3D simulation of the Hierarchical Multi-Mode Molecular Stress Function constitutive model in an abrupt contraction flow
KeywordMolecular stress function Hierarchical multi-mode molecular stress function HMMSF Simulation Abrupt contraction Vortex Birefringence Stress optical coefficient
Molecular stress function
Hierarchical multi-mode molecular stress function (HMMSF)
Stress optical coefficient
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AbstractA recent development of the Molecular Stress Function constitutive model, the Hierarchical Multi-Mode Molecular Stress Function (HMMSF) model has been shown to fit a large range of rheometrical data with accuracy, for a large range of polymer melts. We develop a 3D simulation of the HMMSF model and compare it to experimental data for the flow of Lupolen 1840H LDPE through an abrupt 3D contraction flow. We believe this to be the first finite element implementation of the HMMSF model. It is shown that the model gives a striking agreement with experimental vortex opening angles, with very good agreement to full-field birefringence measurements, over a wide range of flow rates. A method to give fully-developed inlet boundary conditions is implemented (in place of using parabolic inlet boundary conditions), which gives a significantly improved match to birefringence measurements in the inlet area, and in low stress areas downstream from the inlet. Alternative constitutive model parameters are assessed following the principle that extensional rheometer data actually provides a ‘lower bound’ for peak extensional viscosity. It is shown that the model robustly maintains an accurate fit to vortex opening angle and full-field birefringence data, provided that both adjustable parameters are kept such that both shear and extensional data are well fitted.
CitationOlley P, Gough TD, Spares R and Coates PD (2022) 3D simulation of the Hierarchical Multi-Mode Molecular Stress Function constitutive model in an abrupt contraction flow. Journal of Non-Newtonian Fluid Mechanics. 304: 104806.
Link to publisher’s versionhttps://doi.org/10.1016/j.jnnfm.2022.104806
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A study of the quadratic molecular stress function constitutive model in simulationOlley, Peter (2004)Constitutive models that conform to separable KBKZ specification have been shown to fit steady-state strain hardening rheological data in planar and uniaxial elongational flows, but with inaccuracy in the rate of strain hardening. The single parameter Molecular Stress Function model of Wagner [Rheol. Acta, 39 (2000), 97-109] has been shown to accurately fit the rise-rate in experimental data for a number of strain hardening and strain softening materials. We study this models accuracy against the well characterised IUPAC LDPE data, and present a method for full implementation of this model for flow solution which is suitable for incorporating into existing separable KBKZ software. A new method for particle tracking in arbitrarily aligned meshes, which is efficient and robust, is given. The Quadratic Molecular Stress Function (QMSF) model is compared to existing separable KBKZ based models, including one which is capable of giving planar strain hardening; the QMSF is shown to fit experimental rheological and contraction flow data more convincingly. The issue of `negative correction pressures¿ notable in some Doi-Edwards based models is addressed. The cause is identified, and leads to a logical method of calculation which does not give these anomalous results.
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A modification of the convective constraint release mechanism in the molecular stress function model giving enhanced vortex growthOlley, Peter; Wagner, M.H. (2006)The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [J. Rheol. 45 (2001), 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J. non-Newt. Fluid Mech., 3 (1977), 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements.