The detonation-based engine has the key advantage of increased thermodynamic efficiency over the traditional constant pressure combustor. These detonation-based engines are also known as Pressure Gain Combustion systems (PGC) and Rotating Detonation Combustor (RDC) is a form of PGC, in which the detonation wave propagates azimuthally around an annular combustor. Prior researchers have performed a high fidelity 3-D numerical simulation of a rotating detonation combustor (RDC) to understand the flow physics such as detonation wave velocity, pressure profile, wave structure; however, performing these 3-D simulations is computationally expensive. 2-D simulations are a potential alternative to reduce computational cost. In most RDCs, fuel and oxidizer are injected discretely from separate plenums, and this discrete fuel/air injection results in inhomogeneous mixing within the domain. Due to the discrete fuel injection locations, fuel/oxidizer will stratify to form localized pockets of rich and lean mixtures. The motivation of the present study is to investigate the impact of unmixedness and stratification length scales on the performance of an RDC using a 2-D numerical approach. Unmixedness, which is defined as the standard deviation of equivalence ratio normalized by the mean global equivalence ratio, is a measure of the degree of fuel-oxidizer inhomogeneity. To model the effect of unmixedness in a 2-D domain, a lognormal distribution of the fuel mass fraction is generated with a mean equivalence ratio of 1 and varying standard deviations at the inlet boundary as a numerical source term. Moreover, to model the effects of stratification length scales, fuel mass fraction at the inlet boundary cells is bundled for a given length scale, and the mass fractions for these bundles are updated based on the lognormal distribution after every three-time steps. Using this methodology, 2-D numerical analyses are carried out to investigate the performance of an RDC for an H2-air mixture with varying unmixedness and stratification length scales. Results show that mean detonation velocity decreases and wave speed variation increases with an increase in unmixedness. However, with an increase in stratification length scale mean velocity remain relatively unchanged but variation in local velocity increases. The detonation wave front corrugation also increases with an increase in mixture inhomogeneity. The mean detonation cell size increases with an increase in unmixedness. The cell shape becomes more distorted and irregular with an increase in stratification length scale and unmixedness. The combined effect of unmixedness and stratification length scale leads to a decrease in pressure gain. Overall, this concept is able to elucidate the effects of varying unmixedness and stratification length scales on the performance of an RDC. / Master of Science / Pressure Gain Combustion (PGC) system has gained significant focus in recent years due to its increased thermodynamic efficiency over a constant pressure Brayton Cycle. Rotating Detonation Combustor (RDC) is a type of PGC system, which is thermodynamically more efficient than the conventional gas turbine combustor. One of the main aspects of the detonation process is the rapid burning of the fuel-oxidizer mixture, which occurs so fast that there is not enough time for pressure to equilibrate. Therefore, the process is thermodynamically closer to a constant volume process rather than a constant pressure process. A constant volume cycle is thermodynamically more efficient than a constant pressure Brayton cycle. In an RDC, a mixture of fuel and air is injected axially, and a detonation wave propagates continuously through the circumferential section. Numerical simulation of an RDC provides additional flexibility over experiments in understanding the flow physics, detonation wave structure, and analyzing the physical and chemical processes involved in the detonation cycle. Prior researchers have utilized a full-scale 3-D numerical simulation for understanding the performance of an RDC. However, the major challenge with 3-D analyses is the computational expense. Thus, to overcome this, an inexpensive 2-D simulation is used to model the flow physics of an RDC. In most RDCs, the fuel and oxidizer are injected discretely from separate plenums. Due to the discrete fuel injection, the fuel/air mixture is never perfectly premixed and results in a stratified flow field. The objective of the current work is to develop a novel approach to independently investigate the effects of varying unmixedness and stratification length scales on RDC performance using a 2-D simulation.

