35 research outputs found
Introduction to neutron transport
No full textIntitulé de la formation : Master Nuclear Energy, option Nuclear Reactor Physics and EngineeringMaste
Introduction to neutron transport
No full textIntitulé de la formation : Master Nuclear Energy, option Nuclear Reactor Physics and EngineeringMaste
Transport benchmarks for one-dimensional binary markovian mixtures revisited
No full textThe classic benchmarks for transport through a binary markovian mixure are revisited to look at the probability distribution function of the chosen “results”: reflection, transmission and scalar flux. We argue that knowledge of the ensemble averaged results is not sufficient for reliable predictions: a measure of the dispersion must also be obtained. An algorithm to estimate this dispersion is tested
Neutron transport in stochastic geometries. Benchmark calculations and study of a melted reactor core
No full textLAUREA MAGISTRALENegli ultimi anni è andato crescendo l'interesse nella risoluzione dell'equazione del trasporto in mezzi stocastici. In particolare, vengono studiate le miscele binarie stocastiche, utilizzabili in molti campi (diffusione dei contaminanti radioattivi in mezzi geologici, trasporto in mezzi turbolenti per il confinamento della fusione inerziale, attraversamento di schermi di cemento da parte di neutroni e di raggi gamma,..). Le geometrie che trattiamo in questo lavoro sono supposte essere markoviane, cosa che non rispecchia la realtà della maggior parte dei casi che queste geometrie cercano di simulare, ma risulta essere un'approssimazione necessaria. Abbiamo preso in considerazione un problema di trasporto per cui si avevano già dei risultati di riferimento (ottenuti da una geometria planare composta da strati alternati di due materiali). La nostra geometria è invece composta da poligoni creati in modo casuale su un piano ed è markoviana in due dimensioni, cosa che la rende più affine e rappresentativa delle reali geometrie stocastiche. Lo scopo dei nostri calcoli di riferimento è quello di confrontare e analizzare i risultati precedentemente ottenuti e di testare la validità dei modelli del problema che sono stati elaborati. La realizzazione della geometria markoviana è basata sul processo descritto da Switzer nel 1964 che permette di creare una geometria planare con proprietà markoviane. Per ognuna delle molte realizzazioni geometriche effettuate, abbiamo risolto il problema di trasporto neutronico con il codice Monte Carlo creato al CEA, TRIPOLI-4. Abbiamo poi mediato i risultati e costruito gli istogrammi per avere informazioni anche sulle distribuzioni delle quantità cercate.Nella seconda parte della tesi, abbiamo utilizzato la stessa procedura di realizzazione di geometrie markoviane e di risoluzione dell'equazione del trasporto per simulare un nocciolo fuso di un PWR. Anche in questo caso, non conosciamo le distribuzioni dei materiali che compongono il core, ma solo le loro proprietà. Abbiamo analizzato tre diversi casi, ognuno caratterizzato da un certo livello di mescolanza degli elementi del nocciolo e abbiamo cercato il valore del k_eff, per vedere come varia e come si distribuisce quando i materiali si mescolano in modo casuale gli uni con gli altri.The interest in resolving the equation of transport in stochastic media has continued to increase these last years. Binary stochastic mixtures are particularly studied because of their several applications (diffusion of radioactive contaminants in geological media, transport in turbolent media for the inertial confinement fusion, crossing of neutrons or gamma rays throughout concrete shields, ...). The geometries we deal with in this present thesis are assumed to be Markovian, which is never the case in usual environments, but which is a necessary approximation. We consider a two-suite neutron transport problem for which other benchmark results (based on a stochastic geometry composed by a labeled plane filled with two alternating materials) were already performed. The geometry we use is composed by random polygons built in a plane and it is Markovian in two dimensions, thus it better represents a real stochastic geometry. The goal of our benchmark calculations is to compare and analyze the previous obtained results and to test the validity of different elaborated models of the problem. The creation of the Markovian planar geometry is done in accordance with the process described by Switzer in 1964, which allows to construct a two-dimensional geometry with Markovian properties. For each one of the several geometry realizations, we solve the neutron transport problem with the Monte Carlo code TRIPOLI-4, developed at CEA. Then, we average the results and we build histograms to see also the distributions. In the second part of the thesis, we use the same procedure of Markovian geometry creation and stochastic resolution of transport equation to simulate a melted core of a PWR reactor. In this case, we do not know the distributions of the materials composing the core and we study three cases, each one characterized by a different material mixing level. We obtain and analyze the value of k_eff, to see how it varies and distributes depending on the way the materials actually mix after the fusion of the core
Functional Expansion Tallies using Fission Matrix Eigenmodes for Full Core Criticality Simulations
No full textInternational audienceA new Functional Expansion Tally based on the Fission Matrix eigenmodes has been defined, to compute the assembly-integrated power distribution of a large power reactor. This new tally, while giving the same results as the usual assembly-integrated one when all the modes are used (there are as many modes as assemblies in the reactor) can have better performances when a reduced number of modes is used to reconstruct the 2D power map. This is due to the fact that the modes with the larger statistical noise can be discarded, and what is lost in the bias introduced, is gained a few-fold in less statistical noise. This favorable behavior is more pronounced when a limited number of histories is simulated. The new FM-FET can be used effectively when several similar configurations of a same large reactor need to be computed. As an example we used boron variations and temperature variations on a large 2D PWR description, and the numerical results show that a gain of a factor 5-10 can be achieved on the Figure of Merit. Applications to neutronics/thermo-hydraulic coupling are planned where iterative convergence demands to compute several costly Monte-Carlo solutions which are all successively discarded but the last one
Comment converger un calcul Monte-Carlo critique ?
