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Mechanical & Aerospace Engineering Theses & Dissertations

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Full-Text Articles in Aerospace Engineering

Broadband Dynamic Modification Using Feedforward Control, Kendeas Antonis Karantonis Apr 1997

Broadband Dynamic Modification Using Feedforward Control, Kendeas Antonis Karantonis

Mechanical & Aerospace Engineering Theses & Dissertations

The use of feedforward control for dynamic modification is relatively new to the area of structural vibration control. In this thesis the disturbance path dynamics of a flexible aluminum beam, pinned at both ends and under the influence of broadband excitation inputs, are modified through the use of feedforward control. The ideal algebraically determined feedforward control method for response cancellation is first presented. Theoretically, this compensator modifies the disturbance path dynamics to any desired behavior. This ideal algebraic approach can only be used for minimum phase systems. In non-minimum phase systems, right half s-plane plant zeros emerge as unstable poles …


Investigation Of An Alternative Technique For Measuring Turbulence In The Upper Atmosphere, Charles Patrick Leonard Apr 1997

Investigation Of An Alternative Technique For Measuring Turbulence In The Upper Atmosphere, Charles Patrick Leonard

Mechanical & Aerospace Engineering Theses & Dissertations

The capability of the Global Positioning System (GPS) as a tool for measuring turbulence in the upper atmosphere is presented. By studying experimental ground and flight test data, a methodology for extracting macroscale turbulence data from in situ measurements was developed.

A description of the GPS using a single nonprecision receiver is followed by data from ground and flight testing. Ground testing focused on determining the smallest turbulent scales discernible by the GPS receiver. Testing was also undertaken to compare turbulence data from the GPS with that of a simultaneously operating constant-temperature hot-wire anemometer, the conventional tool for making turbulence …


Input Design For Systems Under Identification Using Indirect And Direct Methods, Marco P. Schoen Mar 1997

Input Design For Systems Under Identification Using Indirect And Direct Methods, Marco P. Schoen

Mechanical & Aerospace Engineering Theses & Dissertations

The motivation for system identification can be manifold. In this work, the provocation to identify unknown system characteristics is derived from the control engineering point of view. That is, one intends to design a control strategy based on the identified system properties. The used system identification methods are the Open-Loop Kalman filter System Identification method (OKID) and the Closed-Loop System Identification method (CLID). It is shown that the quantitative largest error of the system identification is given by its model representation, that is the attempt to describe a system with model parameters which poses a linear relationship with the input/output …


The Effectiveness Of Film Cooling In A Hypersonic Flowfield With Favorable Pressure Gradients, Julie A. Young Oct 1996

The Effectiveness Of Film Cooling In A Hypersonic Flowfield With Favorable Pressure Gradients, Julie A. Young

Mechanical & Aerospace Engineering Theses & Dissertations

The impetus of this technical document is to report results of aerothermodynamic cooling of a scramjet nozzle under favorable pressure gradients. The goals of film cooling are to protect the nozzle skin from the high enthalpy combustor flow, reduce regenerative cooling requirements, and decrease nozzle skin friction. A hypersonic nozzle configuration for which experimental data exists was selected as the basis of this numerical study. As a first step, the numerical results of film cooling along a flat plate are compared to previous literature to validate the numerical model. Subsequently, computations are performed to study the effects of varying the …


Parametric Correlations For Generic Scramjet Combustors With Ramp-Type Injectors, Jason Granville Bush Oct 1996

Parametric Correlations For Generic Scramjet Combustors With Ramp-Type Injectors, Jason Granville Bush

Mechanical & Aerospace Engineering Theses & Dissertations

Development of an efficient scramjet combustor requires the use of computational models due to the cost of full-scale physical testing in the speed regime of Mach 10 through Mach 18. This study focuses upon the database generated by one such computational model, SHIP3D, which describes a generic scramjet combustor using ramp-type file! injectors. Three generalized parametric equations have been developed from this database, which describe the fuel-air mixing efficiency within the scramjet combustor as a function of normalized-axial combustor distance, ramp injector-region lift coefficient, and stoichiometry. It is shown that one of the three equations nearly models the trends as …


Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke Oct 1996

Dynamics And Control Of A Three Dimensional Gantry Crane With Cable Flexibility, Uchendu H. Eke

Mechanical & Aerospace Engineering Theses & Dissertations

The control of payload swing in industrial gantry cranes is a topic of widespread interest. In this thesis, the control of the swing of a payload idealized by a point mass assumption is investigated utilizing s, compact robotics matrix/vector representation of the dynamical model. In this form, this particular system can be viewed as sn underactuated manipulator with equal numbers of active and passive degrees of freedom. The full three dimensional model is developed and linearized by modelling the cable as a single thread of fiexible wire and the degree of dynamic coupling between the active and passive coordinates is …


Numerical Prediction Of Turbulent Diffusion Flames Formed By Cylindrical Tube Injector, Ali S. Kheireddine Jul 1996

Numerical Prediction Of Turbulent Diffusion Flames Formed By Cylindrical Tube Injector, Ali S. Kheireddine

Mechanical & Aerospace Engineering Theses & Dissertations

This work summarizes numerical results for a diffusion flame formed from a cylindrical tube fuel injector, issuing gaseous fuel jet vertically in a quiescent atmosphere. Both pure fuels as well as fuel mixtures are examined. The primary objective is to predict the flame base height as a function of the jet velocity. A finite volume scheme is used to discretize the time-averaged Navier-Stokes equations for the reacting flow, resulting from the turbulent fuel jet motion. The turbulent stresses, and heat and mass fluxes are computed from the Reynolds stress turbulence model. A chemical kinetics model involving a two-step chemical reaction …


A Progressive Damage Methodology For Residual Strength Predictions Of Center-Crack Tension Composite Panels, Timothy William Coats Jul 1996

A Progressive Damage Methodology For Residual Strength Predictions Of Center-Crack Tension Composite Panels, Timothy William Coats

Mechanical & Aerospace Engineering Theses & Dissertations

An investigation of translaminate fracture and a progressive damage methodology was conducted to evaluate and develop residual strength prediction capability for laminated composites with through penetration notches. This is relevant to the damage tolerance of an aircraft fuselage that might suffer an in-flight accident such as an uncontained engine failure. An experimental characterization of several composite materials systems revealed an R-curve type of behavior. Fractographic examinations led to the postulate that this crack growth resistance could be due to fiber bridging, defined here as fractured fibers of one ply bridged by intact fibers of an adjacent ply.

The progressive damage …


A Study Of The Numerical Implementation Of Multidisciplinary Design Optimization Strategies, Rodney A. Taylor Jul 1996

A Study Of The Numerical Implementation Of Multidisciplinary Design Optimization Strategies, Rodney A. Taylor

Mechanical & Aerospace Engineering Theses & Dissertations

Design optimization provides an organized, systematic, and efficient method for obtaining design improvements based upon a specified measure of design performance. In the multidisciplinary design optimization (MDO) environment efficient optimization techniques allow complex designs to be improved by managing conflicting disciplinary design goals so as to improve the global design. This thesis studies the implementation issues surrounding MDO techniques and strategies. To facilitate this investigation two testbed problems have been selected for study. These problems consider two approaches to the conceptual design of an aeroelastic wing. The first approach is based on an idealized, two-dimensional representation of an airfoil under …


Unsteady, Transonic Flow Around Delta Wings Undergoing Coupled And Natural Modes Response: A Multidisciplinary Problem, Margaret Anne Menzies Apr 1996

Unsteady, Transonic Flow Around Delta Wings Undergoing Coupled And Natural Modes Response: A Multidisciplinary Problem, Margaret Anne Menzies

