Three-dimensional modelling of generalized Newtonian fluids in domains including obstructions - Noel R.T. Boukanga (2010)
Three dimensional flow regimes are encountered in many types of industrial flow processes such as filtration, mixing, reaction engineering, polymerization and polymer forming as well as environmental systems. Thus, the analyses of phenomena involved fluid flow are of great importance and have been subject of numerous ongoing research projects. The analysis of these important phenomena can be conducted in laboratory through experiments or simply by using the emerging computational fluid dynamics (CFD) techniques. But when dealing with three dimensional fluid flow problems, the complexities encountered make the analysis via the traditional experimental techniques a daunting task. For this reason, researchers often prefer to use the CFD techniques which with some care taken, often produce accurate and stable results while maintaining cost as low as possible. Many CFD codes have been developed and tested in the past decades and the results have been successful and thus encouraging researchers to develop new codes and/or improve existing codes for the solutions of real world problems. In this present project, CFD techniques are used to simulate the fluid flow phenomena of interest by solving the flow governing equations numerically through the use of a personal computer. The aim of this present research is to develop a robust and reliable technique which includes a novel aspect for the solution of three dimensional generalized Newtonian fluids in domains including obstructions, and this must be done bearing in mind that both accuracy and cost efficiency have to be achieved. To this end, the finite element method (FEM) is chosen as the CFD computational method. There are many existing FEM techniques namely the streamline upwind Petrov-Galerkin methods, the streamline diffusion methods, the Taylor-Galerkin methods, among others. But after a thorough analysis of the physical conditions (geometries, governing equations, boundary conditions, assumptions …) of the fluid flow problems to be solve in this project, the appropriate scheme chosen is the UVWP family of the mixed finite element methods. It is scheme originally developed to solve two dimensional fluid flow problems but since the scheme produced accurate and stable results for two dimensional problems, then attempt is made in this present study to develop a new version of the UVWP scheme for the numerical analysis of three dimensional fluid flow problems. But, after some initial results obtained using the developed three dimensional scheme, investigations were made during the course of this study on how to speed up solutions’ convergence without affecting the cost efficiency of the scheme. The outcomes of these investigations yield to the development of a novel scheme named the modified three dimensional UVWP scheme. Thus a computer model based on these two numerical schemes (UVWP and the Modified UVWP) is developed, tested, and validated through some benchmark problems, and then the model is used to solve some complicated tests problems in this study. Results obtained are accurate, and stable, moreover, the cost efficiency of the computer model must be mentioned because all the simulations carried out are done using a simple personal computer.