The production of droplets from jets formed directly at nozzles was used in the lead shot production process where a nozzle was placed in the base of a tank of molten lead. A similar process is now used to obtain fertilizer prills where solid particles are produced from fertilizer melts by liquid jet break-up. This method could be extended to other materials such as metals and polymers where it is advantageous to obtain the material as solid spheres. The extension of this method to such materials requires a knowledge of the break-up behaviour of a wide range of liquids exhibiting both Newtonian and non-Newtonian behaviour. Since the more viscous liquids are difficult to break-up for the method to be successful in handling viscous liquids stronger forces than the naturally occurring capillary forces may be required. It is for this reason that the application of electrohydrodynamic forces to jets is considered in this thesis. It is of prime importance in most applications of jet break-up, after determining the conditions for instability, to determine the size of droplets formed. It is for this reason that this thesis is primarily concerned with the prediction of the size of droplets formed and also concerned with possible methods of monosize droplet production by liquid jet break-up.

This thesis describes the development of a computer program to study the steady two-dimensional laminar incompressible flow in a T-junction, at which one fully-developed channel flow impinges at right angles upon another. The calculation is made by finite differences on a non-uniform mesh. Solutions are presented for varying inlet velocity ratios, and for Reynolds numbers in the range 10[2] to 10[4]. Two further flow problems are also considered briefly using the same program. In the first the side channel is transformed to a square cavity. This allows a direct comparison with the work of previous authors, and good agreement is found. In the second the side channel is transformed to an outlet. The computational problem proves unusually awkward because it is surprisingly difficult to find a method of iteration which converges with a viable expenditure of computer time, and, more importantly, because the flow pattern proves very sensitive to the numerical treatment of the immediate neighbourhood of the 270-degree corners. The convergence difficulty is substantially overcome after a great deal of experimentation. The corner-flow difficulty is treated by a novelmesh configuration. Nevertheless the separated flow proves sensitive to the mesh size at the corner. This sensitivity is investigated, with the aid of analytical solutions, and it is concluded that the mesh size at the corner needs to be of the order of the Stokes radius, which in turn is inversely proportional to the Reynolds number. Considerable attention is given to the accuracy of the finite difference solutions, both theoretically, and practically by duplicating solutions using alternative finite difference equations.

In the last few decades, droplet microfluidics has been developed as a new area of microfluidics, where samples are compartmentalised in another immiscible phase. With these micro-droplets, Taylor dispersion can be minimised between samples and thorough mixing is easy and fast within the droplets themselves. Moreover, the sample consumptions are comparatively low as the samples are limited within nano-litre, pico-litre or even smaller droplets. Due to these attractive features, droplet microfluidics has been widely used as a platform to study various phenomena in chemistry, biology and physics. Droplets are normally generated in a T-junction or flow-focusing with syringe pumps or other pressure sources. An alternative way to generate droplets is to sequentially aspirate aqueous samples and carrier oil under negative pressures. Both of the typical T-junction methods and the current aspiration methods, have limitations in freely introducing/collecting samples into designed droplets, such as continuous sampling where introduction of samples does not affect the droplet generation, and in-situ sampling where samples from environment can be directly introduced into droplets. This ‘sample in’ problem is still a challenge in droplet microfluidics. This thesis addresses the two droplets sampling issues in droplet microfluidics: continuous droplet sampling, and in-situ droplet sampling. To solve the first issue, a novel microfluidic platform was engineered which includes aspiration droplet generators, a peristaltic pumping system and a feedback system which is used to synchronise droplet generation with pulsations of flowrates from the peristaltic pump. The demonstration of this platform successfully shows the capability of continuously generating and pumping droplets. To solve the second issue, a micro peristaltic pump was engineered to realise a robust droplet generation method and a direct sample introduction from ‘out-world’ to chip. The results show that this device is capable of generating droplets in-situ.

