PETROBRAS / O presente trabalho contempla a análise do desenvolvimento de filme de líquido em escoamento ascendente sob a ação dos campos centrífugo e gravitacional, localizado em uma câmara ciclônica de um sistema de distribuição. No estudo foi analisada a dinâmica de um escoamento bifásico líquido-gás a partir de simulações numéricas, tridimensionais e transientes. Na modelagem numérica do escoamento foi utilizado o modelo de dois fluidos euleriano-euleriano junto com o esquema compressivo para a captura da interface líquido-gás e o modelo de turbulência SST (Shear Stress Transport). As equações de balanço foram discretizadas utilizado o método dos volumes finitos baseados em elementos finitos. As simulações numéricas foram realizadas no software comercial ANSYS-CFX 15.0. O modelo numérico desenvolvido foi validado com base em dados experimentais fornecidos pelo NUEM (Núcleo de Escoamento Multifásico). Os resultados obtidos neste trabalho possibilitaram o entendimento da dinâmica do escoamento (formação, espalhamento, estabilidade e desenvolvimento) e como a variação das velocidades superficiais do líquido e do gás (0,5; 1,0; 1,5 e 2,0 m/s para ambas as fases) influenciam na estabilidade e no comportamento do escoamento de filme de líquido ascendente. Foi elaborado ainda um modelo matemático capaz de fornecer condições de comportamento médio de um escoamento no padrão golfadas para os casos analisados. / Flows with free surface compose an important class of two-phase flows in the fluids mechanics. In various applications a thin film of liquid builds up on horizontal or vertical surfaces. This type of flow is denominated as liquid film flow. The present work contemplates the analysis of the development of liquid film in ascendant flow under the action of the centrifugal and gravitational fields, located in a cyclonic chamber of a distribution system. In the study, the dynamics of a liquid film flow were analyzed with the aid of three-dimensional and transient numerical simulations. The numerical model developed was validated based on experimental data provided by NUEM (Centre for Multiphase Flows). In the numerical modeling of the flow, were used the EulerianEulerian two fluid model coupled with the compressive discretization scheme for the capture of the liquid-gas interface and the Shear Stress Transport turbulence model. The balance equations were discretized using the finite volume based on finite elements method. Numerical simulations were supported by the commercial software ANSYS-CFX 15.0. The results obtained in this work enabled the understanding of flow dynamics (formation, spreading, stability and development) and how the superficial velocities of liquid and gas (0.5, 1.0, 1.5 and 2.0 m/s for both phases) influence on the stability and behavior of the ascendant liquid film flow. A mathematical model capable of providing conditions that represent the average behavior of a slug flow pattern was also elaborate.

In a nuclear fuel cask, the heat generating spent fuel rods are packed in a housing and the resulting bundle is placed inside a cask of thick outer shell made of materials like lead or concrete. The cask presents a wide variation in geometrical dimensions ranging from the diameter of the rods to the diameter of the cask. To make the problem tractable, first the heat generating rod bundle alone is considered for analysis and the effective thermal conductance of the bundle is correlated in terms of the relevant parameters. In the second part, the bundle is represented as a solid of equivalent thermal conductance and the attention is focused on the modelling of the cask. The first part, dealing with the effective thermal conductance is solved using Fluent software, considering coupled conduction, natural convection and surface radiation in the heat generating rod bundle encased in a hexagonal sheath. Helium, argon, air and nitrogen are considered as working media inside the bundle. A correlation is obtained for the critical Rayleigh number which signifies the onset of natural convection. A correlation is also developed for the effective thermal conductance of the bundle, considering all the modes of transport, in terms of the maximum temperature in the rod bundle, pitch-to-diameter ratio, bundle dimension (or number of rods), heat generation rate and the sheath temperature. The correlation covers pitch-to-diameter ratios in the range 1.1-2, number of rods ranging from 19 to 217 and the heat generation rates encountered in practical applications. The second part deals with the heat transfer modeling of the cask with the bundle represented as a solid of effective (or equivalent) thermal conductance. The mathematical model describes two-dimensional conjugate natural convection and its interaction with surface radiation in the cask. Both Boussinesq and non-Boussinesq formulations have been considered for convection. Numerical solutions are obtained on a staggered mesh with a pressure correction method using a custom-made Fortran code. The surface radiation is coupled to the conduction and convection at the solid-fluid interfaces. Steady-state results are obtained using time-marching. Results for various quantities of interest, namely, the flow and temperature distributions, Nusselt numbers, and interface temperatures, are presented. The Grashof number based on the volumetric heat generation and gap width is varied from 105 to 5 ×109. The emissivities of the interfaces are varied from 0.2-0.8 for the radiative calculations. The solid-to-fluid thermal conductivity ratio for the inner cylinder is varied in the range 5-20 in the parametric studies. Simulations are also performed with thermal conductivity calculated in an iterative manner from bundle parameters. The dimensionless outer wall conductivity ratio is chosen to correspond to cask walls made of lead or concrete. The dimensionless thickness (with respect to gap width) of the outer shell is in the range of 0.0825-1, while the inner cylinder dimensionless radius is 0.2. Air is the working medium in the cask for which the Prandtl number is 0.71. Correlations are obtained for the average temperatures and Nusselt numbers at the inner interface in terms of the parameters. The radiation heat transfer is found to contribute significantly to the heat dissipation.

