A neutron noise solver based on a discrete ordinates method

A neutron noise transport modelling tool is presented in this thesis. The simulator allows to determine the static solution of a critical system and the neutron noise induced by a prescribed perturbation of the critical system. The simulator is based on the neutron balance equations in the frequency domain and for two-dimensional systems. The discrete ordinates method is used for the angular discretization and the diamond finite difference method for the treatment of the spatial variable. The energy dependence is modelled with two neutron energy groups. The conventional inner-outer iterative scheme is employed for solving the discretized neutron transport equations. For the acceleration of the iterative scheme, the diffusion synthetic acceleration is implemented.The convergence rate of the accelerated and unaccelerated versions of the simulator is studied for the case of a perturbed infinite homogeneous system. The theoretical behavior predicted by the Fourier convergence analysis agrees well with the numerical performance of the simulator. The diffusion synthetic acceleration decreases significantly the number of numerical iterations, but its convergence rate is still slow, especially for perturbations at low frequencies.The simulator is further tested on neutron noise problems in more realistic, heterogeneous systems and compared with the diffusion-based solver. The diffusion synthetic acceleration leads to a reduction of the computational burden by a factor of 20. In addition, the simulator shows results that are consistent with the diffusion-based approximation. However, discrepancies are found because of the local effects of the neutron noise source and the strong variations of material properties in the system, which are expected to be better reproduced by a higher-order transport method such as the one used in the new solver

Investigation of a discrete ordinates method for neutron noise simulations in the frequency domain

During normal operations of a nuclear reactor, neutron flux measurements show small fluctuations around mean values, the so-called neutron noise. These fluctuations may be driven by a variety of perturbations, e.g., mechanical vibrations of core components. From the analysis of the neutron noise, anomalous patterns can be identified at an early stage and corrected before they escalate. For this purpose, the modelling of the reactor transfer function, which describes the core response to a possible perturbation and is based on the neutron transport equation, is often required. In this thesis a discrete ordinate method is investigated to solve the neutron noise transport equation in the frequency domain. When applying the method, two main issues need to be considered carefully, i.e., the performance of the numerical algorithm and possible numerical artifacts arising from the discretization of the equation. For an efficient numerical scheme, acceleration techniques are tested, namely, the synthetic diffusion acceleration and various forms of the coarse mesh finite difference method. To reduce the possible numerical artifacts, the impact of the order of discrete ordinates and the use of a fictitious source method are studied. These analyses serve to develop the higher-order neutron noise solver NOISE-SN. The solver is compared with different solvers and used to simulate neutron noise experiments carried out in the research reactor CROCUS (at EPFL). The solver NOISE-SN is shown to provide results that are consistent with the results obtained from other higher-order codes and can reproduce features observed in neutron noise experiments

On the simulation of neutron noise using a discrete ordinates method

The method of discrete ordinates is investigated for neutron noise simulations in the frequency domain. For this purpose, the solver NOISE-SN is developed and used to simulate two neutron noise problems that are respectively derived from the two-dimensional systems described in the neutron transport simulation benchmarks C4V and C5G7. In the first problem based on the C4V system, NOISE-SN is compared to the diffusion-based simulator CORE SIM+. These results show that NOISE-SN and CORE SIM+ calculate similar spatial distributions of neutron noise, although significant differences can be found at the location of the perturbation and at locations with strong variations of material properties, where the discrete ordinates method is expected to be more accurate than diffusion theory. Then NOISE-SN calculations are performed to test different SN approximations, and the fictitious source method that may be applied to mitigate possible numerical artifacts, known as the ray effect. In the second problem based on the C5G7 system, the choice of a low order of discrete ordinates in NOISE-SN leads to unphysical values of the neutron noise because of the ray effect. The increase of the order of discrete ordinates or introducing a fictitious source in the equations to be solved alleviates the issue. The second option is shown to remove the ray effect without a high order of discrete ordinates and thus without too expensive calculations, even though the strength of the fictitious source needs to be tuned carefully to avoid very slow convergence rates

