Waves and Turbulence in Core-Annular Pipe Flow

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...