Numerical modeling of three-phase (gas-liquid-solid) flows with connectivity-free multi-fluid interface treatment and non-boundary-fitted techniques for fluid-structure interactions

A gas-liquid-solid multiphase flow is an important physical phenomenon that appears in nature and many engineering applications. Numerical modeling of multiphase flows becomes an essential tool to predict and analyze the corresponding flow and solid behaviors and appropriate interfacial responses, and ultimately to study their underlying mechanisms and physics. However, being widely studied, the development of numerical algorithm for three-phase flows is still a challenging field due to the complex nature of the gas-liquid-solid interactions. In this thesis, a computational frame work to model and simulate gas-liquid-solid three-phase flows is established. A non-boundary-fitted approach is developed to easily and efficiently accommodate the moving interfaces and deforming solid. A background fluid mesh is constructed in the whole domain, whereas the gas-liquid multi-fluid interface and the solid structure are represented independently using connectivity-free interfacial points and an Lagrangian mesh, respectively. The gas-liquid interface and the solid mesh can move freely on the background fluid mesh which is represented using an Eulerian frame of reference, which avoids the re-meshing process and simplifies the computation setup significantly. The gas-liquid interface is treated using the connectivity-free front tracking (CFFT) method. It uses explicit interfacial points to represent the interface without the logical connectivity of the interfacial points, while conserving the total volume. Without any connectivity of the points, the interface topology change can be easily handled by adopting a simple points regeneration scheme. An indicator function is used to identify the appropriate (gas or liquid) properties and surface tension force. The reproducing kernel particle method (RKPM) is introduced to perform more accurate interpolations for indicator calculation. To further enhance the accuracy at the interface for microscopic scale, a dynamic contact line model with rough surface hysteresis is coupled to the CFFT method. It is implemented by reconstructing the contact region of the interface to impose the predicted dynamic contact angle. This feature can help us achieve more accurate interfacial representations when the gas-liquid interface contacts with a solid wall. This model allows us to analyze the bubbles and droplets behaviors near the solid wall boundary. To couple the solid into the gas-liquid multi-fluid system, we adopt the immersed finite element method (IFEM), a non-boundary-fitted approach to treat fluid-solid interactions. The IFEM provides a realistic representation for solid motion and deformation by solving the solid governing equations. The concept of indicator function is again adopted to identify the real and artificial fluids where the solid occupies, which naturally combines the IFEM with the CFFT method for the three-phase representation. The coupling of the two algorithms sets a new computational framework for the gas-liquid-solid interactions, where the dynamics of each individual phase is accurately captured and each interface is clearly represented and predicted. This work provides a new means in predicting and analyzing complex physical phenomena.