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航空宇宙技術研究所 16-18 Jun. 1999 東京 日本, National Aerospace Laboratory 16-18 Jun. 1999 Tokyo Japan, 航空機の概念設計では、しばしば非凸面設計空間と複数の局所最適化に帰着する多数の非線形の制約条件を必然的に伴う。高速度民間航空機(HSCT)の設計は、26の設計変数と68の制約条件を持った非常に複雑な概念設計の例として用いられている。本稿では、HSCTの問題および数千の局所最適条件を課せられたテスト問題に関して3つの包括的最適化技術を比較した。1つは逐次2次計画(SQP)またはSnymanの動的探索法を用いた多点開始局所最適化法であり、もう1つはHSCT問題に関するJonesのDIRECT大域的最適化アルゴリズムである。SQPは局所最適化法であり、一方Snymanのアルゴリズムは浅い局所極小値を通って動くことが出来る。DIRECTアルゴリズムは、設計空間で小さな有望な領域を見出し、局所最適化法を用いて最適値に収束させるLipschitzの最適化法をベースにした大域的探索法である。DIRECTアルゴリズムは、ノイズ成分の大きな関数の大域的最適値を見出すのには最も費用効率が良いことが分かった。, The conceptual design of aircraft often entails a large number of nonlinear constraints that result in a nonconvex design space and multiple local optima. The design of the High Speed Civil Transport (HSCT) is used as an example of a highly complex conceptual design with 26 design variables and 68 constraints. This paper compares three global optimization techniques on the HSCT problem and a test problem with thousands of local optima: multistart local optimizations using either Sequential Quadratic Programming (SQP) or Snyman's dynamic search method, and Jones' DIRECT global optimization algorithm on the HSCT problem. SQP is a local optimizer, while Snyman's algorithm is capable of moving through shallow local minima. The DIRECT algorithm is a global search method based on Lipschizian optimization that locates small promising region of design space and uses a local optimizer to converge to the optimum. The DIRECT algorithm is found to be the most cost effective for locating the global optimum of noisy function., 資料番号: AA0001961002, レポート番号: NAL SP-44

The presence of numerical noise in engineering design optimisation problems inhibits the use of many gradient-based optimisation methods. This numerical noise may result in the inaccurate calculation of gradients which in turn slows or prevents convergence during optimisation, or it may promote convergence to spurious local optima. 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 optimisation. To address these issues, a procedure has been developed to create noise-free algebraic models of subsonic and supersonic aerodynamic performance quantities, for use in the optimisation of high-speed civil transport (HSCT) aircraft configurations. This procedure employs methods from statistical design of experiments theory and response surface modelling to create the noise-free algebraic models. Results from a sample HSCT design problem involving ten variables are presented to demonstrate the utility of this method.

Different sources of uncertainty in CFD simulations are illustrated by a detailed study of two-dimensional, turbulent, transonic flow in a converging-diverging channel. Runs were performed with the commercial CFD code GASP using different turbulence models, grid levels, and flux-limiters to see the effect of each on the CFD simulation uncertainties. Two flow conditions were studied by changing the exit pressure ratio: the first is a complex case with a strong shock and a separated flow region, the second is the weak shock case with no separation. The uncertainty in CFD simulations has been studied in terms of four contributions: (1) discretization error, (2) error in geometry representation, (3) turbulence model, and (4) the downstream boundary condition. In this paper, we have quantified the relative contribution and the importance of each source of uncertainty and shown the level of scatter in results that a well informed CFD user may obtain in a typical design activity. The nozzle efficiency results obtained in this study showed that the range of variation for the strong shock case was much larger than that observed in the weak shock case. The discretization errors were up to 6% and the relative uncertainty originating from the selection of different turbulence models was as large as 9% for the strong shock case. Furthermore, the results demonstrated that grid convergence is not achieved with grid levels that have moderate mesh sizes and showed that highly refined grids are required to obtain solutions with an acceptable level of accuracy in design problems that involve simulations of complex flow fields. The results illustrated the interaction of different sources of uncertainty and showed that the magnitudes of numerical errors are influenced by the physical models used.

