scholarly journals ANALYSIS OF TIME-EIGENVALUE AND EIGENFUNCTIONS IN THE CROCUS BENCHMARK

2021 ◽  
Vol 247 ◽  
pp. 04011
Author(s):  
Yasushi Nauchi ◽  
Alexis Jinaphanh ◽  
Andrea Zoia

Time-dependent neutron transport in non-critical state can be expressed by the natural mode equation. In order to estimate the dominant eigenvalue and eigenfunction of the natural mode, CEA had extended the α-k method and developed the generalized iterated fission probability method (G-IFP) in the TRIPOLI-4® code. CRIEPI has chosen to compute those quantities by a time-dependent neutron transport calculation, and has thus developed a time-dependent neutron transport technique based on k-power iteration (TDPI) in MCNP-5. In this work, we compare the two approaches by computing the dominant eigenvalue and the direct and adjoint eigenfunctions for the CROCUS benchmark. The model has previously been qualified for keffs and kinetic parameters by TRIPOLI-4 and MCNP-5. The eigenvalues of the natural mode equations by α-k and TDPI are in good agreement with each other, and closely follow those predicted by the inhour equation. Neutron spectra and spatial distributions (flux and fission neutron emission) obtained by the two methods are also in good agreement. Similar results are also obtained for the adjoint fundamental eigenfunctions. These findings substantiate the coherence of both calculation strategies for natural mode.

Author(s):  
Carlo Fiorina ◽  
Manuele Aufiero ◽  
Sandro Pelloni ◽  
Konstantin Mikityuk

The present paper describes a first step taken at the Paul Scherrer Institut in the development of a new multi-physics platform for reactor analysis. Such platform is based on the finite-volume software OpenFOAM and aims at a tightly coupled description of neutron transport, thermal mechanics and fluid dynamics. For this purpose, a steady-state 3-D discrete ordinates/thermal-mechanics solver was first developed in collaboration with the Politecnico di Milano. The present work briefly discusses such solver and its preliminary validation, which will be described in detail in parallel publications. It then focuses on its extension to time-dependent simulations. The solver is first tested by simulating different step-wise reactivity insertions in a critical configuration constituted by an infinite slab of highly enriched uranium. Subsequently, a super-prompt-critical power burst in the Godiva reactor has been simulated. Godiva was a spherical assembly of highly enriched uranium built and operated at the Los Alamos National Laboratory (US) during the Fifties. A prompt-critical transient in such system configures as a quick power excursion (up to ∼10 GW), which causes a temperature rise, and a subsequent reactivity reduction via expansion of the sphere. The overall transient lasts for few fractions of a millisecond. Results obtained with the newly developed model have been compared to experimental results, showing a relatively good agreement.


Author(s):  
Wankui Yang ◽  
Baoxin Yuan ◽  
Songbao Zhang ◽  
Haibing Guo ◽  
Yaoguang Liu ◽  
...  

Deep penetration problems exist widely in reactor applications, such as SPRR300 (Swimming Pool Research Reactor 300), a light water moderated, enriched uranium fueled research reactor in China. Deterministic transport theory is intrinsically suitable for deep penetration. But there exist some problems when it’s applied in SPRR-300research reactors. First, the reactor core is complicated for geometry description in deterministic theory codes. Monte Carlo method has advantages in complex geometry modeling. And it uses continuous energy cross sections which are independent with specific reactor types and research objections. But usually it’s difficult to converge well enough to deal with deep penetration problems, even though there are a number of variance reduction techniques. Based on the advantages and disadvantages of Monte Carlo and Deterministic method, we proposed a coupled neutron transport calculation method for deep penetration. It combines advantages of these two methods. Firstly, we use Monte Carlo code to finish fine modeling and do the whole reactor core calculation. Domestically developed Monte Carlo code JMCT is used to do the neutron transport calculation. Then homogenized group constants in each mesh are calculated from JMCT output by a self-developed script. Afterwards, we do the whole reactor calculation with deterministic theory code TORT. It directly uses group constants generated by Monte Carlo code. Finally, we can get the deep penetration calculation results from TORT output. Verification is carried out by comparing the group constants of benchmark problem, and by comparing keff calculated by this method with continuous energy Monte Carlo method. Benchmark calculation is conducted with OECD/NEA slab benchmark problem. The comparison shows that group constants generated by this study are in good agreement with results from published references. Then above group constants are applied to 3-dimensional discrete ordinates deterministic theory transport code TORT. But keff calculated by TORT is a little lower than that calculated by Monte Carlo code JMCT. To minimize other influence factors, different Sn/Pn order, and different mesh size in TORT has been tried. Unfortunately the keff difference between these two methods remains. Even though the keff results in this benchmark are less than keff calculated by continuous energy MC method, Benchmark results show that all the group constants generated by this method are in good agreement with existing references. So it can be expected that after further verification and validation, this coupled method can be effectively applied to the deep penetration problem in such kind of research reactors.


