The subject of motions in two-dimensional ideal fluids is treated by numerical methods and the results given an interpretation based on theories as well as numerical experiments. Phenomena in ideal fluids have relevance to flows in realistic fluids when the flow speeds encountered are much smaller than the speed of sound and when dissipative mechanisms play a negligible role. The restriction to consider only motions of two dimensions is established and the resulting mathematical description yields a classical formalism. In terms of the scalar vorticity the motion of a two-dimensional ideal fluid can be interpreted by the flow in phase space of a classical phase fluid. The scalar stream function acts as a Hamiltonian for a system whose phase space corresponds to real space. Two models with respectively an infinite and a finite number of degrees of freedom are used to picture the evolution with time of the vorticity distribution. The former model, the field model, is used in analytic studies, and the latter model, the particle model, is employed in the numerical approach. The field model is reviewed as an introduction to the subject. The particle model is fitted into a numerical scheme that forms the basis of a computer simulation code VORTEX. This numerical scheme is presented in detail and made the subject of a numerical analysis. Controlled numerical experiments are carried out to establish possible inaccuracies of the scheme and the sources of these inaccuracies are revealed by means of the results from the numerical analysis. The general work of preparing controlled numerical experiments is briefly mentioned and by recording the experience from several numerical experiments the quality of these can be assessed. Results of several numerical experiments are then presented. The problem of two-dimensional turbulence is tackled by a precursory study of the interaction between finite area vorticity regions. An analytic calculation is made to support the numerical simulations which demonstrate the non-linear aspects of vortex interactions: fusion of strongly interacting vortices of the same sign and large amplitude oscillations in the flow from two vortices of opposite sign. The numerical experiments that follow, treat the stability and long-time evolution of laminar wakes, and heuristic comparisons are made with wind tunnel experiments that minimise three-dimensional effects. A model of four finite-sized vortices is used to study the stability of von Kármán vortex streets. Comparisons with theory are made and the results show fusion of like-signed vortex regions as well as fission of a vortex in the presence of other vortices. The final study comprises numerical experiments with a model approximating vortex flows in jets. It is concluded that much insight can be gained by using relatively simple flow models combined with suitable numerical scheme in order to understand the non-linear dynamics of vortex flows.

The transport of particulate in a gas flow or pneumatic conveying system 1s widespread in many areas of industry, for example chemical, food processing, cement industries and transportation of pulverised coal in coal-fired power plants. However, a simple and reliable method for monitoring the flow parameters, particularly the mass flow rate, velocity and size of particulate solids in the pipeline, has yet to be developed. This is mainly due to the fact that numerous problems, including insufficient signal generation, particle deposition in sensing vicinity, inhomogeneous particle and velocity profile, can be encountered by flow meters which may affect their readings. Being able to monitor the flow parameters, especially the particulate mass flow rate for example, allows accurate delivery of particulates and hence a better product quality in food processing industrials. In coal-fired power plants, being able to monitor and subsequently control the flow parameters will result in higher combustion efficiency and lower pollutants emission. Furthermore, optimum conveying conditions could also be set, which would result in reduced energy consumption and wear on equipment. This thesis is concerned with the generation of the Acoustic Emission (AE) from particulate flow and an investigation of the potential of implementing AE for flow parameters, namely the solid feed rate, particle velocity and size monitoring. A series of experiments has been conducted to gather AE signals from a laboratory scale single flow-loop pneumatic conveying system. Initially, AE sensors were attached to two steel meshes, which were placed with a fixed axial distance in the pipeline to study the generation of the AE and subsequently the possibility of using those generated AE to determine particle velocity in the pipeline. Particle velocities measured from this approach were compared with theoretical predictions. The results indicated that more than 90% of the measured particle velocities fall within ±10% of the theoretical particle velocity predicted using the modified Hinkle correlation. Since time alone is measured, no calibration is required. The generation of AE on five different sensor mounting locations was also studied. The results showed that sensors mounted on all those locations were able to respond to changes in the flow parameters. However, only two optimum sensor locations (mesh and outer bend) were chosen, based on the higher strength and repeatability, for further investigation. The final experimental results indicated that the AE features, namely Root-Mean-Square (RMS) and energy of the AE, are related to the changes in the flow parameters and good correlations were found. Good correlations between the RMS and energy of the AE with the momentum and kinetic energy of the particles, respectively, were also found. Ringdown count of the time domain signal and centroid frequency and energy ratio of the Power Spectral Density (PSD) are independent of variation in the solid feed rate and conveying air velocity. However, they varied significantly with changes in the mean particle size. This clearly marks the potential of the AE method to detect particle size variation inside pipes and hence the performance of the pulverising mill. Overall, all those features of AE have great potential in gas-solid two phase flow parameter monitoring.