Mechanical & Aerospace Engineering Theses & Dissertations

The unsteady, three-dimensional Navier-Stokes equations coupled with the Euler equations of rigid-body dynamics are sequentially solved to simulate and analyze the aerodynamic response of a high angle of attack delta wing undergoing oscillatory motion. The governing equations of fluid flow and dynamics of the multidisciplinary problem are solved using a time-accurate solution of the laminar, unsteady, compressible, full Navier-Stokes equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-state Runge-Kutta scheme, respectively. The primary model under consideration consists of a 65° swept, sharp-edged, cropped delta wing of zero thickness at 20° angle of attack. In a freestream …


Study Of Surface Heat Exchangers For High-Altitude Atmospheric Research Aircraft, Te-Kang Wang Apr 1996

Study Of Surface Heat Exchangers For High-Altitude Atmospheric Research Aircraft, Te-Kang Wang

Mechanical & Aerospace Engineering Theses & Dissertations

A flush-mounted heat exchanger concept, using the wing surface to dissipate heat, is investigated as a lower drag alternative to conventional ducted plate-fin radiators. A feasibility analysis is made for an unmanned high-altitude aircraft which will reach altitudes up to 25 kilometers. A computer code is used to calculate approximate heat transfer coefficients over the airfoil's surface. A model is tested in the Old Dominion University subsonic wind tunnel to verify the results of the computer code. The results indicate that a flush mounted heat exchanger design is able to provide 20 to 100 percent of the required heat dissipation …


Variational Methods In Sensitivity Analysis And Optimization For Aerodynamic Applications, Adem Ibrahim Hussen Apr 1996

Variational Methods In Sensitivity Analysis And Optimization For Aerodynamic Applications, Adem Ibrahim Hussen

Mechanical & Aerospace Engineering Theses & Dissertations

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function.

The determination of the sensitivity derivatives of …


Sensitivity Analysis And Optimization Of Aerodynamic Configurations With Blend Surfaces, Almuttil Mathew Thomas Apr 1996

Sensitivity Analysis And Optimization Of Aerodynamic Configurations With Blend Surfaces, Almuttil Mathew Thomas

Mechanical & Aerospace Engineering Theses & Dissertations

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point …


An Approach For Multidisciplinary Design Optimization, Robert V. Krueger Apr 1996

An Approach For Multidisciplinary Design Optimization, Robert V. Krueger

Mechanical & Aerospace Engineering Theses & Dissertations

Multidisciplinary Design Optimization (MDO) is an optimization technique that allows complex designs to be improved by managing conflicting goals in such a fashion so as to improve the overall design. This thesis presents a nonhierarchic MDO formulation and gives a general explanation of how it is to be applied to various appropriate problems. In addition, this thesis evaluates the viability of this MDO technique by applying it to two distinct, multidisciplinary problems that have been used as examples in other literature. The first example problem is a combined aerodynamic/structural problem and the second example is an alkylation process problem. First, …


Numerical Simulation Of Complex, Three-Dimensional, Turbulent-Free Jets, Robert V. Wilson Jan 1996

Numerical Simulation Of Complex, Three-Dimensional, Turbulent-Free Jets, Robert V. Wilson

Mechanical & Aerospace Engineering Theses & Dissertations

Three-dimensional, incompressible turbulent jets with rectangular and elliptical cross-section are simulated with a finite-difference numerical method. The full Navier-Stokes equations are solved at low Reynoids numbers, whereas at high Reynolds numbers filtered forms of the equations are solved along with a sub-grid scale model to approximate the effects of the unresolved scales. A 2-N storage, third-order Runge-Kutta scheme is used for temporal discretization and a fourth-order compact scheme is used for spatial discretization. Although such methods are widely used in the simulation of compressible flows, the lack of an evolution equation for pressure or density presents particular difficulty in incompressible …


The Modeling Of Structural-Acoustic Interaction Using Coupled Fe/Be Method And Control Of Interior Acoustic Pressure Using Piezoelectric Actuators, Yucheng Shi Jan 1996

The Modeling Of Structural-Acoustic Interaction Using Coupled Fe/Be Method And Control Of Interior Acoustic Pressure Using Piezoelectric Actuators, Yucheng Shi

