| Gas-liquid two-phase flows in a micro-channel appear in a variety of energy, environ-mental engineering, and engineering applications. These issues are common to problems related to the strategic implementation of sustainable development such as geologic seques-tration of carbon dioxide and clean energy. Owing to its complexity, such as the interaction in and between phases, and the large computational area, significant challenges arise when it comes to deep understanding of the flow pattern and internal mechanism of these complex problems. On this condition, the following work is done using the lattice Boltzmann equa-tion (LBE):the interaction in and between fluids is analysed; the model used to capture the interface distribution is proposed, the boundary condition used to treatment the interaction between the fluid and the solid wall is given, and the boundary condition for the two-phase flows in larger and infinite area is designed. By using the proposed model and boundaries, flow patterns of near-critical CO2in microchannels and the liquid droplet dynamic behavior on a hydrophobic surface of a gas flow channel in the proton exchange membrane fuel cells are studied. The contents of the present thesis include:(1) The effects of the force schemes on interfacial properties of two-phase systems, such as the mass conservation properties, the density at equilibrium state, spurious velocity, and the Galilean invariance, are studied systematically. First, based on the theoretical anal-ysis, we find that the isotropic central scheme can ensure global mass conservation, while the mixed scheme does not. The degree of mass violation is related to the grid resolution, fluid velocity, and density variation. In order to test its correctness, some numerical simu-lations including a static droplet in different lattices, a two-phase flow system subject to a body force, and phase separation process of a two-phase system are performed. Numerical simulation results confirm the theoretical results, and it is observed that due to the effects of discretization errors and the spurious currents, the mass changes with the pressure form of the interaction force are usually larger than those with the potential form. Second, it is found that the liquid and vapor densities at equilibrium predicted by the LBE with the mixed scheme fit better with the theoretical values than that with the isotropic central scheme, and sometimes the spurious currents can be removed with the model. Third, theoretical analysis indicates that the LBE with the mixed scheme may violate the Galilean invariance, and the test of two-phase flows in a moving channel verifies the theoretical prediction.(2) A lattice Boltzmann model for two-phase flows with accurate density profile is proposed. An explicit expression between the density and the interaction force is derived by solving the proposed LBE model directly for a two-phase system with a flat interface. The theoretical result shows that the density errors always exist in the LBE model at the discrete level due to the imbalance between the density and the interaction force, and the errors are proportional to the square of Courant-number. From the theoretical analysis a lattice Boltzmann equation (LBE) model for two-phase flows is proposed based on the lax-Wendrof scheme, which has an adjustable Courant-Friedrichs-Lewy (CFL) number. By adjusting the CFL number, the density profile predicted by this model coincides well with the theoretical result.(3) Wetting boundary condition for two-phase lattice Boltzmann method is studied. A boundary condition used in phase field method is incorporated into the model proposed in this thesis, which not only can specify contact angle prescribed, but also can eliminate the spurious variation in the order parameter seen in previous implementations. The boundary condition is validated through investigations of the dynamic behaviors of a droplet sliding along the wall, capillary intrusion, and a droplet moving in a microchannel. From the simu-lations, we find that a larger range of contact angles can be reproduced at higher accuracy.(4) In order to study the flows in a very large or infinite long channel, outflow boundary conditions are designed and analysed. Three types of OBCs that are widely used in the LBE for single-phase flows, i.e., the Neumann boundary condition, the convective boundary con-dition, and the extrapolation boundary condition, are extended to a two-phase LBE method and their performances are investigated from the view of numerical accuracy and stability. The numerical results indicate that the Neumann boundary condition and the extrapolation boundary condition, with poor numerical stability and accuracy, usually are not able to give satisfactory predictions, while the type of convective boundary conditions work well. Par-ticularly, when the average velocity is chosen as the characteristic velocity, the convective boundary condition seems to be the most satisfactory one.(5) The proposed model and boundary conditions are applied to simulations of flow patterns of near-critical CO2in microchannels, and two effects, i.e., the volume number of CO2and the wettability of the wall on the flow patterns are studied, and four flow patterns, i.e., bubble flow, slug flow, churn flow and annular flow are observed in the simulation. From the numerical results, we find that the influence of the wettability on the flow shape increases with decreasing of the channel width, the flow shape almost can be determined only by the wettability if the channel is small enough. The numerical results also indicate that a thin film is formed more easily with the increase of the volume fraction of the wetting phase. The above findings provide a theoretical guide for underground storage of CO2.(6) Liquid droplets dynamic behavior on the GDL surface is simulated using the pro-posed model and boundary conditions. The effects of a number of key influential parameters, including the capillary number, gas diffusion layer (GDL) surface wetting properties, and inlet velocity, distance between the gas transport pore and water emergence pore, and the pore size of the water emergence pore are analyzed. We draw the following conclusions: Enhancement of the GDL hydrophobicity can facilitate the transport of the water and gas:A small gas flow will result in the blocking up of the gas transport pore, due to the interaction between the adhesive force from the water emergence pore and the draft from the gas trans-port pore, and a fast gas velocity will inhibit the flow of the water to the gas flow channel. Therefore, only a proper gas inlet velocity can guarantee the droplet discharge and the gas transport; It is better to make sure that the droplet is already separated before arrival the gas transport pore when designing the distance between the gas transport pore and the water emergence pore. Furthermore, increasing the size of water emergence pore appropriately can increase the drainage flux of the water. The results of the present study provide insight for understanding the water droplet dynamic behavior in the gas flow channel of proton exchange membrane fuel cells.To sum up, interface dynamic behaviors of the two phase flows in micro-channel using the lattice Boltzmann method, such as the interaction between the fluids, interaction between the fluid and the solid, the large computational area caused by the long channel, are studied. And flow patterns of near-critical CO2in microchannels, and liquid droplets transport on the GDL surface, are studied numerically by the obtained LBE method and boundary conditions in the thesis. The obtained results enhance the understanding of flow pattern and internal mechanism of such complex flows. Several valuable efforts are made in the present thesis to promote the applications of LBE method in gas-liquid flows. |
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