Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 52 11 2019 02 09 Numerical Solution of Viscoplastically Lubricated Multi-layer Core-Annular Flow Using the Spectral Element Method Numerical Solution of Viscoplastically Lubricated Multi-layer Core-Annular Flow Using the Spectral Element Method 3107 3124 3283 10.22060/mej.2019.14961.5984 FA Mehran Parsaei PhD Student/ Yazd University Mohammad Sefid Yazd University Ali Akbar Dehghan Mech. Eng. Dept, Faculty of Engineering, Yazd University, IRAN Azadeh Jafari Assistant Professor, School of Mechanical Engineering Ehsan Izadpanah Assistant Professor, Persian Gulf University Journal Article 2018 09 11 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 Newtonian fluid in the core is surrounded by a viscoplastic fluid of the regularized Bingham type. This simulation is based on the volume of fluid method. Flow and concentration equations are discretized spatially by the spectral element method. The velocity correction scheme, as a high order algorithm, is developed for splitting the velocity and pressure variables. 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,<br />i.e. Bingham number, viscosity ratio and core thickness on the pressure drop and un-yielded region thickness is evaluated. The results show that the Bingham number is the most effective parameter on the pressure drop and un-yielded region thickness. Also the profiles of secondary variables, including apparent viscosity and shear stress, across the channel section are presented and show that in the interface of the fluids, there is a difference between numerical and semi-analytic solutions. 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 Newtonian fluid in the core is surrounded by a viscoplastic fluid of the regularized Bingham type. This simulation is based on the volume of fluid method. Flow and concentration equations are discretized spatially by the spectral element method. The velocity correction scheme, as a high order algorithm, is developed for splitting the velocity and pressure variables. 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,<br />i.e. Bingham number, viscosity ratio and core thickness on the pressure drop and un-yielded region thickness is evaluated. The results show that the Bingham number is the most effective parameter on the pressure drop and un-yielded region thickness. Also the profiles of secondary variables, including apparent viscosity and shear stress, across the channel section are presented and show that in the interface of the fluids, there is a difference between numerical and semi-analytic solutions. https://mej.aut.ac.ir/article_3283_c819904dde95535c60452b16c1c494f6.pdf