No description available.

In the present work, two phase reacting flow in a single cavity Trapped Vortex Combustor (TVC) is studied at atmospheric conditions. KIVA-3V, numerical program for simulating three dimensional compressible reacting flows with sprays using Lagrangian-Drop Eulerian-fluid procedure is used. The stochastic discrete droplet model is used for simulating the liquid spray. In each computational cell, it is assumed that the volume occupied by the liquid phase is very small. But this assumption of very low liquid volume fraction in a computational cell is violated in the region close to the injection nozzle. This introduces grid dependence in predictions of liquid phase in the region close to the nozzle in droplet collision algorithm, and in momentum coupling between the liquid and the gas phase. Improvements are identified to reduce grid dependence of these algorithms and corresponding changes are made in the standard KIVA-3V models. Pressure swirl injector which produces hollow cone spray is used in the current study along with kerosene as the liquid fuel. Modifications needed for modelling pressure swirl atomiser are implemented. The Taylor Analogy Breakup (TAB) model, the standard model for predicting secondary breakup is improved with modifications required for low pressure injectors. The pressure swirl injector model along with the improvements is validated using experimental data for kerosene spray from the literature. Simulations of two phase reacting flow in a single cavity TVC are performed and the temperature distribution within the combustor is studied. In order to identify an optimum configuration with liquid fuel combustion, the following parameters related to fuel and air such as cavity fuel injection location, cavity air injection location, Sauter Mean Diameter (SMD) of injected fuel droplets, velocity of the fuel injected are studied in detail in order to understand the effect of these parameters on combustion characteristics of a single cavity TVC.

The research topic of liquid drop interaction with solid surfaces is being actively pursued to gain in-depth understanding of several practical cases such as the impingement of fuel spray droplets on surfaces like combustion chamber walls and piston top of an I.C. engine, heat transfer via spray impingement, ink-jet printing, etc. In most of the cases, the physical and flow properties of the liquid drop/spray may be fixed whereas it may be possible to tune the physical and chemical properties of the solid surface thereby enabling to control the interaction process. The present work belongs to the study of liquid drop-solid surface interaction process with special focus on the physical characteristics of solid surface. The thesis reports an experimental study of the dynamics of millimetric water drops impacted onto the junction of dual-textured substrates made of stainless steel. The dual-textured substrates consisted of hydrophobic (textured) and hydrophilic (smooth) portions. The entire textured portion comprised of parallel groove-like structures separated by solid posts/pillars. Two dual-textured substrates, which differ only in the geometry of their textured portions, were employed. Surface topography features of the dual-textured substrates were characterized using scanning electron microscopy (SEM) and optical surface profilometer. The wetting behavior of the textured and smooth portions of the substrates, quantified in terms of the equilibrium, advancing, and receding contact angles adopted by a water drop on the surface portions, was characterized experimentally through the methods of sessile drop formation, captive needle volume addition, and drop evaporation under ambient conditions. Free-falling water drops were impacted from a height onto the junction between the hydrophobic (textured) and hydrophilic (smooth) portions of the dual-textured substrates. A set of twelve different impact experiments were conducted on each of the target substrates with drop impact velocity (Uo) ranging from 0.37 to 1.50 m/sec. The dynamics of drop impact were captured using a high speed camera with frame rate ranging