Numerical modelling of agglomerate degradation

In the processing industries particulate materials are often in the form of powders which themselves are agglomerations of much smaller sized particles. During powder processing operations agglomerate degradation occurs primarily as a result of collisions between agglomerates and between agglomerates and the process equipment. Due to the small size of the agglomerates and the very short duration of the collisions it is currently not possible to obtain sufficiently detailed quantitative information from real experiments to provide a sound theoretically based strategy for designing particles to prevent or guarantee breakage. However, with the aid of computer simulated experiments, the micro-examination of these short duration dynamic events is made possible. This thesis presents the results of computer simulated experiments on a 2D monodisperse agglomerate in which the algorithms used to model the particle-particle interactions have been derived from contact mechanics theories and, necessarily, incorporate contact adhesion. A detailed description of the theoretical background is included in the thesis. The results of the agglomerate impact simulations show three types of behaviour depending on whether the initial impact velocity is high, moderate or low. It is demonstrated that high velocity impacts produce extensive plastic deformation which leads to subsequent shattering of the agglomerate. At moderate impact velocities semi-brittle fracture is observed and there is a threshold velocity below which the agglomerate bounces off the wall with little or no visible damage. The micromechanical processes controlling these different types of behaviour are discussed and illustrated by computer graphics. Further work is reported to demonstrate the effect of impact velocity and bond strength on the damage produced. Empirical relationships between impact velocity, bond strength and damage are presented and their relevance to attrition and comminution is discussed. The particle size distribution curves resulting from the agglomerate impacts are also provided. Computer simulated diametrical compression tests on the same agglomerate have also been carried out. Simulations were performed for different platen velocities and different bond strengths. The results show that high platen velocities produce extensive plastic deformation and crushing. Low platen velocities produce semi-brittle failure in which cracks propagate from the platens inwards towards the centre of the agglomerate. The results are compared with the results of the agglomerate impact tests in terms of work input, applied velocity and damage produced.

The application of contact mechanics to the numerical simulation of particulate material

Particulate solids are complex redundant systems which consist of discrete particles. The interactions between the particles are complex and have been the subject of many theoretical and experimental investigations. Invetigations of particulate material have been restricted by the lack of quantitative information on the mechanisms occurring within an assembly. Laboratory experimentation is limited as information on the internal behaviour can only be inferred from measurements on the assembly boundary, or the use of intrusive measuring devices. In addition comparisons between test data are uncertain due to the difficulty in reproducing exact replicas of physical systems. Nevertheless, theoretical and technological advances require more detailed material information. However, numerical simulation affords access to information on every particle and hence the micro-mechanical behaviour within an assembly, and can replicate desired systems. To use a computer program to numerically simulate material behaviour accurately it is necessary to incorporte realistic interaction laws. This research programme used the finite difference simulation program `BALL', developed by Cundall (1971), which employed linear spring force-displacement laws. It was thus necessary to incorporate more realistic interaction laws. Therefore, this research programme was primarily concerned with the implementation of the normal force-displacement law of Hertz (1882) and the tangential force-displacement laws of Mindlin and Deresiewicz (1953). Within this thesis the contact mechanics theories employed in the program are developed and the adaptations which were necessary to incorporate these laws are detailed. Verification of the new contact force-displacement laws was achieved by simulating a quasi-static oblique contact and single particle oblique impact. Applications of the program to the simulation of large assemblies of particles is given, and the problems in undertaking quasi-static shear tests along with the results from two successful shear tests are described.

Numerical modelling of complex femtosecond laser inscribed fiber gratings - comparison wih experiment

We present experimental studies and numerical modeling based on a combination of the Bidirectional Beam Propagation Method and Finite Element Modeling that completely describes the wavelength spectra of point by point femtosecond laser inscribed fiber Bragg gratings, showing excellent agreement with experiment. We have investigated the dependence of different spectral parameters such as insertion loss, all dominant cladding and ghost modes and their shape relative to the position of the fiber Bragg grating in the core of the fiber. Our model is validated by comparing model predictions with experimental data and allows for predictive modeling of the gratings. We expand our analysis to more complicated structures, where we introduce symmetry breaking; this highlights the importance of centered gratings and how maintaining symmetry contributes to the overall spectral quality of the inscribed Bragg gratings. Finally, the numerical modeling is applied to superstructure gratings and a comparison with experimental results reveals a capability for dealing with complex grating structures that can be designed with particular wavelength characteristics.