No full textCe document présente les recherches qui ont étés effectuées autour des problématiques de convergence des codes Monte-Carlo sur les grands systèmes. Une modélisation de la convergence en tant que processus auto-régressif sur les amplitudes des modes propres est proposé. Ce modèle permet de déduire des formules simples qui caractérisent les vitesses de convergence des calculs monte-carlo. Il est également possible de se servir de ce modèle pour expliquer de nombreuses choses telles que la sous-estimation de la variance, les vitesses de convergences observées ou encore le clustering
Competing Energy Lookup Algorithms in Monte Carlo Neutron Transport Calculations and Their Optimization on CPU and Intel MIC Architectures
No full textAbstractThe Monte Carlo method is a common and accurate way to model neutron transport with minimal approximations. However, such method is rather time-consuming due to its slow convergence rate. More specifically, the energy lookup process for cross sections can take up to 80% of overall computing time and therefore becomes an important performance hotspot. Several optimization solutions have been already proposed: unionized grid, hashing and fractional cascading methods. In this paper we revisit those algorithms for both CPU and manycore (Intel MIC) architectures and introduce vectorized versions. Tests are performed with the PATMOS Monte Carlo prototype, and algorithms are evaluated and compared in terms of time performance and memory usage. Results show that significant speedup can be achieved over the conventional binary search on both CPU and Intel MIC. Further optimization with vectorization instructions has been proved very efficient on Intel MIC architecture due to its 512-bit Vector Processing Unit (VPU); on CPU this improvement is limited by the smaller VPU width
A singular integral equation formulation and solution for transport in semi-infinite ducts
No full textMonte Carlo methods for reactor period calculations
No full textInternational audienceSeveral technological issues, such as reactor start-up analysis or kinetics studies of accelerator-driven systems, demand the asymptotic time behaviour of neutron transport to be assessed. Typically, this amounts to solving an eigenvalue equation associated to the Boltzmann operator, whose precise nature depends on whether delayed neutrons are taken into account. The inverse of the dominant eigenvalue can be physically interpreted as the asymptotic reactor period. In this work, we propose a Monte Carlo method for determining the dominant alpha eigenvalue of the Boltzmann operator and the associated fundamental mode for arbitrary geometries, materials, and boundary conditions. Extensive verification tests of the algorithm are performed, and Monte Carlo calculations are finally validated against reactor period measurements carried out at the ORPHEE facility of CEA/Saclay
Prompt alpha eigenvalue calculations with TRIPOLI-4
No full textMonte Carlo criticality analyses aimed at determining reactor parameters have been historically based on iterative algorithms whose outcome is the effective multiplication coefficient (keff), i.e., the fundamental eigenvalue of the transport equation. Less attention has been comparatively paid to Monte Carlo algorithms for the estimation of the so-called (prompt) α eigenvalues, which provide information about the (prompt) time evolution of the system. In recent years, this issue has witnessed a renewed interest, mostly due to increased computer power, allowing for reliable and stable search strategies for assessing the fundamental α eigenvalue. In this work, we revisit the theory behind α eigenvalues and propose a Monte Carlo iterative algorithm for the development version of Tripol
