Kinetic theory based multiphase flow with experimental verification

Gidaspow, Dimitri; Bacelos, Marcelo Silveira

doi:10.1515/revce-2016-0044

Cited by 32 publications

(21 citation statements)

References 39 publications

(41 reference statements)

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“…Γ slip is production rate of granular energy through slip between two phases. σ s is closed by the widely‐used KTGF 5 . Equation ) is an additional transport equation for describing the granular temperature ( Θ s ) of Lun et al 45 The interphase drag coefficient β is given by

β_{micro} = \frac{18 μ_{g} ε_{g} ((), 1 - ε_{g})}{d_{normals}^{2}} F_{normald, micro} ((),, {Re}_{normals}, ε_{normalg})

where the dimensionless drag F d,micro (Re s , ε g ) is described by the more accurate drag model that is formulated by performing extensive Lattice–Boltzmann simulations 46 :

F_{normald, micro} ((),, {Re}_{normals}, ε_{normalg}) = \frac{10 ((), 1 - ε_{g})}{ε_{normalg}^{2}} + ε_{g}^{2} ((), 1 + 1.5 \sqrt{1 - ε_{g}}) + \frac{0.413 {Re}_{s}}{24 ε_{g}^{2}} ([], \frac{ε_{normalg}^{- 1} + 3 ε_{normalg} (1 - ε_{normalg}) + 8.4 {Re}_{normals}^{- 0.343}}{1 + 10^{3 (1 - ε_{normalg})} {Re}_{normals}^{- [1 + 4 (1 - ε_{normalg})] / 2}})

…”

Section: Cfd Model Developmentmentioning

confidence: 99%

“…Following KTGF, we define a filtered particle‐phase Reynolds stress like quantity (

{\overset{true¯}{boldR}}_{normals, normaly}

) along vertical direction by

{\overset{true¯}{boldR}}_{normals, normaly} = ∭ {(v_{s, y} (r, t) - 〈v_{s, y} (r, t)〉)}^{2} G ((), boldr - boldx) normald boldr = \overset{{((), v_{normals, normaly} ((), boldr, t) - (〈〉, v_{normals, normaly} ((), boldr, t)))}^{2}}{true}

where <> denotes a time‐averaging manner.

{\overset{true¯}{boldR}}_{normals, normaly}

involves the square of the particle velocity fluctuations (i.e., the particle‐induced turbulence intensities 5 or saying the particle‐phase fluctuating energy 50 ). Noting that the definition of a particle‐phase Reynolds stress like quantity in Capecelatro and Desjardins 51 includes velocity and SVF fluctuations about their filtered values.…”

Section: Cfd Model Developmentmentioning

confidence: 99%

“…We investigate in this study a dense bubbling fluidized bed (BFB) 57 and a turbulent fluidized bed (TFB), 56 respectively. The underlying gas–solid dynamics is described by the KTGF‐based TFM 5 . The phase‐coupled SIMPLE procedure is chosen for coupling pressure and velocity.…”

Section: Application Of ML Modelmentioning

confidence: 99%

“…Development of accurate and reliable modeling methods for capturing such complex dynamics has been the grand challenge for FBR modelers. One of the broadly‐practiced predictive methods is the kinetic theory of granular flow (KTGF) based two‐fluid model (TFM), which treats the fluid and particle phases as interpenetrating continuums 5 . However, the TFM simulation with sufficiently fine grids is necessitated for resolving all relevant scales of flow hydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Machine learning to assist filtered two‐fluid model development for dense gas–particle flows

2020

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Machine learning (ML) is experiencing an immensely fascinating resurgence in a wide variety of fields. However, applying such powerful ML to construct subgrid interphase closures has been rarely reported. To this end, we develop two data-driven ML strategies (i.e., artificial neural networks and eXtreme gradient boosting) to accurately predict filtered subgrid drag corrections using big data from highly resolved simulations of gas-particle fluidization. Quantitative assessments of effects of various subgrid input markers on training prediction outputs are performed and three-marker choice is demonstrated to be the optimal one for predicting the unseen test set. We then develop a parallel data loader to integrate this predictive ML model into a computational fluid dynamic (CFD) framework. Subsequent coarse-grid simulations agree fairly well with experiments regarding the underlying hydrodynamics in bubbling and turbulent fluidized beds. The present ML approach provides easily extended ways to facilitate the development of predictive models for multiphase flows. K E Y W O R D S coarse-grid simulation, filtered two-fluid model, fine-grid simulation, fluidization, machine learning, subgrid closure model 1 | INTRODUCTION Gas-solid fluidized bed reactors (FBRs) are ubiquitous in process engineering. Unfortunately, inhomogeneous mesoscale flow structures in such reactors are incredibly complex and manifest persistent instabilities in flow properties spanning all sorts of spatiotemporal scales. 1-3 This dynamic nature is of fundamental importance in essential process features such as the interphase momentum, species, and heat transfer. 4 Development of accurate and reliable modeling methods for capturing such complex dynamics has been the grand challenge for FBR modelers. One of the broadly-practiced predictive methods is the kinetic theory of granular flow (KTGF) based two-fluid model (TFM), which treats the fluid and particle phases as interpenetrating continuums. 5 However, the TFM simulation with sufficiently fine grids is necessitated for resolving all relevant scales of flow hydrodynamics. Fullmer and Hrenya 3 indicated that a typical mesh spacing of~3.3d s is required to obtain the grid independency for simulation statistics at intermediate solid phase fraction, and the grid size less than 10d s for dilute clustering flows is demanded for computational accuracy. For dense bubbling FBRs, Wang et al. 6 recommended a grid resolution of 2-4 d s . Such high requirements (10 −5 -10 −3 m) for reactor-scale simulations (10 −1 -10 1 m) are computationally prohibitive.Alternatively, subgrid models (SGMs) for interphase closure corrections such as the energy minimization multi-scale (EMMS), [7][8][9] filtered TFM (fTFM), 2,10-15 spatially-averaged TFM (SA-TFM), 16-18 and gradient-based method, [19][20][21] have been developed to account for effects of unresolved inhomogeneous structures. SGM enables a dramatic reduction of computational overhead by employing coarse grids while still maintaining high accuracy. In the establis...