This thesis contributes an in-depth comparative study of u-tube and coaxial borehole heat exchangers. While it is widely accepted that the lower resistance of the coaxial heat exchanger should result in a performance advantage, the findings of several studies comparing the heat exchanger configurations did not definitively establish the mechanisms causing differences in performance. This study employs numerical modelling to consider heat exchangers over a broad range of time scales and under carefully controlled geometry and flow conditions, resulting in the identification of the key parameters influencing borehole heat exchanger performance. The first part of this study consists of a comparison of u-tube and coaxial heat exchangers under continuous loading. A detailed conjugate heat transfer numerical model was developed in OpenFOAM, designed to capture both short and long time scales of heat exchange, necessary to understand the nuanced differences between designs. A novel transient resistance analysis was employed to understand the dominant factors influencing performance. This study established that marginal differences exist between u-tube and coaxial borehole heat exchangers (BHEs) when operated continuously long term but that greater differences occur early in operation. The second phase of this investigation provided a framework for analysing borehole heat exchanger performance during intermittent operation, while also comparing u-tube and coaxial designs. During this study, it was found that reducing operating time, improving the the rate of the ground's recovery to its original temperature, and lowering the duty cycle improved BHE performance. Transit time was identified as a influential time scale, below which heating at the outlet was limited. Further, the benefits of operating below the transit time were mitigated by design-specific interaction between inlet and outlet flows. Finally, this study found that non-dimensionalizing operating time by transit time causes the differences between u-tube and coaxial performance to vanish, leading to the conclusion that differences in BHE performance are caused by variations in flow rather than thermal mass. / Thesis / Doctor of Philosophy (PhD) / This thesis provides an in-depth comparative study of two different designs of borehole heat exchanger, the u-tube and coaxial, which are used in geothermal applications to transfer heat to and from the ground. While many researchers anticipated that the coaxial design would perform better, several studies comparing the heat exchangers were not able to provide a clear answer about which heat exchanger performed best. This study addressed this gap by using detailed numerical simulations which showed that there was a marginal difference in performance between the two heat exchangers when operated for periods longer than a few hours, but that larger differences occurred early in operation (under 15 minutes). The results also showed that operating intermittently resulted in improvements in performance of the heat exchanger, particularly when operated for periods less than the time it takes fluid to travel the length of the piping.

The gasification of carbonaceous fuel materials offers significant potential for the production of both energy and chemical products. Advancement of gasification technologies may be expedited through the use of computational fluid dynamics, as virtual reactor design offers a low cost method for system prototyping. To that end, a series of numerical studies were conducted to identify a computational modeling strategy for the simulation of coal gasification in fluidized bed reactors. The efforts set forth by this work first involved the development of a validatable hydrodynamic modeling strategy for the simulation of sand and coal fluidization. Those fluidization models were then applied to systems at elevated temperatures and polydisperse systems that featured a complex material injection geometry, for which no experimental data exists. A method for establishing similitude between 2-D and 3-D multiphase systems that feature non-symmetric material injection were then delineated and numerically tested. Following the development of the hydrodynamic modeling strategy, simulations of coal gasification were conducted using three different chemistry models. Simulated results were compared to experimental outcomes in an effort to assess the validity of each gasification chemistry model. The chemistry model that exhibited the highest degree of agreement with the experimental findings was then further analyzed identify areas of potential improvement. / Ph. D. / Efficient utilization of coal is critical to ensuring stable domestic energy supplies while mitigating human impact on climate change. This idea may be realized through the use of gasification systems technologies. The design and planning of next-generation coal gasification reactors can benefit from the use of computational simulations to reduce both development time and cost. This treatise presents several studies where computational fluid dynamics was applied to the problem of coal gasification in a bubbling fluidized bed reactor with focuses on accurate tracking of solid material locations and modeling of chemical reactions.

Computational fluid dynamics and finite element analysis were employed to study vestibular hair cell bundle mechanics under physiologic stimulus conditions. CFD was performed using ANSYS CFX and FEA utilized a custom MATLAB model. Nine varieties of hair cell bundles were modeled using tip-forcing only (commonly used experimentally), fluid-flow only (physiologic for free-standing bundles), and combined loading (physiologic for bundles with tip attachments) conditions to determine how the bundles behaved in each case. The bundles differed in the heights of their components, their length and width, and their number of steriocilia. Tip links were modeled to determine ion-channel opening behavior. Results show that positive pressures, negative pressures, and shear stresses on the exterior of the bundles are of comparable magnitude. Under combined loading, some bundles experienced very high suction pressures on their interior. The bundles with tall steriocilia are hindered by the endolymph while those with short steriocilia and much taller kinocilia are assisted by the fluid flow. Each bundle type has a different range over which it is most sensitive so that the bundles cumulatively cover a very large range of stimuli; the order in which bundles respond from smallest stimulus magnitude to largest is free-standing extrastriolar bundles, attached striolar bundles, attached extrastriolar bundles, and free-standing extrastriolar bundles. A short examination of off-axis loading shows that the prevailing theory suggesting that bundle response is proportional to the cosine of the angle between the stimulus direction and the bundle's direction of maximum excitation is incorrect. / Ph. D.

