Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / An analytical modelling procedure for predicting the streamwise pressure gradient for steady laminar incompressible flow of a Newtonian fluid through homogeneous isotropic granular porous media is introduced. The modelling strategy involves the spatial volume averaging of a statistical representative portion of the porous domain to obtain measurable macroscopic quantities from which macroscopic transport equations can be derived. A simple pore-scale model is introduced to approximate the actual complex granular porous microstructure through rectangular cubic geometry. The sound physical principles on which the modelling procedure is based avoid the need for redundant empirical coefficients. The model is generalized to predict the rheological flow behaviour of non-Newtonian purely viscous power law fluids by introducing the dependence of the apparent viscosity on the shear rate through the wall shear stress. The field of application of the Newtonian model is extended to predict the flow behaviour in fluidized beds by adjusting the Darcy velocity to incorporate the relative velocity of the solid phase. The Newtonian model is furthermore adjusted to predict fluid flow through Fontainebleau sandstone by taking into account the effect of blocked throats at very low porosities. The analytical model as well as the model generalizations for extended applicability is verified through comparison with other analytical and semi-empirical models and a wide range of experimental data from the literature. The accuracy of the predictive analytical model reveals to be highly acceptable for most engineering designs.

Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / The understanding and quantitative description of fluid flowthrough porousmedia, is a science which has been going on for many years and investigated in a variety of disciplines. Studies in this field have primarily been based on models, which can either be described as empirical or theoretical. Part of the current study is to understand fluid flow in porous media through studying three recent theoretical pore-scale models based on the concept of a Representative Unit Cell (RUC), to represent a porous medium. Amongst other assumptions, these models assumed plane Poiseuille flow throughout each pore section of a rectangular RUC. The main objective of this study is to numerically verify this assumption using Computational Fluid Dynamics (CFD) software, FLUENT version 6.2.16. Attention is also paid to comparison between these models with the experimental data, obtained during the model tests of airflow through a timber stack end, undertaken in a wind tunnel. The laminar and intermediate airflow through a timber stack end is simulated using the commercial software FLUENT, and the results are validated against the theoretical pore-scale models and experimental data. Two turbulence models which are, the Standard k − e and Reynolds-Stress models are used in these computations, the aimbeing to determine howwell they are able to reproduce the experimental data. The numerical results are in good agreement with one of the theoretical models presented and the experimental data.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Meteorology and Physical Oceanography, 1982. / Microfiche copy available in Archives and Science / Bibliography: leaves 108-109. / by Lawrence J. Pratt. / Ph.D.

In an emerging energy landscape that increasingly discourages the use of traditional fossil fuels, there remain applications for which the continued use of high energy density liquid fuels is required, such as aviation and other uses where space and weight are critical design factors, or long term energy storage where cost and long term availability are required. To achieve this while transitioning to green sources of energy requires the design of next-generation combustion engines that can burn alternative fuels such as bio-derived or synthetic fuels; this process will be heavily dependent on design tools such as computational fluid dynamics packages, underpinned by accurate chemical kinetic models for the fuels in question. These kinetic models often contain thermodynamic information about hundreds of unique chemical species and thousands of chemical reactions forming an interconnected network between species governing their rates of production and destruction. Historically, generation of such high-fidelity kinetic models has required decades of research---too long for the engines that will require advanced fuels. Development of a kinetic model that is predictive of certain quantities of interest (ignition delay times, flame speeds, etc) can broadly be broken into four distinct stages: 1) initial ``crude'' model generation, 2) experimental design, 3) experiments and ab-initio theory calculations, and 4) kinetic model optimization. Advances in data-enabled science and ever-increasing computing power have offered pathways towards eventually automating this process. This work aims to introduce a collection of tools and building blocks that will assist in the overall aim of automatic kinetic model development, and in doing so fill important gaps in the current capabilities available in the literature. In particular, the work here touches on aspects of all four of the stages in the model development process described above. With regard to 1), while there are tools available in the literature for automatic generation of kinetic models for an increasingly large library of fuels, these models remain subject to the constraints imposed by current chemical kinetic model structures and combustion codes. Here, automatic screening procedures are introduced that investigate the impact on kinetic model prediction errors due to two distinct issues related to pressure-dependent chemistry: the lack of a new class of chemical reaction type in current chemical kinetic models, and effects due to how species-specific energy transfer parameters are represented in pressure-dependent stabilization reactions within kinetic models. With regard to 2) and 3), a Bayesian optimal experimental design algorithm is paired with computer-controllable perfectly-stirred reactor experiments with unique capability to both explore a combinatorically complex experiment parameter space (including flowing up to ten unique gas mixtures simultaneously) and measure dozens of chemical species using rapid, on-line diagnostics. This setup allows for key reaction pathways to be carefully "sensitized'' with the addition of trace quantities of key chemical species, a capability that has not been used elsewhere in literature. Generally speaking, other experimental design algorithms in literature have not explored experimental design spaces that are radically different from those used by experienced researchers in their manual experimental design processes, and the complexity of the mixtures explored by most traditional combustion experiments is limited to two or three different chemical species at most. The sensitization of key reaction pathways unlocks the ability to perform truly transformational parameter inferences with minimal amounts of experimental data. With regard to joining step 3) to 4) in the above process, semi-automated post-processing codes allow for rapid optimizations to be performed for a prior kinetic model on the basis of experiments chosen by our experimental design algorithm. Critically, a combination of the experimental design algorithm developed here and the jet-stirred reactor experiments described was tested on the kinetic model for N₂O decomposition, which has uncertainties for key reaction rates that have persisted for decades (indeed, researchers suggest kinetic rate constants for N₂O+O=N₂+O₂ that differ by at least four orders of magnitude!). Optimizations using the Multi-Scale Informatics (MSI) tool developed by our research group were run on the basis of experimental data obtained in the aforementioned experiments, and used to gain insights about the rate constant for a key reaction in N₂O decomposition chemistry, N₂O+O=N₂+O₂ , serving as a proof-of-concept for key portions of what will form the backbone of an automatic kinetic model development pipeline.

