The work carried out for this thesis represents part of a larger study being followed in the Department of Chemical Engineering, University of Surrey into the processes of heat transfer taking place in rotary kilns with particular emphasis being placed on those in the Cement Industry. A widely used method of investigation of the performance of furnaces is that of partial modelling of the flow taking place within the system. This approach allows predictions to be made from model work concerning the shape and length of the flame within the real furnace. In cases such as the rotary kiln, where the flame may be defined as a turbulent jet diffusion flame, the mixing of the oxidant (air) with the fuel is of the utmost importance in dictating the flame characteristics. Consequently the approach of isothermal partial modelling has been applied to an accurate model of a specific industrial installations from which general conclusions concerning flow patterns in kiln systems can be made. The two most important aspects of such modelling procedures are firstly to obtain an accurate geometric model, and, secondly, to ensure that the flows produced in the model system are representative of actual practice. The first of these is relatively simple to attain; the second is more difficult. In order to overcome the limitations of published literature concerning flowrates in kiln systems, original industrial data was obtained and analysed in some detail, using relevant jet theories to produce a range of operating conditions suitable for use in the model. Isothermal model systems operating on air and water have been designed and constructed. Prom these flow pattern diagrams have been produced and presented in the results. The model studies indicate that the degree of recirculation in kilns is low to moderate and does not take place symmetrically about the kiln axis. The primary jet is deflected by the asymmetry of the secondary flow, the distribution of which is determined by the inlet geometry to the kiln. Jet deflection increases as the velocity ratio, uo /ua is decreased. The flow patterns are of sufficient generality for wide application for within the limits of the rules of isothermal modelling.

A series of compressor blades, aligned as a cascade, situated in a transonic flow has been studied using a two-dimensional Computational Fluid Dynamics (CFD) technique. An objective of the research was to discover, using a CFD code, how the total aerodynamic stability of a compressor cascade was affected by blade pitching oscillations, vibrating at certain interblade phase angles and oscillation frequencies. The analysis focused on the way in which the interblade phase angle, a, is likely to affect the stability of the cascade over a range of oscillation frequencies between 200Hz and 1 OOOHz, for a series of interblade phase angles between 0° and 180°. Two turbulence models were assessed to determine the sensitivity of turbulence coding, namely the Baldwin-Lomax and Johnson-King models. A validation of the CFD code against published data from the NASA Lewis Research Centre was carried out. The interaction of the passage shock, formed between the blades, and on the positive pressure surface of the blade was shown to have the greatest influence on the aerodynamic stability of the cascade; the shocks formed on the suction side had a somewhat smaller effect. Any flow separation, on either the suction or pressure surfaces, was also shown to decrease cascade stability.

The introduction of a new imaging approach for simultaneous multi-phase and multi-constituent velocity measurements is the main focus of this research. The proposed approach is based on the use of a single off-the-shelf colour camera which will enable simultaneous imaging of phases/constituents which are colourtagged using fluorescent droplets and multi-wavelength illumination. Highly efficient florescent tracers used to seed the constituents are presented and their visibility in full field imaging experiments is evaluated. A commonly found problem in experimental systems using laser illumination, known as flare, is discussed and the application of the developed fluorescent tracers for its reduction is presented. A strong focus of the imaging approach proposed is its flexibility and simplicity allowing its extension to stereoscopic imaging to obtain simultaneous multi-phase/constituent 3-component measurements with the addition of a second imaging camera. Proof of principle experiments with spatially separated and well mixed flows are presented for which successful phase discrimination is obtained and the uncertainty of the measurements is estimated. The imaging system developed is applied for simultaneous air and fuel velocimetry measurements in a Gasoline Direct Injection spray for which a more detailed understating of the interaction mechanisms is required to generate improved designs. The modified imaging system and experimental setup are presented and previously unavailable simultaneous air/fuel 2 and 3-component velocity fields are presented and analysed.

