Numerical models for the simulation of longitudinal and transverse Stokes flow in cylindrical periodic porous media are presented. The models, which are based on a finite-volume formulation in primitive variables, utilize digital image representations of the geometries to simulate, making them particularly well-suited for the rapid automated analysis of creeping flow in porous media with complex morphologies. Complete details of the model formulations are given, including extensive treatment of the pressure boundary conditions at the solid-liquid interface needed to guarantee convergence with all possible geometries. The convergence behavior of both models is tested, and the models are shown to be second-order accurate.The models are used to simulate flow over the whole range of volume fractions of liquid in several regular geometries. The longitudinal model is used to simulate flow in square arrays of circular and square ducts, and both models are used to simulate flow in square and hexagonal arrays of circular cylinders and square arrays of square cylinders rotated by varying amounts. For each of the geometries, accurate empirical expressions for the Darcy permeability as a function of volume fraction solid are presented. Where applicable, model predictions of permeability are compared to existing analytical results.Subsequently, the models are used to simulate Stokes flow in random domains over a wide range of fractions liquid. The sequential random packing algorithm is used to generate 1,000 random packings of circular cylinders at each of 14 fractions of liquid, and longitudinal and transverse flow simulations are performed for each geometry. Histograms and summary statistics are computed for the permeability for each fraction liquid, and empirical expressions for mean permeability as a function of fraction liquid are given. The autocorrelation structure of the geometry and of the fluid velocity is analyzed, and an analysis of the scaling of longitudinal permeability variance is presented. In transverse flow at high packing densities, it is found that lightning-like patterns emerge in the fluid velocity. It is also found that the details of flows in such geometries are strongly sensitive to the placement of individual solid obstacles.

Tidal currents can be used as a predictable source of sustainable energy, and have the potential to make a useful contribution to the energy needs of the UK and other countries with such a resource. One of the technologies which may be used to transform tidal power into mechanical power is a vertical axis turbine, the hydrodynamic analysis of which this thesis is concerned with. The aim of this analysis is to gain a better understanding of the power transformation process, from which position there is the possibility of improving the conversion efficiency. A second aim is to compare the results from different modelling approaches. Two types of mathematical modelling are used: a basic blade element momentum model and a more complex Reynolds-averaged Navier Stokes (RANS) model. The former model has been programmed in Matlab by the present author while the latter model uses a commercial computational fluid dynamics (CFD) code, ANSYS CFX. This RANS model uses the SST k-! turbulence model. The CFD analysis of hydrofoils (equally airfoils), for both fixed and oscillating pitch conditions, is a significant proportion of the present work. Such analysis is used as part of the verification and validation of the CFD model of the turbine. It is also used as input to the blade element momentum model, thereby permitting a novel comparison between the blade element momentum model and the CFD model of the turbine. Both types of turbine model were used to explore the variation in turbine efficiency (and other factors) with tip speed ratio and with and without an angle of attack limiting variable pitch strategy. It is shown that the use of such a variable pitch strategy both increases the peak efficiency and broadens the peak. The comparison of the results from the two different turbine modelling approaches shows that when the present CFD hydrofoil results are used as input to the blade element model, and when dynamic effects are small and the turbine induction factor is low, there is generally good agreement between the two models.

Interface tracking methods for segregated flows such as breaking ocean waves are an important tool in marine engineering. With the development in marine renewable devices increasing and a multitude of other marine flow problems that benefit from the possibility of simulation on computer, the need for accurate free surface solvers capable of solving wave simulations has never been greater. An important component of successfully simulating segregated flow of any type is accurately tracking the position of the separating interface between fluids. It is desirable to represent the interface as a sharp, smooth, continuous entity in simulations. Popular Eulerian interface tracking methods appropriate for segregated flows such as the Marker and Cell Method (MAC) and the Volume of Fluid (VOF) were considered. However these methods have drawbacks with smearing of the interface and high computational costs in 3D simulations being among the most prevalent. This PhD project uses a level set method to implicitly represent an interface. The level set method is a signed distance function capable of both sharp and smooth representations of a free surface. It was found, over time, that the level set function ceases to represent a signed distance due to interaction of local velocity fields. This affects the accuracy to which the level set can represent a fluid interface, leading to mass loss. An advection solver, the Cubic Interpolated Polynomial (CIP) method, is presented and tested for its ability to transport a level set interface around a numerical domain in 2D. An advection problem of the level set function demonstrates the mass loss that can befall the method. To combat this, a process known as reinitialisation can be used to re-distance the level set function between time-steps, maintaining better accuracy. The goal of this PhD project is to present a new numerical gradient approximation that allows for the extension of the reinitialisation method to unstructured numerical grids. A particular focus is the Cartesian cut cell grid method. It allows geometric boundaries of arbitrary complexity to be cut from a regular Cartesian grid, allowing for flexible high quality grid generation with low computational cost. A reinitialisation routine using 1st order gradient approximation is implemented and demonstrated with 1D and 2D test problems. An additional area-conserving constraint is introduced to improve accuracy further. From the results, 1st order gradient approximation is shown to be inadequate for improving the accuracy of the level set method. To obtain higher accuracy and the potential for use on unstructured grids a novel gradient approximation based on a slope limited least squares method, suitable for level set reinitialisation, is developed. The new gradient scheme shows a significant improvement in accuracy when compared with level set reinitialisation methods using a lower order gradient approximation on a structured grid. A short study is conducted to find the optimal parameters for running 2D level set interface tracking and the new reinitialisation method. The details of the steps required to implement the current method on a Cartesian cut cell grid are discussed. Finally, suggestions for future work using the methods demonstrated in the thesis are presented.

