The non-interacting, nonuniform electron gas exhibits simplifications in two dimensions, that are of particular interest in the application of density functional theory. The results of linear response theory for an attractive impurity in a two-dimensional gas have been shown to be surprisingly accurate even though there are bound states, and were shown to be exact in the high density limit (Zaremba et al. Phys. Rev. B, 71:125323, 2005 and Zaremba et al. Phys. Rev. Lett., 90(4):046801, 2003). The density resulting from linear response theory and the Thomas-Fermi approximation coincide in the high density limit. As an alternative to linear response theory, the Kirzhnits gradient expansion gives corrections to Thomas-Fermi in gradients of the potential. In two dimensions, all of the gradient corrections vanish at zero temperature, which is a new result presented in this work. We have performed numerical calculations which show that while Thomas-Fermi appears to be a surprisingly accurate approximation in two dimensions, it is not exact. The differences between two and three dimensions that lead to the vanishing of the gradient corrections, however, are of great interest since these may lead to better understanding and simplifications of the corresponding three-dimensional problem. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2007-11-07 09:47:00.316

In this thesis, large-eddy simulation (LES) is used to simulate both Newtonian and non-Newtonian physiological pulsatile flows in constricted channels to gain insights into the physical phenomenon of laminar-turbulent flow transition due to the presence of an artificial arterial stenosis. The advanced dynamic nonlinear subgrid-scale stress (SGS) model of Wang and Bergstrom (DNM) was utilized to conduct numerical simulations and its predictive performance was examined in comparison with that of the conventional dynamic model (DM) of Lilly. An in-house LES code has been modified to conduct the unsteady numerical simulations, and the results obtained have been validated against available experimental and direct numerical simulation (DNS) results. The physical characteristics of the flow field have been thoroughly studied in terms of the resolved mean velocity, turbulence kinetic energy, viscous wall shear stress, and turbulence energy spectra along the central streamline of the domain.

In this thesis, large-eddy simulation (LES) is used to simulate both Newtonian and non-Newtonian physiological pulsatile flows in constricted channels to gain insights into the physical phenomenon of laminar-turbulent flow transition due to the presence of an artificial arterial stenosis. The advanced dynamic nonlinear subgrid-scale stress (SGS) model of Wang and Bergstrom (DNM) was utilized to conduct numerical simulations and its predictive performance was examined in comparison with that of the conventional dynamic model (DM) of Lilly. An in-house LES code has been modified to conduct the unsteady numerical simulations, and the results obtained have been validated against available experimental and direct numerical simulation (DNS) results. The physical characteristics of the flow field have been thoroughly studied in terms of the resolved mean velocity, turbulence kinetic energy, viscous wall shear stress, and turbulence energy spectra along the central streamline of the domain.

Extensive use of stirred vessels in the process industries for various operations has attracted researchers to study the mixing mechanisms and its effects on the processes. Among the various flow-measuring methods, Particle Image Velocimetry (PlV) technique has become more popular in comparison to LDA and HW A methods because of its ability to provide instantaneous velocity fields. The present study uses this technique to investigate the flowfields and turbulent properties in a 290mm vessel stirred by Rushton Disc turbine (RDT) and Pitched blade turbine (PBT) impellers. Angle-resolved instantaneous flow-fields were obtained using 2-D and 3-D PlV technique. Flows in the RDT were examined. The distribution of out-of-plane vorticity and turbulent properties such as rms velocities, Reynolds stresses and turbulent kinetic energy was discussed. The flow number and power number of the RDT impeller were obtained as 0.83 and 5.16 respectively. Flows generated by the PBT impeller were examined in more detail. For this purpose, a multiblock approach was developed which allowed analysing larger fields of view with reasonably higher resolution. Whole vessel was thus mapped and various turbulent properties were examined. The mean flow-fields, out-of-plane vorticity and turbulent properties such as Reynolds stresses, turbulent kinetic energy and turbulent energy dissipation rates were estimated at different angle of blade rotation. The variation of the trailing vortex axis was obtained. The pumping number and power number ofPBT impeller was obtained as 0.86 and 1.52 respectively. Using this information, an integral length scales were estimated using 2-D FFT autocorrelation, which showed that these length scales vary significantly through out the vessel. It is demonstrated that assuming constant length scale through out the vessel could underestimate dissipation rate up to 25% in the impeller discharge. A kinetic energy balance was carried out around the PBT blades. It is shown that around 44% of the total power consumed by the impeller is dissipated within the impeller. The average rate of dissipation of kinetic energy was 39 times higher in the impeller region than the average dissipation rate in the vessel. Using LDA and PIV techniques, macro-instabilities (Ml) were studied. Spectral analysis was done using LOMB algorithm, which showed the presence of a dimensionless frequency of O.013-0.0174N in the RDT and PBT impellers. The frequency of Ml varied linearly with the impeller speed. The maximum broadening of turbulence levels due to the presence of Ml was around 20% for the PBT and 18% for the RDT impeller. The effect of mixing on the feed locations was studied using PlV measurements. Results showed that there is no direct effect of feed coming out of the feed pipe on the flow distribution, however, due to feed pipe, there was a wake formation close to the feed pipe. The low Reynolds number in the wake can affect local mixing conditions close to the feed pipe. At the end, angle-resolved Reynolds stresses were calculated and was noticed that flows in the vessel were isotropic in the bulk of the vessel however, anisotropic flow was noticed in the impeller stream.

