Pressure Vessel Fluence 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).

Validation of 3D discrete ordinate transport code with the practical engineering shielding calculation benchmark problems

This paper introduces extended validation works on JSNT-S code based on two practical engineering shielding calculation problems, the PWR Pressure Vessel Fluence Calculation Benchmark (PWR benchmark) and H. B. Robinson Unit 2 Pressure Vessel Benchmark (HBR-2 benchmark). The benchmarks put forward new challenges to the JSNT-S code, including the complexity of neutron source calculation, strong attenuation of the flux in the shielding material and modeling of complex shield structure geometry. SourceTrans code is developed to convert core pin-by-pin power distribution into neutron source, visual modeling code JLAMT is used to build 3Dfinemodels. Neutronic parameters provided in the benchmark report are validated, including the 47 group neutron flux spectrum, E > 1 MeV flux, E > 0.1 MeV flux, rates of displacement per atom (DPA), activation reaction rate and so on. The results show that JSNT-S code has good accuracy in simulating the practical engineering shielding calculation, and extend the reference solutions for benchmark problems.

EFFECT OF FISSION SOURCE SPECTRUM ON MONTE CARLO CALCULATION OF EX-CORE QUANTITIES

The Consortium for Advanced Simulation of Light Water Reactors (CASL) Virtual Environment for Reactor Applications (VERA) offers unique capabilities to combine highfidelity in-core radiation transport with temperature feedback using MPACT and CTF with a follow-on fixed source transport calculation using the Shift Monte Carlo code to calculate ex-core quantities of interest. In these coupled calculations, MPACT provides a fission source to Shift for the follow-on radiation transport calculation. In past VERA releases, MPACT passed a spatially dependent source without the energy distribution to Shift. Shift then assumed a235U Watt spectrum to sample the neutron source energies. There were concerns that, in cases with burned or mixed oxide (MOX) fuel near the periphery of the core, the assumption of a235U Watt spectrum for the source neutron energies would not be accurate for studying ex-core quantities of interest, such as pressure vessel fluence or detector response. Therefore, two additional options were implemented in VERA for Shift to sample neutron source energies: (1) a nuclide-dependent Watt spectra for235U,238U,239Pu, and241Pu, and (2) to use the standard 51-energy group MPACT spectrum. Results show that the 51-group MPACT spectrum is not suitable for ex-core calculations because the groups have been fine-tuned for in-core calculations. Differences in relative detector response due to235U and nuclide-dependent Watt spectra sampling schemes were negligible; however, the use of nuclide-dependent Watt spectra for vessel fluence calculations was found to be important for fuel cycles with burned and fresh fuel.

Methodology of Fuel Burn Up Fitting in VVER-1000 Reactor Core by Using New Ex-Vessel Neutron Dosimetry and In-Core Measurements and its Application for Routine Reactor Pressure Vessel Fluence Calculations

Paper describes the new approach of fitting axial fuel burn-up patterns in peripheral fuel assemblies of VVER-1000 type reactors, on the base of ex-core neutron leakage measurements, neutron-physical calculations and in-core SPND measured data. The developed approach uses results of new ex-vessel measurements on different power units through different reactor cycles and their uncertainties to clear the influence of a fitted fuel burn-up profile to the RPV neutron fluence calculations. The new methodology may be recommended to be included in the routine fluence calculations used in RPV lifetime management and may be taken into account during VVER-1000 core burn-up pattern correction.

Pressure Vessel Fluence Calculations for the Hungarian VVER-440 Units for the Power Uprate and the Llifetime Extension

A major project was launched at Paks NPP, Hungary, to investigate the possibility of lifetime extension up to 60 years. At the same time, new fuel types with higher enrichment and containing pins with gadolinium have been introduced. Due to these plans, the radiation load of the pressure vessel was evaluated up to 60 years irradiation, taking into account the past and planned future cycles. The computational procedure, elaborated and validated earlier for the fast flux calculation in the pressure vessel was modified for the new fuel types. The neutron source at the core boundaries was taken from core design calculations and the neutron transport from the source to and through the pressure vessel was followed by Monte Carlo calculations. A number of calculations were performed to adequately follow the change of the neutron source. The paper details this procedure, the used Monte Carlo model, the influence of the different reloading schemes on the radiation load and the calculated results.

