Robert Roy

Effect of particle size distribution and packing compression on fluid permeability as predicted by lattice-Boltzmann simulations

Abstract Massive parallel lattice-Boltzmann method simulations of flow through highly polydispersed spherical particle packings formed using Monte-Carlo methods were performed. The computed fluid permeabilities were compared to experimental data obtained from blocks made of three natural ground calcium carbonate powders compressed at different levels. The agreement with experimental measurements is excellent considering the approximations made. A series of flow simulations was also performed for packings of spherical particles compressed at different levels with increasing polydispersity modeled with both lognormal and Weibull size distributions. The predicted permeabilities were found to follow reasonably well the Carman–Kozeny correlation although an increasing deviation towards lower predicted permeabilities with increasing polydispersity was observed. Finally, following a careful analysis of the inherent numerical errors, an expression relating the Kozeny “constant” to the size distribution and compression level was derived from the simulation results, which led to a modified correlation.

Modelling of CANDU reactivity control devices with the lattice code DRAGON

Abstract The lattice code DRAGON has been used for modelling the normal operating conditions in CANDU reactors. The integral transport equation is first solved using the collision probability (CP) formalism for 2-D cluster geometries representing standard CANDU cells. Whereas the usual tracking procedure only permits isotropic reflection at the cell boundary, we investigate the effects on a completely reflected cluster cell of the cyclic-tracking procedure that can also treat specular reflection. For CANDU reactivity devices located perpendicularly to the fuel channels, the standard CP formalism is applied to 3-D supercell geometries containing zones of mixed cylindrical and rectangular geometries. A symmetric two-bundle model allows most of the surfaces to be located in the moderator regions, thus reducing discrepancies introduced by the assumption of isotropic boundary currents. Using a single basic definition for the tracking files, efficient algorithms for computation and normalization of CP pertinent to these cell and supercell models are also described. Numerical results include reactivity worths for adjuster rods and zonal control units (ZCU) of a typical CANDU reactor.

A new characteristics algorithm for 3D transport calculations

Abstract In this paper, we present recent developments based on a characteristics method applied for solving general 3D geometries in the case of isotropic boundary conditions. Assuming isotropic sources and scattering, this characteristics solver involves the calculation of the region-to-region angular flux by scanning the tracking file containing the integration lines. The scalar flux is computed by collecting all mean angular fluxes in terms of the entering angular flux and the source of the region. At the boundary, the entering angular fluxes are linked to the emerging angular fluxes by isotropic albedos. The transport solution is similar to the one obtained by the standard collision probability method. The main advantage of this treatment is to get rid of collision probability matrices which have a dimensionality of the size of the square of the number of regions. For multigroup calculations, the rebalancing scheme was enhanced to take into account the external currents for any value of the albedos. Numerical comparisons are also presented in order to show the accuracy of the characteristics method as compared to the standard collision probability treatment for 3D supercells in the lattice code DRAGON. Several calculations for the incremental cross sections of adjusters and liquid zone controllers show that the characteristics results are accurate for the usual supercell calculations in a CANDU reactor.

A Transport Method for Treating Three-Dimensional Lattices of Heterogeneous Cells

AbstractA new ray-tracing method for the calculation of collision probabilities within arbitrary three-dimensional geometries has been developed. This method is used to discretize the neutron transport equation for heterogeneous rectangular cells containing zones of mixed cylindrical and rectangular geometry. For multicell applications, the interface current (IC) method provides the coupling between cells. The solution to the IC equations over multicell domains consisting of rectangular three-dimensional cells is improved by using an alternate direction implicit iteration scheme with variational acceleration. Results include comparisons of this technique with SHETAN for simple geometries and the analysis of a three-dimensional extension of a two-dimensional 15 × 15 pressurized water reactor benchmark problem.

