The motivation for the present work is to investigate particle-laden turbulent flows using accurate numerical simulations. In the present work, the carrier phase is modeled using direct numerical simulations (DNS) and the particles are tracked in a Lagrangian sense. Investigations of both one-way and two-way coupled particulate flows in homogeneous isotropic turbulence have been carried out. The phenomenon of interest in one-way coupled simulations is preferential accumulation, which refers to the tendency of heavy particles in isotropic turbulence to collect in regions of high strain and low vorticity. Several measures and mechanisms of accumulation have been reported in the literature often showing conflicting scaling with particle and fluid parameters. In the present study, accumulation has been quantified using several indicators to give a unified picture. The present work addresses the scaling of preferential accumulation with Reynolds number and suggests that while the spacing between particle clusters does exhibit a dependence on Reynolds number, the structure of particle clusters as viewed by individual particles shows little dependence on Reynolds number. The effect of adding a gravitational settling force on the particles has also been explored. While the gravity force tends to homogenize the particle distribution at low Stokes numbers, at high Stokes numbers it tends to arrange the originally random distribution into streaks in the direction of gravity. The ability of the Lorentz force to limit preferential accumulation has been the focus of the next part of the study. Charges are placed on particles to produce an electric field when the particles are inhomogeneously distributed. The electric field and thereby the Lorentz force tend to homogenize the particle distribution. It is interesting to note that the particle distribution attains a stationary state determined by the total amount of charge contained in the domain. It is demonstrated that in the presence of gravity, less amount of charge is required to homogenise particle distribution. Good agreement is observed for simulations of settling charged particles with experimental work. The modification of carrier phase turbulence by particles is studied formono-sized particles. The non-uniform modification of the fluid energy spectrum by particles has been demonstrated. It is seen that there is an increase in energy at high wave numbers for microparticles (St k < 1), whereas for high Stokes number particles, energy is damped at all scales. The effect of incorporating two way coupling on particle distribution has also been reported. It is noted that increasing mass loading leads to attenuation of accumulation at low Stokes numbers while the effect is reversed at higher Stokes numbers.

A Free-Lagrange method has been applied to simulate the collapse of single cavitation bubbles near various boundary types. The simulations resemble an underwater explosion or laser- or spark-generated bubble, where the bubble evolution is driven by a high initial pressure difference between the bubble content and the surrounding water. The significant advantages of this method in simulating highly deforming fluid problems are minimal numerical diffusion and that the material interfaces are sharply resolved because the computational mesh moves with the same velocity as the local flow. In addition, the Free-Lagrange approach avoids the classical problem of mesh tangling and distortion faced by conventional Lagrangian schemes as the connectivity of the computational mesh is allowed to evolve naturally. As the collapse of single cavitation bubble near a boundary is typically axisymmetric, a swirl-free axisymmetric Free-Lagrange code was developed. Simulations of conical shock waves for various geometries and axisymmetric shock propagation in a material incorporating strength were carried out for validation purposes. Here, the code, which employs second order space and first order time accurate Godunov-type solvers, has been used to simulate the expansion and collapse of single cavitation bubbles near a planar rigid boundary, an aluminium layer and a free-surface for various collapse parameters. The results clearly capture the phenomena of bubble collapse that are believed to be responsible for cavitation erosion, i.e. high-speed liquid jet impact and shock/blast wave emission. It is concluded that numerical simulations using the Free-Lagrange method are well suited to the study of highly deforming fluid problems, particularly in the study of the growth and collapse of single cavitation bubbles.

