A mathematical model for the determination of the aerodynamic forces acting on an aircraft is presented. The mathematical model is based on the generalization of the idea of aerodynamically steady motions. One important use of these results is the determination of steady (time-invariant) aerodynamic forces and moments. Such aerodynamic forces can be determined using computer simulation by determining numerically the associated steady flows around the aircraft when it is moving along such generalized steady trajectories. The method required the extension of standard (inertial) CFD formulations to general non-inertial reference frames. Generalized Navier-Stokes and Euler equations have been derived. The formulation is valid for all ranges of Mach numbers including transonic flow. The method was implemented numerically for the planar case using the generalized Euler equations. The developed computer codes can be used to obtain numerical flow solutions for airfoils moving in general steady motions (i.e. circular motions). From these numerical solutions it is possible to determine the variation of the lift, drag and pitching moment with respect to the pitch rate at different Mach numbers and angles of attack. One of the advantages of the mathematical model developed here is that the aerodynamic forces become well-defined functions of the motion variables (including angular rates). In particular, the stability derivatives are associated with partial derivatives of these functions. These stability derivatives can be computed using finite differences or the sensitivity equation method. / Ph. D.

Computational solutions are presented for flows ranging from incompressible viscous flows to inviscid transonic flows. The viscous flow problems are solved using the incompressible Navier-Stokes equations while the inviscid solutions are attained using the full potential equation. Results for the viscous flow problems focus on turbulence modeling when separation is present. The main focus for the inviscid results is the development of an unstructured solution algorithm. The subject dealing with turbulence modeling for separated flows is discussed first. Two different test cases are presented. The first flow is a low-speed converging-diverging duct with a rapid expansion, creating a large separated flow region. The second case is the flow around a stationary hydrofoil subject to small, oscillating hydrofoils. Both cases are computed first in a steady state environment, and then with unsteady flow conditions imposed. A special characteristic of the two problems being studied is the presence of strong adverse pressure gradients leading to flow detachment and separation. For the flows with separation, numerical solutions are obtained by solving the incompressible Navier-Stokes equations. These equations are solved in a time accurate manner using the method of artificial compressibility. The algorithm used is a finite volume, upwind differencing scheme based on flux-difference splitting of the convective terms. The Johnson and King turbulence model is employed for modeling the turbulent flow. Modifications to the Johnson and King turbulence model are also suggested. These changes to the model focus mainly on the normal stress production of energy and the strong adverse pressure gradient associated with separating flows. The performance of the Johnson and King model and its modifications, along with the Baldwin-Lomax model, are presented in the results. The modifications had an impact on moving the flow detachment location further downstream, and increased the sensitivity of the boundary layer profile to unsteady flow conditions. Following this discussion is the numerical solution of the full potential equation. The full potential equation assumes inviscid, irrotational flow and can be applied to problems where viscous effects are small compared to the inviscid flow field and weak normal shocks. The development of a code is presented which solves the full potential equation in a finite volume, cell centered formulation. The unique feature about this code is that solutions are attained on unstructured grids. Solutions are computed in either two or three dimensions. The grid has the flexibility of being made up of tetrahedra, hexahedra, or prisms. The flow regime spans from low subsonic speeds up to transonic flows. For transonic problems, the density is upwinded using a density biasing technique. If lift is being produced, the Kutta-Joukowski condition is enforced for circulation. An implicit algorithm is employed based upon the Generalized Minimum Residual method. To accelerate convergence, the Generalized Minimum Residual method is preconditioned. These and other problems associated with solving the full potential equation on an unstructured mesh are discussed. Results are presented for subsonic and transonic flows over bumps, airfoils, and wings to demonstrate the unstructured algorithm presented here. / Ph. D.