Development and Testing of the VITAMIN-B7/BUGLE-B7 Coupled Neutron-Gamma Multigroup Cross-Section Libraries

Abstract The U.S. Nuclear Regulatory Commission’s Regulatory Guide 1.190 states that calculational methods used to estimate reactor pressure vessel (RPV) fluence should use the latest version of the evaluated nuclear data file (ENDF). The VITAMIN-B6 fine-group library and BUGLE-96 broad-group library, which are widely used for RPV fluence calculations, were generated using ENDF/B-VI.3 data, which was the most current data when Regulatory Guide 1.190 was issued. We have developed new fine-group (VITAMIN-B7) and broad-group (BUGLE-B7) libraries based on ENDF/B-VII.0. These new libraries, which were processed using the AMPX code system, maintain the same group structures as the VITAMIN-B6 and BUGLE-96 libraries. Verification and validation of the new libraries were accomplished using diagnostic checks in AMPX, “unit tests” for each element in VITAMIN-B7, and a diverse set of benchmark experiments including critical evaluations for fast and thermal systems, a set of experimental benchmarks that are used for SCALE regression tests, and three RPV fluence benchmarks. The benchmark evaluation results demonstrate that VITAMIN-B7 and BUGLE-B7 are appropriate for use in RPV fluence calculations and meet the calculational uncertainty criterion in Regulatory Guide 1.190.

Application of Ex-vessel Neutron Dosimetry Combined with In-core Measurements for Correction of Neutron Source Used for Reactor Pressure Vessel Fluence Calculations

Abstract This paper deals with calculated and semi-analytical evaluations of VVER-1000 reactor core neutron source distributions and their influence on measurements and calculations of the integral through-vessel neutron leakage. Neutron activation measurements analyzed in the paper were carried out in an ex-vessel air cavity at different nuclear power plant units with VVER-1000 during different fuel cycles. The time-integrated neutron source distributions used for DORT calculations were prepared via two different approaches based on (a) calculated fuel burnup (standard routine procedure) and (b) in-core measurements by means of self-powered detectors (SPDs) and thermocouples (TCs) (new approach). Considering that fuel burnup distributions in operating VVER may be evaluated now by the use of analytical methods (calculations) only, it is necessary to develop new approaches for the testing and correction of calculated evaluations of a neutron source. The results presented in this paper allow one to consider the reverse task of the alternative estimation of fuel burnup distributions. The proposed approach is based on the adjustment (fitting) of time-integrated neutron source distributions, and thus fuel burnup patterns, in some part of the reactor core, taking into account neutron leakage measurements, neutron-physical calculations, and in-core SPD and TC measurement data.

Weld Material Investigations of a WWER-440 Reactor Pressure Vessel: Results From the First Trepan Taken From the Former Greifswald NPP

Between 1973 and 1990 four units of the Russian nuclear power plants type WWER-440/230 were operated in Greifswald (former East Germany). Material probes from the pressure vessels were gained in the frame of the ongoing decommissioning procedure. The investigations of this material started with material from the circumferential core weld of unit 1. First, this paper presents results of the reactor pressure vessel (RPV) fluence calculations depending on different loading schemes and on the axial weld position based on the Monte Carlo code TRAMO. The results show that the use of the dummy assemblies reduces the flux by a factor of 2–5 depending on the azimuthal position. The circumferential core weld (SN0.1.4) received a fluence of 2.4×1019 neutrons/cm2 at the inner surface; it decreases to 0.8×1019 neutrons/cm2 at the outer surface. The material investigations were done using a trepan from the circumferential core weld. The reference temperature T0 was calculated with the measured fracture toughness values, KJc, at brittle failure of the specimen. The KJc values show a remarkable scatter. The highest T0 was about 50°C at a distance of 22 mm from the inner surface of the weld. The Charpy transition temperature TT41J estimated with results of subsized specimens after the recovery annealing was confirmed by the testing of standard Charpy V-notch specimens. The VERLIFE procedure prepared for the integrity assessment of WWER RPV was applied on the measured results. The VERLIFE lower bound curve indexed with the Structural Integrity Assessment Procedures for European Industry (SINTAP) reference temperature, RTT0SINTAP, envelops the KJc values. Therefore for a conservative integrity assessment the fracture toughness curve indexed with a RT representing the brittle fraction of a data set of measured KJc values has to be applied.

