CFD-DEM simulations of solid-liquid flow in stirred tanks using a non-inertial frame of reference

Delacroix, Bastien; Rastoueix, Juliane; Fradette, Louis; Bertrand, François; Blais, Bruno

doi:10.1016/j.ces.2020.116137

Cited by 22 publications

(16 citation statements)

References 64 publications

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“…We used a previously developed unresolved CFD‐DEM model in a rotating frame of references Delacroix et al 45,46 The model is based on the CFDEM platform, 47 which combines two open‐source software packages, that is, LIGGGHTS 48 for granular dynamics using the discrete element method (DEM) and OpenFOAM 49 for the CFD. The CFD part is based on a cell‐centered finite volume approach.…”

Section: Model Descriptionmentioning

confidence: 99%

“…In this section, we briefly recall the essential elements of this model. For more details, the reader is referred to papers specifically devoted to the development of this model 45,50 …”

Section: Model Descriptionmentioning

confidence: 99%

“…Volume‐averaged Navier–Stokes equations (VANS) are commonly used in CFD‐DEM. In the particular context of rotating frames of reference, we previously showed that these equations lead to a destabilization of CFD‐DEM simulations at t = 0 45 . The fluid model was thus based on the Navier–Stokes equations (Equations and ).

\frac{\partial}{\partial t} ((), ρ_{normalf}) + \nabla \cdot ((), ρ_{f} u_{f}) = 0

\begin{matrix} lefttrue \\ \frac{\partial}{\partial t} (ρ_{normalf} {bold-italicu}_{normalf}) + \nabla \cdot (ρ_{normalf} {bold-italicu}_{normalf} \otimes {bold-italicu}_{normalf}) = - \nabla P + \nabla \cdot τ + {bold-italicF}_{normalg} \\ - \underset{F_{pf}}{\underset{\frac{1}{normalΔ V} \sum_{i}^{n_{normalp}} ((), f_{pf, i} - f_{\nabla normalp, i} - f_{\nabla \cdot bold-italicτ, i})}{true}} - \underset{F_{Coriolis}}{\underset{2 ρ_{f} bold-italicΩ \times u_{f}}{true}} - \underset{F_{Centrifugal}}{\underset{ρ_{f} bold-italicΩ \times ((), bold-italicΩ \times q_{f})}{true}} \end{matrix}

with f_{pf, i} = f_{drag, i} + f_{Ar, i} + f_{\nabla \cdot boldτ, i} + f_{\nabla normalp, i} + \sum f_{add,}

…”

Section: Model Descriptionmentioning

confidence: 99%

“…For a quantity ζ , a parabolic filter was applied based on the following equation:

\frac{\partial ζ}{\partial t} = \frac{λ^{2}}{normalΔ t_{CFD}} \nabla^{2} ((), ζ)

where λ is the characteristic smoothing length chosen to be equal to 3 particle diameters to ensure stability. For more details about the stakes of this smoothing process, we refer the reader to Delacroix et al 45 …”

Section: Model Descriptionmentioning

confidence: 99%

“…Modeling rotating geometries, such as impellers is commonly done using methods such as the multiple reference frame, 39,40 sliding mesh, 23,24,41–43 or the immersed boundary 44 . In a previous study, we showed that these methods cannot be used straightforwardly for close‐clearance impellers, which is why we developed a new computational fluid dynamics‐discrete element method (CFD‐DEM) model based on a rotating frame of reference approach that makes it possible to study any axially symmetrical impeller 45 …”

Section: Introductionmentioning

confidence: 99%

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Which impeller should be chosen for efficient solid–liquid mixing in the laminar and transitional regime?

