Local correlated sampling Monte Carlo calculations in the TFM neutronics approach for spatial and point kinetics applications

Abstract

Abstract. These studies are performed in the general framework of transient coupled calculations with accurate neutron kinetics models. This kind of application requires a modeling of the influence on the neutronics of the macroscopic cross-section evolution. Depending on the targeted accuracy, this feedback can be limited to the reactivity for point kinetics, or can take into account the redistribution of the power in the core for spatial kinetics. The local correlated sampling technique for Monte Carlo calculation presented in this paper has been developed for this purpose, i.e. estimating the influence on the neutron transport of a local variation of different parameters such as sodium density or fuel Doppler effect. This method is associated to an innovative spatial kinetics model named Transient Fission Matrix, which condenses the time-dependent Monte Carlo neutronic response in Green functions. Finally, an accurate estimation of the feedback effects on these Green functions provides an on-the-fly prediction of the flux redistribution in the core, whatever the actual perturbation shape is during the transient. This approach is also used to estimate local feedback effects for point kinetics resolution.

Towards spatial kinetics in a low void effect sodium fast reactor: core analysis and validation of the TFM neutronic approach

“…Recent developments [5] extend the application field of this TFM approach to fast reactors with a heterogeneous core such as the sodium fast reactor. For sodium fast reactors with a low void effect based on a sodium plenum, if the density of the sodium decreases, the probability to produce a new fission decreases due to the increased neutron leakage.…”

“…Because the core geometry of such reactors is very heterogeneous, not only must the neutron departure and arrival volumes be taken into account, but also the intermediate volumes crossed by the neutron. Finally, the raw information used is the probability that a fission neutron created in j produces a new fission neutron in i considering a perturbation in the crossed volumes k. The theory and the methodology of this perturbative approach using the correlated sampling technique is detailed in [5], the present paper focuses on the application of this approach to the study of the low void effect sodium fast reactor ASTRID [1] and to its validation with direct Monte Carlo and deterministic S N calculations. The effect of the perturbation in the crossed volume k on the fission matrix G x x n x is namedG den k x x n x for the density effect and G dop k x x n x for the Doppler effect.…”

“…In this way, the effect of the perturbation on the neutron source perturbation is correctly taken into account. As detailed in [5], this perturbed weight propagation is not required for fission matrix generation if the mesh is fine enough since the perturbation of the neutron source is directly taken into account through the eigen vector.…”

“…As presented in [5], the perturbative TFM approach may also be used to calculate the local feedback effects for point kinetics applications. These local feedbacks correspond to the eigen values of the local contributions such as Figures 18 and 19 show the results obtained for cases A and B together with the results of ERANOS.…”

“…For this reason, spatial neutron kinetic models must be developed to verify that the flux redistribution remains limited in such situations. To this end, the spatial kinetic Transient Fission Matrix (called TFM) approach previously developed and presented in [3,4] has been adapted to model the effect of local medium perturbations [5]. The TFM approach is based on a conversion to discretized Green functions of the Monte Carlo response of the system in order to perform kinetic calculations without new reference calculation during the transient and thus with a reduced computation time.…”