With the advantages of high reliability, high power density and long life, small nuclear power reactor has become one of the most excellent space power options in the space missions. TOPAZ-II is the most mature space nuclear power reactor based on thermionic conversion. In this paper, the thermo-physical and transport properties of NaK-78 and heat transfer correlations for liquid metals are implemented into the RELAP5 code. The modified RELAP5 has already been accessed to analyze the thermal-hydraulic characteristics of the space reactor cooled by NaK-78. A RELAP5 model including the core, TFEs, radiator, coolant loop and volume accumulator is developed. Temperature reactivity feedback, TFE emitter, TFE collector, moderator and the reactivity insertion effects of control drums and safety drums are modeled in the point reactor kinetics equations with six-group delayed neutrons. To V&V the integrated TOPAZ-II system model, the steady state is simulated and analyzed. The steady state calculated results are in good agreement with the designed values. On the basis of V&V, a hypothetical reactivity insertion accident is simulated and analyzed. During the accident, the automatic control system is assumed to be malfunctioned, 0.01$ positive reactivity is introduced for 500s and then control drums start to rotate inward. The maximum temperatures of fuel and emitter are below the melting temperature, respectively. The maximum temperature of coolant is 940K with 160K margin from boiling. With the rotating of control drums, the reactor reaches critical again.

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.

Global-local self-shielding calculation scheme is a new high-fidelity resonance calculation model proposed by NECP laboratory of Xi'an Jiaotong University. Neutron Current Method (NCM) is utilized for resonance calculation in the global aspect to obtain Dancoff factors. Then each fuel pin is transformed into individual 1D cylindrical problems by conserving Dancoff factors. The Pseudo-Resonant-Nuclide Subgroup Method (PRNSM) is used to conduct resonance calculation in the local aspect for each 1D cylindrical pin. Global-local self-shielding calculation scheme has been successfully implemented in high-fidelity numerical nuclear reactor physics code NECP-X. Verification results of global-local self-shielding calculation scheme showed good accuracy for UO2 fuels. The maximum relative error of microscopic absorption cross sections (XSs) for 238 U in resonance range was 1.5% compared with MCNP5 [1]. AIC control rods serve as strong absorbers in reactor. Strong self-shielding phenomenon occurs when AIC control rods are inserted. Analysis was performed to determine the effects of AIC control rods on the accuracy of global-local self-shielding calculation scheme and the sources of error. Evaluation results showed that the main part of error was introduced by NCM and radius searching. The relative errors were larger than 10% in several resonance groups. Therefore, a supercell model is proposed to couple with global-local self-shielding calculation scheme to treat resonance calculation for AIC control rods in this paper. Numerical results show that this model improves the accuracy of the global-local self-shielding calculation scheme. The relative errors of microscopic absorption XSs for AIC in most resonance groups were decreased to less than 2%.

Monte Carlo (MC) burnup calculation method, implemented through coupling neutron transport and point depletion solvers, is widely used in design and analysis of nuclear reactor. Burnup calculation is generally solved by dividing reactor lifetime into steps and modeling geometry into numbers of burnup areas where neutron flux and one group effective cross sections are treated as constant during each burnup step. Such constant approximation for neutron flux and effective cross section will lead to obvious error unless using fairly short step. To yield accuracy and efficiency improvement, coupling schemes have been researched in series of MC codes. In this study, four coupling schemes, beginning of step approximation, predictor-corrector methods by correcting nuclide density and flux-cross section as well as high order predictor-corrector with sub-step method were researched and implemented in RMC. Verification and comparison were performed by adopting assembly problem from VERA international benchmark. Results illustrate that high order coupled with sub-step method is with notable accuracy compared to beginning of step approximation and traditional predictor-corrector, especially for calculation in which step length is fairly long.

In this paper the application of the virtual element method (VEM) to the multigroup, neutron diffusion equation will be presented. The VEM is a recently developed Bubnov-Galerkin spatial discretisation method based largely on the mimetic finite difference method (MFD) that preserves the properties of the underlying vector operators. It can discretise elliptic partial differential equations (PDEs) on arbitrary polygonal/polyhedral meshes with arbitrary order and regularity. Deterministic, geometry conforming methods, used to solve multigroup, neutron diffusion, nuclear reactor physics problems have historically used the finite element method (FEM). However, FEM requires high-quality meshes with few highly distorted elements (elements with a poor aspect ratio) or it may may experience convergence problems. The process of creating high quality meshes, even with automated mesh generation algorithms, such as the advancing front and Delaunay methods, is often very time consuming. For these reasons VEM is being studied in this paper as a possible alternative to FEM in the numerical solution of neutron diffusion problems in nuclear reactor physics. A C5G7 UOX pincell problem is presented to demonstrate the application of VEM to mutligroup diffusion problem. The method of manufactured solutions (MMS) is used to determine the order of convergence.

