Numerical Simulation of Rheological Models for Complex Fluids Using Hierarchical Grids

• Published in: Polymers 2022-11, Vol.14 (22), p.4958
• Main Authors: Castillo-Sánchez, Hugo A, de Souza, Leandro F, Castelo, Antonio
• Format: Article
• Language: English
• Subjects: Analysis; Computational fluid dynamics; Convergence; Drilling; Finite difference method; Finite element method; Flow velocity; Fluid dynamics; Fluid flow; Fluids; Interpolation; Mathematical models; Meshless methods; Model accuracy; Numerical analysis; Plug flow; Rheological properties; Rheology; Shear stress; Simulation; Simulation methods; Software; Surfactants; Velocity distribution; Viscoelastic fluids; Viscoelasticity; Viscosity; Vorticity; Yield stress
• ISSN: 2073-4360; 2073-4360
• DOI: 10.3390/polym14224958

In this work, we implement models that are able to describe complex rheological behaviour (such as shear-banding and elastoviscoplasticity) in the system, which is a recently developed Computational Fluid Dynamics (CFD) software that can simulate Newtonian, Generalised-Newtonian and viscoelastic flows using finite differences in hierarchical grids. The system uses a moving least squares (MLS) meshless interpolation technique, allowing for more complex mesh configurations while still keeping the overall order of accuracy. The selected models are the Vasquez-Cook-McKinley (VCM) model for shear-banding micellar solutions and the Saramito model for viscoelastic fluids with yield stress. Development of solvers and numerical simulations of inertial flows of these models in 2D channels and planar-contraction 4:1 are carried out in the system. Our results are compared with those predicted by two other methodologies: the OpenFOAM-based software that uses the Finite-Volume-Method and an in-house code that uses the Vorticity-Velocity-Formulation ( ). We found an excellent agreement between the numerical results obtained by these three different methods. A mesh convergence analysis using uniform and refined meshes is also carried out, where we show that great convergence results in tree-based grids are obtained thanks to the finite difference method and the meshless interpolation scheme used by the . More importantly, we show that our methodology implemented in the system can successfully reproduce rheological behaviour of high interest by the rheology community, such as non-monotonic flow curves of micellar solutions and plug-flow velocity profiles of yield-stress viscoelastic fluids.