Thesis (Ph.D.); Submitted to Old Dominion Univ., Norfolk, VA (US); 1 May 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "JLAB-PHY-03-36" "DOE/ER/40150-2739" Rustam Niyazov. 05/01/2003. Report is also available in paper and microfiche from NTIS.

The work was concerned with the design, analysis and basic demonstration of a novel hydraulically assisted fixed geometry turbocharger system intended to help overcome some of the transient issues associated with current automotive boosting technologies. The novel system was based upon use of relatively lightweight parts, where kinetic energy is recovered during vehicle braking, stored in a simple hydraulic accumulator and then used later on to rapidly accelerate the engine's turbocharger. The turbocharger is fitted with a replacement centre housing enclosing a small impulse turbine, rigidly mounted to the turbocharger shaft and powered by a jet of oil. The aim is one of helping the engine to accelerate the vehicle while operating in a region of much higher brake efficiency due to the reduction in exhaust backpressure when compared with competing variable geometry and/or compound boosting technologies. The specific tasks involved concept design and computational analysis, including specification of the turbine type and geometry together with the associated hydraulic parts. A production turbocharger was reverse engineered to confirm the feasibility of packaging the hydraulic turbine system into the centre housing of a typical fixed geometry design. Finally an experimental rig was designed and manufactured to allow basic demonstration of the system, with speeds of up to ~90000 rpm @ 200 bar pressure from the pump via the accumulator achieved in ~0.8 seconds and clear potential for further optimisation. This hydraulic boosting system is capable of attaining 70% efficiency (a product of 0.85 from the oil pump, 0.95 from the hydraulic accumulator and 0.88 of Pelton wheel). The system has higher power density at low cost compared to the main competitor ‘E Boosting - with efficiency in the region of 90%’. The cost of E boosting and need for 48 volt battery makes it less favourable compared to the hydraulic turbine system. The concept has been shown to offer significant potential to assist a turbocharger to spool up via a Novel Hydraulic Kinetic Energy Recovery System approach.

The air hybrid engine absorbs the vehicle kinetic energy during braking, stores it in an air tank in the form of compressed air, and reuses it to start the engine and to propel a vehicle during cruising and acceleration. Capturing, storing and reusing this braking energy to achieve stop-start operation and to give additional power can therefore improve fuel economy, particularly in cities and urban areas where the traffic conditions involve many stops and starts. In order to reuse the residual kinetic energy, the vehicle operation consists of 3 basic modes, i.e. Compression Mode (CM), Expander Mode (EM) and normal firing mode, as well as stop-start operation through an air starter. A four-cylinder 2 litre diesel engine has been modelled to operate in four air hybrid engine configurations so that the braking and motoring performance of each configuration could be studied. These air hybrid systems can be constructed with production technologies and incur minimum changes to the existing engine design. The regenerative engine braking and starting capability is realised through the employment of an innovative simple one-way intake system and a production cam profile switching (CPS) mechanism. The hybrid systems will allow the engine to be cranked by the compressed air at moderate pressure without using addition starters or dedicated valves in the cylinder head. Therefore, the proposed air hybrid engine systems can be considered as a cost-effective regenerative hybrid powertrain and can be implemented in vehicles using existing production technologies. A novel cost-effective pneumatic regenerative stop-start hybrid system, Regenerative Engine Braking Device (RegenEBD), for buses and commercial vehicles is presented. RegenEBD is capable of converting kinetic energy into pneumatic energy in the compressed air saved in an air tank using a production engine braking device and other production type automotive components and a proprietary intake system design. The compressed air is then used to drive an air starter to achieve regenerative stop-start operations. The proposed hybrid system can work with the existing vehicle transmission system and can be implemented with the retro-fitted valve actuation device and a sandwich block mounted between the cylinder head and the production intake manifold. Compression mode operation is achieved by keeping the intake valves from fully closed throughout the four-strokes through a production type variable valve exhaust brake (VVEB) device on the intake valves. As a result, the induced air could be compressed through the opening gap of intake valves into the air tank through the intake system of proprietary design. The compressed air can then be used to crank the engine directly through the air expander operation or indirectly through the action of an air starter in production. A single cylinder camless engine has been set up and operated to evaluate the compression mode performance of two air hybrid concepts. The experimental results are then compared with the computational output with excellent agreement. In order to evaluate the potential of the air hybrid engine technologies, a new vehicle driving cycle simulation program has been developed using Matlab Simulink. An air hybrid engine sub-model and methodology for modelling the air hybrid engine’s performance have been proposed and implemented in the vehicle driving cycle simulation. The NEDC analysis of a Ford Mondeo vehicle shows that the vehicle can achieve regenerative stop-start operations throughout the driving cycle when it is powered by a 2.0litre diesel engine with air hybrid operation using a 40litre air tank of less than 10bar pressure. The regenerative stop-start operation can lead to 4.5% fuel saving during the NEDC. Finally, the Millbrook London Transport Bus (MLTB) driving cycle has been used to analyse the effectiveness of RegenEBD on a double deck bus powered by a Yuchai diesel engine. The results show that 90% stop-starts during the MLTB can be accomplished by RegenEBD and that a significant fuel saving of 6.5% can be obtained from the regenerative stop-start operations.

