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Methodologies have been developed for accurate numerical simulations of unsteady two layer cocurrent and countercurrent turbulent flows driven by gravity and pressure. The basis of these methodologies is projection method within the bulk of each phase, with rigorously derived boundary conditions being imposed at the gas/liquid interface. A judiciously chosen high – order spatial discretisation allows for direct numerical simulations (DNS) of the turbulence in each phase. A method for conducting simulations with smallscale eddies modelled and largescale eddies resolved (wall – resolved LES), was also implemented. The gas/liquid interface is forced to remain flat so as to allow the a priori constructed structured mesh to adequately resolve the turbulent boundary layer around the interface for the duration of the simulation. The method is numerically efficient when applied to the flows where time scales (andj therefore kinematic viscosities) in the two phases are of the same order of magnitude, but no restriction is placed on the density or viscosity ratio. For example, flow of air over viscous oil can be efficiently simulated. Single phase versions of both the DNS and the LES codes are validated against the literature. Results for the two layer system provide insight into the structure and the energy budget of turbulence near a liquid film on a wall. The turbulence statistics in the less viscous phase are compared to those derived from those collected from singlephase flows over a moving wall. The results are used to validate (and possibly replace) semiempirical profiles used previously in stability analyses and to provide further information that is otherwise unknown.

Experimental and numerical investigations have been conducted in order to evaluate the accuracy of the Mixture Model, a depth-resolved and time-averaged multiphase numerical model, in predicting the behaviour of dilute surge-type turbidity currents. The effects of turbulent dispersion and turbulence modulation upon sediment transport within turbidity currents are directly modelled via their incorporation into the Mixture Model. Modelled predictions of flow front propagation and deposit density are compared against both experimental data and refined two-fluids model from previous studies. When modelled using the formulation of Chen & Wood (1985), turbulence modulation does not affect on the propagation of dilute turbidity currents significantly. Turbulent dispersion can be modelled by incorporating the formulation of Simonin (1991) into the slip equation of the Mixture Model. Its effect is strongest in dilute flows carrying fine particles and diminishes when either grain size or flow concentration increases. Modelled turbulent dispersion effects are too strong in simulations of flows carrying silicon carbide particles; Mixture Model simulations agree poorly with both experimental data or refined two-fluids model results of the deposit mass profile. Yet turbulent dispersion is essential to ensure that model predictions of flows carrying glass beads compare well with experimental data. The reasons for the discrepancy between modelling approaches best suited to each of these flow types remains poorly understood. A new analytical approach is developed to evaluate the effect of the lift force on particles of small, intermediate and large particle Reynolds number immersed in two-dimensional shear flows. The lift force always reduces the magnitude of the particle settling velocity and may push particles forward or backward, depending on the sign of both the lift coefficient and the flow vorticity. Given plausible velocity profiles within natural turbidity currents, the effect of lift force on the sand-like particles immersed in such turbidity currents is negligible. It may become significant when the ratio of the particle density to the flow density approaches unity. New experiments are presented for flows over the flow concentration range 0.25 – 5% and grain size range 58 - 115μm. The data are used to facilitate a more complete validation of the Mixture Model, based on flow front propagation rates, deposit mass density and deposit grain characteristics. Modelling results for first two variables are in good agreement with the experimental data, when turbulent dispersion effects are incorporated. For reasons which remain unclear, the model cannot simulate the unexpected experimental result that deposit grain size is largely unfractionated if the standard deviation of the source material is less than 11 but significantly fractionated if it exceeds 18. This discrepancy requires further work.

This thesis considers the advantages of incorporating laminar kinetic energy modelling into turbulence modelling, in order to predict laminar-turbulent transition. The final aim is to implement an improved transition model into the industrial Finite-Volume code, Code Saturne. The literature review suggests that in order for a RANS-based model to predict transition accurately, modelling of complex, anisotropic phenomena is necessary. The Walters-Cokljat model is shown to compare very well to other transition modelling methods, including correlation-based modelling. The Walters-Cokljat model is a single-point RANS-based model that solves an additional transport equation for laminar kinetic energy. This transition model is especially desirable from an industrial stand-point, due to its single-point RANS basis, with only 3 transport equations. Although this method shows great promise as an industrial tool for transition prediction, results presented here show that there are aspects of the model that require modification. The definition of effective length-scale and the method of accounting for the effects of shear sheltering are the two main areas for consideration. The current definition of effective length-scale is found to be inappropriate for flows with large free-stream length-scales, which are common-place in turbomachinery applications. Another phenomenon commonly found in turbomachinery is separation-induced transition; however, the current function for shear sheltering effects inhibits transition when turbulence intensity is not the forcing factor. Additionally, when reviewed analytically, the definition and placement of the shear sheltering function does not match the observations of Jacobs and Durbin. Alternatives for the definitions of the effective length-scale and the shear sheltering function are proposed. The individual proposals are tested, and steps towards a full working implementation are documented.

