A new set of slip boundary conditions is developed to be used beyond the slip flow-early transition by using more accurate representation of the velocity and temperature gradients at the wall. The new model agrees well with the results from the solution of the Boltzman equation. The effect of rarefaction on steady-state heat transfer in microchannels in the slip flow regime is investigated by the integral transform technique with the implementation of the first order slip boundary conditions. Uniform temperature and/or uniform heat flux boundary conditions are considered for flow between two parallel plates, in circular and rectangular channels and annular sections. Thermal entrance length is solved as well as the fully developed region. Transient effects are obtained by performing the analysis for a cylindrical pipe with a sudden wall temperature change. Two characteristics of rarefaction namely the velocity slip and the temperature jump have opposite effects on heat transfer. It is found that the Nusselt number decreases with increasing rarefaction. Viscous heat dissipation is also included in the analyses and the change in the heat transfer due to this effect is clarified. Viscous heating may increase or decrease the heat transfer coefficient depending on the direction of the external heat transfer.

Wavelet method is applied to the study of radiative heat transfer and combined conductive-radiative heat transfer through the gray and nongray participating medium in one- and two-dimensional (1-D and 2-D) geometries. The participating medium is assumed to have an index of refraction of unity and to be absorbing, emitting, and nonscattering. The surfaces of 1-D infinite parallel plates and 2-D rectangular enclosure are assumed to be black and isothermal. The governing equations are the radiative transfer equation (RTE) and energy equation. The wavelet expansion is used to evaluate the spectral dependence of radiative intensity in RTE. And a set of differential equations about the expansion coefficients are developed by applying Galerkin method and discrete ordinates method (DOM). For 1-D problem, these equations are solved by finite difference method, and for 2-D problem, they are solved by finite volume method. The energy equation is solved simultaneously by applying the modified quasi-linearization algorithm (MQA) to obtain the temperature distribution and heat flux. The results for the cases of radiative equilibrium, uniform internal heat generation, and combined conductive-radiative heat transfer with gray and nongray medium are given and compared with those obtained by other methods. The optical thickness of the medium ranges from optical thin to optical thick. The conduction-radiation parameter varies from radiation-dominated to conduction-dominated situations. The method is proved to be a powerful tool in analyzing the radiative heat transfer through the nongray participating media. The results of 2-D nongray problems are first presented.

In this thesis, a general method was developed to solve the momentum-optimal attitude command trajectory for a given reorientation. The solution method relied on converting a standard two-point boundary-value problem to an unconstrained optimization problem using Lagrange multipliers. This approach was applied to a realistic robotic assembly operation of the International Space Station. Results for the optimization method in this thesis were compared with alternative attitude command strategies. Unlike much of the previous research, the methods developed in this thesis account for spacecraft with arbitrary and/or changing inertia matrices, control torques which do not necessarily coincide with the principal axes of the spacecraft, the full nonlinear rotational dynamics, known external torques that are functions of attitude and changes in angular momentum and mass properties due to repositioning of spacecraft components. Using the methods developed in this thesis, the peak momentum use during a maneuver was minimized. Additionally, optimal maneuvers were able to remove accumulated momentum from the CMG system.

Floating Production, Storage and Offloading (FPSO) Systems are subjected to stochastic wave loads. In this context, an approach for stochastic fatigue analysis of FPSO topside equipment is developed. Proper FPSO transfer functions, and the Ochi-Hubble sea wave elevation spectrum are combined to provide the design spectrum at the topside of the FPSO. The equipment response is simulated by a time series model; it is approximated as the output of digital filters to a band-limited white noise input. The rainflow cycle counting method is applied to the equipment response time history to identify significant cycles that produce fatigue damage. By using a S-N fatigue life curve, and Miner's linear damage accumulation rule, the fatigue life is estimated for a generic piece of equipment. The results of the rainflow cycle counting method are supplemented by results from a power spectrum based, exclusively, approach.

