Numerical solution to the multi- layer core- annular flow of two fluids with different viscosities using Spectral Element Method

The aim of this article is to develop a high order splitting scheme for the simulation of multi- layer core- annular flow of two fluids with different viscosities inside the two-dimensional channel. For this simulation, the incompressible fluids flow equations (Navier- Stokes) and concentration (volume fraction) equation are solved. The two-phase flow is modeled by the volume of fluid technique and with harmonic interpolation. The spectral element method is used for the spatial discretization and Adams- Bashforth method is adopted for the time integration. Velocity correction scheme is developed here as a high order splitting scheme for the coupling issue. To validate the numerical results they are compared with the analytic solution of fully developed flow. This comparison includes outflow velocity profile and pressure gradient. Also, the accuracy of numerical method has been investigated spatially and temporally. The form of core- annular flow has been investigated for various parameters and the results have been compared with experimental and other numerical works. Investigations show that the Reynolds number and core inlet thickness are two important parameters on the pattern of core- annular flow.