This thesis investigates the role of superfluidity in neutron stars and associated phenomena. We model the internal fluid of a neutron star as a two-component system: one of charged particles and one of superfluid neutrons. We derive a set of multi-constituent hydrodynamic equations that allows for a mutual friction between the constituents. We show that when a velocity difference exists between the two constituents the momentum of each constituent is modified by an entrainment parameter. Throughout all of this work we take direction from both theoretical and experimental work on superfluid Helium. This suggests that a force due to vortex lines in the superfluid acts between the two constituents. The hydrodynamic equations are on a scale at which the effect of vortices can be averaged over. The form of the mutual friction between the two constituents depends on the configuration of the vortices. Firstly, we concentrate on an array of vortices. The mutual friction is calculated both for a straight array, and then extended to a ‘moderately’ curved array. We also investigate a turbulent model for the superfluid neutrons in which the vortices are in a tangle. To include rotation in our model we use a phenomenological approach to construct the mutual friction for a polarised tangle. The hydrodynamic equations are used to investigate how entrainment and mutual friction affect plane waves. We show that there are conditions in which the waves are unstable and discuss how this may lead to turbulence. As a first step in considering the neutron star crust we consider how oscillations in the fluid are dissipated on a boundary. As before, we concentrate on the effects of entrainment and mutual friction. Finally, we consider a simple global model of the glitch phenomenon seen in neutron stars in which the important process is a reconfiguration of the vortex array. We use this model to consider how the observational data may constrain parameters.

We investigate equilibrium configurations and oscillation spectra of neutron stars, modelled as rotating magnetised fluid bodies in Newtonian gravity. We also explore the idea that these model neutron stars could have dynamics analogous to rigid-body free precession. In axisymmetry, the equations of magnetohydrodynamics reduce to a purely toroidal-field case and a mixed-field case (with a purely poloidal-field limit). We solve these equations using a nonlinear code which finds stationary rotating magnetised stars by an iterative procedure. We find that despite the general nature of our approach, the mixed-field configurations we produce are all dominated by their poloidal component. We calculate distortions induced both by magnetic fields and by rotation; our results suggest that the relationship between the magnetic energy and the induced ellipticity should be close to linear for all known neutron stars. We then investigate the oscillation spectra of neutron stars, using these stationary configurations as a background on which to study perturbations. This is done by evolving the perturbations numerically, making the Cowling approximation and specialising to purely toroidal fields for simplicity. The results of the evolutions show a number of magnetically-restored Alfv´en modes. We find that in a rotating star pure inertial and pure Alfv´en modes are replaced by hybrid magneto-inertial modes. We also show that magnetic fields appear to reduce the effect of the r-mode instability. Finally, we look at precession-like dynamics in magnetised fluid stars, using both analytic and numerical methods. Whilst these studies are only preliminary, they indicate deficiencies in previous research on this topic. We suggest ways in which the problem of magnetised-fluid precession could be better understood.

Marine anthropogenic noise is increasing, along with concern about its impact on the environment. Hence minimising noise within engineering design is important, including in applications such as ships, submarines and turbines. The desire to mitigate noise may also be related to reducing the detectability of certain types of marine craft. Noise reduction typically focuses on rotating machinery such as propellers, due to the high velocity of the blades. A common source of broadband noise in engineering scenarios is often termed inflow turbulence noise. Resulting from upstream turbulence impinging onto rotor blades, this source typically dominates the low to mid range of the frequency spectrum. This is due to the high turbulence intensity and large length scales present in the inflow turbulence, which exceed those generating competing noise sources. This thesis uses a library of numerical tools to simulate broadband inflow turbulence noise. Synthetic turbulence is generated numerically within the simulations. Turbulence is resolved on the grid by solving the filtered Navier-Stokes equations. Based on the assumption of incompressible flow, noise sources may be predicted without resolving acoustic waves on the grid. This decoupling of hydrodynamic and acoustic processes means that radiated noise may be estimated using an acoustic analogy. Validation of two inflow turbulence generators revealed the importance of obtaining the prescribed turbulence statistics, as well as minimising artificial pressure fluctuations. This is used to simulate homogeneous isotropic turbulence impinging onto a foil, allowing acoustic sources to be located. The far-field sound prediction is in good agreement with experimental measurement data for low frequencies. It is then shown that the effect of foil thickness on noise can successfully be predicted using the proposed methodology. Noise radiation from a tidal turbine is then estimated by fully resolving all turbine blades, both spatially and temporally, in the simulation. A good agreement is seen in comparison to an analytical model, demonstrating that the simulation captures the dominant flow features which affect the acoustic spectrum. These spectral ‘humps’ are a result of turbulence-rotor interaction, which is implicitly included. Full scale noise estimates made from the simulations are then used to inform environmental impact assessment; the turbine hydrodynamic noise is not expected to be an issue in this regard.