Accurate and efficient turbulence simulation in complex geometries is a formidable challenge. Traditional methods are often limited by low accuracy and/or restrictions to simple geometries. We explore the merger of Discontinuous Galerkin (DG) with Variational Multi-Scale (VMS), termed Local VMS (LVMS), to overcome these limitations. DG spatial discretizations support arbitrarily high-order accuracy on unstructured grids amenable for complex geometries. Furthermore, high-order hierarchical representation within DG provides a natural framework for a priori scale separation crucial for VMS implementation, a promising approach to LES. We study the efficacy of LVMS for turbulence simulation using a fully-developed turbulent channel flow. First, a detailed spatial resolution study is undertaken to record the effects of the DG discretization on turbulence statistics. Here, the local hp-refinement capabilities of DG are exploited to obtain reliable low-order statistics efficiently. Then, we explore the effects of enforcing Dirichlet boundary conditions through numerical fluxes in DG that allows solution jumps (slip) at the channel walls. This feature of DG is effective in mitigating the high near-wall resolution requirements in the wall-normal direction that enables reasonable drag predictions even with moderate resolutions. However, using coarse resolutions leads to significant slip at the channel walls that affect drag predictions. Here, modifying the numerical viscous flux to regulate this slip through a penalty is found to improve drag predictions. Thus, demonstrating the potential of the numerical viscous flux to act as a rudimentary wall-model. Next, for reduced-order modeling, we evaluate the merits of Spectral Filtering (SF) and Polynomial Dealiasing (PD) for improving non-linear stability. While both approaches are successful, PD is found to be better suited for Sub-Grid Scales (SGS) modeling. Finally, a VMS model is implemented to account for SGS effects. Results in good agreement with reference are obtained demonstrating the effectiveness of LVMS for wall-bounded turbulence. The locality of DG provides the flexibility to specify model parameters individually on each element. This unique feature of LVMS can be exploited for surgical modeling in a wide range of turbulent flows.

A finite element analysis methodology employing rp-adaptivity is developed. The p-refinement phase is facilitated through the addition and deletion of general serendipity element edge nodes. The r-refinement phase is based on the reduction of error in the solution using element area as the grid optimization design variable. A series of tiered linked list data structure representations are developed for storing and manipulating the model information. The Zienkiewicz-Zhu error estimator is utilized for determining localized error. A modified superconvergent patch recovery technique is implemented to recover highly accurate nodal gradients utilized in the error estimation phase. Numerical results are presented for an idealized fluid flow problem.

Harmonic gear drives have found increasing application in high performance and precision servomechanisms due to their attractive physical and dynamic properties. However all harmonic gear drives exhibit undesireable nonlinear kinematic error and the ability to control and compensate this error is limited to obtaining an appropriately accurate and controllable representative mathematical model. A comprehensive literature search revealed a wide effort towards characterization with little or no effort to modeling and control. This work adopts existing models of kinematic error characterized in the literature and presents modeling techiques such that for any model of kinematic error used, the PD-control law will effectively regulate the control variable to the desired position. Additionally, asymptotic stability result reveals that in case of PD control, sensors should be placed to measure at the load end.

Large Eddy Simulation (LES) is an efficient computational tool for turbulence simulation. Variational Multiscale (VMS) is a new paradigm for LES that uses variational projection instead of spatial filtering that obviates many issues related to spatial filtering in traditional LES. VMS for a fully-developed turbulent channel flow using a constant coefficient Smagorinsky model is implemented in a hybrid-spectral code. Our implementation differs from prior VMS where we apply scale separation only in the homogeneous directions, i.e. in the planes. The results obtained are comparable to prior VMS implementations that show good agreement with Direct Numerical Simulation (DNS) and are superior to dynamic LES. The ability of the VMS method to simulate turbulence control is studied in the context of opposition control. The results show good agreement with DNS and dynamic LES making VMS an attractive method for turbulence control investigations.

Radiative heat transfer analysis requires the consideration of seven independent variables, three spatial directions, two angular directions, frequency and time. Consequently, the solution of radiative transfer problems demands specialized numerical methods in order to deal with each of these independent variables. In this study, a new numerical scheme is developed, which employs wavelet analysis in the evaluation of radiative intensity in the angular domain. The formulation of the method for one- and two-dimensional problems is presented, and the accuracy and effectiveness of the method are tested by case studies. The wavelet analysis is implemented in the treatment of transient radiative transfer problems and as a test case, imaging of inhomogeneties within an absorbing, scattering medium exposed to short-pulse laser irradiation is studied.

The purpose of this work is to develop a singular perturbation-based approach to modeling closed kinematic chains. First, a kinematical analysis is developed to show that closed kinematic chains cannot be modeled in general using only independent generalized coordinates. Second, the Lagrangian formulation is used to develop the DAE system for closed kinematic chains. Next, differential algebraic equations (DAEs) are described, followed by discussion of standard techniques for their solution and the limitations of the standard techniques with respect to model-based control design. Then, a singular perturbation approach to solving the DAE that arise from closed kinematic chains is developed. Using this model makes it possible to solve an ODE which is an approximation of the DAE. Finally, the technique is illustrated using the Rice Planar Delta Robot.