The aim of this research is to examine the transition process between two different wake states of an oscillating circular cylinder in the frame of three-dimensional large eddy simulation (LES). The relationship between the hydrodynamic force and near-wake structure of the fully-submerged cylinder is considered in detail, and results will be used to understand the mechanisms of vortex-induced vibration at high Reynolds flows. The simulations are performed on parallel processing in the University's high performance computing facility. The spanwise- and phase-averaging tools are developed in open source code OpenFOAM environment for qualitative comparisons with the experimental visualisation studies. Verification and validation of the simulations at subcritical Reynolds numbers of 5500-41300 are conducted. The grid resolution and subgrid model, which highly influence on LES solutions, are carefully and properly chosen at the considered Reynolds numbers, and the resulting hydrodynamic forces and pressure are successfully predicted compared to the available experimental or direct numerical simulation data. In these studies, the variations of the near-wake structure and shear-layer frequency are examined with increasing Reynolds number. The numerical results exhibit the characteristic broadband spectral peaks of shear-layer frequency due to small-scale shear-layer vortices inside the freely-separating thin-boundary layers behind the cylinder, and clearly show the dependence of Re0:67 for which the shear-layer instability is fully developing in subcritical flow regime. Based on the careful validations, turbulent flow behind an oscillating cylinder is investigated with various excitation amplitudes and a series of excitation frequencies. In these studies, the well-known flow features of an oscillating cylinder are reproduced and compared to the experimental observations. Two types of transition processes near flow resonance, namely the self-excited and reverse self-excited transitions, are captured first in a set of numerical simulations. Whilst the self-excited transition was only observed in the recent experiment especially at a certain flow condition, high amplitude excitation and lower Reynolds number, the present research shows numerical evidence that the one-time transition is possible even at lower excitation amplitude and higher Reynolds number as well. The change of the ensemble averaged wake patterns during the transition process strongly supports this numerical observation.

Flow-induced vibration (FIV) is an important phenomenon, by which the flow around bluff bodies creates forces that excite vibration. When marine risers are designed in a tandem arrangement, two aspects of FIV including Vortex Induced Vibration (VIV) and Wake-Induced Vibration (WIV) are very important, resulting in strong vibrations and fatigue damage. In this thesis, the simultaneous effects of VIV and WIV are studied for the case of circular cylinders by means of Computational Fluid Dynamics (CFD) software ANSYS Fluent. An Arbitrary Lagrangian-Eulerian (ALE) formulation is applied on a deformable mesh needed for modelling a free vibrating cylinder. The response dynamics and wake interactions are addressed. Major aspects considered in the thesis include: the Reynolds number (Re), the mass-damping parameter, the degrees of freedom of a single cylinder and of a downstream cylinder and the combined effect of VIV and WIV. The current predictions focus on sub-critical Re flow so that turbulence models are applied using two-dimensional Reynolds Averaged Navier-Stokes (RANS) equations. Force coefficients are analysed based on pressure distribution and Strouhal number. The VIV and WIV response is analysed by considering oscillating amplitude, frequencies and motion trajectories. The work concentrates on FIV vibration in three main cases: a single circular cylinder, and a downstream cylinder in tandem and staggered arrangements. The cylinder was elastically mounted on a mass-spring-damper system, with 1 degree of freedom (dof), 1+1dof, 2 dof or 4 dof. The study results showed the cylinder’s vibration is strongly affected by the mass-damping ratio and reduced velocity. The coupling between inline and crossflow vibrations could increase the amplitude of motion dramatically compared to crossflow vibration only. The amplitude of vibration changes the wake pattern as well as the trajectory of the cylinder. The vibration in the inline direction on the downstream cylinder in the wake of the upstream one is remarkably high compared to the crossflow direction. With a 2 dof system, the simultaneous effects of VIV and WIV give rise to vibration in each direction with two natural frequencies. WIV can be observed in the low-frequency response of the cylinder, which is considerably larger than the high-frequency VIV response. The combination of these two components can result in vibrations of the cylinder with higher amplitudes compared to any single form of excitation. The trajectories of the cylinder with a 4 dof system are very chaotic.

