An analytical dispersion model has been derived to determine the distribution of velocities and concentrations of a tracer in a two-dimensional jet in a coflowing ambient fluid. The particular novelty of this model is that it bridges the gap between near-field (where initial momentum dominates behaviour) and far-field (where ambient turbulence is more important) domains. We describe this domain as the ???intermediate field???. In a literature review of coflowing jets we find several laboratory studies and models which can predict the velocities (and in some cases concentrations) in a 2D jet, however they all have shortcomings. None could fully account for ambient turbulence, and all were strictly near-field, i.e. they are unable to describe behaviour when ambient turbulence dominates the initial shear. A brief review of analytical far-field models was also undertaken. There are standard solutions for the dispersion of a 2D continuous source but none that allow for an initial source momentum or non-uniform velocity. As opposed to the near-field coflow approach used by other researchers we start from the far-field, modifying the simple diffusion models by perturbing the governing equations to allow for the initial momentum. Models are developed for both along-stream velocity and the concentration field of a tracer. From the velocity model, a comparison is made with experimental data available from one researcher (Wang, 1996) and an existing near-field coflow model PJCMERG (Davidson, 1989). The initial conditions (width and excess velocity) for our model are determined by Gaussian curve fitting to an arbitrary point in the near-field. The diffusivity parameter is used to adjust (tune) the model until the centreline velocity profile matches. We can always achieve this match and to a much closer degree than PJCMERG. There are no available laboratory or field data for concentrations of a tracer in a 2D coflowing jet although the near-field model PJCMERG does have a tracer component. We demonstrate how PJCMERG cannot converge to any far-field model, while our model provides a neat transition between the near-field and far-field. We have started the extension of the 2D model to the more common 3D situation although we have yet to carry out any comparisons with other models or data. The model development is included in an appendix for other researchers to pick up.

An analytical dispersion model has been derived to determine the distribution of velocities and concentrations of a tracer in a two-dimensional jet in a coflowing ambient fluid. The particular novelty of this model is that it bridges the gap between near-field (where initial momentum dominates behaviour) and far-field (where ambient turbulence is more important) domains. We describe this domain as the ???intermediate field???. In a literature review of coflowing jets we find several laboratory studies and models which can predict the velocities (and in some cases concentrations) in a 2D jet, however they all have shortcomings. None could fully account for ambient turbulence, and all were strictly near-field, i.e. they are unable to describe behaviour when ambient turbulence dominates the initial shear. A brief review of analytical far-field models was also undertaken. There are standard solutions for the dispersion of a 2D continuous source but none that allow for an initial source momentum or non-uniform velocity. As opposed to the near-field coflow approach used by other researchers we start from the far-field, modifying the simple diffusion models by perturbing the governing equations to allow for the initial momentum. Models are developed for both along-stream velocity and the concentration field of a tracer. From the velocity model, a comparison is made with experimental data available from one researcher (Wang, 1996) and an existing near-field coflow model PJCMERG (Davidson, 1989). The initial conditions (width and excess velocity) for our model are determined by Gaussian curve fitting to an arbitrary point in the near-field. The diffusivity parameter is used to adjust (tune) the model until the centreline velocity profile matches. We can always achieve this match and to a much closer degree than PJCMERG. There are no available laboratory or field data for concentrations of a tracer in a 2D coflowing jet although the near-field model PJCMERG does have a tracer component. We demonstrate how PJCMERG cannot converge to any far-field model, while our model provides a neat transition between the near-field and far-field. We have started the extension of the 2D model to the more common 3D situation although we have yet to carry out any comparisons with other models or data. The model development is included in an appendix for other researchers to pick up.

<p>The Large Hadron Collider (LHC) is presently under construction at CERN. The LHC is a circular accelerator that stores proton beams and accelerates them to a 7 TeV beam energy for high energy physics research. The required bending and focusing/defocusing fields are achieved with superconducting magnets.</p><p>Such a superconducting magnet-based accelerator can be controlled only when the field errors of production and installation of all magnetic elements are known to the required accuracy. The ideal way to compensate the field errors is to have direct diagnostics on the beam. For the LHC, however, a system solely based on beam feedback may be too demanding. The present baseline for the LHC control system hence requires an accurate forecast of the magnetic field and the multipole field errors to reduce the burden on the beam-based feedback. The field model is the core of this magnetic prediction system, also known as \emph{the Field Description for the LHC} (FIDEL). The model will provide the forecast of the magnetic field at a given time, magnet operating current, magnet ramp rate, magnet temperature, and magnet powering history. The model is based on the identification and physical decomposition of the effects that contribute to the total field in the magnet aperture of the LHC dipoles.</p><p>This thesis presents the tool that was constructed to ease the detection, identification and finally correction of errors in the raw data from the series measurements of the main dipoles of the LHC. The results after cleaning all measurement data for the over 240 dipoles measured at cold, using this tool, is also presented.</p><p>Another aspect of the Thesis is the presentation of a procedure devised to extract the model parameters for the main dipole magnets of the LHC by using the cleaned data. The procedure and the model are verified and validated by application to the magnets of the 7-8 sector of the LHC.</p>

