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A new noise metric has been developed that may be used for optimization problems involving aerodynamic noise from a clean wing. The modeling approach uses a classical trailing edge noise theory as the starting point. The final form of the noise metric includes characteristic velocity and length scales that are obtained from three-dimensional, steady, RANS simulations with a two- equation k-omega turbulence model. The noise metric is not the absolute value of the noise intensity, but an accurate relative noise measure as shown in the validation studies. One of the unique features of the new noise metric is the modeling of the length scale, which is directly related to the turbulent structure of the flow at the trailing edge. The proposed noise metric model has been formulated so that it can capture the effect of different design variables on the clean wing airframe noise such as the aircraft speed, lift coefficient, and wing geometry. It can also capture three-dimensional effects which become important at high lift coefficients, since the characteristic velocity and the length scales are allowed to vary along the span of the wing. Noise metric validation was performed with seven test cases that were selected from a two-dimensional NACA 0012 experimental database. The agreement between the experiment and the predictions obtained with the new noise metric was very good at various speeds, angles of attack, and Reynolds Number, which showed that the noise metric is capable of capturing the variations in the trailing edge noise as a relative noise measure when different flow conditions and parameters are changed. Parametric studies were performed to investigate the effect of different design variables on the noise metric. Two-dimensional parametric studies were done using two symmetric NACA four-digit airfoils (NACA 0012 and NACA 0009) and two supercritical (SC(2)-0710 and SC(2)-0714) airfoils. The three-dimensional studies were performed with two versions of a conventional transport wing at realistic approach conditions. The twist distribution of the baseline wing was changed to obtain a modified wing which was used to investigate the effect of the twist on the trailing edge noise. An example study with NACA 0012 and NACA 0009 airfoils demonstrated a reduction in the trailing edge noise by decreasing the thickness ratio and the lift coefficient, while increasing the chord length to keep the same lift at a constant speed. Both two- and three-dimensional studies demonstrated that the trailing edge noise remains almost constant at low lift coefficients and gets larger at higher lift values. The increase in the noise metric can be dramatic when there is separation on the wing. Three-dimensional effects observed in the wing cases indicate the importance of calculating the noise metric with a characteristic velocity and length scale that vary along the span. The twist change does not have a significant effect on the noise at low lift coefficients, however it may give significant noise reduction at higher lift values. The results obtained in this study show the importance of the lift coefficient on the airframe noise of a clean wing and favors having a larger wing area to reduce the lift coefficient for minimizing the noise. The results also point to the fact that the noise reduction studies should be performed in a multidisciplinary design and optimization framework, since many of the parameters that change the trailing edge noise also affect the other aircraft design requirements. It's hoped that the noise metric developed here can aid in such multidisciplinary design and optimization studies. Ph. D.

Through this research, a robust aircraft design methodology is developed for analysis and optimization of the Air Vehicle (AV) segment of Unmanned Aerial Vehicle (UAV) systems. The analysis functionality of the AV design is integrated with a Genetic Algorithm (GA) to form an integrated Multi-disciplinary Design Optimization (MDO) methodology for optimal AV design synthesis. This research fills the gap in integrated subsonic fixed-wing UAV AV MDO methods. No known single methodology captures all of the phenomena of interest over the wide range of UAV families considered here. Key advancements include: 1) parametric Low Reynolds Number (LRN) airfoil aerodynamics formulation, 2) UAV systems mass properties definition, 3) wing structural weight methods, 4) self-optimizing flight performance model, 5) automated geometry algorithms, and 6) optimizer integration. Multiple methods are provided for many disciplines to enable flexibility in functionality, level of detail, computational expediency, and accuracy. The AV design methods are calibrated against the High-Altitude Long-Endurance (HALE) Global Hawk, Medium-Altitude Endurance (MAE) Predator, and Tactical Shadow 200 classes, which exhibit significant variations in mission performance requirements and scale from one another. Technology impacts on the design of the three UAV classes are evaluated from a representative system technology year through 2025. Avionics, subsystems, aerodynamics, design, payloads, propulsion, and structures technology trends are assembled or derived from a variety of sources. The technology investigation serves the purposes of validating the effectiveness of the integrated AV design methods and to highlight design implications of technology insertion through future years. Flight performance, payload performance, and other attributes within a vehicle family are fixed such that the changes in the AV designs represent technology differences alone, and not requirements evolution. The optimizer seeks to minimize AV design gross weight for a given mission requirement and technology set. All three UAV families show significant design gross weight reductions as technology improves. The predicted design gross weight in 2025 for each class is: 1) 12.9% relative to the 1994 Global Hawk, 2) 6.26% relative to the 1994 Predator, and 3) 26.3% relative to the 2000 Shadow 200. The degree of technology improvement and ranking of contributing technologies differs among the vehicle families. The design gross weight is sensitive to technologies that directly affect the non-varying weights for all cases, especially payload and avionics/subsystems technologies. Additionally, the propulsion technology strongly affects the high performance Global Hawk and Predator families, which have high fuel mass fractions relative to the Tactical Shadow 200 family. The overall technology synergy experienced 10-11 years after the initial technology year is 6.68% for Global Hawk, 7.09% for Predator, and 4.22% for the Shadow 200, which means that the technology trends interact favorably in all cases. The Global Hawk and Shadow 200 families exhibited niche behavior, where some vehicles attained higher aerodynamic performance while others attained lower structural mass fractions. The high aerodynamic performance Global Hawk vehicles had high aspect ratio wings with sweep, while the low structural mass fraction vehicles had straight, relatively low aspect ratios and smaller wing spans. The high aerodynamic performance Shadow 200 vehicles had relatively low wing loadings and large wing spans, while the lower structural mass fraction counterparts sought to minimize physical size. Ph. D.

The objective of this investigation was to improve the thermal environment for a turbine vane through reduction of passage secondary flows. This was accomplished by modifying the vane/endwall junction to include a leading edge fillet. The problem approach was to integrate optimization methods with computational fluid dynamics to optimize the fillet design. The resulting leading edge fillet was then tested in a large-scale, low speed cascade to verify thermal performance. A combustor simulator located upstream of the cascade was used to generate realistic inlet conditions for the turbine vane. Both computational and experimental results underscore the importance of properly modeling the inlet conditions to the turbine. Results of the computational optimization process indicate that significant reductions in adiabatic wall temperature can be achieved with a leading edge fillet. While the intent of the initial fillet design was to improve the thermal environment for the vane endwall, computational results also indicate thermal benefit to the vane surfaces. Flow and thermal field results show that a fillet can enhance coolant effectiveness, prevent formation of the leading edge horseshoe vortex, and preclude full development of a passage vortex. In experimental testing, four cascade inlet conditions were investigated to evaluate the effectiveness of the fillet in reducing endwall temperature levels. Two tested conditions featured a flush combustor/cascade interface, while the remaining two included coolant injection through a backward-facing slot. With the flush interface, fillet thermal performance was evaluated for two inlet total pressure profiles. For the design profile, the fillet had a positive impact on the endwall temperature distribution as well as on the passage thermal field. For the off-design profile, the fillet was observed to have a slightly detrimental impact on the endwall adiabatic temperature distribution; however, passage thermal field results indicate a thermal benefit for the vane suction surface. With the backward-facing slot, thermal tests were conducted for two slot coolant flow rates. For both slot flow rates, the fillet improved endwall thermal protection and prevented coolant lift-off. While increasing the flow rate of slot coolant enhanced endwall effectiveness, fillet thermal performance was similar for the two slot flow rates. Ph. D.

Conventional airliners use two to four engines in a Cayley-type arrangement to provide thrust, and the thrust from these engines is typically concentrated right behind the engine. Distributed propulsion is the idea of redistributing the thrust across most, or all, of the wingspan of an aircraft. This can be accomplished by using several large engines and using a duct to spread out the exhaust flow to form a jet-wing or by using many small engines spaced along the span of the wing. Jet-wing distributed propulsion was originally suggested by Kuchemann as a way to improve propulsive efficiency. In addition, one can envision a jet-wing with deflected jets replacing flaps and slats and the associated noise. The purpose of this study was to assess the performance benefits of jet-wing distributed propulsion. The Reynolds-averaged, finite-volume, Navier-Stokes code GASP was used to perform parametric computational fluid dynamics (CFD) analyses on two-dimensional jet-wing models. The jet-wing was modeled by applying velocity and density boundary conditions on the trailing edges of blunt trailing edge airfoils such that the vehicle was self-propelled. As this work was part of a Blended-Wing-Body (BWB) distributed propulsion multidisciplinary optimization (MDO) study, two airfoils of different thickness were modeled at BWB cruise conditions. One airfoil, representative of an outboard BWB wing section, was 11% thick. The other airfoil, representative of an inboard BWB wing section, was 18% thick. Furthermore, in an attempt to increase the propulsive efficiency, the trailing edge thickness of the 11% thick airfoil was doubled in size. The studies show that jet-wing distributed propulsion can be used to obtain propulsive efficiencies on the order of turbofan engine aircraft. If the trailing edge thickness is expanded, then jet-wing distributed propulsion can give improved propulsive efficiency. However, expanding the trailing edge must be done with care, as there is a drag penalty. Jet-wing studies were also performed at lower Reynolds numbers, typical of UAV-sized aircraft, and they showed reduced propulsive efficiency performance. At the lower Reynolds number, it was found that the lift, drag, and pitching moment coefficients varied nearly linearly for small jet-flap deflection angles. Master of Science

The purpose of this study is to examine the multidisciplinary design optimization (MDO) of a distributed propulsion blended-wing-body (BWB) aircraft. The BWB is a hybrid shape resembling a flying wing, placing the payload in the inboard sections of the wing. The distributed propulsion concept involves replacing a small number of large engines with many smaller engines. The distributed propulsion concept considered here ducts part of the engine exhaust to exit out along the trailing edge of the wing. The distributed propulsion concept affects almost every aspect of the BWB design. Methods to model these effects and integrate them into an MDO framework were developed. The most important effect modeled is the impact on the propulsive efficiency. There has been conjecture that there will be an increase in propulsive efficiency when there is blowing out of the trailing edge of a wing. A mathematical formulation was derived to explain this. The formulation showed that the jet "fills in" the wake behind the body, improving the overall aerodynamic/propulsion system, resulting in an increased propulsive efficiency. The distributed propulsion concept also replaces the conventional elevons with a vectored thrust system for longitudinal control. An extension of Spence's Jet Flap theory was developed to estimate the effects of this vectored thrust system on the aircraft longitudinal control. It was found to provide a reasonable estimate of the control capability of the aircraft. An MDO framework was developed, integrating all the distributed propulsion effects modeled. Using a gradient based optimization algorithm, the distributed propulsion BWB aircraft was optimized and compared with a similarly optimized conventional BWB design. Both designs are for an 800 passenger, 0.85 cruise Mach number and 7000 nmi mission. The MDO results found that the distributed propulsion BWB aircraft has a 4% takeoff gross weight and a 2% fuel weight. Both designs have similar planform shapes, although the planform area of the distributed propulsion BWB design is 10% smaller. Through parametric studies, it was also found that the aircraft was most sensitive to the amount of savings in propulsive efficiency and the weight of the ducts used to divert the engine exhaust. Ph. D.

