The depth-averaged Saint-Venant equations, which are used for most computational flow models, are adequate in simulating open channel flows with insignificant curvatures of streamlines. However, these equations are insufficient when applied to flow problems where the effects of non-hydrostatic pressure distribution are predominant. This study provides a comprehensive examination of the feasibility of a simple one-dimensional Boussinesq-type model equation for such types of flow problems. This equation, which allows for curvature of the free surface and a non-hydrostatic pressure distribution, is derived using the momentum principle together with the assumption of a constant centrifugal term at a vertical section. Besides, two Boussinesq-type model equations that incorporate different degrees of corrections for the effects of the curvature of the streamline are investigated in this work. One model, the weakly curved flow equation model, is the simplified version of the flow model based on a constant centrifugal term for flow situations that involve weak streamline curvature and slope, and the other, the Boussinesq-type momentum equation linear model is developed based on the assumption of a linear variation of centrifugal term with depth.

The current work has developed a CFD model to characterise a pseudo-annular photocatalytic bubble column reactor. The model development was divided into three stages. Firstly, hydrodynamic assessment of the multiphase fluid flow in the vessel, which incorporated residence time distribution analysis both numerically and experimentally for validation purposes. Secondly, the radiation distribution of the UV source was completed. The final stage incorporated the kinetics for the degradation the model pollutant, sodium oxalate. The hydrodynamics were modelled using an Eulerian-Eulerian approach to the multiphase system with the standard k- turbulence model. This research established that there was significant deviation in the fluid behaviour in the pseudo-annular reactor when compared with traditional cylindrical columns due to the nature of the internal structure. The residence time distribution study showed almost completely mixed flow in the liquid phase, whereas the gas phase more closely represented plug flow behaviour. Whilst there was significant dependence on the superficial gas flow rate the mixing behaviour demonstrated negligible dependence on the liquid superficial velocity or the liquid flow direction, either co- or counter- current with respect to the gas phase. The light distribution was modelled using a conservative variant of the Discrete Ordinate method. The model examined the contribution to the incident radiation within the reactor of both the gas bubbles and titanium dioxide particles. This work has established the importance of the gas phase in evaluating the light distribution and showed that it should be included when examining the light distribution in a gas-liquid-solid three-phase system. An optimal catalyst loading for the vessel was established to be 1g/L. Integration of the kinetics of sodium oxalate degradation was the final step is developing the complete CFD model. Species transport equations were employed to describe the distribution of pollutant concentration within the vessel. Using a response surface methodology it was shown that the reaction rate exhibited a greater dependency on the lamp power that the lamp length, however, the converse was true with the quantum efficiency. This work highlights the complexity of completely modelling a photocatalytic system and has demonstrated the applicability of CFD for this purpose.

Thermal stratification occurs in shallow water bodies because solar energy separates the water column into an upper warm layer, a lower cold layer, and an intermediate layer between the upper and lower layers. In general the intermediate layer exhibits a significant thermal gradient over depth. Because cold water is heavier than warm water, this temperature structure produces a stable stratification, thereby inhibiting circulation from the bottom to the surface. This stable stratification results in a deficit of dissolved oxygen in the lower layer leading to water quality problems. Hence understanding the thermal structure and vertical circulation in shallow water bodies is important for water quality and its management. In this research, a numerical code is developed to examine the three-dimensional flow structure in shallow water bodies. This numerical code is used to solve the governing equations : the Reynolds averaged Navier-Stokes equations for three velocities and pressure, the depth-averaged continuity equation for free surface movement, the equations for turbulence closure, the scalar transport equation for temperature, and the international equation of state for density variation due to temperature. These equations are solved simultaneously using a finite difference method. The mathematical equations are transformed into a generalised coordinate system which allows flexibility for irregular boundaries and the allocation of vertical grid points every time step depending on free surface movements. In order to overcome possible numerical instabilities because of the small vertical length scale in shallow water bodies, an implicit method is used in the vertical direction. Several test cases involving free surface movement are used to verify the numerical code, and numerical solutions compare favourably against analytical solutions and measured data. The numerical code has been applied to the Torrens Lake in Adelaide, South Australia, where algal blooms occur frequently in summer due to thermal stratification. Typical thermal structures have been obtained from the model and these are compared with field data. The current code has been developed to improve upon existing commercial models which may not adequately address shallow water flows because of the high computational burden required to resolve free surface movements and consequential difficulties encountered for models with a small vertical length scale. / Thesis (Ph.D.)--School of Mathematical Sciences, 2007.

Bibliography: leaves 169-178.