Two-dimensional turbulence has been extensively studied over the past years theoretically and numerically since the theory of the dual cascade energy. Numerical studies have revealed an impor- tant feature of two-dimensional turbulence, that is, the predomi- nance of coherent structures, followed by interaction and merger of these isolated vortices in the subsequent evolution. A method of 'vortex census' has been introduced to keep track of the vortices but the relation to reconnection has remained unexplored. In this Thesis, we study the reconnection process of vorticity con- tours associated with coherent vortices in two-dimensional turbu- lence for different Reynolds number. After checking topological integrity by the Euler index theorem, we make use of the critical points and their connectivity (so-called surface networks) to study the topological changes of vorticity contours. Wc show how this method can remarkably distinguish the dynamics of the vortic- ity field in the Navier-Stokes equations and that of the Charney- Hasegawa-Mima equation. We found that the potential vorticity formed vortex crystals. This excites us to study the vortex crystal in details by study a coarse-grained asymptotic equation [Smirnov and Chukbar(2001)]. Self-similar blow-up solutions with an infi- 1 I i :. nite total energy were given. We ask whether or not finite-time blow-up can take place developing from smooth initial data with a finite energy.

For nearly 40 years, engineers, researchers and scientists from the nuclear industry across the World have been trying to understand the behaviors of deposition, bounce and re-suspension of heavy, radioactive particles suspended as a dilute secondary phase in the cooling circuits of primary reactor systems. The aim is to understand the mechanism of transport and deposition of such particles through large, complex geometry systems, so that the risk of dispersal of radioactive particles may be assessed, and confirmed to be acceptably small both in closed containers and in the atmosphere in the case of an accident scenario. The first part of the present work addresses the challenge of robustly and efficiently predicting the behaviors of rigid and spherical particles (referred to as heavy particles) within turbulent boundary layers, the underlying physics of which is the controlling factor on particle deposition in smooth pipes and ducts. In the second component of work we study the deposition and bounce of heavy particles suspended in turbulent flows across heat exchanger tube banks, using Large Eddy Simulation (LES). It was originally proposed to extend the boundary layer work to this application, but it was quickly identified that the deposition mechanisms here are governed by the high core flow turbulence, rather than boundary layer phenomena, so that LES provides the only realistic modelling approach. In both cases the dispersed heavy particles are expressed in a Lagrangian framework solved in an independently developed large-scale parallel code; whilst the fluid phase is described in an Eulerian framework, either based on correlations from published Direct Numerical Simulation (DNS) for the boundary layer models, or from Computational Fluid Dynamics (CFD) simulations for both the boundary layer and tube-bank models, making use of the unstructured-grid based Navier-Stokes solver ANSYS FLUENT. Underpinning this work we implement a complete stochastic Lagrangian particle tracking module, based on a robust and efficient particle localization algorithm which can determine and update the cell containing each particle as the particles move through an unstructured finite volume grid overlying the flow domain. The module can handle correctly the interactions of particles with complex boundaries, and uses a novel numerical scheme for interpolating the carrier-phase velocity field seen by the particles from cell-centred values obtained from CFD computation. It implements a Gear three-level implicit scheme to compute the particle velocity, which is more robust, accurate and efficient than the conventional explicit and implicit schemes. The module has been fully parallelized using MPI (Message Passing Interface) settings on a Linux cluster consisting of 20 single CPU node, and further been successfully integrated with both the steady and unsteady ANSYS FLUENT solvers, complete replacing the built-in Lagrangian particle tracking model provided by ANSYS FLUENT. The algorithm and numerical schemes have been validated against analytical solutions of particle transport in a two-dimensional straining shear flow and other cases. For turbulent boundary layer flows, a simpler but more promising stochastic quadrant model, inspired by the discrete random walk model of Kallio and Reeks and the quadrant analysis of Wu and Willmarth, is developed in order to account for the effects of near wall large-scale coherent structures, e.g. sweeps and ejections, on particle transport. The input parameters for the stochastic quadrant model are educed from the corresponding statistics obtained from a Large Eddy Simulation (LES) of a fully developed channel flow. The model is applied to the prediction of deposition of heavy particles in a turbulent boundary layer; both using a Kallio and Reeks correlation based model of the flow, and also a Reynolds-Averaged Navier-Stokes (RANS) flow solution of using ANSYS FLUENT, the latter flow model having the potential to be extended to complex duct geometries. These solutions are compared to those of by solving an alternative Langevin equation of Dehbi, or continuous random walk model, which satisfies the fully mixed condition and describes the fluid velocity fluctuations seen by heavy particles. Prior to the current work no systematic investigation of the potential errors in particle deposition in turbulent boundary layers due to the modified hydrodynamic forces experienced by particles when very close to the wall has been carried out, possibly because of the complexity of the correlations involved. The effect is explored with the present stochastic quadrant model, using recently published composite correlations of Zeng and Balachandar for the particle drag coefficient CD and lift coefficient CL for near wall particles. This work provides an important first confirmation that for practical cases hydrodynamic effects can reasonably be neglected for particle deposition in turbulent boundary layers. The boundary layer methods developed in the first part of this thesis are applicable to the prediction of heavy particle deposition in fairly complex duct geometries, but are shown to be inappropriate for flow over tube-banks, where the boundary layers are no longer the rate limiting feature. Consequently the parallel Lagrangian stochastic particle tracking model is extended to study the particle impaction efficiency on tube banks in a turbulent flow in the framework of Large Eddy Simulation (LES). The flow field, obtained from Large Eddy Simulation with the dynamic Smagorinsky sub-grid scale model within ANSYS FLUENT, is fully validated against existing experimental data. As far as the dispersed particle phase is concerned, the energy losses when particles impact on and generally, but not always, rebound from cylinders within the tube-bank is taken into account using an empirical critical-impact velocity model. The efficiency of particle impaction is measured for particles of three Stokes number, and the results are compared with existing experimental data.