An investigation was conducted to assess the usefulness of anti-optimization in the process of validating of aerodynamic codes. Anti-optimization is defined here as the intentional search for regions where the computational and experimental results disagree. Maximizing such disagreements can be a useful tool in uncovering errors and/or weaknesses in both analyses and experiments. The codes chosen for this investigation were an airfoil code and a lifting line code used together as an analysis to predict three-dimensional wing aerodynamic coefficients. The parameter of interest was the maximum lift coefficient of the three-dimensional wing, CL max. The test domain encompassed Mach numbers from 0.3 to 0.8, and Reynolds numbers from 25,000 to 250,000. A simple rectangular wing was designed for the experiment. A wind tunnel model of this wing was built and tested in the NASA Langley Transonic Dynamics Tunnel. Selection of the test conditions (i.e., Mach and Reynolds numbers) were made by applying the techniques of response surface methodology and considerations involving the predicted experimental uncertainty. The test was planned and executed in two phases. In the first phase runs were conducted at the pre-planned test conditions. Based on these results additional runs were conducted in areas where significant differences in CL max were observed between the computational results and the experiment — in essence applying the concept of anti-optimization. These additional runs were used to verify the differences in CL max and assess the extent of the region where these differences occurred. The results of the experiment showed that the analysis was capable of predicting CL max to within 0.05 over most of the test domain. The application of anti-optimization succeeded in identifying a region where the computational and experimental values of CL max differed by more than 0.05, demonstrating the usefulness of anti-optimization in process of validating aerodynamic codes. This region was centered at a Mach number of 0.55 and a Reynolds number of 34,000. Including considerations of the uncertainties in the computational and experimental results confirmed that the disagreement was real and not an artifact of the uncertainties. 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.

This work examines the detailed flow characteristics of direct measuring skin friction gages with computational methods. This type of device uses a small movable head mounted flush to a wall such that the head is assumed to be exposed to the same shear stress from the flow as the surrounding wall. The force caused by the action of the shear stress on the head deflects a flexure system monitored by instruments such as strain gages mounted at the base of a beam. The goal of the study was to develop an understanding of the effects that the geometric design and installation parameters of the sensor have on the surrounding flow and the ability of the sensor to reflect the undisturbed shear stress value. Disruption of the external flow due to poor design and/or improper installation of the sensor can take the form of intrusion into the flow, recession into the wall, and/or tilted alignment of the sensor such that the head is not flat in the plane of the wall, as well as flow into or out of the small gap surrounding the sensing head. Further, the performance of a direct measuring skin friction sensor in the presence of a pressure gradient has always been a concern. These effects are studied here with a three-dimensional, Navier-Stokes code based on a finite element method technique. Numerical solutions for cases in which one or more design parameters were varied are shown for a variety of flow situations. These situations include: (a) a laminar fully-developed channel flow at a low Reynolds number, (b) a turbulent flat plate boundary layer flow at a high Reynolds number, and (c) strong favorable and adverse pressure gradient turbulent boundary layer flows created by converging and diverging channels at high Reynolds number. Reported results for all cases include detailed flow visualization and stress field imagery, and total surface forces on the sensing head and gage flexure. Under ideal circumstances, these total forces should reflect as accurately as possible the average value of undisturbed shear stress times the exposed sensing head area (the friction force). Any deviation from this value was considered an "error" in the simulated measurement. The laminar channel flow case with a strong favorable pressure gradient showed the importance of proper alignment of the sensor. Protrusion or recession of the sensing head proved to be the dominant effect on resulting forces seen by the gage, changing the output by up to 15% for head protrusion and 10% for head recession for misalignments up to +/-1% of the head diameter. The thickness of the lip on the edge of the head also proved to have a significant effect on the output, with a smaller lip thickness generally showing better performance than a large one. Zero lip thickness indicated accuracy to within 1% of the desired wall shear result, since the pressure differences had little influence on the sensing head. Finally, the assumption of a linear pressure variation from the surface to the cavity along the lip as has been suggested in the past was investigated. The results indicate that the linear assumption works well only for large ratios of lip thickness to gap size, a fact which is correlated with previous experimental results. For the turbulent external flat plate case, misalignment remained the dominant effect on the sensor response. Results indicated that, in general, protrusion is more costly than the same level of recession, and a protrusion of +1% of the head diameter was shown to cause in excess of 100% error in indicated wall shear output. Both protrusion and recession produced large variations in both force and moment on the sensing flexure, but the outcome was that for protrusion the errors caused by these two effects tended to sum together, while for recession they tended to partially cancel out. The gap size played an increased role in the high Reynolds number boundary layer cases. Gap sizes of 1.67% up to 6.67% of the head diameter were studied and were shown to produce output errors between 4% and 22% (with larger errors corresponding to larger gap sizes), thus showing the importance of minimizing the gap for high Reynolds number flows. The lip was shown to have no significant effect for a flow without a pressure gradient. Finally, the favorable and adverse pressure gradient flows showed reasonable performance of the skin friction gage. Errors in output were shown to be -6% for the favorable pressure gradient case and 17% for the adverse pressure gradient case. Only the baseline gage design was studied for these situations, but the results from the two cases indicate that further reducing the lip thickness may not improve the performance of the gage. The error in output was caused almost entirely by applied moment for the adverse pressure gradient, while the applied force and applied moment had a cancellation effect in the favorable pressure gradient case. As a general result, the use of computational fluid dynamics has been shown to be an effective tool in the design and analysis of skin friction gages. Using a computational approach has the advantage of being able to resolve the small, confined gap regions of the gage, providing information that has been shown to be unavailable from previous experimental studies. This work has contributed to a much better understanding of the detailed flow over, in, and around skin friction gages. This will lead to improved gage design and reduced uncertainty in these important measurements. Ph. D.

Continuous adjoint methods and optimal control theory are applied to a pressure-matching inverse design problem of quasi 1-D nozzle flows. Pontryagin’s Minimum Principle is used to derive the adjoint system and the reduced gradient of the cost functional. The properties of adjoint variables at the sonic throat and the shock location are studied, revealing a logarithmic singularity at the sonic throat and continuity at the shock location. A numerical method, based on the Steger-Warming flux-vector-splitting scheme, is proposed to solve the adjoint equations. This scheme can finely resolve the singularity at the sonic throat. A non-uniform grid, with points clustered near the throat region, can resolve it even better. The analytical solutions to the adjoint equations are also constructed via Green’s function approach for the purpose of comparing the numerical results. The pressure-matching inverse design is then conducted for a nozzle parameterized by a single geometric parameter. In the second part, the adjoint methods are applied to the problem of minimizing drag coefficient, at fixed lift coefficient, for 2-D transonic airfoil flows. Reduced gradients of several functionals are derived through application of a Lagrange Multiplier Theorem. The adjoint system is carefully studied including the adjoint characteristic boundary conditions at the far-field boundary. A super-reduced design formulation is also explored by treating the angle of attack as an additional state; super-reduced gradients can be constructed either by solving adjoint equations with non-local boundary conditions or by a direct Lagrange multiplier method. In this way, the constrained optimization reduces to an unconstrained design problem. Numerical methods based on Jameson’s finite volume scheme are employed to solve the adjoint equations. The same grid system generated from an efficient hyperbolic grid generator are adopted in both the Euler flow solver and the adjoint solver. Several computational tests on transonic airfoil design are presented to show the reliability and efficiency of adjoint methods in calculating the reduced (super-reduced) gradients. Ph. D.

Recent investigations of a strut-braced wing (SBW) aircraft show that, at high positive load factors, a large tensile force in the strut leads to a considerable compressive axial force in the inner wing, resulting in a reduced bending stiffness and even buckling of the wing. Studying the influence of this compressive force on the structural response of SBW is thus of paramount importance in the early stage of SBW design. The purpose of the this research is to investigate the effect of compressive force on aeroelastic stability of the SBW using efficient structural finite element and aerodynamic lifting surface methods. A procedure is developed to generate wing stiffness distribution for detailed and simplified wing models and to include the compressive force effect in the SBW aeroelastic analysis. A sensitivity study is performed to generate response surface equations for the wing flutter speed as functions of several design variables. These aeroelastic procedures and response surface equations provide a valuable tool and trend data to study the unconventional nature of SBW. In order to estimate the effect of the compressive force, the inner part of the wing structure is modeled as a beam-column. A structural finite element method is developed based on an analytical stiffness matrix formulation of a non-uniform beam element with arbitrary polynomial variations in the cross section. By using this formulation, the number of elements to model the wing structure can be reduced without degrading the accuracy. The unsteady aerodynamic prediction is based on a discrete element lifting surface method. The present formulation improves the accuracy of existing lifting surface methods by implementing a more rigorous treatment on the aerodynamic kernel integration. The singularity of the kernel function is isolated by implementing an exact expansion series to solve an incomplete cylindrical function problem. A hybrid doublet lattice/doublet point scheme is devised to reduce the computational time. SBW aircraft selected for the present study is the fuselage-mounted engine configuration. The results indicate that the detrimental effect of the compressive force to the wing buckling and flutter speed is significant if the wing-strut junction is placed near the wing tip. Ph. D.

