A.J.H. Goddard

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 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.

STABLE TRACER AEROSOL DEPOSITION MEASUREMENTS IN A TEST CHAMBER

Abstract In order to provide data for evaluating the exposure of domestic building occupants to particulate pollutants from a variety of sources it is necessary to carry out aerosol deposition experiments in real house environments. To complement such studies in real houses, in which many influences on aerosol deposition exist simultaneously, it is desirable to carry out aerosol deposition experiments in test chambers under controlled conditions. An aerosol test chamber, with the dimensions of a small room, is described. The chamber is fitted with air sampling ports so that aerosol deposition velocities can be inferred by monitoring tracer aerosol concentration decay. The use of neutron-activatable aerosol facilitates simultaneous surface sampling. This is not possible with conventional light-scattering aerosol detection techniques and thus provides valuable information on mass transport limited deposition. Aerosol deposition experiments have been carried out, under turbulent conditions using monodisperse neutron-activatable particles of four sizes. Results are compared with the theory of Corner and Pendlebury (1951, Proc. Phys. Soc. B64 , 645–654). Surface sampling has been used to obtain additional information from average aerosol deposition velocities. The potential of the test chamber as a means of assessing the influence of internal building surface character upon aerosol deposition velocity is illustrated.

Interception of caesium-contaminated rain by vegetation

Abstract A series of experiments were carried out to quantify the interception of rain-borne caesium by crops of grass ( Lolium perenne ), broad beans ( Vicia faba ) and wheat ( Triticum aestivum ) under rainfall intensities typical of those encountered in the U.K. (1–18 mm h −1 ). The fraction of contamination deposited on the vegetation decreased with time, as the plant surface approached a saturation level of contamination. Surface contamination was dependent upon the total amount of rainfall rather than the rainfall intensity. The total surface water storage capacity of wheat and beans was determined, and found to approach a saturation level as total rainfall increased in a manner similar to the measured contamination levels. Total accumulation of caesium from aqueous solution onto bean leaves was found to increase linearly with time over the range of concentrations tested (0.0001–10 mM), the rate of accumulation increasing with concentration according to a power law. The combination of results obtained suggests that deposition of rain-borne contaminants could be modelled appropriately by a water storage capacity term and a “chemical term” derived from the contaminant concentration and its affinity for a particular plant surface.

Experimental Studies of the Effect of Rough Surfaces and Air Speed on Aerosol Deposition in a Test Chamber

Understanding the fate of particles indoors is important for human health assessment because deposited particles, unless resuspended, cannot be inhaled. To complement studies in real buildings, where control of variables is often difficult, an experimental test chamber facility (8 m 3 ) was designed to study particle deposition under well-stirred conditions using monodisperse tracer aerosol particles in the range of 0.7 to 5.4 w m. The use of neutron-activatable tracers facilitated simultaneous surface sampling and aerosol concentration decay measurements. Aerosol deposition on both smooth surfaces and regular arrays of three-dimensional roughness elements under 3 different airflow speeds was investigated in the test chamber.It was expected that the texture of the chamber surface would significantly influence particle deposition, but some counterintuitive results were observed: under the lowest airflow condition and for the smallest particle size, particle deposition onto rough samples was found to be less than on the corresponding smooth surfaces. The ratio of particle deposition on rough surfaces relative to smooth surfaces increased with particle size and magnitude of airflow. For the largest particle size and airflow speed, particle deposition on the rough surfaces exceeded that on the smooth surfaces by a factor of 3.

Long-range atmospheric dispersion of radioisotopes—i. The MESOS model

Abstract The Lagrangian puff trajectory model, MESOS, was initiated in 1976 to simulate the atmospheric transport and dispersal of radionuclides over distances of several hundred km or more. Extensive meteorological data bases have since been constructed from routine reports from European synoptic stations and ships, and used with the model to study large numbers of notional releases from various West European sites. Probability distributions of different levels of contamination have been deduced at several receptor points for hypothetical accidental releases of selected nuclides. Patterns of air contamination and ground deposition have been predicted for continuous releases and used for calculations of collective dose to the population of the EEC countries arising from routine emissions from nuclear installations. In part I of this paper the basic MESOS model is described, together with a comparison study of model predictions and measurements made following the Windscale release in 1957. In part II results obtained with the model for different European sources are presented and discussed.

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.

Radiation dose implications of airborne contaminant deposition to humans

Abstract— In nuclear accident consequence assessment, dose contributions from radionuclide deposition on the human body have in the past generally been either ignored or estimated on the basis of rather simple models. Recent experimental work has improved the state of knowledge of relevant processes and parameter ranges. The results presented in this paper represent a first approach to a detailed assessment of doses from radiopollutant deposition on the human body, based on contaminant-specific data. Both the dose to skin from beta-emitters and the whole-body dose from gamma-emitters on body surfaces were found to give potentially significant contributions to dose. Further, skin penetration of some contaminants could lead to significant internal doses.

Multigroup application of the anisotropic FEM code FELTRAN to one, two, three-dimensions and R-Z problems

Abstract The multigroup even parity form of the neutron transport equation, with anisotropic scattering, has been solved by the Finite Element Method (FEM). The maximum principle for the even parity equation is employed. Spherical harmonics are used to represent the angular dependence of the flux and scattering while finite elements are used in the spatial domain. A finite element code, FELTRAN, has been developed which solves multigroup anisotropic scattering problems in one, two and three dimensions. Angular integrals which appear in the functional are evaluated in a general and modular form within the code; hence any desired order of anisotropic scattering and moments for the even parity flux can be chosen. In the spatial domain various types of elements are used for both regular and irregular geometries. Lagrangian linear, quadratic and cubic rectangular elements are used in X - Y and R - Z regular geometry, while curved geometries are handled by triangular elements. Solutions may also be obtained for the adjoint form of the even parity equation. Some representative examples in one, two and three dimensions are analysed and comparison is made with discrete-ordinates finite-difference codes ANISN and DOT, together with a 22-group problem intended to demonstrate the capabilities of FELTRAN in solving more practical problems.

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.