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The vast majority of solid–liquid mixing studies have focused on high Reynolds number applications with configurations and impeller geometries adapted to this type of regime. However, the mixing of particles in a viscous fluid is an essential element of many contemporary industries. We used the computational fluid dynamics‐discrete element method model previously developed in our group to investigate solid–liquid mixing with close‐clearance impellers in the laminar regime of operation. We compared different geometries, that is, the double helical ribbon, anchor, Paravisc™, and Maxblend™ impellers. We investigated the impact of fluid viscosity and compared the results with those obtained with the pitched blade turbine, a more commonly used impeller, based on power consumption for equivalent mixing states. This study highlights that the higher the viscosity of the fluid, the more interesting it is to use close‐clearance impellers for their ability to generate a strong shear stress and a strong bulk flow in the entire vessel.

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Section: Model Descriptionmentioning

confidence: 99%

“…In this section, we briefly recall the essential elements of this model. For more details, the reader is referred to papers specifically devoted to the development of this model 45,50 …”

Section: Model Descriptionmentioning

confidence: 99%

\frac{\partial}{\partial t} ((), ρ_{normalf}) + \nabla \cdot ((), ρ_{f} u_{f}) = 0

\begin{matrix} lefttrue \\ \frac{\partial}{\partial t} (ρ_{normalf} {bold-italicu}_{normalf}) + \nabla \cdot (ρ_{normalf} {bold-italicu}_{normalf} \otimes {bold-italicu}_{normalf}) = - \nabla P + \nabla \cdot τ + {bold-italicF}_{normalg} \\ - \underset{F_{pf}}{\underset{\frac{1}{normalΔ V} \sum_{i}^{n_{normalp}} ((), f_{pf, i} - f_{\nabla normalp, i} - f_{\nabla \cdot bold-italicτ, i})}{true}} - \underset{F_{Coriolis}}{\underset{2 ρ_{f} bold-italicΩ \times u_{f}}{true}} - \underset{F_{Centrifugal}}{\underset{ρ_{f} bold-italicΩ \times ((), bold-italicΩ \times q_{f})}{true}} \end{matrix}

with f_{pf, i} = f_{drag, i} + f_{Ar, i} + f_{\nabla \cdot boldτ, i} + f_{\nabla normalp, i} + \sum f_{add,}

…”

Section: Model Descriptionmentioning

confidence: 99%

“…For a quantity ζ , a parabolic filter was applied based on the following equation:

\frac{\partial ζ}{\partial t} = \frac{λ^{2}}{normalΔ t_{CFD}} \nabla^{2} ((), ζ)

Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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In order to improve the preparation efficiency of high-purity silicon, a new method of rotary segregation purification has been developed to prepare polysilicon. Numerical simulation based on ANSYS19.0 software and water model experiments were used to study the distribution of flow field and optimize the impurity removal process. A numerical simulation model suitable for rotating interface is established. The simulation result is in good agreement with the water model experiment. A vortex flow is found in the middle of the mold when the mold insertion depth is 90 mm. The vortex is conducive to the thinning of the impurity enrichment layer at the solid-liquid interface. With the mold insertion depth increases from 90 to 170 mm, two vortex flows appear in the middle and bottom of the mold, respectively. Moreover, setting the mold rotation rate at 100 rpm can contribute to a more stable flow field and a higher melt flow velocity. When the diffusion layer thickness is less than 0.1 mm, the impurity segregation coefficient can approach close to its equilibrium segregation coefficient, indicating that impurity segregation be effectively enhanced by increasing the rotation rate of mold, strengthening the effect of solidification rate and increasing the rotational speed. Industrial tests were carried out at the 100 kg level. The result shows that the rotary segregation method and equipment can achieve the removal of very low impurity in silicon (99.999 pct), and SoG-Si (99.9999 pct) was obtained. This method provides a new way for silicon purification, and it is believed that better results can be obtained through continuous improvement.

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CFD-DEM simulations of solid-liquid flow in stirred tanks using a non-inertial frame of reference

Cited by 22 publications

References 64 publications

Which impeller should be chosen for efficient solid–liquid mixing in the laminar and transitional regime?

Which impeller should be chosen for efficient solid–liquid mixing in the laminar and transitional regime?

Computational Fluid Dynamics

Numerical Simulation of Flow Field Optimizing the Rotating Segregation Purification of Silicon for SoG-Si

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