from 3000 to 10000 frames per second. From the captured frames, the temporal variations of the impacting drop parameters were measured using a MATLAB-assisted program. A systematic analysis of experimental data revealed the existence of four distinct regimes of drop dynamics on the dual-textured substrate: (a) early inertia driven drop spreading, (b) primary drop receding, (c) secondary spreading on the hydrophilic portion, and (d) final equilibrium regimes. It is shown that the drop impact dynamics during the early inertia driven impact regime remains unaffected by the dual-texture feature of the substrate. A larger retraction speed of impacting drop liquid observed on the hydrophobic portion of the substrate makes the drop liquid on the higher wettability/hydrophilic portion to advance further (secondary drop spreading). The net horizontal drop velocity towards the hydrophilic portion of the dual-textured substrate decreases with increasing drop impact velocity. The available experimental results suggest that the movement of bulk drop liquid away from the impact point during drop impact on the dual-textured substrate is larger for the impact of low inertia drops. A semi-empirical model, based on the balance of the wettability gradient, contact angle hysteresis, and viscous forces acting on impacted drop liquid on the substrate, is formulated to predict the movement of bulk drop liquid away from the impact point (ξ). A satisfactory comparison between the model predictions and the experimental measurements is reported for the variation of ξ with Uo.

Atomization characteristics of liquid fuel sprays control combustion efficiency and emissions in engines. The present work is motivated by the need to study the atomization and spray structure of vegetable oil biofuels for which no data in the literature exists. In this work, various laser-based diagnostic techniques such as laser shadowgraphy, Particle/Droplet Image Analysis (PDIA) and Laser Sheet Dropsizing (LSD) are applied for studying atomization characteristics, tip penetration, droplet size and liquid volume fraction of Pongamia vegetable oil (SVO) and its blends with diesel. A constant volume high pressure spray visualization chamber is designed and fabricated to study SVO sprays at high gas pressure and temperature conditions. This optical chamber can be used for gas pressures up to 60 bar and temperatures up to 600 K. Optical access inside the chamber is provided through four quartz windows to perform various optical spray diagnostic studies. A high pressure spray injection facility based on components of common rail diesel injection system is designed. This facility can provide an injection pressure of up to 1700 bar with independent control over injection duration and timing. A marked difference is observed between diesel and SVO spray structures under atmospheric gas pressure condition. A very interesting observation related to the behavior of 100% SVO fuel when sprayed into atmospheric pressure is the presence of an intact liquid core even at injection pressure as high as 1600 bar. The presence of liquid core at high injection pressures is attributed to the high viscosity of SVOs and the non-Newtonian behavior of these oils under high pressure and shear. The spray characterization of the oil and its blends at high gas pressure shows that although the atomization is dramatically different from that at atmospheric gas pressure, it is still incomplete even at very high injection pressures. For a gas pressure of 30 bar, it is observed that the Sauter Mean Diameter (SMD) for Pongamia oil is more than twice that of diesel. A new method of simultaneously obtaining two-dimensional droplet size and quantitative liquid volume fraction data in sprays has been developed. Measurements with this method reveal a higher liquid volume fraction at the central axis of spray for Pongamia oil compared to that of diesel indicating potentially poor air-fuel mixing. The experimental data obtained and the spray tip penetration correlations developed for the vegetable oils and blends serve as useful inputs for fuel injection and engine system designers.

