Reactor Physics Calculations Research Articles

Adjoint-Based Sensitivity Analysis of Coupled Criticality Problems

Sensitivity analysis is a technique that is widely used in reactor physics calculations to efficiently obtain first-order changes in responses of interest due to variations of input parameters. This paper presents an extension of the well-known perturbation procedures for the critical eigenvalue and flux functionals. The extended method makes it possible to determine sensitivities in coupled criticality problems with mutual feedback between neutronics and one or more augmenting systems (e.g., thermal hydraulics or fission product poisoning). The technique uses appropriate neutronic and augmenting adjoint functions, which can be obtained by solving a system of coupled adjoint equations.Three different approaches are presented for considering the effects of perturbations in coupled criticality problems with feedback: The steady-state power level is allowed to adjust to maintain criticality with the perturbed parameters (power perturbation), a change is allowed in the critical eigenvalue while the flux is constrained (eigenvalue perturbation), or simultaneous perturbations are made to ensure criticality at the unperturbed power level (control parameter perturbation). In the case of power and eigenvalue perturbations, sensitivities can be obtained with or without power- and k-reset procedures, respectively, yielding identical results to control parameter perturbation.The paper presents the theoretical background, an application to a one-dimensional slab problem with thermal and fission product feedback, and a numerical procedure to obtain the necessary adjoint functions. The proposed technique relies on using the neutronics and augmenting codes separately as a preconditioner for Krylov methods employed to the coupled adjoint problem. This makes the development of new codes unnecessary and provides a means of large-scale implementation.

Monte Carlo Calculations Applied to NRU Reactor and Radiation Physics Analyses

The statistical MCNP (Monte Carlo N-Particle) code has been satisfactorily used for reactor and radiation physics calculations to support NRU operation and analysis. MCNP enables 3D modeling of the reactor and its components in great detail, the transport calculation of photons (in addition to neutrons), and the capability to model all locations in space, which are beyond the capabilities of the deterministic neutronics methods used for NRU. While the simple single-cell model is efficient for local analysis in any site of NRU, the complex full-reactor model is required for calculations of the core physics and beyond-the-core radiation. By supplementing, adjusting or benchmarking the results from the existing NRU codes, the MCNP calculations provide greater confidence that NRU remains within the licence envelope.

Developments in Sensitivity Methodologies and the Validation of Reactor Physics Calculations

The sensitivity methodologies have been a remarkable story when adopted in the reactor physics field. Sensitivity coefficients can be used for different objectives like uncertainty estimates, design optimization, determination of target accuracy requirements, adjustment of input parameters, and evaluations of the representativity of an experiment with respect to a reference design configuration. A review of the methods used is provided, and several examples illustrate the success of the methodology in reactor physics. A new application as the improvement of nuclear basic parameters using integral experiments is also described.

A verification exercise in multiphysics simulations for coupled reactor physics calculations

The modeling of nuclear reactors involves the solution of a multiphysics problem with various time and length scales. Mathematically, this requires solving a system of coupled, nonlinear, stiff, Partial Differential Equations (PDEs). This paper deals with the verification aspects associated with a multiphysics code, i.e., the substantiation that the mathematical description of the multiphysics equations are solved correctly (in time and space). Multiphysics applications have the added complexity that the solution field participates in various physics components, potentially yielding spatial and/or temporal coupling errors. We present a multiphysics framework that tightly couples the various physical models using the Jacobian-free Newton-Krylov technique (JFNK) and show that high-order convergence can be achieved in both space and time. Code verification results are provided.