This paper presents a fast sub-grid scale (SGS) finite element method for the first order neutron transport equation. The spherical harmonics method is adopted for the angular discretization. The sub-grid scale discretization embeds discontinuous component in each element to provide a stabilization term for the continuous finite element formulation. Traditional SGS method uses Riemann decomposition and vacuum boundary assumption to decouple the discontinuous component. Here we propose a new method to perform the decoupling based on the assumption that the convection term of the discontinuous component is proportional to the residual of angular flux in each element. The computing costs for the establishment of the coefficient matrix of discontinuous component are reduced to O (1) from O ( n 3 ). Further more, the computing costs for the inversion of the coefficient matrix are reduced to O ( n ) from O ( n 3 ) by applying mass lumping technique. Numerical results show that the new method is not only more efficient but also yields more accurate solution than traditional sub-grid scale method.

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.

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.

Until recently, interior penalty methods have been applied to elliptic operators using an approach based on the mass matrix of finite elements that possess a constant Jacobian. In the case of isogeometric analysis, such an approach would not always guarantee coercivity of the bilinear form and thus numerical stability of the solution. In this paper, optimal interior penalty parameters [1] are described and applied to the symmetric interior penalty scheme of the discontinuous Galerkin isogeometric spatial discretisation of the neutron diffusion equation. The numerical accuracy of the proposed method is compared against a standard continuous Bubnov-Galerkin isogeometric spatial discretisation of the neutron diffusion equation. Numerical consistency and order of error-convergence is verified by means of the method of manufactured solutions. Numerical results are also presented for a two-dimensional pin-cell test case, based upon the OECD/NEA C5G7 quarter core MOX fuel assembly benchmark for nuclear reactor physics parameters of interest.

Radiation-induced damage and degradation to shielding and structure materials in nuclear reactors is one of the key limiting factors that affect the safety considerations and the lifetime. Neutron radiation damages materials mainly by exciting a number of Primary Knock-on Atom (PKAs). PKAs induce displacement cascades, causing microstructure changes and mechanical degradations in materials. Computer simulations are used to model this complex process. Knowing the PKA spectrum accurately is important because PKA spectrum and the input of computer simulation are coupled. In this work, we aim to obtain the PKA spectrum in Zr-based alloys with relatively low Zr concentration by using the Geant4 software. Some new functions were added by reprogramming in Geant4. We found that the energy spectra of PKA in Zr 2 Cu and Zr 2 Ni are mainly caused by Zr atom, and the shape of the average energy spectra are similar with pure Zr. The number of PKA distributions and the energy deposition in these two Zr-based metals are similar with pure Zr but different than those in pure Ni. These finding indicate that the metallic elements of Cu and Ni have small impact on PKA spectrum in Zr-based alloys, which illustrate that simplified simulation models are feasible when using computer for simulating. Moreover, it has great significant for the calculation of irradiation damage and the computer simulation for the process of collision cascade after one PKA is formed.

This paper designs a measure and analysis system of nuclear noise frequency spectrum for narrow channel research reactor core. Based on high-speed synchronization DAQ which is PXI-1031, the hardware design has been carried out. By using Labview, the data acquisition and analysis code has been developed. In order to verify the function of nuclear noise frequency spectrum measure and analysis system, firstly, through using arbitrary waveform generator which is Fluke-282, two sine signals have been tested. Secondly, by using history operation datum, the prompt neutron decay constant has been measured and analyzed. The simulation experimental and operational datum results show that such measure and analysis system of nuclear noise frequency spectrum is successful and reliable design, which can meet the design requirements. Finally, the preliminary research work between helium bubble and its responding frequency for narrow channel core has just started to monitor safety operation or carry out fault diagnosis.