The internal combustion engine is synonyms with the automobile since its invention in late 19th century. The internal combustion engine today is far more advanced and efficient compared to its early predecessors. An intense competition exists today amongst the automotive OEMs in various countries and regions for stepping up sales and increasing market share. The pressure on automotive OEMs to reduce fuel consumption and emission is enormous which has lead to innovations of many variations in engine and engine-related technologies. However, IC engines are in existence for well more than a century and hence have already evolved to a highly refined state. Changes in IC engine are therefore largely incremental in nature. A deterrent towards development of an engine configuration that is significantly different from its predecessor is the phenomenal cost involved in prototyping. Thus, the only viable alternative in exploring new engine concepts and even optimizing designs currently in operation is through extensive use of CAE. In light of published work in the field of analysis of IC engines, current research effort is directed towards development of a rational methodology for arriving at a weight-optimized engine design, which simultaneously meets performance of various attributes such as thermal, durability, vehicle dynamics and NVH. This is in contrast to the current methodology adopted in industry, according to which separate teams work on aspects of engine design such as combustion, NVH (Noise, Vibration and Harshness), acoustics, dynamics, heat transfer and durability. Because of the involvement of heterogeneous product development groups, optimization of an engine for weight, which can have a significant impact on its power-to-weight ratio, becomes a slow process beset with manual interventions and compromise solutions. Thus, following the traditional approach, it is quite difficult to claim that an unambiguous weight-optimized design has been achieved. As a departure from the practiced approach, the present research effort is directed at the deployment of a single multi-physics explicit analysis solver, viz. LS-DYNA - generally known for its contact-impact analysis capabilities, for simultaneously evaluating a given engine design for heat transfer, mechanical and thermal loading, and vibration. It may be mentioned that only combustion analysis is carried out in an uncoupled manner, using proven phenomenological thermodynamic relations, to initially arrive at mechanical and thermal loading/boundary conditions for the coupled thermo-mechanical analysis. The proposed methodology can thus be termed as a semi-integrated technique and its efficacy is established with the case study of designing a single cylinder air-cooled diesel engine from scratch and its optimization.

Soot is a carbonaceous materials produced as a result of incomplete combustion of fuels (gasoline, diesel, etc). At the present level of automobile technology, emission of soot from combustion in diesel engine appears to be an inevitability. The disadvantage in the diesel combustion is that it is not homogeneous throughout the cylinder. So the fuel-air ratio cannot be maintained constant throughout the flame zone and hence rich combustion zone leads to the formation of soot. Diesel engine combustion processes produce a large amount of soot, which is one of the major pollutant emissions of the exhaust systems. The fraction of combustion particulate, which is soot, is often estimated by finding the insoluble portion of the particulate. Hydrocarbons or other available molecules may also condense on or beads orbed by soot depending on the surrounding conditions. Other particulate matter constituents include partially burned fuel/lubricant oil bound water, wear metal and fuel derived sulfate. In diesel engine lubrication, soot has long been recognized as the major contaminant that is detrimental to engine lubrication, particularly in friction and wear. Different techniques for soot abatement have been investigated by researchers from the field of combustion and fuel. In spite of the large numbers of investigations of soot formation conducted till date, there is relatively little quantitative information is available about the mechanisms and governing rate processes. Some of the studies focused on the combustion chemistry of soot formation while some emphasized on engine design. On the other hand comparatively a few research works are coming out from the tribological point of view. Considering that internal combustion engines play such an important role in industry, investigative research of the parametric influences of particle size, agglomeration, oil viscosity, additives and surfactant as well as chemistry and electrical properties of particles on wear as well as into the wear mechanisms have not perhaps been as extensive as it is detrimental. Existence of a large numbers of variables in tribological contacts makes the situation very complex and difficult to analyze it quantitatively. In this complex scenario, where many opposed effects are playing their roles in soot tribology, the influence of the physical, structural and mechanical properties of soot on engine tribology has limited attention. We focus our study on one of the end effects of engine soot; friction and wear of the engine components. Since a diesel engine is not particularly suitable for use in a laboratory study of the fundamental processes and parameters of combustion due to its inherent difficulties on control and safety as well as data analysis uncertainty, so the most useful studies of soot fundamentals have emerged from studies of processes which have used simplified environments such as diffusion flames. We focus on soot tribology in steel-on-steel interaction in the presence of soot material suspended in relatively simple paraffinic hydrocarbons, hexadecane; with and without an additive. The physical, structural, chemical and mechanical properties of the particle and their changes as a function of tribological parameters are monitored throughout this study. Three type of soot are used in this work. Firstly, commercial grade carbon blacks has been used as soot simulant. Secondly, to enable controlled variations of the physical, mechanical, chemical and geometrical parameters of the particles, soot is generated in-situ by burning ethylene gas and the particles are extracted thermophoretically from different thermal zones of the flame. Thirdly, to establish the validity of the study, two types of diesel soots are extracted from an engine and studied. The objective is to use such an understanding to elucidate the basic mechanisms of friction and wear in the presence of soot which may limit the performance of a diesel engine. From our study we find that these soots have widely different morphologies, crystallographic orders and reactivity. At tribological contact the soot agglomerates fragment to primary level particles. The physical and chemical properties of such particles determine the friction between and wear of mating components. If the soot is strongly graphitic, the friction and wear are moderate. If the soot is made of chemically active organic groups, the friction and wear are high. The hardness, friction and resistance to material removal of the soot collected near the flame tip and diesel soot are found to be high compared to the other types of soot. Besides, the high hardness, irregular primary particle shape, large inter-particle adhesion leading to agglomeration and more abrasive nature of diesel soot influence the metal wear adversely. This trend of soot tribology is profound when these soots are suitably dispersed in the oil by the addition of dispersants, in our case it is polyisobutylene succinimide. Different functional groups present on the soot surface play important role in defining the interaction between surrounding medium and contacts which, in turn define the contact conditions, particle/agglomerate behavior and soot tribology. Finally, agglomeration is simulated using the features of a dissipative particle dynamics package as the simulation technique. Simulations are performed on a sizeable number of particles to observe agglomeration behavior, on simple environment, in future which can be further extended.

