A Space-Time Parallel Method to Solve Space-Dependent Neutron Kinetics Equations in Hexagonal-Z Geometry

Neutron kinetics plays an important role in reactor safety and analysis. The backward Euler method is the most widely used time integration method in the calculation of space-dependent nuclear reactor kinetics. Diagonally Implicit Runge-Kutta (DIRK) method owns high accuracy and excellent stability and it could be applied to the neutron kinetics for hexagonal-z geometry application. As solving the neutron kinetics equations is very time-consuming and the number of available cores continues to increase with parallel architectures evolving, parallel algorithms need to be designed to utilize the available resources effectively. However, it is difficult to parallel in time axis since the later moment is strongly dependent on the previous moment. In this paper, the Parareal method which is a time parallel method and implemented by MPI in the processor level is studied in the hexagonal-z geometry with the help of DIRK method. In order to make good use of the parallelism, a parallel strategy in the space direction is also used. In the coarse nodal method, many same operations are finished in the nodes and these operations could be parallel by OpenMP in the thread level since they are independent. Several transient cases are used to validate this method. The results show that the Parareal method gets a fast-convergent speed such as only 2∼3 iterations are needed to convergent. This space-time parallel method could reduce the cost time compared to the sequential method.

First Steps Towards the Development of a 3D Nuclear Fuel Behavior Solver With OpenFOAM

A new 3D fuel behavior solver is currently under collaborative development at the Laboratory for Reactor Physics and Systems Behaviour of the École Polytechnique Fédérale de Lausanne and at the Paul Scherrer Institut. The long term objective is to enable a more accurate simulation of inherently 3D safety-relevant phenomena which affect the performance of the nuclear fuel. The current implementation is a coupled three-dimensional heat conduction and linear elastic small strain solver, which models the effects of burnup- and temperature dependent material properties, swelling, relocation and gap conductance. The near future developments will include the introduction of a smeared pellet cracking model and of material inleasticities, such as creep and plasticity. After an overview of the theoretical background, equations and models behind the solver, this work focuses on the recent preliminary verification and validation efforts. The radial temperature and stress profiles predicted by the solver for the case of an infinitely long rod are compared against their analytical solution, allowing the verification of the thermo-mechanics equations and of the gap heat transfer model. Then, an axisymmetric model is created for 4 rods belonging to the Halden assembly IFA-432. These models are used to predict the fuel centerline temperature during power ramps recorded at the beginning of life, when the fuel rod performance is still not affected by more complex high burnup effects. Finally, the predictions are compared with the experimental measurements coming from the IFPE database. This first preliminary results allow a careful validation of the temperature-dependent material properties and of the gap conductance models.

Advances in FEMN: The Code for Nuclear Noise Analysis Based on ICEM-CFD

The finite element method based on unstructured mesh has good geometry adaptability, it has been used to solve reactor physics problems, manual description of geometric modeling and meshing makes the current finite element code very complicated, it greatly restricts the application of this method in the numerical calculation of reactor physics. Using the CAD pre-processing software ICEM-CFD, three dimensional geometry is divided into tetrahedral or hexahedral meshes, two dimensional geometry is divided into triangular or quadrilateral meshes, the main code of neutron calculation for nuclear noise analysis based on finite element method is developed. The steady state parameters are calculated and tested through benchmark problem, the test results show that the code has the corresponding computing capabilities. Finally, the neutron noise spectrum is calculated for the 3D PWR benchmark problem published by IAEA, and the noise distribution under given frequency is given.

Influence of Xe-135 Dynamic Behavior on Core Operation Safety for a Molten Salt Reactor

The isotope Xe-135 has a large thermal neutron absorption cross section and is considered to be the most important fission product. A very small amount of such neutron poison may significantly affect the reactor reactivity since they will absorb the neutrons from chain reaction, therefore monitoring their atomic density variation during reactor operation is extremely important. In a molten reactor system, Xe-135 is entrained in the liquid fuel and continuously circulates through the core where the neutron irradiation functions and the external core where only nuclei decay occurs, at the same time, an off-gas removal system operates for online removing Xe-135 through helium bubbling. These unique features of MSR complicate the Xe-135 dynamic behaviors, and the calculation method applied in the solid fuel reactor system is not suitable. From this point, we firstly analytically deduce the nuclei evolution law of Xe-135 in the flowing salt with an off-gas removal system functioning. A study of Xe-135 dynamic behavior with the core power change, shutdown, helium bubbling failure and startup then is conducted, and several valuable conclusions are obtained for MSR design.

Towards Development of Uncertainty Library for Nuclear Reactor Core Simulation

Uncertainty quantification is an indispensable analysis for nuclear reactor simulation as it provides a rigorous approach by which the credibility of the predictions can be assessed. Focusing on propagation of multi-group cross-sections, the major challenge lies in the enormous size of the uncertainty space. Earlier work has explored the use of the physics-guided coverage mapping (PCM) methodology to assess the quality of the assumptions typically employed to reduce the size of the uncertainty space. A reduced order modeling (ROM) approach has been further developed to identify the active degrees of freedom (DOFs) of the uncertainty space, comprising all the cross-section few-group parameters required in core-wide simulation. In the current work, a sensitivity study, based on the PCM and ROM results, is applied to identify a suitable compressed representation of the uncertainty space to render feasible the quantification and prioritization of the various sources of uncertainties. While the proposed developments are general to any reactor physics computational sequence, the proposed approach is customized to the TRITON-NESTLE computational sequence, simulating the BWR lattice model and the core model, which will serve as a demonstrative tool for the implementation of the algorithms.