Computational fluid dynamics (CFD) based Fire Field Modelling (FFM) codes offer powerful tools for fire safety engineers but their operation requires a high level of skill and an understanding of the mode of operation and limitations, in order to obtain meaningful results in complex scenarios. This problem is compounded by the fact that many FFM cases are barely stable and poor quality set-up can lead to solution failure. There are considerable dangers of misuse of FFM techniques if they are used without adequate knowledge of both the underlying fire science and the associated numerical modelling. CFD modelling can be difficult to set up effectively since there are a number of potential problems: it is not always clear what controls are needed for optimal solution performance, typically there will be no optimal static set of controls for the whole solution period to cover all stages of a complex simulation, there is the generic problem of requiring a high quality mesh - which cannot usually be ascertained until the mesh is actually used for the particular simulation for which it is intended and there are potential handling issues, e.g. for transitional events (and extremes of physical behaviour) which are likely to break the solution process. In order to tackle these key problems, the research described in this thesis has identified and investigated a methodology for analysing, applying and automating a CFD Expert user's knowledge to support various stages of the simulation process - including the key stages of creating a mesh and performing the simulation. This research has also indicated an approach for the control of a FFM CFD simulation which is analogous to the way that a FFM CFD Expert would approach the modelling of a previously unseen scenario. These investigations have led to the identification of a set of requirements and appropriate knowledge which have been instantiated as the, so called, Experiment Engine (EE). This prototype component (which has been built and tested within the SMARTFIRE FFM environment) is capable, both of emulating an Expert users' ability to produce a high quality and appropriate mesh for arbitrary scenarios, and is also able to automatically adjust a key control factor of the solution process.

No description available.

Aircraft propellers in any flight condition other than pure axial flight are subject to an incident flowfield that gives rise to time-varying forces. Means of modelling these time-dependent forces have been presented in the literature, to varying degrees of success but a review of the different models is missing, and there is a need for an instructive means of simulation using physically realistic but computationally light methodologies. This dissertation provides a comprehensive overview of the relevant work to date, in addition to providing a logical framework in which the problem of propeller blade cyclic load variation may be assessed. Through this framework, the importance of different aerodynamic features pertinent to this problem are compared, and a new solution methodology based on adaptations of existing models is presented. This research project was commissioned by Dowty Propellers (DP), who chose Glasgow University and the supervisors for their rotorcraft simulation experience. Prediction of the propeller induced flowfield is shown to be of importance for the calculation of blade cyclic loads. Momentum models are fit for purpose owing to relative computational simplicity - this dissertation suggests a new radially-weighted implementation of momentum theory that provides better correlation with wind tunnel data than existing models. Swept propeller blades are discussed and the inherent problems faced by a designer or performance engineer are highlighted. An Euler transform to resolve velocities and forces between disc and blade element axes is presented, along with the assertion that ‘simple’ sweep correction methods can be deleterious to propeller aerodynamic simulation if used naïvely. Fundamentally, representation of a swept propeller blade by a blade element model is described as wholly more problematic than a straight propeller blade owing to the displacement of blade elements with respect to the blade pitch change axis - and that flow information will always be lost with such a representation. Installation effects are simulated and installed load fluctuations are predicted to a reasonable degree of accuracy compared to what little data is available. Different means of resolving installation velocities to disc and, subsequently, blade element axes are compared, and it is shown that representing installation effects by an effective incidence angle as is ‘standard practice’ will most likely underpredict installed load fluctuation. In addition to a varying blade root bending load caused directly by load fluctuation on a propeller at an angle of incidence, the reacted net loads at a propeller hub may include a constant yawing moment and in-plane force. This in-plane force has been well documented in the literature, but the equations for its calculation may miss a component of force due to a tilting of the blade tangential force. New equations for this additional force term are presented that validate well to legacy experimental data.

