A numerical method has been developed for computing the steady state flow about arbitrary shaped three dimensional bodies on or below the free surface using a Boundary Integral Element Method ( Panel Method). The method uses a singularity distribution over the body surface and the free surface. The method can solve for the potential distribution as well as the source density distribution. In this study a constant source distribution is assumed on each panel. The free surface boundary condition is linearized about the uniform undisturbed flow (Kelvin Free Surface condition). Upstream waves are prevented by the use of an one-sided upstream 4-point finite difference operator for the free surface condition. Wave elevations are computed using the linearized free surface condition. In this study two different bodies were considered: a submerged spheroid and a sphere. The wave resistance was computed for different Froude numbers and compares well with existing results. The study has also analyzed the effect of the number of panels on the body surface, the length of the free surface paneling behind the body and the aspect ratio of the free surface panels. / Master of Science

A review of the existing, more prominent velocity profile models for two and three-dimensional incompressible flows was presented, with emphasis placed on those that had previously shown their ability to correlate experimental data taken under various conditions. This review included velocity profile models that seemingly could represent flows in which the cross flow velocity vector reverses direction. The various methods of determining a wall shearing stress by semi-empirical considerations for two and three-dimensional flows was discussed. A direct measurement of the wall shearing stress in a three-dimensional flow field was used to infer the most accurate method of applying two-dimensional techniques to three-dimensional conditions in order to obtain reasonable values for the friction losses in a boundary layer. A discussion of the error in the determination of the skin friction coefficient by use of the Glauser Chart was presented. The experimental constants in the law of the wall formulation are shown to be the basis for an error which may be in excess of 15 per cent in the determination of the skin friction coefficient. Finally, a thorough comparison of the previously reviewed two and three-dimensional velocity profile models was made with some of the most complete sets of experimental data available to date. / Master of Science

Presented in this paper are experiments to test the hypothesis that drag reduction is possible over hydrophobic surfaces in the Wenzel state during laminar and turbulent flows. Quantification of surface drag reduction in rectangular channel flow over walls with specific hydrophobic or hydrophilic properties was obtained with pressure drop measurements along the channel for a range of Reynolds numbers between 350 and 5900. Several commercially available materials and coatings were chosen in order to span a range of contact angles between 30° and 135°. The results are within the bounds of the theoretical values calculated with the Colebrook equation, and do not show any reduction in wall shear stress as a function of material properties or surface chemistry. The differences between this experiment and others measuring pressure drop over hydrophobic surfaces is the macro-scale conditions and the hydrophobic surfaces being fully wetted. These experiments are further proof of the importance of a liquid-vapor interface for increasing the shear free area to produce drag reduction. / Master of Science

The present investigation was undertaken to determine experimentally whether or not instability of the laminar boundary layer on blunt convex bodies exists when the wall-to-stagnation temperature is lowered. It was found that instability existed and theoretical considerations are given to the transition being associated with the formation of ice on the model surface and with an increase in roughness Reynolds numbers due to thinning of the laminar boundary layer at low wall-to-stagnation temperature ratios. The experimental tests were conducted on two-inch diameter spheres at M = 4.95 and free-stream Reynolds numbers per foot of approximately 72. 5 x 10⁶ or 12.1 x 10⁶ based on the model base diameter. Data were obtained tor both the hot wall and cold wall case. The stagnation temperature was approximately 400° F. Initial model wall temperatures were 97°F, for the hot wall test and -320° F for the cold wall tests. / M.S.