Strength Limit of Thimble Tube With Material Plasticity Under Bending Moment and Axial Compression Force

The thimble tube, which is made of Zircaly-4, is one of the main components of a PWR fuel assembly. The thimble tube has an important role as a structural member of the skeleton. Another role of the thimble tube is to guide a rod cluster control assembly (RCCA) for insertion during the reactor operation, and the function has to be assured not only in normal operation but in a seismic event. In a horizontal seismic event, the fuel assembly vibrates laterally, which gives bending moment to the thimble tube. In addition, axial compressive force acts on the thimble tube in a vertical seismic event. The integrity of the thimble tube has to be maintained while this force and moment act. Mitsubishi has confirmed by the elastic stress analysis that the stress of the thimble tube is lower than the limit value requested for the seismic event. The stress evaluation method is based on the ASME code. The ASME code also describes the limit analysis which is available when the predicted stress is beyond elastic region of the material. In the analysis, the material is assumed to be elastic-perfectly plastic, and the maximum load that the structure can carry is calculated. For the reason mentioned above, the allowable limit of the thimble tube should be determined as a function between the force and the moment. We are planning to examine the allowable limit experimentally. As a step before testing, an analytical approach for the limit is discussed in this paper. Firstly, the allowable limit is calculated by a beam model assuming elastic-perfectly plastic material, based on the ASME code. Secondly, a 3D model analysis with elastic-plastic material is performed to predict the practical strength. Based on the comparison with the analysis using elastic-perfectly plastic material, ASME based limit is considerably conservative compared with the one with the actual stress-strain curve. Conversely, this means there is enough room to rationalize the allowable limit. As the future work, the experiment will be conducted to obtain the practical limit of the thimble tube and to verify the analysis results.

Development of Three-Dimensional Neutron Kinetics Code Based on High Order Nodal Expansion Method in Hexagonal-Z Geometry

To solve three-dimensional kinetics problems, a high order nodal expansion method for hexagonal-z geometry (HONEM) and a Runge-Kutta (RK) method are respectively adopted to deal with the spatial and temporal problem. In the HONEM, 1D partially-integrated flux are approximated by using four order polynomial. The two order polynomial is adopted to the approximation of partially-integrated leakages. The Runge-Kutta method is adopted as a tool for dispersing the time term of 3D kinetics equation. A flux weighting method (FWM) is used for obtaining homogenized cross sections of mix node. The three-dimensional hexagonal kinetics code has been developed based on this method and tested with two benchmark problems of VVER which are the control rod ejection without any feedback and with simple adiabatic Doppler feedback. The results calculated by this code agree well with the reference results and the code is validated.

Parallel Computation of the Point Neutron Kinetic Equations Using Parallel Revisionist Integral Deferred Correction

The point kinetics is very important to the safety of the reactor operation. However, these equations are stiff and usually solved with very small time step. These equations are solved by Revisionist integral deferred correction (RIDC), which is a parallel time integration method. RIDC is a highly accurate method, and it reduces the error by iteration. Based on C++ and MPI, a four-core fourth-order RIDC is implemented and tested by several cases, such as step, ramp, and sinusoidal reactivity insertion. Compared with other methods, the time step of RIDC in the step reactivity insertion case is smaller, but it’s larger in the case of the sinusoidal reactivity insertion. RIDC can keep high accuracy while the time step is appropriately large. The numerical results also show that the speed-up ratio can achieve 2 when 4 processors are used.

Analysis on the Dynamic Buckling Behavior of the Spacer Grid Structure

The spacer grid is a key element of the fuel assembly used in the Pressurized water reactor. Due to its structural complexity, the analysis and the design of the spacer grid structure is difficult. This paper discusses the 5 × 5 cell size partial grid analysis including the detailed grid structural elements, through which, the impact force, the rebound velocity and the time history of acceleration and as well as other mechanical properties of grid under different initial impact velocity were obtained. This paper carried out the dynamic buckling criterion studies, and determined the dynamic buckling load of the 5 × 5 cell size partial spacer grid. Based on assuming the impact process is simple harmonic vibration, the method to determine the dynamic stiffness of the spacer grid was proposed. The experiments were also performed for the comparison with the analytical results. It is found that the analytical results are in good agreement with the experimental results. As a result, we can conclude that the analysis model including detailed grid elements is able to yield accurate analytical results.

Multiphysics Modeling of Thorium-Based (Th, U)O2 and (Th, Pu)O2 Fuel Performance in a Light Water Reactor

ThO2 has been considered as a possible replacement for UO2 fuel for future generation of nuclear reactors, and thorium-based mixed oxide (Th-MOX) fuel performance in a light water reactor was investigated due to better neutronics properties and proliferation resistance compared to conventional UO2 fuel. In this study, the thermal, mechanical properties of Th0.923U0.077O2 and Th0.923Pu0.077O2 fuel were reviewed with updated properties and compared with UO2 fuel, and the corresponding fuel performance in a light water reactor under normal operation conditions were also analyzed and compared by using CAMPUS code. The Th0.923U0.077O2 fuel were found to decrease the fuel centerline temperature, while Th0.923Pu0.077O2 fuel was found to have a bit higher fuel centerline temperature than UO2 fuel at the beginning of fuel burnup, and then much lower fuel centerline than UO2 fuel at high fuel burnup. The Th0.923U0.077O2 fuel was found to have lowest fuel centerline temperature, fission gas release and plenum pressure. While the Th0.923Pu0.077O2 fuel was found to have earliest gap closure time with much less fission gas release and much lower plenum pressure compared to UO2 fuel. So the fuel performance could be expected to be improved by applying Th0.923U0.077O2 and Th0.923Pu0.077O2 fuel.