<p>Large Eddy Simulation (LES), where the unsteady motion of the large scales is simulated and models are used to describe the average motion of the small scales, is a promising way for predicting flow dynamics in single phase flow. It is likely that predictions of multiphase flow can follow a similar strategy, but not in a conventional way, where low-pass filter is used to separate the large and small length scales. For multiphase flows where sharp moving phase boundaries separate different fluids or phases, the dynamics of the interface often determines the behavior of the flow. In a coarse, or reduced order model, it may therefore be important to retain a sharp interface for the resolved scales, in a similar way that modeling of disperse flows often retain bubbles or drops as point particles. Equations for the evolution of coarse grained flows are usually derived from equations for the fully resolved flow by adding closure terms to account for the effect of unresolved scales, the coarse field is generated by explicit filtering, and the closure terms constructed using the filtered fully resolved solution. An alternate approach is to find the closure terms directly from the evolution of the coarse field by asking how the traditional fluid equations need to be modified to ensure that the coarse field evolves correctly. The second approach allows the coarsening to be done in a variety of different ways, including using nonconventional coarsening strategies that preserve a sharp interface, without the need of knowing the exact analytical form of the subgrid stress. We describe a systematic process to coarsen fully resolved numerical solutions for multiphase flows while retaining a sharp interface. The different phases are identified by an index function that takes different values in the different phases and is coarsened by solving a constant coefficient diffusion equation, while tracking the interface contour. Small flow scales of one phase, left behind when the interface is moved, are embedded in the other phase by solving another diffusion equation with a modified diffusion coefficient that is zero at the interface location to prevent diffusion across the interface, along with a pseudo pressure equation to preserves the incompressibility of the coarsened volumetric velocity field. Several examples of different levels of coarsening are shown. The dynamics of the small scales in the mixed regions can be modeled in many different ways, including using homogeneous mixture, drift flux, and two fluid Euler-Euler models, as well as Euler-Lagrange models. While classical models for the flow away from the interface can be used, those are usually developed in highly empirical ways and we have started explore the use of data-driven techniques for more systematic development of models for the whole flow field, including the interface. We are currently using simple homogeneous mixture models and examples of evolving the coarsen two-dimensional flow with empirical modeling of subgrid terms will be shown. We end by discussing more advanced approaches, including the implementation of more models for the large scale flow and the use of machine learning to help develop closure for the model equations.</p>

Interface Retaining Coarsening for Data-Driven Modeling of Multiphase Flows

Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2021/volume/85284

ASME 2021 Fluids Engineering Division Summer Meeting (FEDSM2021)

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