<p> This dissertation presents the kinematic design of six-bar linkages for function, motion, and path generation by means of polynomial homotopy continuation algorithms. When no link dimensions are specified beforehand, the synthesis formulations for each design objective yield polynomial systems of degrees in the millions and billions, suggesting a large number of solutions. Complete solution sets to these systems have not yet been obtained and is the topic of this dissertation. Function generation for eleven positions is explored in most detail, in particular the Stephenson II and III function generators, for which we calculate multihomogeneous degrees of 264,241,152 and 55,050,240. A numerical reduction using homotopy estimates these systems to have 1,521,037 and 834,441 roots, respectively. For motion generation, the Watt I linkage can be specified for eight positions, producing a system of a multihomogeneous degree over 19 billion. However, for this work we focus on the smaller case of six positions, numerically reducing this system to an estimated 5,735 roots. For path generation we take a different approach. The design of path generators is formulated as RR chains constrained to have a single degree-of-freedom by attaching six-bar function generators to them. This enables us to use our results obtained on Stephenson II and III function generators to create four types of eleven position path generators: the Stephenson I linkage, two types of Stephenson II linkages, and the Stephenson III linkage. </p>

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The formation and evolution of secondary vortical structures in a plane mixing layer subjected to spanwise-nonuniform excitation has been studied in a closed-return water facility. It is shown that secondary vortices may result from spanwise-nonuniformities in the nominally two-dimensional vorticity layer close to the flow partition, or from spanwise core deformations of the primary vortices further downstream. These distinctly different mechanisms are excited by time-harmonic wavetrains with spanwise amplitude or phase variations, respectively, synthesized by a mosaic of surface film heaters flush-mounted on the flow partition. The appearance of the secondary vortical structures is accompanied by significant distortions in transverse distributions of the streamwise velocity component. Inflection points, which are not present in corresponding velocity distributions of the unforced flow, suggest the formation of locally unstable regions of large shear in which broadband perturbations, already present in the base flow, undergo rapid amplification. This amplification is followed by breakdown to turbulence thus producing the small-scale motion necessary for mixing transition. The present investigation further shows that the flow is extremely receptive to spanwise-periodic amplitude excitation at any wavelength synthesizable by the heater mosaic. Spanwise-periodic phase excitation leads to substantial deformations of the primary vortices, although the receptivity of the flow appears to have a short wavelength cutoff. Spanwise-nonuniform amplitude and phase excitations at a subharmonic frequency of the Kelvin-Helmholtz instability result in complex pairing interactions of the primary vortices.

The problem of formulating and numerically solving the equations of motion of flexible multibody systems for application to structural impact is considered in this dissertation. As an alternative to experimental tests and to numerical procedures such as hybrid models and finite element methods, multibody dynamics contains the ingredients for efficient crash analysis of these problems provided that a proper description of the deformations of the system components is included. Based on the principles of continuum mechanics, updated and total Lagrangian formulations are used to derive the equations of motion for a flexible body. The finite element method is applied to these equations in order to obtain a numerical solution of the problem. It is shown that the use of convected coordinate systems not only simplifies the form of the flexible body equations of motion, but it also lowers the requirements for objectivity of the material law. A simpler form of the finite element equations of motion is obtained when a lumped mass formulation is used, and the nodal accelerations are expressed in a nonmoving reference frame. In this form, not only the geometric and material nonlinear behavior of the flexible body is accounted for, but also the inertial coupling between the gross motion and the distributed flexibility is preserved. A reduction on the number of coordinates describing the flexible body is achieved with the application of the Guyan condensation technique or the modal superposition method. For partially flexible bodies with a small deformable part, an efficient kinetostatic method is derived assuming that the deformable part is massless. The equations of motion of the complete multibody system are formulated in terms of joint coordinates. The necessary velocity transformations between the set of independent velocities and the dependent velocities are derived. Special emphasis is paid to the formulation of the constraint equations of kinematic joints involving flexible bodies. The dynamics of a truck rollover are studied in order to illustrate the efficiency of the developed methodology. Several simulations are performed using a general purpose multibody dynamics analysis code.

