Linear stability analysis and experimental verification of stratified air–water flow in a horizontal bend

Stratified flow in gas–liquid systems is a basic flow configuration which occurs frequently in industries due to the large density differential between the phases that helps to sustain stable stratification for relatively wide ranges of flow rates. The study on stability of stratified flow and the development of transitional criteria to various flow patterns have been very actively pursued for straight pipes, resulting in a broad understanding of the underlying mechanisms. Beside straight pipes, pipelines contain other fittings, which pose abrupt changes to the flow direction, and hence their impact on the flow stability needs to be ascertained.This study attempts to extend the linear stability analysis of stratified flows in a straight pipe to a horizontal bend. A model for the effect of a horizontal elbow on the transition from stratified to non-stratified patterns using the two-fluid approach is presented. The Inviscid Kelvin–Helmholtz (IKH) and Viscous Kelvin–Helmholtz (VKH) stability criteria for stratified flow transition are derived.Experiments are carried out using air and water in a 0.05 m diameter horizontal pipe work containing an intermediate bend of 0.5 m radius of curvature and the flow pattern observed in the bend is compared with the stability theory. The results show that the IKH and VKH stability criteria for stratified flow in a bend have identical forms as their counterparts in an inclined straight pipe, except that the tilt of the liquid lump in the bend which depends on the liquid velocity replaces the inclination angle for a straight pipe. The stable region is over-predicted by the IKH criterion while the VKH criterion shows good agreement for transition from stratified to slug flow if the liquid surface gradient is taken into account in the solution of the flow parameters under fully developed conditions.The work presented in this paper is of tremendous help to oil production engineers who need to know and control the flow regime transitions in order to avoid problems associated during production. These problems are mainly due to the generation of slug flow which leads to severe unwanted jigging.