In-cylinder fuel-air mixing in a compressed natural gas (CNG)-fuelled, single-cylinder, spark-ignited engine is analysed using a transient three-dimensional computational fluid dynamic model built and run using STAR-CD, a commercial CFD software. This work is motivated by the need for strategies to achieve improved performance in engines utilizing gaseous fuels such as CNG. The transient in-cylinder fuel-air mixing is evaluated for a port gas injection fuelling system and compared with that of conventional gas carburetor system. In this work pure methane is used as gaseous fuel for all the computational studies. It is observed that compared to the premixed gas carburetor system, a substantial level of in-cylinder stratification can be achieved with the port gas injection system. The difference of more than 20% in mass fraction between the rich and lean zones in the combustion chamber is observed for the port gas injection system compared to less than 1% for the conventional premixed system. The phenomenon of stratification observed is very close to the “barrel stratification” mode. A detailed parametric study is undertaken to understand the effect of various injection parameters such as injection location, injection orientation, start of injection, duration of injection and rate of injection. Furthermore, the optimum injection timing is evaluated for various load-speed conditions of the engine. It is also observed that the level of stratification is highest at 50% engine load with a reduced level at 100% load. For low engine loads, the level of stratification is observed to be very low. To analyse the effect of stratification on engine performance, the in-cylinder combustion is modeled using the extended coherent flame model(ECFM). For simulating the ignition process, the arc and kernel tracking ignition model(AKTIM) is used. The combustion model is first validated with measured in-cylinder pressure data and other derived quantities such as heat release rate and mass burn fraction. It is observed that there is a good agreement between measured and simulated values. Subsequently, this model is use to simulate both premixed and stratified cases. It is observed that there is a marginal improvement in terms of overall engine efficiency when the stoichiometric premixed case is compared with the lean stratified condition. However, a major improvement in performance is observed when the lean stratified case is compared with lean premixed condition. The stratified case shows a faster heat release rate which could potentially translate to lower cycle-to-cycle variations in actual engine operation. Also, the stratified cases show as much as 20% lower in-cylinder NOx emissions when compared with the conventional premixed case at the same engine load and speed, underscoring the potential of in-cylinder stratification to achieve improved performance and lower NOx emissions.