A methodology for the energy analysis of high temperature lunar manufacturing processes is presented. The Moon's environment creates unique thermodynamic and heat rejection problems due to the absence of an atmosphere and large ambient temperature swing as it goes from lunar day to lunar night; it is a perfect vacuum at the surface. The methodology combines availability analysis, the Pinch technology and a mathematical heat rejection model to minimize energy requirement and the lift-off mass from earth. The availability analysis is used to identify process irreversibilities and to determine the quality of energy from various exit streams. The Pinch technology is used to identify hot and cold streams for potential process heat integration. The heat rejection model is used to optimize the radiator area with temperature as the driving factor. The methodology presented allows one to identify all power consumption, production and rejection in the process, and then determine the feasibility of heat and work integration without a significant mass penalty. It provides a means to design a power system to minimize waste energy. This would result in reduction of the power requirement, cost of power and the power system's mass. The hydrogen reduction of ilmenite process for oxygen production on the Moon is used as a case study to demonstrate the energy analysis methodology. The study was limited to the reduction and electrolysis processes. The availability analysis estimated that the two processes required 56 kW to meet sensible heat and heat of reaction demands but produced 53 kW of process irreversibilities. This 53 kW of unavailability included 9.4 kW of energy potential in the product solid stream and product oxygen stream. The Pinch technology found that the product solid stream and product oxygen stream may be split to help meet the heating demands of the feed ilmenite stream. This would reduce the 56 kW of power demand by 24%. If oxygen were to be brought from 1273 K to 300 K, its entire heat content may be recovered and heat rejection is eliminated. The heat exchanger area requirement is estimated to be more than ten times the radiator area if the radiator were operated at 1273 K.

A finite element numerical method is developed for the modelling of compressible flows with locally incompressible regions, which avoids the pressure oscillations frequently exhibited in these areas. Unification of the modelling of pressure in the finite element approximation of compressible and incompressible flows is investigated through the appropriate combinations of approximation spaces and integration schemes. The penalty method for incompressible flows is re-examined in the context of a slightly compressible fluid, yielding a formulation that is consistent for both the Navier-Stokes and Stokes equations, and providing an accurate method for calculation of pressure that is faster than the solution of a pressure Poisson equation. Extension of concepts from the reformulated penalty method to the compressible Navier-Stokes equations leads to an algorithm using piecewise constant density and pressure, with bilinear velocity and temperature. Further investigation shows that bilinear density with selective reduced integration also avoids pressure oscillations, while providing improved shock capture. Selective reduced integration of all terms related to compressibility is shown to be a key element in the avoidance of pressure oscillations. The identification of the isotropic component of the stress tensor as a compressibility term, not to be combined with viscous terms, is emphasized. Reduced integration of divergence terms is shown to yield conservation of mass on the element level as well as on the assembled level, whereas full integration conserves mass only on the assembled level. The compressible flow algorithm is coupled with a chemistry solver, for the study of chemically reacting flows, where an oscillation free flow solution is essential since unphysical oscillations may cause premature ignition. Computational efficiency is obtained by iterating a fluid flow step with frozen chemistry, and a chemical reaction step with frozen flow. The algorithm is applied to the study of the ram accelerator concept, a technique for accelerating a projectile in a tube to extremely high velocities by using a shock wave to initiate combustion. The viability of the ram accelerator is demonstrated through calculations at various velocities, pressures, and gas mixtures.

The problem of analyzing and estimating transmission losses in ephemeral streams with compound channels was the focus of this research. The Kinematic Runoff and Erosion model KINEROS (Woolhiser et al., 1990) and the Soil Conservation Service SCS model (Lane, 1983) were employed in this study as they represent a range in model complexity. Initial soil moisture and channel wetness conditions were employed to modify channel infiltration capacity in the SCS model and the saturated hydraulic conductivity in KINEROS. Numerically both models have been improved to treat compound channel routing with differential over-bank and main channel infiltration. The KINEROS model was extended by coupling the over-bank and channel one-dimensional kinematic and infiltration equations through the lateral inflow terms with an assumed horizontal water surface. The SCS was extended to incorporate the Manning's equation for flow with the ordinary differential equation employed in the model. Results demonstrate that simulations by multiple trapezoidal and multiple compound cross sections further decrease computed outflow volumes and increase transmission losses as compared to using a single average trapezoidal cross section. Both models simulated observed channel losses with a comparable degree of accuracy for eight carefully checked runoff events. Over-bank losses represented 12.5% of the mean main channel loss in the case of KINEROS model and 13.4% in the SCS model. The evaluation of the performance of both models demonstrated that the best results were obtained by introducing the channel bed capacity term in the analysis to more fully treat pre-runoff channel moisture conditions.