This thesis is directed primarily at a systematic theoretical investigation of gravity-driven thin film flow over various topographical features, the effect of inertia being of particular interest. The problem is solved using a hierarchy of models based, in order of decreasing complexity, on (i) the full Navier-Stokes system of equations; (ii) a depth averaged form of the latter; (iii) the lubrication equations. Every effort has been made to solve the underlying discrete equation set in each case efficiently using state-of-the-art solution strategies, thus guaranteeing accurate and mesh-independent predictions. The solution of models (ii) and (iii) centres on the use of a multigrid methodology together with automatic, error controlled, time-stepping and the proper treatment of any associated nonlinear advective terms. A discrete analogue of model (i), for both two- and three-dimensional flows, is obtained using a finite element formulation with the free surface parametrised via the method of spines and the system solved using a parallel multifrontal method together with a memoryefficient out-of-core storage approach. A comprehensive set of results is presented for flow over both one- and twodimensional topography, generated using models (ii) and (iii); the predictions obtained are contrasted with each other and compared with existing related experimental data. The free-surface disturbance arising for the problems investigated is revealed to be influenced significantly by the presence of inertia which leads to an increase in the magnitude and severity of the resulting capillary ridge, surge and trough formations present. A complementary exploration, using model (i) is undertaken which reveals the attendant internal flow structure. It shows that two-dimensional flow over spanwise topography and three-dimensional flow over localised trench topography can lead to different internal, inertia dependent, flow topologies; findings that are consistent with previously reported results for the well-known lid-driven cavity problem. Finally, the effect of a normal electric field on the free-surface disturbance generated by inertial thin film flow over topography is investigated using model (ii) coupled with a Fourier series separable solution of Laplace’s equation for the electric potential. Results for both two- and three-dimensional flow reveal that a significant electric field strength can be used to effectively planarise the free-surface capillary ridges and depressions that arise. The two-dimensional solutions obtained are consistent with those reported elsewhere for the case when inertia is neglected and highlight the importance attached to choosing an appropriate means of embodying the latter. Furthermore, the novel results generated for three-dimensional flow demonstrate that as Reynolds number increases, larger electric field strengths are required to planarise the associated free-surface disturbance.

No description available.

This work involves an experimental investigation of the spreading of liquids on gel layers in the presence of surfactants. Of primary interest is the instability that accompanies the cracking of gels through the deposition and subsequent spreading of a drop of surfactant solution on their surface. This instability, which has been reported recently in the literature, manifests itself via the shaping of crack-like spreading “arms”, in formations that resemble “starbursts”. The main aim of this study is to elucidate the complex interactions between spreading surfactants and underlying gels and to achieve fundamental understanding of the mechanism behind the observed phenomenon of the cracking pattern formation. This is hoped to be beneficial for improving a wide range of engineering, biological, biomedical and environmental settings where such systems are of central importance. Towards this aim, a parametric experimental work that involves the spreading of different types of surfactants on various types of gels was conducted, in order to explore the ways that system parameters such as the surfactant chemistry and concentration and the gel type and strength can affect the morphology and dynamics of the “starburst” patterns. The surfactants used were SDS (sodium dodecyl sulphate) and Silwet L-77 (a trisiloxane ethoxylate); the former is one of the most common materials used in surfactant-related studies and the latter belongs to a certain class of surfactants, termed “superspreaders” which are known for exhibiting unique spreading behaviour. The different gel substrates were made of agar (a polysaccharide-based gel), and gelatine (a protein-based gel). In terms of the spreading dynamics, the crack propagation was attempted to fit to a power-law by measuring the temporal evolution of the length of the spreading “arms” that form each one of the observed patterns. The values of the exponent of the power law are inside the predicted limits for Marangoni-driven spreading on thick layers. Therefore, Marangoni stresses induced by surface tension gradients between the spreading surfactant and the underlying gel layer are identified to be the main driving force behind these phenomena, while gravitational forces were also found to play an important role. A mechanism that involves the “unzipping” of the gel in a manner perpendicular to the direction of the largest surface tension gradient is suggested. An attempt to quantify the stresses that form the cracks and a detailed rheological characterisation of the gels are also included.

The flow around two identical circular cylinders, arranged in configurations where one of the cylinders is immersed in the wake of the other, is studied using numerical simulations. Two aspects of such flows were considered. The first is the stability of nominally two-dimensional time-periodic wakes to three-dimensional perturbations. We investigated flows around tandem and staggered arrangements with diverse centre-to-centre distances. Direct stability analysis and numerical simulations were employed, and the results are compared to those obtained for the flow around an isolated cylinder. The onsets of the three-dimensional instabilities were calculated and the unstable modes are fully described. In addition, we assess the nonlinear character of the bifurcations and physical mechanisms are proposed to explain the instabilities. The second aspect considered in this thesis is the flowinduced vibration experienced by a rigid cylinder when it is mounted on an elastic base and immersed in the wake of a fixed identical cylinder. Tandem arrangements with centre-to-centre distances varying from 1.5 to 8 cylinder diameters were tested. The flow was simulated using an Arbitrary Lagrangian-Eulerian approach that coupled the solution of the structure equations with that of the flow. Two- and three- dimensional simulations were performed to assess the mutual influence between the three-dimensional flow structures in the wake and the motion of the cylinder. The response of the downstream cylinder is compared to that of an elastically-mounted rigid isolated cylinder. Based on the simulation results we propose physical mechanisms to explain the origin of the excitation.

