4. METHODS
The burnup model is implicit and the overall solution scheme at each burnup step is iterative. The multigroup diffusion equation is approximated by a coarse-mesh fourth-order polynomial method. More precisely, the numerical approximation is represented by coarse-mesh finite-difference equations corrected by discontinuity factors internally computed so as to match the accuracy of a fourth-order polynomial approach. Then, the finite-difference equations are solved for the nodal neutron fluxes by the usual inner/outer scheme.
The equivalent homogenised nuclear parameters including the discontinuity factors correcting for homogenisation errors, according to Henry's generalised equivalence theory, are updated by trilinear interpolation in input libraries of reference values.
The thermal-hydraulic model (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 of hydrodynamic phenomena form a system of coupled nonlinear equations that are solved by the upflow scheme (allowed only when no reverse flow is predicted) or by a Newton-Raphson iteration procedure (needed when the vapor mass continuity equation is added). 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.
