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Abstract
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The aim of this research is to simulate a multi-layer flow of the core-annular type in a two-dimensional channel, in which a viscoelastic fluid with the Oldroyd-B model in the core is surrounded by a visco-plastic fluid of the regularized Bingham type. This simulation is based on the volume of fluid method. Flow, concentration and polymeric stress equations are discretized spatially by spectral element method. The velocity correction scheme, as a high order algorithm, is developed for splitting the velocity, concentration, polymeric stress and pressure variables. The present scheme is developed on the base of the Nektar , an open source code which is used for the solution of one-phase Newtonian fluid. The special cases of the flow regime, including one-phase visco-plastic flow, the flow of two Newtonian fluids and the core/annular visco-elastic/Newtonian flow, is considered and studied. Considering a developed flow leads to a nonlinear equation in the plastic region of the flow, which is numerically solved and is called semi-analytic solution and along with the 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, core thickness, Weissenberg number and Reynolds number on the pressure drop, un-yielded region thickness, outlet core thickness and flow morphology is evaluated. This evaluation is in the range of Reynolds number less than 1000, to ensure that the flow is laminar, the Bingham number less than 50, the Weissenberg number less than 7.5 and the viscosity ratio less than 30. The results show that, for the specified Reynolds number, the Bingham number is the most effective parameter on the pressure drop and un-yielded regionthickness. 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-
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