Recent theoretical studies by Lingwood (1995,1997a,b) on the rotating-disk boundary-layer, have shown, using an analysis that deploys the usual 'parallel-flow' approximation, that there exists a region of absolute instability. However, by taking into account the radial variation of the mean flow, Davies h Carpenter (2003) have shown, using numerical simulations, that the absolute instability does not give rise to an unstable linear global mode. In fact convective behaviour is found to dominate the global response. The aim of the current study is to further the studies of Davies h Carpenter (2003) to other rotating boundary-layers. Uniform suction and a uniform axial magnetic field are known to be stabilizing. However, by considering non-parallel effects, globally unstable behaviour is observed, albeit without the promotion of a fixed global frequency. An investigation is also carried out on the so called BEK family of rotating boundary-layers, which includes the Bodewadt, Ekman and von Karman flows. All of these flows are absolutely unstable, when the parallel flow approximation is applied. However, by considering the genuine non-parallel flow, the numerical simulation results indicate that the kind of behaviour found for the von Karman flow is carried over to other flows in the BEK family. The numerical simulation results of the rotating-disk boundary-layer can be modeled using the linearized complex Ginzburg-Landau equation. By deriving expressions for the stability, convection velocity and diffusion/dispersion effects, in terms of the numerical simulation results, the Green's solutions to the Ginzburg-Landau equation can be successfully matched to the parallel and non-parallel rotating-disk boundary-layer. The results suggest that the long-term behaviour depends on the precise balance of the varying frequency, varying growth rate, and diffusion/dispersion effects. It is then possible for an absolutely unstable disturbance to remain globally stable.

The work commences with a review of the literature on turbulent forced convection heat transfer to supercritical pressure fluids flowing in pipes. Only in the more recent work is any mention made of the effects of free convection on the heat transfer. An extensive programme of experiments is carried out with supercritical pressure carbon dioxide flowing both upwards and downwards in a 1.9 cm bore resistance heated test section. The test section is part of a closed loop system in which mass flow rate, wall heat flux and bulk inlet temperature can be varied systematically. Locally impaired wall temperature profiles occur in upflow whereas downflow profiles appear well behaved. The difference between them is the result of buoyancy effects. The influence of small variations in the test section wall thickness is investigated with regard to large circumferential non-uniformities of wall temperature. Downward flow is identified as being pseudo fully developed but nevertheless dependent upon wall and bulk temperature conditions. The trends in upward flow are recognised by examining the relative effects of free and forced convection. Comparison of upward and downward flow experimental data for supercritical water and carbon dioxide using ideas 01: .. non-dimensional similarity lead to the conclusion that although heat transfer is locally impaired in up~low in large bore pipes when compared with downflow, both upward and downward flow in small bore pipes produce worse heat transfer than in large bore pipes. Theory is produced in .which the influence of free convection on the non-dimensional shear stress in the boundary layer of an upward flow is included. Processing of the data produced in the present experiments and from published data of other workers using other fluids enables locally impaired heat transfer in upflow to be identified as a product of the effect of buoyancy in reducing the shear stress in this region. This method is applicable if buoyancy effects are sufficiently large relative to forced flow effects. Finally, it is shown that for a turbulent flow of air in a pipe, better heat transfer can be obtained for the case of downflow rather than upflow under the influence of variable density alone. The absolute shear stress level in each case relative to the other, rather than the non-dimensional level, is the quantity which is of greater importance in the understanding of these results.

No description available.

Transition to turbulence in polymeric channel flow is investigated, with the FENE-P model used to characterize the viscoelastic behaviour of the flow. Simulations are performed to study transition through both the natural and bypass routes. In the linear growth regime of natural transition, differences in the growth rate of a TS wave are explained by appealing to the production of the perturbation energy budget. At high Weissenberg number, the growth rate is substantially lower in comparison to Newtonian flow. As a result, the transition process is prolonged. Upon the introduction of three dimensional disturbances, Newtonian and non-Newtonian cases undergo transition through the H-type instability. The spanwise extent of the lambda structures during transition is larger in non-Newtonian flow. Bypass transition is initiated by an initially-localized disturbance. In the linear growth regime, the flow response is stabilized by viscoelasticity, and the maximum attainable disturbance-energy amplification is reduced with increasing polymer concentration. The reduction in the energy growth rate is attributed to the polymer work, which plays a dual role: First, a spanwise polymer-work term develops, and is explained by the tilting action of the wall-normal vorticity on the mean streamwise conformation tensor. This resistive term weakens the spanwise velocity perturbation thus reducing the energy of the localized disturbance. The second action of the polymer is analogous, with a wall-normal polymer work term that weakens the vertical velocity perturbation. Its indirect effect on energy growth is substantial since it reduces the production of Reynolds shear stress and in turn of the streamwise velocity perturbation, or streaks. During the early stages of non-linear growth, the dominant effect of the polymer is to suppress the large scale streaky structures which are strongly amplified in Newtonian flows. As a result, the process of transition to turbulence is prolonged and, after transition, a drag reduced turbulent state is attained.

