Multidisciplinary interactions are expected to play a significant role in the design of future high-performance aircraft (Blended-Wing Body, Truss-Braced wing, High Speed Civil transport, High-Altitude Long Endurance aircraft and future military aircraft). Also, the availability of supercomputers has made it now possible to employ high-fidelity models (Computational Fluid Dynamics for fluids and detailed finite element models for structures) at the preliminary design stage. A necessary step at that stage is to calculate the wing angle-of-attack at which the wing will generate the desired lift for the specific flight maneuver. Determination of this angle, a simple affair when the wing is rigid and the flow regime linear, becomes difficult when the wing is flexible and the flow regime non-linear. To solve this inherently nonlinear problem, a Newton's method type algorithm is developed to simultaneously calculate the deflection and the angle of attack. The present algorithm requires the sensitivity of the aerodynamic pressure with respect to each of the generalized displacement coordinates needed to represent the structural displacement. This sensitivity data is easy to determine analytically when the flow regime is linear. The present algorithm uses a finite difference method to obtain these sensitivities and thus requires only the pressure data and the surface geometry from the aerodynamic model. This makes it ideally suited for nonlinear aerodynamics for which it is difficult to obtain the sensitivity analytically. The present algorithm requires the CFD code to be run for each of the generalized coordinates. Therefore, to reduce the number of generalized coordinates considerably, we employ the modal superposition approach to represent the structural displacements. Results available for the Aeroelastic Research Wing (ARW) are used to evaluate the performance of the modal superposition approach. Calculations are made at a fixed angle of attack and the results are compared to both the experimental results obtained at NASA Langley Research Center, and computational results obtained by the researchers at NASA Ames Research Center. Two CFD codes are used to demonstrate the modular nature of this research. Similarly, two separate Finite Element codes are used to generate the structural data, demonstrating that the algorithm is not dependent on using specific codes. The developed algorithm is tested for a wing, used for in-house aeroelasticity research at Boeing (previously McDonnell Douglas) Long Beach. The trim angle of attack is calculated for a range of desired lift values. In addition to the Newton's method algorithm, a non derivative method (NDM) based on fixed point iteration, typical of fixed angle of attack calculations in aeroelasticity, is employed. The NDM, which has been extended to be able to calculate trim angle of attack, is used for one of the cases. The Newton's method calculation converges in fewer iterations, but requires more CPU time than the NDM method. The NDM, however, results in a slightly different value of the trim angle of attack. It should be noted that NDM will converge in a larger number of iterations as the dynamic pressure increases. For one value of the desired lift, both viscous and inviscid results were generated. The use of the inviscid flow model while not resulting in a markedly different value for the trim angle of attack, does result in a noticeable difference both in the wing deflection and the span loading when compared to the viscous results. A crude (coarse-grain) parallel methodology was used in some of the calculations in this research. Although the codes were not parallelized, the use of modal superposition made it possible to compute the sensitivity terms on different processors of an IBM SP/2. This resulted in a decrease in wall clock time for these calculations. However, even with the parallel methodology, the CPU times involved may be prohibitive (approximately 5 days per Newton iteration) to any practical application of this method for wing analysis and design. Future work must concentrate on reducing these CPU times. Two possibilities: (i) The use of alternative basis vectors to further reduce the number of basis vectors used to represent the structural displacement, and (ii) The use of more efficient methods for obtaining the flow field sensitivities. The former will reduce the number of CFD analyses required the latter the CPU time per CFD analysis. NOTE: (03/2007) An updated copy of this ETD was added after there were patron reports of problems with the file. / Ph. D.

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

Creating effective models predicting particle entrainment behavior within axisymmetric turbulent jets is of significant interest to many areas of study. Research into multiphase flows within turbulent structures has primarily focused on specific geometries for a target application, with little interest in generalized cases. In this research, the entrainment characteristics of various particle sizes and densities were simulated by determining the distribution of particles across a surface after the particles had fallen out of entrainment within the jet core. The model was based on an experimental set-up created by Lieutenant Zachary Robertson, which consists of a particle injection system designed to load particles into a fully developed pipe [1]. This pipe flow then exits into an otherwise quiescent environment (created within a wind tunnel), creating an axisymmetric turbulent round jet. The particles injected were designed to test the effect of both particle size and density on the entrainment characteristics. The data generated by the model indicated that, for all particle types tested, the distribution across the bottom surface of the wind tunnel followed a standard Gaussian distribution. Experimentation yielded similar results, with the exception that some of the experimental trials showed distributions with significantly non-zero skewness. The model produced results with the highest correlation to experimentation for cases with the smallest Stokes number (small size/density), indicating that the trajectory of particles with the highest level of interaction with the flow were the easiest to predict. This was contrasted by the high Stokes number particles which appear to follow standard rectilinear motion. / Master of Science

