Tiejun Zu

Heterogeneous Pseudo-Resonant Isotope Method for Resolved Resonance Interference Treatment in Resonance Self-Shielding Calculation

Abstract The theory of resonance interference factor (RIF) method is examined for thermal reactor problems, and the approximations and limitations are identified. To evaluate the interference effect between resonance isotopes, the RIF method establishes an approximate equivalent relationship between a heterogeneous system and a homogeneous system by introducing background cross sections, and the approximation is a source of deviation in self-shielding calculations. Furthermore, each resonance isotope is treated individually in the self-shielding procedure, which requires unnecessary calculation effort, especially for whole-core and burnup cases. Based on the analysis, a heterogeneous pseudo-resonant isotope method (HPRIM) is proposed to overcome these problems. The mixture of resonant nuclides is considered as a pseudo-resonant isotope, and the resonance integral is generated in a one-dimensional heterogeneous system. The numerical results show that HPRIM improves the accuracy of evaluating the resonance interference effect and improves the efficiency of the self-shielding procedure.

The pseudo-resonant-nuclide subgroup method based global–local self-shielding calculation scheme

ABSTRACT The pseudo-resonant-nuclide subgroup method (PRNSM) based global–local self-shielding calculation scheme is proposed to simultaneously resolve the local self-shielding effects (including spatial self-shielding effect and the resonance interference effect) for large-scale problems in reactor physics calculations. This method splits self-shielding calculation into global calculations and local calculations. The global calculations obtain the Dancoff correction factor for each pin cell by neutron current method. Then an equivalent one-dimensional (1D) cylindrical problem for each pin cell is isolated from the lattice system by preserving Dancoff correction factor. The local calculation is to perform self-shielding calculations of the equivalent 1D cylindrical problem by the PRNSM. The numerical results show that PRNSM obtains accurate spatial dependent self-shielded cross sections and improves the accuracy of dealing with the resonance interference over the conventional Bondarenko iteration method and the resonance interference factor method. Furthermore, because both global and local calculation is linearly proportional to the size of problems, the global–local calculation scheme could be applied to large-scale problems.

Total Uncertainty Analysis for PWR Assembly Based on the Statistical Sampling Method

Abstract The nuclear-data uncertainties impact the best-estimate predictions of the nuclear reactor system. In this paper, total uncertainty analyses have been performed for the TMI-1 assembly at both hot zero-power and hot full-power conditions to evaluate the impacts of nuclear-data uncertainties on the predictions of lattice calculations, based on the statistical sampling method. With an improved multigroup cross-section perturbation model, the contributions of various basic cross sections to the uncertainties of k∞ and two-group macroscopic cross sections are obtained. For the total uncertainty analyses, a 172-group cross-section covariance library produced from ENDF/B-VII.1 is used to generate the samples for the multigroup microscopic cross-section library, and DRAGON 5.0 is applied to perform lattice calculations for each sample. The numerical results show that the relative uncertainty of k∞ can reach about 4.7‰ using the vp covariance matrix of 235U-v and 7.1‰ using the vt covariance matrix of 235U-v. The relative uncertainties of two-group macroscopic cross sections vary from about 2.9‰ (for the total cross section of the thermal group) to about 11.9‰ (for the scattering cross section from the fast group to the thermal group). Moreover, through detailed analysis toward uncertainty origins, it has been observed that 235U, 238U, 16O, and 1H are the four most significant contributors, and the uncertainties of 235U-(v, σf, σγ), 238U-(σγ, σ(n,inel), σ(n,elas), v), 16O-(σ(n,elas)), and 1H-(σ(n,elas), σγ) are the most significant cross-section contributors.

Neutron Up-Scattering Effect in Refined Energy Group Structure

Aiming at generating a 361-group library, this paper investigated neutron up-scattering effect in the 361-group Santamarina-Hfaiedh Energy Mesh (SHEM). Firstly, the Doppler Broadening Rejection Correction (DBRC) method is implemented to consider the neutron up-scattering effect in Monte Carlo (MC) method. Then the MC method is employed to prepare resonance integral table and scattering matrix for afterward calculation. Numerical results show that the neutron up-scattering affects kinf by ~200 pcm at most for UO2 pin cell problems in the 361-group SHEM, while the fuel temperature coefficient (FTC) is also influenced by 12~13%. It has also been found that both of the above two influences acts through scattering matrix rather than self-shielded absorption cross sections. In addition, the self-shielding effect of cladding is studied and it’s been found that it affects kinf by 30~70 pcm.

