Session R47: Invited Session: Simulation of Interfaces in Two-Fluid Flows

Accelerated boundary integral simulations of particulate and two-phase flows

In micro-fluidic applications where the scales are small and viscous effects dominant, the Stokes equations are often applicable. The suspension dynamics that is observed already with rigid particles and fibers are very complex also in this Stokesian regime, and surface tension effects are strongly pronounced at interfaces of immiscible fluids. Simulation methods can be developed based on boundary integral equations, which leads to discretizations of the boundaries of the domain only, and hence fewer unknowns compared to a discretization of the PDE. Two main difficulties associated with boundary integral discretizations are to construct accurate quadrature methods for singular and nearly singular integrands, as well as to accelerate the solution of the linear systems, that will have dense system matrices. If these issues are properly addressed, boundary integral based simulations can be both highly accurate and very efficient. We will discuss simulations of periodic suspensions of rigid particles and rigid fibers in 3D, where the simulations are accelerated by a newly developed spectrally accurate FFT based Ewald method, as well as highly accurate simulations of many interacting drops in 2D.   

Direct Numerical Simulations of Multiphase Flows

Many natural and industrial processes, such as rain and gas exchange between the atmosphere and oceans, boiling heat transfer, atomization and chemical reactions in bubble columns, involve multiphase flows. Often the mixture can be described as a disperse flow where one phase consists of bubbles or drops. Direct numerical simulations (DNS) of disperse flow have recently been used to study the dynamics of multiphase flows with a large number of bubbles and drops, often showing that the collective motion results in relatively simple large-scale structure. Here we review simulations of bubbly flows in vertical channels where the flow direction, as well as the bubble deformability, has profound implications on the flow structure and the total flow rate. Results obtained so far are summarized and open questions identified. The resolution for DNS of multiphase flows is usually determined by a dominant scale, such as the average bubble or drop size, but in many cases much smaller scales are also present. These scales often consist of thin films, threads, or tiny drops appearing during coalescence or breakup, or are due to the presence of additional physical processes that operate on a very different time scale than the fluid flow. The presence of these small-scale features demand excessive resolution for conventional numerical approaches. However, at small flow scales the effects of surface tension are generally strong so the interface geometry is simple and viscous forces dominate the flow and keep it simple also. These are exactly the conditions under which analytical models can be used and we will discuss efforts to combine a semi-analytical description for the small-scale processes with a fully resolved simulation of the rest of the flow. We will, in particular, present an embedded analytical description to capture the mass transfer from bubbles in liquids where the diffusion of mass is much slower than the diffusion of momentum. This results in very thin mass-boundary layers that are difficult to resolve, but the new approach allows us to simulate the mass transfer from many freely evolving bubbles and examine the effect of the interactions of the bubbles with each other and the flow. We will conclude by attempting to summarize the current status of DNS of multiphase flows.   

Advances and Challenges in Modeling Interfacial Flows

Interfacial flows are multi-material flows comprised of two or more immiscible materials demarcated by interfaces. They are encountered in several applications of interest to the Department of Energy. Examples of applications include materials processing (e.g. casting), inertial confinement fusion and solvent extraction. We are interested in the development of accurate numerical methods to simulate with high-fidelity interfacial flows. For such simulation, the position of the interface and interface physics need to be predicted as part of the solution of the flow equations. One of the many techniques is known as the volume tracking method. It is a pure Eulerian method that represents the interface with volume fraction and intrinsically ensures mass conservation. In this talk, I will describe several advances that have been made over the past 25 years and discuss remaining challenges in the context of the volume tracking method.   

A moment of fluid method for computing solutions to multiphase/multimaterial flows

We combine the multimaterial Moment-of-Fluid (MOF) work of Ahn and Shashkov with the work of Kwatra et al for removing the acoustic time step restriction in order to solve multimaterial flows in which each material might be compressible or incompressible. The mass weights found in the algorithm of Kwatra et al are computed directly from the multimaterial MOF reconstructed interface. We treat the interface(s) between materials as sharp when discretizing the boundary conditions between materials. The combination of the multimaterial MOF reconstruction together with the cell centered formulation devised by Kwatra et al enable us to robustly compute multimaterial flows with large density ratios, stretching and tearing of interfaces and contact line dynamics at the junction of 3 materials with minimal volume fluctuation of each material (if a given material is incompressible). Simulations for multimaterial flows are presented with applications to combustion (atomization and spray) and microfluidics.