Report Series - Presentations

TransAT CFD/ CMFD

A l g o r i t h m s , S t r u c t u r e & M o d e l s

ASCOMP GmbH

Edited by: Dr Djamel Lakehal

Release Date: Sep., 2014.

Reference: TRS-P/01-2014

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Table of Contents 1. GENERAL DESCRIPTION OF CODE TRANSAT .......................................................... 3

2. MESHING IN TRANSAT ................................................................................... 4

2.1 BFC .................................................................................................... 4

2.2 The Immersed Surfaces Technique (IST) ......................................................... 4

2.3 Block-Mesh Refinement (BMR) .................................................................... 5

2.4 The Sharp Solid Interface Treatment (SSIT) ..................................................... 7

3. DETAILED NUMERICS AND SCALBILITY ............................................................... 8

3.1 Numerical Schemes ................................................................................. 8

3.2 Parallelization ....................................................................................... 8

3.2.1 Single-phase flow ................................................................................ 9

3.2.2 Multi-phase flow ................................................................................ 10

4. THE PHYSICAL MODELS IMPLEMENTED IN TRANSAT .............................................. 12

4.1 Turbulence Modelling ............................................................................. 12

4.1.1 Linear Eddy Viscosity Models (EVM) ......................................................... 12

4.1.2 Explicit Algebraic Stress Models (EASM) ..................................................... 12

4.1.3 Algebraic Heat Flux Models (AHFM) .......................................................... 12

4.2 Turbulence Simulation ............................................................................ 12

4.2.1 LES (Large Eddy Simulation) .................................................................. 12

4.2.2 V-LES (Very Large Eddy Simulation) .......................................................... 13

4.3 Multiphase Flow Modelling ....................................................................... 13

4.3.1 Phase-Average: The Mixture approach ....................................................... 13

4.3.2 Phase-Average: The NPhase approach ........................................................ 13

4.3.3 Interface Tracking: Level Set ................................................................... 14

4.3.4 Interface Tracking: Phase Field ................................................................ 14

4.3.5 Lagrangian Particle Tracking: 1-& 2-way coupling .......................................... 14

4.3.6 Lagrangian Particle Tracking: Dense-packed particle systems ............................ 14

4.4 Multiphase Turbulence ............................................................................ 14

4.4.1 Large Eddy and Interface Simulation (LEIS) ................................................. 15

4.4.2 Large Eddy and Structures Simulation (LESS) ............................................... 15

4.5 Complex Fluids ..................................................................................... 15

4.5.1 Multicomponent flows .......................................................................... 15

4.5.2 Conductive & convective heat transfer ....................................................... 15

4.5.3 Radiative heat transfer ......................................................................... 16

4.5.4 Complex fluids & flows ......................................................................... 16

4.5.5 Reactive flows ................................................................................... 16

4.5.6 Microfluidics flows .............................................................................. 16

4.5.7 Fluid-structure interaction (FSI) .............................................................. 17

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Abstract: This note describes the overall computational framework and structure of the CFD/CMFD code TransAT; in particular it describes the numerical techniques and physical models implemented in the code, without providing all the details. Selected results of code parallel scaling are presented.