With optimization increasingly used in engineering applications, a series of optimization runs may be required, and it may be too expensive to converge them to very high accuracy. A procedure for estimating average optimization convergence errors from a set of poorly converged optimization runs is developed. A probabilistic model is fitted to the errors in optimal objective function values of poorly converged runs. The Weibull distribution was identified as a reasonable error model both for the Rosenbrock function problem and the structural optimization of a high speed civil transport. Once a statistical model for the error is identified, it can be used to estimate average errors from a set of pairs of runs. In particular, by performing pairs of optimization runs from two starting points, accurate estimates of the mean and standard deviation of the convergence errors can be obtained.

Surrogate functions have become an important tool in multidisciplinary design optimization to deal with noisy functions, high computational cost, and the practical difficulty of integrating legacy disciplinary computer codes. A combination of mathematical, statistical, and engineering techniques, well known in other contexts, have made polynomial surrogate functions viable for MDO. Despite the obvious limitations imposed by sparse high fidelity data in high dimensions and the locality of low order polynomial approximations, the success of the panoply of techniques based on polynomial response surface approximations for MDO shows that the implementation details are more important than the underlying approximation method (polynomial, spline, DACE, kernel regression, etc.). This paper surveys some of the ancillary techniques—statistics, global search, parallel computing, variable complexity modeling—that augment the construction and use of polynomial surrogates.

The preliminary design space exploration for large,interdisciplinary engineering problems is often a difficult and time-consuming task. General techniques are needed that efficiently and methodically search the design space. This work focuses on the use of parallel load balancing techniques integrated with a global optimizer to reduce the computational time of the design space exploration. The method is applied to the multidisciplinary design of a High Speed Civil Transport (HSCT). A modified Lipschitzian optimization algorithm generates large sets of design points that are evaluated concurrently using a variety of load balancing schemes.The load balancing schemes implemented in this study are: static load balancing, dynamic load balancing with a master-slave organization, fully distributed dynamic load balancing, an fully distributed dynamic load balancing via threads. All of the parallel computing schemes have high parallel efficiencies. When the variation in the design evaluation times is small, the computational overhead needed for fully distributed dynamic load balancing is substantial enough so that it is more efficient to use a master-slave paradigm. However, when the variation in evaluation times is increased, fully distributed load balancing is the most efficient.

We describe a problem solving environment (PSE) named VizCraft that aids aircraft designers during the conceptual design stage. At this stage,an aircraft design is defined by a vector of 10-30 parameters. The goal is to find a vector that minimizes a performance-based objective function while meeting a series of constraints. VizCraft integrates the simulation code that evaluates a design with visualization for analyzing a design individually or in contrast to other designs. VizCraft allows the designer to easily switch between the view of a design in the form of a parameter set, and a visualization of the corresponding aircraft geometry. The user can easily see which, if any, constraints are violated. VizCraft also allows the user to view a database of designs using parallel coordinates. Keywords: Problem solving environment,scientific data visualization, mutlidiimensional visualization, aircraft design, multidisciplinary design optimization.

A method has been developed to generate and use polynomial approximations to the range and cruise drag components in a highly constrained, multidisciplinary design optimization of a High Speed Civil Transport configuration. The method improves optimization performance by eliminating the numerical noise present in the analyses through the use of response surface methodology. In our implementation, we fit quadratic polynomials within variable bounds to data gathered from a series of numerical analyses of different aircraft designs. Because the HSCT optimization process contains noise and suffers from a nonconvex design space even when noise is filtered out, multiple optimization runs are performed from different starting points with and without the response surface models in order to evaluate their effectiveness. It is shown that response surface methodology facilitates design space exploration, allowing improvements in terms of both convergence performance and computational effort when multiple starting points are required.