No description available.

No description available.

Droplet behaviour influences significantly the quality of emulsions and the performance of microfluidics applications. Despite the numerous studies on droplet behaviour, the interactions between the suspended droplet and its surrounding walls, especially for non-Newtonian fluids, are not yet fully understood. Here, we investigate the behaviour of isolated droplets subjected to a simple shear in a wide range of capillary numbers, confinement ratios and viscosity relations between the droplet and the carrier fluid. Simulations are performed using the colour-gradient lattice Boltzmann method (LBM), which is also adapted to handle power-law fluids. Findings on the Newtonian droplets in a Newtonian carrier fluid show that droplet deformation and orientation to the flow, i.e. tumbling, are enhanced with increasing confinement. Even more, with a larger viscosity ratio the rate of the deformation increases more significantly while the rate of tumbling becomes smaller. Noteworthy, the largest deformation is presented by droplets of the same viscosity as the matrix fluid. We also find that in a shear-thickening carrier fluid droplet deformation and tumbling are enhanced while they are reduced in a shear-thinning fluid. Additionally, with increasing confinement, the lowest capillary number a droplet breaks increases in the low viscosity ratio cases, contrary to the high viscosity ratio ones. At unity viscosity ratio this critical capillary number is slightly affected while droplets are found to break at a lower capillary number in a power-law carrier fluid. Simulations are performed to examine the behaviour of power-law droplets sheared in a Newtonian carrier fluid. The results are correlated well with the ones of the Newtonian droplets when the droplets obtain ellipsoidal shapes. However, upon slight deviation from the ellipsoidal shape the behaviour of power-law droplets differs substantially from their Newtonian counterparts.

No description available.

In this study, 2D and 3D numerical models based on the Smoothed Particle Hydrodynamics (SPH) approach have been developed to simulate turbulent open channel flows over a fixed rough bed. Both models were then used to simulate free surface turbulent flow over a rough boundary, including the free surface dynamic behaviour. The numerical code is based on the open source code SPHysics (http://www.sphysics.org) and during this study significant improvements have been made to this code on the modelling of turbulence and rough bed treatment. A modified sub-particle-scale (SPS) eddy viscosity model is proposed to reflect the turbulence transfer mechanisms and drag force equations are included into the momentum equations to account for the existence of roughness elements on the bed and on sidewalls. The computed results of flow velocity, shear stress and free surface elevations have been compared with detailed laboratory measurements under different flow conditions. The comparison has demonstrated that the modified SPH models can accurately simulate the free surface flows over a fixed rough bed. It was found that the modified 3D model is more accurate than the modified 2D model in predicting the flow velocity, shear stress profiles and the dynamic behaviour of the free surface. The capabilities and limitations of each model to simulate such free surface flow are highlighted and discussed.

We investigate the interaction of colloidal particles with ice-water interfaces. To this end, the experimental setup we use consists of a directional solidification stage, a light microscope, and thin sample cells, which allows for the possibility of particles to be viewed at the single particle level, and thermally in two dimensions (2D). First, the interaction of single particles with a moving ice-water interface is studied. We show that speed, ice growth facets and grain boundaries are important parameters in determining the way in which particles are incorporated into the ice. Secondly, once a particle is trapped, as along as it is not too cold, it is still free to move. This is due to the presence of premelted liquid trapped within the ice, surrounding the particles in a thin layer. Particle movement is measured by use of tracking algorithms, and related to theoretical predictions, which use a balance between a thermomolecular and a viscous force to describe the motion. The extracted premelted layer thickness and its dependence on the undercooling implies that for the particle--ice system, non--retarded van der Waals interactions dominate. However, we find that the forces in the model should be modified for particles trapped in grain boundaries, and along cellular instabilities, or if impurities are present. Thirdly, the thermomolecular motion is also key to understanding how segregated ice, ice which is devoid of particles, can form in concentrated suspensions of particles, where the pore space between particles can also stay liquid below the bulk melting temperature. We study segregated ice growth both at the macroscopic scale and at the particle level. Regular ice lenses form in a regime defined by the temperature gradient and cooling rate, and these formations cause large structural changes in freezing colloidal suspensions. We explore how changing conditions such as the packing, size, shape and polydispersity of the particles, and the impurity concentration affect this process. Finally, due to the confinement of the system, the particles are in quasi 2D, whereas the ice--water system is in 3D. Consequently, we investigate the ice-water meniscus in 3D, both theoretically and experimentally using laser scanning confocal microscopy. The capillary length we measure is of the order of a colloidal particle.