One of the largest sources of error in a CFD simulation is the discretization error. One of the least computationally expensive ways of reducing the discretization error in a simulation is by performing mesh adaptation. In this work, the mesh adaptation processes are driven by the truncation error, which is the local source of the discretization error. Because this work is focused on methods for structured grids, r-adaptation is used as opposed to h-adaptation. A new method for performing the r-adaptation based on an optimization process is developed and presented here. This optimization process was applied to simple 1D and 2D Euler problems as a method of testing the approach. The mesh optimization approach is compared to the more common equidistribution approach to determine which produces more accurate results as well as the costs associated with each. It is found that the optimization process is able to reduce the truncation error than equidistribution. However, in the 2D cases optimization does not reduce the discretization error sufficiently to warrant the significant costs of the approach. This indicates that the much cheaper equidistribution process provides a cost-effective manner to reduce the discretization error in the solution. Further, equidistribution is able to achieve the bulk of the potential reductions in discretization error possible through r-adaptation. This work also develops a new framework for reducing the cost of performing truncation error based r-adaptation. This new framework also addresses some of the issues associated with r-adaptation. In this framework, adaptation is performed on a coarse mesh where it is faster to perform, creating a mapping function for this mesh, and finally evaluating this mapping at a fine enough mesh to meet the error target. The framework is used for 2D Euler and 2D laminar Navier-Stokes problems and shown to be the most cost-effective way to meet a desired error target. Finally, the multi-mesh CFD method is introduced and applied to a wide variety of problems from quasi-1D nozzle to 2D laminar and turbulent boundary layers. The multi-mesh method allows the system of equations to be solved on a system of meshes. With this method, each equation is solved on a mesh that is adapted specifically for it, meaning that more accurate solutions for each equation can be obtained. This work shows that, for certain problems, the multi-mesh approach is able to achieve more accurate results in less time compared to using a single mesh. / Doctor of Philosophy / Computational fluid dynamics (CFD) describes a method of numerically solving equations that attempt to model the behavior of a fluid. As computers have become cheaper and more powerful and the software has become more capable, CFD has become an integral part of the engineering process. One of the goals of the field is to be able to bring these higher fidelity simulations into the design loop earlier. Ideally, using CFD earlier in the design process would allow design engineers to create new innovative designs with less programmatic risk. Likewise, it is also becoming necessary to use these CFD tools later in the final design process to replace some physical experiments which can be expensive, unsafe, or infeasible to run. Both of these goals require the CFD codes to meet the accuracy requirements for the results as fast as possible. This work discusses several different methods for improving the accuracy of the simulations as well as ways of obtaining these more accurate results for the cheapest cost. In CFD, the governing equations modeling the flow behavior are solved on a computer. As a result, these continuous differential equations must be approximated as a system of discrete equations, so that they can be solved on a computer. These approximations result in discretization error, the difference between the exact solutions to the discrete and continuous equations, which is typically the largest type of numerical error in a CFD solution. The source of the discretization error is the truncation error, which is composed of the terms left out of the approximations made when discretizing the continuous equations. Thus, if the truncation error can be reduced, the discretization error in the solution should also be reduced. In this work, several different ways of reducing this truncation error through mesh adaptation are discussed, including the use of optimization methods. These mesh optimization methods are compared to a more common way of performing adaptation, namely equidistribution. It is determined that equidistribution is able to reduce the discretization error by a similar amount while being significantly faster than mesh optimization. This work also presents a framework for making the adaptation process faster overall by performing the adaptation on a coarse mesh and then refining the mesh enough to meet the error tolerance for the application. This framework was the cheapest method investigated to meet a given error target. This work also introduces a new technique called multi-mesh CFD, which allows each equation (conservation of mass, momentum, energy, etc.) to be solved on a separate mesh. This allows each equation to be solved on a mesh that is specifically adapted for it, resulting in a more accurate solution. Here, it is shown that, for certain problems, the multi-mesh technique is able to obtain a solution with lower error than only using a single mesh. This work also shows that these more accurate results can be obtained in less time using multiple meshes than on a single mesh.