The thesis presents a Probability Density Function (PDF)-derived Eulerian/Eulerian model for the prediction of dispersed two-phase (solid/gas) flows. Continuum equations for the dispersed phase are formulated from the Kinetic Model (KM) PDF transport equations. The Kinetic stresses of the dispersed phase are determined from an algebraic stress model (ASM) together with a KM-based transport equation for the fluctuating kinetic energy. The continuum equations for the continuous phase are assumed to be the same as those in the Eulerian two-fluid model except for the interfacial momentum and energy transfer terms. Closures for these terms are derived from the PDF KM and mirror their counterparts in the dispersed phase equations. Also, the carrier phase turbulence is modelled by the standard k-ε model. These transport equations are solved using the numerical framework of an existing two-fluid approach. Furthermore, the current two-fluid model practice of applying wall functions to impose boundary conditions is adapted for application to the particulate phase. Such wall functions are calculated from the PDF KM itself. In this approach, the PDF equations are pre-integrated using the fully developed flow assumption along the wall to relate wall fluxes to values of the relevant variables in the interior of the flow. Such integration is utilised to create a wall functions database for a range of mean flow conditions. The model is validated against a range of both unbounded and bounded flow cases. Comparisons are made with experimental data as well as the results of other computational methods. It was found that the proposed model performs very well in capturing particulate behaviour and improves, in certain aspects, on the performance of traditional two-fluid models while retaining the practicality of the latter model for industrial applications. In particular, a reasonable capture of the particulate dispersion was observed within jet flows. Improvements were also seen in the prediction of mass flux distribution in shear layers and an accurate capture of near-wall mass distributions in bounded flows.

This thesis presents a methodology for the numerical solution of one-dimensional (1D) and two-dimensional (2D) compressible flows via a discontinuous Galerkin (DG) formulation. The 1D Euler equations are used to assess the performance and stability of the discretisation. The explicit time restriction is derived and it is established that the optimal polynomial degree, p, in terms of efficiency and accuracy of the simulation is p = 5. Since the method is characterised by minimal diffusion, it is particularly well suited for the simulation of the pressure wave generated by train entering a tunnel. A novel treatment of the area-averaged Euler equations is proposed to eliminate oscillations generated by the projection of a moving area on a fixed mesh and the computational results are validated against experimental data. Attention is then focussed on the development of a 2D DG method implemented using the high-order library Nektar++. An Euler and a laminar Navier–Stokes solvers are presented and benchmark tests are used to assess their accuracy and performance. An artificial diffusion term is implemented to stabilise the solution of the Euler equations in transonic flow with discontinuities. To speed up the convergence of the explicit method, a new automatic polynomial adaptive procedure (p-adaption) and a new zonal solver are proposed. The p-adaptive procedure uses a discontinuity sensor, originally developed as an artificial diffusion sensor, to assign appropriate polynomial degrees to each element of the domain. The zonal solver uses a modification of a method for matching viscous subdomains to set the interface conditions between viscous and inviscid subdomains that ensures stability of the flow computation. Both the p-adaption and the zonal solver maintain the high-order accuracy of the DG method while reducing the computational cost of the simulation.

The natural mechanism for transition to turbulence in flat-plate boundary layers is the growth and breakdown of Tollmien-Schlichting (TS) waves. In the presence of significant free-stream turbulence (FST) however, streamwise velocity perturbations, known as Klebanoff modes or streaks, amplify inside the boundary layer. These distortions alter the stability characteristics of the boundary layer, and the natural mechanism is bypassed, leading to earlier transition. Herein, a model is employed to describe the Klebanoff distortions: one Fourier component of the FST is used along with its signature inside the shear region to force the boundary layer and stimulate streaks. Varying the parameters of the forcing mode causes streaks with different frequencies and amplitudes. A base flow which is periodic in two dimensions is formed, and its linear stability is investigated using Floquet theory. Two modes emerge as the most unstable, and their eigenvalues are tracked whilst varying streak frequency and amplitude. The ‘inner’ mode, is related to the TS wave, but its growth rate is enhanced by unsteady streaks. The ‘outer’ mode is a high-frequency instability of the streaks at the edge of the boundary layer. It has no counterpart in the undisturbed boundary-layer. The critical streak amplitude for the outer mode is calculated for different streak frequencies and it agrees more closely with experiments than previous analyses which assumed the streaks to be steady. The current analysis indicates that increasing the frequency of the streaks can enhance their instability. In fact an optimum frequency exists for free-stream disturbances to penetrate the shear and stimulate unstable streaks. Direct numerical simulations with streaks and secondary-instability eigenmodes are conducted. The simulations show that both the inner and outer mode can grow to nonlinear amplitudes and cause boundary-layer transition to turbulence.