Characteristic Finite Element Method For Convection Diffusion Problem & Numerical Simulation Of Bubble Behavior

AbstrFive different finite elements for the convection-diffusion problem with a modified charac-teristic finite element scheme are studied in this paper. Then numerical simulations are studied to investigate the motion of bubbles in ionic liquids using an improved volume-of-fluid (VOF) model and DPM model. A coupled Computational Fluid Dynamic (CFD) model and Population Balance Model(PBM) have been applied to study the mass transfer properties for capturing CO2 with ionic liquids solvents.In Chapter 2, firstly, finite element method for the convection-diffusion problem with a mod-ified characteristic finite element scheme is studied. We discuss five-node element, the constrained rotated Q1 element, bilinear finite element and the popular ratated Q1 element. The O(h2) or-der error estimate in L2-norm with respect to the space, one order higher than the expanded characteristic-mixed finite element scheme with order O(h), and the same as the conforming case for a modified characteristic finite element scheme under regular meshes, is obtained by use of some distinct properties of the interpolation operator and the mean value technique, instead of the so-called elliptic projection, which is an indispensable tool in the convergence analysis of the previous literature. Then some numerical results are provided to verify our theoretical analy-sis. Secondly, we apply a nonconforming finite element to the same equation with the expanded characteristic-mixed finite element scheme with respect to the space. When the requirement of the exact solution's regularity is lower, the optimal estimates are obtained as the same as the pre-vious literature for the conforming finite element under regular meshes. We verify our theoretical analysis with some numerical results.In Chapter 3, a numerical simulation is studied to investigate the motion of bubbles in ionic liquids using an improved volume-of-fluid (VOF) model and DPM model. In the improved method, besides the gravity and surface tension, a new force between two phases is added to the momentum equation in order to describe the gas-liquid interaction much rigorously in the ionic liquids which possess some special properties compared with the traditional solvents. In DPM model, a new drag force model is added. The deformation, velocity and equivalent diameter of bubble rising in three ionic liquids, i.e., bmimBF4, bmimPF6 and omimBF4 are simulated and the calculation results are agreed well with the experimental data. Furthermore, the detailed velocity fields and pressure fields around the bubble are also predicted with the proposed numerical simulation models. This work is important for understanding the fluid dynamic performance of bubbles in ionic liquids, and could provide a useful tool for designing a bubble column with ionic liquids as its solvents.Although separating CO2 from flue gas with ionic liquids has been regarded as a new and effective method, the mass transfer properties of the CO2 absorption in these new solvents have still been rarely researched. In Chapter 4, a coupled Computational Fluid Dynamic (CFD) model and Population Balance Model (PBM) have been applied to study the mass transfer properties for capturing CO2 with ionic liquids solvents. Considering the unique properties of ionic liquids, the Eulerian-Eulerian two-flow model with a new drag model is employed for the gas-liquid fluid dynamic simulation. The bubble size distribution is predicted by the PBM method. The gas holdup, interfacial area and bubble size distribution in the bubble column reactor are predicted. The mass transfer rates are estimated with the Higbie's penetration model. Furthermore, the velocity field and pressure field in the reactor are also predicted.