Core-annular flow through a horizontal pipe
The purpose of the MSc-project is to study the flow of a high-viscosity liquid surrounded by a low viscosity liquid through a horizontal pipe (an example is given in figure 1). This core-annular flow is very interesting from a practical and scientific point of view. It can, for instance, be used to transport a very viscous oil through a pipeline by lubricating it with water. There is also a growing interest in the literature to use this flow pattern for micro-fluidic applications.
Much attention has been paid in the literature to core-annular flow. Joseph and Renardy [1] have written a book about it. There are several review articles, see for instance Oliemans and Ooms [2] and Joseph et al. [3]. Most publications deal with the development of waves at the interface between the high-viscosity liquid and the low-viscosity one, see Bai et al. [4] and Li and Renardy [5]. These studies deal with vertical core-annular flow (the core has a concentric position in the pipe). In that case the buoyancy force on the core, due to a density difference between the two liquids, is in the axial direction of the pipe. It is also important to pay attention to core-annular flow through a horizontal pipe. When the densities of the two liquids are different, gravity will push the core off-center in that case. Experimental results suggest that under normal conditions a steady eccentric core-annular flow (rather than a stratified flow) is achieved. Attention must be given to the explanation of the levitation mechanism. The following will happen if the core moves from a concentric position to a slightly eccentric one owing to a small difference in density between the core liquid and annular liquid. The pressure distribution in the liquid in the narrow part of the annulus will intensify and the pressure in the wide part of the annulus will relax due to the movement of the waves at the core-annular interface with respect to the pipe wall. A larger pressure will be generated in the narrow part of the annulus which can levitate the core. This explanation was indeed proved by Ooms et al. [6]. In their numerical calculations they studied two different cases: in one case they started with a smooth interface between the core and the annulus and in the other they started with an interface on which already a wave of finite amplitude was present. Levitation occurred in both cases.
An experimental set-up has been constructed (see figure 2) to study in detail core-annular flow in a horizontal pipe with special attention for the levitation mechanism. The pipe has an inner diameter of 21 mm and is about 8 m long. There are also bends, so that also core-annular flow in a bend can be investigated. The liquids are a very viscous oil (with a viscosity that is 2700 times larger than the water viscosity at room temperature) and water. The pressure drop over the pipe has been measured as a function of the throughputs of oil and water. The pressure drop reduction of core-annular flow compared to the flow of oil alone at the same oil throughput has been studied in detail. Also measurements have been made of the core eccentricity and wave shape at the interface. The experimental results were compared with the numerical ones derived using the method as described by Ooms et al. [6]. The purpose of the new study is to investigate the influence of the oil viscosity. This viscosity depends strongly on the oil temperature. So the plan is to extend the experimental set-up in such a way, that the oil temperature can be raised to a value between 30 ◦C and 40 ◦C. The oil viscosity is then about 3 to 4 times lower than the one at room temperature. The expectation is that with decreasing oil viscosity core-annular flow becomes increasingly difficult and at too low viscosity even impossible. It is important (from a scientific and practical point of view) to find out where this transition is and which phenomena then occur. This experimental study will again be supported by numerical calculations.
[1] D.D. Joseph and Y.Y. Renardy, Fundamentals of two-fluid dynamics, part II: Lubricated transport, drops and miscible liquids, Springer-Verlag, New York, (1993).
[2] R.V.A. Oliemans and G. Ooms, Core-annular flow of oil and water through a pipeline, Multiphase Science and Technology (ed. G.F. Hewitt, J.M. Delhaye and N. Zuber), vol. 2, Hemisphere, (1986), Washington.
[3] D.D. Joseph, R. Bai, K.P. Chen and Y.Y. Renardy, Core-annular flows, Ann. Rev. Fluid Mech. 29, (1999), 65
[4] R. Bai, K. Kelkar and D.D. Joseph, Direct simulation of interfacial waves in a high-viscosityratio and axisymmetric core-annular flow, J. Fluid Mech. 327, (1996), 1.
[5] J. Li and Y.Y. Renardy, Direct simulation of unsteady axisymmetric core-annular flow with high viscosity ratio, J. Fluid Mech. 391, (1999), 123.
[6] G. Ooms, M.J.B.M. Pourquie and J.C. Beerens, On the levitation force in horizontal coreannular flow with a large viscosity ratio and small density ratio, Phys. Fluids 25, (2013), 032102.