Neste trabalho, estuda-se uma abordagem de caráter analítico para problemas bidimensionais de transporte de nêutrons que são descritos pela equação linear de Boltzmann. Neste sentido, aplica-se o método ADO, método Anal tico de Ordenadas Discretas, para resolver as equações unidimensionais nodais, obtidas a partir da integração da formulação bidimensional. Nesta derivação, necessita-se de equações auxiliares para os fluxos desconhecidos no contorno. Assim, duas propostas são apresentadas: na primeira, relações entre o fluxo integrado e o fluxo desconhecido são introduzidas e na segunda, os termos desconhecidos são tratados como fonte do problema. Resultados numéricos são apresentados e comparados com resultados existentes na literatura. / In this work, an analytical approach for two dimensional transport problems, describeb by the linear Boltzmann Equation, is proposed. In this sense, the ADO method, Analytical Discrete Ordinates, is applied to solve the one dimensional equations obtained by the application of a nodal scheme. In this derivation, auxiliary equations are needed for the unknown uxes at the boundary. So two proposals are presented: rst, relations between the integrated ux and the unknown ux are introduced and the second, the unknown terms are treated as source of the problem. Numerical results are presented and compared with available results in the literature.

The present work deals with the development of a direct simulation strategy for solving the motion of spherical particles in non-Newtonian liquids. The purely viscous (non-elastic) non-Newtonian liquids are described by Bingham and thixotropy models. Validation of the strategy is performed for single phase (lid driven cavity flow) and two phase flows (sphere sedimentation). Lid driven cavity flow results illustrate the flow evolution of thixotropic liquid and subtle differences between thixotropic rheology and pseudo Bingham rheology. Single sphere sedimentation in Bingham liquid is shown to be influenced by the yield stress of the liquid. Time-dependent properties such as aging prominently affect the settling of a sphere in thixotropic liquid. The hydrodynamic interactions between two spheres are also studied at low and moderate Reynolds numbers. In thixotropic liquid, an intriguing phenomenon is observed where the separation distance between the spheres first increases and then rapidly decreases. / Chemical Engineering

As the operating conditions of the pressurized water reactor (PWR) have been increased towards the thermal limits of the core for economics, the subcooled boiling heat transfer performance of the rod bundles under normal operating conditions has become an increasingly important design focus. Effective field models such as two-fluid model, on which most previous numerical studies in the nuclear fields have focused, cannot predict detailed phenomenon of subcooled boiling because it involves complex multiphase dynamics, such as nucleation, growth, detachment bubbles from a wall, deformation, break-up, coalescence, and condensation. It also requires numerous, additional closure relations. On the other hand, direct numerical simulations with interfacial tracking enable us to capture specific two-phase flow and do not require additional empirical closure relations. In this thesis, we simulate isothermal, two-dimensional bubble dynamics as a starting point toward direct simulation of the subcooled boiling. We adopt a lattice Boltzmann method with the phase-field model. The lattice Boltzmann method is a mesoscopic approach well-adapted to the simulation of complex fluids and is simple to implement. The phase field model can capture complex topological deformation, such as coalescence and break-up, with better numerical stability than other interfacial tracking methods like Volume of Fluid (VOF) and level set methods. We validate the present method for stationary and moving two-phase interfaces by comparing with theoretical solutions for a single static bubble in a stationary liquid and a capillary wave, respectively. In addition, the capability of the current method to simulate the coalescence of two bubbles and droplets is validated by comparing with experimental data. To see the applicability of the method to problems involving complex bubble behaviors and interactions with a high-density ratio as in subcooled boiling water, we simulate rising single and double bubbles in a viscous fluid. For a single bubble problem, the bubble shapes and terminal velocity agreed well with the experimental results for different fluid dynamic conditions. For a double bubble case, the current method can capture the interaction and dynamics of the bubbles. Thus, it is expected that this study can serve as a stepping-stone extension to convective subcooled boiling heat transfer in the nuclear reactor core.

Advancements in electronic performance lead to a decrease in device size and an increase in power density. Because of these changes, current cooling mechanisms for electronic devices are beginning to be ineffective. Microchannels, with their large heat transfer surface area to volume ratio, cooled with either gas or liquid coolant, have shown some potential in adequately maintaining a safe surface temperature. By modifying the walls of the microchannel with fins, the cooling performance can be improved. Using computational fluid dynamics software, microfins placed in a staggered array on the bottom surface of a rectangular minichannel are modeled in order to optimize microstructure geometry and maximize heat transfer dissipation through convection from a heated surface. Fin geometry, dimensions, spacing, height, and material are analyzed. Correlations describing the Nusselt number and the Darcy friction factor are obtained and compared to recent studies. These correlations only apply to short fins in the laminar regime. Triangular fins with larger fin height, smaller fin width, and spacing double the fin width maximizes the number of fins in each row and yields better thermal performance. Once the effects of microfins were found, an experiment with multi-walled carbon nanotubes (MWNTs) grown on the surface were tested using both water and Al2O3/H2O nanofluid as the working medium. Minichannel devices containing two different MWNT structures – one fully coated surface of MWNTs and the other with a circular staggered fin array of MWNTs - were tested and compared to a minichannel device with no MWNTs. It was observed that the sedimentation of Al2O3 nanoparticles on a channel surface with no MWNTs increases the surface roughness and the thermal performance. Finally, using the lattice Boltzmann method, a two dimensional channel with suspended particles is modeled in order to get an accurate characterization of the fluid/particle motion in nanofluid. Using the analysis based on an ideal fin, approximate results for nanofluids with increase surface roughness was obtained. Microchannels have proven to be effective cooling systems and understanding how to achieve the maximum performance is vital for the innovation of electronics. Implementation of these modified channel devices can allow for longer lasting electronic systems.