1. GENERAL DESCRIPTION OF CODE TRANSAT

The CFD/CMFD code TransAT© developed at ASCOMP Switzerland is a multiscale, multi-physics, conservative finite-volume code based on solving the singe- and multi-fluid Navier-Stokes equations. TransAT exists in two versions: Single Block (TransAT-SB) and Multi-block (TransAT-MB). While TransAT-SB is parallelized using the OpenMP-Protocol on personal computers and laptops, TransAT-MB uses MPI on can run on non-shared memory supercomputer clusters. The code uses structured multi-block meshes¸ with the grids having 2 layers of ghost cells where information from neighboring blocks is received. MPI parallel based algorithm is used in connection with multi-blocking. The grid arrangement is collocated and can thus handle more easily curvilinear skewed grids. The solver is pressure based (Projection Type), corrected using the Karki-Patankar technique for low-Mach number compressible flows. High-order time marching and convection schemes can be employed; up to 3rd order Monotone schemes in space and 5th order in time. Turbulent flows can be treated in three ways: RANS statistical models, Scale Resolving Approaches like LES and its DES and VLES, and pure DNS. RANS models could be applied in steady and transient, and are in general built within the Implicit arm of the code. RANS models span one- and two-equations models, from linear to non-linear EASM models up to the quartic presentation of the stresses and heat & scalar fluxes. Near wall treatment is achieved using Low-Re schemes, two-layer approach and fixed and adaptive wall functions approach. LES (and DNS) is built within another arm of the code; that is the Explicit version, with its proper routines for pressure coupling, boundary conditions, diffusive fluxes and near-wall stress integration. The VLES variant is though implemented within the Implicit arm of the code, since it requires solving turbulence scalar equations. A variety of schemes and techniques were developed to treat multiphase flows: Interfacial flows are tackled using Interface Tracking Methods (ITM) for both laminar and turbulent flows. Specifically, the Level-Set approach, the phase-field variant and the Volume-of-Fluid –with interface reconstruction- methods can be employed. Static or dynamic angle treatment is also possible. Dispersed multiphase flows (bubbly flows) are treated using the One- and N-phase, phase-averaged mixture approach with Algebraic Slip to account for phase drift. Particle laden flows are handled using the Lagrangian particle tracking scheme, with one-to-four way coupling, including heat transfer. The four-way coupling approach is actually built within the dense-gas Eulerian-Lagrangian formulation that accounts for inter-particle collision forces. As to the level set, use is made of the 3rd order Quick scheme for convection, and 3rd order WENO for re-distancing. Mass conservation is enforced using global and local mass-conserving schemes. Turbulent multiphase flows can be tackled within both the RANS and LES (and V-LES) frameworks. All multiphase flows schemes (ITM, 1-& N-Phase, and Particle Tracking) are coded within the RANS and LES contexts; though in implicit form for the first and explicit for the latter. LES of interfacial turbulent flows includes specific interfacial treatments; a technique that is very specific to TransAT, and is known as LEIS, short for Large Eddy & Interface Simulation.

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2. MESHING IN TRANSAT

Mesh generation in TransAT can be accomplished either using traditional Boundary Fitted Coordinates (BFC), including for Cartesian-grid meshing, with the help of external professional tools like Gridgen, ICEM and Gambit, or using the IST/BMR methods described next, for which the TransAT Suite has a specific grid generator: TransAT-MESH. In most of the cases a CAD file is needed. ASCOMP relies on Rhinoceros to generate CAD files. TransAT-MESH handles Cartesian grids with a specific feature to generate blocked regions.

2.1 BFC

The selected BFC grids shown in Figure 1 below have been generated using external professional meshing tools like ICEM. In most cases, BFC grids are multiblock in nature and are preferred to mesh 3D piping systems.

(a): Flow in an inclined pipe bended on top

Figure 1: Example of multi-block BFC grids used by TransAT. (b): Flow in a T-junction

2.2 The Immersed Surfaces Technique (IST)

Immersed boundary (IB) techniques were developed in the late 70s for flows interacting with solid boundary under various formulations (Mittal & Iaccarino, 2005). The mostly known formulation employs a mixture of Eulerian and Lagrangian variables, where the solid boundary is represented by discrete Lagrangian markers embedding in and exerting forces to the Eulerian fluid domain. The interactions between the markers and the fluid variables are linked by a simple discretized delta function. IB methods are all based on direct momentum forcing (penalty approaches) on the Eulerian grid. The forcing should be performed such as it ensures the satisfaction of the no-slip boundary condition on the immersed boundary in the intermediate time step. This procedure involves thus solving a banded linear system of equations whose unknowns consist of the boundary forces on the Lagrangian markers; thus, the order of the unknowns is 1D lower than the fluid variables.

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Figure 2: Representation of solid and fluid components using IST.

The Immersed Surfaces Technology (IST) has been developed by ASCOMP GmbH (to the best of our knowledge), although other similar approaches have been developed in parallel. The underpinning idea is inspired from Interface Tracking techniques for two-phase flows (notably the Level Set variant). In IST the solid is described as the second ‘phase’, with its own thermo-mechanical properties. The technique differs substantially from the IB method of Peskin in that the jump condition at the solid surface is implicitly accounted for, not via direct momentum forcing. The solid is first immersed into a cubical Cartesian grid. The solid is defined by its external boundaries using the solid level set function. Like in fluid-fluid flows, this function represents a distance to the wall surface; is zero at the surface, negative in the fluid and positive in the solid. The treatment of viscous shear at the solid surfaces is handled very much the same way as in all CFD codes, where the wall normal vector needed to estimate the wall shear ( ) is obtained from . The wall-normal vector is initially stored in a specific array. The momentum and energy equations within the multi-component formulation (gas, liquid, solid) can simply be written under the form:

where the RHS source terms marked by Dirac functions in the momentum equation indicate the forces at the fluid-fluid interface (surface tension), and fluid(s)-wall force (wall shear). The fluid(s) and the solid have their own material properties, based on the solid Level Set function: density, heat capacity, thermal conductivity and viscosity in the equations:

2.3 Block-Mesh Refinement (BMR)

The BMR technique was developed in the TransAT code to help better solve the boundary layer zone when use is made of the IST technique discussed above. In BMR, more refined sub-blocks are automatically generated around solid surfaces; with dimensions made

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dependent on the Reynolds number (based on the boundary layer thickness). An unlimited number of sub-blocks of various refinements can be generated, with connectivity between the blocks matching up to 1-to-8 cells. This method can save up to 75% grid cells in 3D, since it prevents clustering grids where unnecessary.

Figure 3: IST/BMR setup of an electronic cooled board.

For the hierarchical BMR method - a hierarchical solution methodology is used. The coarse level is solved first everywhere (even inside fully overlapping fine grid domains). This gives Dirichlet boundary conditions to the finer levels and so on. The effect of the fine grid on the coarse grid is accounted for using the modified LDC method (Local Defect Correction - Anthonissen). The LDC coupling is very strong. Along the coarse-fine block boundaries all discrete fluxes are conserved. Numerically, there is though a requirement to better couple the pressure solver between BMR blocks. TransAT-MB-BMR has an Explicit and an Implicit arm. Explicit pressure solver and the implicit equation solver and pressure solver are all treated the same way. Each block is iteratively solved using the SIP (approximate LU) method. Each iteration of the Stone’s SIP solver has two diagonal loops - information between blocks is exchanged after each diagonal sweep. This is the only coupling that exists between blocks, which is not very strong. The implicit method is segregated and uses the SimpleC method (or Simple). The combined IST/BMR technique has various major advantages over traditional methods; these are enumerated below (including ongoing developments): Rapid gridding of complex geometries & set-up of flow boundary conditions Suitable for moving bodies, fluid-structure interactions Suitable for conjugate heat transfer Retain high-order scheme accuracy (Cartesian grids) No need to change discretization Local Defect Correction (LDC) – fully conservative Automated refinement per block: where needed Scalable parallelization; save up to 70% cells in 3D

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2.4 The Sharp Solid Interface Treatment (SSIT)

The IST algorithm described in Section 1.2 may have drawback in some case, in that objects have to be resolved on the grid, using a minimum of 2-3 grid cells completely inside the solid to fully block the flow. If there are less cells inside the solid, the flow feels the presence of the solid only partially. To resolve this issue, the code TransAT has been recently upgraded using the so-called sharp solid interface formulation, which modifies the original IST algorithm by decoupling the equations at surfaces based on surface normals that are dependent on the solid level set function (gradients). With this, even an infinitely thin solid perceives the full blocking effect on the oncoming flow. The mathematical background of the approach is beyond the scope of this document; below we present a couple of illustrative examples.

Figure 4: IST grid representation of a thin flat plane across flow. Solution of the flow past the plate

The first example shown in Fig. 4 involves the 3D flow past a thin solid plate located in the cross flow. As shown in the grid, the resolution is rather coarse, but still with this the flow past the obstacle is well resolved, as displayed in the right panel. The next practical example involves the flow past a ventilation issue, containing very thin plates. Results are shown in Fig. 5 below. The formulation is capable to treat such complicated situations, for which traditional grid generation technique will fail.

Figure 5: Flow and pressure past the thin flat plane.

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3. DETAILED NUMERICS AND SCALBILITY

3.1 Numerical Schemes

TransAT has the unique feature to run either in explicit or implicit, depending on the test problems considered, for both single and multiphase flows, depending on the turbulence models employed. In implicit solutions, the user can resort to steady state or transient time marching schemes. TransAT uses high order schemes for convection and diffusion processes in the linearized, discretized transport equations. Briefly, the schemes employed for convection in all equations are: HLPA (2nd order) CENTRAL (2nd order) QUICK (3rd order) TVD-based Schemes (2nd order)

The schemes employed for time marching are: EULER (1st and 2nd order) TLFI (2nd order) TVD Runge-Kutta (2nd , 3rd and 4th order)

The schemes employed for re-distancing of level set equation are: WENO (3rd order) FAST MARCHING (1st & 2nd order) NARROW BAND

The schemes employed for interface reconstruction & advection of VOF equation are: PLIC (2nd order) CVTNA (3rd order)

The schemes employed for compressible advection of density equation are: UPWIND (1st & 2nd order) CENTRAL (2nd order)

The schemes employed for pressure-velocity coupling are: SIP GMRES GMG & AMG PetsC Library

3.2 Parallelization

TransAT software is parallelized using Message Passing Interface (MPI) and domain decomposition methods. TransAT contains its own parallelized Elliptic solver based on the Strongly Implicit Procedure (SIP). It is augmented using the parallel PETSc solver library.

