<p> The main objective of this thesis is to study the flow characteristics of a rotary cylinder with a symmetric end plate. We performed the simulations for different velocity ratios (0, 5, 10, and 15), aspect ratios (9.053 and 18) at high Reynolds numbers (1.15 x 10⁴ &le; Re &ge; 6.44 x 10⁵). We then studied the wake structure, the vortices formed in the wake region, the effect of vortex formation on the aerodynamic forces such as lift and drag. We performed computational fluid dynamics (CFD) simulations using a CFD solver, STAR-CCM+ from CD-Adapco. The results show that when the circular cylinder is stationary, the vortex shedding frequency is high; the upper and lower vortices show an asymmetrical process with the wake centerline. A significant vortex pairing can also be seen. But, with the rotation and increase in velocity ratio, the strength of vortex shedding decreases and after velocity ratio 5 the periodic vortex shedding is suppressed. The structure of the wake also modifies depending on the direction of the rotation. When aspect ratio of the circular cylinder is increased, the lift force generated on the cylinder surface is decreased. When an end plate is introduced in the region close to the stationary circular cylinder, it creates interference in the vortex formation and hence, the instabilities in the fluid flow due to vortices are decreased. The geometry of the stationary circular cylinder with an end plate seems to behave similar to a symmetric airfoil at zero angle of attack. Hence, aerodynamic forces generated on the geometry are constant. When the circular cylinder with the end plate is given a constant rotation, then the vortex formation is suppressed, the wake moves further downstream due to the end plate, the lift force generated on the surface increases and a significant decrease in drag force is also observed.</p>

<p> The objective of the present study is to investigate the characteristics of a flow around a rotating circular cylinder with and without an end plate near a wall boundary. The different cases which are taken into consideration in the current investigations were with gap ratios of 0.1d, 0.5d, 1.0d, 1.5d and 2.0d. A symmetric end plate is attached behind the rotating circular cylinder at a distance of 0.1d from the cylinder and a gap ratio of 1.5d. We performed Computational Fluid Dynamics (CFD) simulation of the flow around a rotating circular cylinder near a plane wall boundary using a CFD solver, STAR-CCM+. Free-stream velocity is kept constant at 5 m/s and the Reynolds number calculated is 3.24X10⁴. We then studied the flow characteristics such as lift and drag generated on the circular cylinder with and without an end plate and the wake structure. We observed that the vortex suppression is increased when the gap ratio is reduced, i.e., when the circular cylinder is nearer to the plane wall boundary. As the gap ratio increases the drag force generated decreases and the lift force increases considerably. In the case of rotating circular cylinder with an end plate, the wake area has moved upwards and the lift generated has increased manifold.</p>

<p> The objective of this study was to determine the deflected wing shape and the out-of-plane loads of a large-scale carbon-composite wing of an ultralight aerial vehicle using Fiber Bragg Grating (FBG) technology. The composite wing was instrumented with an optical fiber on its top and bottom surfaces positioned over the main spar, resulting in approximately 780 strain sensors bonded to the wings. The strain data from the FBGs was compared to that obtained from four conventional strain gages, and was used to obtain the out-of-plane loads as well as the wing shape at various load levels using NASA-developed real-time load and displacement algorithms. The composite wing measured 5.5 meters and was fabricated from laminated carbon uniaxial and biaxial prepreg fabric with varying laminate ply patterns and wall thickness dimensions. A three-tier whiffletree system was used to load the wing in a manner consistent with an in-flight loading condition.</p>

<p> Although multiphase gas and liquid phenomena occurs widely in engineering problems, many aspects of multiphase interaction like within droplet dynamics are still not quantified. This study aims to qualify the Lattice Boltzmann (LBM) Interparticle Potential multiphase computational method in order to build a foundation for future multiphase research. This study consists of two overall sections. </p><p> The first section in Chapter 2 focuses on understanding the LBM method and Interparticle Potential model. It outlines the LBM method and how it relates to macroscopic fluid dynamics. The standard form of LBM is obtained. The perturbation solution obtaining the Navier-Stokes equations from the LBM equation is presented. Finally, the Interparticle Potential model is incorporated into the numerical LBM method. </p><p> The second section in Chapter 3 presents the verification and validation cases to confirm the behavior of the single-phase and multiphase LBM models. Experimental and analytical results are used briefly to compare with numerical results when possible using Poiseuille channel flow and flow over a cylinder. While presenting the numerical results, practical considerations like converting LBM scale variables to physical scale variables are considered. Multiphase results are verified using Laplaces law and artificial behaviors of the model are explored. </p><p> In this study, a better understanding of the LBM method and Interparticle Potential model is gained. This allows the numerical method to be used for comparison with experimental results in the future and provides a better understanding of multiphase physics overall.</p>