Modeling noise experiments performed at AKR-2 and CROCUS zero-power reactors

CORTEX is a EU H2020 project (2017-2021) devoted to the analysis of ’reactor neutron noise’ in nuclear reactors, i.e. the small fluctuations occurring around the stationary state due to external or internal disturbances in the core. One important aspect of CORTEX is the development of neutron noise simulation codes capable of modeling the spatial variations of the noise distribution in a reactor. In this paper we illustrate the validation activities concerning the comparison of the simulation results obtained by several noise simulation codes with respect to experimental data produced at the zero-power reactors AKR-2 (operated at TUD, Germany) and CROCUS (operated at EPFL, Switzerland). Both research reactors are modeled in the time and frequency domains, using transport or diffusion theory. Overall, the noise simulators managed to capture the main features of the neutron noise behavior observed in the experimental campaigns carried out in CROCUS and AKR-2, even though computational biases exist close to the region where the noise-inducing mechanical vibration was located (the so-called ”noise source”). In some of the experiments, it was possible to observe the spatial variation of the relative neutron noise, even relatively far from the noise source. This was achieved through reduced uncertainties using long measurements, the installation of numerous, robust and efficient detectors at a variety of positions in the near vicinity or inside the core, as well as new post-processing methods. For the numerical simulation tools, modeling the spatial variations of the neutron noise behavior in zero-power research reactors is an extremely challenging problem, because of the small magnitude of the noise field; and because deviations from a point-kinetics behavior are most visible in portions of the core that are especially difficult to be precisely represented by simulation codes, such as experimental channels. Nonetheless the limitations of the simulation tools reported in the paper were not an issue for the CORTEX project, as most of the computational biases are found close to the noise source

Novel Y-chromosomal microdeletions associated with non-obstructive azoospermia uncovered by high throughput sequencing of sequence-tagged sites (STSs)

Y-chromosomal microdeletion (YCM) serves as an important genetic factor in non-obstructive azoospermia (NOA). Multiplex polymerase chain reaction (PCR) is routinely used to detect YCMs by tracing sequence-tagged sites (STSs) in the Y chromosome. Here we introduce a novel methodology in which we sequence 1,787 (post-filtering) STSs distributed across the entire male-specific Y chromosome (MSY) in parallel to uncover known and novel YCMs. We validated this approach with 766 Chinese men with NOA and 683 ethnically matched healthy individuals and detected 481 and 98 STSs that were deleted in the NOA and control group, representing a substantial portion of novel YCMs which significantly influenced the functions of spermatogenic genes. The NOA patients tended to carry more and rarer deletions that were enriched in nearby intragenic regions. Haplogroup O2* was revealed to be a protective lineage for NOA, in which the enrichment of b1/b3 deletion in haplogroup C was also observed. In summary, our work provides a new high-resolution portrait of deletions in the Y chromosome.National Key Scientific Program of China [2011CB944303]; National Nature Science Foundation of China [31271244, 31471344]; Promotion Program for Shenzhen Key Laboratory [CXB201104220045A]; Shenzhen Project of Science and Technology [JCYJ20130402113131202, JCYJ20140415162543017]SCI(E)[email protected]; [email protected]; [email protected]

A discrete ordinates solver with diffusion synthetic acceleration for simulations of 2-D and 2-energy group neutron noise problems

A neutron transport solver for 2-D, 2-energy-group neutron noise problems is presented. The simulator allows to determine: 1) the static neutron flux associated with a critical system; 2) the neutron noise in the frequency domain, according to a prescribed perturbation of the critical system. The perturbation is modeled as stationary fluctuations of the macroscopic nuclear cross-sections. The solution algorithm is based on a diamond finite difference scheme, discrete ordinates method, and it is accelerated using a diffusion synthetic acceleration technique. The solver is tested on 2-D homogeneous and heterogeneous systems with a localized neutron noise source. Its convergence is analyzed and compared to the case without acceleration

Development of a frequency-domain reactor noise simulator based on a neutron transport method

