Uncertainty treatment of a coupled model of thermohydraulics and neutronics using special functions solutions

Abdelqoddous Moussa, Olivier D. Lafitte

Abstract: This paper is a followup of the paper of Dellacherie et al. in [2], where we were able to obtain an analytic solution of a monodimensional stationary system coupling two simplified models, one solving the thermohydraulic equations, the other one solving the neutronic diffusion equation with one energy group. An approximation of the analytic solution using incomplete Jacobi elliptic integrals was derived as well as the calculation of the neutron multiplication factor $k_{eff}$, and we use this explicit approximation in a more general case with uncertainties on the data, which are the values of some physical functions (of the temperature $T$) of the fluid characterizing the problem (namely the diffusion coefficient $D$, the absorption cross-section $\Sigma_{a}$ and the fission cross section $\nu\Sigma_{f}$). A thorough numerical study has been done. Using it, we demonstrate that the physical hypotheses on these function must hold for any Monte-Carlo sampling of the values, for example the values of the fission cross section must be increasing if the temperature $T$ increases.