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Solving the neutron kinetic equations
Let us recall the system
(1) to be solved for
Φ,Cj in each plane
z.
Coefficients F, D, ρ, ... are weighted planar averages depending on the current core physical condition and radial distributions of static direct and adjoint fluxes in each core plane.
Physical state {u2ck, vm2ck, b2ck} is calculated by means of do, core on the "thermodynamic" nodes ck of the core.
For given values of these planar variables, the corresponding neutronic values depend on their radial distribution over the various assemblies , in each z plane. This distribution depends also of the way the heating mode.
As the transient radial distribution is not solved in SAFPWR, it is only possible to correlate the plane physical state with its corresponding neutronic state for limit heating modes which can be reproduced in the design diffusion program.
For example, a stationary heating, as modeled in the neutronic calculation, where the radial distributions of water density and fuel temperature depend only on current radial distribution of assembly power and moderator density.
Or the neutronic program can easily be adapted to simulate adiabatic heating from a given stationary condition. Then the fuel temperature increment will result from the "historical" evolution of radial power distribution.
For actual situations, transient heating evolution depart from those limiting heating modes; for example, in case of rapid reactivity insertion, heating is firstly quasi adiabatic, to change progressively to stationary heating as the transient stabilizes to steady state.
Nodes ck
Core m,h,b-balances (do, core) are carried out on the nodes ck=(1, k9c) where the thermodynamic state (u2ck, vm2ck, b2ck, t1ck, u2ck) is calculated from the nuclear power f2ck deposited into the slice ck of core, and the flows w(_,h,b)entering the core.
ci neutronic meshing
For discretizing the axial diffusion operator, each node ck is, in turn, partitioned into a number of equal "Core Intervals ci" or "meshes", specified by entering i9ck(ck), index of last interval of ck.
It is on this ci meshing that the planar neutronic variables phci (flux), cjci (concentration cj at ci of delayed emitters of family j), fission source sfci will be calculated.
It is also on the ci partition that we will apply correction terms for accounting for the physical effects (Xenon and Sm poisoning, fuel exposure axial distribution, rods separation grids), which are not explicitly modeled in SAFPWR.
Core configuration groups and levels
Neutronic correlations (or "tables") are entered for each of the axial confiGuration "g" which may be differentiated according to the control and safety groups insertion and, possibly, axial neutronic differentiation due to exposure, burnable poisons.
Generally, we enter g9 configurations "g" whose localization in the are delimited by their upper level zg(g), starting from core bottom.
For a given application, we need to enter all the configurations which will be potentially present; the currently present configurations are ranked into cn9 layers (levels: Niveaux) cn.
kn partition
At last, for programming convenience, an additional partition kn is defined by intersecting the ck, ci and cn partitions.
An element ckn of such a partition includes all intervals belonging to a same node ck and configuration level cn and any interval covering a configuration transition ("transition interval") defined its own element ckn (ex: kn=7) where the macroscopic constants of the groups transiting in it are volume homogenized in it.