4. METHODS
The TRAC two-phase, two-fluid nonequilibrium hydrodynamics model with a noncondensable gas field is based on six partial differential equations that describe the transfer of mass, energy and momentum between the water liquid and vapor phases and the interaction of the individual phases with the system structures. Because these interactions are dependent on the flow topology, a flow-regime dependent constitutive equation package has been incorporated into the code.
The one-dimensional (z) or three-dimensional (r, *, z) fluid dynamics equations as well as the one-dimensional (r or z) or two-dimensional (r, z) equations that model the heat transfer in solid structures are approximated by finite differences. The fluid dynamics equations in the one-dimensional components use a multistep procedure that allows the material Courant condition to be violated. The optional three-dimensional component (vessel) uses a semi-implicit scheme, subject to the Courant condition, The finite-difference equations for hydrodynamic phenomena form a system of coupled nonlinear equations that are solved by a Newton-Raphson iteration procedure. The heat-transfer equations are treated implicitly in the radial direction and explicitly in the axial direction.
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 and coded in the QUANDRY program, but, instead of solving the nodal equations for node-averaged fluxes and directional leakages, it adopts the more efficient approach of solving Coarse-Mesh Finite-Difference (CMFD) equations corrected by Equivalence Theory Discontinuity Factors which are internally computed so as to match just the accuracy of the Analytical Nodal Method.
The cross-sections and the discontinuity factors correcting for homogenisation effects are updated for thermal (fuel temperature) and thermal-hydraulic feedback (coolant temperature and density) and 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.
At each thermal-hydraulic (TRAC) time step whose size is automatically selected by inhibitive and promotional algorithms between input minimum and maximum values, the coefficients of the neutronic nodal equations are recomputed and a refined logic to control also the neutronic (QUANDF) substeps is applied.