This thesis presents extensive experimental data that systematically examines the wakes and the drag forces of canopy patches with different densities, immersed in turbulent boundary layers. The patches are circular (with outer diameter D) and are made of several identical circular cylinders (height, H and diameter, d). The bulk aspect ratio of all the patches (AR = H~D)was fixed at 1 and the patch density ([phi] = Ncd2~D2) is altered by varying the number of cylinders(Nc) in the patch. Drag measurements show that the patch drag coefficient increases with increasing density. The drag coefficient of the highest investigated density ([phi]= 0.25) is greater than the drag coefficient of a solid patch (i.e. [phi] = 1, which is a solid cylinder with AR = 1). PIV measurements were carried out along streamwise-wall-normal (x - y) plane along the centreline of patch and in the streamwise-spanwise (x - z) plane at its mid height (i.e. y = H~2). Mean velocity fields show that the porosity of the patch promotes bleeding along all directions. It was observed that bleeding along the vertical/horizontal direction increases/decreases with increasing [phi]. Furthermore, it was also observed that bleeding along the lateral direction dictates the point of flow separation along the sides of the patch and makes it independent of [phi]. All these aspects make wakes for porous patches markedly different from their solid counterpart and provide a basis to explain the observed trends in the drag coefficient. The wakes generating behind three-dimensional porous patches can be divided in two distinct regions: the very near wake, where the wake properties are constant along the height of the model, as a first approximation, and the near wake, where the velocity profiles for different patches collapse, regardless of patch density. Scaling laws and parameters for the velocity profiles are introduced. Subsequently, an analysis of the trend of these parameters with [phi] and y is carried out and, where possible, a predictive model is evaluated. The wakes are also found to be self similar at the mid height horizontal plane, if scaled with appropriate scaling parameters, and the trend of these parameter with patch density is analysed. The analysis of fluctuating quantities confirms the presence of two distinct regions in the patches’ wakes, and suggests the presence of an alternate vortex street whose intensity and coherence increases with increasing patch density.

In the present work the investigations of non linear effects, in the context of potential flow theory, are investigated. These effects are caused by three main reasons, namely: the changes of the wetted geometry of the floating body, the water line dynamics and the fully non linear nature of the free surface boundary conditions. In order to understand the importance of tackling the non linear effects, a three dimensional frequency study of the S175 conteinership is carried out, at different Froude numbers, using linear frequency domain methods and a partly non linear time domain method. A time domain analysis, with the aid of an unstructured mixed Eulerian Lagrangian (MEL) description of the fluid flow, is implemented aiming in exploring potential low non linear effects. In this framework, the mixed boundary value problem of the Eulerian phase of the MEL scheme is tackled by means of a Boundary Element Method using constant elements (or a direct Rankine panel method). At given time step, on Neumann boundaries the impervious boundary condition is specified whereas, on Dirichlet boundaries, the potential on the free surface is prescribed. The solution of the Boundary Value problem yields the potential on the Neumann boundaries and its normal derivative on Dirichlet boundaries. In the Lagrangian phase, the free surface boundary conditions are then integrated in time. This method was used to solve the linear time domain radiation, i.e by applying linearized free surface boundary conditions on the exact free surface and solving the mixed boundary value problem on the mean undisturbed free surface, for the case of forced motions of a hemisphere and a Wigley hull. In addition, the linear time domain method is also extended to the unified hydroelastic analysis in time domain for the cases of 2 and 3 nodes bending. Results are presented for the the Wigley hull, undergoing prescribed forced oscillations for both rigid and exible mode shapes. The extension of the MEL scheme to a numerical tool capable of addressing several degrees of non linearities (from body nonlinear to fully nonlinear) is also discussed. In this context, two numerical formulations to calculate the time derivative of the velocity potential are implemented, namely: a backward finite scheme and an exact calculation based in the time harmonic property of the velocity potential. In latter case, a second boundary value problem is constructed and solved for the time derivative of the potential on Neumann boundaries and for the normal acceleration on Dirichlet boundaries. Results of both approaches are compared for the case of a sphere undergoing force oscillations in heave are compared to results obtained by other time domain methods. Moreover, after the boundary value problem is solved, a radial basis function representation of the velocity potential and free surface elevation is constructed, this approach allows for the estimation of the gradient of the velocity potential (body nonlinear and fully nonlinear simulations) and free surface steepness (fully nonlinear simulations). The results of the body non linear analysis, for large amplitude of oscillation in heave, are presented for the both the sphere and Wigley hull. For the latter, body non linear results of the coupling between heave into the first distortion mode (2-node) are also presented. The results of the fully non linear simulations are presented for the case of a sphere. An investigation of the suitability of two unstructured meshing libraries is also performed in the context of the MEL simulation scheme. Practical issues related to (re)meshing at each time step, the representation of ship like geometries, free surface evolution and numerical stability are highlighted for both libraries.