Multilevel converters are finding increased attention in industry and academia as the preferred choice of electronic power conversion for high power applications. They have a wide application area in a variety of industries involving transportation and energy management, a significant portion of which comprises of multilevel inverter fed induction motor drives. Multilevel inverters are ideally suitable for high power drives, since the switching frequency of the devices is limited for high power applications. In low power drives, the switching frequency is often in the range of tens of kHz, so that switching frequency harmonics are pushed higher in the frequency spectrum thereby the size and cost of the filter are reduced. But higher switching frequency has its own drawbacks, in particular for high voltage, high power applications. They cause large dv/dt stress on the motor and the devices, increased EMI problems and higher switching losses. An engineering trade-o is thus needed to select the minimum switching frequency without compromising on the output voltage quality. The present work is an alternate approach in this direction. Here, new inverter topologies and PWM strategies are developed that can eliminate a set of harmonics in the phase voltage using 12-sided polygonal space vector diagrams, also called dodecagonal space vector diagrams. A dodecagonal space vector diagram has many advantages over a hexagonal one. Switching space vectors on a dodecagon will not produce any harmonics of the order 6n 1, (n=odd) in the phase voltage. The next set of harmonics thus reside at 12n 1, (n=integer). By increasing the number of samples in a sector, it is also possible to suppress the lower order harmonics and a nearly sinusoidal voltage can be obtained. This is possible to achieve at a low switching frequency of the inverters. At the same time, a dodecagon is closer to a circle than a hexagon; so the linear modulation range is extended by about 6.6% compared to the hexagonal case. For a 50 Hz rated frequency operation, under constant V/f ratio, the linear modulation can be achieved upto a frequency of 48.3 Hz. Also, the harmonics of the order 6n 1, (n=odd) are absent in the over-modulation region. Maximum fundamental voltage is obtained from this inverter at the end of over-modulation region, where the phase voltage becomes a 12-step waveform. The present work is developed on dodecagonal space vector diagrams. The entire work can be summarized and explained through Fig. 1. This figure shows the development of hexagonal and dodecagonal space vector diagrams. It is known that, 3-level and 5-level space vector diagrams have been developed as an improvement over 2-level ones. They Figure 1: Development of hexagonal and dodecagonal space vector diagrams have better harmonic performance, reduced dv/dt stress on the motor and devices, better electromagnetic compatibility and improvement of efficiency over 2-level space vector diagrams. This happens because the instantaneous error between the reference vector and the switching vectors reduces, as the space vector density increases in the diagram. This is shown at the top of the figure. In the bottom part, the development of the dodecagonal space vector diagram is shown, which is the contribution of this thesis work. This is explained in brief in the following lines. Initially, a space vector diagram is proposed which switches on hexagonal space vectors in lower-modulation region and dodecagonal space vectors in the higher modulation region. As the reference vector length increases, voltage vectors at the vertices of the outer dodecagon and the vertices from the outer most hexagon is used for PWM control. This results in highly suppressed 5th and 7th order harmonics thereby improving the harmonic profile of the motor current. This leads to the 12-step operation at rated voltage where all the 5th and 7th order harmonics are completely eliminated. At the same time, the linear range of modulation extends upto 96.6% of base speed. Because of this, and the high degree of suppression of lower order harmonics, smooth acceleration of the motor upto rated speed is possible. The presence of multilevel space vector structure also limits the switching frequency of the inverters. In the next work, the single dodecagonal space vector diagram is improved upon to form two concentric dodecagons spanning the space vector plane (Fig. 1). The radius of the outer dodecagon is double the inner one. It reduces the device rating and the dv/dt stress on the devices to half compared to existing 12-sided schemes. The entire space vector diagram is divided into smaller sized isosceles triangles. PWM switching on these smaller triangles reduces the inverter switching frequency without compromising on the output voltage quality. The space vector diagram is further refined to accommodate six concentric dodecagons in the space vector plane (Fig. 1). Here the space vector diagram is characterized by alternately placed dodecagons which become closer to each other at higher radii. As such the harmonics in the phase voltage are reduced, in particular at higher modulation indices. At the same time, because of the dodecagonal space vector structure, all the 6n ± 1, (n=odd) harmonics are eliminated from the phase voltage. A nearly sinusoidal phase voltage can be generated without resorting to high frequency switching of the inverters. The above space vector diagrams are developed using different inverter circuits. The first work is developed from cascaded combination of three 2-level inverters, while the second and third works use 3-level NPC inverters feeding an open end induction motor drive. The circuit topologies are explained in detail in the respective chapters. Apart from this, PWM switching schemes and detailed analysis on duty cycle calculations using the concept of volt-second balance are also presented. They show that with proper switching schemes, the proposed configurations can substantially reduce the overall loss of the inverter. Other operational issues like capacitor voltage balancing of 3-level NPC inverters and improvement of input current drawn from the grid are also covered. All the above propositions are first simulated by MATLAB and subsequently verified by an experimental laboratory prototype. Motor current waveforms both at steady state and transient conditions during motor acceleration show that the induction motor can be fed from nearly sinusoidal voltage at all operating conditions. Simplified comparative studies are also made with the proposed converters and higher level inverters in terms of output voltage quality and losses. These are some of the constituents for chapters 2, 3 and 4 in this thesis. Additionally, the first chapter also covers a brief survey on some of the recent progresses made in the field of multilevel inverter. The thesis concludes with some interesting ideas for further thought and exploration.