Computational simulations of multiphase flow are challenging because many practical applications require adequate resolution of not only interfacial physics associated with moving boundaries with possible topological changes, but also around three-dimensional, irregular solid geometries. In this paper, we focus on the simulations of fluid/fluid dynamics around complex geometries, based on an Eulerian-Lagrangian framework. The approach uses two independent but related grid layouts to track the interfacial and solid boundary conditions, and is capable of capturing interfacial as well as multiphase dynamics. In particular, the stationary Cartesian grid with time dependent, local adaptive refinement is utilized to handle the computation of the transport equations, while the interface shape and movement are treated by marker-based triangulated surface meshes which freely move and interact with the Cartesian grid. The markers are also used to identify the location of solid boundaries and enforce the no-slip condition there. Issues related to the contact line treatment, topological changes of multiphase fronts during merger or breakup of objects, and necessary data structures and solution techniques are also highlighted. Selected test cases including spacecraft fuel tank flow management, and movement and rupture of interfaces associated with liquid plug flow are presented.

SUMMARYLiquid plug propagation and rupture occurring in lung airways can have a detrimental effect on epithelial cells. In this study, a numerical simulation of a liquid plug in an infinite tube is conducted using an Eulerian-Lagrangian approach and the continuous interface method. A reconstruction scheme is developed to allow topological changes during plug rupture by altering the connectivity information about the interface mesh. Results prior to the rupture are in reasonable agreement with the study of Fujioka et al. in which a Lagrangian method is used. For unity non-dimensional pressure drop and a Laplace number of 1000, rupture time is shown to be delayed as the initial precursor film thickness increases and rupture is not expected for thicknesses larger than 0.10 of tube radius. During the plug rupture process, a sudden increase of mechanical stresses on the tube wall is recorded, which can cause tissue damage. The peak values of those stresses increase as the initial precursor film thickness is reduced. After rupture, the peaks in mechanical stresses decrease in magnitude as the plug vanishes and the flow approaches a fully developed behavior. Increasing initial pressure drop is shown to linearly increase maximum variations in wall pressure and shear stress. Decreasing the pressure drop and increasing the Laplace number appear to delay rupture because it takes longer for a fluid with large inertial forces to respond to the small pressure drop.

Multiphase flow computations involve coupled momentum, mass and energy transfer between moving and irregularly shaped boundaries, large property jumps between materials, and computational stiffness. In this study, we focus on the immersed boundary technique, which is a combined Eulerian-Lagrangian method, to investigate the performance improvement using the multigrid technique in the context of the projection method. The main emphasis is on the interplay between the multigrid computation and the effect of the density and viscosity ratios between phases. Two problems, namely, a rising bubble in a liquid medium and impact dynamics between a liquid drop and a solid surface are adopted. As the density ratio increases, the single grid computation becomes substantially more time-consuming; with the present problems, an increase of factor 10 in density ratio results in approximately a three-fold increase in CPU time. Overall, the multigrid technique speeds up the computation and furthermore, the impact of the density ratio on the CPU time required is substantially reduced. On the other hand, the impact of the viscosity ratio does not play a major role on the convergence rates.

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Numerical simulations of flows involving moving boundaries are challenging as they need to address the location and the conditions of the interface that interacts with the flow field. We have developed a unified, marker-based approach, which can treat moving solid and multiphase fluid dynamics using adaptively refined Cartesian grids. The interfaces separating the fluid phases are modeled using a continuous interface method, while the noslip condition on solid interfaces is imposed by a sharp interface method. A smoothly varying Heaviside-like function is used for handling discontinuous material properties between fluids and for identifying the solid-fluid interface location. Furthermore, a distance-based formulation is adopted to treat solid-fluid interface intersections. A domain decomposition method via Hilbert space filling curves and preconditioned multigrid solvers are incorporated into the staggered grid arrangement for scalar and velocity variables. To highlight the performance of the present approach, case studies are conducted for (i) interface shapes, residual volumes, formation of sloshes and corresponding wave periods in draining tank with different control parameters and flow regimes, (ii) fluid dynamics around a flapping airfoil, and (iii) fluid flow around complex solid geometries.

Multiphase flows are marked by the presence of interfacial dynamics, steep jump in fluid-properties across the interface and moving boundaries between different phases and materials. Presence of moving boundaries and nonlinear coupling of phases across interface makes three-dimensional numerical simulations a difficult and expensive task. The presented work uses a continuous interface combining marker points on a stationary Eulerian grid. For an efficient computation an adaptive Cartesian grid is used to resolve local length scales of the flow. The interface location and flow solution are used as the adaptation criteria. The multiphase-interface is tracked using unstructured surface grid representation. A volume preserving interface reorganization procedure has been developed to maintain the desired interface surface grid resolution. Also, a momentum-source computation technique improving the performance of immersed boundary treatment in the governing field equation has been investigated.