The Large Eddy Simulation (LES) technique with the Smagorinsky-Lilly dynamic subgrid model and two-equation Standard k-ω Transitional turbulence model are applied to investigate non-spiral and spiral blood flow through three dimensional models of arterial stenosis and aneurysm. A spiral pattern of blood flow is thought to have many beneficial effects on hemodynamics. Previous computational studies on spiral blood flow involve only steady spiral flow in a straight stenosed pipe without considering an upstream curved section of the artery. But a spiral pattern in the blood flow may exist due to the presence of an upstream curved section in the artery. On the other hand, pressure is generally considered a constant quantity in studies on pulsatile flow through either arterial stenosis or aneurysm; however, blood pressure is a waveform in a physiological flow. Although cosine-type or smooth regular stenoses are generally taken in investigations of blood flow in a three-dimensional model of arterial stenosis, in reality, stenoses are of irregular shape. Besides stenosis and aneurysm, another abnormal condition of the artery is the presence of stenosis with an adjacent aneurysm in the same arterial segment, especially in the posterior circulation. A study on (steady or pulsatile) flow through such arterial stenosis with an adjacent aneurysm in the same arterial segment is not available so far. Therefore, taking above things into consideration, thorough investigations of steady and unsteady pulsatile non-spiral and spiral blood flow in three-dimensional models of stenosis and aneurysm are needed to give a sound understanding of the transition-to-turbulence of blood flow due to stenosis and aneurysm and to study the the effects of spiral velocity on the transition-to-turbulence. The LES technique has mostly been used to investigate turbulent flow in engineering fields other than bio-fluid mechanics. In the last decade, LES has seen its excellent potential for studying the transition-to-turbulence of physiological flow in bio-fluid mechanics. Though the k-ω Transitional model is used in few instances, mainly LES is applied in this study. Firstly, investigations of steady non-spiral and spiral blood flow through threedimensionalmodels of cosine-type regular stenosed tube without and with upstream curved segment of varying angles of curvature are performed by using the k-ω Transitional model and LES. A fully developed Poiseuille velocity profile for blood is introduced at the inlets of the models. To introduce a spiral effect at the inlet, onesixth of the bulk velocity is taken as the tangential velocity at the inlet along with the axial velocity profile there. Secondly, physiological pulsatile non-spiral and spiral blood flow through a three-dimensional model of a straight tube having cosine-type regular stenosis are investigated by using mainly LES. A two-equation k-ω Transitional model is also used in one non-spiral flow case. The first four harmonics of the Fourier series of pressure pulse are used to generate physiological velocity profiles at the inlet. At the outlet, a pressure waveform is introduced. The effects of percentage of area reduction in the stenosis, length of the stenosis, amplitude of pulsation and Womersley number are also examined. Thirdly, transient pulsatile non-spiral and spiral blood flow through a threedimensional model of irregular stenosis are investigated by applying LES and comparison is drawn between non-spiral flow through a regular stenosis and that through an irregular stenosis. Lastly, pulsatile non-spiral and spiral blood flow through a three-dimensional model of irregular stenosis with an adjacent post-stenotic irregular aneurysm in the same arterial segment are studied by applying LES and the k-ω Transitional model. The effects of variation in spiral velocity are also examined. The results presented in this thesis are analysed with relevant pathophysioloical consequences. In steady flow through the straight stenosed tube, excellent agreement between LES results for Re = 1000 and 2000 and the corresponding experimental results are found when the appropriate inlet perturbations are introduced. In the models with an upstream curved segment, no significant effect of spiral flow on any flow property is found for the investigated Reynolds numbers; spiral pattern disappears before the stenosis – which may be due the rigid wall used in the models and/or a steady flow at the inlet. The effects of the curved upstream model can be seen mainly in the maximum turbulent kinetic energy (TKE), the maximum pressure drop and the maximum wall shear stress (WSS), which in the curved upstream models generally increase significantly compared with the corresponding results in the straight stenosed tube. The maximumcontributions of the SGS motion to the large-scale motion in both non-spiral and spiral flow through a regular stenosis, an irregular stenosis and an irregular stenosis with an adjacent post-stenotic irregular aneurysm are 50%, 55%and 25%, respectively, for the highest Reynolds number investigated in each model. Although the wall pressure and shear stress obtained from the k-ω Transitional model agree quite well with the corresponding LES results, the turbulent results obtained from the k-ω Transitional model differ significantly from the corresponding LES results – this shows unsuitability of the k-ω model for pulsatile flow simulation. Large permanent recirculation regions are observed right after the stenosis throat in both non-spiral and spiral flow, which in the model of a stenosis with an adjacent post-stenotic aneurysm are stretched beyond the aneurysm and the length of the recirculation regions increases with spiral velocity. This study shows that, in both steady and unsteady pulsatile flow through the straight tube model having either a stenosis (regular or irregular) or an irregular stenosis with an adjacent post-stenotic irregular aneurysm, the TKE rises significantly at some locations and phases if a spiral effect is introduced at the inlet of the model. However, the maximum value of the TKE in a high spiral flow drops considerably compared with that in a low spiral flow. The maximum wall pressure drop and shear stress occur around the stenosis throat during all the phases of the pulsatile cycle. In the model of a stenosis only, the wall pressure rises in the immediate post-stenotic region after its drop at the stenosis throat. However, in the model of a stenosis with an adjacent aneurysm, the wall pressure does not rise to regain its undisturbed value before the start of the last quarter of the aneurysm. The effects of the spiral flow on the wall pressure and WSS are visible only in the downstream region where they take oscillatory pattern. The break frequencies of energy spectra for velocity and pressure fluctuations from −5/3 power slope to −10/3 power slope and −7/3 power slope, respectively, are observed in the downstream transition-to-turbulence region in both the non-spiral and spiral flow. At some locations in the transition region, the velocity spectra in the spiral flow has larger inertial subrange region than that in non-spiral flow. The effects of the spiral flow on the pressure spectra is insignificant. Also, the maximum wall pressure drop, the maximum WSS and the maximum TKE in the non-spiral flow through the irregular stenosis rise significantly compared with the corresponding results in the non-spiral flow through the regular stenosis. When the area reduction in the stenosis is increased, the maximum pressure drop, the maximumWSS and the TKE rise sharply. As for the effects of the length of the stenosis, the maximum WSS falls significantly and the maximum TKE rises sharply due to the increase in the length of the stenosis; but the maximum pressure drop is almost unaffected by the increase in the stenosis length.

