In this work, flow through synthetic arrangements of contacting spheres is studied as a model problem for porous media and packed bed type flows. Direct numerical simulations are performed for moderate pore Reynolds numbers in the range, 10 ≤ Re ≤ 600, where non-linear porescale flow features are known to contribute significantly to macroscale properties of engineering interest. To first choose and validate appropriate computational models for this problem, the relative performance of two numerical approaches involving body conforming and non-conforming grids for simulating porescale flows is examined. In the first approach, an unstructured solver is used with tetrahedral meshes, which conform to the boundaries of the porespace. In the second approach, a fictitious domain formulation (Apte et al., 2009. J Comput. Phys. 228 (8), 2712-2738) is used, which employs non-body conforming Cartesian grids and enforces the no-slip conditions on the pore boundaries implicitly through a rigidity constraint force. Detailed grid convergence studies of both steady and unsteady flow through prototypical arrangements of spheres indicate that for a fixed level of uncertainty, significantly lower grid densities may be used with the fictitious domain approach, which also does not require complex grid generation techniques. Next, flows through both random and structured arrangements of spheres are simulated at pore Reynolds numbers in the steady inertial ( 10 ≲ Re ≲ 200) and unsteady inertial (Re ≈ 600) regimes, and used to analyze the characteristics of porescale vortical structures. Even at similar Reynolds numbers, the vortical structures observed in structured and random packings are remarkably different. The interior of the structured packings are dominated by multi-lobed vortex rings structures that align with the principal axes of the packing, but perpendicular to the mean flow. The random packing is dominated by helical vortices, elongated parallel to the mean flow direction. The unsteady dynamics observed in random and structured arrangements are also distinct, and are linked to the behavior of the porescale vortices. Finally, to investigate the existence and behavior of transport barriers in packed beds, a numerical tool is developed to compute high resolution finite-time Lyapunov exponent (FTLE) fields on-the-fly during DNS of unsteady flows. Ridges in this field are known to correspond to Lagrangian Coherent Structures (LCS), which are invariant barriers to transport and form the skeleton of time dependent Lagrangian fluid motion. The algorithm and its implementation into a parallel DNS solver are described in detail and used to explore several flows, including unsteady inertial flow in a random sphere packing. The resulting FTLE fields unambiguously define the boundaries of dynamically distinct porescale features such as counter rotating helical vortices and jets, and capture time dependent phenomena including vortex shedding at the pore level. / Graduation date: 2013

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1979. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / by Paul David Bayless. / M.S.

Call number: LD2668 .T4 1985 F69 / Master of Science

Dissertation (PhD)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: A mathematical model is presented which conceptualises fluid flow and heat transfer in cellular metallic foams completely saturated with a fluid in motion. The model consists of a set of elliptic partial differential governing equations describing, firstly, a momentum balance in the fluid by the spatial distribution of its locally mean velocity, and secondly, an energy balance in the fluid and in the solid matrix of the metallic foam, by the spatial and temporal distribution of their locally mean temperatures. The separate energy balance descriptions for the fluid and the solid matrix extend the application of the model to conditions of thermal equilibrium and thermal non-equilibrium between the fluid and the solid matrix. A computational solution algorithm is presented which allows the universal application of the model to porous domains of arbitrary shape, with spatially and temporally variable heat loads in a variety of forms. / AFRIKAANSE OPSOMMING: 'n Wiskundige model word voorgestel wat vloei en warmteoordrag voorspel in sellulêre metaalsponse wat in geheel gevul is deur 'n bewegende vloeier. Die vloeier kan in gasof vloeistoffase verkeer. Die model bestaan uit 'n stel elliptiese parsiële differensiaalvergelykings wat in die eerste plek 'n momentum-ewewig in die vloeier beskryf in terme van 'n ruimtelike, lokaal-gemiddelde snelheidsveld, en wat tweedens 'n energie-ewewig in die vloeier en in die soliede matriks van die metaalspons beskryf in terme van ruimtelike en tydelike lokaal-gemiddelde temperatuur verspreidings. Die aparte energie-ewewig beskrywings vir die vloeier en vir die soliede matriks van die metaalspons brei die aanwending van die model uit na gevalle waar die vloeier en die soliede matriks in termiese ewewig of in termiese onewewig verkeer. 'n Numeriese oplossingsalgoritme word ook voorgestel vir die universele toepassing van die model op ruimtelik-arbitrêre metaalspons geometrië wat onderwerp word aan 'n aantal verskillende ruimtelik-en tydveranderlike termiese laste.