The behaviour of gas-liquid two-phase flow has been studied extensively in the past at near atmospheric pressure in small diameter pipes. However, the industrial reality is the utilisation of large diameter pipes at elevated pressures and there is significantly less information available in this area due principally to the cost of investigating large diameter pipes. This research relied on using large-scale laboratory facilities at the University of Nottingham, and on using newly developed state of the art multiphase instrumentation. This study tested and applied the wire mesh sensor (WMS). The work included in this thesis utilised the two variants of the WMS; the already established Conductivity WMS and the recently developed Capacitance WMS and the two sensors were compared against each other. The Capacitance WMS was recently supplied by HZDR (Research Institution, Germany) to the University of Nottingham. Extensive experimental campaigns were carried out with this novel sensor. The WMS was initially tested and validated against several other instruments such as high speed camera and gamma densitometry. It was subsequently applied to a large diameter bubble column and large diameter pipe with two phase flow. The aims of this project was to gain a better understanding of the flow patterns and their transitions in large diameter pipes and to provide real experimental data to assist researchers and engineers in producing relevant and physically sound models for use in larger diameter pipes. As a result of this study, novel and interesting structures which have been labelled as wisps were discovered in large diameter pipes. In addition the WMS was used extensively for the first time on bubble columns in order to assess its suitability for such an application.

This thesis describes the application of novel swirl inducing pipe to various pipe configurations, when pumping a range of fluids and fluid / particle mixtures. An extensive experimental programme, incorporating particle image velocimetry and photography, was implemented using a pipe flow loop designed specifically for the purpose. Experimental data was obtained on the effect of a 4-lobe near-optimal swirl pipe on coal-water, sand-water and magnetite-water slurries of various particle size. Results indicated that swirl induction produced greater benefit for denser slurries and higher concentrations, and that swirl induced into slurries containing larger and denser particles decayed more rapidly. At low velocity, experimental data highlighted a reduction in the total pressure drop experienced across a 3.0m horizontal pipe section, a downward sloping section and vertical pipe bends, when the swirl-inducing pipe was present. PIV was used to measure the axial and tangential velocity of swirling flows downstream of a near-optimal swirl-inducing pipe. It was confirmed that a significant tangential velocity was generated when pumping water in the turbulent regime, however, when the fluid viscosity was increased, leading to laminar flow, no significant tangential velocity was detected.

In oil industrial applications, the modem practice in the drilling of oil wells, deviated drilling, results in inclinations from the vertical to the horizontal being present in such wells. Their design requires an accurate knowledge of the pressure drop/flowrates/physical-properties relationships. The measurement of wet-gas streams can be improved significantly by the use of a Venturi flow meter with an "overreading" correction. Moreover, at high gas mass fractions, knowledge of the liquid distribution about the well tubing cross section is required to inform policy on the use of inhibitors to protect the tubing from corrosion. Therefore, the aims of this study are to address aspects of two-phase gas/liquid flow in the pipe upstream the Venturi and in the Venturi. The main thrust of the project is to examine the effects of stratification that occur in annular flow when the pipe inclination is from horizontal to much higher inclinations. The study of annular flow includes the prediction of the three principal dependent variables – film flowrate, film thickness and pressure drop - as a function of position along the channel. All experiments were carried out with air and water in an inclinable rig. It consisted of a 5 m long stainless steel pipe of 38 mm internal diameter. The pipe could be positioned at any angle between horizontal and vertical in intervals of 5 degrees. The Venturi, located downstream the pipe, had a 19 mm i.d. throat and angles of convergent and diffuser respectively of 32° and 4°. Measurements on liquid film flowrate and liquid film thickness were carried on with two conductance probe techniques and sintered porous wall units. Measurements on pressure drop were conducted with the use of two differential pressure cells. In all experiments described, gas and liquid flowrates and pipe orientation were varied. Another aim of the study was to develop computer modelling for the prediction of air-water pressure gradient and liquid film thickness along the Venturi. The models of Azzopardi et al. (1991) regarding pressure drop and the models of Fukano and Ousaka (1988) for film thickness circumferential variations have been analysed and modified according to the characteristics of the system.