A vortex-panel method for potential flow is used as a basis for modeling surface effects and creating a finite-element interface so that an arbitrary body can be analyzed. The basic model consists of triangular panels of linearly varying vorticity which represent the body, vortex cores on the lifting edges of the body, and vortex filaments representing the wake. The interface modification is made by using a finite-element application's output as the basis for an input file for the model, executing the main program, and writing body and wake output readable by the finite-element application. The surface-effect modification is made by including an image of the body below the real body to create a surface boundary condition through symmetry. / Master of Science

No description available.

In this thesis I study a variety of two-dimensional turbulent systems using a mixed analytical, phenomenological and numerical approach. The systems under consideration are governed by the two-dimensional Navier-Stokes (2DNS), surface quasigeostrophic (SQG), alpha-turbulence and magnetohydrodynamic (MHD) equations. The main analytical focus is on the number of degrees of freedom of a given system, defined as the least value $N$ such that all $n$-dimensional ($n$ ≥ $N$) volume elements along a given trajectory contract during the course of evolution. By equating $N$ with the number of active Fourier-space modes, that is the number of modes in the inertial range, and assuming power-law spectra in the inertial range, the scaling of $N$ with the Reynolds number $Re$ allows bounds to be put on the exponent of the spectrum. This allows the recovery of analytic results that have until now only been derived phenomenologically, such as the $k$[superscript(-5/3)] energy spectrum in the energy inertial range in SQG turbulence. Phenomenologically I study the modal interactions that control the transfer of various conserved quantities. Among other results I show that in MHD dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo inverse flux partially neutralises the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. These theoretical results are backed up by high resolution numerical simulations, out of which have emerged some new results such as the suggestion that for alpha turbulence the generalised enstrophy spectra are not closely approximated by those that have been derived phenomenologically, and new theories may be needed in order to explain them.

Abstract not available

In this study, numerical simulations of a low emission lab-scale non-premixed combustor are conducted and analyzed. The objectives are to provide new insight into the physical phenomena in the SPRF (Stagnation Point Reverse Flow) combustor built in the Georgia Tech Combustion Lab, and to compare three Large Eddy Simulation (LES) combustion models (Eddy Break-Up [EBU], Steady Flamelet [SF] and Linear Eddy Model [LEM]) for non-premixed combustion. The nominal operating condition of the SPRF combustor achieves very low NOx and CO emissions by combining turbulent mixing of exhaust gases with preheated reactants and chemical kinetics. The SPRF numerical simulation focuses on capturing the complex interaction between turbulent mixing and heat release. LES simulations have been carried out for a non-reactive case in order to analyze the turbulent mixing inside the combustor. The LES results have been compared to PIV experimental data and the code has been validated. The dominating features of the operational mode of the SPRF combustor (dilution of hot products into reactants, pre-heating and pre-mixing) have been analyzed, and results from the EBU-LES, SF-LES and LEM-LES simulations have been compared. Analysis shows that the LEM-LES simulation achieves the best agreement with the observed flame structure and is the only model that captures the stabilization processes observed in the experiments. EBU-LES and SF-LES do not predict the correct flow pattern because of the inaccurate modeling of sub-grid scale mixing and turbulence-combustion interaction. Limitations of these two models for this type of combustor are discussed.

Large Eddy Simulation (LES) of bluff body stabilized premixed and partially premixed combustion close to the flammability limit is carried out in this thesis. The LES algorithm has no ad-hoc adjustable model parameters and is able to respond automatically to variations in the inflow conditions. Algorithm validation is achieved by comparison with reactive and non-reactive experimental data. In the reactive flow, two scalar closure models, Eddy Break-Up (EBULES) and Linear Eddy Mixing (LEMLES), are used and compared. Over important regions, the flame lies in the Broken Reaction Zone regime. Here, the EBU model assumptions fail. The flame thickness predicted by LEMLES is smaller and the flame is faster to respond to turbulent fluctuations, resulting in a more significant wrinkling of the flame surface. As a result, LEMLES captures better the subtle effects of the flame-turbulence interaction. Three premixed (equivalence ratio = 0.6, 0.65, and 0.75) cases are simulated. For the leaner case, the flame temperature is lower, the heat release is reduced and vorticity is stronger. As a result, the flame in this case is found to be unstable. In the rich case, the flame temperature is higher, and the spreading rate of the wake is increased due to the higher amount of heat release Partially premixed combustion is simulated for cases where the transverse profile of the inflow equivalence ratio is variable. The simulations show that for mixtures leaner in the core the vortical pattern tends towards anti-symmetry and the heat release decreases, resulting also in instability of the flame. For mixtures richer in the core, the flame displays sinusoidal flapping resulting in larger wake spreading. More accurate predictions of flame stability will require the use of detailed chemistry, raising the computational cost of the simulation. To address this issue, a novel algorithm for training Artificial Neural Networks (ANN) for prediction of the chemical source terms has been implemented and tested. Compared to earlier methods, the main advantages of the ANN method are in CPU time and disk space and memory reduction.