In this thesis, we study the effects of weak compressibility on staggered vortex streets, which are a ubiquitous phenomenon observed in nature. They are formed by fluid flowing past an obstacle, and can be found at several different length scales ranging from human length scales such as in water flowing under a bridge, to astronomical length scales such as planetary atmospheres, and beyond. They are of fundamental importance in fluid flows of interest to engineers and applied mathematicians alike. Yet, these vortex streets have not been studied as much theoretically. The classical exact solutions of Kármán are more than a century old, and used singular vortex models. The studies by Saffman and co-workers considered a vortex patch street, thus removing the singularity, however this study was numerical. Part of the difficulty in de-singularised models arises because of the unknown shape of the free-boundary of a finite-sized vortex. In particular, the effects of compressibility have not been taken into account in any theoretical investigation from first principles. We undertake a theoretical study of weakly compressible vortex streets, and obtain solutions to first-order for the velocity field. The vortices are modelled as hollow vortices, which are bounded regions of constant pressure with a non-zero circulation around them. For incompressible hollow vortex streets, exact solutions based on a conformal mapping approach were found by Crowdy and Green (2011). We perform a Rayleigh-Jansen (perturbation) analysis on these solutions, assuming isentropic flow of an ideal gas. We develop a novel method involving a rare use of complex analysis in studying compressible flows of this type. We utilise the Imai-Lamla formula [Imai (1942)] for the complex potential, which reduces the solution of the weakly compressible flow to computing analytic functions. Combining this with a conformal mapping approach, we solve the free-boundary problem by obtaining boundary value problems in multiply-connected pre-image domains (an annulus), which are solved through modern applications of classical methods. We utilise the machinery of the Schottky-Klein prime function for this domain, which helps in solving the boundary value problems for the analytic functions. We find that the speed of the vortex street changes due to compressibility, but the details of this change depends importantly on the area of the vortices. The vortex street is found to speed up for smaller areas and slow down at larger areas. The critical area of transition is found to be further dependant on the vortex configuration in the flow. We discuss the relationship of the present results with a few other known results in the context of different flows. We compare our results in the zero vortex size limit, to the results from a weakly compressible point vortex analysis undertaken in Crowdy and Krishnamurthy (2017b) and find agreement. Parts of the results in this thesis are reported as a paper Crowdy and Krishnamurthy (2017a). It is hoped that the present study leads to further studies on related problems such as the stability of vortex streets and vortex wake modelling for both incompressible and compressible flows. Other related problems likely to be influenced by this study include the free compressible vortex pair, which is important from the point-of-view of the theory of vortex sound.