Multidisciplinary design optimization (MDO) for large-scale engineering problems poses many challenges (e.g., the design of an efficient concurrent paradigm for global optimization based on disciplinary analyses, expensive computations over vast data sets, etc.) This work focuses on the application of distributed schemes for massively parallel architectures to MDO problems, as a tool for reducing computation time and solving larger problems. The specific problem considered here is configuraton optimization of a high speed civil transport (HSCT), and the efficient parallelization of the embedded paradigm for reasonable design space identification. Two distributed dynamic load balancing techniques (random polling and global round robin with message combining) and two necessary termination detection schemes (global task count and token passing) were implemented and evaluated in terms of effectiveness and scalability to large problem sizes and a thousand processors. The effect of certain parameters on execution time was also inspected. Empirical results demonstrated stable performance and effectiveness for all schemes, and the parametric study showed that the selected algorithmic parameters have a negligible effect on performance.

A method has been developed to generate and use polynomial approximations to the range and cruise drag components in a highly constrained, multidisciplinary design optimization of a High Speed Civil Transport configuration. The method improves optimization performance by eliminating the numerical noise present in the analyses through the use of response surface methodology. In our implementation, we fit quadratic polynomials within variable bounds to data gathered from a series of numerical analyses of different aircraft designs. Because the HSCT optimization process contains noise and suffers from a nonconvex design space even when noise is filtered out, multiple optimization runs are performed from different starting points with and without the response surface models in order to evaluate their effectiveness. It is shown that response surface methodology facilitates design space exploration, allowing improvements in terms of both convergence performance and computational effort when multiple starting points are required.

A method has been developed to efficiently implement supersonic aerodynamic predictions from Euler solutions into a highly constrained, multidisciplinary design optimization of a High-Speed Civil Transport. The method alleviates the large computational burden associated with performing computational fluid dynamics analyses through the use of variable-complexity modeling techniques, response surface methodologies, and coarse grained parallel computing. Using information gained from lower fidelity aerodynamic models, reduced term response surface models representing a correction to the linear theory response surface model predictions are constructed using Euler solutions. Studies into five, ten, fifteen, and twenty variable design problems show that accurate results can be obtained with the reduced term models at a fraction of the cost of creating the full term quadratic response surface models. Specifically, a savings of 255 CPU hours out of 392 CPU hours required to create the full term response surface model is obtained for the twenty variable problem on a single 75 MHz IP21 processor of a SGI Power Challenge.

A procedure for generating and using polynomial approximations to the range or to the cruise drag components in terms of 29 design variables for a High Speed Civil Transport configuration design is presented. Response surface methodology is used to fit quadratic polynomials to data gathered from a series of numerical analyses of different aircraft 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 aircraft designs could occur and response surface models are built using higher fidelity analysis results of designs in this "reasonable" region. This is a means of using results from advanced CFD methods at the early design stage. Regression analysis and analysis of variance are used to reduce the number of polynomial terms in the response surface model functions. Optimization runs of the aircraft configuration are then carried out with the response surface models and compared to the previous optimization runs without the response surface models. It is shown that considerable reduction of the amount of numerical noise in optimization is achieved with response surface models and the convergence rate is improved. Careful attention was required to keep the accuracy of the models at an acceptable level.

The presence of numerical noise in engineering design optimization problems inhibits the use of many gradient-based optimization methods. This numerical noise may result in the inaccurate calculation of gradients which in turn slows or prevents convergence during optimization, or it may promote convergence to spurious local optima. 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 expenses 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 noise-free algebraic models of subsonic and supersonic aerodynamic performance qualities for use in the optimization of high-speed civil transport (HSCT) aircraft configurations. This procedure employs methods from statistical design of experiments theory and response surface modeling to create the noise-free algebraic models. Results from a sample HSCT design problem involving ten variables are presented to demonstrate the utility of this method.

The presence of numerical noise inhibits gradient-based optimization and therefore limits the practicality of performing aircraft multidisciplinary design optimization (MDO). To address this issue, a procedure has been developed to create noise free algebraic models of subsonic and supersonic aerodynamic performance for use in the MDO of high-speed civil transport (HSCT) configurations. This procedure employs methods from statistical design of experiments theory to select a set of HSCT wing designs (fuselage/tail/engine geometry fixed) for which numerous detailed aerodynamic analyses are performed. Polynomial approximations (i.e., response surface models) are created from the aerodynamic data to provide analytical models relating aerodynamic quantities (e.g., wave drag and drag-due-to-lift) to the variables which define the HSCT wing configuration. A multidisciplinary design optimization of the HSCT is then performed using the response surface models in lieu of the traditional, local gradient based design methods. The use of response surface models makes possible the efficient and robust application of MDO to the design of an aircraft system. Results obtained from five variable and ten variable wing design problems presented here demonstrate the effectiveness of this response surface modeling method.