The three-dimensional rendezvous between two spacecraft is considered: a target spacecraft on a circular orbit around the Earth and a chaser spacecraft initially on some elliptical orbit yet to be determined. The chaser spacecraft has variable mass, limited thrust, and its trajectory is governed by three controls, one determining the thrust magnitude and two determining the thrust direction. We seek the time history of the controls in such a way that the propellant mass required to execute the rendezvous maneuver is minimized. Two cases are considered: (i) time-to-rendezvous free and (ii) time-to-rendezvous given, respectively equivalent to (i) free angular travel and (ii) fixed angular travel for the target spacecraft. The above problem has been studied by several authors under the assumption that the initial separation coordinates and the initial separation velocities are given, hence known initial conditions for the chaser spacecraft. In this paper, it is assumed that both the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given so as to prevent the occurrence of trivial solutions. Two approaches are employed: optimal control formulation (Part A) and mathematical programming formulation (Part B). In Part A, analyses are performed with the multiple-subarc sequential gradient-restoration algorithm for optimal control problems. They show that the fuel-optimal trajectory is zero-bang, namely it is characterized by two subarcs: a long coasting zero-thrust subarc followed by a short powered max-thrust braking subarc. While the thrust direction of the powered subarc is continuously variable for the optimal trajectory, its replacement with a constant (yet optimized) thrust direction produces a very efficient guidance trajectory. Indeed, for all values of the initial distance, the fuel required by the guidance trajectory is within less than one percent of the fuel required by the optimal trajectory. For the guidance trajectory, because of the replacement of the variable thrust direction of the powered subarc with a constant thrust direction, the optimal control problem degenerates into a mathematical programming problem with a relatively small number of degrees of freedom, more precisely: three for case (i) time-to-rendezvous free and two for case (ii) time-to-rendezvous given. In particular, we consider the rendezvous between the Space Shuttle (chaser) and the International Space Station (target). Once a given initial distance SS-to-ISS is preselected, the present work supplies not only the best initial conditions for the rendezvous trajectory, but simultaneously the corresponding final conditions for the ascent trajectory. In Part B, an analytical solution of the Clohessy-Wiltshire equations is presented (i) neglecting the change of the spacecraft mass due to the fuel consumption and (ii) and assuming that the thrust is finite, that is, the trajectory includes powered subarcs flown with max thrust and coasting subarc flown with zero thrust. Then, employing the found analytical solution, we study the rendezvous problem under the assumption that the initial separation coordinates and initial separation velocities are free except for the requirement that the initial chaser-to-target distance is given. The main contribution of Part B is the development of analytical solutions for the powered subarcs, an important extension of the analytical solutions already available for the coasting subarcs. One consequence is that the entire optimal trajectory can be described analytically. Another consequence is that the optimal control problems degenerate into mathematical programming problems. A further consequence is that, vis-a-vis the optimal control formulation, the mathematical programming formulation reduces the CPU time by a factor of order 1000. Key words. Space trajectories, rendezvous, optimization, guidance, optimal control, calculus of variations, Mayer problems, Bolza problems, transformation techniques, multiple-subarc sequential gradient-restoration algorithm.

This thesis uses linear covariance analysis to model a landmark tracking camera for lunar navigation on manned missions during a loss of communication scenario. The research provides evidence that this method satisfies Crew Exploration Vehicle requirements for autonomous navigation for returning astronauts safely to Earth from lunar orbit. This study broadens NASA's existing research efforts by creating a 6-degree-of-freedom linear covariance analysis tool to simulate the navigation errors generated in lunar orbit in the absence of ground updates. This methodology is capable of generating results which approximate those of a Monte Carlo study in a fraction of the time. Evidence is shown that landmark tracking can substantially reduce position and velocity errors while actively tracking a realistic set of lunar features.