This study is concerned with the modelling of single-phase and two-phase turbulent flows in a square duct over a range of Reynolds numbers with attention focused on the deposition, dispersion and re-suspension of particles. Reynolds averaged Navier Stokes (RANS) modelling is used in conjunction with a Lagrangian particle tracker (LPT). Modelling and simulation of single- and two-phase turbulent flows in circular pipes with the presences of stationary flat beds are also considered using the previously stated methodologies, as well as large eddy simulation (LES). The performance of the RANS modelling technique is evaluated against available experimental, simulation and empirical data. The RANS modelling technique is seen to perform with qualitative accuracy across all of the test cases considered within this thesis, and it can be said that this approach is capable of reproducing many of the key feature' associated with these flows. In almost all cases, qualitative agreement is seen between the RANS modelling results and the available experimental data, simulation results and empirical correlations. A key failing of the RANS modelling technique is the inaccurate representation of the magnitude of the secondary velocities found in square ducts and pipes with variable bed height. The RANS modelling technique with a Reynolds stress model (RSM) for turbulence, coupled with a LPT, can be usefully used in modelling particle-laden duct and pipe flow. across a range of conditions. Important qualitative information can be gained from this technique in terms of particle deposition, dispersion and re-suspension. For more detailed studies on the physics of these flows, the preferred methodologies are the more advanced simulation techniques of LES and direct numerical simulation CDNS), while there is also a clear need for further experimental investigations of such particle- laden flows.

The work presented concerns the way small particles attached to a surface are resuspended when exposed to a turbulent flow. Of particular concern to this work is the remobilization of radioactive particles as a consequence of potential nuclear accidents. In this particular case the focus is on small particles, < 5 microns in diameter, where the principal force holding such particles onto a surface arises from van der Waals inter-molecular forces. Given its suitable treatment of the microphysics of small particles, it was decided here to aim to develop improved versions of the Rock’n’Roll (R’n’R) model; the R’n’R model is based on a statistical approach to resuspension involving the rocking and rolling of a particle about surface asperities induced by the moments of the fluctuating drag forces acting on the particle close to the surface. Firstly, a force (moment) balance model has been modified by including the distribution of the aerodynamic force instead of considering only its mean value. It was also possible to improve the representation of the adhesive-force distribution where it is customary to include a substantial reduction factor to take account of surface roughness. The R’n’R model is significantly improved by using realistic statistical fluctuations of both the stream-wise fluid velocity and acceleration close to the wall obtained from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of turbulent channel flow; in the standard model a major assumption is that these obey a Gaussian distribution. The flow conditions are translated into the moments of the drag force acting on the particle attached to the surface (using O’Neill’s formula for the aerodynamic drag forces in terms of the local flow velocities). In so doing the influence of highly non-Gaussian forces (associated with the sweeping and ejection events in a turbulent boundary layer) on the resuspension rate has been examined along with the sensitivity of the fluctuation statistics to LES and DNS. We have found most importantly that the statistics of both fluctuating forces and its derivative (normalized on their rms values) are noticeably independent of the normalized distance from the wall, y+ within the viscous sublayer (y+ < 6) – if this were not the case then modelling fluctuations with different particle sizes would be far more complex. In particular as a result of the analysis of our DNS/LES data 3 distinct features of the modified R’n’R model have emerged as playing an important part in the resuspension. The first is the typical forcing frequency ω due to the turbulent (fluctuating) aerodynamic drag forces acting on the particle attached to a surface (in the modified R’n’R model based on the DNS results (y+ = 0.1) it is a factor of 4 > the value in the original model based on Hall’s measurements of the lift force). This naturally has a significant effect of increasing the fraction resuspended for very short times (ωt ~< 1) iv and is the controlling influence over the entire range of times from short to long term resuspension. The second is the value of the ratio of the root-mean-square (rms) drag force to its mean value which in the modified model is nearly twice (1.8) than that in the original. This feature of the model is largely responsible for the greater fraction resuspended after times ~ 1s (times which are sufficient to include the transition period from short term resuspension to long term resuspension rates (~t-1). The third feature introduces changes in the resuspension because the distribution of aerodynamic drag forces in the modified model is distinctly non-Gaussian behaving more like a Rayleigh distribution. This means that the distribution of the drag force decays much more slowly in the wings of the distribution than the equivalent Gaussian (with the same rms) so that for very large values of the adhesive force / rms drag force ~ 8 (at the extreme end of the DNS measurements), the resuspension rate constant is a factor of 30 larger than that for an equivalent Gaussian model. Thus although the fraction of particles resuspended is very small in these instances, the differences between the modified and original models can be very large. This is particularly important when we consider resuspension from multilayer deposits. When we consider these influences in the context of a broad range of adhesive forces due to surface roughness, we find that in general, the modified model gives around 10% more for the fraction of particle resuspension fraction than the original R’n’R model (for an initial log normal distribution of adhesive forces), however the difference could become significant (3 to 7 times greater depending on the range of values of the adhesive-force spread factor) when the friction velocity is small (i.e., smaller resuspension fraction). As for the short-term resuspension rate, the difference between the modified and original model becomes significant when this is dominated by the typical forcing frequency (ω+ is 0.0413 for the original model, 0.08553 for LES approach and 0.127143 for DNS for y+ = 6). The sensitivity to the adhesive-force spread factor has also been studied and the results indicate that the modified model removes particles much more easily than the original model in conditions of small friction velocity and a smoother surface (i.e., small spread factor). Finally in this phase of the work, the correlation between the distribution of the fluctuating force and its derivative has been checked for both LES and DNS statistics. The results demonstrate that this correlation has a very slight effect on particle resuspension compared with the result from the uncorrelated curve-fitted model. In view of recent numerical data for lift and drag forces in turbulent boundary layers (Lee & Balachandar), the lift and drag we have considered and the impact of these data on predictions made by the non-Gaussian R’n’R model are compared with those based on O’Neill formula. The results indicate that, in terms of the long-term resuspension fraction, the difference is minor. It is concluded that as the particle size decreases the L&B method will lead to less-and-less long-term resuspension. Finally the ultimate model that has been developed in this work is a hybrid version of the R’n’R model adapted for application to multilayer deposits based on the Friess and Yadigaroglu multilayer v approach. The deposit is modelled in several overlying layers where the coverage effect (masking) of the deposit layers has been studied; in the first instance a monodisperse deposit with a coverage ratio factor was modelled where this was subsequently replaced by the more general case of a polydisperse deposit with a particle size distribution. The results indicate that, in general, as the number of modelled layers increases the resuspension fraction of the whole deposit after a certain time decreases significantly. In other words, it takes a much longer time to resuspend a thicker deposit. Taking account of the particle size distribution slightly increases the short-term resuspension. However, this change decreases the long-term resuspension significantly. The model results have been compared with data from the STORM SR11 test (ISP-40) and the BISE experiments. In general, both comparisons indicate that with smaller spread of the adhesive force distribution (i.e., the range of adhesive force distribution is narrower) the new multilayer model agrees very well with the experimental data. It can be inferred that multilayer deposits lead to much narrower distributions of adhesive force.