Two algorithms commonly used for solving low-speed flow fields are evaluated using an unsteady turbulent flow formulation. The first algorithm is the method of artificial compressibility which solves the incompressible Navier-Stokes equations. The second is a preconditioned system for solving the compressible Navier-Stokes equations. Both algorithms have been implemented into GASP Version 4, which is the flow solver used in this investigation. Unsteady numerical simulations of unsteady, 2-D flow over square cylinders are performed with comparisons made to experimental data. Cases studied include both a single-cylinder and a three-cylinder configuration. Two turbulence models are also used in the computations, namely the Spalart-Allmaras model and the Wilcox k-ω (1998) model. The following output data was used for comparison: aerodynamic forces, mean pressure coefficient, Strouhal number, mean velocity magnitude and turbulence intensity. The main results can be summarized as follows. First, the predictions are more sensitive to the turbulence model choice than to the choice of algorithm. The Spalart-Allmaras model overall produced better results with both algorithms than the Wilcox k-ω model. Second, the artificial compressibility algorithm produced slightly more consistent results compared with experiment. / Master of Science

The current demands for higher performance in gas turbine engines can be reached by raising combustion temperatures to increase thermal efficiency. Hot combustion temperatures create a harsh environment which leads to the consideration of the durability of the combustor and turbine sections. Improvements in durability can be achieved through understanding the interactions between the combustor and turbine. The flow field at a combustor exit shows non-uniformities in pressure, temperature, and velocity in the pitch and radial directions. This inlet profile to the turbine can have a considerable effect on the development of the secondary flows through the vane passage. This thesis presents a computational study of the flow field generated in a non-reacting gas turbine combustor and how that flow field convects through the downstream stator vane. Specifically, the effect that the combustor flow field had on the secondary flow pattern in the turbine was studied. Data from a modern gas turbine engine manufacturer was used to design a realistic, low speed, large scale combustor test section. This thesis presents the results of computational simulations done in parallel with experimental simulations of the combustor flow field. In comparisons of computational predictions with experimental data, reasonable agreement of the mean flow and general trends were found for the case without dilution jets. The computational predictions of the combustor flow with dilution jets indicated that the turbulence models under-predicted jet mixing. The combustor exit profiles showed non-uniformities both radially and circumferentially, which were strongly dependent on dilution and cooling slot injection. The development of the secondary flow field in the turbine was highly dependent on the incoming total pressure profile. For a case with a uniform inlet pressure in the near-wall region no leading edge vortex was formed. The endwall heat transfer was found to also depend strongly on the secondary flow field, and therefore on the incoming pressure profile from the combustor. / Master of Science

Detonation cycles are identified as an efficient alternative to the Brayton cycles used in power and propulsion applications. Rotating Detonation Engine (RDE) operating on a detonation cycle works by compressing the working fluid across a detonation wave, thereby reducing the number of compressor stages required in the thermodynamic cycle. Numerical analyses of RDEs are flexible in understanding the flow field within the RDE, however, three-dimensional analyses are expensive due to the differences in time-scale required to resolve the combustion process and flow-field. The alternate two-dimensional analyses are generally modeled with perfectly premixed fuel injection and do not capture the effects of improper mixing arising due to discrete injection of fuel and oxidizer into the chamber. To model realistic injection in a 2-D analysis, the current work uses an approach in which, a Probability Density Function (PDF) of the fuel mass fraction at the chamber inlet is extracted from a 3-D, cold-flow simulation and is used as an inlet boundary condition for fuel mass fraction in the 2-D analysis. The 2-D simulation requires only 0.4% of the CPU hours for one revolution of the detonation compared to an equivalent 3-D simulation. Using this method, a perfectly premixed RDE is comparing with a non-premixed case. The performance is found to vary between the two cases. The mean detonation velocities, time-averaged static pressure profiles are found to be similar between the two cases, while the local detonation velocities and peak pressure values vary in the non-premixed case due to local pockets fuel rich/lean mixtures. The mean detonation cell sizes are similar, but the distribution in the non-premixed case is closer due to stronger shock structures. An analytical method is used to check the effects of fuel-product stratification and heat loss from the RDE and these effects adversely affect the local detonation velocity. Overall, this method of modeling captures the complex physics in an RDE with the advantage of reduced computational cost and therefore can be used for design and diagnostic purposes. / Master of Science / The conventional Brayton cycle used in power and propulsion applications is highly optimized, at cycle and component levels. In pursuit of higher thermodynamic efficiency, detonation cycles are identified as an efficient alternative and gained increased attention in the scientific community. In a Rotating Detonation Engine (RDE), which is based on the detonation cycle, the compression of gases occurs across a shock wave. This method of achieving high compression ratios reduces the number of compressor stages required for operation. In an RDE (where combustion occurs between two coaxial cylinders), the fuel and oxidizer are injected axially into the combustion chamber where the detonation is initiated. The resultant detonation wave spins continuously in the azimuthal direction, consuming fresh fuel mixture. The combustion products expand and exhaust axially providing thrust/mechanical energy when coupled with a turbine. Numerical analyses of RDEs are flexible over experimental analysis, in terms of understanding the flow physics and the physical/chemical processes occurring within the engine. However, three-dimensional numerical analyses are computationally expansive, and therefore demanding an equivalent, efficient two-dimensional analysis. In most RDEs, fuel and oxidizer are injected from separate plenums into the chamber. This type of injection leads to inhomogeneity of the fuel-air mixture within the RDE which adversely affects the performance of the engine. The current study uses a novel method to effectively capture these physics in a 2-D numerical analysis. Furthermore, the performance of the combustor is compared between perfectly premixed injection and discrete, non-premixed injection. The method used in this work can be used for any injector design and is a powerful/efficient way to numerically analyze a Rotating Detonation Engine.