This thesis focuses on modelling of wind turbine wakes when they are affected by real complex terrain features, such as hills and forests, and also examines the effect of the rotational momentum imparted to the downstream wake from the rotor blades. Modelling work is carried out using the commercial Computational Fluid Dynamics (CFD) solver FLUENT. Motivation for this project was the fact that there is currently limited knowledge on several issues that affect the operation of a wind farm in a complex terrain environment. Wind developers normally use commercial, easy-to-use software (such as WAsP) to predict the potential wind farm output , which are based on simple linear models to model wakes and wind flow orographic effects and have been calibrated for cases of simple terrain. In cases of complex terrain, they are expected to give errors due to arising non-linearities. After a review of the relevant literature, the chosen CFD procedure is explained. This involves the use of 3-D Reynolds Averaged Navier-Stokes equations using the Reynolds Stress Model for the turbulence closure, in order to account for the anisotropy in atmospheric turbulence. The Virtual Blade Model in FLUENT is demonstrated as a useful tool for modelling the rotor effects without the need of meshing the rotor geometry in detail and avoiding significant computational cost. The approach is initially validated with the widely documented Nibe measurements, which involved full-scale observations of a single wake over at terrain. The model is also tested in the case of a wind turbine operating at the summit of an ideal, Gaussian hill. The wake development is examined in detail and in comparison with another CFD approach. Most notably, a slight divergence is found in the wake path as it evolves downwind. Additionally, the proposed approaches of modelling the neutral atmospheric ow over a real hill and over a forest are validated with full-scale measurements. Ultimately, the work includes the modelling of real wind farms over complex terrain and validating the results with measurements. A coastal complex terrain wind farm is initially examined and results are validated with SCADA measurements and compared with results using the WAsP wind modelling software. Finally, a wind farm over hilly terrain and near forests is also considered and the effect of the forest in the wake is studied. Results are also validated with full-scale measurements.

Atherosclerosis is often diagnosed using an ultrasound (US) examination in the carotid and femoral arteries and the abdominal aorta. A decision to operate requires two measures of disease severity: the degree of stenosis measured using B-mode US; and the blood flow patterns in the artery measured using spectral Doppler US. However other biomechanical factors such as wall shear stress (WSS) and areas of flow recirculation are also important in disease development and rupture. These are estimated using an image-guided modelling approach, where a three-dimensional computational mesh of the artery is simulated. To generate a patient-specific arterial 3D computational mesh, a 3D ultrasound (3DUS) system was developed. This system uses a standard clinical US scanner with an optical position sensor to measure the position of the transducer; a video capture card to record video images from the scanner; and a PC running Stradwin software to reconstruct 3DUS data. The system was characterised using an industry-standard set of calibration phantoms, giving a reconstruction accuracy of ± 0.17 mm with a 12MHz linear array transducer. Artery movements from pulsatile flow were reduced using a retrospective gating technique. The effect of pressure applied to the transducer moving and deforming the artery was reduced using an image-based rigid registration technique. The artery lumen found on each 3DUS image was segmented using a semi-automatic segmentation technique known as ShIRT (the Sheffield Image Registration Toolkit). Arterial scans from healthy volunteers and patients with diagnosed arterial disease were segmented using the technique. The accuracy of the semi-automatic technique was assessed by comparing it to manual segmentation of each artery using a set of segmentation metrics. The mean accuracy of the semi-automatic technique ranged from 85% to 99% and depended on the quality of the images and the complexity of the shape of the lumen. Patient-specific 3D computational artery meshes were created using ShIRT. An idealised mesh was created using key features of the segmented 3DUS scan. This was registered and deformed to the rest of the segmented dataset, producing a mesh that represents the shape of the artery. Meshes created using ShIRT were compared to meshes created using the Rhino solid modelling package. ShIRT produced smoother meshes; Rhino reproduced the shape of arterial disease more accurately. The use of 3DUS with image-guided modelling has the potential to be an effective tool in the diagnosis of atherosclerosis. Simulations using these data reflect in vivo studies of wall shear stress and recirculation in diseased arteries and are comparable with results in the literature created using MRI and other 3DUS systems.