A novel method for calculating the linear fluid-structure interaction of a cantilevered flexible surface centrally positioned in an ideal channel flow, incorporating the effects of vorticity shed downstream, is described. The perturbation pressure is modelled using a linearised boundary-element method. The flexible surface deflection is modelled using linearised one-dimensional beam theory. The shed vorticity is modelled using a linearised discrete vortex method. The computational model can therefore be used to conduct numerical experiments where no presupposition of the flexible surface deflection is made. This linear model can accurately capture the onset of instability in this fluid-structure system. The flexible surface is infinitely thin; the upper and lower sides of the surface can therefore be considered stream lines of the flow, with a step jump in pressure between them across the surface. The discontinuity of tangential velocity across the flexible surface generates lift. The flexible surface is therefore modelled by a distribution of vortex singularities with a Kutta condition applied at the surface’s trailing edge. The individual models of the flexible surface and the fluid velocity and vorticity, together with the action of the individual hydrodynamic pressure components created when the models are combined to form a single unsteady model, are validated via a series of numerical experiments and by quantitative comparison with an appropriate, previously developed computational model. Unique, highly detailed investigations into the ideal fluid-structure phenomena observed in numerical experiments conducted over a wide range of mass ratio and inlet velocity are documented. For the first time, detailed numerical investigation of the effect on this fluid-structure interaction of channel walls, a rigid central surface (upstream and adjacent to the flexible surface), unsteady mean flow, the variation of stiffness and damping properties along the flexible surface and the vorticity shed at the trailing edge of the flexible surface have been quantified. Calculations of the critical velocity show good correlation with other published work and examples of the possible application of the unsteady model to different physical fluid-structure phenomena are outlined. Of central importance is the application of the unsteady model to the investigation of the human snoring phenomenon. Further insight into the operation of two types of snore is made and a new type of snore is discovered, incorporating the effects of inhalation. The numerical experiments demonstrate that the location (on the flexible surface) of the destabilising phase shift between the flexible surface velocity and fluid pressure leading to instability change drastically for a small shift in mass ratio. Coupled with knowledge of further snore mechanisms from other published work, these results show the uniqueness of treatment required to provide effective surgical treatment to individual patients suffering from snoring; furthermore, this highlights the need for more realistic fluid-structure models to be created.

The thesis introduces a new version of an elliptic-blending low-Reynolds-number eddy-viscosity Reynolds-averaged Navier Stokes model. It is a model intended to be implemented in an industrial solver. It will be argued that there is still room for such a simple model, though eddy-viscosity models must rely on developments specificallymade for higher order formulations. It is the aim of the v2-f model to integrate elements of Reynolds-stress modelling developments into a simpler formulation, but the former paradoxically suffers from numerical stiffness, which kept it out of reachof industry researchers everyday simulations. The v2-f formulation endeavours to reproduce the near-wall asymptotic behaviour of the turbulent quantities, as sounder alternative to empirical damping functions, and the required near-wall balance of small terms represents a numerical challenge. The present work first provides a comprehensive review of v2-f developments proposed over the past twenty years, and the different remedies for the numericalstiffness linked to the original formulation. The review focuses on ten v2-f variants, proposed between 1991 and 2006, whose behaviour is compared in some fundamental flows: the channel flow for five different Reynolds numbers, the asymptotic case of the logarithmic layer at infinite Reynolds number and the case of a flow with homogeneous sheared turbulence. Based on the conclusions of the review, the thesis proposes new developments. Firstly, the derivation of a new model, namely the φ - α model, is introduced. It relies on the resolution of two non-dimensional variables: φ represents the wall-normal anisotropy and α is a wall-proximity sensor. It is argued that only this formulation can address the numerical problems already mentioned without altering the predictions. Secondly, additional upgrades of the φ - α model are proposed to correct the dissipation rate equation. The aim is to improve the model behaviour in some specific regions of a boundary layer, by isolating some viscous terms and by improving the representation of turbulent transport at the edge of a boundary layer. Final developments are combined in a new model, the BL-v2/k model. The φ - α and BL-v2/k models are then validated for a set of two pressure induced separated flows and two buoyant flows, and beneficial effects of the proposed developments on the predictions are demonstrated. The numerical properties of the convergency of the BL-v2/k model are also reported at the end of this work.