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, simple analysis techniques are used to find regions of the design space where reasonable HCST 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.

Modern aerospace vehicle design requires the interaction of multiple discipines, traditionally processed in a sequential order. Multidisciplinary optimization (MDO), a formal methodology for the integration of these disciplines, is evolving towards methods capable of replacing the traditional sequential methodology of aerospace vehicle design by concurrent algorithms, with both an overall gain in product performance and a decrease in design time. A parallel MDO paradigm using variable-complexity modeling and multipoint response surface approximations is presented here for the particular instance of the design of a high speed civil transport (HSCT). This paradigm interleaves the disciplines at one level of complexity, and processes them hierarchically at another level of complexity, achieving parallelism within disciplines, rather than across disciplines. A master-slave paradigm manages a coarse grained parallelism of the analysis and optimization codes required by the disciplines showing reasonable speedups and efficiencies on an Intel Paragon.

A parallel variable-complexity modeling approach, permitting the efficient use of emerging parallel computing in multidisciplinary optimization (MDO) technology, is presented for the particular instance of High Speed Civil Transport (HSCT) design. In this method simple analyses are used to limit the approximation domain based on the D-optimality criterion through the use of a genetic alogorithm. At the D-optimal points, a refined analysis is performed. The optimization code is composed of a sequence of analysis cycles between aerodynamic and structural calculations. Results for coarse grained parallelization of the aerodynamic and structural codes on an Intel Paragon are presented for an example HSCT design problem involving only two variables. The full HSCT design problem employs twenty-eight design variables.

Convergence difficulties were encountered in our recent efforts towards a combined aerodynamic-structural optimization of the High Speed Civil Transport (HSCT). The underlying causes of the convergence problems were traced to numerical noise in the calculation of aerodynamic drag components for obstacles to convergence. The first technique employed a sequential approximation optimization method which used large initial move limits on the design variables. This helped dislodge the optimizer out of the local minima in the design space created by the noisy drag data. The second method utilized the aircraft. Two techniques were developed to circumvent the response surface methods to construct smooth approximations to the noisy data. The response surfaces were formed by analyzing several individual HSCT configuration and then fitting polynomial functions to selected objective function data. A simplified example design problem was used to demonstrate the response surface technique and to investigate various other issues relating to the construction of the response surfaces.