This thesis describes experiments conducted in 3He-B to investigate the properties of quantum turbulence created by an oscillating grid. The turbulence is detected using an array of vibrating wire resonators. We have measured various steady-state properties of the turbulence includ- ing fluctuations, and investigated how turbulence propagates and evolves by examining the correlations between pairs of detectors. The quantum turbu- lence generated in our experiment is found to decay in a way similar to that found in classical fluids, as described by the Richardson cascade.

The present research focuses on the development and computer implementation of a novel threedimensional, anisotropic turbulence model not only capable of handling complex geometries but also the turbulence driven secondary currents. The model equations comprise advanced algebraic Reynolds stress models in conjunction with Reynolds Averaged Navier-Stokes equations. In order to tackle the complex geometry of compound meandering channels, the body-fitted orthogonal coordinate system is used. The finite volume method with collocated arrangement of variables is used for discretization of the governing equations. Pressurevelocity coupling is achieved by the standard iterative SIMPLE algorithm. A central differencing scheme and upwind differencing scheme are implemented for approximation of diffusive and convective fluxes on the control volume faces respectively. A set of algebraic equations, derived after discretization, are solved with help of Stones implicit matrix solver. The model is validated against standard benchmarks on simple and compound straight channels. For the case of compound meandering channels with varying sinuosity and floodplain height, the model results are compared with the published experimental data. It is found that the present method is able to predict the mean velocity distribution, pressure and secondary flow circulations with reasonably good accuracy. In terms of engineering applications, the model is also tested to understand the importance of turbulence driven secondary currents in slightly curved channel. The development of this unique model has opened many avenues of future research such as flood risk management, the effects of trees near the bank on the flow mechanisms and prediction of pollutant transport.

The first part is the derivation of one-particle vertical diffusion for stably stratified turbulence with or without rapid rotation. Nicolleau & Vassilicos (2000) have analytically calculated vertical one-particle diffusion in stably stratified turbulence without rotation. One-particle vertical diffusion for turbulence with stable stratification and with or without rapid rotation has been derived here analytically using the solutions of the linearized equations of motions. The second part is an attempt to explain the depletion of horizontal pair diffusion in strongly stratified turbulence. "Recently, Nicolleau et al. (2005) have shown that in their Kinematic Simulations (KS) of vertically stably and strongly stratified homogeneous turbulence (Froude number smaller than 1). horizontal pair diffusion is significantly depleted by comparison to unstratified isotropic and homogeneous two- and three-dimensional turbulence. We have seeked to explain this depletion of horizontal pair diffusion by vertical stratification in terms of the probability density function of the horizontal divergence of the velocity field and the statistics of stagnation points following the recent approach to Richardson pair diffusion by Davila & Vassilicos (2003), Goto & Vassilicos (2004), Goto et al. (2005) and Osborne et al. (2005). We measure the number density of stagnation points in the KS of three-dimensional strongly stratified turbulence and find that it is virtually identical to what it is in KS of three-dimensional isotropic turbulence The third part is a study of the vertical motions of small, spherical inertial particles in strongly stratified turbulence.