A pilot scale study of the dynamics of the break-up of curved liquid jets is presented. This work is motivated by an industrial process called prilling which is used in the manufacture of pellets. In this process a sieve-like cylindrical can spins rapidly on its central vertical axis. Molten liquid is pumped into the top of the can and flows from the holes in the form of curved liquid jets. Experiments are described which were carried out on a pilot scale rig. Some differences between the break-up modes observed in this study and previous work using a small laboratory scale rig are discussed. Previous theories describing break-up mechanisms of curved liquid jets were extended to include viscosity and gravity. Break-up lengths and drop sizes were obtained theoretically and compared with experimental results. Experiments were carried out using insonification, a process where sound waves are fired at the jet to control satellite drop formation. Three different frequencies of wave were used, 10, 100 and 200 Hz at four different rotation rates. It was observed that insonification was successful at eliminating satellite drops at low rotation rates and when frequencies of 100 or 200 Hz were used. Insonification was included in the theory. The theory predicted that insonification eliminated satellite drops for a large range of frequencies in the experimental regimes for sufficiently large acoustic volume. The theory also predicted that satellite drops were eliminated in parameter regimes outside the experimental regimes. The trajectory of the jet was allowed to become unsteady, in a rotating frame of reference. Simulations were carried out in inviscid and viscous regimes.

Includes bibliography. / 374 leaves, [7] leaves of plates : 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 Mechanical Engineering, 1985

Extensive use of stirred vessels in the process industries for various operations has attracted researchers to study the mixing mechanisms and its effects on the processes. Among the various flow-measuring methods, Particle Image Velocimetry (PlV) technique has become more popular in comparison to LDA and HW A methods because of its ability to provide instantaneous velocity fields. The present study uses this technique to investigate the flowfields and turbulent properties in a 290mm vessel stirred by Rushton Disc turbine (RDT) and Pitched blade turbine (PBT) impellers. Angle-resolved instantaneous flow-fields were obtained using 2-D and 3-D PlV technique. Flows in the RDT were examined. The distribution of out-of-plane vorticity and turbulent properties such as rms velocities, Reynolds stresses and turbulent kinetic energy was discussed. The flow number and power number of the RDT impeller were obtained as 0.83 and 5.16 respectively. Flows generated by the PBT impeller were examined in more detail. For this purpose, a multiblock approach was developed which allowed analysing larger fields of view with reasonably higher resolution. Whole vessel was thus mapped and various turbulent properties were examined. The mean flow-fields, out-of-plane vorticity and turbulent properties such as Reynolds stresses, turbulent kinetic energy and turbulent energy dissipation rates were estimated at different angle of blade rotation. The variation of the trailing vortex axis was obtained. The pumping number and power number ofPBT impeller was obtained as 0.86 and 1.52 respectively. Using this information, an integral length scales were estimated using 2-D FFT autocorrelation, which showed that these length scales vary significantly through out the vessel. It is demonstrated that assuming constant length scale through out the vessel could underestimate dissipation rate up to 25% in the impeller discharge. A kinetic energy balance was carried out around the PBT blades. It is shown that around 44% of the total power consumed by the impeller is dissipated within the impeller. The average rate of dissipation of kinetic energy was 39 times higher in the impeller region than the average dissipation rate in the vessel. Using LDA and PIV techniques, macro-instabilities (Ml) were studied. Spectral analysis was done using LOMB algorithm, which showed the presence of a dimensionless frequency of O.013-0.0174N in the RDT and PBT impellers. The frequency of Ml varied linearly with the impeller speed. The maximum broadening of turbulence levels due to the presence of Ml was around 20% for the PBT and 18% for the RDT impeller. The effect of mixing on the feed locations was studied using PlV measurements. Results showed that there is no direct effect of feed coming out of the feed pipe on the flow distribution, however, due to feed pipe, there was a wake formation close to the feed pipe. The low Reynolds number in the wake can affect local mixing conditions close to the feed pipe. At the end, angle-resolved Reynolds stresses were calculated and was noticed that flows in the vessel were isotropic in the bulk of the vessel however, anisotropic flow was noticed in the impeller stream.