This thesis discusses optimal trajectories for hypervelocity flight of interest in aeroassisted orbital transfer. Both coplanar orbital transfer and noncoplanar orbital transfer are studied. For these cases, the GEO-to-LEO transfer, the HEO-to-LEO transfer, and the LEO-to-LEO transfer are considered in connection with a spacecraft which is controlled during the atmospheric pass via the angle of attack (coplanar case) or via the angle of attack and the angle of bank (noncoplanar case). For the noncoplanar case, three transfer maneuvers are studied. Type 1 involves four impulses and four space plane changes; Type 2 involves three impulses and three space plane changes; and Type 3 involves three impulses and no space plane change. In Type 1, the initial impulse directs the spacecraft away from Earth, and then is followed by an apogee impulse propelling the spacecraft toward Earth; in Types 2 and 3, the initial impulse directs the spacecraft toward Earth. A common element of these maneuvers is that they all include an atmospheric pass, with velocity depletion coupled with plane change. Within the framework of classical optimal control, the following problems are studied: (P1) minimize the energy required for orbital transfer; (P2) maximize the time of flight during the atmospheric portion of the trajectory; and (P3) minimize the time integral of the square of the path inclination. Within the framework of minimax optimal control, the following problem is studied: (P4) minimize the peak heating rate. Numerical solutions for Problems (P1), (P2), (P3), (P4) are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. The engineering implications of the results obtained are discussed. In particular, it is shown that the nearly-grazing solution (namely, the trajectory solving Problem (P3)) is a useful engineering compromise between energy requirements and aerodynamic heating requirements.

A geometric nonlinear filter (GNF) is designed for application to the problem of tracking a maneuvering aircraft. The aircraft tracking problem is a state estimation problem and a state prediction problem. A nonlinear aircraft maneuver model is proposed for use in the state estimation as well as the state prediction. This nonlinear model is based on the so-called coordinated turn and describes planar trajectories. The GNF design approach involves state transformations with output injection to transform the nonlinear system model to a linear form, known as the observer canonical form. For many nonlinear systems, such as the proposed aircraft maneuver model, this linearizing transformation does not exist. Therefore, for the maneuvering aircraft model, a transformation to an approximate observer canonical form is given. Utilizing a Lyapunov stability approach, sufficient conditions for stability of the GNF estimation error are derived. No such conditions exist for the extended Kalman filter (EKF). The GNF was found to be stable in cases where the EKF was not stable. The tracking performance of the GNF compares favorably with the EKF for various levels of measurement noise. However, the GNF offers a substantial savings in computational time making it more attractive than the EKF for use in a fire control computer.

The application of the sequential gradient-restoration algorithm (SGRA) to the estimation of the windshear along the trajectory of an aircraft is studied. Based on the measured trajectory data obtained from the digital flight data recorder (DFDR) of Flight Delta 191 (August 2, 1985, Dallas-Fort Worth International Airport), a nonlinear least-square problem is formulated. The performance index being minimized measures the deviation of the experimental trajectory (the altitude, the relative velocity, and the pitch attitude angle) from the computed trajectory, obtained by integrating the equations of motion of an aircraft in a vertical plane. Since the thrust and the aerodynamic forces enter directly in this dynamic formulation, a clear picture of the forces acting on the aircraft can be seen. This leads to a good understanding of the behavior of the aircraft during the windshear encounter. The angle of attack is treated as a control, and the power setting is regarded as a known input. By assuming that the manufacturer-supplied aerodynamic and thrust data are dependable, the dynamically estimated vertical wind shows reasonable agreement with that obtained with the kinematic approach. However, the results obtained for the horizontal wind are less satisfactory. Upon modifying the manufacturer-supplied thrust and aerodynamic data with unknown multiplicative factors, a better agreement between the measured and computed trajectory can be achieved. As a consequence, the estimated winds exhibit better accuracy. The inclusion of penalty terms in the performance index being minimized forces the values of the unknown multiplicative factors to be close to unity. The estimation of these factors is important, because it might explain some unusual effects, such as the presence of rain. Upon employing different combinations of the measured trajectory data, the relative importance of each data can be established. The horizontal distance data and the relative velocity data are found to have minor effect on the estimation results. The altitude data affect mostly the vertical wind, and the pitch attitude angle data are crucial to the estimation of both the horizontal and vertical winds.

The problem considered here involves a functional I subject to differential constraints, nondifferential constraints, and general boundary conditions. It consists of finding the state x(t), control u(t), and parameter $\pi$ so that the functional I is minimized, while the differential constraints, nondifferential constraints, and boundary conditions are satisfied to a predetermined accuracy. Here, I is a scalar, x an n-vector, u an m-vector, and $\pi$ a p-vector. Four types of gradient-restoration algorithms are considered, and their relative efficiency in terms of the number of iterations for convergence and CPU time is evaluated. The algorithms considered are as follows: sequential gradient-restoration algorithm, complete restoration (SGRA-CR); sequential gradient-restoration algorithm, incomplete restoration (SGRA-IR); combined gradient-restoration algorithm, no restoration (CGRA-NR); and combined gradient-restoration algorithm, incomplete restoration (CGRA-IR).