Despite the amount of research into the cavity flow problem the prediction of the flow patterns, associated forces and acoustic phenomena remains an unsolved problem. The coupling of the shear layer dynamics, the internal vortical structures and the acoustics of the cavity make it a very complex flow despite the simple geometry. Once doors, stores and release mechanism are added the problem is compounded, thus accurate prediction methods are a necessity. The cavity has been shown to oscillate in different modes depending on the flow conditions and the geometry of the cavity. Two modes of oscillation were examined in detail, these being the wake and shear layer mode, using computational fluid dynamics and experimental data where available. The flow code used is the in-house CFD solver PMB and the experimental data has been provided by DERA. The cavity geometry was for a 1VD=5 cavity with a W/D ratio of 1 for the 3D investigation. For the wake mode the Reynolds number has been varied from 5,000 to 100,000 and the Mach number has been varied from 0.3 to 1.0 in order to examine the effect of changing conditions on this mode of oscillation. The characteristics of this mode of oscillation have been identified and a stable region within the varying Mach and Reynolds numbers has been shown. Outside of this stable region a blended flow has been identified. For the shear layer mode of oscillation the open cavity environment has been examined. This cavity is of great interest as examples of it can be found in current airframes, the H- 111 for example. This flow type is characterised by intense acoustic noise at distinct frequencies which could cause structural fatigue and damage sensitive electronics. However, this cavity type also has a relatively benign pressure distribution along the length of the cavity making it ideal for store separation. The flow cycle predicted shows that the separated shear layer impact on the rear wall generates strong acoustic waves. These waves are further enhanced by the interaction of the wave with the vortices and upstream wall of the cavity. The flow conditions of interest for this case are M=0.85 and Re=6.783 million. A study of the effect of time step, grid refinement and turbulence model has been performed. It has been seen that the density of the grid and the turbulence model chosen must be considered as a pair; if the grid is too fine it may resolve scales being modelled by the turbulence model and result in a double counting of energy resulting in spurious results. One area of cavity studies that has received only sparse investigation is the effect of 3-Dimensionality on the flow. One objective of this work was to try and rectify this. However, it was found that the choice of solver could play a significant role in the accurate prediction of the 3D cavity flow. For cases where the acoustic spectrum is broad, typical URANS codes may have difficulty in predicting these flows. Under such conditions DES or LES would be more appropriate choices. However, when the frequency spectrum is not as spread out URANS can provide good results. This can be seen in the 3D cavity case where doors are present and aligned vertically. The wake mode, while identified in 2D. has received little attention in 3D. It is generally thought that the effect of the third dimension would be to trip the wake mode to shift to another mode of oscillation. This study has shown that this is indeed the case. The flow cycle shown is more reminiscent of the blended flows shown in some 2D cases.

Of particular interest are the flow structure and dynamics associated with open shallow rectangular cavities at low Mach numbers for various length-to-depth ratios. At the Reynolds number investigated, it is the presence of convective instabilities through the process of feedback disturbance that gives rise to a globally unstable flowfield. Using an instrumental wing model with a cut-out an experimental investigation of a cavity flowfield exhibiting ‘fluid-dynamic’ phenomenon has been completed. A post-processing module for the PIV image data was constructed which optimised the data fidelity and accuracy while improving upon velocity spatial resolution. These improvements were necessary to capture the flow scales of interest and minimise the measurement error for the presentation of velocity, velocity-derivative and turbulent statistics. It is shown that the hydrodynamics that is intrinsic to the cavity flowfield at these inflow conditions organises the oscillation of small- and large-scale vortical structures. The impingent scenario at the downstream edge is seen to be crucially important to the cavity oscillation and during the mass addition phase a jet-edge is seen to form over the rear bulkhead and floor. In some instances this jet-like flow is observed to traverse the total internal perimeter of the cavity and interact with the shear layer at the leading edge of the cavity, this disturbs the normal growth of the shear layer and instigates an increase in fluctuation. The coexistence and interplay between a lower frequency mode dominant within the cavity zone and the shear layer mode is seen to shed large-scale eddies from the cavity. This modulation imposes a modification to the feedback signal strength such that two distinct states of the shear layer are noted. Concepts for the passive reduction of internal cavity fluctuation are successful although modifications to the shear layer unsteadiness are encountered; an increase in drag is implied.

No description available.