A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. The scalar test cases include advected shear, circular advection, non-linear advection with coalescing shock and expansion fans, and advection-diffusion. For all scalar cases the fluctuation splitting scheme is more accurate, and the primary mechanism for the improved fluctuation splitting performance is shown to be the reduced production of artificial dissipation relative to DMFDSFV. The most significant scalar result is for combined advection-diffusion, where the present fluctuation splitting scheme is able to resolve the physical dissipation from the artificial dissipation on a much coarser mesh than DMFDSFV is able to, allowing order-of-magnitude reductions in solution time. Among the inviscid test cases the converging supersonic streams problem is notable in that the fluctuation splitting scheme exhibits superconvergent third-order spatial accuracy. For the inviscid cases of a supersonic diamond airfoil, supersonic slender cone, and incompressible circular bump the fluctuation splitting drag coefficient errors are typically half the DMFDSFV drag errors. However, for the incompressible inviscid sphere the fluctuation splitting drag error is larger than for DMFDSFV. A Blasius flat plate viscous validation case reveals a more accurate vertical-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. A viscous Mach 17.6 (perfect gas) cylinder case demonstrates solution monotonicity and heat transfer capability with the fluctuation splitting scheme. While fluctuation splitting is recommended over DMFDSFV, the difference in performance between the schemes is not so great as to obsolete DMFDSFV. The second half of the dissertation develops a local, compact, anisotropic unstructured mesh adaption scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. This alignment behavior stands in contrast to the curvature clustering nature of the local, anisotropic unstructured adaption strategy based upon a posteriori error estimation that is used for comparison. The characteristic alignment is most pronounced for linear advection, with reduced improvement seen for the more complex non-linear advection and advection-diffusion cases. The adaption strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization. The system test case for the adaption strategy is a sting mounted capsule at Mach-10 wind tunnel conditions, considered in both two-dimensional and axisymmetric configurations. For this complex flowfield the adaption results are disappointing since feature alignment does not emerge from the local operations. Aggressive adaption is shown to result in a loss of robustness for the solver, particularly in the bow shock/stagnation point interaction region. Reducing the adaption strength maintains solution robustness but fails to produce significant improvement in the surface heat transfer predictions. Ph. D.

A series of direct-measuring skin friction gages were developed for a high-speed, high-temperature environment of the turbulent boundary layer in flows such as that in supersonic combustion ramjet (scramjet) engines, with a progression from free-jet ground tests to a design for an actual hypersonic scramjet-integrated flight vehicle. The designs were non-nulling, with a sensing head that was flush with the model wall and surrounded by a small gap. Thus, the shear force due to the flow along the wall deflects the head, inducing a measurable strain. Strain gages were used to detect the strain. The gages were statically calibrated using a direct force method. The designs were verified by testing in a well-documented Mach 2.4 cold flow. Results of the cold-flow tests were repeatable and within 15% of the value of Cf estimated from simple theory. The first gage design incorporated a cantilever beam with semiconductor strain gages to sense the shear on the floating head. Cooling water was routed both internally and around the external housing in order to control the temperature of the strain gages. This first gage was installed and tested in a rocket-based-combined-cycle (RBCC) engine model operating in the scramjet mode. The free-jet facility provided a Mach 6.4 flow with P0 = 1350 psia (9310 kPa) and T0 = 2800 °R (1555 °K). Local wall temperatures were measured between 850 and 900 °R (472-500 °K). Output from the RBCC scramjet tests was reasonable and repeatable. A second skin friction gage was designed for and tested in a wind tunnel model of the Hyper-X flight vehicle scramjet engine. These unsuccessful tests revealed the need for a radically different skin friction gage design. The third and final skin friction gage was specifically developed to be installed on the Hyper-X flight vehicle. Rather than the cantilever beam and semiconductor strain gages, the third skin friction gage made use of a flexure ring and metal foil strain gages to sense the shear. The water-cooling and oil-fill used on the previous skin friction sensors were eliminated. It was qualified for flight through a rigorous series of environmental tests, including pressure, temperature, vibration, and heat flux tests. Finally, the third skin friction gage was tested in the Hyper-X Engine Model (HXEM), a full-scale-partial-width wind tunnel model of the flight vehicle engine. These tests were conducted at Mach 6.5 enthalpy with P0 = 555 psia (3827 kPa) and h0 = 900 Btu/lbm in a freejet facility. The successful testing in the wind tunnel scramjet model provided the final verification of the gage before installation in the flight vehicle engine. The development, testing, and results of all three skin friction gages are discussed. Ph. D.

A three-dimensional unstructured incompressible RANS code has been developed using artificial compressibility and Spalart-Allmaras eddy viscosity model. A node-based finite volume method is used in which all flow variables are defined at the vertices of tetrahedrons in an unstructured grid. The inviscid fluxes are computed by using the Roe's flux difference splitting method, and higher order accuracy is attained by data reconstruction based on Taylor series expansion. Gauss theorem is used to formulate necessary gradients. For time integration, an implicit scheme based on linearized Euler backward method is used. A tetrahedral unstructured grid generation code has been also developed and applied to the tip clearance flow in a highly staggered cascade. Surface grids are first generated in the flow passage and blade tip by using several triangulation methods including Delaunay triangulation, advancing front method and advancing layer method. Then the whole computational domain including tip gap region is filled with prisms using the surface grids. Each prism is divided into three tetrahedrons. To accomplish this division in a consistent manner, connectivity pattern is assigned to each triangle in the surface grids. A new algorithm is devised to assign the connectivity pattern without reference to the particular method of triangulation. This technique offers great flexibility in surface grid generation. The code has been validated by comparisons with available computational and experimental results for several test cases: invisicd flow around NACA section, laminar and turbulent flow over a flat plate, turbulent flow through double-circular arc cascade and laminar flow through a square duct with 90° bend. For the laminar flat plate case, the velocity profile and skin friction coefficient are in excellent agreement with Blasius solution. For the turbulent flat plate case, velocity profiles are in full agreement with the law of the wall up to Reynolds number of 1.0E8, however, the skin friction coefficient is under-predicted by about 10% in comparison with empirical formula. Blade loading for the two-dimensional circular arc cascade is also compared with experiments. The results obtained with the experimental inflow angle (51.5° ) show some discrepancies at the trailing edge and severely under-predict the suction peak at the leading edge. These discrepancies are completely remedied if the inflow angle is increased to 53.5° . The code is also capable of predicting the secondary flow in the square duct with 90° bend, and the velocity profiles are in good agreement with measurements and published Navier-Stokes computations. Finally the code is applied to a linear cascade that has GE rotor B section with tip clearance and a high stagger angle of 56.9° . The overall structure of the tip clearance flow is well predicted. Loss of loading due to tip leakage flow and reloading due to tip leakage vortex are presented. On the end wall, separation line of the tip leakage vortex and reattachment line of passage vortex are identified. The location of the tip leakage vortex in the passage agrees very well with oil flow visualization. Separation bubble on the blade tip is also predicted. Mean streamwise velocity contours and cross sectional velocity vectors are compared with experimental results in the near wake, and good agreements are observed. It is concluded that Spalart-Allmaras turbulence model is adequate for this type of flow field except at locations where the tip leakage vortex of one blade interacts with the wake of a following blade. This situation may prevail for blades with longer span and/or in the far wake. Prediction of such an interaction presents a challenge to RANS computations. The effects of blade span on the flow structure have been also investigated. Two cascades with blades of aspect ratios of 0.5 and 1.0 are considered. By comparing pressure distributions on the blade, it is shown that the aspect ratio has strong effects on loading distribution on the blade although the tip gap height is very small (0.016 chord). Grid convergence study has been carried out with three different grids for pressure distributions and limiting streamlines on the end wall. Ph. D.

This investigation, in consideration of the sudden separation increase involved in wing drop, was to determine if the incorporated 2-D airfoil exhibits abnormal shock sensitivity. A comparative airfoil study was used to determine if this particular transonic airfoil is prone to abrupt shock movement, resulting in increased regions of separation. Master of Science

Errors of computational simulations in design of a high-speed civil transport (HSCT) are investigated. First, discretization error from a supersonic panel code, WINGDES, is considered. Second, convergence error from a structural optimization procedure using GENESIS is considered along with the Rosenbrock test problem. A grid converge study is performed to estimate the order of the discretization error in the lift coefficient (CL) of the HSCT calculated from WINGDES. A response surface (RS) model using several mesh sizes is applied to reduce the noise magnification problem associated with the Richardson extrapolation. The RS model is shown to be more efficient than Richardson extrapolation via careful use of design of experiments. A programming error caused inaccurate optimization results for the Rosenbrock test function, while inadequate convergence criteria of the structural optimization produced error in wing structural weight of the HSCT. The Weibull distribution is successfully fit to the optimization errors of both problems. The probabilistic model enables us to estimate average errors without performing very accurate optimization runs that can be expensive, by using differences between two sets of results with different optimization control parameters such as initial design points or convergence criteria. Optimization results with large errors, outliers, produced inaccurate RS approximations. A robust regression technique, M-estimation implemented by iteratively reweighted least squares (IRLS), is used to identify the outliers, which are then repaired by higher fidelity optimizations. The IRLS procedure is applied to the results of the Rosenbrock test problem, and wing structural weight from the structural optimization of the HSCT. A nonsymmetric IRLS (NIRLS), utilizing one-sidedness of optimization errors, is more effective than IRLS in identifying outliers. Detection and repair of the outliers improve accuracy of the RS approximations. Finally, configuration optimizations of the HSCT are performed using the improved wing bending material weight RS models. Ph. D.

Steady and unsteady flow over a generic Suboff submarine model is studied. The skin-friction magnitudes are measured by using hot-film sensors each connected to a constant temperature anemometer. The local minima in the skin-friction magnitudes are used to obtain the separation locations. Steady static pressure measurements on the model surface are performed at 10° and 20° angles of attack. Steady and unsteady results are presented for two model configurations: barebody and sail-on-side case. The dynamic plunge-pitch-roll model mount (DyPPiR) is used to simulate the pitchup maneuvers. The pitchup maneuver is a linear ramp from 1° to 27° in 0.33 seconds. All the tests are conducted at ReL=5,500,000 with a nominal wind tunnel speed of 42.7±1 m/s. Steady results show that the flow structure on the leeward side of the barebody can be characterized by the crossflow separation. In the sail-on-side case, the separation pattern of the non-sail region follow the barebody separation trend closely. The flow on the sail side is strongly affected by the presence of the sail and the separation pattern is different from the crossflow separation. The flow in the vicinity of the sail-body junction is dominated by the horseshoe type separation. Unsteady results of the barebody and the non-sail region of the sail-on-side case show significant time lags between unsteady and steady crossflow separation locations. These effects produce the difference in separation topology between the unsteady and steady flowfields. A first-order time lag model approximates the unsteady separation locations reasonably well and time lags are obtained by fitting the model equation with the experimental data. The unsteady separation pattern of the sail side does not follow the quasi-steady data with a time lag and the unsteady separation structure is different from the unsteady crossflow separation topology observed for the barebody and the non-sail region of the sail-on-side case. Master of Science