Life-extension of EDF Energy's existing nuclear fleet is based on an assumption of continued safe operation. Potential fracture of graphite bricks in the nuclear reactor core of a power station represents an unknown variable in the equation. An understanding of the nature of this phenomenon and the impact on operation of the power station is desired. This work prepares the way for the future study of fracture in graphite bricks in a reactor core subject to dynamic excitation. Methodology to couple a multi-body finite element contact code to a crack propagation code is thus developed. Three important scientific contributions have been made: (i) An optimisation problem formulated on a smooth manifold to yield the rotation responsible for infinitesimal rigid body motion. This involves an iterative scheme in the form of Newton's method that takes into account the geometry of the underlying parameter space. There are no issues with singularities or additional computations in each iteration to scale the solution onto the manifold. (ii) An energy consistent crack initiation criterion for brittle material where nucleation is treated as a sudden and discrete rupture event at the macroscopic level. At the heart of the criterion is the finite difference form of the energy release rate; an expression for the characteristic length is derived and the change in total potential energy is obtained from an asymptotic argument involving the topological derivative. The criterion can predict crack onset at a sharp or blunt notch. Fracture toughness and material strength are the only input requirements. (iii) Algorithms related to the detection of sharp notches in a tetrahedral finite element mesh and a general computational procedure for evaluation of non-local crack initiation criteria. The only tool in the implementation of these algorithms is C++11. There is no need for a complex data structure storing all incidence information. Unordered associative containers in the standard library are exploited in the design of these rather efficient algorithms, which cover surface extraction and provide connectivity of the edges representing a sharp notch tip. A mesh re-generation routine for purposes of refinement at the sharp notch tips has also been developed.