Nondestructive burnup measurements by gamma-ray spectroscopy on spent fuel elements of the RP-10 research reactor

Gamma-ray spectroscopy is an important nondestructive method for the qualification of irradiated nuclear fuels. Regarding research reactors, the main parameter required in the scope of such qualification is the average burnup of spent fuel elements. This work describes the measurement, using nondestructive gamma-ray spectroscopy, of the average burnup attained by Material Testing Reactor (MTR) fuel elements irradiated in the RP-10 research reactor. Measurements were performed at the reactor storage pool area using 137Cs as the only burnup monitor, even for spent fuel elements with cooling times much shorter than two years. The experimental apparatus was previously calibrated in efficiency to obtain absolute average burnup values, which were compared against corresponding ones furnished by reactor physics calculations. The mean deviation between both values amounts to 6%.

Uncertainty evaluation of calculated and measured kinetics parameters of Tehran Research Reactor

Effective delayed neutron fraction β eff and neutron generation time Λ are important factors in reactor physics calculation and transient analysis. In the first stage of this research, these kinetics parameters have been calculated for two states of Tehran Research Reactor (TRR), i.e. cold (fuel, clad and coolant temperature 20 °C) and hot (fuel, clad and coolant temperature 65, 49 and 44 °C, respectively) states using MTR_PC computer code. The ratio of ( β eff ) i /( β eff ) core plays an important role in reactivity accident analysis codes. This parameter and its contribution to effective delayed neutron fraction from each nucleus have been calculated in cold and hot reactor states. Uncertainty of effective delayed neutron fraction is evaluated in terms of following four quantities; basic delayed neutron constants, delayed neutron spectra, energy dependence of delayed neutron yield ( ν d ) and fission cross-section of 235U and 238U. In the second stage, these parameters have been measured with an experimental method based on Inhour equation. The calculated and measured values are in good agreement. Relative Percent Errors (RPEs) are 2.8% for β eff and 5.7% for Λ in the cold state.

Calculation, measurement and sensitivity analysis of kinetic parameters of Tehran Research Reactor

Effective delayed neutron fraction β eff and neutron generation time Λ are important factors in reactor physics calculation and transient analysis. In the first stage of this research, these kinetic parameters have been calculated for two states of Tehran Research Reactor (TRR), i.e. cold (fuel, clad and coolant temperatures equal to 20 °C) and hot (fuel, clad and coolant temperatures of 65, 49 and 44 °C, respectively) states using MTR_PC code. In the second stage, these parameters have been measured with an experimental method based on Inhour equation. For the cold state, calculated β eff and Λ by MTR_PC code are 0.008315 and 30.190 μs, respectively. In the hot state, these parameters being 0.008303 and 33.828 μs, respectively. The measured β eff and Λ for the cold state (reactor power in the range of 100–200 W) being 0.008088 and 32.001 μs, respectively. The calculated and measured values are in good agreement. Relative percent errors are about 2.8% for β eff and 5.7% for Λ which are smaller than the other reported results. In the third stage of the research, variations of β eff and Λ vs. fuel enrichment are investigated in cold and hot states. Comparative analysis shows that both β eff and Λ increase as fuel enrichment decreases. However, the variation rate of β eff is not the same in the two conditions. β eff in the hot state is larger than that calculated in the cold state when fuel enrichment is more than 83.91%, while the situation is vice versa for the enrichments smaller than the aforementioned value. Calculated neutron generation time shows normal behavior for all different fuel enrichments. All variables involved in kinetic parameters calculations (i.e., neutron fission cross section, fuel enrichment, etc.) are investigated theoretically to evaluate the results of calculations in cold and hot states. Variations of β eff and Λ with fuel burnup are also studied.

