Numerical simulations are conducted for the wave initiation, growth, and saturation at the oil-water interface in core-annular flow (CAF). The focus is on conditions with a turbulent water annulus, but the laminar water annulus is also considered. The simulation results are compared with lab measurements. The growth rate for the linear instability of different wavelengths in the case of a turbulent water annulus is obtained from two-dimensional (2D) axisymmetric Reynolds-averaged Navier-Stokes (RANS) simulations with the Launder-Sharma low-Reynolds number k-ϵ model. The latter simulation results provide the most unstable wavelength for the turbulent water annulus. Our study also shows the following. The maximum wave growth rate for a turbulent water annulus is significantly higher than for a laminar water annulus. The most unstable wavelength in the simulations is about 25% smaller than in the experiments. The wave amplitude for the different wavelengths in the simulations is typically 17% lower than in the experiments.

DNS and RANS simulations were carried out for core-annular flow in a horizontal pipe and results were compared with experiments carried out with water and oil in our lab. In contrast to most existing studies for core-annular flow available in the literature, the flow annulus is not laminar but turbulent. This makes the simulations more challenging. As DNS does not contain any closure correlations, this approach should give the best representation of the flow (provided a sufficiently accurate numerical mesh and numerical method is used). Various flow configurations were considered, such as without gravity (to enforce an on-average concentric oil core) and with gravity (to allow for eccentricity in the oil core location). Both single-phase and two-phase conditions were considered; single-phase flow refers to the water annulus with imposed wavy wall, whereas two-phase flow includes the determination of the wavy interface. Mesh refinement was carried out to assess the numerical accuracy of the simulation results.

The Reynolds-Averaged Navier Stokes (RANS) with the Launder & Sharma low-Reynolds number k−ε model was used to simulate core-annular flow in the same configuration with vertical upflow as considered by Kim & Choi (2018), who carried out Direct Numerical Simulations (DNS), and by Vanegas Prada (1999), who performed experiments. The DNS are numerically very accurate and can thus be used for benchmarking of the RANS turbulence model. There is a large ratio between the oil and water viscosities, and the density difference between the water and oil is only small. The frictional pressure drop was fixed and the water holdup fraction was varied. Differences between the RANS and DNS predictions, e.g. in the wave structure and in the Reynolds stresses, are discussed. Despite the shortcomings of the considered Launder & Sharma low-Reynolds number k−ε model in RANS, in comparison to DNS, the RANS approach properly describes the main flow structures for upward moving core-annular flow in a vertical pipe, like the travelling interfacial waves in combination with a turbulent water annulus. The Fanning friction factor with RANS is 18% lower than with DNS, and the holdup ratio with RANS is only slightly higher than with DNS (i.e. it has a slightly larger tendency to accumulate water in RANS than in DNS).

When a very viscous liquid (like oil) and a far less viscous liquid (like water) both flow through a pipeline, under certain conditions, the more viscous liquid will migrate to the core of the pipe, while being surrounded by an annulus with the less viscous liquid. This typical flow pattern, referred to as core-annular flow (CAF), was discovered a few decades ago and has drawn much attention from researchers. The less viscous liquid functions as a lubrication layer to reduce the pressure drop, which thus requires far less energy to transport a certain amount of viscous liquid than when the annulus flow is absent. Often oil is used for the laminar core flow and water is used for the laminar or turbulent annulus flow. The main research question in this PhD thesis is how the turbulence in the annulus and the waves at the interface determine the key hydraulic parameters that characterize the core-annular flow. Thereto, a large number of Computational Fluid Dynamics (CFD) simulations were carried out. These are mainly 1D, 2D, and 3D RANS simulations (Reynolds-Averaged Navier Stokes, with the Launder & Sharma low-Reynolds number 𝑘 − 𝜖 model)), but also some DNS were carried out (Direct Numerical Simulations). The simulation results are also compared with experiments carried out in the Delft lab. Four crucial hydraulic quantities are involved in the core-annular flow study, namely: pressure drop, hold up ratio, watercut, and total flow rate. The pressure drop can be non-dimensioned to a Fanning friction factor. From the Fanning friction factor, the lubrication strength of CAF is shown, since the value of the Fanning friction factor is comparable to water only pipe flow under the same mixturebased Reynolds number. The holdup ratio indicates the apparent slip effect between the oil and water; its value is between 1 and 2, because water somewhat accumulates in the core-annular flow. In both the numerical simulations and lab experiment, two parameters are set as input and two parameters appear as output. Understanding the correlation between the four parameters can help to properly design the pipe flow system. The study of the correlation between these four parameters will be presented in Chapter 3 and in the Appendix. The effect of gravity on the CAF depends on the inclination of the pipe. For horizontal pipe flow, gravity acts perpendicular to the pipe wall and introduces a buoyancy force on the oil core. Our simulation starts with concentric oil-water CAF with a flat interface. This flow configuration is unstable for a horizontal pipe and will finally develop into an eccentric oil core with a wavy interface. The waves create a downward force to balance the buoyancy force. Due to the movement of the oil core, a secondary flow will appear in the water layer. From our simulation results, we found how the inertia effect redistributes the pressure on the interface, creating a net downward pressure force that balances the buoyancy force, and prevents the oil core to touch the upper pipe wall. This part will be illustrated in Chapters 2 and 3. For the vertical pipe, gravity acts in the streamwise direction. Detailed DNS simulations were presented by Kim & Choi (2018). In Chapter 5, we repeat the work of Kim & Choi by using RANS, and find a rather good agreement for the Fanning friction factor and holdup ratio between RANS and DNS. Different is that the waves in the RANS simulations are more regular and that RANS predicts higher turbulence than DNS...