In the recent years, researchers have discovered a multitude of applications using nanofibers in fields like composites, biotechnology, environmental engineering, defense, optics and electronics. This increase in nanofiber applications needs a higher rate of nanofiber production. Electrospinning has proven to be the best nanofiber manufacturing process because of simplicity and material compatibility. Study of effects of various electrospinning parameters is important to improve the rate of nanofiber processing. In addition, several applications demand well-oriented nanofibers. Researchers have experimentally tried to control the nanofibers using secondary external electric field. In the first study, the electrospinning process is modeled and the bending instability of a viscoelastic jet is simulated. For this, the existing discrete bead model is modified and the results are compared, qualitatively, with previous works in literature. In this study, an attempt is also made to simulate the effect of secondary electric field on electrospinning process and whipping instability. It is observed that the external secondary field unwinds the jet spirals, reduces the whipping instability and increases the tension in the fiber. Lattice Boltzmann method (LBM) has gained popularity in the past decade as the method is easy implement and can also be parallelized. In the second part of this thesis, a hybrid numerical scheme which couples lattice Boltzmann method with finite difference method for a Oldroyd-B viscoelastic solution is proposed. In this scheme, the polymer viscoelastic stress tensor is included in the equilibrium distribution function and the distribution function is updated using SRT-LBE model. Then, the local velocities from the distribution function are evaluated. These local velocities are used to evaluate local velocity gradients using a central difference method in space. Next, a forward difference scheme in time is used on the Maxwell Upper Convected model and the viscoelastic stress tensor is updated. Finally, using the proposed numerical method start-up Couette flow problem for Re = 0.5 and We = 1.1, is simulated. The velocity and stress results from these simulations agree very well with the analytical solutions.

This research develops an extendible framework for reproducing watercolor in a digital environment, with a focus on interactivity using the GPU. The framework uses the lattice Boltzmann method, a relatively new approach to fluid dynamics, and the Kubelka-Munk reflectance model to capture the optical properties of watercolor. The work is demonstrated through several paintings produced using the system.

Zugl.: Erlangen, Nürnberg, Univ., Diss., 2008

Reaction-diffusion-convection (R-D-C) problems are governed by wide spectrum of spatio-temporal scales associated with ranges of physical and chemical processes. Such Problems are called multiscale, multiphysics problems. The challenge associated with R-D-C problems is to bridge these scales and processes as seamlessly as possible. For this purpose, we develop a wavelet-based multiscale simulation framework that couples diverse scales and physics.In a first stage we focus on R-D models. We treat the `fine' reaction-scales stochastically, with kinetic Monte Carlo (kMC). The transport via diffusion possesses larger spatio-temporal scales which are bridged to the kMC with the Compound Wavelet Matrix (CWM) formalism. Since R-D-C problems are dynamical we extend the CWM method via the dynamic-coupling of the kMC and diffusion models. The process is approximated by sequential increments, where the CWM on each increment is used as the starting point for the next, providing better exploration of phase-space. The CWM is extended to two-dimensional diffusion with a reactive line-boundary to show that the computational gain and error depends on the scale-overlap and wavelet-filtering. We improve the homogenization by a wavelet-based scheme for the exchange of information between a reactive and diffusive field by passing information along fine to coarse (up-scaling) and coarse to fine (down-scaling) scales by retaining the fine-scale statistics (higher-order moments, correlations). Critical to the success of the scheme is the identification of dominant scales. The efficiency of the scheme is compared to the homogenization and benchmark model with scale-disparity.To incorporate transport by convection, we then couple the Lattice Boltzmann Model (LBM) and kMC operating at diverse scales for flows around reactive block. Such model explores markedly different physics due to strong interplay between these time-scales. `Small' reaction induced temperature variations are considered for multiscale coupling of the reactions with the flow, showing the discrepancies in the evolutions and yield comparing to the conventional model. The same framework is used to study the reactions induced by hydrodynamic bubble collapse which shows the similar features of the kinetics and yield comparing to conventional models.We culminate to some problems that could be solved using the developed framework and preliminary results are presented as "proof of concept."

No description available.

No description available.