In a wide range of industries, machine condition monitoring is one of the most cost effective ways to minimise maintenance efforts and machine downtime. To implement such a system, wireless solutions have increasingly become an attractive proposition due to the ease of installation and minimal infrastructure alternation. However, currently most wireless sensors in the world are powered by a finite battery source. The dependence of batteries not only requires frequent maintenance, but also has adverse environmental consequences associated with battery disposal. These reasons render massive deployment of wireless sensors in the industry problematic. With the advances in semiconductors, power consumption of wireless sensors has been continuously decreasing. It is an inevitable trend for self-powered wireless sensors to emerge and become the norm for machine and environmental monitoring. In this research, vibration is chosen to be the energy source to enable self-powered wireless sensors due to its ubiquitousness in machinery and industrial environments. As a result of relying on resonance, the biggest challenge for vibration-based energy harvesters is their narrow bandwidth. Even a small deviation of the vibration frequency can dramatically reduce the power output. The primary goal of this research is to address this problem. In particular, Piezoelectric generators are identified to be the most suitable technology. In this work, extensive theoretical and experimental studies are conducted in single mass and multi-modal harvesters, and in resonance tuning harvesters by modulus and impedance matching as well as by mechanical actuation. Mathematical modelling plays a significant role in energy harvester designs. A dynamic model that generalises the single degree of freedom models and the continuum models is derived and validated by experiments. The model serves as the building block for the whole research, and it is further refined for the investigation of modulus and impedance matching. In the study of multi-modal harvesters, a continuum model for double-mass piezoelectric cantilever beams is derived and experimentally validated. To study the feasibility of resonance tuning by mechanical means, prototypes were built and performance evaluated. This document details the theoretical basis, concepts and experimental results that extend the current knowledge in the field of energy harvesting. This research work, being highly industrially focused, is believed to be a very significant step forward to a commercial energy harvester that works for a wide range of vibration frequencies.

This thesis investigates the computation of invariance kernels for planar nonlinear systems with one input, with application to wind turbine stability. Given a known bound on the absolute value of the input variations (possibly around a fixed non-zero value), it is of interest to determine if the system's state can be guaranteed to stay within a desired region K of the state space irrespective of the input variations. The collection of all initial conditions for which trajectories will never exit K irrespective of input variations is called the invariance kernel. This thesis develops theory to characterize the boundary of the invariance kernel and develops an algorithm to compute the exact boundary of the invariance kernel. The algorithm is applied to two simplified wind turbine systems that tap kinetic energy of the turbine to support the frequency of the grid. One system provides power smoothing, and the other provides inertial response. For these models, limits on speed and torque specify a desired region of operation K in the state space, while the wind is represented as a bounded input. The theory developed in the thesis makes it possible to define a measure called the wind disturbance margin. This measure quantifies the largest range of wind variations under which the specified type of grid support may be provided. The wind disturbance margin quantifies how the exploitation of kinetic energy reduces a turbine's tolerance to wind disturbances. The improvement in power smoothing and inertial response made available by the increased speed range of a full converter-interfaced turbine is quantified as an example.

Following successful implementation of inerters for passive mechanical control in racing cars, this research studies potential innovative solutions for railway vehicle suspensions by bringing the inerter concept to the design of mechatronic systems. The inerter is a kinetic energy storage device which reacts to relative accelerations; together with springs and dampers, it can implement a range of mechanical networks distinguished by their frequency characteristics. This thesis investigates advantages of inerter-based novel devices to simplify the design of active solutions. Most of the research work is devoted to the enhancement of vertical ride quality; integrated active-plus-novel-passive solutions are proposed for the secondary suspensions. These are defined by different active control strategies and passive configurations including inerters. By optimisation of the suspension parameters, a synergy between passive and active configurations is demonstrated for a range of ride quality conditions. The evidence of cooperative work is found in the reduction of the required active forces and suspension travelling. This reveals a potential for reducing the actuator size. Benefits on power requirements and actuator dynamic compensation were also identified. One of the strategies features a nonlinear control law proposed here to compensate for 'sky-hook' damping effects on suspension deflection; this, together with inerter-based devices attains up to 50% in active force reduction for a setting providing 30% of ride quality enhancement. The study is developed from both, an analytical and an engineering perspective. Validation of the results with a more sophisticated model is performed. The lateral stability problem was briefly considered towards the end of the investigation. A potential use of inerter-based devices to replace the static yaw stiffness by dynamic characteristics was identified. This leads to a synergy with 'absolute stiffness', an active stability solution for controlling the wheelset 'hunting' problem, for reducing the creep forces developed during curve negotiation.