Pool Critical Assembly Research Articles

PCA Benchmark Analysis with ADVANTG3.0.1. and MCNP6.1.1b Codes

The Pool Critical Assembly Pressure Vessel (PCA) benchmark is a well known benchmark in the reactor shielding community which is described in the Shielding Integral Benchmark Archive and Database (SINBAD). It is based on the experiments performed at the PCA facility in the Oak Ridge National Laboratory (ORNL) and it can be used for the qualification of the pressure vessel fluence calculational methodology. The measured quantities to be compared against the calculated values are the equivalent fission fluxes at several experimental access tubes (A1 to A8) in front, behind, and inside the pressure-vessel wall simulator. This benchmark is particularly suitable to test the capabilities of the shielding calculational methodology and cross-section libraries to predict invessel flux gradients because only a few approximations are necessary in the overall analysis. This benchmark was analyzed using a modern hybrid stochastic-deterministic shielding methodology with ADVANTG3.0.1 and MCNP6.1.1b codes. ADVANTG3.0.1 is an automated tool for generating variance reduction (VR) parameters for Monte Carlo (MC) calculations with MCNP5v1.60 code (and higher versions). It is based on the multigroup, discrete ordinates solver Denovo, used for approximating the forward-adjoint transport fluxes to construct VR parameters for the final MC simulation. The VR parameters in form of the weight windows and the source biasing cards can be directly used with unmodified MCNP input. The underlining CADIS methodology in Denovo code was initially developed for biasing local MC results, such as point detector or a limited region detector. The FW-CADIS extension was developed for biasing MC results globally over a mesh tallies or multiple point/region detectors. Both CADIS and FW-CADIS are based on the concept of the neutron importance function, which is a solution of the adjoint Boltzmann transport equation. The equivalent fission fluxes calculated with MCNP are based on several highenergy threshold reactions from international dosimetry libraries IRDF-2002 and IRDFF-2014, distributed by the IAEA Nuclear Data Section. The obtained results show a good agreement with referenced PCA measurements. Visualization of the deterministic solution in 3D was done using the VisIt code from the Lawrence Livermore National Laboratory (LLNL).

Reactor pressure vessel damage (dpa/s) calculation and testing of 56Fe data libraries based on PCA benchmark model simulations using the SuperMC 3.4 code

Reactor Pressure Vessel (RPV) damage determination is important for reactor (power plant) safety and power economics, as its determination informs plant integrity and end-of-life extension. Irradiation damage determination is indirectly derived from the measurement/calculation of neutron fluence at or close to the pressure vessel system. The labyrinth procedure for experimentally determining the fluence by online operating plants makes theoretical (calculation) applications attractive. However, the calculation process must be validated via benchmark analysis, particularly according to the U.S Nuclear Regulatory Guide (Guide 1.190) for RPV dosimetry methods. One such related benchmark is the Pool Critical Assembly (PCA) of Oak Ridge. In this work, a detailed 3D model of the PCA facility and the calculated threshold reaction rate(s) have been achieved using the SuperMC code. Since iron (i.e., 56Fe) forms the major components of RPV, its evaluated data is key for benchmark calculations. Therefore, the calculation compares the 56Fe data from ENDF/BVII.1, ENDF/BVIII.0, and a modified 56Fe-data by CIELO group (post-ENDF/BVIII.0). The calculated threshold reaction rates were achieved within 5%–10% deviation. The deviations were also identified to be dependent on the selected detectors’ energy response spectrum. A detailed demonstration of displacement-per-atom rate (dpa/s) calculation is also presented, it showed contribution of about 5% and 95% for neutron energy <0.1 MeV and >0.1 MeV respectively.

Contributon-Based Mesh-Reduction Methodology for Hybrid Deterministic-Stochastic Particle Transport Simulations Using Block-Structured Grids

In neutral-particle transport shielding problems, variance-reduction methods are used in Monte Carlo (MC) simulations to bias the progression of tracked particles toward user-defined detectors or regions of interest. These biasing techniques allow for converged results in areas that would otherwise be poorly sampled due to low neutron or gamma fluxes relative to the fixed source. One widely used state-of-the-art methodology in shielding simulations is the Consistent Adjoint-Driven Importance Sampling (CADIS) method, which is a hybrid transport methodology that uses deterministic adjoint solutions to define weight window (WW) targets for particle splitting, rouletting, and source biasing during MC. However, for large problems, the WW data can require prohibitively large amounts of memory (tens to hundreds of gigabytes). This can make the simulation not feasible with the available computational resources, or it can restrict execution to a small fraction of nodes with large enough memory, thus significantly reducing the available resources and increasing the turnaround time needed to complete intended analyses.A novel methodology and data structure have been developed and implemented within the MONACO and MAVRIC sequences of the Scale 6.1 code package that greatly reduces memory requirements for storing WW maps by orders of magnitude. The data structure is accompanied with an algorithm that determines mesh reduction through coarsening and refinement using contributon response theory. Large memory savings are achieved by using separate block-structured grids for each energy group. The implementation of this methodology leads to a fractional increase in biased MC simulation time due to tracking particles through a more complex data structure storing the WW targets. For large shielding problems, enhanced parallelism enabled by memory reduction more than compensates for the decline in biased MC performance resulting in an effective speedup in solution time. Here, the improvements and drawbacks in the methodology are demonstrated on the relatively small but well-known Pool Critical Assembly shielding benchmark. The methodology showed a reduction in memory of from 163 to 194 times, with only a limited slowdown in biasing efficiency between 1% and 9%.

