Rotating Flow of Two Immiscible Liquids in a Vertical Concentric Annulus

This paper conducts a numerical and analytical investigation into the impact of the rotation rate on the dynamics of two immiscible liquids flow between vertical concentric cylinders. The governing momentum and energy equations are solved using numerical method. The discretization of momentum and energy equations is realized employing the finite volume method. The correlation between velocity and pressure fields is established using the SIMPLER algorithm, ensuring interface continuity. The flow is induced by radial density gradients resulting from thermal boundary conditions. The inner cylinder is characterized by a dimensionless temperature of 0.5, while the outer cylinder is at -0.5. The adiabatic condition is maintained for horizontal boundaries. The vertical equation of motion incorporates the buoyancy term, assuming axisymmetric flow. The analytical solution considers the flow in one dimension focusing on azimuthal velocity profile. The study explores the impact of an analytical and numerical rotational Reynolds numbers on flow patterns and heat transfer. Both numerical and analytical findings converge effectively, particularly at low rotational rates. The observation that the rotation of the inner cylinder exerts centrifugal forces, impacting the flow of water and oil differentially, serves to validate the assumption of a planar interface.