A New Methodology for Adjustment of Iron Scattering Cross Sections Using Time-of-Flight Spectroscopy

Abstract Monte Carlo analysis of a time-of-flight experiment was performed to investigate the iron scattering cross section. Experimental data were utilized to build a Monte Carlo source for simulation of a time-of-flight (ToF) experiment with a spherical iron shell, different source spectra, and different angular beam source alignments. For this study, two pointwise cross section libraries, ENDF/B-VI and JEFF 3.0 are examined. Comparison of calculation and experimental results indicates differences that are larger than experimental and calculation errors. To reduce the observed discrepancy, pointwise data in the ENDF/B-VI iron scattering cross section file were adjusted at a few energy intervals using a utility code developed for this purpose. Adjusted cross sections resulted in closer agreement of calculated results with the experimental Time-of-Flight data. Multigroup cross sections were generated with the adjusted cross sections and results indicate pressure vessel fluence may be underestimated.

Effect of Transverse Neutron Leakage on the Attenuation of the Displacements per Atom in the Reactor Pressure Vessel

The changes in the energy dependence of the neutron removal cross section at the vessel inner wall water/steel interface produce a substantial shift in the neutron spectrum as the fluence propagates into the pressure vessel. To account for this spectral shift, Regulatory Guide 1.99, Revision 2 requires that the fluence used in determining the reference temperature for nil-ductility transition RTNDT be extrapolated from the pressure vessel inner surface using the displacements per atom (dpa).The strong azimuthal and axial variation of the fluence at the vessel inner wall results in a substantial redistribution of the fluence as it propagates through the vessel due to transverse neutron leakage (i.e., perpendicular to the radial direction through the vessel). This transverse leakage tends to increase the dpa radial attenuation in regions of high fluence and reduce the attenuation in regions of low fluence.A series of pressure vessel fluence calculations has been carried out to determine the effect of (a) the transverse neutron leakage and (b) the plant-specific reactor design configuration on the radial attenuation of the dpa through the vessel. The calculations were performed for four operating pressurized water reactors and were carried out using the methods described in U.S. Nuclear Regulatory Commission Regulatory Guide 1.190. The calculations were performed with the DORT discrete ordinates transport code using ENDF/B-VI neutron transport and dpa cross sections.The transverse leakage is found to introduce a substantial variation of the dpa attenuation rate over the inner surface of the vessel. In the belt-line region opposite the core, the transverse leakage results in an ~6 to 14% azimuthal variation and an ~3 to 11% axial variation in the dpa at a 15-cm depth into the vessel, depending on the plant configuration.In order to simplify the determination of ΔRTNDT in probabilistic fracture mechanics analyses, conservative belt-line and reflector region dpa attenuation rates have been determined. Plant-specific analytic expressions for the radial dependence of the dpa through the vessel have also been determined.

Statistical Analysis of Reactor Pressure Vessel Fluence Calculation Benchmark Data Using Multiple Regression Techniques

