Necessary corrections to an inelastic mixed-viscosity model to efficiently and accurately solve for the flow of polymer solutions around a sphere

It is well known from existing literature that the molecular constitutive models face convergence issues in CFD simulations at higher flow rates. Hence, this article investigates the viability of a numerically efficient approximation that potentially replaces such models by a GNF-based approach, by closely mimicking flow and stress profiles. As a test case, we use the flow of polymer solutions, modelled by FENE-P, around a sphere. Note, the FENE-P is frequently used as a constitutive model for polymer solutions. First, the flow fields predicted by FENE-P are compared with an equivalent GNF model (with the Carreau-Yasuda serving as the representative GNF in this study). Despite efforts to align the viscosity-shear rate dependence and thus creating equivalent models, the GNF model exhibits notable shortcomings, particularly due to neglect of chain stretching, especially near the stagnation points. Subsequently, an attempt is made to address this limitation by introducing extensional components to the local viscosity. Various inelastic models exist in literature for this aspect, among which the most recent one, the GNF-X formulation [Journal of Rheology 64, 493 (2020)] is selected. However, this formulation predicts significantly large stresses at the stagnation regions relative to FENE-P as well as fails to exhibit the asymmetry in stress and flow profiles. Consequently, we propose appropriate corrections to be added (termed as GNF-XM), which enables successful predictions. The asymmetry and drag coefficients from the GNF-XM agree well with the predictions from FENE-P across all flow rates. Notably, being inelastic and easier to converge, computational times are significantly lower than those for FENE-P, particularly at higher flow rates. This suggests a promising, highly efficient GNF-based approximation to FENE-P, with potential applicability to other complex constitutive models. Note, such an inelastic model would be helpful for polymer processing applications, particularly for faster design estimates. The corrections are physical in origin and independent of the details of the GNF-X formulation, which can be added to any given inelastic mixed-viscosity formulation.

Graphical abstract