An accurate and efficient numerical method for Compressible Vorticity Confinement (CVC) was developed. The methodology follows from Steinhoff's vorticity confinement approach that was developed for incompressible flows. In this research, the extension of this approach to compressible flows has been developed by adding a vorticity confinement term as a "body force" into the governing compressible flow equations. This vorticity confinement term tends to cancel the numerical dissipative errors inherently related to the numerical discretization in regions of strong vorticity gradients. The accuracy, reliability, efficiency and robustness of this method were investigated using two methods. One approach is directly applying the CVC method to several real engineering problems involving complex vortex structures and assessing the accuracy by comparison with existing experimental data and with other computational techniques. Examples considered include supersonic conical flows over delta wings, shock-bubble and shock-vortex interactions, the turbulent flow around a square cylinder and the turbulent flow past a surface-mounted 3D cube in a channel floor. A second approach for evaluating the effectiveness of the CVC method is by solving simplified "model problems" and comparing with exact solutions. Problems that we have considered are a two-dimensional supersonic shear layer, flow over a flat plate and a two-dimensional vortex moving in a uniform stream. The effectiveness of the compressible confinement method for flows with shock waves and vortices was evaluated on several complex flow applications. The supersonic flow over a delta wing at high angle of attack produces a leeward vortex separated from the wing and cross flow, as well as bow shock waves. The vorticity confinement solutions compare very favorably with experimental data and with other calculations performed on dense, locally refined grids. Other cases evaluated include isolated shock-bubble and shock-vortex interactions. The resulting complex, unsteady flow structures compare very favorably with experimental data and computations using higher-order methods and highly adaptive meshes. Two cases involving massive flow separation were considered. First the two-dimensional flow over a square cylinder was considered. The CVC method was applied to this problem using the confinement term added to the inviscid formulation, but with the no-slip condition enforced. This produced an unsteady separated flow that agreed well with experimental data and existing LES and RANS calculations. The next case described is the flow over a cubic protuberance on the floor of a channel. This flow field has a very complex flow structure involving a horseshoe vortex, a primary separation vortex and secondary corner vortices. The computational flow structures and velocity profiles were in good agreement with time-averaged values of the experimental data and with LES simulations, even though the confinement approach utilized more than a factor of 50 fewer cells (about 20,000 compared to over 1 million). In order to better understand the applicability and limitations of the vorticity confinement, particularly the compressible formulation, we have considered several simple model problems. Classical accuracy has been evaluated using a supersonic shear layer problem computed on several grids and over a range of values of confinement parameter. The flow over a flat plate was utilized to study how vorticity confinement can serve as a crude turbulent boundary layer model. Then we utilized numerical experiments with a single vortex in order to evaluate a number of consistency issues related to the numerical implementation of compressible confinement. Ph. D.

A non-intrusive direct-measuring skin friction device with a rubber RTV sheet over the surface of the floating head, gap and housing was developed for application in 3D, unsteady, transonic flight conditions. Design conditions required optimum gage performance at altitudes ranging from 15,000 to 45,000 feet, Mach numbers ranging from 0.6 to 0.99 resulting in shear values of 0.3 to 1.5 psf. under vibration conditions up to 8.0 grms over a 15 - 2,000 Hz frequency range. The gage consisted of a rubber RTV sheet-coated floating element attached to an aluminum cantilevered beam. A dual-axis, full bridge strain gage configuration was used with the application of semi-conductor strain gages to increase instrument sensitivity. The gage was studied with and without a viscous liquid (glycerin) fill in the housing. Vibration verification testing was performed at 1.0 grms in the Virginia Tech modal analysis lab to ensure adequate damping performance over a 0−3200 Hz frequency range. Tests revealed that the rubber RTV compound sheet provided adequate viscoelastic damping, with or without viscous liquid fill. Gage performance verification testing was performed on in the Virginia Tech supersonic wind tunnel at shear levels of tw = 3.9 to 5.3 psf in a Mach 2.4 flow. Skin friction values in good agreement with previous testing and analytical predictions were obtained from the tests with adequate damping in the low vibration environment of the Virginia Tech supersonic wind tunnel. The gage proved robust as it survived repeated runs including the violent start and unstart processes typical of a supersonic, blowdown wind tunnel. Flight tests were performed at NASA Dryden Flight Research Center, with the gage mounted in a plate suspended below an F-15 aircraft. This provided a mildly 3D, turbulent boundary layer on a vibrating surface. The gage was tested without liquid fill in the gage cavity, and it performed satisfactorily in this high vibration environment. The gage demonstrated adequate damping and good robustness, surviving the complete flight test intact and remained fully operational. The sensor measured skin friction values 30%-50% higher than those predicted by indirect methods and analogies generally valid for 2D, steady flows. The gage indicated trends in skin friction values for different flight conditions in good agreement with the other methods. Possible reasons for the differences in numerical values are discussed in detail, including potential uncertainties in the gage output and limitations and uncertainties in the methods used for comparison. Finally, suggestions for further development of such gages are provided for flight test applications. Master of Science

The classic minimum induced drag spanload is not necessarily the best choice for an aircraft. For a single aircraft configuration, variations from the elliptic, minimum drag optimum load distribution can produce wing weight savings that result in airplane performance benefits. For a group of aircraft flying in formation, non-elliptic lift distributions can give high induced drag reductions both for the formation and for each airplane. For single aircraft, a discrete vortex method which performs the calculations in the Trefftz plane has been used to calculate optimum spanloads for non-coplanar multi-surface configurations. The method includes constraints for lift coefficient, pitching moment coefficient and wing root bending moment. This wing structural constraint has been introduced such that wing geometry is not changed but the modified load distributions can be related to wing weight. Changes in wing induced drag and weight were converted to aircraft total gross weight and fuel weight benefits, so that optimum spanloads that give maximum take-off gross weight reductions can be found. Results show that a reduction in root bending moment from a lift distribution that gives minimum induced drag leads to more triangular spanloads, where the loads are shifted towards the root, reducing wing weight and increasing induced drag. A slight reduction in root bending moment is always beneficial, since the initial increase in induced drag is very small compared to the wing weight decrease. Total weight benefits were studied for a Boeing 777-200IGW type configuration, obtaining take-off gross weight improvements of about 1% for maximum range missions. When performing economical, reduced-range missions, improvements can almost double. A long range, more aerodynamically driven aircraft like the Boeing 777-200IGW will experience lower benefits as a result of increasing drag. Short to medium range aircraft will profit the most from more triangular lift distributions. Formation flight configurations can also result in large induced drag reductions for load distributions that deviate from the elliptical one. Optimum spanloads for a group of aircraft flying in an arrow formation were studied using the same discrete vortex method, now under constraints in lift, pitching moment and rolling moment coefficients. It has been shown that large general improvements in induced drag can be obtained when the spanwise and vertical distances between aircraft are small. In certain cases, using our potential flow vortex model, this results in negative (thrust) induced drag on some airplanes in the configuration. The optimum load distributions necessary to achieve these benefits may, however, correspond to a geometry that will produce impractical lift distributions if the aircraft are flying alone. Optimum separation among airplanes in this type of formation is determined by such diverse factors as the ability to generate the required optimum load distributions or the need for collision avoidance. Master of Science

The purpose of this study is to examine the multidisciplinary design optimization (MDO) of a strut-braced wing (SBW) aircraft compared to similarly designed cantilever wing aircraft. In this study, four different configurations are examined: cantilever wing aircraft, fuselage mounted engine SBW, wing mounted engine SBW, and wingtip mounted engine SBW. The cantilever wing design is used as a baseline for comparison. Two mission profiles were used. The first called for a 7380 nmi range with a 305 passenger load based on a typical Boeing 777 mission. The second profile was supplied by Lockheed Martin Aeronautical Systems (LMAS) and has a 7500 nmi range with a 325 passenger load. Both profiles have a 0.85 cruise Mach number and a 500 nmi reserve range. Several significant refinements and improvements have been made to the previously developed MDO code for this study. Improvements included using ADIFOR (Automatic Differentiation for FORTRAN) to explicitly compute gradients in the design code. Another major change to the MDO code is the improvement of the optimization architecture to allow for a more robust optimization process. During the Virginia Tech SBW study, Lockheed Martin Aeronautical Systems (LMAS) was tasked by NASA Langley to evaluate the results of previous SBW studies. During this time, the original weight equations which were obtained from NASA Langley's Flight Optimization System (FLOPS) was replaced by LMAS proprietary equations. A detailed study on the impact of the equations from LMAS on the four designs was done, comparing them to the designs that used the FLOPS equations. Results showed that there was little difference in the designs obtained using the new equations. An investigation of the effect of the design constraints on the different configurations was performed. It was found that in all the design configurations, the aircraft range proved to be the most crucial constraint in the design. However, results showed that all three SBW designs were less sensitive to constraints than the cantilever wing aircraft. Finally, a double-deck fuselage concept was considered. A double deck fuselage configuration would result in a greater wing/strut intersection angle which would, in turn, reduce interference drag at that section. Due to the lack of available data on double deck fuselage aircraft, a detailed study of passenger and cargo layout was done. Optimized design showed that there was a small improvement in takeoff gross weight and fuel weight over the single-deck fuselage SBW results when compared with a similarly designed cantilever wing aircraft. Master of Science

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.

In transonic flow, the aerodynamic interference that occurs on a strut-braced wing airplane, pylons, and other applications is significant. The purpose of this work is to provide relationships to estimate the interference drag of wing-strut, wing-pylon, and wing-body arrangements. Those equations are obtained by fitting a curve to the results obtained from numerous Computational Fluid Dynamics (CFD) calculations using state-of-the-art codes that employ the Spalart-Allmaras turbulence model. In order to estimate the effect of the strut thickness, the Reynolds number of the flow, and the angle made by the strut with an adjacent surface, inviscid and viscous calculations are performed on a symmetrical strut at an angle between parallel walls. The computations are conducted at a Mach number of 0.85 and Reynolds numbers of 5.3 and 10.6 million based on the strut chord. The interference drag is calculated as the drag increment of the arrangement compared to an equivalent two-dimensional strut of the same cross-section. The results show a rapid increase of the interference drag as the angle of the strut deviates from a position perpendicular to the wall. Separation regions appear for low intersection angles, but the viscosity generally provides a positive effect in alleviating the strength of the shock near the junction and thus the drag penalty. When the thickness-to-chord ratio of the strut is reduced, the flowfield is disturbed only locally at the intersection of the strut with the wall. This study provides an equation to estimate the interference drag of simple intersections in transonic flow. In the course of performing the calculations associated with this work, an unstructured flow solver was utilized. Accurate drag prediction requires a very fine grid and this leads to problems associated with the grid generator. Several challenges facing the unstructured grid methodology are discussed: slivers, grid refinement near the leading edge and at the trailing edge, grid convergence studies, volume grid generation, and other practical matters concerning such calculations. Ph. D.

