The Distinctive Cfd Challenges of Computational Rheology

In this general lecture, we shall rst outline the way computational non-Newtonian uid mechanics di ers from conventional CFD. We do this by brie y outlining the major historical developments in this relatively new eld of science, which is conveniently called Computational Rheology. To illustrate essential features, we limit the discussion to the Oldroyd B, UCM and Phan-Thien/Tanner constitutive models. In order to provide a serious challenge to existing numerical codes, we describe some recent unpublished experimental results on ow through a contraction of constant-viscosity (Boger) and also shear-thinning elastic liquids. Both planar and axisymmetric contractions are of interest, and pressure drops and observed ow structures provide the relevant points of contact between experiment and numerical production. Numerical codes, developed at UWS involving a hybrid nite element/ nite volume scheme for Oldroyd B and Phan-Thien/Tanner constitutive models, are applied to the contractionow problems and an encouraging agreement is demonstrated between theory and experiment. Speci cally, the dramatic experimental di erences between ow in planar and axisymmetric contractions and between constant-viscosity and shear-thinning polymer solutions are mirrored in the numerical predictions, at least in a qualitative sense. Notwithstanding these encouraging developments, the review ends with a realistic assessment of the challenges still awaiting computational rheologists, with particular reference to the choice of constitutive model and the possibility of further re nements to the numerical techniques.