Stationary core-annular flow through a horizontal pipe.

Area of Science:

• Fluid dynamics
• Multiphase flow

Background:

• Core-annular flow is a configuration where a high-viscosity liquid core is surrounded by a low-viscosity annular liquid layer in a horizontal pipe.
• Buoyancy forces arise from density differences between the core and annular layer, influencing flow stability.
• Surface instabilities on the core, such as bamboo and snake waves, are known to generate secondary flows and pressure variations.

Purpose of the Study:

• To theoretically investigate the core-annular flow of immiscible liquids in a horizontal pipe.
• To determine how buoyancy forces acting on the core are counterbalanced by hydrodynamic forces generated by surface waves.
• To compare the effectiveness of snake waves versus bamboo waves in counteracting buoyancy.

Main Methods:

• Theoretical investigation using hydrodynamic-lubrication theory.
• Modeling the core as a rigid body.
• Analyzing the generation of secondary flows and hydrodynamic forces by surface waves.

Main Results:

• Snake waves on the core surface generate lubrication forces that can effectively counterbalance the buoyancy force.
• Bamboo waves on the core surface do not generate sufficient hydrodynamic forces to counteract the buoyancy force.
• Secondary flows induced in the annular layer play a crucial role in force generation.

Conclusions:

• The shape of surface waves significantly impacts the stability of core-annular flow.
• Snake waves provide a mechanism for stabilizing the core against buoyancy-driven displacement.
• Hydrodynamic-lubrication theory is a valuable tool for analyzing forces in such complex fluid systems.