Effects of head loss, surface tension, viscosity and density ratio on the Kelvin–Helmholtz instability in different types of pipelines

Highlights: • The Kelvin–Helmholtz instability in different types of pipelines is analyzed. • The effects of head losses are different in different types of pipelines. • When the elbow angle is close to 80, the head loss reaches its maximum. We report the effects of head loss, surface tension, viscosity and density ratio on the Kelvin–Helmholtz instability (KHI) in two typical pipelines, i.e., straight pipeline with different cross-sections and bend pipeline. The dynamic governing equations for upper and lower fluids in the two pipes are solved analytically. We find in the straight pipeline with different cross-sections that the relative tangential velocity of fluid decreases with the increase of the head loss, viscosity and density ratio of upper and lower fluids, but it increases with the surface tension; the amplification factor decreases with the increase of the head loss and surface tension but increases with the density ratio of upper and lower fluids; the higher the height of fluid interface is, the more both the relative tangential velocity of fluid and the amplification factor are depressed. In the bend pipeline, the critical tangential velocity of fluid is found to decrease with the increase of the head loss, viscosity and density ratio of upper and lower fluids, but it increases with the surface tension; the amplification factor increases with the head loss and density ratio of upper and lower fluids, but it decreases with the increase of the surface tension; when the elbow angle is close to $80^{\circ }$, the head loss reaches its maximum. The results provide guidance for pipeline design and theoretical prediction for flooding velocity in different types of tubes.