An immersed computational framework for multiphase fluid-structure interaction. - Liang Yang (2015)
"The objective of this thesis is to further extend the application range of immersed computational approaches in the context of hydrodynamics and present a novel general framework for the simulation of fluid-structure interaction problems involving rigid bodies, flexible solids and multiphase flows. The proposed method aims to overcome shortcomings such as the restriction of having to deal with similar density ratios among different phases or the restriction to solve single-phase flows. The new framework will be capable of coping with large density ratios, multiphase flows and will be focussed on hydrodynamic problems. The two main challenges to be addressed are: - the representation, evolution and compatibility of the multiple fluid-solid interface - the proposition of unified framework containing multiphase flows, flexible structures and rigid bodies with possibly large density ratios First, a new variation of the original IBM is presented by rearranging the governing equations which define the behaviour of the multiple physics involved. The formulation is compatibile with the "one-fluid" equation for two phase flows and can deal with large density ratios with the help of an anisotropic Poisson solver. Second, deformable structures and fluid are modelled in a identical manner except for the deviatoric part of the Cauchy stress tensor. The challenging part is the calculation of the deviatoric part the Cauchy stress in the structure, which is expressed as a function of the deformation gradient tensor. The technique followed In this thesis is that original ISP, but re-expressed in terms of the Cauchy stress tensor. Any immersed rigid body is considered as an incompressible non-viscous continuum body with an equivalent internal force field which constrains the velocity field to satisfy the rigid body motion condition. The "rigid body" spatial velocity is evaluated by means of a linear least squares projection of the background fluid velocity, whilst the immersed force field emerges as a result of the linear momentum conversation equation. This formulation is convenient for arbitrary rigid shapes around a fixed point and the most general translation- rotation. A characteristic or indicator function, defined for each interacting continuum phase, evolves passively with the velocity field. Generally, there are two families of algorithms for the description of the interfaces, namely, Eulerian grid based methods (interface tracking). In this thesis, the interface capturing Level Set method is used to capture the fluid-fluid interface, due to its advantages to deal with possible topological changes. In addiction, an interface tracking Lagrangian based meshless technique is used for the fluid-structure interface due to its benefits at the ensuring mass preservation. From the fluid discretisation point of view, the discretisation is based on the standard Marker-and-Cell method in conjunction with a fractional step approach for the pressure/velocity decoupling. The thesis presents a wide range of applications for multiphase flows interacting with a variety of structures (i.e. rigid and deformable) Several numerical examples are presented in order to demonstrate the robustness and applicability of the new methodology. (Abstract shortened by ProQuest.)."