Numerical simulation of a thixotropic-viscoelastic model in contraction geometries

Abstract

This work presents a comprehensive numerical implementation of a viscoelastic thixotropic model known as the modified-Bautista–Manero (MBM) model (a model widely used to characterize the rheological behavior of wormlike micellar solutions). This implementation is integrated into the OpenFOAM computational fluid dynamics software, specifically using the rheoTool library. In contrast to previous studies, our approach includes simulations of inertial flows and we account for convective terms within all the governing equations. Moreover, we use two numerical techniques that have been proven to be efficient methods in computational simulations of viscoelastic fluids through a planar contraction: (1) the high-resolution scheme called convergent and universally bounded interpolation scheme for the treatment of advection to discretize the convective terms of the momentum, viscoelastic, and thixotropic equations; and (2) the logarithm-conformation reformulation to tackle the high-Weissenberg number problem. This expansion of the model's scope results in a more realistic representation of the fluid's behavior and, consequently, more accurate computational results. To validate the implementation of the MBM model, we performed numerical simulations in two different industrial-relevant geometries: the planar 4:1 contraction and the 4:1:4 contraction–expansion configurations. Two fluids with different structural responses are studied: one with quick structural recovery and the other with mildly slow recovery. The numerical method developed in this work allowed us to run stable simulations of these fluids up to Reynolds and Deborah number values of Re = 1.11 and De = 14.0, respectively, and the influence of inertial, viscoelastic, and thixotropic effects on various flow field variables is investigated. These variables include velocity, viscosity, normal stresses, and corner vortex size. Transient and steady solutions of corner vortexes across a range of Deborah and Reynolds numbers are also presented. In addition, the results obtained in this work are also directly compared with numerical simulations obtained using the non-thixotropic rubber network-based exponential Phan-Thien–Tanner model. For the planar 4:1 contraction simulations, the analysis of the results is based on three dimensionless numbers (the viscoelastic Mach, the elasticity, and the thixoelastic numbers), which allows to conclude that vortex enhancement is mainly seen when high elasticity is coupled with quick structural reformation and very low inertial effects. We further report from the planar 4:1:4 contraction–expansion results that an increase in inertia leads both to vortex inhibition in the upstream channel and to slight vortex enhancement in the downstream channel. Finally, we demonstrate the strong influence of fluid convection on fluidity profiles and on the size of the upstream/downstream corner vortex.