Finite element computations of viscoelastic two-phase flows using local projection stabilization

Venkatesan, J and Ganesan, S (2020) Finite element computations of viscoelastic two-phase flows using local projection stabilization. In: International Journal for Numerical Methods in Fluids .

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Abstract

A three-field local projection stabilized (LPS) finite element method is developed for computations of a three-dimensional axisymmetric buoyancy driven liquid drop rising in a liquid column where one of the liquid is viscoelastic. The two-phase flow is described by the time-dependent incompressible Navier-Stokes equations, whereas the viscoelasticity is modeled by the Giesekus constitutive equation in a time-dependent domain. The arbitrary Lagrangian-Eulerian (ALE) formulation with finite elements is used to solve the governing equations in the time-dependent domain. Interface-resolved moving meshes in ALE allows to incorporate the interfacial tension force and jumps in the material parameters accurately. A one-level LPS based on an enriched approximation space and a discontinuous projection space is used to stabilize the numerical scheme. A comprehensive numerical investigation is performed for a Newtonian drop rising in a viscoelastic fluid column and a viscoelastic drop rising in a Newtonian fluid column. The influence of the viscosity ratio, Newtonian solvent ratio, Giesekus mobility factor, and the Eötvös number on the drop dynamics are analyzed. The numerical study shows that beyond a critical Capillary number, a Newtonian drop rising in a viscoelastic fluid column experiences an extended trailing edge with a cusp-like shape and also exhibits a negative wake phenomena. However, a viscoelastic drop rising in a Newtonian fluid column develops an indentation around the rear stagnation point with a dimpled shape.

Item Type:	Journal Article
Publication:	International Journal for Numerical Methods in Fluids
Publisher:	John Wiley and Sons Ltd
Additional Information:	The copyright of this article belongs to Wiley
Keywords:	Drops; Finite element method; Navier Stokes equations; Newtonian liquids; Stabilization; Steady flow; Two phase flow, ALE approach; Drop dynamics; Giesekus model; Local projection stabilizations; Vis-coelastic fluids, Viscoelasticity
Department/Centre:	Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited:	16 Jun 2020 09:26
Last Modified:	16 Jun 2020 09:26
URI:	http://eprints.iisc.ac.in/id/eprint/64597

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