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β_{micro} = \frac{18 μ_{g} ε_{g} ((), 1 - ε_{g})}{d_{normals}^{2}} F_{normald, micro} ((),, {Re}_{normals}, ε_{normalg})

where the dimensionless drag F d,micro (Re s , ε g ) is described by the more accurate drag model that is formulated by performing extensive Lattice–Boltzmann simulations 46 :

F_{normald, micro} ((),, {Re}_{normals}, ε_{normalg}) = \frac{10 ((), 1 - ε_{g})}{ε_{normalg}^{2}} + ε_{g}^{2} ((), 1 + 1.5 \sqrt{1 - ε_{g}}) + \frac{0.413 {Re}_{s}}{24 ε_{g}^{2}} ([], \frac{ε_{normalg}^{- 1} + 3 ε_{normalg} (1 - ε_{normalg}) + 8.4 {Re}_{normals}^{- 0.343}}{1 + 10^{3 (1 - ε_{normalg})} {Re}_{normals}^{- [1 + 4 (1 - ε_{normalg})] / 2}})

…”

Section: Cfd Model Developmentmentioning

confidence: 99%

“…Following KTGF, we define a filtered particle‐phase Reynolds stress like quantity (

{\overset{true¯}{boldR}}_{normals, normaly}

) along vertical direction by

{\overset{true¯}{boldR}}_{normals, normaly} = ∭ {(v_{s, y} (r, t) - 〈v_{s, y} (r, t)〉)}^{2} G ((), boldr - boldx) normald boldr = \overset{{((), v_{normals, normaly} ((), boldr, t) - (〈〉, v_{normals, normaly} ((), boldr, t)))}^{2}}{true}

where <> denotes a time‐averaging manner.

{\overset{true¯}{boldR}}_{normals, normaly}

Section: Cfd Model Developmentmentioning

confidence: 99%

Section: Application Of ML Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Machine learning to assist filtered two‐fluid model development for dense gas–particle flows

2020

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“…In the E-E approach, each phase is treated as an interpenetrating continuum, and the concept of phase volume fraction is used. The governing equations based on the conservation of the mass, momentum, and energy are solved for both liquid and solid phases based on the kinetic theory of granular flow (Sinclair and Jackson 1989, Gidaspow 1994, Enwald et al 1996, Gidaspow and Bacelos 2017. In the case of two-phase flow in SLCFB where the number of solid particles is huge, the E-E method is attractive and practical.…”

Section: Computational Fluid Dynamic Modelsmentioning

confidence: 99%

Solid-liquid circulating fluidized bed: a way forward

Thombare

Chavan

Bankar

et al. 2017

Reviews in Chemical Engineering

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AbstractSolid-liquid circulating fluidized beds (SLCFBs) offer several attractive features over conventional solid-liquid fluidized beds such as efficient liquid-solid contact, favorable mass and heat transfer, reduced back-mixing of phases, and integrated reactor and regenerator design. These unique features have stimulated theoretical and experimental investigations over the past two decades on transport phenomena in SLCFBs. However, there is a need to compile and analyze the published information with a coherent theme to design and develop SLCFB with sufficient degree of confidence for commercial application. Therefore, the present work reviews and analyzes the literature on hydrodynamic, mixing, heat transfer, and mass transfer characteristics of SLCFBs comprehensively. Suitable recommendations have also been made for future work in concise manner based on the knowledge gaps identified in the literature. Furthermore, a novel multistage SLCFB has been proposed to overcome the limitations of existing SLCFBs. The proposed model of SLCFB primarily consists of a single multistage column which is divided into two sections wherein both the steps of utilizationviz.loading (adsorption, catalytic reaction, etc.) and regeneration of solid phase could be carried out simultaneously on a continuous mode.

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Data‐driven modeling of mesoscale solids stress closures for filtered two‐fluid model in gas–particle flows

2021

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This study performs data‐driven modeling of mesoscale solids stress closures for filtered two‐fluid model (fTFM) in gas–particle flows via an artificial neural network (ANN) based machine learning method. The data used for developing the ANN‐based predictive data‐driven modeling framework is systematically filtered from fine‐grid simulations. The loss function optimization result reveals that coupling two loss functions promotes more accurate predictions of the mesoscale solids stresses than using a single loss function. Further comprehensive assessments of closure markers demonstrate a systematic dependence of the mesoscale solids stresses on the filtered particle velocity and its gradient as additional anisotropic markers, instead of using the conventional isotropic filtered rate of solid phase deformation as a closure marker. An optimal three‐marker mesoscale closure is thus proposed. Comparative analysis of the conventional filtered model and present three‐marker model shows that the data‐driven model can substantially enhance the prediction accuracy.

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Kinetic theory based multiphase flow with experimental verification

Cited by 32 publications

References 39 publications

Machine learning to assist filtered two‐fluid model development for dense gas–particle flows

Machine learning to assist filtered two‐fluid model development for dense gas–particle flows

Solid-liquid circulating fluidized bed: a way forward

Data‐driven modeling of mesoscale solids stress closures for filtered two‐fluid model in gas–particle flows

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