In this paper, preliminary neutron physical properties of ceramic fast reactor (CFR) are simulated and analyzed. The CFR core consists of ceramic materials, including nuclear fuels, coolants, structural materials, reflective and absorption materials. These ceramics improve inherent safety levels substantially, increase breeding performance, and enhance the power-generation efficiency. The CFR has the potential to operate and breed more than 30 years. The performance of the CFR was simulated focusing on neutron-related effects. The parameters discussed contain fast neutron energy spectrum, the ideal effective multiplication-factor, nuclides mass changes, breeding performance, operation mode, etc. Furthermore, the strengths of the proposed reactor system are discussed. In the future nuclear energy system, CFR may be one of the existing alternative novel reactor type.

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.

Heat pipe-segmented thermoelectric module converters space reactor power system (HP-SMTCs SRPS) is a promising candidate for space nuclear power system. An examination was taken to discuss the criticality safety of HP-SMTCs reactor core in several accident conditions. In the original nuclear design, the case that reactor core is submerged in wet sand while the voids inside the core are filled with sea water and the BeO reflector are dismantled is defined as the worst status with the highest risk of supercritical. However, recent Monte Carlo transport calculation result shows that reactivity in the case that the core is submerged in water while the voids inside are empty is even higher than those cases with the voids full of sea water, which means that the reactor may encounter high risk of supercritical when some particular accidents occur. Detailed analysis about the neutron energy spectrum and absorption reaction rate is made in order to find out the potential reason of these unexpected results. According to the discussion about the criticality safety issues in some accidents, further evaluations may be necessary for the neutronics design of HP-SMTCs space reactors.

The computing power available nowadays to the average Monte-Carlo-code user is sufficient to perform large-scale neutron transport simulations, such as full-core burnup or high-fidelity multiphysics. In practice however, software limitations in the majority of the available Monte Carlo codes result in a low efficiency when running in High Performance Computing (HPC) environments, the main issues being inadequate memory utilization and poor scalability. The traditional parallel processing scheme based of splitting particle histories among processes requires domain replication across nodes, and therefore the memory demand for each computing node does not scale, and a memory bottleneck appears for large-scale problems. The scalability of this approach usually limits the resources that can be used efficiently to a small number of nodes/processors. Consequently, massively parallel execution is not viable with particle-based parallelism, at least not by itself. In this work we propose a Spatial Domain Decomposition (SDD) approach to develop an efficient and scalable Monte Carlo neutron transport algorithm. Breaking down the geometry into subdomains, a distributed memory scheme can be used to reduce the in-node memory demand, allowing the simulation of large-scale memory-intensive problems. Additionally, with an efficient neutron tracking algorithm the overall speedup can be significantly improved.

Deep penetration problems exist widely in reactor applications, such as SPRR300 (Swimming Pool Research Reactor 300), a light water moderated, enriched uranium fueled research reactor in China. Deterministic transport theory is intrinsically suitable for deep penetration. But there exist some problems when it’s applied in SPRR-300research reactors. First, the reactor core is complicated for geometry description in deterministic theory codes. Monte Carlo method has advantages in complex geometry modeling. And it uses continuous energy cross sections which are independent with specific reactor types and research objections. But usually it’s difficult to converge well enough to deal with deep penetration problems, even though there are a number of variance reduction techniques. Based on the advantages and disadvantages of Monte Carlo and Deterministic method, we proposed a coupled neutron transport calculation method for deep penetration. It combines advantages of these two methods. Firstly, we use Monte Carlo code to finish fine modeling and do the whole reactor core calculation. Domestically developed Monte Carlo code JMCT is used to do the neutron transport calculation. Then homogenized group constants in each mesh are calculated from JMCT output by a self-developed script. Afterwards, we do the whole reactor calculation with deterministic theory code TORT. It directly uses group constants generated by Monte Carlo code. Finally, we can get the deep penetration calculation results from TORT output. Verification is carried out by comparing the group constants of benchmark problem, and by comparing k eff calculated by this method with continuous energy Monte Carlo method. Benchmark calculation is conducted with OECD/NEA slab benchmark problem. The comparison shows that group constants generated by this study are in good agreement with results from published references. Then above group constants are applied to 3-dimensional discrete ordinates deterministic theory transport code TORT. But k eff calculated by TORT is a little lower than that calculated by Monte Carlo code JMCT. To minimize other influence factors, different Sn/Pn order, and different mesh size in TORT has been tried. Unfortunately the k eff difference between these two methods remains. Even though the k eff results in this benchmark are less than k eff calculated by continuous energy MC method, Benchmark results show that all the group constants generated by this method are in good agreement with existing references. So it can be expected that after further verification and validation, this coupled method can be effectively applied to the deep penetration problem in such kind of research reactors.

