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**DEM-CFD modeling of solid-fluid flows **

*Paul Golz and John Favier DEM Solutions Ltd, 20 York Place, Edinburgh, EH1 3EP, UK Corresponding Author: jfavier@dem-solutions.com www.dem-solutions.com *

Effective modeling of solid-fluid flow requires methods for adequately characterizing the discrete nature of the solid phase and representing the interaction between solids and fluids. CFD multi-phase models such as the Euler-Lagrange Method and the Euler-Granular method address the problem within a continuum framework. In continuum models, contact between fluid, particles and boundary surfaces is not considered explicitly with respect to particle inertial and mechanical properties. This can limit the ability of CFD multiphase models to adequately represent particle-particle and fluid-particle interactions and therefore can reduce the accuracy of the prediction of both the fluid and the particle dynamics. This limitation can be overcome by explicit calculation of the particle contact mechanics in a particle-scale reference frame using a Lagrangian approach such as the Discrete Element Method (DEM). Coupling of DEM and CFD provides a means of momentum and energy exchange between solids and fluid, which, in principle, removes the need for some of the semi-empirical approximations employed in CFD solid-fluid models.

Coupled DEM-CFD simulation has potentially a very wide range of application and is attracting increasing interest from industry. DEM-CFD models reported in the literature have largely been applied to simulation of fluidised beds and more recently to pneumatic transport of particles. A feature of most of these models is the simple boundary surface geometry and use of mapped, usually Cartesian, meshes. Many industrial processes involved complex geometry, often with moving parts, and complex flow dynamics. Simulation of such systems requires use of unstructured fluid meshes, and the ability to handle energy as well as momentum exchange, turbulent flow, and chemical reactions. This capability is now possible in a commercial environment using co-simulation of EDEM discrete element modeling software with FLUENT. EDEM is an advanced particle mechanics simulation tool employed for modeling of industrial particulate handling and processing operations. It uses a surface mesh to represent boundary surfaces which enables a one-to-one coupling with the boundary surface elements of the CFD fluid volume mesh. EDEM-FLUENT cosimulation is being used to investigate systems such as particle agglomeration and clumping in fluidised beds, dense phase conveying, filtration, solid-liquid mixing, pipe erosion, spray coating and many others. Here we show some applications and assess the opportunities and limitations for application of DEM-CFD simulation of industrial solid-fluid system.

**DEM-CFD modeling of solid-fluid flows **

*Paul Golz and John Favier DEM Solutions Ltd, 20 York Place, Edinburgh, EH1 3EP, UK Corresponding Author: jfavier@dem-solutions.com www.dem-solutions.com *

Effective modeling of solid-fluid flow requires methods for adequately characterizing the discrete nature of the solid phase and representing the interaction between solids and fluids. CFD multi-phase models such as the Euler-Lagrange Method and the Euler-Granular method address the problem within a continuum framework. In continuum models, contact between fluid, particles and boundary surfaces is not considered explicitly with respect to particle inertial and mechanical properties. This can limit the ability of CFD multiphase models to adequately represent particle-particle and fluid-particle interactions and therefore can reduce the accuracy of the prediction of both the fluid and the particle dynamics. This limitation can be overcome by explicit calculation of the particle contact mechanics in a particle-scale reference frame using a Lagrangian approach such as the Discrete Element Method (DEM). Coupling of DEM and CFD provides a means of momentum and energy exchange between solids and fluid, which, in principle, removes the need for some of the semi-empirical approximations employed in CFD solid-fluid models.

Coupled DEM-CFD simulation has potentially a very wide range of application and is attracting increasing interest from industry. DEM-CFD models reported in the literature have largely been applied to simulation of fluidised beds and more recently to pneumatic transport of particles. A feature of most of these models is the simple boundary surface geometry and use of mapped, usually Cartesian, meshes. Many industrial processes involved complex geometry, often with moving parts, and complex flow dynamics. Simulation of such systems requires use of unstructured fluid meshes, and the ability to handle energy as well as momentum exchange, turbulent flow, and chemical reactions. This capability is now possible in a commercial environment using co-simulation of EDEM discrete element modeling software with FLUENT. EDEM is an advanced particle mechanics simulation tool employed for modeling of industrial particulate handling and processing operations. It uses a surface mesh to represent boundary surfaces which enables a one-to-one coupling with the boundary surface elements of the CFD fluid volume mesh. EDEM-FLUENT cosimulation is being used to investigate systems such as particle agglomeration and clumping in fluidised beds, dense phase conveying, filtration, solid-liquid mixing, pipe erosion, spray coating and many others. Here we show some applications and assess the opportunities and limitations for application of DEM-CFD simulation of industrial solid-fluid system.

