An adaptation of the separable KBKZ equation for comparable response in planar and axisymmetric flow

A specialisation of the 'separable' form of the KBKZ equation [M.H. Wagner, J. Non-Newtonian Fluid Mech. 4 (1978) 39-55] is presented that allows stra in-hardening response to both planar and uniaxial elongation, while simulta neously giving shear-thinning behaviour. The specialisation expresses the s train-damping function in terms of a single invariant measure of strain. It is demonstrated that comparable planar and uniaxial elongational viscositi es are predicted for IUPAC LDPE, with an over-prediction of the first norma l stress difference in shear flow. It is shown that it is possible to fit t ransient data, for an LDPE melt that exhibits strain-hardening, for both pl anar and uniaxial elongational data simultaneously. It is shown that the new damping model gives vortex growth for simulations of both planar and axisymmetric contraction flows of LDPE, in contrast to a popular existing model that has been demonstrated to fail to predict vorte x growth in planar contraction flow [P. Olley, R. Spares, P.D. Coates, J. N on-Newtonian Fluid Mech. 86 (1999) 337-357]. The finite-element based method used to find the flow solution is described including a novel method for implementing streamline tracking. Details are given of the iterative method used to compute flow fields, according to th e stress field, and for the associated method to implement under-relaxation . Two new vortex measures are defined in order to quantify simulated vortic es that can have an 'hourglass' shape (a shape that has been reported exper imentally for LDPE contraction flows). To allow a broad assessment, comparisons are given as geometry type, contra ction ratio, damping model, and the number of available strain-damping para meters are varied. Results for planar and axisymmetric contractions are com pared, and contraction ratios of 8:1 and 4:1 are studied for planar flow. R esults obtained using the new damping model are compared with well-establis hed results obtained using an existing damping model for 4:1 axisymmetric c ontraction flow. The quantitative effects on flow simulations from using 's ingle-beta' and 'multiple-beta' damping functions are assessed. (C) 2000 El sevier Science B.V. All rights reserved.