The calculated >1-MeV pressure vessel fluence is used to determine the fracture toughness and integrity of the reactor pressure vessel. It is therefore of the utmost importance to ensure that the fluence prediction is accurate and unbiased. In practice, this assurance is provided by comparing the predictions of the calculational methodology with an extensive set of accurate benchmarks. A benchmarking database is used to provide an estimate of the overall average measurement-to-calculation (M/C) bias in the calculations (<M/C>). This average <M/C> is used as an ad-hoc multiplicative adjustment to the calculations to correct for the observed calculational bias. However, this average only provides a well-defined and valid adjustment of the fluence if the M/C data are homogeneous; i.e., the data are statistically independent and there is no correlation between subsets of M/C data.Typically, the identification of correlations between the errors in the database M/C values is difficult because the correlation is of the same magnitude as the random errors in the M/C data and varies substantially over the database. In this paper, an evaluation of a reactor dosimetry benchmark database is performed to determine the statistical validity of the <M/C> adjustment to the calculated pressure vessel fluence. Physical mechanisms that could potentially introduce a correlation between the subsets of M/C ratios are identified and included in a multiple regression analysis of the M/C data. Rigorous statistical criteria are used to evaluate the homogeneity of the M/C data and determine the validity of the <M/C> adjustment.For the database evaluated, the M/C data are found to be strongly correlated with dosimeter response threshold energy and dosimeter location (e.g., cavity versus in-vessel). It is shown that because of the inhomogeneity in the M/C data, for this database, the benchmark data do not provide a valid basis for adjusting the pressure vessel fluence.The statistical criteria and methods employed in this analysis are generic and may be applied in benchmarking applications where the M/C comparisons are used to determine an adjustment of the calculations.

Fast Tree Multigrid Transport Application for the Simplified P3 Approximation

Calculation of neutron flux in three-dimensions is a complex problem. A novel approach for solving complicated neutron transport problems is presented, based on the tree multigrid technique and the Simplified P3 (SP3) approximation. Discretization of the second-order elliptic SP3 equations is performed for a regular three-dimensional octree grid by using an integrated scheme. The octree grid is generated directly from STL files, which can be exported from practically all computer-aided design-systems. Marshak-like boundary conditions are utilized. Iterative algorithms are constructed for SP3 approximation with simple coarse-to-fine prolongation and fine-to-coarse restriction operations of the tree multigrid technique. Numerical results are presented for a simple cylindrical homogeneous one-group test case and for a simplistic two-group pressurized water reactor pressure vessel fluence calculation benchmark. In the former homogeneous test case, a very good agreement with 1.6% maximal deviation compared with DORT results was obtained. In the latter test case, however, notable discrepancies were observed. These comparisons show that the tree multigrid technique is capable of solving three-dimensional neutron transport problems with a very low computational cost, but that the SP3 approximation itself is not satisfactory for all problems. However, the tree multigrid technique is a very promising new method for neutron transport.

Uniform Gauss-Weight Quadratures for Discrete Ordinate Transport Calculations

Recently, a uniform equal-weight quadrature set, UEn, and a uniform Gauss-weight quadrature set, UGn, have been derived. These quadratures have the advantage over the standard level-symmetric LQn quadrature sets in that the weights are positive for all orders,and the transport solution may be systematically converged by increasing the order of the quadrature set. As the order of the quadrature is increased,the points approach a uniform continuous distribution on the unit sphere,and the quadrature is invariant with respect to spatial rotations. The numerical integrals converge for continuous functions as the order of the quadrature is increased.The numerical characteristics of the UEn quadrature set have been investigated previously. In this paper, numerical calculations are performed to evaluate the application of the UGn quadrature set in typical transport analyses. A series of DORT transport calculations of the >1-MeV neutron flux have been performed for a set of pressure-vessel fluence benchmark problems. These calculations employed the UGn (n = 8, 12, 16, 24, and 32) quadratures and indicate that the UGn solutions have converged to within ~0.25%. The converged UGn solutions are found to be comparable to the UEn results and are more accurate than the level-symmetric S16 predictions.