Mechanical & Aerospace Engineering Theses & Dissertations

A coupled finite element (FE) and boundary element (BE) approach is presented to model full coupled structural/acoustic/piezoelectric systems. The dual reciprocity boundary element method is used so that the natural frequencies and mode shapes of the coupled system can be obtained, and to extend this approach to time dependent problems. The boundary element method is applied to interior acoustic domains, and the results are very accurate when compared with limited exact solutions. Structural--acoustic problems are then analyzed with the coupled finite element/boundary element method, where the finite element method models the structural domain and the boundary element method models the …


An Experimental Investigation Of Wall Cooling Effects On Hypersonic Boundary Layer Stability In A Quiet Wind Tunnel, Alan E. Blanchard Oct 1995

An Experimental Investigation Of Wall Cooling Effects On Hypersonic Boundary Layer Stability In A Quiet Wind Tunnel, Alan E. Blanchard

Mechanical & Aerospace Engineering Theses & Dissertations

One of the primary reasons for developing quiet tunnels is for the investigation of high-speed boundary-layer stability and transition phenomena without the transition-promoting effects of acoustic radiation from tunnel walls. In this experiment, a flared-cone model under adiabatic- and cooled-wall conditions was placed in a calibrated, 'quiet' Mach 6 flow and the stability of the boundary layer was investigated using a prototype constant-voltage anemometer. The results were compared with linear-stability theory predictions and good agreement was found in the prediction of second-mode frequencies and growth. In addition, the same 'N=10' criterion used to predict boundary-layer transition in subsonic, transonic, and …


Buckling Analysis And Optimum Design Of Multidirectionally Stiffened Composite Curved Panel, Navin R. R. Jaunky Oct 1995

Buckling Analysis And Optimum Design Of Multidirectionally Stiffened Composite Curved Panel, Navin R. R. Jaunky

Mechanical & Aerospace Engineering Theses & Dissertations

Continuous filament grid-stiffened structure is a stiffening concept that combines structural efficiency and damage tolerance. However, buckle resistant design optimization of such structures using a finite element method is expensive and time consuming due to the number of design parameters that can be varied. An analytical optimization procedure which is simple, efficient and supports the preliminary design of grid-stiffened structures for application to combined loading cases is needed.

An analytical model for a general grid-stiffened curved panel is developed using an improved smeared theory with a first-order, shear-deformation theory to account for transverse shear flexibilities and local skin-stiffener interaction effects. …


Experimental Investigation Of The Inlet Deflector Configuration Variation In The Flow Field At Mach 1.9, Kyu C. Hwang Oct 1995

Experimental Investigation Of The Inlet Deflector Configuration Variation In The Flow Field At Mach 1.9, Kyu C. Hwang

Mechanical & Aerospace Engineering Theses & Dissertations

In recent years, active research has been conducted to study the technological feasibility of supersonic laminar flow control on the wing of the High Speed Civil Transport (HSCT). For this study, the F-16XL has been chosen due to its highly swept crank wing planform that closely resembles the HSCT configurations. During flights, it is discovered that the shock wave generated from the aircraft inlet introduces disturbances on the wing where the data acquisition is conducted. The flow field about a supersonic inlet is characterized by a complex three-dimensional pattern of shock waves generated by the geometrical configuration of a deflector …


Numerical Investigation Of Shock-Induced Combustion Past Blunt Projectiles, Jagjit K. Ahuja Jul 1995

Numerical Investigation Of Shock-Induced Combustion Past Blunt Projectiles, Jagjit K. Ahuja

Mechanical & Aerospace Engineering Theses & Dissertations

A numerical study is conducted to simulate shock-induced combustion in premixed hydrogen-air mixtures at various free-stream conditions and parameters. Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock-induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A seven-species, seven reactions finite rate hydrogen-air chemical reaction mechanism is used combined with a finite-difference, shock-fitting method to solve the complete set of Navier-Stokes and species conservation equations. In this approach, the bow shock represents a boundary of the computational domain and is treated as a discontinuity across which Rankine-Hugoniot conditions are applied. All interior details of …