In light of rising global temperatures and energy needs, nuclear power is uniquely positioned to offer carbon-free and reliable electricity. In many markets, nuclear power faces strong headwinds due to competition with other fuel sources and prohibitively high capital costs. Small Modular Reactors (SMRs), such as the proposed Advanced Fast Reactor (AFR) 100, have gained popularity in recent years as they promise economies of scale, reduced capital costs, and flexibility of deployment. Fast sodium reactors commonly feature an upper plenum with a large inventory of sodium. When temperatures change due to transients, stratification can occur. It is important to understand the stratification behavior of these large volumes because stratification can counteract natural circulation and fatigue materials. This work features steady-state and transient simulations of thermal stratification and natural circulation of liquid sodium in a simple rectangular slice using a commercial CFD code (ANSYS FLUENT). Different inlet velocities and their effect on stratification are investigated by changing the inlet geometry. Stratification was observed in the two cases with the lowest inlet velocities. An approach for tracking the stratification interface was developed that focuses on temperature gradients rather than differences. Other authors have developed correlations to predict stratification in three dimensional enclosures. However, these correlations predict stratified conditions for all simulations even the ones that did not stratify. The previous models are modified to reflect the two-dimensional nature of the flow in the enclosure. The results align more closely with the simulations and correctly predict stratification in the investigated cases. / Master of Science

Eugene Clement created a design method for swept-back cambered step hulls with deadrise. The cambered step is designed to carry 90% of the planing vessels weight with the remaining 10% being support by a stern mounted hydrofoil. The method requires multiple design iterations in order to achieve an optimal design. Clement stated that the method was not suitable for cambered planing surfaces with high deadrise angles greater than 15 degrees. The goal of this thesis is to create a design procedure for swept-back cambered planing surfaces with high deadrise angles that does not require multiple iterations to obtain an optimal design. Computational fluid dynamics (CFD) program STAR CCM+ is used to generate a database for performance characteristics for a wide range of designs varying deadrise angle, load requirements, trim angle, and different camber values. The simulations are first validated with experimental data for two different cambered steps designed by Stefano Brizzolara and tested in the tow tank at the United States Naval Academy. A series of validation studies utilizing fixed and overset meshes led to a final simulation set up with an overset mesh that allowed for accurate prediction of drag, trim moment, wetted keel length, and the wake profile aft of the cambered planing surface. The database is fitted such that the final equations for optimal design values such as camber, trim angle, drag (shear and pressure), wetted keel length, wetted surface area, and trim moment are in terms of deadrise angle and lift. The optimized design equations are validated with CFD simulation. / Master of Science / Eugene Clement developed a new design method to improve the performance of ultra-fast planing crafts. A planing craft uses the force generated from the flow of water over the bottom to lift the vessel without the use of the static buoyancy force that classic boat designs rely on. Clement wanted to improve the performance of the planing vessel by reducing the total drag force caused by the flow of water on the bottom of the vessel. Clement's design method involves reducing the wetted surface area which reduces drag. Reducing the wetted surface area would normally cause the lifting force on the vessel to reduce, but with the addition of curvature in the smaller wetted surface area, the lifting force would remain the same. Clement's new design method requires multiple iterations to obtain an optimal design. The method limits the angle of the vessels bottom relative to horizontal to under 15 degree. The goal of this thesis is to create a new design method for planing vessels with bottoms that have an incline of 15 degrees or more relative to horizontal. The design method is created using Computational Fluid Dynamics (CFD) solver to model the planing surface moving through water. The CFD solver is validated with experimental test performed at the United States Naval Academy. The improved design method uses equations that can predict the forces and other design characteristics based on the desired vessel weight and seakeeping requirements.

