Brendan Kochunas

Stability and accuracy of 3D neutron transport simulations using the 2D/1D method in MPACT ☆

A consistent “2D/1D” neutron transport method is derived from the 3D Boltzmann transport equation, to calculate fuel-pin-resolved neutron fluxes for realistic full-core Pressurized Water Reactor (PWR) problems. The 2D/1D method employs the Method of Characteristics to discretize the radial variables and a lower order transport solution to discretize the axial variable. This paper describes the theory of the 2D/1D method and its implementation in the MPACT code, which has become the whole-core deterministic neutron transport solver for the Consortium for Advanced Simulations of Light Water Reactors (CASL) core simulator VERA-CS. Several applications have been performed on both leadership-class and industry-class computing clusters. Results are presented for whole-core solutions of the Watts Bar Nuclear Power Station Unit 1 and compared to both continuous-energy Monte Carlo results and plant data.

Analysis of the Core Power Response During a PWR Rod Ejection Transient Using the PARCS Nodal Code and the DeCART MOC Code

Abstract The current state of the art in the analysis of a control rod ejection event in a pressurized water reactor (PWR) relies on homogenization methods in which the assembly-averaged power from a whole-core nodal neutronics simulator is used with some type of flux reconstruction to estimate the individual fuel rod power. Recently, there has been interest in taking advantage of methods that do not require homogenization, such as the DeCART code, to perform time-dependent neutron transport calculations. These calculations could provide not only more accurate pin power results but also intrapin power information during the transient. The work described in this paper is the analysis of a PWR control rod ejection transient using the nodal core simulator PARCS, which employs homogenization methods, and the method of characteristics (MOC) code DeCART, which treats the explicit geometry. Higher-fidelity methods such as those used by DeCART have the potential to quantify the homogenization and modeling errors inherent in the lower-order methods. The methods used in PARCS and DeCART are briefly described as well as the approach to generate the temperature feedback for the rod ejection event. The results are compared and discussed. For the considered transient scenario, PARCS and DeCART are in generally good agreement for the predicted global and local powers as well as for the temperature.

VERA Core Simulator methodology for pressurized water reactor cycle depletion

This paper describes the methodology developed and implemented in the Virtual Environment for Reactor Applications Core Simulator (VERA-CS) to perform high-fidelity, pressurized water reactor (PWR), multicycle, core physics calculations. Depletion of the core with pin-resolved power and nuclide detail is a significant advance in the state of the art for reactor analysis, providing the level of detail necessary to address the problems of the U.S. Department of Energy Nuclear Reactor Simulation Hub, the Consortium for Advanced Simulation of Light Water Reactors (CASL). VERA-CS has three main components: the neutronics solver MPACT, the thermal-hydraulic (T-H) solver COBRA-TF (CTF), and the nuclide transmutation solver ORIGEN. This paper focuses on MPACT and provides an overview of the resonance self-shielding methods, macroscopic-cross-section calculation, two-dimensional/one-dimensional (2-D/1-D) transport, nuclide depletion, T-H feedback, and other supporting methods representing a minimal set of the capabilities needed to simulate high-fidelity models of a commercial nuclear reactor. Results are presented from the simulation of a model of the first cycle of Watts Bar Unit 1. The simulation is within 16 parts per million boron (ppmB) reactivity for all state points compared to cycle measurements, with an average reactivity bias of <5 ppmB for the entire cycle. Comparisons to cycle 1 flux map data are also provided, and the average 2-D root-mean-square (rms) error during cycle 1 is 1.07%. To demonstrate the multicycle capability, a state point at beginning of cycle (BOC) 2 was also simulated and compared to plant data. The comparison of the cycle 2 BOC state has a reactivity difference of +3 ppmB from measurement, and the 2-D rms of the comparison in the flux maps is 1.77%. These results provide confidence in VERA-CSs capability to perform high-fidelity calculations for practical PWR reactor problems.

Space-dependent wielandt shifts for multigroup diffusion eigenvalue problems

Abstract We present a new concept—the space-dependent Wielandt shift (SDWS)—for accelerating the convergence of the power iteration (PI) scheme for multigroup diffusion k-eigenvalue problems. The SDWS improves on standard Wielandt shift (WS) techniques, which are empirical in nature and are typically effective only when the current estimate of the solution is reasonably converged. By accounting for the physics of the problem through SDWS, we are able to improve the acceleration for the initial iterates when the current estimate of the solution is not close to convergence. Numerical results from one-dimensional problems suggest that, compared to standard WS techniques, the new SDWS techniques can provide upward of a 46% reduction in the number of PIs required for convergence and a 40% reduction in the computational time required. This improvement is sensitive to several problem-dependent factors, such as the geometry and energy-dependence of the problem, the spatial discretization, and the initial guess. The reduction in computational time is also dependent on the linear solver in the PI scheme, as it is well known that WSs can significantly worsen the conditioning of the diffusion linear system. In this paper, we provide a detailed study of the impact of WSs on the performance of several iterative linear solvers. Results from our implementation of SDWS in the three-dimensional (3D) code MPACT show that SDWS can provide similar speedups for 3D multigroup diffusion eigenvalue problems. These results also show that moderate speedups can be obtained by applying SDWS to the coarse mesh finite difference (CMFD) solver in a CMFD-accelerated transport scheme. However, the benefit of doing this may be limited because all but the first few CMFD solves are relatively easy to converge, regardless of the WS used.

