow is predicted) or by a Newton-Raphson iteration procedure (needed when the vapor continuity equation is involved). The heat-transfer equations in the solid structures are treated implicitly. Moreover, a full boiling curve is provided, comprising the basic heat-transfer regimes, each represented by a set of optional correlations for the heat-transfer coefficient between a solid surface and the coolant bulk.