Verification and validation of numerical models of the transport of insulation debris

Damage to insulation materials located near to a primary circuit coolant leak may compromise the operation of the emergency core cooling system (ECCS). Insulation material in the form of mineral wool fiber agglomerates (MWFA) maybe transported to the containment sump strainers, where they may block or penetrate the strainers. Though the impact of MWFA on the pressure drop across the strainers is minimal, corrosion products formed over time may also accumulate in the fiber cakes on the strainers, which can lead to a significant increase in the strainer pressure drop and result in cavitation in the ECCS. An experimental and theoretical study performed by the Helmholtz-Zentrum Dresden-Rossendorf and the Hochschule Zittau/Görlitz is investigating the phenomena that maybe observed in the containment vessel during a primary circuit coolant leak. The study entails the generation of fiber agglomerates, the determination of their transport properties in single and multi-effect experiments and the long-term effect that corrosion and erosion of the containment internals by the coolant has on the strainer pressure drop. The focus of this paper is on the verification and validation of numerical models that can predict the transport of MWFA. A number of pseudo-continuous dispersed phases of spherical wetted agglomerates represent the MWFA. The size, density, the relative viscosity of the fluid-fiber agglomerate mixture and the turbulent dispersion all affect how the fiber agglomerates are transported. In the cases described here, the size is kept constant while the density is modified. This definition affects both the terminal velocity and volume fraction of the dispersed phases. Note that the relative viscosity is only significant at high concentrations. Three single effect experiments were used to provide validation data on the transport of the fiber agglomerates under conditions of sedimentation in quiescent fluid, sedimentation in a horizontal flow and suspension in a horizontal flow. The experiments were performed in a rectangular column for the quiescent fluid and a racetrack type channel that provided a near uniform horizontal flow. The numerical models of sedimentation in the column and the racetrack channel found that the sedimentation characteristics are consistent with the experiments. For channel suspension, the heavier fibers tend to accumulate at the channel base even at high velocities, while lighter phases are more likely to be transported around the channel.

Numerical investigation of the impact of reflectors on spectral performance of Raman fibre laser

Using a cavity mode model we study numerically the impact of bandwidth and spectral response profile of fibre Bragg gratings on four-wave-mixing-induced spectral broadening of radiation generated in 6 km and 22 km SMF-based Raman fibre lasers.

Comparison of BER estimation methods in numerical simulation of 40 Gbit/s RZ-DPSK transmission

This study analyzes the validity of different Q-factor models in the BER estimation in RZ-DPSK transmission at 40 Gb/s channel rate. The impact of the duty cycle of the carrier pulses on the accuracy of the BER estimates through the different models has also been studied.

Comparative analysis of BER estimation methods in numerical simulation of 40-Gb/s RZ-DPSK transmission with in-line SOAs

Applying direct error counting, we compare the accuracy and evaluate the validity of different available numerical approaches to the estimation of the bit-error rate (BER) in 40-Gb/s return-to-zero differential phase-shift-keying transmission. As a particular example, we consider a system with in-line semiconductor optical amplifiers. We demonstrate that none of the existing models has an absolute superiority over the others. We also reveal the impact of the duty cycle on the accuracy of the BER estimates through the differently introduced Q-factors.

Comparative numerical study of energy deposition in femtosecond laser microfabrication with fundamental and second harmonics of Yb-doped laser

We present the results of comparative numerical study of femtosecond laser inscription for fundamental and second harmonic of Yb-doped laser. We have found that second harmonic is more efficient in terms of amount of absorbed energy which leads to lower inscription threshold. Hence this regime is more attractive for applications in femtosecond laser microfabrication. We observed the different size of modified domain on initial pulse energy and different spectrum dynamics during the pulse propagation for fundamental and second harmonics.

