The European Journal of Physics N (EPJ-N)
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Application of the EGPT methodology in the analysis of small-sample reactivity worth experiments
No full textIn the current paper, we investigate the application of the Equivalent Generalized Perturbation Theory (EGPT) to derive trends and associated covariances on the neutron capture cross section of one major fission product for both light water reactors and sodium-cooled fast reactors which is Rhodium-103. To do so, we have considered the ERMINE-V/ZONA1 & ZONA3 fast spectrum experiment and the MAESTRO thermal-spectrum experiment, where samples of these materials were oscillated in the MINERVE facility. In the paper, the theoretical formulation of EPGT is described and its derivation in the special case of the close loop oscillation technique where the reactivity worth is determined thanks to a power control system. A numerical benchmark is presented to assess the relevance of sensitivity coefficients provided by EGPT against direct perturbations where the microscopic cross sections are manually changed before calculating the adjoint and forward flux. The breakdown between direct and indirect contributions in the sensitivity analysis of the sample reactivity worth is presented and discussed, with the impact of using a calibration reference sample to normalize the measured reactivity worth. Finally, the assimilation of integral trends is done with the CONRAD code, using C/E comparisons between TRIPOLI4/JEFF3.2 calculations and experimental results and the sensitivity coefficients provided by the EGPT. Preliminary results of this study are showing that the JEFF3.2 evaluation of 103Rh gives satisfactory agreements in both thermal and fast spectrum experiments and that the combination of them can lead to a significant uncertainty reduction on the capture cross section, from ±5% to ±3% in the resolved resonance range (1 eV–10 keV) and from ±8% to ±5% in the unresolved resonance range (10 keV–1 MeV)
Resonance parameter covariance representation: file32 versus file33
No full textSensitivity and uncertainty analysis in error propagation studies are carried out based on nuclear data uncertainty information available in the basic nuclear data libraries such as ENDF, JEFF, JENDL and others. The uncertainty files (covariance matrices) are generally obtained from analysis of experimental data. In the resonance region, the computer code SAMMY is used for analyses of experimental data and generation of resonance parameters. In addition to resonance parameters evaluation, SAMMY also generates resonance parameter covariance matrices (RPCM). The intent of this paper is to discuss the use of the RPCM in contrast to the use of a cross section covariance matrix (CSCM) representation. For so, the resonance evaluation for 48Ti in the resonance range from 10−5 eV to 400 keV is used. The RPCM is translated into two distinct CSCM by using a coarser and a finer group structures. The results are presented and discussions of the feasibility of using these covariance representations are depicted
Template for estimating uncertainties of measured neutron-induced fission cross-sections
No full textA template for estimating uncertainties (unc.) of measured neutron-induced fission, (n,f), cross-sections (cs) is presented. This preliminary template not only lists all expected unc. sources but also supplies ranges of unc., estimates for correlations between unc. of the same and different experiments which can be used if the information is nonexistent. If this template is applied systematically when estimating experimental covariances for an evaluation, it may help in pinpointing missing unc. for individual datasets, identifying unreasonably low unc., and estimating correlations between different experimental datasets. Thus, a detailed unc. estimate – usually, a time-intensive procedure – can be undertaken more consistently and efficiently. As an example, it is shown that unc. and correlations of 239Pu(n,f) by Merla et al. [Proceedings of the Conference on Nuclear Data for Science and Technology 1991 Jülich (Springer-Verlag, Berlin, 1992) pp. 510–513], which are questionably low in the GMA database underlying the neutron cs standards evaluations, are distinctly larger at 14.7 MeV and more strongly correlated if this template is used for reestimating the associated covariances
An optimization methodology for heterogeneous minor actinides transmutation
No full textIn the case of a closed fuel cycle, minor actinides transmutation can lead to a strong reduction in spent fuel radiotoxicity and decay heat. In the heterogeneous approach, minor actinides are loaded in dedicated targets located at the core periphery so that long-lived minor actinides undergo fission and are turned in shorter-lived fission products. However, such targets require a specific design process due to high helium production in the fuel, high flux gradient at the core periphery and low power production. Additionally, the targets are generally manufactured with a high content in minor actinides in order to compensate for the low flux level at the core periphery. This leads to negative impacts on the fuel cycle in terms of neutron source and decay heat of the irradiated targets, which penalize their handling and reprocessing. In this paper, a simplified methodology for the design of targets is coupled with a method for the optimization of transmutation which takes into account both transmutation performances and fuel cycle impacts. The uncertainties and performances of this methodology are evaluated and shown to be sufficient to carry out scoping studies. An illustration is then made by considering the use of moderating material in the targets, which has a positive impact on the minor actinides consumption but a negative impact both on fuel cycle constraints (higher decay heat and neutron) and on assembly design (higher helium production and lower fuel volume fraction). It is shown that the use of moderating material is an optimal solution of the transmutation problem with regards to consumption and fuel cycle impacts, even when taking geometrical design considerations into account
Efficient use of Monte Carlo: the fast correlation coefficient