In this thesis, we have used a phase field model for studying the effect of atomic mobility inside the precipitate phase on coarsening behaviour in two dimensional (2D) systems. In all the available coarsening theories, the diffusivity inside the precipitate phase is not explicitly taken into account; this would imply that there is no chemical potential gradient inside the precipitate. This assumption is valid if (a) the atomic mobility inside the precipitate is much higher than that in the matrix, or (b) the precipitate volume fraction is small (i.e. the interparticle spacing is far higher than the average particle size). We undertook this study to evaluate the potential effect of diffusivity in the precipitate on coarsening in situations where conditions (a) and (b), above, do not hold, by studying systems with moderate volume fractions (20% and 30%) and with low atomic mobilities in the precipitate. In our study, we have fixed the atomic mobility in the matrix at a constant value. We have used the well known Cahn-Hilliard model in which the microstructure is described in terms of a composition field variable. The evolution of microstructure is studied by numerically solving a non-classical diffusion equation known as the Cahn-Hilliard equation. We have used a semi-implicit Fourier spectral technique for solving the CH equation using periodic boundary conditions. The coarsening behaviour is tracked and analyzed using number density of particles, their average size and their size distribution. The main conclusion from this study is that, contrary to expectations, the atomic mobility in the precipitate phase has only a small effect on coarsening behavior. Specifically, with decreasing atomic mobility in the precipitate phase, we report a small increase in the number density, a slightly wider size distribution and a slightly smaller coarsening rate. We also add that these effects are too small to allow experimental verification. These results indicate that the need for chemical potential equilibration within each precipitate is not an important factor during coarsening.

No description available.

No description available.

Point defects control many properties of technological importance in intermetallic compounds such as atomic diffusion, creep, hardness, mechanical properties and sintering. Farther, since intermetallic compounds are characterized by long range atomic order, the point defects in these compounds can be qualitatively different from those in pure metals and disordered alloys. In the present study, we have chosen β-NiAl for our point defect studies since it is a potential candidate for high temperature applications and a model system for the study of basic phenomena in ordered alloys. We have used a mean field formulation for studying point defect concentrations. The outline of the formulation is as follows: We divide the rigid, body centred cubic lattice into two interpenetrating cubic sublattices called α and j3 which are made up of the cube corners and body centres respectively. We write a generic free energy function (G) that involves the temperature T and the six sublattice occupancies viz., the A (Ni), B (Al) and vacancies (V) on the two sublattices α andβ. We use the constraints on the number of α and β sublattice sites viz., the number of α sublattice sites is equal to the number of β sublattice sites, to write G as a function of four of the six sublattice occupancies and T. We define three auxiliary parameters η1, η2 and η3 which correspond to the vacancy concentration, the differential B species population on the two sublatices (the chemical or atomic order), and the differential vacancy population on the two sublattices, respectively. We then rewrite G as a function of T, xB and ηi. The G can now be minimized with respect to the three auxiliary variables so that we recover the free energy (G) as a function of XB and T only. The formulation requires as inputs the Ni-Ni, Al-Al, Ni-Al, Ni-V and Al-V interaction energies in the nn and nnn shells. We have obtained the Ni-Ni, Al-Al and Ni-Al interaction energies from the effective pair potentials reported in the literature. For the Ni-V and Al-V interaction energies we have used a bond breaking model in which we have assumed that the Ni-V and Al-V interaction energies in the nnn shell to be zero. Using the above interaction parameters in our mean field formulation we have determined the concentrations of various types of point defects in β-NiAL We have specifically chosen the temperature range of 800 - 2000 K and the composition range of 45 - 55 atomic% Al. Our results can be summarised as follows: 1.The predominant defect in the stoichiometric alloy is a combination of an Ni-antisite defect and two vacancies on the Ni sublattice. 2.The Al-rich alloys of composition (50 + ∆) atomic% contain 2∆% vacancies;since the alloys are almost perfectly ordered, these vacancies predominantly occupy the Ni sublattice. Similarly, the Ni-rich alloys of composition (50 — ∆)atomic% contain ∆% Ni antisites. 3.Both the vacancies on the Ni sublattice (in Al-rich alloys) and Ni-antisites (in Ni-rich alloys) show negligible temperature dependence, and hence owe their origin to the off-stoichiometry. 4.In all the alloys, the Al-antisites have the lowest concentration (of the order 10-6 even at 2000 K) and the concentration of the vacancies on the β sublattice is the next lowest. Thus, our results support the view that β-NiAl is a triple defect B2 and, if we consider constitutional vacancies as those which have a little or no temperature dependence, there exist constitutional vacancies in Al-rich β-NiAl. This conclusion is in agreement with some of the experimental results. However, it must be pointed out that there is considerable disagreement among experimental results from different groups.