Numerical investigation of the effect of the temporal pulse shape on modification of fused silica by femtosecond pulses

We report the results of numerical studies of the impact of asymmetric femtosecond pulses focused in the bulk of the material on the femtosecond modification of fused silica. It is shown that such pulses lead to localisation of absorption in the process of femtosecond modification and to a decrease in the threshold energy of modification. It is found that the optimal asymmetry parameters for reaching the maximum plasma density in the focusing region depend on the pulse energy: at an initial energy of about 100 nJ, it is preferable to use pulses with positive TOD; however, when the energy is increased, it is preferable to use pulses with negative TOD. This is explained by differences in the dynamics of the processes of absorption of energy of a pulse propagating in the material.

Comparative numerical study of efficiency of energy deposition in femtosecond microfabrication with fundamental and second harmonics of Yb-doped fiber laser

We present the results of comparative numerical study of energy deposition in single shot femtosecond laser inscription for fundamental and second harmonic of Yb-doped fiber laser. We have found that second harmonic is more efficient in absorbing energy which leads to lower inscription threshold. Hence this regime is more attractive for applications in femtosecond laser microfabrication.

Numerical modeling of holmium-doped fluoride fiber lasers

We combine all the known experimental demonstrations and spectroscopic parameters into a numerical model of the Ho3+ -doped fluoride glass fiber laser system. Core-pumped and cladding-pumped arrangements were simulated for all the population-bottlenecking mitigation schemes that have been tested, and good agreement between the model and the previously reported experimental results was achieved in most but not in all cases. In a similar way to Er3+ -doped fluoride glass fiber lasers, we found that the best match with measurements required scaled-down rate parameters for the energy transfer processes that operate in moderate to highly concentrated systems. The model isolated the dominant processes affecting the performance of each of the bottlenecking mitigation schemes and pump arrangements. It was established that pump excited-state absorption is the main factor affecting the performance of the core-pumped demonstrations of the laser, while energy transfer between rare earth ions is the main factor controlling the performance in cladding-pumped systems.

High performance numerical modeling of ultra-short laser pulse propagation based on multithreaded parallel hardware

The focus of this study is development of parallelised version of severely sequential and iterative numerical algorithms based on multi-threaded parallel platform such as a graphics processing unit. This requires design and development of a platform-specific numerical solution that can benefit from the parallel capabilities of the chosen platform. Graphics processing unit was chosen as a parallel platform for design and development of a numerical solution for a specific physical model in non-linear optics. This problem appears in describing ultra-short pulse propagation in bulk transparent media that has recently been subject to several theoretical and numerical studies. The mathematical model describing this phenomenon is a challenging and complex problem and its numerical modeling limited on current modern workstations. Numerical modeling of this problem requires a parallelisation of an essentially serial algorithms and elimination of numerical bottlenecks. The main challenge to overcome is parallelisation of the globally non-local mathematical model. This thesis presents a numerical solution for elimination of numerical bottleneck associated with the non-local nature of the mathematical model. The accuracy and performance of the parallel code is identified by back-to-back testing with a similar serial version.

On the numerical solution of a Cauchy problem for the Laplace equation via a direct integral equation approach

We investigate the problem of determining the stationary temperature field on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the temperature (or the heat flux) is known, and, additionally, on a portion of this exterior boundary the heat flux (or temperature) is also given. We propose a direct boundary integral approach in combination with Tikhonov regularization for the stable determination of the temperature and flux on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green’s functions, and properties of these equations are shown in an L2-setting. An effective way of discretizing these boundary integral equations based on the Nystr¨om method and trigonometric approximations, is outlined. Numerical examples are included, both with exact and noisy data, showing that accurate approximations can be obtained with small computational effort, and the accuracy is increasing with the length of the portion of the boundary where the additionally data is given.

On the numerical solution of a Cauchy problem in an elastostatic half-plane with a bounded inclusion

We propose an iterative procedure for the inverse problem of determining the displacement vector on the boundary of a bounded planar inclusion given the displacement and stress fields on an infinite (planar) line-segment. At each iteration step mixed boundary value problems in an elastostatic half-plane containing the bounded inclusion are solved. For efficient numerical implementation of the procedure these mixed problems are reduced to integral equations over the bounded inclusion. Well-posedness and numerical solution of these boundary integral equations are presented, and a proof of convergence of the procedure for the inverse problem to the original solution is given. Numerical investigations are presented both for the direct and inverse problems, and these results show in particular that the displacement vector on the boundary of the inclusion can be found in an accurate and stable way with small computational cost.