Numerical simulation of thixotropic–viscoelastic models for structured fluids in hierarchical grids

Abstract

In the present work, we implement thixotropic–viscoelastic models in the HiGFlow system, which is a recently developed Computational Fluid Dynamics software that is able to simulate Newtonian, Generalized-Newtonian and viscoelastic flows using finite differences in tree-based grids. The system uses a moving least squares meshless interpolation technique, allowing to use more complex mesh configurations, still keeping the overall order of accuracy. We provide here a brief introduction to each of the implemented models (the Bautista–Manero–Puig, the Modified-Bautista, the NM_τp and NM_T models), where we describe their parameters, their strengths and their limitations. Unlike previous numerical works focused on this kind of fluids, non-zero Reynolds number numerical simulations of these models are carried out here in HiGFlow using different geometries like 2D channels, planar contraction 4:1 and 4:1:4 and our results are compared with those predicted by RheoTool, an open-source toolbox based on OpenFOAM. Although the transient numerical solutions differ, we observe that there is an excellent agreement in the steady-state profiles obtained in both software. A discussion of our results and their physical interpretation, a comparison with previously published results in the literature and a deep analysis of the corner vortex behaviour in the contraction geometries are also presented. Moreover, we show that our methodology offers flexibility and stability in the numerical simulations of thixotropic–viscoelastic flows for structured fluids, which allows the users to accurately simulate rheological behaviour of interest.