Youqi Zheng

Studies on the molten salt reactor: code development and neutronics analysis of MSRE-type design

The molten salt reactor is characterized by its use of the fluid-fuel, which serves both as a fuel and as a coolant simultaneously. The position of delayed neutron precursors continuously changes both in the core and in the external loop due to the fuel circulation, and the fission products are extracted by an online fuel reprocessing unit, which all lead to the modeling methods for the conventional reactors using solid fuel not applicable. This study establishes suitable calculation models for the neutronics analysis of the molten salt reactor and develops a new code named MOREL based on the three-dimensional diffusion steady and transient calculations. Some numerical tests are chosen to verify the code and the numerical results indicate that MOREL can be used for the analysis of the molten salt reactor. After verification, it is applied to analyze the characteristics of a typical molten salt reactor, including the steady characteristics, the influence of fuel circulation on the kinetic behaviors. Besides, the influence of online fuel reprocessing simulation is also examined. The results show that inherent safety is the character of the molten salt reactor from the aspect of reactivity feedback and the fuel circulation has great influence on the kinetic characteristics of molten salt reactor.

An Improved Resonance Self-Shielding Calculation Method Based on Equivalence Theory

Abstract The deviation of the effective resonance cross section obtained by conventional equivalence theory for a heterogeneous system is analyzed. It is shown that several approximations commonly adopted in conventional equivalence theory account for the deviation at different levels, with the narrow resonance (NR) approximation being the main source of deviation. Based on the analysis, an improved method based on equivalence theory is proposed. It utilizes the resonance fine flux integral table to minimize the deviation caused by NR approximation. The validity of the method is confirmed by test calculations of effective resonance cross sections in different geometries and different energy group structures. The results of eigenvalue calculations on typical fuel pin cells show that the proposed improvement is effective in reducing the error of infinite multiplication factors of the pin cell. Since the resonance fine flux integral used in this method has already been obtained in calculating the resonance integral table and can be pre-tabulated in the process of generating the library, the implementation of the proposed method is simple and requires no additional calculations. It is useful for improving the accuracy of lattice physics codes based on the equivalence theory.

Daubechies Wavelet Method for Angular Solution of the Neutron Transport Equation

Abstract This paper describes Daubechies’ wavelet method (DWM) for the discretization of the angular variable in the neutron transport equation. Two special features are introduced: (a) the azimuthal angle is discretized using the Daubechies’ scaling function as the basis function, while the polar angle is decoupled and discretized using the discrete ordinates in a standard manner, and (b) the construction of Daubechies’ wavelets on an interval is used to get around the edge effect between subdomains in the angular variable. In addition, two acceleration methods, namely, coarse mesh rebalance and coarse mesh finite difference, are implemented in DWM. The test results on several benchmark problems indicate that DWM described in this paper is capable of treating transport problems exhibiting angularly complicated behaviors, effective in mitigating ray effect, and versatile in handling transport phenomena in a variety of structured media.

Improvements and validation of the transient analysis code MOREL for molten salt reactors

ABSTRACT The liquid fuel salt used in the molten salt reactors (MSRs) serves as the fuel and coolant simultaneously. On the one hand, the delayed neutron precursors circulate in the whole primary loop and part of them decay outside the core. On the other hand, the fission heat is carried off directly by the fuel flow. These two features require new analysis method with the coupling of fluid flow, heat transfer and neutronics. In this paper, the recent update of MOREL code is presented. The update includes: (1) the improved quasi-static method for the kinetics equation with convection term is developed. (2) The multi-channel thermal hydraulic model is developed based on the geometric feature of MSR. (3) The Variational Nodal Method is used to solve the neutron diffusion equation instead of the original analytic basis functions expansion nodal method. The update brings significant improvement on the efficiency of MOREL code. And, the capability of MOREL code is extended for the real core simulation with feedback. The numerical results and experiment data gained from molten salt reactor experiment (MSRE) are used to verify and validate the updated MOREL code. The results agree well with the experimental data, which prove the new development of MOREL code is correct and effective.

A new approach to three-dimensional neutron transport solution based on the method of characteristics and linear axial approximation

Abstract A new approach based on the method of characteristics (MOC) is proposed to solve the neutron transport equation. A new three-dimensional (3D) spatial discretization is applied to avoid the instability issue of the transverse leakage iteration of the traditional 2D/1D approach. In this new approach, the axial and radial variables are discretized in two different ways: the linear expansion is performed in the axial direction, then, the 3D solution of the angular flux is transformed to be the planar solution of 2D angular expansion moments, which are solved by the planar MOC sweeping. Based on the boundary and interface continuity conditions, the 2D expansion moment solution is equivalently transformed to be the solution of the axially averaged angular flux. Using the piecewise averaged angular flux at the top and bottom surfaces of 3D meshes, the planes are coupled to give the 3D angular flux distribution. The 3D CMFD linear system is established from the surface net current of every 3D pin-mesh to accelerate the convergence of power iteration. The STREAM code is extended to be capable of handling 3D problems based on the new approach. Several benchmarks are tested to verify its feasibility and accuracy, including the 3D homogeneous benchmarks and heterogeneous benchmarks. The computational sensitivity is discussed. The results show good accuracy in all tests. With the CMFD acceleration, the convergence is stable. In addition, a pin-cell problem with void gap is calculated. This shows the advantage compared to the traditional 2D/1D MOC methods.