A study was conducted on the measurement of skin friction, the least under-stood component of drag. Skin friction is considered the "last frontier" in drag reduction for supersonic flight, but to understand skin friction, it must be accurately measured. This study utilized the direct measuring technique for skin friction. A small de-vice, termed a skin friction gage, measures the stress on a cantilever beam topped with a movable surface piece as a shear flow passes over the flush surface. The improvement of these devices for various flow fields is ongoing. A problem that arose with many designs was leakage of a gap-filling liquid. The typical direct measuring skin friction gage uses oil in a gap between the cantilever beam and the encasement to dampen vibrations, to create an even flow over the surface, and for temperature compensation. In high speed testing the oil leaks out; therefore, a gage with rubber to fill the gap instead of oil was introduced This study employed a finite element method model to fully understand the strains involved with the rubber and the skin friction gage. The development of a calibration device, called the Calibration Rig, for the rubber skin friction gages was constructed. The Calibration Rig was successful, but deemed to be more cumbersome than initially expected. This led to the development of a thin rubber sheet to cover the face of the gage instead of rubber filling the entire gap. More finite element method modeling was done to finalize the design of a gage with a rubber sheet. The design consisted of a plastic skin friction gage with an approximately 0.015 in. thick rubber sheet, a 0.0625 in. wide gap between the floating head on the cantilever beam and the encasement to be filled with oil, and semi-conductor strain gages to measure the beam deflection. Vibration tests were performed to determine if the rubber sheet produced the required damping. These tests were successful, and so much so, that the oil for damping was not necessary. However, supersonic wind tunnel tests at Mach 2.4 which were done at Virginia Polytechnic Institute and State University, initially yielded unfavorable results. The rubber sheet failed during the violent process of starting and unstarting of the tunnel. More study on the adhesive mounting of the rubber sheet to the skin friction gage face is needed. Master of Science

This dissertation presents experimental measurements and analysis of the surface pressure fluctuations beneath several turbulent boundary layers of practical interest. Pressure fluctuations in turbulent boundary layers are a source of noise and vibration that can accelerate structural fatigue. Pressure fluctuations and their correlation with velocity fluctuations is an important diffusive mechanism of turbulence transport. The approach was to study the statistics of both the surface pressure and the velocity field through new measurements of the fluctuating surface pressure and existing measurements of the velocity field and the covariance of the surface pressure and fluctuating velocity components. Measurements were made in three types of flows. The first type of flow was a zero pressure gradient, two-dimensional, turbulent boundary layer (Re(theta) = 7300 and Re(theta) = 23400). The two-dimensional flows serve as a baseline for comparison to the other three-dimensional flows and validate the experimental techniques used in the present study through comparison with existing measurements. The second type of flow was a three-dimensional, pressure-driven, turbulent boundary layer that forms away from a wing-body junction. Two of this type of boundary layer were studied - Re(theta) = 5940 and Re(theta) = 23200. The third type of flow was the separating flow about the leeside of a 6:1 prolate spheroid at angle of attack. Measurements were made at two angles of attack, 10° and 20°, and two axial locations, x/L = 0.600 and x/L = 0.772, in this type of flow. Spectral scaling is discussed and various scaling combinations of the spectral power density of surface pressure fluctuations beneath two-dimensional boundary layers that cover a wide range of Reynolds number (1400 < Re(theta) < 23400) are presented. The spectral power density of surface pressure fluctuations beneath the separating flow on the leeside of a 6:1 prolate spheroid at 10° angle of attack collapse when normalized using viscous scales. However, the spectral power density of surface pressure fluctuations beneath highly three-dimensional flow contain nearly constant spectral levels within a middle to high frequency range. The nearly constant spectral levels are due to a lack of overlapping frequency structure between the large-scale motions and the viscous-dominated motions since each of these types of motion may have different flow histories due to the three-dimensional flow structure. This effect amplifies the importance of the middle frequency range to p' as compared to two-dimensional flows. In terms of instrumentation, accurate p' measurements in a three-dimensional flow require accurate high frequency (f > 20 kHz) p measurements. The lack of similarity in the shape of the spectral power density preclude a direct extension of "universal" generalizations that are true for surface pressure fluctuations beneath two-dimensional boundary layers. The resulting RMS surface pressure fluctuation distributions reflect the importance of the high frequency wall region contributions. Scaling parameters for the p spectra beneath three-dimensional flows must incorporate local flow structure in order to be successful. Analysis based on the Poisson equation shows that variation of the high frequency spectral levels are related to the variation in near-wall mean velocity gradients and v² structure. In the 6:1 prolate spheroid flow, near regions of crossflow separation there is a local minimum in RMS surface pressure fluctuations, whereas around reattachments and under the large shed vortices there is a local maximum in RMS surface pressure fluctuations. Measurements of the correlation coefficient between surface pressure and velocity fluctuations show that there can be sources of p away from the wall in three-dimensional flows. Sources of p away from the wall are significant in terms of fluid-structure interaction since they contribute low frequency fluctuations. Structures typically have low resonant frequencies. Sources of p away from the wall are also significant in terms of radiated sound since they are likely to interact with the free-stream and be radiated away as sound. Ph. D.

Recent transonic airliner designs have generally converged upon a common cantilever low-wing configuration. It is unlikely that further large strides in performance are possible without a significant departure from the present design paradigm. One such alternative configuration is the strut-braced wing, which uses a strut for wing bending load alleviation, allowing increased aspect ratio and reduced wing thickness to increase the lift to drag ratio. The thinner wing has less transonic wave drag, permitting the wing to unsweep for increased areas of natural laminar flow and further structural weight savings. High aerodynamic efficiency translates into reduced fuel consumption and smaller, quieter, less expensive engines with lower noise pollution. A Multidisciplinary Design Optimization (MDO) approach is essential to understand the full potential of this synergistic configuration due to the strong interdependency of structures, aerodynamics and propulsion. NASA defined a need for a 325-passenger transport capable of flying 7500 nautical miles at Mach 0.85 for a 2010 date of entry into service. Lockheed Martin Aeronautical systems (LMAS), our industry partner, placed great emphasis on realistic constraints, projected technology levels, manufacturing and certification issues. Numerous design challenges specific to the strut-braced wing became apparent through the interactions with LMAS, and modifications had to be made to the Virginia Tech code to reflect these concerns, thus contributing realism to the MDO results. The SBW configuration is 9.2-17.4% lighter, burns 16.2-19.3% less fuel, requires 21.5-31.6% smaller engines and costs 3.8-7.2% less than equivalent cantilever wing aircraft. Master of Science

Turbulent wakes generated from an aircraft or submarine vehicles has been of main interest to researchers due to the broad band noise associated with such wakes. One such case is the noise generated by spiral vortices shed of from one blade interacting with another oncoming blade of helicopter rotor. Consequently, researchers have been trying to understand the basic physics and evolution of such wakes. Although there has been numerous studies done on plane wakes, there has been little research being done on laterally curved wakes. Single and two-point velocity measurements were taken on a plane and laterally curved turbulent wakes to understand the evolution and effect of lateral curvature into the far wake region. The analyses provide useful information in modeling curved or spiral wakes such as turbulence field surrounding tip vortices shed from a wing. In order to achieve our objectives, the Virginia Tech 3’ x 2’ subsonic wind tunnel was used to take velocity measurements of toroidal ring model and a straight cylinder as a control case. Velocity measurements were done using four sensor hot-wire anemometers, to obtain all mean velocity, Reynolds stress, triple product components of the turbulence field. Single point, spectra and two-point measurements of the wakes were performed throughout the development into the far wake region. The single point results reveal the universality of the mean axial velocity, however the Reynolds stresses and triple products were not universal illustrating that the turbulence field has its own length and velocity scales different from that of the mean flow. The effect of lateral curvature is mainly evidenced in the early development of the curved ring wake. The turbulent energy budget reveals similar trend for both wakes and plane wake achieves approximate equilibrium. The spectra result reveals for the plane wake that self-preservation is achieved for all scales of motion, while the ring wake does not achieve such a state. While the longitudinal correlations of both wakes are similar in form, in general difference in form and orientation prevailed over all indicating the difference in the turbulent structure of both wakes. Linear stochastic estimation reveals the presence of spanwise and double-roller eddy structures in the plane wake and only spanwise eddies were detected for the ring wake. Master of Science

Simultaneous two-point three-component four-sensor hot-wire velocity measurements taken in three flows of aeroacoustic interest are here analyzed. The analyses provide information on the turbulence structure of the flows as it would be encountered by hypothetical noise producing blades passing through the flows. Two-point measurements taken in the first flow, a lifting wake from a rectangular NACA 0012 half wing, are used to calculate space-time correlation functions and 'pointwise' wave number frequency spectra. Two upwash spectra, calculated for locations in the region of the wake that is roughly homogenous in the spanwise direction, are direct estimates of the full wave number frequency spectra at their locations. As such, they are used to perform aeroacoustic calculations, and the results are compared to results achieved using the von Kármán isotropic spectrum. Amiet's approximation, where the wave number frequency spectra can be represented by the correlation length scales is found to hold reasonably well for the measured spectra. The two-point measurements in the second flow, a vortex/blade-tip interaction, are analyzed to provide information useful to researchers of blade-wake interaction noise produced by helicopter rotors. Space-time correlation functions and wave number frequency spectra are calculated for five cuts through the region of interaction. The correlation functions provide information concerning the turbulence length scales found in the interaction region. The spectra are compared to the von Kármán isotropic spectrum and found to be greatly different. However, the spectra do bear some resemblance to spectra calculated in the spanwise homogenous region of the lifting wake. The two-point measurements taken in the third flow, the wake from a fan cascade, are analyzed to provide information of use to modelers of broadband noise produced through rotor wake/stator interactions. In particular, space-time correlation functions are calculated for a grid of two-point measurements, which allows the estimation of the turbulence structure as seen by a passing stator blade. Space-time correlation functions and wave number frequency spectra are calculated for various stator configurations. The implications of engine operating speed and stator configuration for broadband noise production are discussed. [Vita removed March 2, 2012. GMc] Master of Science

A procedure for generating and using a polynomial approximation to wing bending material weight of a High Speed Civil Transport (HSCT) is presented. Response surface methodology is used to fit a quadratic polynomial to data gathered from a series of structural optimizations. Several techniques are employed in order to minimize the number of required structural optimizations and to maintain accuracy. First, another weight function based on statistical data is used to identify a suitable model function for the response surface. In a similar manner, geometric and loading parameters that are likely to appear in the response surface model are also identified. Next, rudimentary analysis techniques are used to find regions of the design space where reasonable HSCT designs could occur. The use of intervening variables along with analysis of variance reduce the number of polynomial terms in the response surface model function. Structural optimization is then performed by the program GENESIS on a 28-node Intel Paragon. Finally, optimizations of the HSCT are completed both with and without the response surface. Master of Science

