Development of an efficient finite volume computational platform for the simulation of complex flows of complex fluids governed by the Rolie-Poly model - Abuga, Jade Gesare (Department of Mathematics and Applied Mathematics, 2019)
The flow of non-Newtonian fluids, also known as complex fluids, is an important area of fluid mechanics due to their applications in industries such as food processing, mining, chemical and plastic industries. It is therefore essential to understand the flow and general behaviour of such fluids. Examples of these include polymeric liquids (both solutions and melts), immiscible polymer blends, emulsions, suspensions of rigid and deformable particles (such as biological cells, capsules or lipid vesicles) and colloidal dispersions. Polymer melts are a category of fluids known as viscoelastic fluids and it is only recently that different forms of constitutive equations derived as simplified versions of molecular reptation-based models have been developed to describe molten polymers. The most adept mathematical models being the tube-based models which are derived from the Doi-Edwards tube-based model. These constitutive equations are able to replicate experimental data is some fairly complex flows but are not able to do so in some cases, shear-banding phenomena being one of them. Under certain flow conditions, some complex fluids have been shown to exhibit different shear bands in the flow field due to flow-induced material non-homogeneities. It is becoming increasingly clear that non-homogeneities should not be ignored in polymers or other complex fluids since flow-induced nonhomogeneities may, in some instances, be as important as the complex rheology in differentiating the flow behaviour of Newtonian and complex fluids. Thus, with the use of technology to simulate fluid flows, there has been an increase in the research towards viscoelastic models and shear banding. This has also led to an increase in the development of CFD tools to solve such flows. One of the CFD tools is the OpenFOAM CFD viscoelastic solver that has already been developed. Therefore, the development of an efficient finite volume computation platform for complex flows governed by the Rolie-Poly constitutive equation has been presented in this thesis. The test cases of the lid-driven cavity flow and the planar 4:1 contraction flow were used to validate the solver which was used with the OpenFOAM CFD package. Discrete Elastic Viscous Stress Splitting (DEVSS) technique and the Log-conformation Reformulation (LCR) methodology of Fattal and Kupferman were employed to stabilise the numerical algorithm at high Weissenberg number. For the 4:1 planar contraction flow, it is observed that the numerical results using the LCR stabilazation technique are in good agreement for a range of Weissenberg numbers whereas the DEVSS method shows good agreement for low Weissenberg numbers. The numerical results for the lid-driven cavity flow are in good agreement with the existing literature for low Weissenberg numbers for both stabilization techniques. In the course of this thesis however, capacity to deal with Rolie-Poly constitutive equation was added to the rheoTool which is a tool box for simulation viscoelastic fluid flows in OpenFOAM. A subsequent comparison of the numerical results with those from the rheoTooL solver show good agreement. Furthermore, this thesis uses a two-fluid model by coupling the stress to concentration equation to study the shear banding phenomena in Rolie-Poly fluid flow. Validation is done by comparing existing literature of shear bands using the Giesekus and Johnson-Segalman constitutive equations. The numerical results show good agreement with existing literature for the DEVSS stabilization technique.