2021 ◽  
Vol 247 ◽  
pp. 04008
Author(s):  
F. Filiciotto ◽  
A. Jinaphanh ◽  
A. Zoia

Time eigenvalues emerge in several key applications related to neutron transport problems, including reactor start-up and reactivity measurements. In this context, experimental validation and uncertainty quantification would demand to assess the variation of the dominant time eigenvalue in response to a variation of nuclear data. Recently, we proposed the use of a Generalized Iterated Fission Probability method (G-IFP) to compute adjoint-weighted tallies, such as kinetic parameters, perturbations and sensitivity coefficients, for Monte Carlo time (or alpha) eigenvalue calculations. With the massive use of parallel Monte Carlo calculations, it would be therefore useful to trade the memory burden of the G-IFP method (which is comparable to that of the standard IFP method for k-eigenvalue problems) for computation time and to rely on history-based schemes for such adjoint-weighted tallies. For this purpose, we investigate the use of the super-history method as applied to estimating adjoint-weighted tallies within the α-k power iteration, based on previous work on k-eigenvalue problems. Verification of the algorithms is performed on some simple preliminary tests where analytic solutions exist. In addition, the performances of the proposed method are assessed by comparing the super-history and the G-IFP methods for the same sets of benchmark problems.


2019 ◽  
Vol 33 (22) ◽  
pp. 1950258 ◽  
Author(s):  
Rıza Erdem ◽  
Songül Özüm

We have presented the time-dependent behaviors of a spin-1 Ising model (with both bilinear and biquadratic interactions) in the neighborhood of the equilibrium states via the path probability method. The rate equations as introduced by Keskin and co-workers (1989) have been linearized to obtain the characteristic relaxation times. The temperature variations of these times were produced in accordance with the Tanaka and Mannari’s work (1976) on the equilibrium properties. Results are compared to one using Onsager’s phenomenological theory and a good agreement is achieved.


1964 ◽  
Vol 22 (3) ◽  
pp. 613-621 ◽  
Author(s):  
William Perl

Clusters of ribosomes observed by electron microscopy in thin sections of rabbit reticulocytes are of the same order of size as the section thickness of 600 A. Many of the observed clusters must therefore have been transected by the section surfaces and observed as clusters containing fewer ribosomes. A probability method of correcting for this effect is given. Comparison of the results with grid observations of ribosome distributions indicates sufficiently good agreement for application to cell section observations.


2021 ◽  
Author(s):  
Xiangbiao Wang ◽  
Chun Bao Li ◽  
Ling Zhu

Abstract Ship collision accidents occur from time to time in recent years, and this would cause serious consequences such as casualties, environmental pollution, loss of cargo on board, damage to the ship and its equipment, etc. Therefore, it is of great significance to study the response of ship motion and the mechanism of structural damage during the collision. In this paper, model experiments and numerical simulation are used to study the ship-ship collision. Firstly, the Coupled Eulerian-Lagrangian (CEL) was used to simulate the fluid-structure interaction for predicting structural deformation and ship motion during the normal ship-ship collision. Meanwhile, a series of model tests were carried out to validate the numerical results. The validation presented that the CEL simulation was in good agreement with the model test. However, the CEL simulation could not present the characteristics the time-dependent added mass.


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