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The present thesis describes the advances made in modelling two-phase flows in inclined pipes using a transient one-dimensional approach. The research is a developement of an existing numerical methodology, capable of simulating stratified and slugging two-phase flows in horizontal or inclined single pipes. The aim of the present work is to extend the capabilities of the approach in order (i) to account for the effect of the pipe topography in the numerical solution of the two-fluid model, and (ii) to simulate vertical bubbly twophase flows at various pressures in large diameter pipes, and (iii) to model stratified and terrain-induced slugging in two-phase flow pipelines made of several uphill, downhill and level sections. A transient compressible two-fluid model based on the one-dimensional form of the mass and momentum conservation equations for the gas and liquid phases, is developed to predict those flow configurations. The wall to fluid and the interphase interactions are accounted for by constitutive relations which are flow regime dependent. The conservation equations are discretized using a finite volume method. An algorithm is created to enable simulations on pipelines made of several sections, and account for the effect of the topography in the simulations. The methodology is applied to the compressible model in order to evaluate the robustness and accuracy of the numerical schemes, especially for the high-resolution Advection Upwinding Splitting Method (AUSM) associated to the compressible model. It also assesses the ability of the method to predict three physical flow regimes, namely stratified, bubbly and terrain-induced slug flows. The terrain-induced slugging study is performed on a slightly inclined (±1.5°) V-section system. The use of hydrodynamic slug correlations for hilly-terrain slugging is discussed. It shows to be conclusive with a good agreement with experimental measurements obtained for slug frequency and slug length predictions. Mechanisms such as the wave formation at the interface, the slug growth and propagation as well as merging slugs, can also be observed by the model. The bubbly model is extensively tested against available data collected by Nottingham University from experimental systems of 70mm and 189mm vertical pipes. In some cases, void fraction predictions are within 10% with experimental data, and pressure predictions within 4%. The simulation results compare well in overall with the measurements. In large diameter pipes, some variations are observed between the numerical and the measured results: especially the model underpredicts the flow at the bottom of the pipe. Limitations of the model for this particular case are highlighted. It is also observed that, in fully-developed flows, the model does give satisfactory predictions.

A new methodology was developed for the numerical simulation of transient two-phase flow in pipes. The method combines high-resolution numerical solvers and adaptive mesh refinement (AMR) techniques, and can achieve an order of magnitude improvement in computational time compared to solvers using conventional uniform grids. After a thorough analysis of the mathematical models used to describe the complex behaviour of two-phase flows, the methodology was used with three specific models in order to evaluate the robustness and accuracy of the numerical schemes developed, and to assess the ability of these models to predict two physical flow regimes, namely stratified and slug flows. The first stage of the validation work was to examine the physical correlations required for an accurate modelling of the stratified smooth and wavy flow patterns, and a new combination of existing correlations for the wall and interfacial friction factors was suggested in order to properly predict the flow features of the experimental transient case investigated. The second and final phase of the work dealt with the complex and multi-dimensional nature of slug flow. This flow regime remains a major and expensive headache for oil producers, due to its unsteady nature and high-pressure drop. The irregular flow results in poor oil/water separation, limits production and can cause flaring. The modelling approached that was adopted here is based on the two-fluid model, which can theoretically follows each formed slug and predicts its evolution, growth and decay, as it moves along the pipe. However, the slug flow study, performed here through a test case above the Inviscid Kelvin-Helmholtz transition from stratified to slug flow, showed that the incompressible two-fluid model used is unable to accurately predict most of the features of this complex flow. Mechanisms such as the interfacial wave formation, the slug growth and propagation, although observed from the simulations, cannot be accurately determined by the model.

This thesis is concerned with the effect of wall waviness on shear flow instability, specifically for the incomprehensiblc flow in a channel. We investigate the stability of the flow in a channel with fixed wavy boundaries using two methods. Firstly the disturbance evolution is calculated using the parabolised stability equations (PSE), which apply to the flow stability at finite Reynolds number, and are solved using a finite-difference marching scheme, marching in the downstream direction. Secondly we employ the triple-deck formulation for channel flow which is valid at asymptotically high Reynolds number and the problem is solved using Floquet theory, making use of the periodic coefficients appearing in the disturbance equations. The mean flow for the PSE analysis is obtained by linearising the Navier-Stokes equations using a perturbation method, valid for small amplitude boundary waviness, Δ. We solve the linear PSE using this periodic mean flow, and it is found that increasing Δ stabilises plane Poiseuille flow near the nose of the neutral curve but has a destabilising effect on the lower branch for higher Reynolds numbers. The nonlinear PSE are used to study thc stability of 2-D finite amplitude waves, and are able to demonstrate the existence of suporcritical equilibrium amplitude solutions, as well as threshold amplitudes separating growing and decaying solutions in the subcritical regime. Wall waviness is found to have a stabilising effect on subcritical disturbances, raising the amplitude needed for instability to occur. Using Floquet theory and decomposing the disturbance equations into Fourier modes enables the high Reynolds number problem to be formulated as an eigenvalue problem. The waviness is found to be able to produce a destabilising effect in agreement with the results for the linear PSE near the lower branch. The method of multiple scales is used to study the wavy channel flow stability at high Reynolds number in the limit of small Δ, which gives an O(Δ 2) correction to the flat boundary eigenvalue, λ. When λ = ±i μ, for boundary wavenumber, μ, we find a degeneracy in the intermediate O(Δ) system of equations due to a resonance ktween a neutrally stable flat-boundary T-S wave and the boundary wave of equal wave-length. New asymptotic scalings are derived in this case to obtain a valid solution.

We have performed direct numerical simulations (DNS) of quasi-2D (that is with flow parameters independent of longitudinal coordinate) decaying and forced turbulence and 3D turbulent channel flows in order to ascertain the sustenance mechanism of near-wall turbulence by investigating the mechanism of streak formation. We found the existence of streaks in quasi-2D flows thus demonstrating that contrary to many proposed theories, feedback from longitudinal flow is not necessary for streak formation. Passive scalars having different mean scalar profiles were introduced in forced quasi-2D and 3D turbulent flows in order to compare the streak spacing of the scalars deduced from two-point correlations of DNS results with results obtained theoretically. It has been found that even for the same vortex structure for all the passive scalars there is a marked variation in streak spacing implying that the preferential streak spacing is not necessarily equal to twice the vortex spacing, as has been suggested by several proposed theories. Moreover, the formation of scalar streaks in a velocity field prescribed as s sum of a mean turbulent velocity profile and random potential perturbations, conclusively supports the fact that organised vortices are not needed for generation of near-wall streaks. It has also been demonstrated that the lift-up mechanism responsible for generation of streaks is also responsible for the cross-flow spacing. The obtained qualitative numerical results are in favour of theory of streak formation based on optimal perturbations (Butler and Farrell, 1993) but at the same time the quantitative agreement is poor. So a modification of the same - Generalized optimal perturbation (Chernyshenko and Baig, 2003) theory has been proposed and it offers significantly better agreement with the DNS results.