Numerical methods for the simulation of shock-induced turbulent mixing have been investigated, focussing on Implicit Large Eddy Simulation. Shock-induced turbulent mixing is of particular importance for many astrophysical phenomena, inertial confinement fusion, and mixing in supersonic combustion. These disciplines are particularly reliant on numerical simulation, as the extreme nature of the flow in question makes gathering accurate experimental data difficult or impossible. A detailed quantitative study of homogeneous decaying turbulence demonstrates that existing state of the art methods represent the growth of turbulent structures and the decay of turbulent kinetic energy to a reasonable degree of accuracy. However, a key observation is that the numerical methods are too dissipative at high wavenumbers (short wavelengths relative to the grid spacing). A theoretical analysis of the dissipation of kinetic energy in low Mach number flows shows that the leading order dissipation rate for Godunov-type schemes is proportional to the speed of sound and the velocity jump across the cell interface squared. This shows that the dissipation of Godunov-type schemes becomes large for low Mach flow features, hence impeding the development of fluid instabilities, and causing overly dissipative turbulent kinetic energy spectra. It is shown that this leading order term can be removed by locally modifying the reconstruction of the velocity components. As the modification is local, it allows the accurate simulation of mixed compressible/incompressible flows without changing the formulation of the governing equations. In principle, the modification is applicable to any finite volume compressible method which includes a reconstruction stage. Extensive numerical tests show great improvements in performance at low Mach compared to the standard scheme, significantly improving turbulent kinetic energy spectra, and giving the correct Mach squared scaling of pressure and density variations down to Mach 10−4. The proposed modification does not significantly affect the shock capturing ability of the numerical scheme. The modified numerical method is validated through simulations of compressible, deep, open cavity flow where excellent results are gained with minimal modelling effort. Simulations of single and multimode Richtmyer-Meshkov instability show that the modification gives equivalent results to the standard scheme at twice the grid resolution in each direction. This is equivalent to sixteen times decrease in computational time for a given quality of results. Finally, simulations of a shock-induced turbulent mixing experiment show excellent qualitative agreement with available experimental data.

A parallel CFD code to solve incompressible fluid flow on unstructured Cartesian meshes has been developed almost from ground up. Turbulence statistics have been computed using the Large Eddy Simulation technique. The new code was subjected to some validation where results are compared to available reference data. An analysis on the iteration and discretisation errors was carried out. This code was then applied to predict the lid driven cubical cavity flow in at a bulk Reynolds number of 10,000. Three different mesh sizes were used to investigate independence of results on grid size. Amongst others, turbulence statistics were checked against Kolmogorov -5/3 law. A detailed study of synthetic turbulence methods was carried out and applied to the prediction of flow in a duct with square cross section using an inlet and outflow boundaries. Three different turbulence generation methods were investigated namely the artificial turbulence generation method, random perturbation method and a novel hybrid particle-wave method also termed as the enhanced vortex particle method in this study. The mean and instantaneous field variables together with the turbulence statistics from each method were compared and analysed. Finally, the code was used to solve turbulent flow over arrays of wall-mounted obstacles with mesh densities comparable to previous studies. The velocity profiles and vector fields at various locations in the domain were compared to data obtained from recent LES simulations. The artificial turbulence generation case was applied for the first time to produce turbulence at the inlet. The turbulence kinetic energy spectrum distribution agrees well with reference data. Important findings from this study are clarified and some suggestions for future work are given in the conclusions section.