Compound Aircraft Transport (CAT) flight involves two or more aircraft using the resources of each other; a symbiotic relationship exists consisting of a host, the mothership aircraft and a parasite, the hitchhiker aircraft. Wingtip-docked flight is just as its name implies; the two aircraft are connected wingtip-to-wingtip. Formation flight describes multiple aircraft or flying objects that maintain a pattern or shape in the air. There are large aerodynamic advantages in CAT flight. The aforementioned wingtip-docked flight increases total span of the aircraft system, and formation flight utilizes the upwash from the trailing wingtip vortex of the lead aircraft (mothership) to reduce the energy necessary to achieve and/or maintain a specific flight goal for the hitchhiker and the system. The Stability Wind Tunnel (6 X 6 X 24 foot test section) at Virginia Tech, computational aerodynamic analysis with the vortex lattice method (VLM), and a desktop aircraft model were used to answer questions of the best location for a hitchhiker aircraft and analyze stability of the CAT system. Wind tunnel tests implemented a 1/32 scale F-84E model (hitchhiker) and an outboard wing portion representing a B-36 (mothership). These models were chosen to simulate flight tests of an actual wingtip-docked project, Tom Tom, in the 1950s. That project was terminated after a devastating accident that demonstrated a possible "flapping" motion instability. The wind tunnel test included a broad range of hitchhiker locations: varying spanwise gap distance, longitudinal or streamwise distance, and vertical location (above or below wing) with respect to a B-36-like wing. The data showed very little change in the aerodynamic forces of the mothership, and possibilities of large benefits in lift and drag for the hitchhiker when located slightly aft and inboard with respect to the mothership. Three CAT flight configurations were highlighted: wingtip-docked, close formation, and towed formation. The wingtip-docked configuration had a 20-40 percent performance benefit for the hitchhiker compared to solo flight. The close formation configuration had performance benefits for the hitchhiker approximately 10 times that of solo flight, and the towed formation was approximately 8 times better than solo flight. The VLM analysis completed and reenforced the experimental wind tunnel data. A modified VLM program (VLM CAT) incorporated multiple aircraft in various locations as well as additional calculations for induced drag. VLM CAT results clearly followed the trends seen in the wind tunnel data, but since VLM did not model the fuselage, has assumptions like a flat wake, and is an inviscid computation it did not predict the large benefits or excursions as seen in the wind tunnel data. Increases in performance for the hitchhiker in VLM CAT were on the order of 3 to 4 times that of the hitchhiker in solo flight, while the wind tunnel study saw up to 10 times that of solo flight. VLM CAT is a valuable tool in supplying quick analysis of position and planform effects in CAT flight. Modifications to a desktop F-16 dynamic simulation have been developed to investigate the stability of wingtip-docked flight. These modifications analyze the stability issues linked with sideslip angle as seen by the Tom Tom Project test pilot, when he entered docking maneuvers with 5 degrees yaw to simulate a ``tired pilot". The wingtip-docked system was determined to have an unstable aperiodic mode for sideslip angle greater than 0.0 degrees and an unstable oscillatory mode for sideslip angle greater than 2.0 degrees. There is a small range of sideslip angle that is a stable oscillatory mode, sideslip angle between 0.0 and 2.0 degrees. The variables, altitude and speed, yield little effect on the stability of the system. The sensitivity analysis was indeterminate in distinguishing a state driving the instability, but the analysis was conclusive in verifying the lateral-longitudinal (roll-pitch) coupled motion observed by test pilots in wingtip-docked flight experiments. The parameter with the largest influence on the instability was the change in pitch angular acceleration with respect to roll angle. The aerodynamic results presented in this study have determined some important parameters in the location of a hitchhiker with respect to a mothership. The largest aerodynamic benefits are seen when the hitchhiker wingtip is slightly aft, inboard and below the wingtip of the mothership. In addition, the stability analysis has identified an instability in the CAT system in terms of sideslip angle, and that the wingtip-docked hitchhiker is coupled in lateral and longitudinal motion, which does concur with the divergent "flapping" motion about the hinged rotational axis experienced by the Tom Tom Project test pilot. Ph. D.

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated, and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences and a complex-variable approach. Several simplifying approximations to the complete linearization of the residual are also presented. A first-order approximation to the dependent variables is implemented in the adjoint and design equations, and the effect of a "frozen" eddy viscosity and neglecting mesh sensitivity terms is also examined. The resulting derivatives from these approximations are all shown to be inaccurate and often of incorrect sign. However, a partially-converged adjoint solution is shown to be sufficient for computing accurate sensitivity derivatives, yielding a potentially large cost savings in the design process. The convergence rate of the adjoint solver is compared to that of the flow solver. For inviscid adjoint solutions, the cost is roughly one to four times that of a flow solution, whereas for turbulent computations, this ratio can reach as high as ten. Sample optimizations are performed for inviscid and turbulent transonic flows over an ONERA M6 wing, and drag reductions are demonstrated. Ph. D.

The Streamline Upwind/Petrov-Galerkin (SU/PG) method is applied to higher-order finite-element discretizations of the Euler equations in one dimension and the Navier-Stokes equations in two dimensions. The unknown flow quantities are discretized on meshes of triangular elements using triangular Bezier patches. The nonlinear residual equations are solved using an approximate Newton method with a pseudotime term. The resulting linear system is solved using the Generalized Minimum Residual algorithm with block diagonal preconditioning. The exact solutions of Ringleb flow and Couette flow are used to quantitatively establish the spatial convergence rate of each discretization. Examples of inviscid flows including subsonic flow past a parabolic bump on a wall and subsonic and transonic flows past a NACA 0012 airfoil and laminar flows including flow past a a flat plate and flow past a NACA 0012 airfoil are included to qualitatively evaluate the accuracy of the discretizations. The scheme achieves higher order accuracy without modification. Based on the test cases presented, significant improvement of the solution can be expected using the higher-order schemes with little or no increase in computational requirements. The nonlinear system also converges at a higher rate as the order of accuracy is increased for the same number of degrees of freedom; however, the linear system becomes more difficult to solve. Several avenues of future research based on the results of the study are identified, including improvement of the SU/PG formulation, development of more general grid generation strategies for higher order elements, the addition of a turbulence model to extend the method to high Reynolds number flows, and extension of the method to three-dimensional flows. An appendix is included in which the method is applied to inviscid flows in three dimensions. The three-dimensional results are preliminary but consistent with the findings based on the two-dimensional scheme. Ph. D.

The objective of this study is to use Multidisciplinary Design Optimization (MDO) to investigate the use of truss-braced wing concepts in concert with other advanced technologies to obtain a significant improvement in the performance of transonic transport aircraft. The truss topology introduces several opportunities. A higher aspect ratio and decreased wing thickness can be achieved without an increase in wing weight relative to a cantilever wing. The reduction in thickness allows the wing sweep to be reduced without incurring a transonic wave drag penalty. The reduced wing sweep allows a larger percentage of the wing area to achieve natural laminar flow. Additionally, tip-mounted engines can be used to reduce the induced drag. The MDO approach helps the designer achieve the best technology integration by making optimum trades between competing physical effects in the design space. To perform this study, a suite of approximate analysis tools was assembled into a complete, conceptual-level MDO code. A typical mission profile of the Boeing 777-200IGW was chosen as the design mission profile. This transport carries 305 passengers in mixed class seating at a cruise Mach number of 0.85 over a range of 7,380 nmi. Several single-strut configurations were optimized for minimum takeoff gross weight, using eighteen design variables and seven constraints. The best single-strut configuration shows a 15% savings in takeoff gross weight, 29% savings in fuel weight, 28% increase in L/D, and a 41% increase in seat-miles per gallon relative to a comparable cantilever wing configuration. In addition to the MDO work, we have proposed some innovative, unconventional arch-braced and ellipse-braced concepts. A plastic solid model of one of the novel configurations was created using the I-DEAS solid modeling software and rapid prototyping hardware. Master of Science

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 framework for understanding the fundamental physics of flowfields over forebody type shapes at low speed, high angle of attack conditions with special emphasis on sideslip has been established. Computational Fluid Dynamics (CFD) has been used to study flowfields over experimentally investigated forebodies: the Lament tangent-ogive forebody, the F-5A forebody and the Erickson chine forebody. A modified version of a current advanced code, CFL3D, was used to solve the Euler and thin-layer Navier-Stokes equations. The Navier-Stokes equations used a form of the Baldwin-Lomax turbulence model modified to account for massive crossflow separation. Using the insight provided by the solutions obtained using CFD, together with comparison with limited available data, the aerodynamics of forebodies with positive directional stability has been revealed. An unconventional way of presenting the results is used to illustrate how a positive contribution to directional stability arises. Based on this new understanding, a parametric study was then conducted to determine which shapes promote a positive contribution to directional stability. Ph. D.

A method to efficiently introduce supersonic drag predictions from computational fluid dynamics (CFD) calculations in a combined aerodynamic-structural optimization of a High-Speed Civil Transport (HSCT) is presented. To achieve this goal, the method must alleviate the large computational burden associated with performing CFD analyses and reduce the numerical noise present in the analyses. This is accomplished through the use of response surface (RS) methodologies, a variation of the variable-complexity modeling (VCM) technique, and coarse grained parallel computing. Variable-complexity modeling allows one to take advantage of the information gained from inexpensive lower fidelity models while maintaining the accuracy of the more expensive high fidelity methods. The utility of the method is demonstrated on HSCT design problems of five, ten, fifteen, and twenty design variables. Motivation for including CFD predictions into the HSCT optimization comes from studies detailing the differences in supersonic aerodynamic predictions from linear theory, Euler, and parabolized Navier-Stokes (PNS) calculations for HSCT configurations. The effects of these differences in integrated forces and distributed loads on the aircraft performance and structural weight are investigated. These studies indicate that CFD drag solutions are required for accurate HSCT performance and weight estimates. Response surface models are also used to provide useful information to the designer with minimal computational effort. Investigations into design trade-offs and sensitivities to certain design variables, available at the cost of evaluating a simple quadratic polynomial, are presented. In addition, a novel and effective approach to visualizing high dimensional, highly constrained design spaces is enabled through the use of RS models. NOTE: An updated copy of this ETD was added in July 2012 after there were patron reports of problems with the original file. Ph. D.