The Large Hadron Collider (LHC) is presently under construction at CERN. The LHC is a circular accelerator that stores proton beams and accelerates them to a 7 TeV beam energy for high energy physics research. The required bending and focusing/defocusing fields are achieved with superconducting magnets. Such a superconducting magnet-based accelerator can be controlled only when the field errors of production and installation of all magnetic elements are known to the required accuracy. The ideal way to compensate the field errors is to have direct diagnostics on the beam. For the LHC, however, a system solely based on beam feedback may be too demanding. The present baseline for the LHC control system hence requires an accurate forecast of the magnetic field and the multipole field errors to reduce the burden on the beam-based feedback. The field model is the core of this magnetic prediction system, also known as \emph{the Field Description for the LHC} (FIDEL). The model will provide the forecast of the magnetic field at a given time, magnet operating current, magnet ramp rate, magnet temperature, and magnet powering history. The model is based on the identification and physical decomposition of the effects that contribute to the total field in the magnet aperture of the LHC dipoles. This thesis presents the tool that was constructed to ease the detection, identification and finally correction of errors in the raw data from the series measurements of the main dipoles of the LHC. The results after cleaning all measurement data for the over 240 dipoles measured at cold, using this tool, is also presented. Another aspect of the Thesis is the presentation of a procedure devised to extract the model parameters for the main dipole magnets of the LHC by using the cleaned data. The procedure and the model are verified and validated by application to the magnets of the 7-8 sector of the LHC.

Numerous efforts have contributed to the study of phase-change problems for over a century|both analytical and numerical. Among those numerical approximations applied to solve phase-transition problems, phase-field models attract more and more attention because they not only capture two important effects, surface tension and supercooling, but also enable explicitly labeling the solid and liquid phases and the position of the interface. In the research of this dissertation, a phase-field model has been employed to simulate 2-D dendrite growth of pure nickel without a flow, and 2-D ice crystal growth in a high-Reynolds-number lid-driven-cavity flow. In order to obtain the details of ice crystal structures as well as the flow field behavior during freezing for the latter simulation, it is necessary to solve the phase-field model without convection and the equations of motion on two different scales. To accomplish this, a heterogeneous multiscale method is implemented for the phase-field model with convection such that the phase-field model is simulated on a microscopic scale and the equations of motion are solved on a macroscopic scale. Simulations of 2-D dendrite growth of pure nickel provide the validation of the phase-field model and the study of dendrite growth under different conditions, e.g., degree of supercooling, interface thickness, kinetic coefficient, and shape of the initial seed. In addition, simulations of freezing in a lid-driven-cavity flow indicate that the flow field has great effect on the small-scale dendrite structure and the flow eld behavior on the large scale is altered by freezing inside it.

An analytical dispersion model has been derived to determine the distribution of velocities and concentrations of a tracer in a two-dimensional jet in a coflowing ambient fluid. The particular novelty of this model is that it bridges the gap between near-field (where initial momentum dominates behaviour) and far-field (where ambient turbulence is more important) domains. We describe this domain as the ???intermediate field???. In a literature review of coflowing jets we find several laboratory studies and models which can predict the velocities (and in some cases concentrations) in a 2D jet, however they all have shortcomings. None could fully account for ambient turbulence, and all were strictly near-field, i.e. they are unable to describe behaviour when ambient turbulence dominates the initial shear. A brief review of analytical far-field models was also undertaken. There are standard solutions for the dispersion of a 2D continuous source but none that allow for an initial source momentum or non-uniform velocity. As opposed to the near-field coflow approach used by other researchers we start from the far-field, modifying the simple diffusion models by perturbing the governing equations to allow for the initial momentum. Models are developed for both along-stream velocity and the concentration field of a tracer. From the velocity model, a comparison is made with experimental data available from one researcher (Wang, 1996) and an existing near-field coflow model PJCMERG (Davidson, 1989). The initial conditions (width and excess velocity) for our model are determined by Gaussian curve fitting to an arbitrary point in the near-field. The diffusivity parameter is used to adjust (tune) the model until the centreline velocity profile matches. We can always achieve this match and to a much closer degree than PJCMERG. There are no available laboratory or field data for concentrations of a tracer in a 2D coflowing jet although the near-field model PJCMERG does have a tracer component. We demonstrate how PJCMERG cannot converge to any far-field model, while our model provides a neat transition between the near-field and far-field. We have started the extension of the 2D model to the more common 3D situation although we have yet to carry out any comparisons with other models or data. The model development is included in an appendix for other researchers to pick up.