Molecular dynamics simulations of the diffusion process in ordered B2 compounds at high temperature were performed using an embedded atom interatomic potential developed to fit NiAl properties. Diffusion in the bulk occurs through a variety of cyclic mechanisms that accomplish the motion of the vacancy through nearest neighbor jumps restoring order to the alloy at the end of the cycle. The traditionally postulated six-jump cycle is only one of the various cycles observed and some of these are quite complex. Diffusion at the grain boundary mainly takes place through sequences of coordinated nearest neighbor jumps yielding to a rearrangement of the grain boundary structure. Two distinct mechanisms resulting in a structural unit migration of the vacancy are also identified. The results are analyzed in terms of the activation and configuration energies calculated using molecular statics simulations. / Master of Science

Systems engineering has many subdisciplines which would be useful to study in terms of complex system behavior. However, it is the interactions between a complex system and its operating environment which drive the motivation for this analysis. Specifically, this work introduces a new approach to assessing these interactions called "boundary resilience." While classical resilience theory measures a system's internal reaction to adverse event, boundary resilience evaluates the impacts such an event may have on the surrounding environment. As the scope of this analysis is quite large, it was deemed appropriate to conduct a case study to determine the fundamental tenants of boundary resilience. SpaceX's satellite Internet mega-constellation (StarLink) was chosen due to its large potential to impact the space environment as well as its size and complexity. This study produced two boundary resilience measures, one for local boundary resilience of a single component and one for the global boundary behavior of the entire system. The local metric measures the likelihood of an adverse event occurring at that boundary location as well as its potential to impact the surrounding environment. The global boundary resilience metric reflects a nonlinear relationship among the system components. / Doctor of Philosophy / It is no secret that the world and the systems which enable it to function have become increasingly complex in recent decades. This complexity has the potential to create both innovative uses as well as unplanned and unexpected behaviors in these systems. As they interact with their environment, complex systems can produce equally complex and unpredictable behaviors which have potential to have a negative impact on their environment. This work seeks to study one component of this behavior: resilience. Resilience usually measures a system's ability to continue providing a service in the event of a disruption, or to recover the ability to provide the service after some amount of time. Boundary resilience, on the other hand, takes the perspective of potential environmental damage caused by an adverse event, rather than damage to the system's functionality. This study uses a case study of the StarLink satellite constellation to examine this phenomenon. The outcome of the analysis shows that the size of a complex system negatively impacts its potential to cause damage to the surrounding environment, but increasingly mature components can mitigate this degradation.

Instability waves in a free shear layer formed by two parallei compressibie streams are analyzed using the linear spatial stability theory. Both viscous and inviscid disturbances are considered. The basic state is obtained by solving the compressibie laminar boundary-layer equations or is specified by the hyperbolic tangent velocity profile. The effects of viscosity, Mach number, the velocity and temperature ratios on the growth rate are determined. Unlike the boundary layer flow, viscosity has a stabilizing effect on the mixing layer flow. Increasing the temperature ratio produces a strong stabilizing effect on the growth of the mixing flow; this stabilization does not, however, persist at higher Mach numbers. Whereas the maximum growth rate of the Incompressible mixing layer varies linearly with the velocity ratio, the maximum growth rate of the compressible mixing flow varies nonlinearly with the velocity ratio. The numerical results substantiate the fact that the convective Mach number Is the appropriate parameter for correlating the compressibility effects on the spreading rate of the mixing layer. The ratio of the spreading rate of a compressible layer to that of an incompressible layer at the same velocity and density ratios depends primarily on the convective Mach number. Three-dimensional waves become important when the convective Mach number is greater than 0.6. The influence of nonparallelism on the spatial growth rate of two-dimensional disturbances is evaluated and is found to be negligible. Linear subharmonic Instabilities of a compressible mixing layer, which Is spatially periodic in a translating frame of reference, are analyzed by using Floquet theory. The basic state is obtained by the linear superposition ofa steady mean flow, which is given by a solution to the compressible boundary-layer equations or by a hyperbolic tangent velocity profile approximation, and the neutral primary wave of that mean flow. The results show that the growth rates of two-dimensional subharmonic instabilities (pairing mode) increase with increasing amplitude of the periodicity but decrease with increasing the convective iVIach number. In the incompressible flow case, the most amplified subharmonic wave is a two-dimensional mode, which is in agreement with the published results. For subsonic convective Mach numbers, the presence of the periodicity enhances the growth rates of three-dimensional subharmonic waves over a wide range of spanwise wavenumber which shows a preferred band over which the growth rate is maximum. However, when the convective IVIach number is greater than one, the interaction between the subharmonic wave and the primary wave marginally increases the maximum growth rate of the subharmonic. Nevertheless, that interaction dramatically increases the range of amplified spanwise wave numbers. Fourth-order compact finite-difference codes are developed for solving the compressible boundary-layer equations and investigating their primary and subharmonic instabilities. The codes proved to be very accurate and versatile. / Ph. D.