The objective of this study is to develop a CFD tool for performing reliable large eddy simulation (LES) of the compressible evaporating two-phase turbulent flow in a gas turbine combustor. The KIVA-3V code originally developed by Los Alamos National Laboratory is used as a baseline code. The KIVA-3V code has been modified to facilitate LES calculations. Both the temporal and spatial accuracies of the original KIVA-3V code have been improved to second order. A one-equation subgrid scale (SGS) turbulence model is implemented to describe the unresolved turbulent subgrid effect. To ensure that there are sufficient particle numbers to capture the dynamic droplet dispersion process, the ETAB breakup model coupled with a new hybrid droplet-particle algorithm is also implemented into the code. Furthermore, the effect of the subgrid scale (SGS) velocity on the droplet dispersion is included. The SGS velocity is computed from the subgrid turbulent kinetic energy predicted by the one-equation SGS turbulence model. A new collision model based on the concept of "particle cloud" is proposed and implemented in the code. The new model greatly reduces the grid-dependence of the original O'Rourke model in a Cartesian mesh. The gas solver of the new LES version of KIVA-3V code, which will be referred as KIVA-LES hereby) is validated against large eddy simulations of natural and forced plane impinging jets. Predictions were carried out for different inflow conditions, which include a natural plane impinging jet with a random perturbation on the inflow plane and a forced plane impinging jet with a Strouhal number of 0.36, locked both in phase and laterally in space. The first simulation was performed to quantitatively study the mean flow and turbulence statistics. The computed field variables and turbulence intensity of streamwise velocity agreed well with the experimental results. The second simulation was performed to study the vortex structures of a forced plane impinging jet. The predictions captured the typical vortex structures of this kind of flow, such as spanwise rollers, successive ribs, cross ribs and wall ribs were reproduced by the simulation, which were also previously detected by the experiment of Sakakibara et al. (103) with digital particle image velocimetry (DPIV) system, but to our -best knowledge never wholly reproduced by numerical simulations to date. Moreover, the study has also led to some new findings related to the formation and evolution of successive ribs, cross ribs and wall ribs. The new collision model is tested against analytical solutions of simplified realistic collision problems in a box volume. The grid-dependence of the model is also checked against some spray test cases. The new collision scheme is computationally more efficient than the frequently used O'Rourke's (87) scheme since it abandons a sampling procedure to compute the collision number. The new model delivers sufficient accuracy in calculating the collision numbers in cases with uniformly distributed droplets although O'Rourke's model seems to perform better for these scenarios. However, for the prediction of a real spray in Cartesian gird, the new model has delivered much improved results. The predictions of the new model do not show any grid-dependent artefacts. KIVA-LES with the Lagrangian spray models is used to predict non-evaporating and evaporating diesel fuel sprays. The computed results are compared with the experimental data by Hiroyasu and Kadota (55) and Naber and Siebers (81), as well as the predictions of the original KIVA-3V. The predictions are in good agreement with the data. The large scale vortical structures are reproduced by the LES simulations, which cause "branch-like" spray shape and influence the spray penetration depth. The predictions have also captured the differences between the dense and dilute regions of the sprays. The LES analysis of diesel sprays has also demonstrated that SGS velocity has significant influence on the predicted spray angles. Most importantly, grid-convergent results, which were difficult to obtain with the original KIVA-3V, have been obtained in the present study. Finally, the validated code is used to study evaporating two-phase spray flow in a coaxial gas turbine model combustor. The predictions were compared with some published experimental data. This is a first step towards a more comprehensive numerical analysis of practical industrial combustors where multiple inlets and more complex combustor geometry are encountered. Good agreement with the data is achieved. The predictions have captured the "ring-like" vortex just downstream the annulus and "worm-like" streamwise vortical structure further downstream. The axial droplet mass flux and Sauter mean radius (SMR) are well predicted. Overall the present study has demonstrated the capability of KIVA-LES with the newly developed collision model to provide reasonably accurate predictions of evaporating two-phase flows in coaxial gas turbine combustors.

To develop a complete numerical model for predicting fluid flow and mass transfer in domains with porous walls such as those found in cross flow filtration is not an easy task to undertake. Many gaps in theory exist that undermine any attempt to build a reliable representation of this process and a sensible effort to solving this problem must be built on sound and logical assumptions. The difficulties with modelling interacting particles, with simulating multiphase flow and with prescribing accurate boundary conditions are very much the essence of the problem. From a comprehensive literature search into areas of combined free and porous flow, mass transfer in porous domains and into the fields of rheology, and mathematical modelling of crossflow filtration it was discovered that present research although great in quantity, is overall limited by the difficulties described above. As well, the present research found in the literature is also limited for use in industrial applications as it generally considers dilute suspensions, it is often found to look at simple flow profiles for Newtonian fluids, the research scarcely looks into the dependency of flow profiles and mass transfer profiles on each other via rheology and many researchers who study crossflow filtration concentrate solely on the porous wall to solve the flux paradox situation and do not generally consider the whole domain. The purpose of the present thesis is to describe the concept, procedure and results behind the integration of a solids transport model into a previously developed flow algorithm and the explanation of ideas for solving the problem of prescribing appropriate concentration boundary conditions at the porous wall. The aim of the research is to develop a fast and cost effective tool for solving the given problem based on rational assumptions.