I have carried out three-dimensional numerical simulations of self-gravitating discs to determine under what circumstances they fragment to form bound clumps that may grow into giant planets. Through radiation hydrodynamical simulations using a Smoothed Particle Hydrodynamics code, I find that the disc opacity plays a vital role in determining whether a disc fragments. Specifically, opacities that are smaller than interstellar Rosseland mean values promote fragmentation (even at small radii, R < 25AU) since low opacities allow a disc to cool quickly. This may occur if a disc has a low metallicity or if grain growth has occurred. Given that the standard core accretion model is less likely to form planets in a low metallicity environment, I predict that gravitational instability is the dominant planet formation mechanism in a low metallicity environment. In addition, I find that the presence of stellar irradiation generally acts to inhibit fragmentation (since the discs can only cool to the temperature defined by stellar irradiation). However, fragmentation may occur if the irradiation is sufficiently weak that it allows the disc to attain a low Toomre stability parameter. With specific reference to the HR 8799 planetary system, I find that it is only possible for fragments to form in the radial range where the HR 8799 planets are located (approximately 24-68 AU) if the disc is massive. In such a high mass regime, mass transport occurs in the disc causing the surface mass density to alter. Therefore, fragmentation is not only affected by the disc temperature and cooling, but also by any restructuring due to the gravitational torques. The high mass discs also pose a problem for the formation of this system because the protoplanets accrete from the disc and end up with masses greater than those inferred from observation and thus, the growth of planets would need to be inhibited. In addition, I find that further subsequent fragmentation at small radii also takes place. By way of analytical arguments in combination with hydrodynamical simulations using a parameterised cooling method, I explore the fragmentation criteria which in the past, has placed emphasis on the cooling timescale in units of the orbital timescale, beta. I find that at a given radius the surface mass density (i.e. disc mass and profile) and star mass also play a crucial role in determining whether a disc fragments or not as well as where in the disc fragments form. I find that for shallow surface mass density profiles (p<2, where the surface mass density is proportional to R^{-p}), fragments form in the outer regions of the disc. However for steep surface mass density profiles (p is greater than or similar to 2), fragments form in the inner regions of a disc. In addition, I find that the critical value of the cooling timescale in units of the orbital timescale, beta_crit, found in previous simulations is only applicable to certain disc surface mass density profiles and for particular disc radii and is not a general rule for all discs. I obtain an empirical fragmentation criteria between the cooling timescale in units of the orbital timescale, beta, the surface mass density, the star mass and the radius. Finally, I carry out crucial resolution testing by performing the highest resolution disc simulations to date. My results cast some serious doubts on previous conclusions concerning fragmentation of self-gravitating discs.

Approved for public release, distribution unlimited / Steam leakage from an aircraft carrier catapult is sometimes ingested into the aircraft engines upon launch which may induce compressor stall. Investigation of this phenomenon is of particular interest to the Navy with its new F35C, the aircraft carrier variant of the joint strike fighter. The single engine configuration of the F-35C makes this aircraft particularly vunerable to steam-induced stall. The present study examined both throttle-induced stall and steam-induced stall in a compressor at 90% and 95% speed through the use of 9 Kulite and 2 hot-film pressure transducers. The use of Fast Fourier Transform waterfall plots of the transient data before and during stall proved invaluable in determining stall precursors as well as the mode of rotor stall. In addition, a new computational fluid dynamic model was designed using CFX-5 software to represent a single blade passage of the compressor rotor, in order to predict compressor performance. The computed results were compared to experimental results gathered at various throttle settings. An accurate model will enable researchers to predict compressor performance for various and multiple gases. / Outstanding Thesis