The present work was conducted with the intent of developing a high-fidelity numerical model of a unique combustion flow problem combining multi-phase fuel injection with substantial momentum and temperature into a highly complex turbulent flow. This important problem is very different from typical and more widely known liquid fuel combustion problems and is found in practice in pulverized coal combustors and ducted rocket ramjets. As the ducted rocket engine cycle is only now finding widespread use, it has received little research attention and was selected as a representative problem for this research. Prior to this work, a method was lacking domestically and internationally to effectively model the ducted rocket engine cycle with confidence. In the ducted rocket a solid fuel gas generator is used to deliver a fuel-rich multi-phase mixture to the combustion chamber. When a valve is used to vary the fuel generator pressure, and thereby the delivered fuel flowrate, the engine is known as a Variable Flow Ducted Rocket (VFDR). The Aerojet MARC-R282 ramjet engine represents the worlds first VFDR flown, and the first in operational use. Although performance requirements were met, improvements are sought in the understanding of the ramjet combustion process with a future aim of reducing the visible exhaust and correcting uneven combustor heating patterns. For this reason the MARC-R282 combustor was selected as the baseline geometry for the present research, serving to provide a documented baseline case for numerical modeling and also being a good candidate to benefit from an improved understanding of the combustion process. In order to proceed with the present research, experiments were first carried out to characterize the gas generator particulate exhaust in terms of composition and particle size. Equilibrium thermochemistry was used to supplement these data to develop a gas phase combustion model. The gas phase reactions and resulting particle definition were modeling using the FLUENT Computational Fluid Dynamics (CFD) code for the baseline GQM-163A Supersonic Sea Skimming Missile (SSST) operating conditions. These results were compared to direct-connect ramjet ground tests in order to validate the analysis tool. Data were developed to understand the gas and solid phase fuel exhaust characteristics at the propellant surface, exiting the gas generator injector, and following secondary combustion with air. Particles were collected and analyzed from the fuel generator exhaust. While exhibiting some variation with time in the firing, they were roughly an average of 20 microns in diameter, in line with prior experience with pulverized coal combustion experiments. A computational model was developed based on coal combustion parameters using FLUENT. However, despite considerable effort, the CFD analysis was not able to predict effective burning of the carbon particles to the degree seen in testing. In addition, using equilibrium thermochemistry as a basis for determining the carbon particle content in the fuel exhaust, the CFD analysis resulted in trends in performance opposite to the test results. These facts led to a hypothesis that there was actually a significant fraction of small particles or much less carbon produced than equilibrium thermochemistry would predict. A parametric analysis was performed replacing the 20 micron soot particles with fine fraction particles, representing a fraction of the predicted equilibrium carbon soot being still in the gas phase as higher molecular weight hydrocarbons, or in the form of sub-micron particles. When almost all particles were replaced with fine fraction particles, the model was able to correctly predict absolute values of combustion efficiency as well as trends for different injector geometries. The presence of particles was apparent from the visible exhaust and collection data, however they were found not to play a significant role in the combustion process for this fuel and engine configuration. The robustness of the computational model was also evaluated by examining the effects of turbulence model, order of discretization, and grid size. Comparable trends and results were seen for all cases examined. With the successful development of this modeling tool and an improved understanding of the combustion process, future work is enabled to develop improved combustor flow management and fuel injection schemes to improve existing designs and develop new configurations. This research has served to advance the field of combustion modeling by providing: 1) a solid ducted rocket combustion modeling tool considering solid and gas phase combustion, 2) a correlation between primary combustion theory and particulate exhaust sampling, 3) low length/diameter ratio ducted rocket combustor modeling, and 4) combustor CFD coupled with solid particle tracking and combustion models. Ph. D.