We are interested in the onset of instability of the axisymmetric flow between two concentric spherical shells that differentially rotate about a common axis in the narrow-gap limit. The expected mode of instability takes the form of roughly square axisymmetric Taylor vortices which arise in the vicinity of the equator and are modulated on a latitudinal length scale large compared to the gap width but small compared to the shell radii. At the heart of the difficulties faced is the presence of phase mixing in the system, characterised by a non-zero frequency gradient at the equator and the tendency for vortices located off the equator to oscillate. This mechanism serves to enhance viscous dissipation in the fluid with the effect that the amplitude of any initial disturbance generated at onset is ultimately driven to zero. In this thesis we study a complex Ginzburg-Landau equation derived from the weakly nonlinear analysis of Harris, Bassom and Soward [D. Harris, A. P. Bassom, A. M. Soward, Global bifurcation to travelling waves with application to narrow gap spherical Couette flow, Physica D 177 (2003) p. 122-174] (referred to as HBS) to govern the amplitude modulation of Taylor vortex disturbances in the vicinity of the equator. This equation was developed in a regime that requires the angular velocities of the bounding spheres to be very close. When the spherical shells do not co-rotate, it has the remarkable property that the linearised form of the equation has no non-trivial neutral modes. Furthermore no steady solutions to the nonlinear equation have been found. Despite these challenges Bassom and Soward [A. P. Bassom, A. M. Soward, On finite amplitude subcritical instability in narrow-gap spherical Couette flow, J. Fluid Mech. 499 (2004) p. 277-314] (referred to as BS) identified solutions to the equation in the form of pulse-trains. These pulse-trains consist of oscillatory finite amplitude solutions expressed in terms of a single complex amplitude localised as a pulse about the origin. Each pulse oscillates at a frequency proportional to its distance from the equatorial plane and the whole pulse-train is modulated under an envelope and drifts away from the equator at a relatively slow speed. The survival of the pulse-train depends upon the nonlinear mutual-interaction of close neighbours; as the absence of steady solutions suggests, self-interaction is inadequate. Though we report new solutions to the HBS co-rotation model the primary focus in this work is the physically more interesting case when the shell velocities are far from close. More specifically we concentrate on the investigation of BS-style pulse-train solutions and, in the first part of this thesis, develop a generic framework for the identification and classification of pulse-train solutions. Motivated by relaxation oscillations identified by Cole [S. J. Cole, Nonlinear rapidly rotating spherical convection, Ph.D. thesis, University of Exeter (2004)] whilst studying the related problem of thermal convection in a rapidly rotating self-gravitating sphere, we extend the HBS equation in the second part of this work. A model system is developed which captures many of the essential features exhibited by Cole's, much more complicated, system of equations. We successfully reproduce relaxation oscillations in this extended HBS model and document the solution as it undergoes a series of interesting bifurcations.

This thesis examines chaotic mixing in wavy-type channels and two-layer shallow water flow. For wavy-type channels, the equations of motion for vortices and fluid particles are derived assuming two-dimensional irrotational, incompressible flow. Instantaneous positions of the vortices and particles are determined using Lagrangian tracking, and are conformally mapped to the physical domain. Unsteady vortex motion is analysed, and vortex-induced chaotic mixing in the channels studied. The dynamics of mixing associated with the evolution of the separation bubble, and the invariant manifolds are examined. Mixing efficiencies of the different channel configurations are compared statistically. Fractal enhancement of productivity is identified in the study of auto-catalytic reaction in the wavy channel. For the two-layer shallow water model, an entropy-correction free Roe type two-layer shallow water solver is developed for a hyperbolic system with non-conservative products and source terms. The scheme is well balanced and satisfies the C-property such that smooth steady solutions are second order accurate. Numerical treatment of the wet-dry front of both layers and the loss of hyperbolicity are incorporated. The solver is tested rigorously on a number of 1D and 2D benchmark test cases. For 2D implementation, a dynamically adaptive quadtree grid generation system is adopted, giving results which are in excellent agreement with those on regular grids at a much lower cost. It is also shown that algebraic balancing cannot be applied directly to a two-layer shallow water flow due to the lack of simultaneous referencing for the still water position for both layers. The adaptive two-layer shallow water solver is applied successfully to flow in an idealised tidal channel and to tidal-driven flow in Tampa Bay, Florida. Finally, chaotic advection and particle mixing is studied for wind-induced recirculation in two-layer shallow water basins, as well as Tampa Bay, Florida.