II. THEORY: COUPLING METHOD

Here we present two methods of coupling: Lagrangian and Eulerian. The Lagrangian coupling allows only for momentum exchange between the fluid and the solid phases. As well as momentum exchange, the Eulerian coupling also accounts for the volume fraction of the particles. Lagrangian coupling is considerably less compute intensive than the Eulerian coupling but is only valid where the local solid volume fraction, i.e. the solid fraction within a fluid control volume, remains below 10%.

The Lagrangian coupling scheme is shown in Fig.1. The CFD is performed as a single phase, transient calculation which is iterated to convergence for a time step. A drag force is then calculated on the DEM particles using the fluid velocity in the mesh cell within which each particle is located. The DEM then takes control of the simulation and performs one or more iterations. After the DEM finishes iterating, control is passed back to the CFD. A momentum sink is added to each of the mesh cells to represent the effect of energy transfer to the DEM particles.

The magnitude of the momentum sink, *P*, of the CFD mesh cell can be calculated from

where F is the force on a particle in a particular iteration from the fluid. The sum is over the number of DEM iterations carried out between each CFD iteration. This momentum transfer is typically under-relaxed on the CFD side to provide greater stability of the CFD solution.

The Eulerian coupling model is based on FLUENT’s existing Euler-Granular model. The solver is run with two interpenetrating phases and additional sets of continuity equations must be introduced to account for the interaction of these phases. The individual phase continuity equations must also be modified to account for the volume fraction, α, of the individual phases. For this form of coupling, energy is not transferred between the phases meaning that only mass and momentum need to be conserved. Consider the mass continuity equation for the fluid phase:

where the subscript *F *refers to the fluid and *P *to the particulate phase. *v**F *is the velocity of the fluid phase. Since time is discretised, the change in the particulate mass in any grid cell is given by:

where τ is the CFD time-step. A similar equation exists for the conservation of momentum:

Another good test of the coupled solution is entrainment and deposition. The entrainment of sand particles by a jet of water passing over a packed bed of sand was modeled. Using an Eulerian method, the EDEM-FLUENT co-simulation correctly predicts both particle pick-up and transport, and also the circulation of the fluid as a result of the particles. Figure 4 (left) shows a vortex forming directly above the bed as a result of the presence of the growing wall of particles to the right of the bed. On the same figure (right) the circulation at the exit of the flow pipe is able to penetrate the packed bed only slightly.

Industrial applications of this coupling include filtration, slurry flow, aeration, deposition and entrainment. This methodology is also expected to be useful in applications such as ball mills, cyclones, drying, spray coating, jet-milling and particle inhalation devices. In order to further increase the range of industrial applications, ongoing development is incorporating rotational forces (e.g. Saffman, Magnus forces), irregularly shaped particles, heat transfer, turbulent scattering, incorporation of a free surface and mass transfer between the solid and fluid phase. This will enable simulation of such processes as crystallisation and chemical reactions.

VI. NOTES

The examples described in this paper were produced using co-simulation of EDEM 1.1 (DEM Solutions Ltd) and FLUENT 6.2.16 (Fluent Inc.) using an EDEM-FLUENT coupling module available from DEM Solutions Ltd. For further information visit www.dem-solutions.com.

VII. REFERENCES

Kuipers, J.A.M, Prins, W. and van Swaaij, W.P.M., Chem Eng Sci (1991) **46**, 2881-2894 Tsuji, Y., Kawaguchi, T. and Tanaka, T., Powder Technology (1993) **77**, 79-83

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