Theoretical Convergence Rate Lower Bounds for Variants of Coarse Mesh Finite Difference to Accelerate Neutron Transport Calculations

Abstract The lower bounds for the theoretical convergence rate of variants of the Coarse Mesh Finite Difference (CMFD) method for neutron transport acceleration are studied in this paper by generalization of the method into three categories: artificially diffusive CMFD, flux relaxation, and higher-order spatial prolongation operators. A Fourier analysis of the methods demonstrates that artificial diffusion and flux relaxation are mathematically equivalent and arbitrarily scale the coarse mesh to fine mesh projection (CMP) vector. The high-order spatial prolongation method is shown to affect the shape of the CMP vector. As a result, any of the CMFD variants based on these three sets of modifications correspond to a specific CMP vector. The optimization process is performed for the multidimensional vector, and the minimum spectral radius among all possible CMP vectors is shown to be the theoretical lower bound for the CMFD convergence rate. The spectral radius associated with the CMFD convergence rate lower bound is found to be slightly smaller (less than 0.04) than optimally diffusive CMFD (odCMFD), and the difference between odCMFD to the CMFD lower bound is much smaller than the difference between both standard CMFD and partial current–based CMFD to the CMFD lower bound. In addition, the odCMFD method has a distinct advantage in ease of implementation and minimal overhead. Conversely, the implementation necessary to achieve the CMFD lower bound would be very complicated, especially for two- and three-dimensional problems.

Improved Accuracy in the 2-D/1-D Method with Anisotropic Transverse Leakage and Cross-Section Homogenization

Abstract The Two-Dimensional (2-D)/One-Dimensional (1-D) method allows pin-resolved computational transport solutions for large, full-core light water reactor simulations at relatively low computational cost compared to a true three-dimensional (3-D) transport method. The 2-D/1-D method constructs an approximation to the 3-D transport equation with (1) a 2-D transport equation in the radial variables and , discretized on a fine radial spatial grid, and (2) a 1-D transport (or approximate PN) equation in the axial variable , discretized on a radially coarse spatial grid. The 2-D and 1-D equations are coupled through transverse leakage (TL) terms. In this paper, a new 2-D/1-D P3 method with anisotropic transverse leakages and anisotropic homogenized 1-D cross sections (XSs) is proposed to improve the accuracy of conventional 2-D/1-D with pin homogenization. It is shown that only the polar component of the anisotropic homogenized XS has a significant effect on the solution; the azimuthal component is negligible. However, the polar and azimuthal components of the leakage terms are both important. The new method is implemented in the 2-D/1-D code Michigan PArallel Characteristics Transport (MPACT). The method in this paper is shown to achieve nearly 3-D transport accuracy with sufficient refinement in space and angle. The improvement of this new method compared to the previous 2-D/1-D method in MPACT is most notable in problems with strong axial leakage and sharp axial discontinuities, such as control rod tips or part-length rods. The method is computationally more expensive than the existing 2-D/1-D method with isotropic TL and XSs, but this additional cost may be justified when the axial flux shape does not vary smoothly due to axial heterogeneity and needs to be resolved well.

Fourier analysis of iteration schemes for k-eigenvalue transport problems with flux-dependent cross sections

Abstract A central problem in nuclear reactor analysis is calculating solutions of steady-state k -eigenvalue problems with thermal hydraulic feedback. In this paper we propose and utilize a model problem that permits the theoretical analysis of iterative schemes for solving such problems. To begin, we discuss a model problem (with nonlinear cross section feedback) and its justification. We proceed with a Fourier analysis for source iteration schemes applied to the model problem. Then we analyze commonly-used iteration schemes involving non-linear diffusion acceleration and feedback. For each scheme we show (1) that they are conditionally stable, (2) the conditions that lead to instability, and (3) that traditional relaxation approaches can improve stability. Lastly, we propose a new iteration scheme that theory predicts is an improvement upon the existing methods.

Coupled Thermal-Hydraulic/Neutronics/Crud Framework in Prediction of Crud-Induced Power Shift Phenomenon

A thermal-hydraulics (TH)/neutronics/crud multiphysics coupling framework to simulate the crud deposits’ impact on crud-induced power shift (CIPS) phenomenon is proposed in this paper. The coupling among three essential physics (i.e., TH, crud, and neutronics) was implemented by coupling the computational fluid dynamics software STAR-CCM+, a newly developed crud module, and the neutronics code DeCART. A typical 3 × 3 pressurized water reactor fuel pin problem was analyzed with this framework and simulation results are presented. Time-dependent results are provided for a 12-month simulation. Simulation results provide the history of crud deposits inventory and their distributions on fuel rods, boron hideout amount inside crud deposits, and power shape changing over time. The obtained results clearly showed the power shape suppression in regions where crud deposits exist, a clear indication of CIPS phenomenon.