A new uncertainty arising in reactor pressure vessel fluence calculation

To identify and estimate a discrepancy of the reactor pressure vessel (RPV) fast neutron fluence between heterogeneous and homogeneous assembly models, Kori Unit 1 cycle 1 core was modeled on three-dimensional representations by MCNP4A. While all fuel rods were represented exactly in the heterogeneous model, the assemblies of the homogeneous model consisted of uniform compositions which were homogenized by volume fractions of components i.e. fuel, cladding, and water. In the conventional RPV fluence calculations of the deterministic methods, the homogenized assemblies have been used to model on the reactor core region. Because an uncertainty associated with the assembly modeling has not been revealed, it was identified and estimated by full-scope Monte Carlo simulations in this study. The MCNP version 4A was consistenly used in all procedures such calculations as criticality, source terms, and RPV fluence. The heterogeneous model converges to a k value of 1.00039±0.00084 and the relative assembly power distributions were nearly the same as that of the Kori Unit 1 FSAR. In the MCNP criticality calculation, pin-by-pin source terms were also calculated to use in RPV fluence calculations. Each calculation of the heterogeneous and the homogeneous models were performed by the MCNP. The results showed that the RPV fast neutron fluence of the homogeneous model were higher than that of the heterogeneous model. A new uncertainty associated with the assembly modeling was found to be 10∼20%, which is too high to be ignored. It is concluded that the homogeneous model of the assembly region should be one cause of the uncertainty in the RPV fluence calculations.

Neutron Fluence at the Pressure Vessel of a Pressurized Water Reactor Determined by the MCNP Code

Pressure vessel fluence and reaction rates for dosimetry foils in the cavity surrounding the pressure vessel of a pressurized water reactor were determined with a Monte Carlo calculation using the ...

Transport Analysis of Several Cross-Section Libraries Used for Reactor Pressure Vessel Fluence Calculations

Several neutron cross-section libraries used for fluence calculations at the reactor pressure vessel (RPV) based on one-dimensional S[sub N] transport calculations are analyzed. It is demonstrated the BUGLE-80, SAILOR, and ELXSIR libraries yield similar results, while the CASK library predicts significantly different results through and beyond the RPV. The use of the revised ENDF/B-V iron cross sections yields a significant increase in the neutron fluxes beyond the iron-containing regions. This result has direct impact on the reactor cavity dosimetry that is being considered for the RPV fluence estimation.

Transport calculations of neutron transmission through steel using ENDF/B-V, revised ENDF/B-V and ENDF/B-VI iron evaluations

The ENDF/B-VI evaluated nuclear data file has been recently released by the U.S. National Nuclear Data Center during 1990. Among the most eagerly awaited new cross-section evaluations in this data collection are those for the natural iron isotopes, due to their importance in nuclear systems analysis and because the previous ENDF/B data (version V, which was released in 1979) are known to underestimate the transmission of fast neutrons through steel structures such as reactor pressure vessels and radiation shielding. In this paper, a comparison is made of results obtained from neutron transport calculations performed with these two ENDF/B versions (V and VI) of iron data as well as an intermediate, revised version V evaluation that was proposed in 1986. Several different response parameters that are sensitive to high-energy neutrons are examined, for a variety of geometrical configurations and source spectra. It is found that the two newer iron evaluations substantially increase the transmission of high-energy neutrons through steel components with an incident fission spectrum source. Preliminary estimates indicate that the version VI iron evaluation will considerably improve the agreement between calculations and experimental dosimeter measurements used in light water reactor pressure vessel fluence analysis. The calculated leakage spectrum of D-T fusion neutrons from an iron sphere is also improved for energies above 4 MeV, but large discrepancies with the measured spectrum are still observed at lower energies.

Comments on “Application of Neutron Transport Green’s Functions to the Calculation of Pressure Vessel Fluence”

Comments on “Application of Neutron Transport Green’s Functions to the Calculation of Pressure Vessel Fluence”

Application of Neutron Transport Green's Functions to the Calculation of Pressure Vessel Fluence

A simple and accurate analytic method for calculating pressure vessel neutron damage >1-MeV fluence has been derived. The method employs asymptotic expressions for the one-speed neutron transport Green's function together with an effective removal cross section, to propagate the neutron source from the core out to the pressure vessel. The spatial integration over the core neutro source is performed using a multipole expansion of the transport Green's function. The analytic method reproduces detailed (DOT) numerical calculations in both (r, theta) and (r, z) geometries to within less than or equal to5%, and similar accuracy is expected in three dimensions.