TRIGA fuel burn-up calculations and its confirmation

The Cesium (Cs-137) isotopic concentration due to irradiation of TRIGA Fuel Elements FE(s) is calculated and measured at the Atominstitute (ATI) of Vienna University of Technology (VUT). The Cs-137 isotope, as proved burn-up indicator, was applied to determine the burn-up of the TRIGA Mark II research reactor FE. This article presents the calculations and measurements of the Cs-137 isotope and its relevant burn-up of six selected Spent Fuel Elements SPE(s). High-resolution gamma-ray spectroscopy based non-destructive method is employed to measure spent fuel parameters. By the employment of this method, the axial distribution of Cesium-137 for six SPE(s) is measured, resulting in the axial burn-up profiles. Knowing the exact irradiation history and material isotopic inventory of an irradiated FE, six SPE(s) are selected for on-site gamma scanning using a special shielded scanning device developed at the ATI. This unique fuel inspection unit allows to scan each millimeter of the FE. For this purpose, each selected FE was transferred to the fuel inspection unit using the standard fuel transfer cask. Each FE was scanned at a scale of 1 cm of its active length and the Cs-137 activity was determined as proved burn-up indicator. The measuring system consists of a high-purity germanium detector (HPGe) together with suitable fast electronics and on-line PC data acquisition module. The absolute activity of each centimeter of the FE was measured and compared with reactor physics calculations. The ORIGEN2, a one-group depletion and radioactive decay computer code, was applied to calculate the activity of the Cs-137 and the burn-up of selected SPE. The deviation between calculations and measurements was in range from 0.82% to 12.64%.

Development of MCBurn and its application in the analysis of SCWR physical characteristics

The MCBurn, a coupled code system linking the Monte Carlo N-particle transport code (MCNP) and Oak Ridge isotope generation and depletion code (ORIGEN), can resolve the basic calculation problems in reactor physical design and analysis, such as criticality, power distribution, nuclide burn up, and neutron fluence. It has been verified in the pressurized water reactor (PWR) pin model, fast reactor (FR) burn up model, and boiling water reactor (BWR) assemble model with benchmarked results. In supercritical water reactor (SCWR) physical calculations, the calculation conditions such as the geometry, the neutron spectrum, and the fuel materials, etc., are more complex than those in traditional reactors, which is a great challenge to reactor physics calculation code. However, the MCBurn code is a possible solution. In this paper, several update functions of the MCBurn in new neutron cross-section lib, code interface, and neutron flux distribution were described. The application of the MCBurn in SCWR were verified on a supercritical water reactor assemble. The calculation results show that the MCBurn is accurate and adaptable in the SCWR calculation.

Compact extended model for Doppler broadening of neutron absorption resonances

We present a simplified compact model for calculating Doppler broadening of neutron absorption resonances in an incoherent Debye solid. Our model extends the effective temperature gas model to cover the whole range of energies and temperatures, and reduces the information of the dynamical system to a minimum content compatible with a much better accuracy of the calculation. This model is thus capable of replacing the existing algorithm in standard codes for resonance cross-sections preparation aimed at neutron and reactor physics calculations. The model is applied to the 238U 6.671 eV effective broadened cross-section. We also show how this model can be used for thermometry in an improved fashion compared to the effective temperature gas model.

Computation of some transport theory expressions for a line source in an infinite half-space

In a previous paper, Williams [Williams, M.M.R., 2007. The transport and diffusion theory of a line source in an infinite half-space with internal reflection. Ann. Nucl. Energy 34, 910–921] has obtained transport theory closed form expressions for the particle density for a problem in which a filamentary source is placed within a half-space, perpendicular to the surface (this “line source” problem is closely related to the classical “searchlight” problem of radiative transfer). Some numerical results for limiting cases (surface, z → 0), where the expressions reduce to a single integral were also reported. In this paper, we report additional numerical results for arbitrary internal positions in the medium by evaluating the closed form expressions which have required efficient and accurate evaluations of the generalized H function and subsequent two fold integrations. We have verified the accuracy of the techniques and the results through comparisons with both the limiting case ( z → 0) reported in Williams [Williams, M.M.R., 2007. The transport and diffusion theory of a line source in an infinite half-space with internal reflection. Ann. Nucl. Energy 34, 910–921] and also independent results obtained by numerical solutions of the related integral equation via use of the singularity subtraction technique and quadratures. The present work should further aid in progress on related problems with Fresnel reflections and other complications, as well as to the validation of standard commercial reactor physics computer codes. For completeness, we should mention the recent book by Ganapol [Ganapol, B.D., 2008. Analytical benchmarks for nuclear engineering applications: case studies in transport theory, NEA, OECD] in which a number of three-dimensional transport problems are solved with special reference to acceleration techniques.