A new approach in which element reference frames are placed at each element and deformed with the elements at all times is introduced with the purpose of computing large deformations in the dynamic analysis of highly deformable bodies. Since the deformation rate of a deformable body is generally not zero, the time derivatives of the motions of these element frames do not vanish. This co-rotational-time-dependent frame approach (named CRTD in this work) is applied to flexible rotating beams undergoing large deformations. A novel numerical scheme based on the Newmark method is presented for the fast integration of the nonlinear equations obtained from the CRTD approach, and mesh partitioning/recombining algorithms are investigated as a means of achieving computational efficiency. A flexible rotating plate undergoing large and fast rotation but small deformation is also examined. Numerical results, which include comparisons between the CRTD approach and other related approaches including nonlinear finite element approaches are presented. The effects of bending stiffness and density on the maximum deflection of highly deformable rotating beams, and differences between the rotating plate and rotating beam approaches are discussed.

A control system for the enhancement and regulation of mixing in a nonreactive plane shear layer has been developed in a two-stream closed-return water facility. Mixing of a passive scalar is estimated using a thermal analog in which the two streams have uniform, steady temperatures differing by 3°C. The position of the temperature interface between the two streams is measured in the plane of its cross stream Schlieren image by an optical sensor which is placed upstream of the rollup of the primary vortices. Control is effected via an array of surface heaters flush-mounted on the flow partition and cross-stream temperature distributions are measured with a resolution of 0.03°C using an array of closely-spaced cold wire sensors. In closed-loop experiments the output from the interface position sensor is fed back to the surface heaters. A transfer function is used to predict the effect of feedback on the interface motion. The dependence of various measures of mixing on the feedback gain k and the total delay time Δ between the actuators and the sensors is studied. The feedback gain k is adaptively modified to maximize mixing at a given streamwise station. These experiments indicate that feedback control of the motion of the temperature interface can be used for controlling the nominally 2D entrainment by the primary vortices and thus enhancing mixing.

The objective of this study was to determine how border irrigation performance is affected by inflow hydrograph shape. Sloping borders with open end boundary condition were selected for the study. A computer program called SRFR was used for simulations with the choice of zero inertia model as the mathematical model describing the movement of water along the border run. Five inflow hydrograph shapes were chosen from over fifteen shapes for evaluation. They are named as follows: constant (CON), cutback (CB), cablegation (CG), modified cutback (MCB), and modified cablegation (MCG). Different ranges of the input parameters were used to cover a wide spectrum of field conditions. Input parameters ranges and values are four infiltration families, 0.25, 0.5, 1.0, and 2.0; three slopes, 0.001, 0.0025, and 0.005; two field lengths, 650 ft and 1300 ft; three Manning's roughnesses, 0.04, 0.15, and 0.25; and three volumes, low, med., and high, which reflect 2, 4, and 6 inches of required depth. It has been found that the inflow hydrograph shape has a substantial influence on the maximum application efficiency, maximum Eₐ. Values of maximum Eₐ range from 61 percent to 80 percent. While CG gives the lowest average value of maximum Eₐ, 61 percent, CB and MCB give the highest average maximum Eₐ at 80 percent. CON gives an average value equal to 71 percent. MCG has an average value close to those given by CB and MCB and equal to 78 percent. The maximum Eₐ values range from low of zero to as high as 95 percent. Fortunately, more than 90 percent of the 216 values for each inflow hydrograph are above 70 percent for all shapes except CG. Most values fall between 70 to 80 percent for CON, 75 to 90 percent for CB, 80 to 95 for MCB, and 75 to 85 for MCG. CG has a much wider range with most maximum Eₐ values falling between 40 and 85 percent. CB and MCB are more sensitive to changes in the input parameters than CON and MCC, but far less than CG, which is the most sensitive.