This thesis is concerned with the development of meshless methods using radial basis functions for solving fluid flow problems. The advantage of meshless methods over traditional mesh-based methods is that they make use of a scattered set of collocation points in the physical domain and no connec- tivity information is required. An important objective of the present research is to develop novel meshless methods for unsteady flow problems. Symmetric/unsymmetric radial basis function collocation schemes are proposed for solving an unsteady convection-diffusion equation for various Peclet numbers. Both global and compactly supported radial basis functions are used and the convergence behaviours of various radial basis functions are studied. The performance of the presented schemes is shown by using both uniform as well as scattered distribution of points. Numerical results suggest that these schemes are capable of obtaining accurate results for low and medium Peclet numbers. Next, two directions have been explored in this thesis for using radial basis functions to solve large scale problems encountered in fluid flow problems. They are namely, domain decomposition schemes and radial basis functions in finite difference mode. These schemes are shown to be computationally efficient and also aid in circumventing the ill-conditioning problem. The performance of both schemes are evaluated by solving the unsteady convection-diffusion problem. The last part of this thesis is concerned with the solution of the 2D Navier-Stokes equations. Meshless methods based on radial basis collocation and scattered node finite difference schemes are formulated for solving steady and unsteady incompressible Navier-Stokes equations. A novel ghost node strategy is proposed for incor- porating the no-slip boundary conditions. Optimisation strategies based on residual error objective and leave-one-out statistical criterion are proposed to evaluate the optimal shape parameter value in case of the multiquadric RBF for collocation and scattered finite difference approaches respectively. Standard benchmark problems like the driven cavity flows in square and rectangular domains and backward facing step flow problem are solved to study the performance of the developed schemes. Finally, a higher order radial basis function based scattered node finite difference method is proposed for solving the incompressible Navier-Stokes equations.

A 3D parallel CFD code is written to investigate the characteristics of and differences between Large Eddy Simulation (LES) models in the context of simulating a thermal buoyant plume. An efficient multigrid scheme is incorporated to solve the Poisson equation, resulting from the fractional step, projection method used to solve the Low Mach Number (LMN) Navier-Stokes equations. A wide range of LES models are implemented, including a variety of eddy models, structure models, mixed models and dynamic models, for both the momentum stresses and the temperature fluxes. Generalised gradient flux models are adapted from their RANS counterparts, and also tested. A number of characteristics are observed in the LES models relating to the thermal plume simulation in particular and turbulence in general. Effects on transition, dissipation, backscatter, equation balances, intermittency and energy spectra are all considered, as are the impact of the governing equations, the discretisation scheme, and the effect of grid coarsening. Also characteristics to particular models are considered, including the subgrid kinetic energy for the one-equation models, and constant histories for dynamic models. The argument that choice of LES model is unimportant is shown to be incorrect as a general statement, and a recommendation for when the models are best used is given.

Two-phase flow in small tubes and channels is becoming a common phenomenon in industrial processes. However, the study of two-phase flow regimes in small tubes is still at its infancy. The previous studies are reviewed and discussed in the literature section. The problems and inconsistencies encountered in the earlier studies are presented and discussed. The experimental facility is introduced in the chapters that follow. They include a section on the design of the experimental system and the test sections, the selection of the experimental parameters and the introduction of the purposely-developed programs to control the experiments and collect and process the data. The methodology of the calibration and the uncertainty analysis, the problems encountered and their solutions and the single-phase validation experiments are also described. In this project we studied the effect of tube diameter and fluid flow parameters on flow patterns in small tubes using R134a as the working fluid. The tested tube diameters were 1.10, 2.01, 2.88 and 4.26 mm; the fluid pressures were 6, 10 and 14 bar; the liquid and gas superficial velocities covered a range of 0.04-5.0 m/s and 0.01-10.0 m/s respectively. The observed flow patterns included bubbly, dispersed bubble, confined bubble, slug, chum, annular and mist flow. Twelve integrated flow maps are sketched in this report. The obtained results were compared with earlier experiments by other workers and with existing models, with obvious differences in the prediction of the transition boundaries. A set of new models and correlations were developed, based on the new data for boiling R134a presented in this thesis, to predict the effect of tube diameter and fluid properties on the transition boundaries. Some also agreed with the limited data available from earlier studies for adiabatic air-water flow in small to normal size tubes.