C.R.E. de Oliveira

Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations

A method for optimising a pre-existing mesh of tetrahedral finite elements is described. It is based on a series of mesh connectivity and node position searches of the landscape defining mesh quality. A Riemannian metric, reflecting the a posteriori error measure, is used to calculate element size and shape. A functional is defined which embodies both shape and size quality of an element with respect to the metric, and is used to gauge mesh quality. A heuristic-based local search strategy is adopted – local in the sense that it has no hill-climbing abilities. The paper presents applications of the method to complex, steady-state and time-dependent problems which highlight its anisotropic, feature-capturing abilities. Numerical evidence is provided which suggests that the computational complexity (time) of the proposed algorithm varies linearly with the number of elements or nodes of the finite element mesh.

A study of bubbling and slugging fluidised beds using the two-fluid granular temperature model

Abstract This paper reports finite element numerical simulations of gas–solid fluidised beds using the two-fluid granular temperature model. The aim of the study has been to investigate the various phenomena that have been observed in fluidised beds but have not been subject to numerical investigation. Two fluidised beds, operating in the slugging and bubbling regimes, were modelled, and the formation, elongation, coalescence and eruption of bubbles described. The effect of an obstruction on the fluidisation efficiency in a fluidised bed was investigated. Granular temperature distribution inside the fluidised bed provided an indication of the regions on the obstruction, which could be susceptible to erosion by particle impact.

A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method

Most researchers choose the diffusion approximation to the transport equation as the model to describe photon migration in biological tissues. However, the applicability of this approximation is limited and, in certain cases, invalid. In this paper we introduce a two-dimensional, finite element-spherical harmonics (FE-P(N)) radiation transport method for the simulation of light propagation in tissue. The propagation of light is investigated first in a layered cylinder, which can be seen as a very simplistic approximation of a human head. Effects of the anisotropy factor g on the photon migration is then examined in homogeneous and heterogeneous media for different values of g and mu(s). The influence of void-like heterogeneities and channels in which absorption and scattering are very small compared with the surrounding medium on the transport of photons is also investigated. Significant differences between transport and diffusion calculations are shown to occur in all cases.

A finite element-spherical harmonics radiation transport model for photon migration in turbid media

Abstract In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE-PN) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, (μa/μs′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.

A Subcritical, Gas-Cooled Fast Transmutation Reactor with a Fusion Neutron Source

A design is presented for a subcritical, He-cooled fast reactor, driven by a tokamak D-T fusion neutron source, for the transmutation of spent nuclear fuel (SNF). The reactor is fueled with coated transuranic (TRU) particles and is intended for the deep-burn (>90%) transmutation of the TRUs in SNF without reprocessing of the coated fuel particles. The reactor design is based on the materials, fuel, and separations technologies under near-term development in the U.S. Department of Energy (DOE) Nuclear Energy Program and on the plasma physics and fusion technologies under near-term development in the DOE Fusion Energy Sciences Program, with the objective of intermediate-term (~2040) deployment. The physical and performance characteristics and research and development requirements of such a reactor are described.

Transient Criticality in Fissile Solutions - Compressibility Effects

Abstract Research on the incorporation of compressibility effects, for both the liquid and radiolytic gas phases, into the Finite Element Transient Criticality (FETCH) coupled neutronics/computational fluid dynamics code is described. The code has been developed to simulate criticality transients in multiphase media and is applied here to fissile solution transient criticality. The predicted fission and pressure transients obtained by the enhanced numerical model are benchmarked against the results from the SILENE series of experiments on criticality transients in uranium solutions. The amplitude and the form of the first pressure peak, following a step reactivity change, are well represented, and insight is gained into the form of subsequent pressure oscillations. An explanation is given on the absence of these oscillations in more energetic transients.

Space-dependent kinetics simulation of a gas-cooled fluidized bed nuclear reactor

In this paper we present numerical simulations of a conceptual helium-cooled fluidized bed thermal nuclear reactor. The simulations are performed using the coupled neutronics/multi-phase computational fluid dynamics code finite element transient criticality which is capable of modelling all the relevant non-linear feedback mechanisms. The conceptual reactor consists of an axi-symmetric bed surrounded by graphite moderator inside which 0.1 cm diameter TRISO-coated nuclear fuel particles are fluidized. Detailed spatial/temporal neutron flux and temperature profiles have been obtained providing valuable insight into the power distribution and fluid dynamics of this complex system. The numerical simulations show that the unique mixing ability of the fluidized bed gives rise, as expected, to uniform temperature and particle distribution. This uniformity enhances the heat transfer and therefore the power produced by the reactor.

Finite element simulations of incompressible flow past a heated/cooled sphere

SUMMARY This paper reports numerical simulation of the flow past a heated:cooled sphere. A Galerkin finiteelement method is used to solve the 3D incompressible Boussinesq equations in primitive variable form.Numerical simulations of flow around the sphere for a range of Grashof numbers and moderateReynolds numbers, were conducted. The drag coefficient for adiabatic flow shows good agreement withstandard correlations over the range of the Reynolds numbers investigated. It is shown that the drag canvary considerably with heating of the sphere and that computational fluid dynamics methods can be usedto derive constitutive laws for macroscopic momentum and heat exchange in multiphase flow.

Non-linear space-dependent kinetics for the criticality assessment of fissile solutions

Abstract A deterministic model for calculating the time dependent fission yield from solutions has been developed. The model is based on transient finite element methods and couples radiation transport modelling with computational fluid dynamics. Non-linear space dependent kinetic equations are derived, in which the non-linearities arise due to radiolytic gas generation, geometical changes in the liquid, the temperature dependent densities, cross sections and thermally/gas induced fluid motion. The latter advects the delayed neutron precursor concentrations together with the energy fields. Applications focus on the role of radiolytic gas evolution and buoyancy induced fluid motion on the criticality of fissile liquids with delayed and prompt supercritical step reactivity insertions. The analysis is performed with uranyl nitrate solutions. The theory behind the modelling is presented, together with numerical results, to validate the approach. The resulting computer code, which we call FETCH (finite element transient criticality), is validated against point kinetics based models for right cylinders and against experiment for both low (delayed supercritical) and high powered (usually prompt supercritical) transients. The term ‘low powered’ in this context will be used to describe transients in fissile liquids in which the rate of radiolytic gas generation is so small that it can be ignored without sacrificing the accuracy of the simulations. Modelling can then be conducted in a single fluid phase. The term “high powered’ refers to transients in which gas evolution and ensuing free surface motion play an important part in their dynamics and are thus solved using the multi-phase mode of FETCH. The simulations presented here provided extensive insights into the dynamics of these transients which can be difficult to study in detail with experiment.

A NEURAL NETWORK GRAPH PARTITIONING PROCEDURE FOR GRID-BASED DOMAIN DECOMPOSITION

This paper describes a neural network graph partitioning algorithm which partitions unstructured finite element/volume meshes as a precursor to a parallel domain decomposition solution method. The algorithm works by first constructing a coarse graph approximation using an automatic graph coarsening method. The coarse graph is partitioned and the results are interpolated onto the original graph to initialize an optimization of the graph partition problem. In practice, a hierarchy of (usually more than two) graphs are used to help obtain the final graph partition. A mean field theorem neural network is used to perform all partition optimization. The partitioning method is applied to graphs derived from unstructured finite element meshes and in this context it can be viewed as a multi-grid partitioning method. Copyright