The blood flow through the Bidirectional Glenn shunt (BGS) and modified Blalock-Taussig shunt (mBTS) to the pulmonary arteries (PAs) was analyzed using Computational Fluid Dynamics. This study consisted of the steady and pulsatile cases. In case one, the results of blood flow through the BGS for the Newtonian and non-Newtonian viscosity models were compared. Case two focused on having an additional pulsatile blood flow through the mBTS using the non-Newtonian Carreau viscosity model. The geometries were created based on the angiograms. In case one, boundary conditions to be specified at the inlets were obtained from the flow rate measurements via Doppler flow studies in children and young adults. The averaged velocities were obtained from these flow rates and specified as parabolic velocity profiles at the inlets. The average PA pressures were obtained from the catheterization data and specified at the branches of the PA outlets. In case two, boundary conditions at the same inlets were constant during the cardiac cycle. The pulsatile PA and aortic pressure tracings obtained from the catheterization data were specified at the outlets and mBTS inlet, respectively. A comparison is made between the first and second case results.

<p>This research investigates the forced response of mistuned rotor blades that can lead to excessive vibration, noise, and high cycle fatigue failure in a turbomachine. In particular, an embedded rotor in the Purdue Three-Stage Axial Compressor Research Facility is considered. The prediction of the rotor forced response contains three key elements: the prediction of forcing function, damping, and the effect of frequency mistuning. These computational results are compared with experimental aerodynamic and vibratory response measurements to understand the accuracy of each prediction.</p><p>A state-of-the-art time-marching computational fluid dynamic (CFD) code is used to predict the rotor forcing function. A highly-efficient nonlinear frequency-domain Harmonic Balance CFD code is employed for the prediction of aerodynamic damping. These allow the compressor aerodynamics to be depicted and the tuned rotor response amplitude to be predicted. Frequency mistuning is considered by using two reduced-order models of different levels of fidelity, namely the Fundamental Mistuning Model (FMM) and the Component Mode Mistuning (CMM) methods. This allows a cost-effective method to be identified for mistuning analysis, especially for probabilistic mistuning analysis.</p><p>The first topic of this work concerns the prediction of the forcing function of the embedded rotor due to the periodic passing of the neighboring stators that have the same vane counts. Superposition and decomposition methods are introduced under a linearity assumption, which states that the rotor forcing function comprises of two components that are induced by each neighboring stator, and that these components stay unchanged with only a phase shift with respect to a change in the stator-stator clocking position. It is found that this assumption captures the first-order linear relation, but neglects the secondary nonlinear effect which alters each stator-induced forcing functions with respect to a change in the clocking position.</p><p>The second part of this work presents a comprehensive mistuned forced response prediction of the embedded rotor at a high-frequency (higher-order) mode. Three steady loading conditions are considered. The predicted aerodynamics are in good agreement with experimental measurements in terms of the compressor performance, rotor tip leakage flow, and circumferential distributions of the stator wake and potential fields. Mistuning analyses using FMM and CMM models show that the extremely low-cost FMM model produces very similar predictions to those of CMM. The predicted response is in good agreement with the measured response, especially after taking the uncertainty in the experimentally-determined frequency mistuning into consideration. Experimentally, the characteristics of the mistuned response change considerably with respect to loading. This is not very well predicted, and is attributed to un-identified and un-modeled effects. A significant amplification factor over 1.5 is observed both experimentally and computationally for this higher-order mode.</p> / Dissertation

Numerical simulation allows investigation into the influence of separation distance and rotation on the performance of two vertical-axis hydrokinetic turbines. Compu- tational fluid dynamics is applied to calulate the lift and drag coefficients acting upon interacting NACA 0021 turbine blades for a Reynolds number of Red = 10, 000. To understand the effect of separation distance, large-eddy simulation of the flow around side-by-side and staggered cylinders, ReD = 3,000, and airfoils, Rec = 3,000, are also performed. Based upon the simulations, a drag reduction of 11.3% and 19.8% is determined for the downstream cylinder and airfoil, respectively. A reduction in Reynolds stresses is also observed for the staggered configuration compared to the side-by-side configuration. Due to computational resources of large-eddy simulation, the Reynolds averaged Navier-Stokes method is also applied to investigate the influence of separation distance and rotation on two vertical axis hydrokinetic turbines. The numerical simulations show that a drag reduction of 15.5% occurs when the non-dimensional spanwise and streamwise separation distances, based on turbine diameter, reach 1 and 2, respectively. / October 2016