Numerical prediction of extensional flows in contraction geometries: hybrid finite volume/element method

Numerical simulation of viscoelastic contraction flows

“…Two rheological equations are considered, namely the constantviscosity Oldroyd-B and the shear-thinning Phan-Thien/Tanner (PTT) models. Accurate solutions are presented over a wide range of the Deborah number (a measure of the elasticity of the flow) extending the attainable values of previous studies [1]. Vortex enhancement was observed for the axisymmetric contraction, with both rheological models, while for the planar contraction vortex enhancement is only observed for the shear-thinning PTT model.…”

“…Concerning fluid rheology, similar parameters are chosen as in previous studies [1,4]. Creeping flow is assumed (Re = 0), with solvent viscosity fraction η S /η 0 = 1/9.…”

“…Several benchmark test cases have emerged in the last decade, such as the viscoelastic flow through contractions (both axisymmetric and planar configurations), the flow through corrugated channels, around cylinders or spheres, stick-slip flows, just to cite a few [2,3]. While for most of these test cases accurate solutions are now established through the independent validation of the results by different research groups (although over a limited range of Deborah numbers), there is still a lack of accurate numerical results for the difficult benchmark flow through contractions [1,4]. Nowadays, another emergent challenge is to establish quantitative agreement between numerical results and experimental observations [5].…”

Time‐dependent algorithms for viscoelastic flow: Finite element/volume schemes

“…The closer the advection velocity is to any given side, the more contribution is sent to the downstream vertex of that side. Our previous work on steady-state problems has proven the efficiency of LDB schemes in dealing with model problems, as well as some complex flows [1,4].…”

“…These schemes were applied successfully to flow past cylinder [1], and to the benchmark flow of an Oldroyd-B fluid through a planar sharp 4:1 contraction [2]. Subsequently, application was extended to various Phan-Thien/Tanner model fluids, contrasting planar and axisymmetric flows through sharp and rounded-corner contractions [3,4]. Such advances were achieved by ensuring consistency in the treatment of flux and complex sourceterms (solution and velocity-gradient dependent), which arise in the constitutive equation.…”