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Figure 6: Flow solution obtained with level set and VLES.

The results of the scaling are shown in Fig. 7. Deviations from the super-linear scaling are observed starting with 128 cores only; negative scaling appeared at 192 cores. Better scaling are obtained for problems treated using IST/BMR methods. The collaboration with INTEL is underway to find the best compilation and execution parameters.

Figure 7: Speedup and parallel efficiency analysis of the upslope test case.

3.2.1 Single-phase flow

The test problem selected for this MPI scaling exercise is the turbulent flow in a channel 8. The problem was simulated

using LES (explicit scheme). The problem was simulated in 3D on the ORNL supercomputer Jaguar, using various grids and memory allocation, as described in Tables 1 & 2.

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Figure 8: LES results of instantaneous cross-flow velocity and thermal fields in a channel

(Lakehal et al., 2011)

As is shown in Table 1, the case was running well up to 960 processors, with an allocation of 10,950 cells per processor, showing a perfect scaling and 100-138% efficiency. Because MPI-messages become smaller as the number of processors increases the MPI parameter (MPI_MAX_SHORT_MSG_SIZE) on the ORNL Jaguar cluster for small messages had to be changed, which slowed down the simulation. Reducing the MPI parameter to 4,000 decreases the efficiency from 104% to 84%; the numbers in Table 1 are colored in red. The reason for > 100% efficiency is because the work per time step does not remain constant if the blocking is changing. In summary, the efficiency is very good until 1,920 processors or 5,475 cells per Proc. (Fig. 9). The conclusion to be drawn here is not ‘TransAT scales up to 1,920 processors’, but rather ‘TransAT-MB using explicit schemes has the potential to outperform in terms of parallel scaling for very large grids & loading’. This result could be different for larger grids with maximum loading.

Figure 9: Speedup efficiency analysis for turbulent channel flow

3.2.2 Multi-phase flow

The test selected for this scaling exercise is the turbulent stratified flow in a pipe of diameter 0.5m and of length 5m (Lakehal et al., 2011). The grid is IST type; LEIS (Lakehal, 2010) was employed, where LES is coupled with level set to track the interface. The pipe contains water at a water holdup of hL/D = 0.14, injected at a velocity of 0.2m/s. Air is

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injected at a bulk velocity of 20m/s (ReG=1.6.105). Flow stratification and surface entrainment is shown in Fig. 10.

Figure 10: Surface deformations in the stratified flow showing droplet entrainment

Figure 11: Speedup efficiency analysis for turbulent single- & two-phase flow in a pipe

The case was simulated on ORNL Jaguar, using various grids and memory allocation as described in Tables 2 & 3. In contrast to previous cases, here the implicit variant of the code has been employed. The single-phase flow variant of the problem was simulated as well. Important to note is that the new OS of Jaguar no longer requires adjusting the MPI parameter; the algorithms in TransAT have been modified to cope with this change. The tables indicate that both single and multiphase flow simulations scale very well, up to 1’024 processors, for an allocation of 13’824 cells per processor. Scaling efficiency reached is more than 100%, for the multiphase flow. Increasing to 2’048 processors with a lower loading per cell (6’912) decreases the efficiency to 70% and 60%, respectively for the two flows. The reason for lower efficiency than in the explicit case is because there is more communication needed to solve a linear system per equation. Multiphase case scales better than the single-phase because more work is performed per time step (level set equation advection and re-distancing, material properties updates, etc.).

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4. THE PHYSICAL MODELS IMPLEMENTED IN TRANSAT

4.1 Turbulence Modelling TransAT can be employed using RANS (from EVM to EASM‘s, for all type of wall resolutions) as well as Scale-Resolving methods, including LES, V-LES and DNS, for all class of grids. Details on these models are provided below.

