#### Structure

The CMFD version of TransAT©, known as TransAT Multiphase© is finite-volumes based, solving the multi-fluid Navier-Stokes equations. This version of the code uses the same meshing means as HPC (IST/BMR or BFC). It is parallelized on HPC systems using MPI. Multiphase flows can be treated using a variety of techniques and models, depending on the nature of the flow; see next section.

#### Topology Prediction

Multiphase gas-liquid flows can be tackled using either interface tracking methods (ITM) or phase-average models, for both laminar and turbulent flows. Specifically, the Level-Set approach, the phase-field variant and the Volume-of-Fluid methods can be employed as ITM’s. Static or dynamic angle treatment is also possible. Particle laden flows rely and the Lagrangian framework, under one-, two- or four-way coupling (granular flows). Expand

#### Phase-Average: The Mixture approach

In the Mixture (Homogeneous) approach applied to gas-liquid systems, the transport equations are solved for the mixture quantities rather than for the phase-specific quantities (subscripts G and L), unlike the two-fluid model. This implies that one mixture momentum equation is solved for the entire flow system, reducing the number of equations to be solved in comparison to the two-fluid model. In many situations however, the model must employed with a prescribed closure law for the interphase slip velocity and associated stresses. In this case, the model is known as Homogeneous ASM. Various slip Pressure-gradient & gravity slip closure models can be used in TransAT, including for instance the Tomiyama drag & lift models, augmented by a turbulent dispersion mechanism.

#### Phase-Average: The NPhase approach

The N-Phase approach is an extension of the Homogeneous ASM introduced above, and is invoked in situations involving more than two fluid phases, e.g. methane-water-oil-hydrate, with the oil phase comprising both light and heavy components (06 phases). The N-Phase approach could as well be used in the two-fluid flow context. In the Homogeneous ASM framework, the N-Phase features a modified scheme where mass conservation and energy equations are solved for each phase to better cope with interphase mass transfer, whereas the momentum is solved for the mixture. Further, the model could be used in TransAT either under this homogeneous form or by adding an algebraic slip velocity to separate the phases.

#### Interface Tracking : Level Set

The level set consists in solving a hyperbolic equation to track the interface on a fixed Eulerian grid, using a smooth signed-distance function referring to the shortest distance to the front. Negative values correspond to one of the fluids and positive values to the other. The exact location of the interface corresponds to the zero level. Material properties are updated in time using this distance function. The advantage of the method is that it dispenses with interface reconstruction employed in VOF, it can handle merging and fragmentation and it permits identification of the exact location of the interface, which helps treat interfacial physics (e.g. interfacial turbulence decay, interphase mass exchange). Our Level Set method works on both Cartesian and BFC grids. It uses various re-distancing schemes, including fast marching on narrow bands for BFC grids, conserving mass up to 0.1%. For practical problems, use is made of the global conservation scheme of Lakehal et al. (2002, IJHFF).

#### Lagrangian Particle Tracking: 1-& 2-way coupling

The Eulerian-Lagrangian formulation applies to particle-laden (non-resolved component entities) flows, under one-way and two-way coupling. Individual particles are tracked in a Lagrangian way in contrast to the former two approaches, where the flow is solved in the Eulerian manner, on a fixed grid. One-way coupling refers to particles cloud not affecting the carrier phase, because the field is dilute, in contrast to the two-way coupling, where the flow and turbulence are affected by the presence of particles. The turbulent dispersion of the particles is treated using the Langevin model.

#### Lagrangian Particle Tracking: Dense-packed particle systems

The four-way coupling refers to dense particle systems with mild-to-high particle volume fractions (?p >5%), where the particles interact with each other. The model accounts for particle-particle collision with the so-called inter-particle stress as a source term (Gidaspow, 1986), while the momentum equation explicitly should account for the presence of particles through the fluid volume fraction. The model is used for fluidized beds and other dense-packed particle-flow systems. This set of Eulerian transport equations for the carrier phase is also combined with the Lagrangian particle equation of motion. Both approaches include particle wall interaction, and particle-flow heat transfer.

#### Multiphase Turbulence

As in the HPC module, turbulent multiphase flows can in this product be tackled within both the RANS and Scale-Resolving contexts, including LES, V-LES. Statistical RANS models are used in the context of the Mixture and N-Phase techniques, which could also benefit from the versatility of scale-resolving strategies (LESS). The ITM context, however, can only be employed in connection with LES or V-LES (LEIS). The Lagrangian particle module can be used within RANS or LES. Expand

#### Large Eddy and Interface Simulation (LEIS)

The LEIS idea, short for Large Eddy & Interface Simulation, is specific to TransAT, and is based on coupling the LES strategy for turbulent flows with either VOF or Level Sets for interface tracking. The combination (Lakehal, 2010, Nucl. Eng. Design) could lead to the simulation of the large-scale physics of interfacial flows down to the grid-resolved level. The idea consists of grid-filtering each phase separately; the resulting sub-grid scale (SGS) stresses are modelled. Special treatment is necessary at the interface though, taking advantage of the fact that the lighter phase perceives the interfaces like deformable walls. A rigorous near-interface treatment is included, taking into account turbulence decay on both sides of the interface (Liovic & Lakehal, 2007, JCP).

#### Large Eddy and Structures Simulation (LESS)

In LESS, phase-average models can be combined or employed within the LES or V-LES approaches in order to take full advantage of turbulence-dispersed structures interaction, which are hindered when use is made of RANS. LESS is well suited for bubbly flows in particular, as shown by Lakehal, Smith and Millelli, 2002, JoT). A bubble-induced subgrid scale model is also introduced.