Interfacial waves in core-annular pipe flow are studied through two-phase numerical simulations. Here the water annulus is turbulent, whereas the oil core stays laminar. The low-Reynolds number Launder & Sharma k−ε model is applied. By extracting the moving wave shape from the two-phase results and imposing this as a solid boundary in a single-phase simulation for the water annulus gives single-phase results (for the pressure drop and holdup ratio) that are in close agreement with values obtained from the two-phase approach. The influence of wave amplitude and wave length on the pressure drop and hold up ratio is then studied by using the single-phase flow model. This gives insight in the appearance of core-annular flow, where the water-based Fanning wall-friction factor and the hold-up ratio are selected as the most important quantities. The effect of watercut and eccentricity on these quantities is also investigated.

1D, 2D and 3D numerical simulations were carried out with the Reynolds-Averaged Navier-Stokes equations (RANS) for horizontal oil-water core-annular flow in which the oil core stays laminar while the water layer is turbulent. The turbulence is described with the Launder-Sharma low-Reynolds number k−ϵ model. The simulation results are compared with experiments carried out in our lab in a 21 mm diameter pipe using oil and water with a viscosity ratio of 1150 and a density ratio of 0.91. The 1D results represent perfect turbulent CAF (i.e. no gravity, no interfacial waves), the 2D results represent axi-symmetric CAF (i.e. no gravity, with interfacial waves), and the 3D results represent eccentric CAF (i.e. with gravity, with interfacial waves). The simulation results typically show a turbulent water annulus in which the structure of the (high-Reynolds number) inertial sublayer can be recognized. The pressure drop reduction factor (which is the ratio between the pressure drop for CAF and the pressure drop for single phase viscous oil flow) for the 2D and 3D results is about the same, but its value is about 35% higher than in the experiment. The hold-up ratio in the 3D model is close to the experimental value, but the 2D prediction is slightly lower. The eccentricity predicted by the 3D simulations is much higher than in the experiment. Most likely, the observed differences between the simulations and the experiments are due to limitations of using a low-Reynolds number k−ϵ model. In particular the water layer at the top in the 3D results shows a relaminarization, which might be absent in the experiment.

Core-annular flow is an efficient way of transporting viscous oil through a pipeline. A sharp increase in the pressure drop will occur when the oil waves at the water-oil interface touch the pipe wall. Depending on the oil and pipe material physical properties, the oil may adhere to the wall leading to fouling. Therefore, a necessary requirement for the onset of oil fouling of the pipe wall is that the flow hydrodynamics allow the oil to reach and touch the wall. With respect to the problem statement, this study deals with finding the hydrodynamic conditions under which core-annular flow becomes unstable and the oil waves touch the pipe wall. The method that is followed is to resolve the first-principle set of equations that describe the hydrodynamics: the Reynolds-Averaged Navier-Stokes (RANS) equations are solved using Computational Fluid Dynamics (CFD) in the opensource package OpenFOAM. Simulations were carried out for the horizontal pipe with two diameters (10.5 and 21 mm), at a range of imposed pressure drops and water holdup fractions (giving the mixture velocity and watercut as output). Most simulations were carried out for an oil to water viscosity ratio of 1040 (but also a variation of this was considered). For each value of the pressure drop (or mixture velocity) there is a critical value of the watercut below which the oil reaches the pipe wall. This critical value of the watercut is lower for the larger pipe diameter of 21 mm, namely about 9.6%, than for the smaller pipe diameter of 10.5 mm, namely about 14% (for a viscosity ratio m = 1040). Wall touching occurs when the mixture velocity is too low, but this lower limit is significantly higher for the larger pipe diameter of 21 mm, namely about 1.1 m/s, than for the smaller pipe diameter, namely about 0.3 m/s (for a viscosity ratio m = 1040). The main conclusion is that a state-of-art CFD approach is capable of simulating the growth of waves at the oil-water interface until they touch the pipe wall, which is a necessary condition for the onset of fouling.