4.1.1 Linear Eddy Viscosity Models (EVM) The Eddy-viscosity models implemented in TransAT are essentially based on the k- model, coded for steady & unsteady flows, using adaptive wall functions and low-Re variants (3 models). The base RANS model is augmented with important modifications such as:

Kato & Launder modification Realizable k- Yap correction RNG

TransAT resorts to the dynamic two-layer approach, whereby the core flow is solved using the 2-equation k- model, whereas the near-wall region is treated using a one-equation model. Two-layer schemes are preferred to low-Re models for practical applications, and encompass the following variants:

TLK: k-based one equation TLV : <v’2> based one equation TLVA: Anisotropic <v’2> based one equation

4.1.2 Explicit Algebraic Stress Models (EASM) To alleviate the difficulty of treating complex fluid flows featuring rotation, anisotropy, buoyancy effects, TransAT adopts the Explicit Algebraic Stress Modelling (EASM) concept, with different variants, ranging from the quadratic up to the quartic versions. The models are all coded for steady & unsteady flows, using adaptive wall functions, two-layer, or low-Re variants. EASM are shown to often return similar results to full RSM’s, with lower computational costs and higher stability.

4.1.3 Algebraic Heat Flux Models (AHFM) In several situations where the heat (or scalar) transfer does not scale with the flow motion, be it for non-unity Prandtl number fluids, for natural convection, etc., the base EVM models are known to return low-quality results. TransAT adopts a series of high-order models for convective heat transfer to alleviate this difficulty, including:

SGGD, and GGDH (anisotropic used with EVM or EASM) WET (anisotropic used with EVM or EASM) AFM (anisotropic used with EVM or EASM)

4.2 Turbulence Simulation

4.2.1 LES (Large Eddy Simulation) The limits of the RANS approach for both single phase and multi-phase flow (in particular) have been reached. ASCOMP has decided to build an added-value modelling strategy based on LES, in complement of RANS. This observation applies in particular to industries in which reactive and multi-phase flow control the design. Many other industries are in search for similar new developments, too, namely oil & gas, thermal hydraulics of nuclear reactors

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and chemical and process engineering. This added to the constant growth of computer resources in terms of speed and storage helps replace the LES concept at the front stage of applied CFD. The LES strategy built in TransAT is very stable and highly accurate. It follows the guidelines of top literature, be it in terms of wall modelling, grid refinement, unsteady inflow boundary conditions (using synthetic models), numerical schemes. Our LES works for both explicit (CFL ~0.1) and implicit schemes (CFL up to 1). The SGS models employed in connection to LES are the following:

Smagorinsky Model Dynamic Model WALE Model

4.2.2 V-LES (Very Large Eddy Simulation) The Very Large-Eddy Simulation approach represents an excellent compromise between efficiency and precision as to capturing unsteady turbulence, and may thus be used for industrial problems for which LES remains computationally expensive. It can also be used for gas-liquid two-phase flows such as pressurized thermal shocks. The method is a sort of blend between U-RANS and LES, in that it resolves very large structures – way larger than the grid size – and models all subscale of turbulence using a two-equation model, by reference to RANS. This modelling approach is proved to provide the flow unsteadiness in three-dimensions, while saving computational cost compared to LES. The method is computationally efficient (it can be applied using an implicit solver which permits a higher CFL than with LES), and numerically robust. The computational cost decreases with increasing filter width, which in contrast to LES is not dependent on the grid size, but based on the characteristics length of the flow. The Subscale models used in connection with V-LES are the basic 1 & 2 Equation RANS Models.

4.3 Multiphase Flow Modelling 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).

4.3.1 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.

4.3.2 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

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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.

4.3.3 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).

4.3.4 Interface Tracking: Phase Field The Phase Field method is applicable to microscale two-phase flows involving complex fluids, by solving the Cahn-Hilliard Navier-Stokes equations, modified by the addition of a continuum forcing term (stresses, Kortoweg stresses) to account for surface forces. An order parameter provides a measure of the two phases, and can be the relative mass density or the species concentration. The phases are separated by an interfacial region called the diffuse interface thickness, where the order parameter changes rapidly, but smoothly. In our formulation, the order parameter is an independent thermodynamic variable on which the free energy of the system is based. On comparison with the Level-Set method, Phase Field requires a larger number of computational grid points in order to capture the diffuse interface. The presence of the diffuse interface means that the spurious currents which develop in the surface tension formulation are virtually non-existent.

4.3.5 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.

4.3.6 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.

4.4 Multiphase Turbulence As in the HPC module described earlier, turbulent multiphase flows can in this product be tackled within both the RANS and Scale-Resolving contexts, including LES, V-LES. Statistical

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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.