A numerical investigation of the performance of two candidate designs for injection into supersonic flow, including a comparison of two renormalized group theory (RNG) based k-epsilon turbulence models with a more conventional k-epsilon model. The chosen designs were an unswept ramp injector with four injection ports and a novel nine-hole injector array. The objectives of the investigation were to provide reliable computational solutions to the flowfields in question using both RNG and standard k-epsilon turbulence models and to compare the solutions to experiment, thereby to judge the relative performance of the turbulence models. A second objective of the investigation was to use the computed data to provide design insights for the nine-hole injector array. This investigation made use of GASP(tm) version 2.2, a commercial computational fluid dynamics code that was augmented by the addition of one RNG-based k-epsilon turbulence model derived by Zhou, et. al. and one variant of Zhou's model, which was derived by the author. Mesh sequencing studies were performed to measure solution quality, with the fine mesh for the injector array containing roughly one million grid nodes and the fine mesh for the ramp injector containing more than six million grid nodes. Results of these studies indicated that the injector-array solution was significantly under-resolved in the farfield, though the quality was better in the vicinity of the injector itself. The ramp-injector solution, while not perfectly grid-resolved, showed much better grid convergence in both the nearfield and farfield. Accordingly, comparison with experiment was better for the ramp injector than for the injector array. For both injectors, the differences between solutions generated with RNG-based k-epsilon and standard k-epsilon turbulence models were negligibly small." Despite inadequate grid resolution in the farfield, the computational investigation of the nine-hole injector array did yield several important design insights. Particularly, the significance to mixing and losses of the placement of the outer injectors of the second and third rows was determined. Ph. D.

With advanced subsonic transports and military aircraft operating in the transonic regime, it is becoming important to determine the effects of the coupling between aerodynamic loads and elastic forces. Since aeroelastic effects can contribute significantly to the design of these aircraft, there is a strong need in the aerospace industry to predict these aero-structure interactions computationally. To perform static aeroelastic analysis in the transonic regime, high fidelity computational fluid dynamics (CFD) analysis tools must be used in conjunction with high fidelity computational structural dynamics (CSD)analysis tools due to the nonlinear behavior of the aerodynamics in the transonic regime. There is also a need to be able to use a wide variety of CFD and CSD tools to predict these aeroelastic effects in the transonic regime. Because source codes are not always available, it is necessary to couple the CFD and CSD codes without alteration of the source codes. In this study, an aeroelastic coupling procedure is developed which will perform static aeroelastic analysis using any CFD and CSD code with little code integration. The aeroelastic coupling procedure is demonstrated on an F/A-18 Stabilator using NASTD (an in-house McDonnell Douglas CFD code)and NASTRAN. In addition, the Aeroelastic Research Wing (ARW-2) is used for demonstration of the aeroelastic coupling procedure by using ENSAERO (NASA Ames Research Center CFD code) and a finite element wing-box code (developed as a part of this research). The results obtained from the present study are compared with those available from an experimental study conducted at NASA Langley Research Center and a study conducted at NASA Ames Research Center using ENSAERO and modal superposition. The results compare well with experimental data. In addition, parallel computing power is used to investigate parallel static aeroelastic analysis because obtaining an aeroelastic solution using CFD/CSD methods is computationally intensive. A parallel finite element wing-box code is developed and coupled with an existing parallel Euler code to perform static aeroelastic analysis. A typical wing-body configuration is used to investigate the applicability of parallel computing to this analysis. Performance of the parallel aeroelastic analysis is shown to be poor; however with advances being made in the arena of parallel computing, there is definitely a need to continue research in this area. Ph. D.

A procedure for generating and using polynomial approximations to the range or to the cruise drag components in terms of 29 design variables for the High Speed Civil Transport (HSCT) configuration and performance design is presented. Response surface model methodology is used to fit quadratic polynomials to data gathered from a series of numerical analyses of different HSCT designs. Several techniques are employed to minimize the number of required analyses and to maintain accuracy. Approximate analysis techniques are used to find regions of the design space where reasonable HSCT designs could occur and response surface models are built using higher fidelity analysis results of the designs in this "reasonable" region. Regression analysis and analysis of variance are then used to reduce the number of polynomial terms in the response surface model functions. Optimizations of the HSCT are then carried out both with and without the response surface models, and the effect of the use of the response surface models is discussed. Results of the work showed that considerable reduction of the amount of numerical noise in optimization is achieved with response surface models and the convergence rate was slightly improved. Careful attention was required to keep the accuracy of the models at an acceptable level. NOTE: (07/2012) An updated copy of this ETD was added after there were patron reports of problems with the file. Master of Science

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 procedure for generating a customized weight function for wing bending material weight of a High Speed Civil Transport (HSCT) is described. The weight function is based on HSCT configuration parameters. A response surface methodology is used to fit a quadratic polynomial to data gathered from a large number of structural optimizations. To reduce the time of performing a large number of structural optimizations, coarse-grained parallelization with a master-slave processor assignment on an Intel Paragon computer is used. The results of the structural optimization are noisy. Noise reduction in the structural optimization results is discussed. It is shown that the response surface filters out this noise. A statistical design of experiments technique is used to minimize the number of required structural optimizations and to maintain accuracy. Simple analysis techniques are used to find regions of the design space where reasonable HSCT designs could occur, thus customizing the weight function to the design requirements of the HSCT, while the response surface itself is created employing detailed analysis methods. Analysis of variance is used to reduce the number of polynomial terms in the response surface model function. Linear and constant corrections based on a small number of high fidelity results are employed to improve the accuracy of the response surface model. Configuration optimization of the HSCT employing a customized weight function is compared to the configuration optimization of the HSCT with a general weight function. Ph. D.

Design engineers often employ numerical optimization techniques to assist in the evaluation and comparison of new aircraft configurations. While the use of numerical optimization methods is largely successful, the presence of numerical noise in realistic engineering optimization problems often inhibits the use of many gradient-based optimization techniques. Numerical noise causes inaccurate gradient calculations which in turn slows or prevents convergence during optimization. The problems created by numerical noise are particularly acute in aircraft design applications where a single aerodynamic or structural analysis of a realistic aircraft configuration may require tens of CPU hours on a supercomputer. The computational expense of the analyses coupled with the convergence difficulties created by numerical noise are significant obstacles to performing aircraft multidisciplinary design optimization. To address these issues, a procedure has been developed to create two types of noise-free mathematical models for use in aircraft optimization studies. These two methods use elements of statistical analysis and the overall procedure for using the methods is made computationally affordable by the application of parallel computing techniques. The first modeling method, which has been the primary focus of this work, employs classical statistical techniques in response surface modeling and least squares surface fitting to yield polynomial approximation models. The second method, in which only a preliminary investigation has been performed, uses Bayesian statistics and an adaptation of the Kriging process in Geostatistics to create exponential function-based interpolating models. The particular application of this research involves modeling the subsonic and supersonic aerodynamic performance of high-speed civil transport (HSCT) aircraft configurations. The aerodynamic models created using the two methods outlined above are employed in HSCT optimization studies so that the detrimental effects of numerical noise are reduced or eliminated during optimization. Results from sample HSCT optimization studies involving five and ten variables are presented here to demonstrate the utility of the two modeling methods. Ph. D.

The research presented in this dissertation investigates the use of all-at-once methods applied to aerodynamic design. All-at-once schemes are usually based on the assumption of sufficient continuity in the constraints and objectives, and this assumption can be troublesome in the presence of shock discontinuities. Special treatment has to be considered for such problems and we study several approaches. Our all-at-once methods are based on the Sequential Quadratic Programming method, and are designed to exploit the structure inherent in a given problem. The first method is a Reduced Hessian formulation which projects the optimization problem to a lower dimension design space. The second method exploits the sparse structure in a given problem which can yield significant savings in terms of computational effort as well as storage requirements. An underlying theme in all our applications is that careful analysis of the given problem can often lead to an efficient implementation of these all-at-once methods. Chapter 2 describes a nozzle design problem involving one-dimensional transonic flow. An initial formulation as an optimal control problem allows us to solve the problem as as two-point boundary problem which provides useful insight into the nature of the problem. Using the Reduced Hessian formulation for this problem, we find that a conventional CFD method based on shock capturing produces poor performance. The numerical difficulties caused by the presence of the shock can be alleviated by reformulating the constraints so that the shock can be treated explicitly. This amounts to using a shock fitting technique. In Chapter 3, we study variants of a simplified temperature control problem. The control problem is solved using a sparse SQP scheme. We show that for problems where the underlying infinite-dimensional problem is well-posed, the optimizer performs well, whereas it fails to produce good results for problems where the underlying infinite-dimensional problem is ill-posed. A transonic airfoil design problem is studied in Chapter 4, using the Reduced SQP formulation. We propose a scheme for performing the optimization subtasks that is based on an Euler Implicit time integration scheme. The motivation is to preserve the solution-finding structure used in the analysis algorithm. Preliminary results obtained using this method are promising. Numerical results have been presented for all the problems described. Ph. D.

Laser Doppler velocimetry (LDV) measurements and hydrogen-bubble flow-visualization techniques were used to examine the near-wall flow structure of 2-D and 3-D turbulent boundary layers (TBLs) over a range of low Reynolds numbers. The goals of this research were (1) an increased understanding of the flow physics in the near wall region of turbulent boundary layers, (2) to observe and quantify differences between 2-D and 3-D TBL flow structures, and (3) to document Reynolds number effects for 3-D TBLs. An ultimate application of this work would be to improve turbulence modeling for 3-D flows. The LDV data have provided results detailing the turbulence structure of the 2-D and 3-D TBLs, as well as low uncertainty skin friction estimates. These results include mean Reynolds stress distributions, flow skewing results, and U and V spectra. Effects of Reynolds number for the 3-D flow were examined when possible. Comparison to results with the same 3-D flow geometry but at a significantly higher Reynolds number provided unique insight into the structure of 3-D TBLs. While the 3-D mean and fluctuating velocities were found to be highly dependent on Reynolds number, a previously defined shear stress parameter was discovered to be invariant with Reynolds number. The hydrogen-bubble technique was used as a flow-visualization tool to examine the near-wall flow structure of 2-D and 3-D TBLs. Both the quantitative and qualitative results displayed larger turbulent fluctuations with more highly concentrated vorticity regions for the 2-D flow. The 2-D low-speed streaky structures experienced greater interaction with the outer region high-momentum fluid than observed for the 3-D flow. The near-wall 3-D flow structures were generally more quiescent. Numerical parameters quantified the observed differences, and characterized the low-speed streak and high-speed sweep events. All observations indicated a more stable near-wall flow structure with less turbulent interactions occurring between the inner and log regions for a 3-D TBL. Ph. D.

