An approximation to the KBKZ constitutive equation

Abstract This work describes an approximation to a KBKZ based equation which completely separates shear and elongational contributions to visco-elastic stresses. This approximation has two significant advantages over a normal KBKZ implementation: (i) computationally intensive procedures associated with computing the Finger-strain tensor are largely avoided, and (ii) the approximation is relatively easy to understand intuitively, hence illustrating some important mechanisms implicit in the KBKZ. Time stepping issues are examined, of relevance to all time-integral flow equations. The approximation is applied to an established problem for which quantitative numerical and experimental results are available in the literature (Kiriakidis et al. [1]). The results of the approximation are compared directly to results simulated using its parent KBKZ equation—this in turn is compared directly with independent published results. It is concluded that the approximation has computational benefits over a full KBKZ solution, notably as flow rates increase. Results from the approximation compare closely with results from the full KBKZ solution for normal stresses in regions of low shear, and shear stresses generally. Vortex intensity is significantly over-predicted as a result of isolating shear and normal strains. Due to the intuitive nature of the approximation, the method could constitute a valuable conceptual ‘bridge’ for workers developing time integral codes.

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