4. METHODS
The thermal-hydraulic model 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 original upflow scheme (when no reverse flow is predicted) or by a Newton-Raphson iteration procedure. 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.
The neutronic module is based on the Analytical Nodal Method (ANM) for two-group neutron diffusion equation in three-dimensional cartesian geometry, developed by A. F. Henry and his coworkers at MIT, which approximates the diffusion equation by analytical formulae that are exact in one dimension and solves the resulting nodal equations for node-averaged fluxes and directional leakages by a triple level of iteration.
The cross-sections and the discontinuity factors correcting for homogenisation errors are updated for thermal (fuel temperature) and thermal-hydraulic feedback (coolant temperature and density) and, also, for dilute Boron effect, either by applying temperature and density coefficients (quadratic at the most) or by interpolating in input multiple-entry libraries of reference values.