An experimental investigation was conducted to compare the supersonic mixing performance between a novel aerodynamic ramp injector and a physical ramp injector. The aerodynamic ramp injector consisted of nine, flush-wall jets arranged to produce multiplicative fuel-vortex interactions for mixing enhancement in a supersonic main flow. The physical ramp injector was a previously optimized and tested swept-ramp design. Test conditions included a Mach 2.0 freest ream of air with a Reynolds number of 3.63 x 10⁷ per meter and helium injection with jet-to-freestream momentum flux ratios of 1.0 and 2.0. Planar-laser Rayleigh scattering and conventional probing techniques including species composition sampling were employed to interrogate the flow field at several downstream locations. Results show that with increasing jet momentum, the aero-ramp exhibited a significant increase in penetration while the physical ramp showed no discernible change. The near-field mixing of the aero-ramp was superior to that of the physical ramp. At the higher jet momentum, the far-field mixing of the aero-ramp was comparable to the physical ramp. In all cases, the total pressure losses suffered with the aero-ramp were less than those incurred with the physical ramp. For both injectors, the total pressure losses decreased with increasing jet momentum. Finally, an analytical relationship predicting the Rayleigh scattering intensity as a function of helium concentration, pressure, and temperature was derived and experimentally validated. It is concluded that these results merit further studies and parametric optimization of the aero-ramp or similar configurations. It is also concluded that further studies may be conducted to establish the absolute quantitative nature of the Rayleigh scattering technique. Ph. D.

The design of the landing gear is one of the more fundamental aspects of aircraft design. The design and integration process encompasses numerous engineering disciplines, e.g., structure, weights, runway design, and economics, and has become extremely sophisticated in the last few decades. Although the design process is well-documented, no attempt has been made until now in the development of a design methodology that can be used within an automated environment. As a result, the process remains to be a key responsibility for the configuration designer and is largely experience-based and graphically-oriented. However, as industry and government try to incorporate multidisciplinary design optimization (MDO) methods in the conceptual design phase, the need for a more systematic procedure has become apparent. The development of an MDO-capable design methodology as described in this work is focused on providing conceptual designer with tools to help automate the disciplinary analyses, i.e., geometry, kinematics, flotation, and weight. Documented design procedures and analyses were examined to determine their applicability, and to ensure compliance with current practices and regulations. Using the latest information as obtained from industry during initial industry survey, the analyses were in terms modified and expanded to accommodate the design criteria associated with the advanced large subsonic transports. Algorithms were then developed based on the updated analysis procedures to be incorporated into existing MDO codes. Master of Science

A procedure for incorporating a key non-linear aerodynamic characteristic into the design optimization of a high-speed civil transport has been developed. Previously, the tendency of a high-speed aircraft to become uncontrollable (pitch-up) at high angles-of-attack during landing or takeoff for some wing shapes could not be included directly in the design process. Using response surface methodology, polynomial approximations to the results obtained from a computationally expensive estimation method were developed by analyzing a set of statistically selected wing shapes. These response surface models were then used during the optimization process to approximate the effects of wing planform changes on pitch-up. In addition, response surface approximations were used to model the effect of horizontal tail size and wing flaps on the performance of the aircraft. Optimizations of the high-speed civil transport were completed with and without the response surfaces. The results of this study provide insight into the influence of nonlinear and more detailed aerodynamics on the design of a high-speed civil transport. Master of Science

Numerous trim, control requirements and mission generalizations have been made to our previous multidisciplinary design methodology for a high speed civil transport. We optimize the design for minimum take off gross weight, including both aerodynamics and structures to find the wing planform and thickness distribution, fuselage shape, engine placement and thrust, using 29 design variables. While adding trim and control it was found necessary to simultaneously consider landing gear integration. We include the engine-out and crosswind landing requirements, as well as engine nacelle ground strike for lateral-directional requirements. For longitudinal requirements we include nose-wheel lift-off rotation and approach trim as the critical conditions. We found that the engine-out condition and the engine nacelle ground strike avoidance were critical conditions. The addition of a horizontal tail to provide take-off rotation resulted in a signiffcant weight penalty, and that penalty proved to be sensitive to the position of the landing gear. We include engine sizing with thrust during cruise and balanced field length conditions. Both the thrust during cruise and balanced field length constraints were critical. We include a subsonic leg in our mission analysis. The addition of a subsonic mission requirement also results in a large weight penalty. Master of Science

Several different time-integration algorithms for the Euler equations are investigated on two distributed-memory parallel computers using an explicit message-passing paradigm: these are classic Euler Explicit, four-stage Jameson-style Runge-Kutta, Block Jacobi, Block Gauss-Seidel, and Block Symmetric Gauss-Seidel. A finite-volume formulation is used for the spatial discretization of the physical domain. Both two- and three-dimensional test cases are evaluated against five reference solutions to demonstrate accuracy of the fundamental sequential algorithms. Different schemes for communicating or approximating data that are not available on the local compute node are discussed and it is shown that complete sharing of the evolving solution to the inner matrix problem at every iteration is faster than the other schemes considered. Speedup and efficiency issues pertaining to the various time-integration algorithms are then addressed for each system. Of the algorithms considered, Symmetric Block Gauss-Seidel has the overall best performance. It is also demonstrated that using parallel efficiency as the sole means of evaluating performance of an algorithm often leads to erroneous conclusions; the clock time needed to solve a problem is a much better indicator of algorithm performance. A general method for extending one-dimensional limiter formulations to the unstructured case is also discussed and applied to Van Albada’s limiter as well as Roe’s Superbee limiter. Solutions and convergence histories for a two-dimensional supersonic ramp problem using these limiters are presented along with computations using the limiters of Barth & Jesperson and Venkatakrishnan — the Van Albada limiter has performance similar to Venkatakrishnan’s. Ph. D.

The current state of transition region modeling is investigated through a literature search. The six most promising transition region models from the literature search were implemented in the Navier-Stokes code GASP. Baldwin-Lomax is an algebraic turbulence model in which the authors discuss how it can be used to simulate the transition region. Wilcox developed a procedure to use the low-Reynolds number k - w model as a transition region model where a roughness strip is used to fix the transition point. Schmidt and Patankar developed production term modifications for low-Reynolds number k - e models to correct for the problems these models have in simulating the transition region. Warren, Harris and Hassan developed a one equation turbulence model that accounts for the first and second mode disturbances in the transition region. The algebraic transition region model of ONERA/CERT controls the amount of eddy viscosity added to the molecular viscosity. The linear combination model of Dey and Narasimha combines a fully laminar and fully turbulent flow field through the indeterminacy to form the transitional flow field. GASP is a compressible Navier-Stokes code which has a practical lower working limit of M = .1. The majority of experimental data for transitional flow exists below this limit. The test cases found above this limit and used here were all in the hypersonic regime. The results from the six transition region models were compared against the experimental test cases found for a variety of cones and ramps. Two models produced inadequate results on these test cases. The Wilcox model did not function as it was intended. The algebraic transition region model overpredicted the heat transfer in the turbulent region for several cases and did not transition in regions of large adverse pressure gradients. Several models performed adequately. The Baldwin and Lomax model provide fast estimates of the transition region. The Warren, Harris and Hassan model, the Schmidt and Patankar model, and the linear combination model produced adequate results on the test cases for this work and are worthy of attention on other test cases. Modifications were made to the Schmidt and Patankar model and the algebraic transition region model to improve their predictions on the current test cases. A turbulent spot was introduced into the boundary layer for the Schmidt and Patankar model which facilitated in the use of the model. Also, the maximum production allowed was recalibrated and allowed to grow exponentially to improve transition region simulating for the test cases presented here. The empirical transition function from the algebraic transition region model was recalibrated for the hypersonic test cases used in this work. Ph. D.

Design for prevention of aeroelastic instability (that is, the critical speeds leading to aeroelastic instability lie outside the operating range) is an integral part of the wing design process. Availability of the sensitivity derivatives of the various critical speeds with respect to shape parameters of the wing could be very useful to a designer in the initial design phase, when several design changes are made and the shape of the final configuration is not yet frozen. These derivatives are also indispensable for a gradient-based optimization with aeroelastic constraints. In this study, flutter characteristic of a typical section in subsonic compressible flow is examined using a state-space unsteady aerodynamic representation. The sensitivity of the flutter speed of the typical section with respect to its mass and stiffness parameters, namely, mass ratio, static unbalance, radius of gyration, bending frequency and torsional frequency is calculated analytically. A strip-theory formulation is newly developed to represent the unsteady aerodynamic forces on a wing. This is coupled with an equivalent plate structural model based on a Rayleigh-Ritz formulation and the aeroelastic equations are solved as an eigenvalue problem to determine the critical speed of the wing. The sensitivity of divergence and flutter speeds to shape parameters, namely, aspect ratio, area, taper ratio and sweep angle are computed analytically. The aeroelastic equations are also integrated with respect to time using the Wilson-θ method at different values of freest ream speed, to observe the aeroelastic phenomena in real time. of divergence and flutter speeds to shape parameters, namely, aspect ratio, area, taper ratio and sweep angle are computed analytically. The aeroelastic equations are also integrated with respect to time using the Wilson-B method at different values of freest ream speed, to observe the aeroelastic phenomena in real time. Flutter analysis of the wing is also carried out using a lifting-surface subsonic kernel function aerodynamic theory (FAST) and an equivalent plate structural model The flutter speed is obtained using a V-g type of solution. The novel method of automatic differentiation using ADIFOR is implemented to generate exact derivatives of the flutter speed with respect to shape and modal parameters of the wing. Finite element modeling of the wing is done using NASTRAN so that wing structures made of spars and ribs and top and bottom wing skins could be analyzed. The free vibration modes of the wing obtained from NASTRAN are input into FAST to compute the flutter speed. The derivatives of flutter speed with respect to shape parameters are computed using a combination of central difference scheme and ADIFOR and the sensitivity to modal parameters is calculated using ADIFOR. An equivalent plate model which incorporates first-order shear deformation theory is then examined so it can be used to model thick wings, where shear deformations are important. The sensitivity of natural frequencies to changes in shape parameters is obtained using ADIFOR. A simple optimization effort is made towards obtaining a minimum weight design of the wing, subject to flutter constraints, lift requirement constraints for level flight and side constraints on the planform parameters of the wing using the IMSL subroutine NCONG, which uses successive quadratic programming. Ph. D.