Benchmark solutions of the stabilized computations of flows of fluids governed by the Rolie-Poly constitutive model

Abstract

Recent studies demonstrate that flow induced non-uniformities of concentration can trigger shear banding in the flow of certain viscoelastic fluids. These studies show that the driving mechanisms for such shear banding are related to the coupling of the polymer stresses to an inhomogeneous concentration profile. The Rolie-Poly (RP) viscoelastic constitutive model has been used in such studies since it has been comprehensively subjected to extensive experimental validation with regards to shear banding and has the demonstrated ability to accurately express the rheology of polymer solutions for a wide range of strain rates. The primary aim of this work is to develop an efficient computational methodology that could be used to accurately simulate the flow of complex fluids governed by the Rolie-Poly constitutive equation. The development of such a computational platform is crucially important for the purposes of our follow up studies on the computational analysis of shear banding phenomena by coupling polymer stress with inhomogeneous concentration profile. Our numerical algorithms will be based on the finite volume method (FVM) and will be implemented on the open source software package OpenFOAM®. In this paper, we will present both validation results as well as new benchmark results from our FVM based OpenFOAM®numerical solver for flow of fluids governed by the Rolie-Poly constitutive model. We use two well-known benchmark problems, the lid-driven cavity flow and the 4:1 planar contraction flow problems. In order to stabilize the numerical algorithm at high Weissenberg numbers, we employ either of two stabilization techniques; the Discrete Elastic Viscous Stress Splitting (DEVSS) technique as well as the Log-Conformation Reformulation (LCR) methodology. Validation of our results is done by comparing our (stabilized) numerical results, against data from existing literature. The numerical results obtained for the contraction flow using the LCR stabilization approach are in good agreement with the existing literature for a wider range of Weissenberg numbers. The DEVSS method shows a good agreement only for lower Weissenberg numbers. For the lid-driven cavity flow, good agreement with the existing literature is observed for low Weissenberg numbers using either of the two stabilization techniques.

Numerical Study of Shear Banding in Flows of Fluids Governed by the Rolie-Poly Two-Fluid Model via Stabilized Finite Volume Methods

“…The Finite volume method (FVM) implemented in OpenFOAM is used to discretize the governing equations. For more details, please refer to [37]. The viscoelastic constitutive models, in particular, the Johnson-Segalman, Giesekus, and Rolie-Poly models are added to the viscoelastic solver and the appropriate momentum equations are also built into the solver as necessary.…”

“…where k is a positive constant related to the parameters of the constitutive model. As in Abuga et al [37], we take k = η p , where η p is the polymer viscosity.…”

Computational Analysis of Shear Banding in Simple Shear Flow of Viscoelastic Fluid-Based Nanofluids Subject to Exothermic Reactions

“…Such widespread use of the viscoelastic (polymeric) fluids, for the improvement and enhancement of, say, HTR and Therm-C, emulsion-polymerization, drag-reduction, etc. can be found for example in [1,4,6,[23][24][25][26][27][28][29][30][31][32][33][34].…”

“…Fluid viscoelasticity has indeed received wide attention in this regard, specifically for the improvement of certain industrial, domestic, and medical applications. Such widespread use of the viscoelastic (polymeric) fluids, for the improvement and enhancement of, say, HTR and Therm-C, emulsion polymerization, drag reduction, etc., can be found, for example, in [1,4,6,[23][24][25][26][27][28][29][30][31][32][33][34].…”

Computational-Analysis of the Non-Isothermal Dynamics of the Gravity-Driven Flow of Viscoelastic-Fluid-Based Nanofluids Down an Inclined Plane

“…Noting the fundamental importance of the rheology of the base fluid to the modern applications of nanofluids, the studies, say in [1][2][3] focus attention on non-Newtonian (specifically polymeric) base-fluids under various flow conditions. The widespread importance of non-Newtonian fluids, both the Generalized Newtonian Fluids (GNF) as well as the polymeric (viscoelastic) fluids, in contemporary application is quite straightforward for example [1][2][3]6,8,[25][26][27][28][29][30][31][32][33][34].…”