In two-phase gas-liquid flow a variety of flow patterns may be encountered during the distribution of two phases (Bubbly, slug, annular and stratified). Slug flow is one of the most complicated flow patterns observed. The slug flow in vertical, horizontal, and inclined tubes has been reported both experimentally and numerically by number of investigators in the literature. Though, curved tubes or connections are very common in the process industry less attention has been made on the slug flow patterns in curved tubes (e.g. hairpin and U-tube bundle in shell-and-tube application and refrigerator heat exchangers). The curved tubes are used in the process industry for single phase flow due to their high efficiency as heat and mass transfer device and compactness in their structure. The better performance of curved tubes is due to the generation secondary flow when fluid flows across the curve channel [1]. Due to the secondary flow, the fluid flow characteristics are rather complicated since the centrifugal force drives the more rapid fluid in the outer wall of the curve tube while the fluid in the inner wall is slowing down.

In case of two-phase flow, the fluid dynamics get even more complex due to the density difference, phase velocity, and fluid properties. There are some investigations focused on the heat transfer, and frictional performance with the presence of U-tube configurations. The detailed flow patterns in across return bend, [2-3] are relevant to slug flow development in curved tubes. Both studies conducted two-phase flow pattern visualization for the air-water mixtures through horizontal return bends having curvature ratios of 3 - 7.1. They reported some qualitative description about the two-phase flow across the horizontal return bends.

The computational fluid dynamics (CFD) provides the mechanistic insight for the slug flow in pipes. The most of the CFD studies was mainly focused on one unit slug cell, implementing either single phase model with void gas or two phase VOF (Volume of Fraction) model to investigate bubble shape, bubble velocity, film thickness, mass transfer, pressure drop and velocity profile inside the liquid slug.

From the literature it can be seen that practically very little attention has been focused on slug flow development in curved tubes. In the present work the investigation of gas and liquid slugs for Taylor flow in curved tubes has been carried out numerically using CFD. In case of curved tubes due to the curvature the flow is 3D, therefore 2D geometry can not be used to predict the slug flow development. The 3D models for curved tube with premixed feed is considered for the slug flow development study. The development of the gas and liquid slugs in the model geometry at various operating and fluid conditions is investigated.

An empty curved tube with cross-sectional diameter d, coil diameter D, and curvature ratio (D/d) are considered. The gas and liquid are supplied through a single inlet. The mixing and the outlet zones have a length of 10d while the curved zone has an arc of 180⁰. The slug flow studies are carried out considering room temperature, and atmospheric pressure at the exit. The set of governing equations for mass and momentum conservation for the two-phase flow through out the domain were solved using the commercial CFD software package, FLUENT 6.1 [4] which is based on the Control Volume Finite Difference Method (CVFDM). The interface between the two slugs is important in evaluating the performance of the reactor and therefore free surface modelling is necessary. In the present work the Volume of fluid (VOF) is used to track the interface between gas and liquid slugs, which is an implicit free surface reconstruction method. It is a surface-capturing technique applied to a fixed Eulerian mesh, which allows the computation of two-phase flow under the condition that the phases do not mix, i.e. there is a clear interface between air and water.

A segregated time dependent unsteady solver in FLUENT is used. The boundary conditions are: velocity inlet for the gas and liquid feeds, specified as uniform entrance velocity, and outflow for the reactor outlet which treats the flow as fully developed at the exit. The curved geometry is first filled with water, and then the streams are introduced at time zero. The PRESTO (pressure staggering option) scheme is used for the pressure interpolation, the PISO (pressure-implicit with splitting of operators) scheme for the pressure-velocity coupling, second-order up-wind differencing scheme for the momentum equation, the geometric reconstruction scheme for the interface interpolation, implicit body force treatment for the body force formulation, and Courant number 0.25 for the volume fraction calculation. In addition, the time step, the maximum number of iterations per time step, and the relaxation factors is carefully adjusted to ensure convergence.

The grid test is carried out for the curved tube to use an appropriate grid for the slug flow development. The grid sensitivity carried out in the present is in terms of grid density, i.e. number of cells per mm³. A few thousand to ten thousand time steps are required for each run. The slug flow study is carried out by varying parameter values: coil diameter, D, mass flow flux, surface tension, σ (0.03 - 0.1), liquid viscosity, μ_L (0.0001 - 0.001), and wall contact angle of liquid, θ (30 - 150).

A code validation exercises have been carried out by comparing the slug flow development in curved channel with the experimental data reported in the literature. The geometrical parameters and experimental conditions of Wang et. al. [2] are considered, i.e., the tube diameter as 6.9, coil diameters as 3 and 7 mm, the mixture is entering at 50 kg/m².s with vapour quality of 0.001.

It is observed that the present predictions of slug flow development display the phenomenon of flow reversal and slug freezing. As the slug approaching the curved section, the air slug makes a turn to climb up the curved zone by both centrifugal and buoyancy forces. Due to the significant difference in density and the influence of gravity the speed of the air slug is comparatively higher than that of the liquid that is initially in front of the slug. Therefore, the air slug is forced to penetrate the liquid in front of it. The liquid is forced to the outer wall of the curved tube because of the presence of the centrifugal force. The resultant interactions of the air slug and the liquid at the outer wall, air slug is unable to climb the curved zone and is further pushed backwards to become a reversed flow. The original elongated gas slug is separated into two smaller slugs due to the amplitude of reversed liquid in the curved zone.

Further due to the resistance of the buoyancy force the elongated slug entering at the upper tube for the air slug is forced to flow downwards. The portion of slug nose continues to moves further downstream while its main body is still trapped in the curved zone due to buoyancy force (slug freezing). This eventually leads to a separation of the air slug. These phenomenons of flow reversal and slug freezing observed in the present study are in good agreement with the experimental observations of Wang et. al. [2]. For the similar process conditions, the flow reversal phenomenon is not observed with an increases of curvature ratio to 10, which may be due to the comparatively smaill centrifugal forces.

The variation of fluid viscosity, surface tension and wall adhesion is also carried out for slug flow development in curved tubes. It is observed that the viscosity, surface tension and wall surface adhesion moderately impact the slug development. The present study will provide insight into the hydrodynamics in curved tubes and will help in further prediction of heat and mass transfer in such devices.

References

[1] Dean W R, (1927) Note on the motion of fluid in curved pipe. Philosophical Magazine 4, 208 - 223.

[2] Wang, C. C., Chen, I. Y., Huang P-S, (2005) Two-phase slug flow across small diameter tubes with the presence of vertical return bend. International Journal of Heat and Mass Transfer 48 2342 - 2346.

[3] Chen I Y, Yang Y W, Wang C C, (2002) Influence of horizontal return bend on the two-phase flow pattern in a 6.9 mm diameter tube. Canadian Journal Chemical Engineering 80(3), 478 - 484.

[4] FLUENT 6.1 documentation, 2003. Fluent Incorporated, Lebanon, New Hampshire.

Key words: Slug Flow, CFD, Curved tube, Two-phase.