Evaluation of the Pool Critical Assembly Benchmark with Explicitly Modeled Geometry Using MCNP6

Despite being one of the most widely used benchmarks for qualifying light water reactor (LWR) radiation transport methods and data, no benchmark calculation of the Oak Ridge National Laboratory (ORNL) pool critical assembly (PCA) pressure vessel wall benchmark facility (PVWBF) using MCNP6 with explicitly modeled core geometry exists. As such, this paper provides results for such an analysis. First, a criticality calculation is used to construct the fixed source term. Next, ADVANTG-generated variance reduction parameters are used within the final MCNP6 fixed source calculations. These calculations provide unadjusted dosimetry results using three sets of dosimetry reaction cross sections of varying ages (those packaged with MCNP6, from the IRDF-2002 multigroup library, and from the ACE-formatted IRDFF v1.05 library). These results are then compared to two different sets of measured reaction rates. The comparison agrees in an overall sense within 2% and on a specific reaction and dosimetry location basis within 5%. Except for the neptunium dosimetry, the individual foil raw calculation-to-experiment comparisons usually agree within 10% but are typically greater than unity. Finally, in the course of developing these calculations, geometry that has previously not been completely specified is provided herein for the convenience of future analysts.

A Broad-Group Cross-Section Library Based on ENDF/B-VII.0 for Fast Neutron Dosimetry Using the CPXSD Methodology

Abstract A new ENDF/B-VII.0-based coupled 44-neutron, 20-gamma-ray-group cross-section library was developed to investigate the latest evaluated nuclear data file (ENDF) ,in comparison to ENDF/B-VI.3 used in BUGLE-96, as well as to generate an objective-specific library. The objectives selected for this work consisted of dosimetry calculations for in-vessel and ex-vessel reactor locations, iron atom displacement calculations for reactor internals and pressure vessel, and 58Ni(n,γ) calculation that is important for gas generation in the baffle plate. The new library was generated based on the contributon and point-wise cross-section-driven (CPXSD) methodology and was applied to one of the most widely used benchmarks, the Oak Ridge National Laboratory Pool Critical Assembly benchmark problem. In addition to the new library, BUGLE-96 and an ENDF/B-VII.0-based coupled 47-neutron, 20-gamma-ray-group cross-section library was generated and used with both SNLRML and IRDF dosimetry cross sections to compute reaction rates. All reaction rates computed by the multigroup libraries are within ± 20 % of measurement data and meet the U. S. Nuclear Regulatory Commission acceptance criterion for reactor vessel neutron exposure evaluations specified in Regulatory Guide 1.190.

Application of Quadruple Range Quadratures to Three-Dimensional Model Shielding Problems

A widely used numerical method for discretizing the direction variable in the transport equation is the discrete ordinates technique. Here, we test various discrete ordinates quadrature sets on two three-dimensional (3-D) (X-Y-Z) shielding problems: the doglegged void neutron model and the pool critical assembly model. Commonly used quadrature sets, including the standard level symmetric sets and double Gauss-Chebyshev sets, produce significant ray effects associated with material discontinuities in both models. Abu-Shumays designed the quadruple range (QR) sets specifically for these types of problems and showed that they perform well in two-dimensional X-Y geometry. Here, we show that compared to more commonly used quadrature sets, the 3-D QR sets substantially reduce ray effects associated with material discontinuities in 3-D X-Y-Z discrete ordinates calculations.

Direct Integration Method for Solving the Neutron Transport Equation in Three-Dimensional Geometry

A numerical method is presented for calculating neutron transport problems in three-dimensional (x,y,z) geometry on the basis of a method of direct integration of the integral transport equation. Several new techniques are introduced to the method to make it well adapted to practical neutron transport calculations in three-dimensional geometry. A technique for evaluating the scattering source based on an estimated spectral shape in each material region allows use of coarse energy mesh intervals without reducing calculational accuracy as compared with the calculation with fine meshes. A quadratic function approximation for the source spatial distribution in each spatial mesh interval is found to improve the mathematical error in direct integration of the source term over the spatial variable as compared with the linear- or exponential-function approximation used in the original method. In addition, Lagrange’s interpolation formula is applied instead of the linear interpolation used in the original method for more accurate estimation of both flux and source.Comparisons are made of the calculations with experiments for three neutron transport problems, the pool critical assembly experiment, the Winfrith iron benchmark experiment, and the annular duct neutron streaming experiment, and also with the three-dimensional Sn calculation to verify the validity of the present method for neutron transport calculations in (x,y,z) geometry.

Reactivity Effects of Large Voids in the Reflector of a Light-Water-Moderated and -Reflected Reactor

Reactivity effects of large voids in the reflector of the Pool Critical Assembly (PCA), an enricheduranium, light-water-moderated and -reflected, pooltype reactor were investigated experimentally and were the variations of reactivity of voids at the center of a core face, void position on core face, and separation distance between void and core face. Superposability of the reactivity effects of multiple voids was neutron flux distribution was measured. (W.D.M.)