Multiphase flows involving bubbles and droplets are ubiquitous in nature and in many industrial processes. Detailed information of such flows can be acquired from direct numerical simulations that directly resolve the flow on the bubble or droplet scale. In recent years, the lattice Boltzmann method (LBM) has emerged as a novel numerical method for multiphase flow simulation. While having many favorable features such as incorporation of physics on the more fundamental level and efficient algorithm for fast computation, the current multiphase LBM still faces challenges in issues such as numerical instability and narrow parameter window, which severely restrict its application in a broad range of real world engineering problems.
This dissertation presents the development of a novel multiphase LBM which significantly expands the application of the method in various flow problems. Specifically, three techniques are developed to achieve enhanced performance in three aspects: First, new interaction potential functions are developed for multi-component LBM model to improve numerical stability at high density ratios between the liquid and gas phase. Second, an adaptive mesh refinement (AMR) scheme is developed to provide sufficient resolution of the gas-liquid interface. Third, the multi-relaxation time
(MRT) scheme is incorporated into the interaction potential model to enhance the numerical stability at low viscosities. The above new techniques are presented in detail, and simulations are performed in both 2D and 3D to evaluate their performance. It is demonstrated that the new interaction potential model is able to raise the stable density ratio from below 50 to over 1000. The AMR can provide accurate predictions of the interface, while reduce the computation cost by about 50% in real computations. In addition, with the MRT algorithm the maximum Reynolds number in bubble simulations can be increased from 100 to about 1000.
The performance of the newly developed LBM technique is further illustrated in different applications. In the study of the buoyant rise of a gas bubble in a viscous liquid, simulations are carried out to investigate the shape and rise velocity of the bubble. Particularly, both bubbles with large deformation and bubbles with high Reynolds number are studied. Good agreement is found between the model predictions and experimental results in the literature. Then the collision between a liquid droplet and a porous surface is investigated. Using the adaptive mesh approach, the flows on both the droplet scale and the pore scale are direct resolved simultaneously. The deformation of the droplet on the porous surfaces is compared to that on impermeable surfaces. Finally, the LBM simulation is performed for bubble formation in microchannels. The bubble shape and formation mechanism are discussed in different regimes and compared with experimental results.
In summary, a systematic investigation is conducted to improve the stability and accuracy of the LBM for multiphase simulations. A novel LBM model is developed and its performance is studied in various test problems. The application of the new model in the simulation of bubble rise, droplet collision, and microchannel bubble formation further illustrates the enhanced capability of the current LBM model.