Dynamic Unstructured Method For Prescribed And Aerodynamically Determined Relative Moving Boundary Problems, Kamakhya Prasad Singh Jul 1995

Dynamic Unstructured Method For Prescribed And Aerodynamically Determined Relative Moving Boundary Problems, Kamakhya Prasad Singh

Mechanical & Aerospace Engineering Theses & Dissertations

A new methodology is developed to simulate unsteady flows about prescribed and aerodynamically determined moving boundary problems. The method couples the fluid dynamics and rigid-body dynamics equations to capture the time-dependent interference between stationary and moving boundaries. The unsteady, compressible, inviscid (Euler) equations are solved on dynamic, unstructured grids by an explicit, finite-volume, upwind method. For efficiency, the grid adaptation is performed within a window around the moving object. The Eulerian equations of the rigid-body dynamics are solved by a Runge-Kutta method in a non-inertial frame of reference. The two-dimensional flow solver is validated by computing the flow past a …


Aerodynamic Design Optimization With Consistently Discrete Sensitivity Derivatives Via The Incremental Iterative Method, Vamshi M. Korivi Apr 1995

Aerodynamic Design Optimization With Consistently Discrete Sensitivity Derivatives Via The Incremental Iterative Method, Vamshi M. Korivi

Mechanical & Aerospace Engineering Theses & Dissertations

In this study which involves advanced fluid-flow codes, an incremental iterative formulation (also known as the "delta" or "correction" form), together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently …


Finite Element Nonlinear Random Response Of Composite Panels Of Arbitrary Shape To Acoustic And Thermal Loads Applied Simultaneously, Roger R. Chen Apr 1995

Finite Element Nonlinear Random Response Of Composite Panels Of Arbitrary Shape To Acoustic And Thermal Loads Applied Simultaneously, Roger R. Chen

Mechanical & Aerospace Engineering Theses & Dissertations

The nonlinear random response of composite plates to the simultaneously applied, combined acoustic/thermal loads are investigated in this dissertation. A finite element formulation for the nonlinear random response is developed. The three-node Mindlin plate element with improved transverse shear is extended and employed. The extension includes the development of the thermal geometric matrix, the mass matrix, the first- order and second-order nonlinear stiffness matrices, and the thermal and mechanical load vectors. An innovative solution procedure has been created which is believed to be the first attempt to analyze nonlinear random response of complex composite panels subjected to simultaneous acoustic and …


Wing-Section Optimization For Supersonic Viscous Flow, Cem Cihan Item Apr 1995

Wing-Section Optimization For Supersonic Viscous Flow, Cem Cihan Item

Mechanical & Aerospace Engineering Theses & Dissertations

The recent interest in the High Speed Civil Transport (HSCT) has resulted in renewed research studies of optimized supersonic cruise transport configurations. Incorporation of flow viscosity effects in the design process of such a supersonic wing is currently under investigation. This may lead to more accurate problem formulations and, in tum, greater aerodynamic efficiency than can be obtained by the traditional, inviscid, linear theories. In this context, for a design code to be a candidate for a complex optimization problem, such as three-dimensional viscous supersonic wing design, it should be validated using simpler building-block shapes.

To optimize the shape of …


Assumed-Stress Hybrid Beam Element For Nonlinear Elastic Stress Analysis, William Scott Carron Apr 1995

Assumed-Stress Hybrid Beam Element For Nonlinear Elastic Stress Analysis, William Scott Carron

Mechanical & Aerospace Engineering Theses & Dissertations

An assumed-stress hybrid 2-node beam element is formulated using the Hellinger-Reissner variational principle. Independent approximations are made for the stresses and displacements. The stress field is assumed to be consistent with the force and moment equilibrium equations. The displacement field is assumed to be linear except that the transverse deflections vary quadratically using the rotational freedoms, The element is implemented in COMET and coupled with its corotational utilities. This enables an analyst to extend the element to problems involving geometric nonlinearities. Excellent performance of the element for nonlinear behaviors of both a stiffening and softening behavior is demonstrated.


