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The unsteady two-dimensional flow around an array of circular cylinders submerged in a uniform onset flow is analyzed. The fluid is taken to be viscous and incompressible. The array of cylinders consists of two horizontal rows extending to infinity in the upstream and downstream directions. The center-to-center distance between adjacent cylinders is a constant. The Biot-Savart law of induced velocities is used to determine the velocity field due to the free vorticity in the surrounding fluid and the bound vorticity distributed on the surface of each cylinder. The bound vorticity is needed to enforce the no-penetration condition and to account for the production of free vorticity in the solid surfaces. It is governed by a Fredholm integral equation of the second kind. This equation is solved by numerical techniques. The transport of free vorticity in the flow field is governed by the vorticity transport equation. This equation is discretized for a control volume and is solved numerically. Advantage is taken of spatially periodic boundary conditions in the flow direction. This reduces the computational domain to a rectangular region surrounding a single circular cylinder, but necessitates use of a non-orthogonal grid. In order to test the numerical techniques, the simpler case of unsteady flow over a single circular cylinder at various Reynolds numbers if first considered. Results compare favorably with previous experimental and numerical data. Three cases for Reynolds numbers of 10², 10³, and 10⁴ are presented for the array of cylinders. The center-to-center distance is fixed at three diameters. The time development of constant vorticity contours as well as drag, lift, and moment coefficients are shown for each Reynolds number. The motion of stagnation and separation points with time is also given. It is found that the drag for a cylinder in the array may be as low as five percent of that for flow over a single cylinder at the same Reynolds number.

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In this work, we develop an extension of the generalized Fourier transform for exterior domains due to T. Ikebe and A. Ramm for all dimensions n>2 to study the Laplacian, and fractional Laplacian operators in such a domain. Using the harmonic extension approach due to L. Caffarelli and L. Silvestre, we can obtain a localized version of the operator, so that it is precisely the square root of the Laplacian as a self-adjoint operator in L2 with DIrichlet boundary conditions. In turn, this allowed us to obtain a maximum principle for solutions of the dissipative two-dimensional quasi-geostrophic equation the exterior domain, which we apply to prove decay results using an adaptation of the Fourier Splitting method of M.E. Schonbek. / by Leonardo Kosloff. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

A sudden expansion combustor (SUE) is analyzed using computation fluid dynamics (CFD). CO emissions and NOx emissions are computed for various operating conditions of the SUE combustor using a can type and an annular type geometrical configurations. The goal of this thesis is to see if the SUE combustor is a viable alternative to conventional combustors which utilize swirlers. It is found that for the can type combustor the NOx emissions were quite low compared to other combustor types but the CO emissions were fairly high. The annular combustor shows better CO emissions compared to the can type, but the CO emissions are still high compared to other combustors. Emissions can be improved by providing better mixing in the primary combustion zone. The SUE combustor design needs to be further refined in order for it to be a viable alternative to conventional combustors with swirlers. / by Daniel Rodriguez. / Thesis (M.S.C.S.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

Ice accretion is a purely unsteady phenomenon that is presently approximated by most icing codes using quasi-steady modeling. The accuracy of ice prediction is thus directly related to the arbitrarily prescribed time span during which the impact of ice growth on both flow and droplets is neglected. The objective of this work is to remove this limitation by implementing a cost-effective unsteady approach. This is done by fully coupling, in time, a diphasic flow (interacting air and droplet particles) with the ice accretion model. The two-phase flow is solved using the Navier-Stokes and Eulerian droplet equations with dual-time stepping in order to improve computational time. The ice shape is either obtained from the conservation of mass and energy within a thin film layer for glaze and mixed icing conditions, or from a mass balance between water droplets impingement and mass flux of ice for rime icing conditions. The iced surface being constantly displaced in time, Arbitrary Lagrangian-Eulerian terms are added to the governing equations to account for mesh movement. Moreover, surface smoothing techniques are developed to prevent degradation of the iced-surface geometric discretization. For rime ice, the numerical results clearly show that the new full unsteady modeling improves the accuracy of ice prediction, compared to the quasi-steady approach, while in addition ensuring time span independence. The applicability of the unsteady icing model for predicting glaze ice accretion is also demonstrated by coupling the diphasic model to the Shallow Water Icing Model. A more rigorous analysis reveals that this model requires the implementation of local surface roughness and that previous quasi-steady validations cannot be carried out using a small number of shots, therefore the need for unsteady simulation.

Even though the power of supercomputers has increased extraordinarily, there is still an insatiable need for more advanced multi-disciplinary CFD simulations in the aircraft analysis and design fields. A particular current interest is in the realistic three-dimensional fully viscous turbulent flow simulation of the highly non-linear aspects of aero-icing. This highly complex simulation is still computationally too demanding in industry, especially when several runs, such as parametric studies, are needed. In order to make such compute-intensive simulations more affordable, this work presents a reduced order modeling approach, based on the "Proper Orthogonal Decomposition", (POD), method to predict a wider swath of flow fields and ice shapes based on a limited number of "snapshots" obtained from complete high-fidelity CFD computations. The procedure of the POD approach is to first decompose the fields into modes, using a limited number of full-calculations snapshots, and then to reconstruct the field and/or ice shapes using those decomposed modes for other conditions, leading to reduced order calculations. The use of the POD technique drastically reduces the computational cost and can provide a more complete map of the performance degradation of an iced aircraft over a wide range of flight and weather conditions.

Computational fluid dynamic (CFO) modelling has been applied to examine the operation of the prc-ozonation system at Wiggins Waterworks, operated by Umgeni Water in Durban, South Africa. Ozonation is employed in water treatment process primarily to achieve the oxidation of iron and manganese, the destruction of micro-organisms and the removal of taste and odour causing compounds. It also aids in the reduction of the colour of the final water, enhancement of algae removal and possible reduction of coagulant demand. A hydrodynamic model has been satisfactorily verified by experimental tracer tests. The effect of the gas injection was modelled by increasing the level of turbulence intensity at the ozone contactor inlet. The model prediction of the overall tracer response corresponded closely to the experimental results. The framework of ozone reaction modelling was subsequently established using values of rate constants from the literature. An accurate prediction of the ozone concentration profile requires the application of the correct ozone kinetics involved. In raw waters, the depletion of ozone is influenced by the presence of natural organic matters (NOM). The observed ozone decay was found in good agreement using the pseudo first-order rate law. By measuring the total organic carbon (TOC) as a surrogate for NOM, the experimentally determined rate constants can be calculated to account for the effects of the ozone doses and the water quality. The characterisation study also aimed to provide sufficient information on ozone depletion and to be operated easily, without the lengthy and costly analyses ofa detailed kinetics study. The predicted profile of residual ozone concentration suggests the current operating strategy can be improved to optimise the ozone utilisation. The proposed monitoring point was suggested to be at the end of second companment where most ozone reactions have been completed. By coupling the transport equations of the target compounds with their chemical reaction rates, the concentration profile of these compounds such as ozone can be predicted in order to assist the understanding of an operation and to attain better interpretation of experimental results. / Thesis (Ph.D.)-University of KwaZulu-Natal, 2005.

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