No full textRandom sampling methods are used for nuclear data (ND) uncertainty propagation, often in combination with the use of Monte Carlo codes (e.g., MCNP). One example is the Total Monte Carlo (TMC) method. The standard way to visualize and interpret ND covariances is by the use of the Pearson correlation coefficient,
Covariance analysis for total neutron cross sections based on a microscopic optical model potential
No full textThe deterministic simple least square (LS) approach is employed in the covariance analysis of the total neutron cross section (n,tot) calculated by a microscopic optical potential, CTOM, which is based on a fundamental theory − Dirac Brueckner Hartree Fock. The sensitivity to the CTOM parameters is firstly systematically calculated for 77 stable nuclei in the range 12C–208Pb within neutron energy 5–200 MeV. Then, an equivalent covariance of experimental data (EVexp) is constructed to describe the experimental data uncertainties and the systematic difference between experimental data and CTOM calculation. The variance and covariance of EVexp matrix are both evaluated via the Gaussian analysis to the ratios of measured (n,tot) cross sections and the CTOM calculations. In addition, a technique named “selection of effective points (SEP)” is suggested additionally to reduce the influence of the Peelle's Pertinent Puzzle problem in this work
Cauchy’s theorem and generalization
No full textIt has already been established that the mean length travelled by a neutral particle in a body containing a diffusing but not absorbing material is independant of its cross section, and consequently equal to the mean chord of the body. An elegant demonstration of this curious feature is presented and analysed thanks to Monte-Carlo simulations
Nuclear data correlation between different isotopes via integral information
No full textThis paper presents a Bayesian approach based on integral experiments to create correlations between different isotopes which do not appear with differential data. A simple Bayesian set of equations is presented with random nuclear data, similarly to the usual methods applied with differential data. As a consequence, updated nuclear data (cross sections,
ν‾
, fission neutron spectra and covariance matrices) are obtained, leading to better integral results. An example for 235U and 238U is proposed taking into account the Bigten criticality benchmark
A multi-physics analysis for the actuation of the SSS in opal reactor
No full textOPAL is a 20 MWth multi-purpose open-pool type Research Reactor located at Lucas Heights, Australia. It was designed, built and commissioned by INVAP between 2000 and 2006 and it has been operated by the Australia Nuclear Science and Technology Organization (ANSTO) showing a very good overall performance. On November 2016, OPAL reached 10 years of continuous operation, becoming one of the most reliable and available in its kind worldwide, with an unbeaten record of being fully operational 307 days a year. One of the enhanced safety features present in this state-of-art reactor is the availability of an independent, diverse and redundant Second Shutdown System (SSS), which consists in the drainage of the heavy water reflector contained in the Reflector Vessel. As far as high quality experimental data is available from reactor commissioning and operation stages and even from early component design validation stages, several models both regarding neutronic and thermo-hydraulic approaches have been developed during recent years using advanced calculations tools and the novel capabilities to couple them. These advanced models were developed in order to assess the capability of such codes to simulate and predict complex behaviours and develop highly detail analysis. In this framework, INVAP developed a three-dimensional CFD model that represents the detailed hydraulic behaviour of the Second Shutdown System for an actuation scenario, where the heavy water drainage 3D temporal profiles inside the Reflector Vessel can be obtained. This model was validated, comparing the computational results with experimental measurements performed in a real-size physical model built by INVAP during early OPAL design engineering stages. Furthermore, detailed 3D Serpent Monte Carlo models are also available, which have been already validated with experimental data from reactor commissioning and operating cycles. In the present work the neutronic and thermohydraulic models, available for OPAL reactor, are coupled by means of a shared unstructured mesh geometry definition of relevant zones inside the Reflector Vessel. Several scenarios, both regarding coupled and uncoupled neutronic & thermohydraulic behavior, are presented and analyzed, showing the capabilities to develop and manage advanced modelling that allows to predict multi-physics variables observed when an in-depth performance analysis of a Research Reactor like OPAL is carried out
Bayesian optimization of generalized data
No full textDirect application of Bayes' theorem to generalized data yields a posterior probability distribution function (PDF) that is a product of a prior PDF of generalized data and a likelihood function, where generalized data consists of model parameters, measured data, and model defect data. The prior PDF of generalized data is defined by prior expectation values and a prior covariance matrix of generalized data that naturally includes covariance between any two components of generalized data. A set of constraints imposed on the posterior expectation values and covariances of generalized data via a given model is formally solved by the method of Lagrange multipliers. Posterior expectation values of the constraints and their covariance matrix are conventionally set to zero, leading to a likelihood function that is a Dirac delta function of the constraining equation. It is shown that setting constraints to values other than zero is analogous to introducing a model defect. Since posterior expectation values of any function of generalized data are integrals of that function over all generalized data weighted by the posterior PDF, all elements of generalized data may be viewed as nuisance parameters marginalized by this integration. One simple form of posterior PDF is obtained when the prior PDF and the likelihood function are normal PDFs. For linear models without a defect this PDF becomes equivalent to constrained least squares (CLS) method, that is, the χ2 minimization method