Neutronics studies on the feasibility of developing fast breeder reactor with flexible breeding ratio

This paper investigates the feasibility of designing a flexible fast breeder reactor from the view of neutronics. It requires that the variable breeding ratio can be achieved in operating a fast reactor without significant changes of the core, including the minimum change of fuel assembly design, the minimum change of the core configuration and the same control system arrangement in the core. The sodium cooled fast reactor is investigated. Two difficulties are overcome: (1) the different excess reactivity is well controlled for different cores, especially for the one with small breeding ratio; (2) the maximum linear power density is well controlled while the breeding ratio changes. The optimizations are done to meet the requirements. The U–Pu–Zr alloy is applied to enhance the breeding. The enrichment-zoning technique with unfixed blanket assembly loading position is searched to get acceptable power distributions when the breeding ratio changes. And the control system is designed redundantly to fulfill the control needs. Then, the achieved breeding ratio can be adjusted from 1.1 to 1.4. The reactivity coefficients, temperature distributions and preliminary safety performances are evaluated to investigate the feasibility of the new concept. All the results show that it is feasible to develop the fast reactor with flexible breeding ratios, although it still highly relies on the advancement of the coolant flow control technology.

Studies on LLFP transmutation in a pressurized water reactor

A systematic study on the long-lived fission product (LLFP) transmutation in a pressurized water reactor (PWR) is performed, aiming at an optimal transmutation strategy for present nuclear energy development. The LLFPs selected in the analysis include 99Tc and 129I discharged from light water reactors (LWRs). The isotope 127I is also considered to avoid the difficulties in isotopes separation. To minimize the negative impacts of LLFPs on the core performance and safety parameters, metallic technetium or MgI2 target pins mixed with ZrH2 are designed and investigated. Through the numerical analysis on equilibrium cycles, the transmuted amounts of 99Tc and 129I equal to the yields from 1.94 and 4.22 PWRs with a power of 1000 MWe, respectively. Numerical results indicate that both 99Tc and 129I can be transmuted conveniently in present PWRs in the form of target pins.

A hybrid method to generate few-group cross sections for fast reactor analysis

ABSTRACT The accuracy of fast reactor core calculation is usually determined by the accuracy of self-shielded few-group cross sections. To further improve the accuracy of cross section generation, a hybrid method is proposed. In the hybrid method, the Monte-Carlo method is used to deal with the resonance effect in both the resolved and unresolved resonance range. The self-shielded ultrafine-group total, fission and elastic scattering cross sections are tallied by the Monte-Carlo method. The scattering transfer matrices are then generated in a synthesis way by using the tallied elastic scattering cross sections and a problem-independent elastic scattering function. The angular flux moments for the group condensation are calculated in an explicit deterministic way. Several tests are done to verify the hybrid method. The results show that the hybrid method avoids the disadvantages of both the traditional deterministic method and the pure Monte-Carlo method. It is a more accurate method to generate the few-group cross sections for fast reactor cores.

Study on Improvement of Analytic Depletion Calculation Method

The transmutation trajectory analysis (TTA) method is a traditional analytic depletion calculation algorithm. It’s capable of providing very accurate solutions with cutoff value being sufficiently small, but the main drawback is expensive time consumption. In this paper, the depletion problem was rephrased as a directed-graph module with additional properties attributed to vertices and edges. Based on this model a new approach for TTA implementation was conducted, to which dynamic programming technique could be introduced easily. Besides it, a new analytic algorithm is proposed based on the above model, which gives each nuclide a time dependent concentration function instead of a scalar value that other algorithms could only offer. One of the advantages brought by this algorithm is making time integration value calculations straightforward. Both of these two approaches are programmed. The resulting TTA code was proved to be very efficient, the running time for a typical ORIGEN2 problem with cutoff equals to 10−15 could be of the same magnitude with time spent on library reading process. The codes are analyzed in terms of time and space complexities, which could offer a theoretical point of view on their behaves.Copyright

Improved Variational Nodal Method Based on Symmetry Group Theory

Abstract To reduce the calculation effort and memory requirement for high-order PN expansion calculation in the Variational Nodal Method (VNM), the surficial irreducible basis functions based on the symmetry group theory have been employed to block-diagonalize one of the four nodal response matrices. Its effectiveness encourages our further investigation on the application of the symmetry group theory to volumetric expansion to block-diagonalize the remaining three of the nodal response matrices in this paper. By using the symmetry group theory, the neutron transport problem for each node can be decoupled into several independent subproblems as long as both the geometry and the material distribution of the node are symmetric. Each of these subproblems can be solved by using variational principles as in the traditional VNM, providing their nodal response matrices as the diagonal blocks of the corresponding entire ones. For hexagonal-z node, each nodal response matrix can be reduced into 16 diagonal blocks, among which only 12 have to be calculated due to the properly selected irreducible basis functions. In addition, it is also proved that the response matrices with anisotropic scattering can also be block-diagonalized as the same. Calculation results based on typical problems demonstrate that the new method reduces the time cost for the response matrice calculation by one order of magnitude compared with our previous work. For the total computing time, the speedup ratio is about 2 for P3 calculation and 4 for P5 calculation. Furthermore, almost 40% of the memory requirement can be saved.