Static pressure and mean velocity data were obtained in a relaxing shear driven three-dimensional incompressible turbulent boundary layer flow produced by a swept rectangular step. The nominally 10 cm (4 in.) thick boundary layer had a freestream velocity of approximately 25 m/sec (80 ft/sec). The two steps investigated were each 3.8 cm (1.5 in.) high by 18.4 cm (7 .25 irt.) long and at angles of 30° and 45° to the transverse wind tunnel direction. Pressure gradients were determined by taking the derivative of least-squares curve fits to the static pressure data. Close to the trailing edge reattachment region, the maximum·gradient was·0.8 kPa/m (5 psf/f) for the 30° step and 0.4 kPa/m (2.5 psf/f) for the 45°step. As expected, a region of nominal pressure gradient (0.03 kPa/m or 0.2 psf/f compared to 1.6 kPa/m or 10 psf/f for a pressure driven flow) was found at greater than 36 cm (14 in.) down.stream of the trailing edge of each step. The wall crossflow angle decayed from 67° at 15 cm (6 in.) behind the trailing edge to 9° at 66 cm (26 in.) for the 30° step. In the same region, the crossflow angle decayed from 45° to 6° for the 45° step. The decay or relaxation was found to be much faster in the near-wall region and in the region close to the trailing edge. A defect in the streamwise velocity profiles indicated that the flow was dominated by the separation and reattachment over the step. For future shear driven investigations, a lower, more streamlined wing-type body is recommended to produce a moderately skewed boundary layer without dominant separation effects. / Master of Science

Static pressure, mean velocity, indirect wall shear from Preston tubes, direct wall shear using a two-dimensional (single line of action) floating element device, and direct wall shear measurements from an omnidirectional floating element capable of simultaneously determining magnitude and direction of a wall shear vector were completed over a modest range of two-dimensional, (near-zero) pressure gradient flows. Static pressure, mean velocity, and direct wall shear measurements using the omnidirectional meter were completed in a pressure driven, and two different shear driven three-dimensional flows. These data were combined to evaluate ten of eleven three-dimensional similarity models found in the literature. Uncertainty estimates on all the data are presented. Two-dimensional experimental results show that the constants in the two-dimensional law of the wall formula appear to be slightly dependent on Reynolds number, and the Patel calibration formulas for Preston tubes to be better than any other available formulas. Three-dimensional results show (1) the Perry and Joubert and the White, Lessmann, and Christoph three-dimensional similarity models to give limited but overall better agreement with experimental data, (2) none of the proposed models adequately model experimental results for y⁺ < 50, (3) near-wall collateral flow does not exist, and (4) pressure gradient effects on the omnidirectional meter appear to be negligible. / Ph. D.

This project proposes a performing arts center in Chattanooga, Tennessee, a 170-year old industrial city. As part of the city revitalization, the design seeks to build up a "stage", and create a piece of edge at the city's northern boundary. Two folded bands, one made of skeletal steel and surfaced with copper connecting the river and the mountainous landscape beyond with the city, the other made of reinforced concrete folded to form a spatial intersection housing a series of activities: performing, spectating, and exhibiting. A curved metal screened circulation wall opens at the bottom to allow the copper band to pass as an entrance into the lobby to develop its folded intersection. Through it, an industrial stack in the middle of the site is isolated from busy city, and anchored with the building as a monument. Along the west side, an additional element characterized as the education box hovers over the ground, with unobstructed views of the river and the old steel bridge on one end, and the green hill on the other. / Master of Architecture