Conventional understanding of quality of energy suggests that heat is a low grade form of energy. Hence converting this energy into useful form of work was assumed difficult. However, this understanding was challenged by researchers over the last few decades. With advances in solar, thermal and geothermal energy harvesting, they believed that these sources of energy had great potential to operate as dependable avenues for electrical power. In recent times, waste heat from automobiles, oil and gas and manufacturing industries were employed to harness power. Statistics show that US alone has a potential of generating 120,000 GWh/year of electricity from oil , gas and manufacturing industries, while automobiles can contribute upto 15,900 GWh/year. Thermoelectric generators (TEGs) can be employed to capture some of this otherwise wasted heat and to convert this heat into useful electrical energy. This field of research as compared to gas turbine industry has emerged recently over past 30 decades. Researchers have shown that efficiency of these TEGs modules can be improved by integrating heat transfer augmentation features on the hot side of these modules. Gas turbines employ advanced technologies for internal and external cooling. These technologies have applications over wide range of applications, one of which is thermoelectricity. Hence, making use of gas turbine technologies in thermoelectrics would surely improve the efficiency of existing TEGs. This study makes an effort to develop innovative technologies for gas turbine as well as thermoelectric applications. The first part of the study analyzes heat transfer augmentation from four different configurations for low aspect ratio channels and the second part deal with characterizing improvement in efficiency of TEGs due to the heat transfer augmentation techniques. / Master of Science

Computational fluid dynamics (CFD) has proven to be an invaluable tool for both engineering design and analysis. As the performance of engineering devices become more reliant upon the accuracy of CFD simulations, it is necessary to not only quantify and but also to reduce the numerical error present in a solution. Discretization error is often the primary source of numerical error. Discretization error is introduced locally into the solution by truncation error. Truncation error represents the higher order terms in an infinite series which are truncated during the discretization of the continuous governing equations of a model. Discretization error can be reduced through uniform grid refinement but is often impractical for typical engineering problems. Grid adaptation provides an efficient means for improving solution accuracy without the exponential increase in computational time associated with uniform grid refinement. Solution accuracy can be improved through local grid refinement, often referred to as h-adaptation, or by node relocation in the computational domain, often referred to as r-adaptation. The goal of this work is to examine the effectiveness of several r-adaptation techniques for reducing discretization error. A framework for geometry preservation is presented, and truncation error is used to drive adaptation. Sample problems include both subsonic and supersonic inviscid flows. Discretization error reductions of up to an order of magnitude are achieved on adapted grids. / Master of Science

The research conducted was a feasibility study using Lithium Fluoride-Beryllium Fluoride (LiF-BeF2) or FLiBe as a coolant with a natural uranium neutron spallation source applied to an accelerator driven sub-critical molten salt reactor. The study utilized two different software tools, MCNPX 2.6 and FLUENT 12.1. MCNPX was used to determine the neutronics and heat deposited in the spallation target structure while FLUENT was used to determine the feasibility of cooling the target structure with FLiBe. Several target structures were analyzed using a variety of plates and large cylinders of natural uranium with a proton beam incident on a Hastelloy-N window. The supporting structures were created from Hastelloy-N due to their anti-corrosive properties of molten salts such as FLiBe and their resistance to neutron damage. The final design chosen was a "Sandwich" design utilizing a section of thick plates followed by several smaller plates then finally a section of thick plates to stop any protons from irradiating the bottom of the target support structure or the containment vessel of the reactor. Utilizing a proton beam with 0.81 MW of proton beam power at 1.35 mA with proton kinetic energies of 600 MeV, the total heat generated in the spallation target was about 0.9 MW due to fissions in the natural uranium. Additionally, the neutrons produced from the final design of the spallation target were approximately 1.25x1018 neutrons per second which were mainly fast neutrons. The use of a natural uranium target proved to be very promising. However, cooling the target using FLiBe would require further optimization or investigation into alternate coolants. Specifically, the final design developed using FLiBe as a coolant was not practically feasible due to the hydraulic forces resulting from the high flow rates necessary to keep the natural uranium target structures cooled. The primary reason for the lack of a feasible solution was the FLiBe as a coolant; FLiBe is unable to pull enough heat generated in the target out of the target structure. Due to the high energy density of a natural uranium spallation target structure, a more effective method of cooling will be required to avoid high hydraulic forces, such as a liquid metal coolant like lead-bismuth eutectic. / Master of Science