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Fully ceramic micro-encapsulated (FCM) fuel is a kind of fuel that employs tri-structural isotropic (TRISO) particles to enhance safety. The FCM fuel assembly is a double heterogeneous system. The conventional self-shielding calculation methods cannot treat the DH effect. In this paper, three methods based on equivalent homogenization of the TRISO particle and the matrix are studied and compared: the hyper-fine energy group cross sections (XSs) homogenization based hyper-fine energy group method (HHM), the hyper-fine energy group XSs homogenization based subgroup method (HSM) and the subgroup XSs homogenization based subgroup method (SSM). These methods are implemented in a high-fidelity neutronics code NECP-X. Numerical results show that these methods are able to treat the double heterogeneity of the FCM fuel. The precision of the HHM and HSM is higher than that of the SSM.

The subgroup methods based on partial cross section fit scheme (PXSFS) and simplified partial cross section fit scheme (SPXSFS) are proposed in this paper to treat problems with non-uniform temperature distribution. These methods fit the cross sections at different temperatures as partial cross sections and share a same set of subgroup probabilities. The new methods are compared to the pre-existing methods: conventional subgroup method (CSM), the correlation model (CM), the subgroup level adjustment scheme (SLAS) and the number density adjustment scheme (NDAS). The numerical results show that the new methods can better predict the spatially dependent reaction rates than pre-existing methods. Within the new methods, the simplified scheme consumes less computation time and is more numerically stable. Additionally, the superhomogenization (SPH) correction method is studied, which is used to treat the multi-group (MG) equivalence effect. It is found that the subgroup-one-group (subgroup-1G) calculation can fully capture the MG equivalence effect. [ABSTRACT FROM AUTHOR]

The subgroup method is improved in several aspects to address challenges brought on by design features of the Fluoride salt-cooled High-temperature Reactor (FHR). Firstly, the Dancoff correction is applied to resolve the double heterogeneity arising from embedding TRISO fuel particles in the matrix of pebbles. Secondly, a fast Resonance Interference Factor (RIF) scheme is proposed to treat the resonance interference effect in the FHR. In this scheme, the heterogeneous system is converted into a homogeneous one according to self-shielded cross section conservation of the dominant resonant nuclide. The resonance interference effect is considered in the equivalent homogenous system by correcting the non-interfered self-shielded cross sections with RIFs which are obtained by solving the slowing down equation in hyper-fine energy group (∼1M number of energy groups). Finally, the resonance elastic scattering effect becomes considerable due to high temperatures in the FHR. This effect is considered by substitution of the conventional Resonance Integral (RI) table with that generated by the Monte Carlo method. The Monte Carlo method is modified via the Doppler Broadening Correction Rejection (DBRC) method to implement the Doppler broadened scattering kernel. The numerical results show that the Dancoff correction can significantly reduce errors brought about by the double heterogeneity. The fast RIF scheme provides more accurate effective self-shielded cross sections than the conventional iteration scheme. In addition, the speedup ratio of the fast RIF scheme is ∼3.3 compared with the conventional on-the-fly RIF schemes for TRU TRISO. The scheme to generate RI table can resolve the resonance elastic scattering effect encountered by the conventional scheme. [ABSTRACT FROM AUTHOR]

• A one-dimensional model for computing partial current discontinuity factor (PCDF) in subgroup method; • The multi-group equivalence effect can be captured in an acceptable precision by the PCDF based on 1D model; • There is negligible increase in computational time brought by the model. In the previous study, a non-iterative equivalence method is proposed, which guarantees that the reaction rates calculated by subgroup method in self-shielding calculation are preserved in subgroup-collapsed one-group calculation. This method shows advantage in efficiency over the Super-Homogenization (SPH) method. However, one-group fixed-source calculations are still needed for obtaining multi-group (MG) equivalence parameters. In this paper, a one-dimensional model is employed for obtaining the MG equivalence parameters in subgroup method. Based on the one-dimensional model, the one-group fixed-source calculation is simplified to one-angle tracking sweeping, which is time-saving. The numerical results show that the reaction rates can be preserved with the MG equivalence parameters obtained based on the one-dimensional model for pin cell problems. For fuel assembly problems, the k inf is improved by 140 pcm ∼ 187 pcm with negligible increase in computational time. [ABSTRACT FROM AUTHOR]

• Two extension schemes of subgroup method are proposed to treat double heterogeneity. • Both of the schemes can treat double heterogeneity. • The subgroup XS correction scheme can be easily implemented in subgroup method. Two extension schemes based on the subgroup method are proposed to treat the double heterogeneity (DH) of fully ceramic micro-encapsulated (FCM) fuels. The first one is the hyper-fine energy group cross section (XS) correction scheme (HFCS), which corrects the hyper-fine energy group XSs with hyper-fine energy group disadvantage factors (DFs) before generation of resonance XS table and physical probability table. The second one is the subgroup XS correction scheme (SGCS), which corrects the subgroup XSs with subgroup DFs calculated by the equivalent homogenization method. These two scheme are implemented in the high-fidelity neutronics code NECP-X. A series cases are tested and the numerical results show that both of the HFCS and the SGCS can treat the DH and the precision of the HFCS is higher than that of the SGCS. [ABSTRACT FROM AUTHOR]

The pseudo-resonant-nuclide subgroup method (PRNSM) based global-local self-shielding calculation scheme was recently developed to resolve the spatial self-shielding and resonance interference effects for large-scale problems. But the PRNSM is not able to treat non-uniform temperature distribution. The reason is that the PRNSM generates physical probability tables at different temperatures with inconsistent subgroup probabilities. To overcome this defect, the on-the-fly subgroup method (OSM), which is an improvement of the PRNSM, is proposed. The new method generates the physical probability tables for different temperatures with shared subgroup probabilities and is able to treat non-uniform temperature distribution. This method replaces the PRNSM in the global-local self-shielding calculation scheme and is implemented in the high-fidelity neutronics code NECP-X. The numerical results show that the OSM can treat the spatial self-shielding effect, the resonance interference effect and the non-uniform temperature effect simultaneously. Besides, NECP-X is able to predict fuel temperature coefficients with high accuracy. • The on-the-fly subgroup method is proposed. • The new method generates physical probability tables for different temperatures with shared subgroup probabilities. • The new method can treat spatial self-shielding, resonance interference and temperature distribution effects. [ABSTRACT FROM AUTHOR]

• A non-iterative equivalence method is proposed to resolve the multi-group equivalence effect. • The new method is implemented into the resonance calculations of the Bamboo-Lattice code. • The new method guarantees less computational cost as compared to the SPH method. Multi-group heterogeneous reaction rates calculated by the subgroup method in resonance calculations are not reproduced, when subgroup-collapsed one-group homogeneous calculations are conducted for the same problem, giving rise to a multi-group equivalence effect. In this paper, a new non-iterative equivalence method introducing partial current discontinuity factors (PCDFs) is proposed to resolve this effect and employed into the Bamboo-Lattice code. Its validity was tested and verified through several fixed-source as well as eigenvalue problems for both single pin-cell and assembly geometries. The numerical results show that preservation of scalar flux, partial currents, neutron leakage and reaction rates is guaranteed by implementing this new method. Moreover, the computational time comparison for different equivalence methods shows that the newly proposed non-iterative equivalence method promises a significantly less computational cost compared to the traditional iterative super-homogenization (SPH) method in treating multi-group equivalence effect. [ABSTRACT FROM AUTHOR]