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Shallow water equations (SWEs) are a set of hyperbolic partial differential equations that describe the flow below a pressure surface in a fluid. They are widely applicable in the domain of fluid dynamics. To meet the needs of engineers working on the area of fluid dynamics, a method known as spectral/hp element method has been developed which is a scheme that can be used with complicated geometry. The use of discontinuous Galerkin (DG) discretisation permits discontinuity of the numerical solution to exist at inter-element surfaces. In the DG method, the solution within each element is not reconstructed by looking to neighbouring elements, thus the transfer information between elements will be ensured through the numerical fluxes. As a consequence, the accuracy of the method depends largely on the definition of the numerical fluxes. There are many different type of numerical fluxes computed from Riemann solvers. Four of them will be applied here respectively for comparison through a 2D Rossby wave test case. / AFRIKAANSE OPSOMMING: Vlakwatervergelykings (SWEs) is ’n stel hiperboliese parsiële differensiaalvergelykings wat die vloei onder ’n oppervlak wat druk op ’n vloeistof uitoefen beskryf. Hulle het wye toepassing op die gebied van vloeidinamika. Om aan die behoeftes van ingenieurs wat werk op die gebied van vloeidinamika te voldoen is ’n metode bekend as die spektraal /hp element metode ontwikkel. Hierdie metode kan gebruik word selfs wanneer die probleem ingewikkelde grenskondisies het. Die Diskontinue Galerkin (DG) diskretisering wat gebruik word laat diskontinuïteit van die numeriese oplossing toe om te bestaan by tussenelement oppervlakke. In die DG metode word die oplossing binne elke element nie gerekonstrueer deur te kyk na die naburige elemente nie. Dus word die oordrag van informasie tussen elemente verseker deur die numeriese stroomterme. Die akkuraatheid van hierdie metode hang dus grootliks af van die definisie van die numeriese stroomterme. Daar is baie verskillende tipe numeriese strometerme wat bereken kan word uit Riemann oplossers. Vier van hulle sal hier gebruik en vergelyk word op ’n 2D Rossby golf toets geval.

published_or_final_version / abstract / Mechanical Engineering / Doctoral / Doctor of Philosophy

Two-dimensional flow in a viscous incompressible fluid, generated by a circular cylinder executing large-amplitude rectilinear oscillations in a plane perpendicular to its axis and parallel to one of the sides of a surrounding rectangular box filled with incompressible fluid is studied numerically. The circular cylinder moves back and forth through its own wake, resulting in an extremely complex flow field. For ease of implementing boundary conditions, a numerically generated body-fitted coordinate system is used. At each time step, the physical domain is doubly-connected, and a cut is introduced in order to map it into a rectangular computational domain. A body-fitted grid is generated by solving a pair of Laplace equations with a simple grid spacing control method which preserves the essential one-to-one property of the mapping. A finite difference/pseudo-spectral technique is used in this work to solve the Navier-Stokes equations in velocity-vorticity formulation. The time integration of the vorticity transport equation is handled by a fully explicit three-level Adams-Bashforth method. The two Poisson equations for the velocity components are 11-banded and block-diagonal in form, and are solved by a preconditioned biconjugate gradient routine. An integral constraint on the vorticity field is used to determine the boundary vorticity that simultaneously satisfies the no-slip and no-penetration conditions. The surface vorticity is uniquely determined by a general solution procedure developed in this study which is valid for flows over multiple solid bodies. With this approach, the physical process of vorticity generation on the solid boundary is properly simulated and the principle of vorticity conservation is satisfied. Results for various test cases and the complex vortex shedding phenomena generated by an oscillating circular cylinder are presented and discussed.