The thesis explores the potential of Genetic Algorithms (GAs) for optimising the operation of electric power systems. It discusses methods which have resulted in significant direct cost saving in operating an electric power system. In particular, the thesis demonstrates the simple search procedure and the powerful search ability of Gas in multi-modal, multi-objective problems, which are resisted by the most well known conventional techniques. Special emphasis has been given to the effectiveness of the enhanced genetic based algorithms and the importance of sophisticated problem structures. Finally, the feasibility and suitability of genetic based algorithms for power system optimisations are verified on a real power supply system. The basic requirement in operating a power system is to ensure that the whole system is run at the minimum possible cost, and the lowest possible pollution level, while reliability and security are maintained. These requirements have resulted in a wide range of power system optimisation problems. In this work, a selection of problems concerning operation economy, security and environmental impact have been dealt with by Genetic Algorithms. These problems are in order of increasing complexity as the project progresses: they range from static problems to dynamic problems, single objective to multi-objectives, softly constrained problems to harshly constrained problems, simple problem structure to more rigorous problem structure. Despite the diversity, GAs consistently produce solutions comparable to conventional techniques over the wide range of problem spectrum. It has been clearly demonstrated that a sophisticated problem structure can bring significant financial benefits in system operation, it has however added further complexity to the problem, where the best result may only be sought from the genetic based algorithms. The enhancements of Genetic Algorithms have been investigated with the aim of further improving the quality and speed of the solution. They have been enhanced in two levels: the first is to develop advanced genetic strategies, and this is subsequently refined by choosing optimal parameter values to further improve the strategies. The outcome of the study clearly indicates that genetic based algorithms are very attractive techniques for solving the ever more complicated optimisations of electric power systems. The basic requirement in operating a power system is to ensure that the whole system is run at the minimum possible cost, and the lowest possible pollution level, while reliability and security are maintained. These requirements have resulted in a wide range of power system optimisation problems. In this work, a selection of problems concerning operation economy, security and environmental impact have been dealt with by Genetic Algorithms. These problems are in order of increasing complexity as the project progresses: they range from static problems to dynamic problems, single objective to multi-objectives, softly constrained problems to harshly constrained problems, simple problem structure to more rigorous problem structure. Despite the diversity, GAs consistently produce solutions comparable to conventional techniques over the wide range of problem spectrum. It has been clearly demonstrated that a sophisticated problem structure can bring significant financial benefits in system operation, it has however added further complexity to the problem, where the best result may only be sought from the genetic based algorithms. The enhancements of Genetic Algorithms have been investigated with the aim of further improving the quality and speed of the solution. They have been enhanced in two levels: the first is to develop advanced genetic strategies, and this is subsequently refined by choosing optimal parameter values to further improve the strategies. The outcome of the study clearly indicates that genetic based algorithms are very attractive techniques for solving the ever more complicated optimisations of electric power systems.

The work presented in this thesis develops techniques, employing the Finite Volume discretisation method, which allow the numerical simulation of three dimensional heat transfer and fluid flow problems using unstructured meshes. The method solves and stores all variables at the element centres which lowers storage requirements and generally shortens run times compared with the Control Volume-Finite Element approach. Correction terms are formulated which address two of the main forms of errors caused by mesh skewness. To allow a generic handling of any unstructured mesh the Cartesian components of velocity are solved under all circumstances. This leads to the requirement to adjust the discretisation of the momentum equations when there is significant flow curvature. The changes are presented in this study both when the position of the flow axis is known prior to the simulation and when its position is known only as a result of the simulation, this being the case when there is more than one source of swirling flow. These original features contribute to a Computational Fluid Dynamics code which is capable of solving swirling, turbulent fluid flow and reactive, radiative heat transfer on highly complex geometries. Specifically the techniques are applied to the simulation of processes occurring in the direct smelting of iron. The use of the Finite Volume method makes it relatively easy to employ many techniques and physical models developed for structured codes. The evaluation of the face convective fluxes is effected through the Rhie - Chow interpolation method. The SIMPLE algorithm is used in the pressure - velocity coupling. In the simulation of swirling flows it is shown that both the standard and ReNormalisation Group k-e models fail to accurately predict turbulent effects. An anisotropic hybrid (k-e and mixing length) model is developed which produces excellent numerical results for the flows of interest. The Simple Chemical Reaction Scheme is used to evaluate the transport of the various chemical species. Radiation effects are simulated through the use of the radiosity model. A series of simulation results are presented which show the capabilities of the methods in test cases ranging from simple heat transfer problems through to the simulation of two swirling jets in a three dimensional unstructured mesh.