Eigenvalue Implicit Sensitivity Calculation and Analysis for Lattice-Physics Calculation

Accurate nuclear cross-section sensitivity-coefficient evaluation is important for sensitivity and uncertainty analysis, similarity analysis, cross-section adjustment et al. A crosssection perturbation will affect the lattice-physics calculation results through the transport calculation directly and through the resonance calculation indirectly. The indirect effect was found to be important in some cases in the previous studies. To quantify the indirect effect on the lattice-physics calculation results for subgroup resonance calculation method, a sensitivity and uncertainty analysis code COLEUS was developed based the GPT-based method. The eigenvalue sensitivity to nonresonance nuclide cross sections was investigated. Numerical results show that in the traditional LWR, the sensitivity coefficients will be overestimated if implicit sensitivity is neglected. And in the BWR, the implicit sensitivity will become more important along with the temperature rise. But if resonance fission and resonance capture play a coequal role or the background cross section is big, the implicit sensitivity can be small.

Propagation of Nuclear Data Uncertainties for PWR Burnup Calculation

As the nuclear data are from either the experiment measurements or the estimation models, uncertainties would arise from the insufficient measurements and/or modeling uncertainties. The uncertainties in nuclear data would have effects on the best-estimated prediction results of the reactor system. In this paper, our home-developed code UNICORN, which has the capability of uncertainties analysis for the neutron physics calculations, has been applied to quantify the response uncertainties of the PWR burnup calculation introduced by the uncertainties of multigroup microscopic cross-section libraries. The burnup benchmark proposed by UAM (“Uncertainty Analysis in Modeling”) is selected for the demonstration purpose. Relative uncertainties of k ∞ , two-group constants and isotope concentrations with the fuel burnup introduced by the nuclear data uncertainties are quantified. It is observed that the relative uncertainty of the eigenvalue is 0.5%; the relative uncertainties of the two-group constants vary between 0.3% (for the Σ t,2) and 1.9% (for the vΣ f,2); the relative uncertainties for the isotope concentrations can reach 30%. These relative uncertainties introduced by the nuclear data are significant for the neutron physics calculations and cannot be ignored.

Thermal-Hydraulics Design of Water-Cooled Pressure Tube Blanket for a Fusion Driven Subcritical Reactor

A Water-cooled Pressure Tube Blanket (WPTB) for fusion driven subcritical reactor has been designed, the design goal of the blanket is to achieve 3000MW thermal power with self-sustaining tritium cycle. Pressurized water has a great advantage in the energy production; however the high pressure may cause some severe structure design issues. This paper proposed a brand new concept of water cooled blanket. As result of adopting pressure-tube, the thickness of the first wall can be significantly reduced. The numerically simulating and calculating of temperature, stress distribution and flow analyses were carried out and the feasibility of using water as coolant were discussed. The results demonstrated the engineering feasibility of the water-cooled fusion-fission hybrid reactor blanket module.Copyright

Wavelets Scaling Function Expansion Resonance Self-Shielding Calculation Based on the DDPM

The continuous-energy resonance self-shielding calculation method based on wavelets scaling function expansion method is a valuable potential method to solve the complex resonance problem. Within the fast and thermal energy ranges, the standard multi-group treatment is applied, while Daubechies’ wavelets scaling function expansion method is used to discretize the energy variable of neutron flux within the resonant energy range. In this method, the neutron transport equation is transformed to a set of expansion coefficients equations of wavelets scaling functions. Calculation of the coefficients is very time consuming so that a powerful neutron transport calculation method is needed for better calculation efficiency. In this paper, the discrete direction probability method (DDPM) is employed as a tool for solving the wavelet scaling function expansion coefficients. The DDPM combines the desirable features of interface current method as well as the method of characteristics.Copyright