The flow properties of several polymer melts have been investigated in steady shear flow and when shear flow was applied or removed. The results have been compared with the predictions of three rheological equations of state which have been proposed to describe the behaviour of elastic fluids. In steady shear flow the viscosity eta and the normal stress differences alpha1 and alpha2 have been determined for two polyisobutylenes (Vistanex LM-MH and Vistanex LM-MS) and a depolymerised natural rubber (Lorival R25). There is some disagreement about the magnitude of alpha2 and the main objective was to determine if it was zero or not. The data were obtained from total thrust and torque measurements in a Weissenberg Rheogoniometer using cone-plate and parallel plate geometries. For the polyisobutylenes alpha2 was negative but small compared with alpha1; the ratio |alpha[2]/alpha[1]| was less than 0.3. The Lorival R25 data were not inconsistent with these conclusions. Attempts have been made to measure stress relaxation on the cessation of shear flow and stress growth at the onset of shear flow. The measurements were carried out on the Weissenberg Rheogoniometer. For Vistanex LM-MH the form of the relaxation depended on the stiffness of the torque measuring system. This is shown to be due to illdefined boundary conditions for transient measurements with high viscosity fluids. However reliable data could be obtained on the lower viscosity polyisobutylene (Vistanex LM-MS) provided a stiff torsion bar was used. For this material the shear stress relaxation and growth were more rapid as the shear rate increased. The normal stress transient measurements were unreliable but it appeared that relaxation and growth times for p[21] were less than for alpha1. A cone-plate rheometer, which can measure the steady shear viscosity and elastic recovery of polymer melts, is described. The form of the recovery curve can also be obtained. A constant shear stress is applied to the sample and the resultant rotation and recovery when the stress is removed are measured by a capacitance technique. Data obtained on the two polyisobutylenes are reported. It is shown that the Weissenberg and Lodge theories of elastic recovery are not valid. Die swell measurements have been carried out on an elastic fluid (Lorival R25) and a high viscosity Newtonian fluid (Paralac 385, a modified alkyd resin). The measurements were made on a capillary rheometer at shear rates below 1 sec[-1]. Both fluids showed a significant amount of die swell. For the Newtonian fluid the average die swell was 13.5% and independent of the capillary radius, viscosity and volume rate of flow. Die swell increased with shear rate for the elastic fluid but did not depend on the capillary radius, and at low shear rates was asymptotic to the Newtonian value. It is shown that the momentum balance theory of die swell is not appropriate to high viscosity fluids of any type. The data obtained on the two polyisobutylenes have been compared with the predictions of the WJFLMB, OWFS and Kaye integral rheological equations of state. The OWFS theory is not an appropriate model for high viscosity elastic fluids such as polymer melts. It predicts elastic recovery values which are much too high and in stress growth experiments it is incapable of predicting stress overshoot which has been reported in the literature. The agreement between theory and experiment for the WJFLMB and Kaye models is reasonable for steady shear flow, stress relaxation, stress growth and total elastic recovery. However these theories do not describe the form of the recovery curve well. Both the WJFLMB and Kaye models predict stress overshoot in stress growth experiments at high shear rates. There is some evidence that the Kaye theory might be a more useful model than the WJFLMB theory in some applications.

This thesis focuses on the use of systems theory to study the stability of viscous channel flow. In the first part of the thesis, the flow is modelled as a feedback connection between a linear dynamical subsystem and a memoryless nonlinear subsystem. After discretisation, the system is approximated by a finite-dimensional model and its global stability is analysed using the passivity theorems, which are extended from finite-dimensional Euclidean spaces to finite-dimensional Hilbert spaces. The passivity analysis leads to the Reynolds number below which the flow is globally stable and the flow can be unstable above this number because of possible energy amplification. The thesis then addresses inaccuracy of the numerical methods that are typically used in the literature to calculate the energy amplification in the flow. It is identified that the inaccuracy is caused by the presence of spurious eigenvalues with negative real parts of large magnitude and numerical integration errors. A remedy to this problem is given in the thesis. In the second part of the thesis, the effects of riblets on the linear stability and the energy amplification in channel flow are investigated numerically. Riblets are small protrusions aligned with the direction of the flow and it is known that the use of riblets on an aerodynamic body can result in significant reduction in drag, although the mechanism of drag reduction by riblets is not yet clear. Three types of riblets (sinusoidal, triangular and semi-circular ones) are considered and in order to use spectral methods to discretise the governing equations, the complex geometry associated with the riblets is transformed to a standard domain by a change of coordinates. The differential equations also have to be transformed into the new coordinate system and the presence of riblets poses a serious difficulty in representing the fluid flow by a state space model. To circumvent this difficulty, a novel formulation of the Navier-Stokes equations is derived.