The neutron flux measured in a nuclear reactor is characterized by fluctuations around a main trend. These fluctuations are known as reactor neutron noise, and they may allow to identify anomalies in the reactor core. In this context, the CORTEX – COre monitoring Techniques and EXperimental validation and demonstration project, supported by the European Commission, aims at studying reactor neutron noise induced by different types of perturbations (e.g. vibrations of reactor components), and developing core monitoring techniques from the analysis of reactor neutron noise. When simulating reactor neutron noise, the reactor transfer function is needed. The reactor transfer function describes the system response to possible perturbations, and it can be modelled with the neutron transport equation. Most of the past work in this area relies on neutron diffusion theory. However, recent efforts focus on advanced computational capabilities that can provide more detailed insights into neutron noise problems and be used to assess the limitations of the diffusion approach.In the CORTEX project, Chalmers University of Technology is building a neutron noise simulator with a high-order approximation of the neutron transport equation. The equations are discretized according to a finite difference scheme for the spatial variable, a discrete ordinates approximation for the angle, and a multi-group formalism for the neutron energy. The simulation consists of two steps. The first step solves the criticality problem and calculates the static neutron flux. The second step determines the neutron noise in the frequency domain with respect to the prescribed neutron noise source and the static neutron flux previously estimated.The numerical solution of the equations is obtained from an iterative procedure. This is a computationally intensive task because a converged solution may require a very large number of iterations. A crucial factor in the reduction of the iterations is the implementation of a technique for the acceleration of the algorithm. For static calculations, methods such as the Diffusion Synthetic Acceleration (DSA) and the Coarse Mesh Finite Difference (CMFD) acceleration have been widely investigated. To some extent, these techniques have also been \ua0applied to time-dependent problems. On the other hand, no study on acceleration of neutron noise calculations in the frequency domain have been reported in the open literature. The current work also explores the extension of DSA and CMFD methods to the case of frequency-domain neutron noise simulations. Preliminary results will be presented for neutron noise calculations in a 2-dimensional heterogeneous system, with 2-energy groups

ACCELERATION OF A 2-DIMENSIONAL, 2-ENERGY GROUP NEUTRON NOISE SOLVER BASED ON A DISCRETE ORDINATES METHOD IN THE FREQUENCY DOMAIN

The acceleration of the convergence rate is studied for a neutron transport solver to simulate 2-D, 2-energy-group neutron noise problems in the frequency domain. The Coarse Mesh Finite Difference (CMFD) method is compared to the Diffusion Synthetic Acceleration (DSA) method. Numerical tests are performed using heterogeneous system configurations with different boundary conditions. The CMFD scheme leads to a better convergence rate. The results also show that CMFD can accelerate neutron noise problems in a wide range of perturbation frequencies with almost equal efficiency. An unstable convergence behavior is nevertheless observed in problems with purely reflective boundary conditions. Stabilization techniques such as performing multiple transport sweeps, underrelaxing the flux update, and using the lpCMFD method are investigated and improvements can be obtained

A sensitivity study for reactor neutron noise calculations with a neutron absorber of variable strength

The paper presents a sensitivity study for reactor neutron noise simulations. The objective is to investigate different modelling choices of the input uncertainties and to assess the influence of possible uncertainties in the nuclear macroscopic cross-sections and in the neutron noise source. A simplified light water reactor core with a localized thermal neutron absorber of variable strength is considered. For this analysis, the neutronic tool CORE SIM is combined with a statistical methodology for uncertainty and sensitivity analysis. Modelling the input uncertainties as uniformly or normally distributed is found to make no relevant difference in terms of the calculated neutron noise. The uncertainties of the thermal capture and removal cross-sections at the location of the neutron noise source affect the induced neutron noise at the location of the neutron noise source and at other locations. The effect of the uncertainty in the thermal fission cross-section at the position of the neutron noise source is mainly on the fast neutron noise and it tends to disappear far from the neutron noise source. The uncertainties of the cross-sections at a position away from the neutron noise source have a small impact on the induced neutron noise taken at the same location away from the neutron noise source (except for the removal cross-section) or at other locations. The uncertainty in the neutron noise source amplitude can significantly affect the neutron noise amplitude over the reactor, although the effect decreases with the distance from the source. Similar outcomes are obtained in the adjoint problems