06/02390 On the accuracy of reactor physics calculations for square HPLWR fuel assemblies: Jatuff, F. et al. Annals of Nuclear Energy, 2006, 33, (2), 198–207.

06/02390 On the accuracy of reactor physics calculations for square HPLWR fuel assemblies: Jatuff, F. et al. Annals of Nuclear Energy, 2006, 33, (2), 198–207.

Sensitivity study on determining an efficient set of fuel assembly parameters in training data for designing of neural networks in hybrid genetic algorithms

Neural Networks (NNs) were applied as a tool for simulating several nuclear reactor physics parameters during core depletion calculations. The main objective was to develop NNs models capable of simulating useful reactor physics parameters to filter out the bad designs created in Genetic Algorithms (GAs) run without the need to perform reactor physics calculations for evaluation of individuals. Applying GAs to optimize both the nuclear reactor Loading Pattern (LP) and Burnable Poison (BP) designs for their respective performance characteristics creates many unwanted results along the way. New population individuals are normally analyzed with a reactor physics code to determine its fitness or applicability for future use. Significant time was required for each reactor physics code calculation and because most of the solution individuals created by GAs result in unusable designs, analyzing every solutions involves prohibitive computational times. Such long computational times can be greatly reduced by applying NNs to filter out most of the unwanted designs. A detailed description of the selection process of the NN architecture, training method, and adequate ranges of data are also presented. Finally, a hybrid GA algorithm is proposed in which two NNs are used to discard most of the worse LP and BP designs.

On the accuracy of reactor physics calculations for square HPLWR fuel assemblies

Although the supercritical-pressure or high-performance light water reactor (HPLWR) concept is largely based on the well-established technological experience available with conventional light water reactors, there is still no consensus on various key design features such as an optimal layout for the fuel assembly. This results mainly from the very large density variations of supercritical-pressure water in the core, which render it difficult to ensure reliable values for parameters such as power peaking factors and reactivity worths. The present paper describes studies carried out to compare deterministic and Monte Carlo codes for analysing a representative square HPLWR lattice with uniform 5%-enriched UO 2 fuel. The main purpose has been to assess the prediction accuracies achievable for integral parameters such as the multiplication factor, control absorber effectiveness, moderator/coolant density reactivity feedback and pin power distributions. The results show good agreement between the deterministic and stochastic calculations for the unperturbed lattice. However, for certain perturbed situations involving, for example, local coolant density changes in the assembly or control absorber insertion, the observed discrepancies are large enough to question the basic viability of the reactor physics design, e.g. with respect to the thermal performance.

Models for reactor physics calculations for HTR pebble bed modular reactors

For reactor physics calculations for modular pebble bed reactors program systems and nuclear data have to be used to get reliable results for important operational and safety related parameters. For cylindrical or annular core geometry such parameters can be calculated with the modular program system ZIRKUS and additionally with common reactor physics programs based on S N and Monte Carlo theory. The modules of the ZIRKUS system were developed by Framatome ANP GmbH and extensively used for design calculations for the 200 MW el HTR-MODUL and verified by means of experiments and operational data mainly from AVR. The models used in ZIRKUS will be described and discussed for typical design calculations for HTR pebble bed reactors.

