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eulerianFilteredTFM - Documentation

A filtered Two Fluid Model library for OpenFOAM®

eulerianFilteredTFM is C++ library based on the open source finite volume library OpenFOAM® developed to solve the three dimensional unsteady spatially averaged Euler-Euler equations that describe a two phase system composed of a continuous phase (fluid) and a dispersed phase (solid particles).

The library features several closures for the interphase transfer coefficients, the phase stress tensor and additional user defined equations.

Basic structure

The eulerianFilteredTFM library stems from the twoPhaseEulerFoam solver included in OpenFOAM®, but its structure is more in line with the physics and the terminology used in fluid-solid suspensions. The library can be subdivided in modules as follows:

• twoPhaseSystem: Similarly to twoPhaseEulerFoam, it is the main module that provides access to relevant quantities or operations and manages the two phases. The module is also solving the phase volume fraction equations.

• interphase closures: Provides closure models for the filtered interphase transfer coefficients (i.e., drag and heat transfer coefficients). Interphase closures are calculated as functions of:

• micro closures: They are the microscopic closures corresponding to the functional form of the interphase transfer coefficients for the unfiltered model.

• heterogeneity corrections: They are corrections based on the fact that highly heterogeneous structures (like clusters) that affect the interphase exchange may exist at a sub-grid level.

• stress closures: Provides closure models for the phase filtered stress tensor. Such tensor is expressed as the sum of three tensors representing the multiscale nature of the non-linear term in the transport equations:

• meso-scale stress: At the meso-scale, only homogenous structures are considered. These homogeneous structures are triggered by two kind of instabilities: one inertial due to the relative motion between the gas and particle phases, and one diffusive that arise from the dumping of particle velocity fluctuations due to collisions or interstitial fluid. These structures are namely clusters and streamers of particles.

• frictional stress (particle phase only): It is the stress arising by frictional effects due to high particle packing. It is generally associated with band-like heterogeneous structures arising at a sub-grid scale.

• micro-scale stress: It is the stress induced by kinetic phenomena like binary collisions (both for particle or fluid phases). This stress can be related to the formation of clusters at a sub-grid scale.

• equation closures: Additional closures for user-defined transport equations like granular temperature or phase fraction variance.

• auxiliary equations: This module allows to define additional equations to be solved alongside with mass and momentum conservation.

• dynamic parameters: Allows dynamic calculation of quantities to simplify the implementation of advanced closures.

Additionally, the library features the eulerianFilteredTFM solver and verification cases.

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Basics	Closures	Auxiliary Equations	dynamic Parameters
Installation	Stress Closures	Defining a new equation	Usage
Dictionary	Interphase Closures
Solvers	Equation Closures
Tutorials	Equation Closures