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A high resolution spectral element approximation of viscoelastic flows in axisymmetric geometries using a DEVSS-G/DG formulation

Kynch, Ross and Phillips, Timothy Nigel 2017. A high resolution spectral element approximation of viscoelastic flows in axisymmetric geometries using a DEVSS-G/DG formulation. Journal of Non-Newtonian Fluid Mechanics 240 , pp. 15-33. 10.1016/j.jnnfm.2016.12.008

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Abstract

The discretisation of benchmark viscoelastic flow problems in axisymmetric geometries using the spectral element method is considered. The computations are stabilized using the DEVSS-G/DG formulation of the governing equations. A decoupled approach is employed in which the conservation equations are solved for velocity and pressure and the constitutive equation (Oldroyd-B and Giesekus) are solved for the polymeric component of the extra-stress tensor. The method is validated for the start-up of transient Poiseuille flow for which an analytical solution exists. A comprehensive set of results is presented for flow past a fixed sphere for the Oldroyd B and Giesekus models. Excellent agreement is found with results in the literature on the drag experienced by the sphere. Evidence is provided which shows the existence of a limiting Weissenberg number due to the inability to resolve the high gradients in axial stress in the wake of the sphere through polynomial enrichment. The shear-thinning property of the Giesekus model leads to a reduction in drag compared to the Oldroyd B model at equivalent values of the Weissenberg number and viscosity ratio. The numerical simulations eventually fail to converge for the Giesekus model which suggests that factors other than solely extensional properties are responsible for this behaviour. The influence of the Reynolds number and, for the Giesekus model, the mobility parameter on the drag coefficient is also investigated and discussed.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Advanced Research Computing @ Cardiff (ARCCA)
Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Viscoelastic fluid; Flow past a sphere; Drag; Spectral element method; DEVSS-G; Discontinuous Galerkin
Publisher: Elsevier
ISSN: 0377-0257
Funders: Engineering and Physical Sciences Research Council (EPSRC)
Date of First Compliant Deposit: 3 January 2017
Date of Acceptance: 28 December 2016
Last Modified: 25 May 2018 14:17
URI: http://orca.cf.ac.uk/id/eprint/97136

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