00/03306 Reactor physics calculations and their experimental validation for conversion and upgrading of a typical swimming pool type research reactor

00/03306 Reactor physics calculations and their experimental validation for conversion and upgrading of a typical swimming pool type research reactor

Gamma-ray spectroscopy on irradiated MTR fuel elements

The availability of burnup data is an important requirement in any systematic approach to the enhancement of safety, economics and performance of a nuclear research reactor. This work presents the theory and experimental techniques applied to determine, by means of nondestructive gamma-ray spectroscopy, the burnup of Material Testing Reactor (MTR) fuel elements irradiated in the IEA-R1 research reactor. Burnup measurements, based on analysis of spectra that result from collimation and detection of gamma-rays emitted in the decay of radioactive fission products, were performed at the reactor pool area. The measuring system consists of a high-purity germanium (HPGe) detector together with suitable fast electronics and an on-line microcomputer data acquisition module. In order to achieve absolute burnup values, the detection set (collimator tube+HPGe detector) was previously calibrated in efficiency. The obtained burnup values are compared with ones provided by reactor physics calculations, for three kinds of MTR fuel elements with different cooling times, initial enrichment grades and total number of fuel plates. Both values show good agreement within the experimental error limits.

Reactor physics calculations and their experimental validation for conversion and upgrading of a typical swimming pool type research reactor

Detailed neutronic analysis of a typical swimming pool type research reactor, Pakistan Research Reactor-1 (PARR-1), was carried out for conversion of its core from 93% highly enriched uranium to 20% low enriched uranium fuel with power upgrading from 5 to 10 MW. Standard computer codes WIMS-D/4 and CITATION were employed to calculate core excess reactivity, power defect, reactivity effect of xenon and samarium, reactivity worth of fuel element, worth of control rods, shutdown margin, reactivity feedback coefficients, neutron flux and power peaking factors. A series of low and high power tests were performed on the newly converted core to determine its performance. A comparison between the calculated and measured results is presented in this article. The agreement is generally good.

Kainate and isoproterenol evoke synergistically glutamate release in the mouse striatum

The Cesium (Cs-137) isotopic concentration due to irradiation of TRIGA Fuel Elements FE(s) is calculated and measured at the Atominstitute (ATI) of Vienna University of Technology (VUT). The Cs-137 isotope, as proved burn-up indicator, was applied to determine the burn-up of the TRIGA Mark II research reactor FE. This article presents the calculations and measurements of the Cs-137 isotope and its relevant burn-up of six selected Spent Fuel Elements SPE(s). High-resolution gamma-ray spectroscopy based non-destructive method is employed to measure spent fuel parameters. By the employment of this method, the axial distribution of Cesium-137 for six SPE(s) is measured, resulting in the axial burn-up profiles. Knowing the exact irradiation history and material isotopic inventory of an irradiated FE, six SPE(s) are selected for on-site gamma scanning using a special shielded scanning device developed at the ATI. This unique fuel inspection unit allows to scan each millimeter of the FE. For this purpose, each selected FE was transferred to the fuel inspection unit using the standard fuel transfer cask. Each FE was scanned at a scale of 1 cm of its active length and the Cs-137 activity was determined as proved burn-up indicator. The measuring system consists of a high-purity germanium detector (HPGe) together with suitable fast electronics and on-line PC data acquisition module. The absolute activity of each centimeter of the FE was measured and compared with reactor physics calculations. The ORIGEN2, a one-group depletion and radioactive decay computer code, was applied to calculate the activity of the Cs-137 and the burn-up of selected SPE. The deviation between calculations and measurements was in range from 0.82% to 12.64%.

Design and Development of Fast Breeder Reactor Passive Reactivity Control Systems: LEM and LIM

To enhance the inherent safety of the fast breeder reactor (FBR), unique attempts are being made in reactivity control systems design to achieve maintenance-free and reliable performance at the Central Research Institute of the Electric Power Industry. The design involves the lithium expansion module (LEM) for inherent reactivity feedback and the lithium injection module (LIM) for inherent ultimate shutdown. Reactor physics calculation revealed the reactivity worth of LEM and LIM in a 60-MW(electric), metal-fueled FBR and a 1000-MW(electric) mixed-oxide-fueled FBR. The system dynamics analyses revealed that LEM and LIM are effective to avoid sodium boiling in unprotected transient overpower and unprotected loss-of-flow transients. Reliability, maintainability, and real-time monitoring for LEM and LIM are also discussed.