Application and development of numerical methods for the modelling of innovative gas cooled fission reactors

Innovative gas cooled reactors, such as the pebble bed reactor (PBR) and the gas cooled fast reactor (GFR) offer higher efficiency and new application areas for nuclear energy. Numerical methods were applied and developed to analyse the specific features of these reactor types with fully three dimensional calculation models. In the first part of this thesis, discrete element method (DEM) was used for a physically realistic modelling of the packing of fuel pebbles in PBR geometries and methods were developed for utilising the DEM results in subsequent reactor physics and thermal-hydraulics calculations. In the second part, the flow and heat transfer for a single gas cooled fuel rod of a GFR were investigated with computational fluid dynamics (CFD) methods. An in-house DEM implementation was validated and used for packing simulations, in which the effect of several parameters on the resulting average packing density was investigated. The restitution coefficient was found out to have the most significant effect. The results can be utilised in further work to obtain a pebble bed with a specific packing density. The packing structures of selected pebble beds were also analysed in detail and local variations in the packing density were observed, which should be taken into account especially in the reactor core thermal-hydraulic analyses. Two open source DEM codes were used to produce stochastic pebble bed configurations to add realism and improve the accuracy of criticality calculations performed with the Monte Carlo reactor physics code Serpent. Russian ASTRA criticality experiments were calculated. Pebble beds corresponding to the experimental specifications within measurement uncertainties were produced in DEM simulations and successfully exported into the subsequent reactor physics analysis. With the developed approach, two typical issues in Monte Carlo reactor physics calculations of pebble bed geometries were avoided. A novel method was developed and implemented as a MATLAB code to calculate porosities in the cells of a CFD calculation mesh constructed over a pebble bed obtained from DEM simulations. The code was further developed to distribute power and temperature data accurately between discrete based reactor physics and continuum based thermal-hydraulics models to enable coupled reactor core calculations. The developed method was also found useful for analysing sphere packings in general. CFD calculations were performed to investigate the pressure losses and heat transfer in three dimensional air cooled smooth and rib roughened rod geometries, housed inside a hexagonal flow channel representing a sub-channel of a single fuel rod of a GFR. The CFD geometry represented the test section of the L-STAR experimental facility at Karlsruhe Institute of Technology and the calculation results were compared to the corresponding experimental results. Knowledge was gained of the adequacy of various turbulence models and of the modelling requirements and issues related to the specific application. The obtained pressure loss results were in a relatively good agreement with the experimental data. Heat transfer in the smooth rod geometry was somewhat under predicted, which can partly be explained by unaccounted heat losses and uncertainties. In the rib roughened geometry heat transfer was severely under predicted by the used realisable k − epsilon turbulence model. An additional calculation with a v2 − f turbulence model showed significant improvement in the heat transfer results, which is most likely due to the better performance of the model in separated flow problems. Further investigations are suggested before using CFD to make conclusions of the heat transfer performance of rib roughened GFR fuel rod geometries. It is suggested that the viewpoints of numerical modelling are included in the planning of experiments to ease the challenging model construction and simulations and to avoid introducing additional sources of uncertainties. To facilitate the use of advanced calculation approaches, multi-physical aspects in experiments should also be considered and documented in a reasonable detail.

Two matrix-based lattice construction techniques

Let m and n be integers greater than 1. Given lattices A and B of dimensions m and n, respectively, a technique for constructing a lattice from them of dimension m+n-1 is introduced. Furthermore, if A and B possess bases satisfying certain conditions, then a second technique yields a lattice of dimension m+n-2. The relevant parameters of the new lattices are given in terms of the respective parameters of A,B, and a lattice C isometric to a sublattice of A and B. Denser sphere packings than previously known ones in dimensions 52, 68, 84, 248, 520, and 4098 are obtained. © 2012 Elsevier Inc. All rights reserved.

A new number field construction of the lattice E8

Known number theoretical constructions of the lattice E8 use the cyclotomic fields Q(ζ15), Q(ζ20), and Q(ζ24). In this work, an infinite family of Abelian number fields yielding rotated versions of the lattice E 8 is exhibited. © 2012 The Managing Editors.

A family of asymptotically good lattices having a lattice in each dimension

A new constructive family of asymptotically good lattices with respect to sphere packing density is presented. The family has a lattice in every dimension n >= 1. Each lattice is obtained from a conveniently chosen integral ideal in a subfield of the cyclotomic field Q(zeta(q)) where q is the smallest prime congruent to 1 modulo n.

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.

Metallochlorophylls of magnesium, copper and zinc: evaluation of the influence of the first coordination sphere on their solvatochromism and aggregation properties

In this study the role of different metal centers (magnesium, zinc and copper) on the enhancement of the hydrophilic character of metallochlorophylls, was evaluated. The solvatochromism as well as the aggregation process for these compounds in water/ethanol mixtures at different volume ratios were evaluated using Fluorescence, and Resonant Light Scattering (RLS) measurements, aiming to characterize the behavior of these compounds. Independently on the studied metallochlorophyll, the presence of at least 60% of water results in a considerable increase in the fluorescence emission, probably a direct consequence of a lower aggregation of these compounds, which is confirmed by the results from RLS measurements. Additionally, the results suggest that magnesium and zinc chlorophyll should be promising phototherapeutic agents for Photodynamic Therapy.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

Flat tori, lattices and bounds for commutative group codes

We show that commutative group spherical codes in R(n), as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.

Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

On the applicability of the Aris' equivalent sphere in multicomponent reacting systems

The validity of the concept of equivalent sphere introduced by Aris in 1957 to multicomponent reacting systems is investigated in this paper. A network of C6 hydrocarbon reforming reaction and a fixed bed reactor are taken as the model reaction network and the reactor configuration, respectively.

Maximum packings of K-v-K-u with triples

We construct, for all positive integers u, and v with u less than or equal to v, a decomposition of K-v - K-u (the complete graph on v vertices with a. hole of size u) into the maximum possible number of edge disjoint triangles.