Two-Fluid Pipe Flow.

The study of two-fluid pipe flow was largely inspired by the potential application of using less viscous fluid to lubricate very viscous fluids such as heavy crude oil in oil transporting system. In this thesis, starting from the basic assumptions and mathematical formations of the governing equations for general two-phase flows, we first discuss the simple steady solutions of two immiscible fluids flowing coaxially in a pipe. There are basically two types of solutions, one is the stratified solution, and the other is the core-annular solution, in which the viscous phase stays in the center while the less viscous phase forms an annular around it. This solution is favored from the perspective of lubricated pipelining. The numerical results of the linear stability analysis of these solutions are then obtained using a finite element approximation with an iterative eigenvalue solver for the large matrices generated by the approximation. The core-annular flow configuration is, in general unstable due to capillarity, interfacial friction force and Reynolds stress or the combination of the three. In most of the industrial practices, the Reynolds number is so high that the flow of the less viscous phase is turbulent. For these cases we apply a k - epsilon turbulence model to the less viscous phase while assume the viscous core is still laminar and solve for the steady solution. The friction factor, which measures the drag in a pipe system, and the holdup ratio are computed for typical cases. The results are compared with available experimental data and the agreement is rather good.