CODES

H. H. Cho, H. Hong, H. G. Lee and H. G. Joo, "Preliminary Development of Simplified P3 based Pin-by-pin Core Simulator, SPHINCS," in KNS 2019 Spring, Jeju, Korea, 2019.

SPHINCS is developed aiming for pin-wise two-step core analysis system. SPHINCS stands for Simplified P3 Pin Homogenized Innovative Neutronics Core Simulator. A part from conventional assembly-wise nodal method, SPHINCS has been developed increasing the energy group from 2G to 8G at pin-level structure. Also, apart from conventional diffusion theory, SP3 theory is introduced as it is well known as a great solution compared with diffusion theory. Its formulation is similar so that it has advantage in implementation as well as not a big computational burden but much more powerful in analyzing large spatial flux variation.

In this regard, nTRACER/SPHINCS pin-wise two-step core analyses has been developed. Throughout single assembly level calculations with nTRACER, pin-homogenized multi-group cross sections are generated. With those group constants, SPHINCS generates corresponding SPH factors as pre-process and performs core analyses after incorporating those SPH factors into group constants. SPHINCS performs core calculation based on pin-homogenized group constants with SPH factors solving SP3 equation which is properly reformulated to be applicable to the finite difference method (FDM) solver. It employs pin-wise 2D-1D synthesis method within the framework of assembly-wise coarse mesh finite difference (CMFD) method.

While utilizing pin-wise group constants generated from nTRACER, from pin-homogenization based on single assembly level calculation, neutron balance would not be preserved in each pin boundary as the spatial homogenization is done. Due to these reduction of spatial scale, super homogenization (SPH) factors are introduced preserving reaction rates of every pins. SPH factors are defined as the ratio of heterogeneous flux to homogeneous flux and heterogeneous flux is provided with group constants from nTRACER. Throughout iterative procedures, group-wise SPH factors for every pins are updated so that all the reaction rates preserved. Those SPH factors are incorporated into group constants and utilized in core analyses. In general, FDM should employ very fine-mesh in order to achieve its accuracy but utilization of SPH factors makes pin-sized FDM available.

For a reactor core design and analyses, it is required to analyze various states of core conditions. Therefore pin-wise closed-channel simple T/H method is employed and functionalization of effective cross sections are performed concerning various branch conditions such as burn-up, fuel temperature, moderator temperature and boron concentration. In each branch conditions, SPH factors are considered as well.

SPHINCS also has pin-wise depletion capability for a reactor design that material composition and corresponding isotope number density becomes changed from steady state initial core condition. The depletion module is implemented with 70 nuclides and 4 fissile nuclides while 19 nuclides with 4 fissile nuclides are used for steady state calculation. Krylov subspace expansion method is used to solve matrix exponential problem. For all the depletion time steps, SPH factors are considered as well.

Time-dependent SP3 equation which is properly reformulated applicable to the FDM solver of SPHINCS is implemented and precursor balance equation is also considered so that coupled kinetics equations is solved. Transient fixed source problem is solved for various core state conditions corresponding to control rod ejection, withdrawal or core moderator density. Especially for 3D modeling, approximate flux weighting method is introduced for robust control rod movements modeling.