Numerical solution of visco-plastically lubricated multi-layer core-annular flow using Spectral Element Method

The aim of this research is the simulation of multi-layer flows of the core-annular type in a 2-dimensional channels, in which the Newtonian fluid in the core is surrounded by a viscoplastic fluid of the regularized Bingham type as a lubricant. This simulation is based on the volume of fluid technique and in the mixing regions of the two fluids, the stress is achieved by harmonic interpolation. Flow and concentration equations are discretized spatially by spectral element method. The velocity correction scheme, as a high order algorithm, is developed for splitting the velocity and pressure variables for the viscoplastically lubricated two phase flow. Applying the developed flow considerations leads to a nonlinear equation in the plastic region of the flow, which is solved numerically and is called semi-analytic solution. This solution, along with previously published works, is used to validate the spectral element results. The effect of the main parameters of the flow, i.e. Bingham number, viscosity ratio and core thickness on the pressure drop and un-yielded region thickness is evaluated. The results show that, for constant Reynolds number, the Bingham number is the most effective parameter on the pressure drop and un-yielded region thickness, respect to the core flow thickness and viscosity ratio. Also the profiles of secondary variables, including apparent viscosity and shear stress, across the channel section is presented and show that in the interface of the fluids, there is a difference between numerical and semi-analytic solutions due to the mixing of the two fluids.