In presence of a weak neutron source, the initial growth of neutron population in a supercritical system exhibits a significant stochastic feature, both initiation and burst waiting times are uncertain. As a result, the energy released during criticality excursions is stochastic, obeying a probability distribution. When criticality accidents and pulsed reactor experiments are analyzed, it is important to estimate this kind of stochastic feature, including assessing the initiation probability and then the fission energy probability distribution. Thus a Monte Carlo direct simulation method has been proposed and the corresponding code MES has been developed. By taking random factors during criticality excursions into account in dynamic Monte Carlo simulations, this method is capable of simulating the whole process from source injection to exponential growth of the neutron population, and finally to extinction of the neutron pulse. A set of static initiation probability problems and a figurative criticality excursion problem have been applied to validate this method and MES. Results demonstrate that with the proposed method MES is able to simulate stochastic transient neutron fields in multiplying systems during criticality excursions.

The adjoint neutron flux is vital in the analysis of reactor kinetics parameters and reactor transient events. Both deterministic and Monte Carlo methods have been developed for the adjoint neutron flux calculation on the basis of multi-group cross sections which may vary significantly among different types of reactors. The iterated fission probability (IFP) method is introduced to calculate the neutron importance which is able to represent the adjoint neutron flux in continuous energy problem and have been applied to the calculation of kinetics parameters. However, the adjoint neutron flux can’t be obtained directly and applied to both Monte Carlo transient event analysis and deterministic methods. In this study, a method based on IFP is studied and implemented in Monte Carlo code RMC. The multi-group adjont neutron flux can be obtained directly through the discretization of energy and space with the modification of fission neutrons through continuous energy Monte Carlo calculations. The obtained multi-group adjoint neutron flux can be used in both Monte Carlo transient analysis and deterministic methods.

Accelerator used for Boron Neutron Capture Therapy (BNCT) is the development trend of cancer treatment in the future. Neutron generator is a neutron source with compact structure, easy to operate, and lower price in accelerator (the structure of neutron tube is more compact). It has a high feasibility of establishing in the hospital when compared with other types of accelerator. At present, the D-D reaction has higher neutron yield than other reactions, more easy to get D material. Therefore, the epithermal neutron beam based on D-D neutron generator is studied for BNCT usage. First, the calculation model is established by MCNP program, including the neutron source model, the geometric model of the irradiation device. The specific neutron energy spectrum and angular distribution of the D-D reaction are theoretically analyzed when establishing the D-D reaction neutron source model. The basic structure models of typical irradiation devices are designed, and then the optimal suitable moderator material for the irradiation device is studied from the neutron reaction cross section, the combination of iron and Fluental materials is optimum. The irradiation device with multi D-D neutron tubes’ combination as BNCT neutron source is designed. It can be concluded by study that the parameters at the beam exit are epithermal neutron flux density 2.01 × 10 8 n/cm 2 · s, fast neutron contamination 1.33 × 10 −11 Gy · cm 2 /n, γ contamination 5.79 × 10 −17 Gy · cm 2 /n, for the combination with 6 neutron tubes. The result can meet IAEA’s requirements for BNCT epithermal neutron beam quality.

The efficient solution of the neutron diffusion equation for large scale whole core calculations is of paramount importance; especially if the detailed pin-level power distribution and reaction rates are required. For heterogeneous whole core calculations finite element based techniques have been one approach to modelling the detailed pin geometry in whole core calculations. A new approach, pioneered in the last few years, is isogeometric analysis (IGA) methods which enable the exact geometry of fuel pins to be modelled. In order to efficiently solve elliptic partial differential equations (PDEs), such as the neutron diffusion equation, typically multi-grid or multi-level iterative solution techniques are used such as the algebraic multi-grid method. However, using IGA methods it is possible to develop true geometric multi-grid techniques which are potentially much more efficient than the standard algebraic multi-grid methods. In this paper we explore the use of IGA methods to develop a scalable, multi-level, iterative algorithm which is then used to solve the neutron diffusion equation over several geometries. This multilevel solution algorithm utilises a single patch multi-grid framework suggested by Hofreither and Takacs that takes advantage of the tensor product construction to provide scalability with respect to spatial, and polynomial refinement. Furthermore, a two-level balancing Neumann-Neumann solver is used to extend the solver to multiple patches in a scalable way. It is seen that the number of iterations required depends on the mapping between the unit square and the physical geometry, as well as the material coefficients.