Bibliography: leaves 70-72 / vi, 73 leaves : ill ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1987

"February 2004" / Includes bibliographical references (leaves 216-227) / Each accompanying profile sheet is named and numbered individually. / xvi, 245 leaves : ill. (some col.), maps (col.), charts ; 30 cm. + 1 location map ( 22 x 30 cm. folded to 22 x 15 cm.) + 4 geologic profiles ( 56 x 100 cm. folded to 20 x 29 cm.) ; in pocket inside back cover. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, School of Earth and Environmental Sciences, Discipline of Geology and Geophysics, 2004

The depth-averaged Saint-Venant equations, which are used for most computational flow models, are adequate in simulating open channel flows with insignificant curvatures of streamlines. However, these equations are insufficient when applied to flow problems where the effects of non-hydrostatic pressure distribution are predominant. This study provides a comprehensive examination of the feasibility of a simple one-dimensional Boussinesq-type model equation for such types of flow problems. This equation, which allows for curvature of the free surface and a non-hydrostatic pressure distribution, is derived using the momentum principle together with the assumption of a constant centrifugal term at a vertical section. Besides, two Boussinesq-type model equations that incorporate different degrees of corrections for the effects of the curvature of the streamline are investigated in this work. One model, the weakly curved flow equation model, is the simplified version of the flow model based on a constant centrifugal term for flow situations that involve weak streamline curvature and slope, and the other, the Boussinesq-type momentum equation linear model is developed based on the assumption of a linear variation of centrifugal term with depth.

The unsteady nature of coastal hydrodynamics is associated with complex boundary layer dynamics and hence engineering predictions of shear stresses and sediment transport are difficult. This thesis explores some of the complex hydrodynamic problems and boundary layer behaviour in the coastal zone and seeks to provide new and improved modelling approaches. The latest experimental results are used to inform the model development process. New laboratory experiments carried out as part of this thesis illustrate the value of convolution integral calculations for both pressure and skin friction forces on particles on the bed. The experiments also highlight the importance of the phase differences between free stream velocity and boundary layer shear stresses. The use of a “bed” shear stress as a model input is found to be problematic whenever there is a large vertical gradient in the boundary layer shear stress. New experimental and modelling work has helped to improve our understanding of sheet flow boundary layer dynamics. This thesis builds on some of these new discoveries to propose a new simplified model framework for sheet flow sediment transport prediction using convolution integrals. This time domain technique has the advantage of simplicity while incorporating the most important physical processes from more detailed models. The new model framework could be incorporated into any depth averaged coastal hydrodynamic modelling software package. Boundary layer analysis techniques presented in the thesis provide an improved understanding of the effective roughness of mobile beds and can be used to calculate instantaneous shear stress profiles throughout the mobile bed boundary layer. New solutions for swash zone hydrodynamics are presented which illustrate the limitations of the previous benchmark analytical model for swash hydrodynamics. It is shown that real swash necessarily involves a much larger influx of mass and momentum than the analytical solution which was previously used by many in the swash sediment transport research community. Models for swash boundary layer development are also presented.

<p>Simulating fluid behavior has proven to be a demanding challenge which requires complex computational models and highly efficient data structures. Smoothed Particle Hydrodynamics (SPH) is a particle based computational model used to simulate fluid behavior that has been found capable of producing convincing results. However, the SPH algorithm is computational heavy which makes it cumbersome to work with.</p><p>This master thesis describes how the SPH algorithm can be accelerated by utilizing the GPU’s computational resources. It describes a model for how to distribute the work load on the GPU and presents a suitable data structure. In addition, it proposes a method to represent and handle moving objects in the fluids surroundings. Finally, the performance gain due to the GPU is evaluated by comparing processing times with an identical implementation running solely on the CPU.</p>

Complex oscillations including chaotic motions have been identified in off-shore and submerged mooring systems characterized by nonlinear fluid-structure interactions and restoring forces. In this paper, a means of controlling these nonlinear oscillations is addressed. When applied, the controller is able to drive the system to periodic oscillations of arbitrary periodicity. The controller applies a perturbation to the nonlinear system at prescribed time intervals to guide a trajectory towards a stable, periodic oscillatory state. The controller utilizes the pole placement method, a state feedback rule designed to render the system asymptotically stable. An outline of the proposed method is presented and applied to the fluid-structure interaction system and several examples of the controlled system are given. The effects of random noise in the excitation force are also investigated and the subsequent influence on the controller identified. A means of extending the controller design is explored to provide adequate control in the presence of moderate noise levels. Meanwhile, in the presence of over powering noise or system measurements that are not well defined, certain filtering and estimation techniques are investigated for their applicability. In particular, the Iterated Kalman Filter is investigated as a nonlinear state estimator of the nonlinear oscillations in these off-shore compliant structures. It is seen that although the inclusion of the nonlinearities is theoretically problematic, in practice, by applying the estimator in a judicious manner and then implementing the linear controllers outlined above, the system is able to estimate and control the nonlinear systems over a wide area of pseudo-stochastic regimes. / Graduation date: 2006