A numerical study of a proposed innovative jet interaction configuration is presented. This work aimed at improving present-day jet interaction configurations in their applications as control thrusters on hypersonic vehicles. Jet thrusters are a useful control system for fast-moving vehicles flying in the upper layers of the atmosphere because of their effectiveness and responsiveness. They produce a strong and responsive lateral force on the vehicle through the interaction of two main mechanisms. The first mechanism comes from the momentum of the injectant itself, basically the thrust of the jet. The second and subtler contribution comes from the jet interaction flowfield, the interaction of the expanding injectant with the crossflow. This interaction produces areas of high pressure ahead of the injector and areas of low pressure in the region aft of the jet. The combination of the high-pressure regions in front of and low-pressure regions aft of the injector produces an undesirable nose-down pitching moment on the vehicle. In order to counterbalance the nose-down attitude, modern-day thruster designs include a large secondary injector far aft of the center of gravity of the vehicle. The thrust of this second injector acting far aft of the primary injector neutralizes the nose-down pitching moment. This is not an efficient method to obviate the problem since it requires the vehicle to be designed to carry two large thrusters and double the quantity of fuel necessary for one thruster. In light of these considerations, this study aimed at developing a jet interaction configuration that can dispense from the need of a large secondary injector to compensate for the nose-down pitching moment. The cases studied here were first a primary jet alone and then a primary jet with pairs of smaller jets. This configuration was based on the notion that the interaction of the secondary jets, conveniently located immediately aft of the thruster, with the barrel shock and the wake of the primary jet can drastically reduce the nose-down pitching moment. Because of the complexity of the jet interaction flowfield the investigation of the feasibility and the assessment of the efficiency of the new jet interaction configurations combined the present numerical effort with experimental studies of jet interaction flowfields performed in the supersonic wind tunnel at Virginia Tech. During the present numerical study the jet interaction flowfield associated with the sonic injection of a gas into a high-speed crossflow was simulated by numerically solving the Reynolds Averaged Navier Stokes (RANS) equations. Turbulence was modeled through a first-order model, the Wilcox's 1988 k-w turbulence model. The computations made use of the finite volume code General Aerodynamic Simulation Program (GASP) Version 4. For simplicity and to keep the study general, the jet interaction flowfield was studied on a flat plate instead of a body of revolution as on a vehicle. Calculations were run for a number of jet interaction configurations consisting of a primary jet alone, a primary jet and one pair of secondary jets, and a primary jet and two pairs of secondary jets. The flow conditions of the simulations ranged from a Mach number of 2.1 up to a Mach number of 4.5 and jet total pressure to freestream static pressure ratios of 14 to 680. A large effort was dedicated to the development of an efficient computational grid that could capture most of the flow-physics with a minimum number of cells. To this end , Chimera or overset grids were employed in the simulation of the secondary injectors. Grid convergence was shown to be achieved for the case of single injection by conducting a thorough convergence study. The discretization error was calculated through a modified Richardson extrapolation to be low. The numerical solutions were compared to the experimental results in order to assess the capability of RANS equations and of first-order turbulence models to properly simulate the complex flowfield. The k-w turbulence model proved to be reliable and robust and the results it provided for this type of flowfield were accurate enough from an engineering standpoint to make informed decisions about the configuration layout. In spite of the overall good performance, the k-w turbulence model failed to correctly predict the flow in the regions of strong adverse pressure gradients. Comparisons with experimental results showed that the separation region was often under-predicted thus highlighting the need to employ better turbulence models for more accurate results. The RANS equations were found accurate enough to provide physical mean-flow solutions. Further, the numerical simulations provided information about the detailed physics of the flowfield that is impossible to obtain through experimental work. The analysis of the numerical solutions highlighted the existence of a complex system of counter-rotating trailing vortices that are responsible for the mixing of the injectant with the freestream. The typical features of the flowfield created by an under-expanded jet exhausting in a quiescent medium were visible in the jet interaction flowfield with the difference of the existence of a crossflow and a non-uniform back-pressure. The region of low pressure aft of the injector was shown to be generated by the detachment of the barrel shock from the surface of the flat plate that leaves a large volume to be filled by the surrounding fluid. The simulations showed that the innovative configuration with one primary jet and an array of smaller secondary jets can effectively decrease the nose-down pitching moment by as much as 160%. In some cases, it also increased the total normal force acting on the flat plate (namely the thrust) by as much as 3%. This effect was found to be caused by the reduction in size and intensity of the low-pressure region aft of the primary injector. / Ph. D.

Buoyancy driven underwater gliders, which locomote by modulating their buoyancy and their attitude with moving mass actuators and inflatable bladders, are proving their worth as efficient long-distance, long-duration ocean sampling platforms. Gliders have the capability to travel thousands of kilometers without a need to stop or recharge. There is a need for the development of methods for hydrodynamic modeling. This thesis aims to determine the hydrodynamic parameters for the governing equations of motion for three autonomous underwater vehicles. This approach is two fold, using data obtained from computational flight tests and using a semi-empirical approach. The three vehicles which this thesis focuses on are two gliders (Slocum and XRay/Liberdade), and a third vehicle, the Virginia Tech Miniature autonomous underwater vehicle. / Master of Science

The Deverson rotor, a single stage axial compressor designed to simulate a multistage axial compressor, was studied computationally using a 3-D Navier-Stokes solver, the Moore Elliptic Flow Program. A one equation, q-L, transitional turbulence model was used with MEFP for closure of the transport equations. The calculation was used to study the physics and flow mechanisms affecting hub corner stall. Preprocessing and post processing programs were written to aid this study, a grid generation program and a streakline visualization program, respectively. First, computational 2-D cascade studies were performed to study the effects of free stream turbulence level and incidence angle on suction surface boundary layer development. The results showed the correct trends in boundary layer transition and separation, loss production, and deviation angles. Velocity measurements taken at the exit of the Deverson rotor were made available by Rolls-Royce for comparison with the 3-D calculation results. The q-L turbulence model predicted the existence of the hub comer stall, but under predicted the size of the corner stall. It failed to predict the radial migration of the associated loss core. However, the calculation did reveal details of the flow that affect comer stall. These included boundary layer transition and separation on the suction surface, hub and suction surface secondary flows, and radial relief. Streaklines were useful in visualizing and understanding these flow details. A preliminary 3-D calculation was performed with a two-equation, q-w, turbulence model. This turbulence model more accurately predicted the comer stall including radial migration of the loss core. / Master of Science

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