The objective of this research is to examine how to design low-noise transport aircraft using Multidisciplinary Design Optimization (MDO). The subject is approached by designing for low-noise both implicitly and explicitly. The explicit design approach involves optimizing an aircraft while explicitly constraining the noise level. An MDO framework capable of optimizing both a cantilever wing and a Strut-Braced-Wing (SBW) aircraft was developed. The framework employs aircraft analysis codes previously developed at the Multidisciplinary Design and Analysis (MAD) Center at Virginia Tech (VT). These codes have been improved here to provide more detailed and realistic analysis. The Aircraft Noise Prediction Program (ANOPP) is used for airframe noise analysis. The objective is to use the MDO framework to design aircraft for low-airframe-noise at the approach conditions and quantify the change in weight and performance with respect to a traditionally designed aircraft. The results show that reducing airframe noise by reducing approach speed alone, will not provide significant noise reduction without a large performance and weight penalty. Therefore, more dramatic changes to the aircraft design are needed to achieve a significant airframe noise reduction. Another study showed that the trailing-edge (TE) flap can be eliminated, as well as all the noise associated with that device, without incurring a significant weight and performance penalty. To achieve approximately 10 EPNdB TE flap noise reduction the flap area was reduced by 82% while the wing reference area was increased by 12.4% and the angle of attack increased from 7.6 degrees to 12.1 degrees to meet the required lift at approach. The wing span increased by approximately 2.2%. Since the flap area is being minimized, the wing weight suffers only about a 2,000 lb penalty. The increase in wing span provides a reduction in induced drag to balance the increased parasite drag due to a lower wing aspect ratio. As a result, the aircraft has been designed to have minimal TE flaps without any significant performance penalty. If noise due to the leading-edge (LE) slats and landing gear are reduced, which is currently being pursued, the elimination of the flap will be very significant as the clean wing noise will be the next 'noise barrier'. Lastly, a comparison showed that SBW aircraft can be designed to be 10% lighter and require 15% less fuel than cantilever wing aircraft. Furthermore, an airframe noise analysis showed that SBW aircraft with short fuselage-mounted landing gear could have similar or potentially a lower airframe noise level than comparable cantilever wing aircraft. The implicit design approach involves selecting a configuration that supports a low-noise operation, and optimizing for performance. A Blended-Wing-Body (BWB) transport aircraft has the potential for significant reduction in environmental emissions and noise compared to a conventional transport aircraft. A BWB with distributed propulsion was selected as the configuration for the implicit low-noise design in this research. An MDO framework previously developed at the MAD Center at Virginia Tech has been refined to give more accurate and realistic aircraft designs. To study the effects of distributed propulsion, two different BWB configurations were optimized. A conventional propulsion BWB with four pylon mounted engines and two versions of a distributed propulsion BWB with eight boundary layer ingestion inlet engines. A 'conservative' distributed propulsion BWB design with a 20% duct weight factor and a 95% duct efficiency, and an 'optimistic' distributed propulsion BWB design with a 10% duct weight factor and a 97% duct efficiency were studied. The results show that 65% of the possible savings due to 'filling in' the wake are required for the 'optimistic' distributed propulsion BWB design to have comparable $TOGW$ as the conventional propulsion BWB, and 100% savings are required for the 'conservative' design. Therefore, considering weight alone, this may not be an attractive concept. Although a significant weight penalty is associated with the distributed propulsion system presented in this study, other characteristics need to be considered when evaluating the overall effects. Potential benefits of distributed propulsion are, for example, reduced propulsion system noise, improved safety due to engine redundancy, a less critical engine-out condition, gust load/flutter alleviation, and increased affordability due to smaller, easily-interchangeable engines. Ph. D.

In recent years, the aircraft industry has begun to focus its research capabilities on reducing emissions and noise produced by aircraft. Modern aircraft use two to four engines arranged on the wing or behind to produce thrust that is concentrated directly behind the engine. Kuchemann suggested a way to improve the propulsive efficiency by changing the normal configuration of engine and aircraft. This concept is the jet-wing distributed propulsion idea, which redistributes the thrust across the span of the wings. Distributed propulsion is accomplished by using many smaller engines spread across the wings or several large engines to duct the exhaust flow in a jet-wing. The jet-wing concept can be used to reduce noise and also as a replacement for flaps and slats by deflecting the jet. Since the distributed propulsion concept is also a method to reduce noise, it's important to have a simplified method of calculating the trailing edge noise of a wing. One of the purposes of this paper was to study the effect of adding jet-wing distributed propulsion to a thick "inboard" airfoil. The two-dimensional jet-wing model was analyzed by parametric computational fluid dynamic (CFD) studies using the Reynolds-averaged, finite-volume, Navier-Stokes code GASP. The model was set up to be self-propelled by applying velocity and density boundary conditions to the blunt edge of the airfoil. A thick "inboard" airfoil from a realistic transonic wing was needed for the study and so the span station of the EET Wing was chosen. This airfoil was thick with a thickness to chord ratio of 16%. In adding distributed propulsion to this thick airfoil, it was found that there was an increase in the propulsive efficiency as compared to typical modern high-bypass-ratio turbofan engines with no negative aerodynamic consequences. The other purpose of this study was to create and assess a simplified method to calculate the trailing edge noise metric value produced by an airfoil. Existing methods use RANS CFD, which is computationally expensive and so it seemed important to find a less expensive method. A method was formed using the Virginia Tech Boundary Layer Java Codes which calculated the characteristic turbulent velocity and characteristic turbulent length scale. A supercritical airfoil, SC(2)-0714, was used to assess the simplified method as compared to the more computationally expensive GASP runs. The results showed that this method has trends that follow those of the GASP results with the method compare well up to modest lift coefficients. Master of Science

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