Simulation Of Active Control Of Asymmetric Flows Around Slender Pointed Forebodies, Hazem Sharaf El-Din Oct 1994

Simulation Of Active Control Of Asymmetric Flows Around Slender Pointed Forebodies, Hazem Sharaf El-Din

Mechanical & Aerospace Engineering Theses & Dissertations

At high angles of attack, the flowfield over slender forebodies becomes asymmetric with substantial side force, which may exceed the available control capability. The unsteady compressible Navier-Stokes equations are used to investigate the effectiveness of different active control methods to alleviate and possibly eliminate the flow asymmetry and the subsequent side force. Although the research work focuses on active control methods, a passive control method has been investigated. The implicit, Roe flux-difference splitting, finite volume scheme is used for the numerical computations. Both locally-conical and three-dimensional solutions of the Navier-Stokes equations are obtained.

The asymmetric flow over five-degree semi-apex angle …


Investigation Of Wall Injectors For Supersonic Mixing Enhancement, Yaacov Haimovitch Jul 1994

Investigation Of Wall Injectors For Supersonic Mixing Enhancement, Yaacov Haimovitch

Mechanical & Aerospace Engineering Theses & Dissertations

A comparative study of the interaction between wall mounted swept-ramp injectors and injector nozzle shape has been conducted in a constant area duct to explore techniques to enhance mixing in scramjet combustors. The scramjet combustors are currently being developed for propulsion systems applications on the envisioned hypersonic vehicles. Short combustor residence time, a requirement for fuel injection parallel to the main flow in the combustor, and an overall strong sensitivity of the vehicle performance to the propulsion system motivated the investigation. The swept-ramp injector investigated in this study produces vortex shedding and local separation downstream of the injector's nozzle exit, …


Investigation Of Computational And Spectral Analysis Methods For Aeroacoustic Wave Propagation, Florence Odile Vanel Jul 1994

Investigation Of Computational And Spectral Analysis Methods For Aeroacoustic Wave Propagation, Florence Odile Vanel

Mechanical & Aerospace Engineering Theses & Dissertations

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular …


Flow Simulations About Steady-Complex And Unsteady Moving Configurations Using Structured-Overlapped And Unstructured Grids, James Charles Newman Iii Apr 1994

Flow Simulations About Steady-Complex And Unsteady Moving Configurations Using Structured-Overlapped And Unstructured Grids, James Charles Newman Iii

Mechanical & Aerospace Engineering Theses & Dissertations

The limiting factor in simulating flows past realistic configurations of interest has been the discretization of the physical domain on which the governing equations of fluid flow may be solved. In an attempt to circumvent this problem, many Computational Fluid Dynamic (CFD) methodologies that are based on different grid generation and domain decomposition techniques have been developed. However, due to the costs involved and expertise required, very few comparative studies between these methods have been performed. In the present work, the two CFD methodologies which show the most promise for treating complex three-dimensional configurations as well as unsteady moving boundary …


Three-Dimensional Aerodynamic Shape Optimization Using Discrete Sensitivity Analysis, Gregory Wayne Burgreen Apr 1994

Three-Dimensional Aerodynamic Shape Optimization Using Discrete Sensitivity Analysis, Gregory Wayne Burgreen

Mechanical & Aerospace Engineering Theses & Dissertations

An aerodynamic shape optimization procedure based on discrete sensitivity analysis is extended to treat three-dimensional geometries. The function of sensitivity analysis is to directly couple computational fluid dynamics (CFD) with numerical optimization techniques, which facilitates the construction of efficient direct-design methods. The development of a practical three-dimensional design procedures entails many challenges, such as: (1) the demand for significant efficiency improvements over current design methods; (2) a general and flexible three-dimensional surface representation; and (3) the efficient solution of very large systems of linear algebraic equations. It is demonstrated that each of these challenges is overcome by: (1) employing fully …