Accurate offline synchronization of distributed traces using kernel-level events

Tracing has proven to be a valuable tool for identifying functional and performance problems. In order to use it on distributed nodes, the timestamps in the traces need to be precisely synchronized. The objective of this work is to improve synchronization of traces recorded on distributed nodes. We aim for high precision and low intrusiveness. In this paper, we present an offline trace synchronization algorithm that is directly applicable to pairs of nodes and that can report approximate bounds on accuracy over short tracing durations. We also present an efficient implementation of this algorithm and an experimental study of parameters that affect synchronization accuracy.

Reactor Core Methods

This chapter addresses the simulation flow chart that is currently used for reactor-physics simulations. The methodologies presented are more appropriate to the context of power reactors, and the chapter focuses particularly on the three-dimensional (3D) aspect of core calculations. Software design that is currently used to achieve accurate numerical simulations of reactor cores is also studied from a practical nuclear engineering point of view. The focus here is on processes and the needs for reactor physicists or nuclear engineers to use modern-day software with confidence and reliability.

Parallel Solver Based on the Three-Dimensional Characteristics Method: Design and Performance Analysis

Abstract Recent advances in parallel software development for solving three-dimensional (3-D) neutron transport problems using the characteristics method are presented. The characteristics method solves the transport equation by collecting local angular fluxes along neutron paths. In order to be able to solve large 3-D transport problems in a reasonable time frame, the characteristics solver needs to be accelerated. After applying adequate numerical acceleration techniques, the only issue is to parallelize the solver. The parallelization of this solver is based on distributing a group of tracks, generated by a ray-tracing procedure, on several processors. Different distributing schemes and load-balancing techniques based on a calculation load model are presented. A message-passing model is used to communicate the local solutions between processes participating in solving a problem. Both analytical models of this parallel algorithm and performance analysis are presented and illustrated by several examples.

Analytic reductions for transmission and leakage probabilities in finite tubes and hexahedra

Analytic reductions are used to simplify evaluation of the transmission probabilities in a hexahedron and of the five independent probabilities (two transmission and three leakage probabilities) that are required for a finite tube. The four- and five-dimensional numerical integrations required for transmission and leakage probabilities are reduced to one and two dimensions, respectively.

Acceleration techniques for trajectory-based deterministic 3D transport solvers

Abstract In this paper, we present new acceleration techniques for solving the linear transport equation in general 3D unstructured domains with isotropic boundary conditions. First, a track merging algorithm is used to consistently gather trajectories crossing similar regions. This domain-decomposition algorithm uses the generic geometrical concept of 3D microbands, where trajectories are classified by subsets of their region-crossing numbers. Secondly, a new local rebalancing technique is used to reduce the total number of iterations for multigroup calculations.This technique uses the self-collision probabilities of every spatial region to perform local group rebalancing. Based on approximations similar to the usual interface-current formalism, the out-going boundary currents are adjusted according to the rebalanced fluxes. Assuming isotropic sources and scattering, both techniques needs little programming effort and can be implemented into any characteristics or collision-probability solver. The main advantage of these techniques is that they are not memory intensive, requiring only new arrays of the size of the multigroup flux. Numerical comparisons show the accuracy of these algorithms for 3D supercells in a CANDU reactor. These algorithms were found particularly useful for speeding up transport calculations with high-scattering ratios.

Collision Probability Calculation and Multigroup Flux Solvers Using PVM

Collision probability evaluation and flux computation are the most time-consuming aspects of applications based on the linearized time-independent transport equation. Parallelization for collision probability calculation and multigroup flux computation are investigated. Particular techniques pertinent to the two-step energy/space iterative process of solving a multigroup transport equation are described. The parallel performance is studied in cases where the cyclic tracking technique is used to integrate collision probability. Parallelization is achieved by distributing either different energy groups or different regions on a set of processors. These algorithms were tested on a four-processor IBM SP2 and an eight-processor SPARC 1000 as well as on networks of workstations using the public domain PVM library. Typical run times are provided for unit cell calculations.