Hot-wire measurements taken in the turbulent wake of a flat plate are presented. Symmetrical and antisymmetrical perturbations at various amplitudes and frequencies were introduced into the wake by small flap oscillations. As predicted by linear stability theory, the sinuous (antisymmetric) mode was observed to be more significant than the varicose (symmetric) mode. When the amplitude of the perturbation was low, the spatial development of the introduced coherent perturbation was predicted well by linear stability theory. At high forcing levels, the wake spreading showed dramatic deviations from the well known square-root behavior of the unforced case. Measured coherent Reynolds stresses changed sign in the neighborhood of the neutral point of the perturbation, as predicted by the linear theory. However, the linear theory failed to predict the disturbance amplitude and transverse shapes close to the neutral point. Some nonlinear aspects of the evolution of instabilities in the wake are discussed. Theoretical predictions of the mean flow distortion and the generation of the first harmonic are compared to experimental measurements. Given the unforced flow and the amplitude of the fundamental wave, the mean flow distortion and the amplitude of the first harmonic are predicted remarkably well.

Under static of dynamic loadings, the junction (interface) between a structure-foundation system can experience contact, slip, separation and rebonding modes of deformations. Two interface models are proposed for simulation of interface behavior in finite element analysis of dynamic soil-structure interaction problems. The first element called the thin-layer element has (small) finite thickness. Geometrically, this element is similar to the continuum (soil or structural) element; however, its constitutive relations are defined differently. The normal behavior is defined as a function of the material properties and stress-strain characteristics of the neighboring continuum element. The shear behavior is defined in terms of observed shear stress-relative displacement behavior expressed as function of factors such as normal stress, number of cycles of loading and amplitude of load (or displacements). Mohr-Coulomb criterion is used to define activated sliding strength of interface. Modes of deformations are simulated by using appropriate stress redistribution iterative schemes. The second model called the mixed interface element has zero thickness. Both displacements and tractions are treated as primary unknowns. Constraints associated with modes of deformations are included using a variational approach. An incremental solution scheme is proposed. Material parameters related to the proposed models are evaluated from the results of sand-concrete interface tests in a Cyclic Multi-Degree-of-Freedom shear device. Accuracy of the proposed models are verified with respect to a number of example problems. In general, consistent and satisfactory results are obtained. For further verification and evaluation of these models, several soil-structure interaction problems are solved and detailed results are presented. It is observed that behavior of structure-foundation systems can be significantly influenced by interface conditions. An analysis based on bonded interface condition appears to underestimate actual response. Hence, it will be appropriate to include interface behavior in the analysis and design of structures subjected to dynamic and earthquake loadings.

A mathematical model has been developed which describes the fluid exchange from a capillary network of realistic topology, and calculates the spatial distribution of extravascular pressure. In this model, the capillaries are represented by a superposition of sources and sinks, resulting from a D'Arcy's Law description of flow in tissue of uniform fluid conductivity. The combination of this representation and Starling's Hypothesis, which relates the forces influencing transmural fluid exchange, yields an integral equation of the second kind which is solved numerically for the source strength distribution. Two important features of this approach are that: (i) it allows for interaction between the local tissue pressure field and fluid exchange (the model is called, therefore, the tissue pressure interaction model); and (ii) complex network morphologies are easily modeled. In single capillaries, this interaction, which decreases the predicted fluid exchange, increases with the magnitude of the ratio of capillary wall to extravascular fluid conductivities. For multiple capillaries, in addition to the "self" interaction of a capillary with the local extravascular pressure field, there is the possibility of interaction between capillaries ("capillary-capillary" interaction). The ratio of conductivities, and the additional factors of intercapillary distance and the number of capillaries, also affect interaction in capillary networks. Although interaction is only a weak function of intercapillary distance, it depends strongly on the number of capillaries. The major result from this work is that for the entire physiological range of conductivity ratios, interaction cannot be neglected in predicting fluid exchange. Although tissue pressure interaction affects the magnitude of fluid exchange, it does not greatly alter the pattern of extravascular flow. Therefore, previous models which neglected interaction are not invalidated by the present findings. The effect of interaction on planar capillary networks within a semi-infinite tissue space was also investigated. Flow boundary conditions were imposed at opposed planar boundaries, parallel with the capillary network. Interaction was found to decrease with decreasing distance between the boundary and plane of the capillaries. It still exerted a large effect, however, for distances greater than one-fourth the reference capillary length.