4.4.1 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 model combination (Lakehal, 2010) 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).

4.4.2 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.

4.5 Complex Fluids This version of the code solves the single- and multi-fluid/component Navier-Stokes equations with addition of various models to account for fluid flow with complex physics ubiquitous to specific industry verticals, like oil & gas, microfluidics, etc. This version of the code uses multiblock grids as well, in both the IST/BMR and the BFC contexts, and is parallelized on HPC systems using MPI. TransAT Multiphysics© is an upgrade of TransAT Multiphase©, in that the multiphase flow module is incorporated here, too, with all its modelling features. TransAT Multiphysics© deals with intricate fluid-flow situations involving multi-components, conductive, convective and radiative heat transfer, reactive flows, microfluidics flow, Non-Newtonian flows, sedimentation, hydrates, porous media, etc.

4.5.1 Multicomponent flows Gas-liquid mixtures Bubbly flows Interfacial gas-liquid & liquid-liquid flows Particle & droplet laden flows Dense particle clouds agglomeration & deposition Multi-component flows with heat & mass transfer Phase change: models & interface flux integration Fluid-solid-particle flows

4.5.2 Conductive & convective heat transfer Conductive & convective heat transport Surface & volumetric heat sources Convective heat transfer models at boundaries Anisotropic heat conduction Boussinesq flows – including in turbulence equations Conjugate heat transfer in 2D and 3D Heat transfer with multiphase-flow

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Variable thermo-mechanical properties of fluids Advanced Equations of State (Peng & Robinson)

4.5.3 Radiative heat transfer Monte Carlo technique

o Surface to surface radiation (non-participating) o Diffuse and spectral reflections o Semi-transparent boundaries

Diffusive approximation (Rosseland model) o Appropriate for optically thick situations

Participating media o absorbing-emitting media o scattering media (arbitrary scattering phase functions) o non-grey media

4.5.4 Complex fluids & flows Settling and sedimentation Non-Newtonian visco-plastic fluids Non-Newtonian Thixotropic fluids Hydrocarbon constitutive laws Binary mixtures Porous media Hydrate & slurries formation

4.5.5 Reactive flows Infinitely Fast Chemistry (non-premixed)

o EDC o EDC-SDT (Scalar Dissipation Timescale) o EDC-MTS (Multiple Timescale)

Finite Rate Chemistry (non-premixed) o Arrhenius (volumetric and surface reaction) o Flamelet based on Mixture Fraction o Progress Variable & Scalar Dissipation Rate o DQMOM (in progress)

Coupling with CANTERA (derived from Chemkin) o Evaluate thermodynamic and transport properties o Import Chemkin reaction mechanisms o Evaluate reaction rates o Pressure dependent reactions o Third body reaction o Surface reactions (heterogeneous) o Build Flamelet libraries

4.5.6 Microfluidics flows Interfacial flow with heat & mass transfer Phase change (boiling, condensation, evaporation) Wetting: static & dynamic contact angle Phase separation via phase field Marangoni effects Electrowetting Effects Subgrid-scale thin-film & lubrication Nano-particle tracking

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Surface tension highly dominated flows

4.5.7 Fluid-structure interaction (FSI) Rigid body motion Solid-solid collision Solid-wall collision Imposed solid vibration

References R. Mittal R., Iaccarino G., Immersed Boundary Methods, Ann. Rev. Fluid Mech, Vol. 37, pp. 239–261, 2005 D. Lakehal et al., Progress in the Prediction of Non-unity Pr Number Flows using TransAT, Proc. NURETH 14, Toronto, Sep. 2011.

D. Lakehal, LEIS for the prediction of turbulent multifluid flows applied to thermal-hydraulics applications, Nuclear Engineering and Design, Elsevier, 2010.

D Lakehal, M Meier, M Fulgosi , Interface tracking towards the direct simulation of heat and mass transfer in multiphase flows, International Journal of Heat and Fluid Flow, Volume 23,

Issue 3, Pages 242–257, June 2002.

D Gidaspow, Hydrodynamics of fiuidizatlon and heat transfer: Supercomputer modeling, Applied Mechanics Reviews 39 (1), 1-23, 1986. P. Liovic, D. Lakehal, “Multi-Physics Treatment in the Vicinity of Arbitrarily Deformable Fluid-Fluid Interfaces”, J. Comp. Physics, 222, 504-535, 2007b.

D Lakehal, BL Smith, M Milelli, Large-eddy simulation of bubbly turbulent shear flows,

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