Lattice Boltzmann Method for Single-phase and Multiphase Systems
Creators: name: Baakeem, Saleh S.
Publisher: name: Schulich School of Engineering
Year: 2022
Subjects: subject: Lattice Boltzmann method
subject: Multiphase flow
subject: Shan–Chen model
subject: Equation of State
subject: Forcing scheme
subject: Chapman-Enskog analysis
subject: General discretization
subject: Unit conversion
subject: Physical Sciences

description: The thesis is dedicated to improving a few shortcomings of the lattice Boltzmann method (LBM). Particularly, the thesis deals with mapping quantities’ units between scales, source term, and multiphase models to lend more flexibility and simplicity to the LBM when simulating single-phase and multiphase systems. Mapping quantities’ units between the macroscopic scale and mesoscopic scale is of extreme importance and it should be correctly performed, where the geometric and dynamics similarity conditions must be conserved. The Buckingham ? theorem and the principle of corresponding states (i.e., scaling) are the popular methods used for unit conversion processes in the LBM. These methods are successful for single-phase systems. However, using these traditional methods for complicated flow problems, such as multiphase flows, is not a straightforward task. In the present work, a dimensional analysis approach is developed to handle the unit conversion processes in the LBM for single-phase and multiphase systems. The approach is characterized by its flexibility in selecting parameters to ensure the stability of the LBM, as well as its flexibility to map properties’ units between scales. Several benchmark examples are used to test the feasibility and accuracy of the proposed approach. It can be concluded that the proposed approach is flexible in mapping the quantities’ units between macroscopic and mesoscopic scales and vice versa.The source term is mainly used to implement complex physics to the governing equations. The literature review shows that there are twelve forcing schemes proposed to deal with the source term in the LBM. It is found that the extra physics can be also added to LBM governing equation by modifying the equilibrium distribution function. The analysis shows that all forcing schemes are suitable for single-phase problems. However, a few of these schemes are applicable to multiphase systems. To analyze the previously published forcing schemes theoretically, a unified forcing scheme is developed based on the general discretization of the LBM. This unified scheme can recover all previously published forcing schemes. Furthermore, it can predict and correct the error in the momentum equation of each scheme. It is found that most of the previously published schemes do not recover the correct Navier-Stokes equations. After correcting the error, the schemes are classified into continuity-conserving and continuity-non-conserving forcing schemes. As a result, the continuity-conserving forcing schemes become applicable to multiphase systems and have the same performance.The last section of the thesis deals with the modeling of single-component and multi-component multiphase systems. Owing to its simplicity and flexibility, the Shan–Chen model (SC) is considered in this study. For single-component multiphase systems, a method to couple the Equation of State (EoS) with the SC model is proposed. The difference between previously proposed approaches and the developed one is in the way of determining parameters of the EoS. As a result, the parameters in each EoS become functions of the critical properties in the lattice scale, i.e., each physical material has its critical values on the lattice scale. Four EoSs—the SC EoS, van der Waals EoS, Redlich–Kwong EoS, and Carnahan and Starling EoS—are considered. Moreover, a methodology for differentiating between different types of fluids is developed. Furthermore, an approach that handles the multi-component multiphase systems is also developed. The fluids and mixtures are treated as real, where the mixing rules are used for modeling mixtures. Three benchmark problems, namely, 2D stationary droplet, 2D layered Poiseuille flow, and 2D falling droplet on a liquid film, are presented for validating the model’s capability in simulating the single-component and multi-component multiphase systems. One can conclude that the developed models show the ability in distinguishing between different kinds of fluids and reduce the computational effort in simulating single-component and multi-component multiphase systems.