The distinctive CFD challenges of computational rheology

In this general lecture, we shall first outline the way computational non-Newtonian fluid mechanics differs from conventional computational fluid dynamics (CFD). We do this by briefly outlining the major historical developments in this relatively new field 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 In order to provide a serious challenge to existing numerical codes, we describe some recent unpublished experimental results on flow through a contraction of constant viscosity (Boger) and also shear-thinning elastic liquids.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 flow structures provide the relevant points of contact between experiment and numerical prediction. Numerical codes developed at UWS involving a hybrid finite-element/finite-volume scheme for Oldroyd B and Phan-Thien/Tanner constitutive models are applied to the contraction-flow problems and an encouraging agreement is demonstrated between theory and experiment. Specifically, the dramatic experimental differences between flow 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 refinements to the numerical techniques.