Towards filtered drag force model for non-cohesive and cohesive particle-gas flows

Özel, Ali; Gu, Yile; Milioli, Christian C.; Kolehmainen, Jari; Sundaresan, Sankaran

doi:10.1063/1.5000516

Cited by 75 publications

(57 citation statements)

References 75 publications

(131 reference statements)

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“…The macroscopic variables are spatially averaged using different filter sizes ( ∆ filter ). The spatially averaged volume fraction is defined as 10,25,47

{\overset{true¯}{ε}}_{q} = ∭ ε_{q} ((), boldr, t) G ((), boldr bold- boldx, t) normald boldr

Here, G ( r − x ) denotes a filter weight function satisfying ∭ G ( r )d r = 1. The box filter kernel applied in this study is described by

G ((), boldr - boldx) = ({, \begin{matrix} \frac{1}{∆_{filter}^{3}}, italicif (||, boldr - boldx) \leq ∆_{filter} / 2 \\ 0, otherwise \end{matrix})

Analogously, we can compute the filtered phase velocity by

{\overset{true¯}{ε}}_{q} ((), boldr, t) {\overset{false\sim}{bold-italicv}}_{q} ((), boldr, t) = ∭ ε_{q} ((), boldr, t) v_{q} ((), boldr, t) G ((), boldr - boldx) normald boldr = \overset{ε_{q} ((), boldr, t) v_{q} ((), boldr, t)}{true}

where “−” is the volume‐averaged variable and “~” denotes the Favre‐averaged quantity.…”

Section: Cfd Model Developmentmentioning

confidence: 99%

“…Since the subgrid scale stress terms are less important as revealed by the budget analysis of Parmentier et al 13 and Jiang et al, 25 the present study is focused on the much more important drag correction term. For modifications to stress terms, interested readers can refer to open reports 10,11,13,16,31,47,48 . Noting that the fluctuations in the SVF and the fluid phase pressure gradient (

ε_{g}^{'} \nabla \cdot σ_{g}^{'}

Section: Cfd Model Developmentmentioning

confidence: 99%

“…For modifications to stress terms, interested readers can refer to open reports 10,11,13,16,31,47,48 . Noting that the fluctuations in the SVF and the fluid phase pressure gradient (

ε_{g}^{'} \nabla \cdot σ_{g}^{'}

) involving in the filtered drag coefficient is not considered in this work, which follows the study of Ozel et al 47 In general, one can model the anisotropic drag closure by processing the filtered data in either the vertical or horizontal direction. The role of this physical anisotropy has been well identified by the work of Cloete et al 30,31 In the current study, we will concentrate on the drag correction term solely along the vertical flow direction ( y ) that is of the key importance as pointed out by the literature 8,10,16,25,49 .…”

Section: Cfd Model Developmentmentioning

confidence: 99%

See 2 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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“…The macroscopic variables are spatially averaged using different filter sizes ( ∆ filter ). The spatially averaged volume fraction is defined as 10,25,47

{\overset{true¯}{ε}}_{q} = ∭ ε_{q} ((), boldr, t) G ((), boldr bold- boldx, t) normald boldr

Here, G ( r − x ) denotes a filter weight function satisfying ∭ G ( r )d r = 1. The box filter kernel applied in this study is described by

G ((), boldr - boldx) = ({, \begin{matrix} \frac{1}{∆_{filter}^{3}}, italicif (||, boldr - boldx) \leq ∆_{filter} / 2 \\ 0, otherwise \end{matrix})

Analogously, we can compute the filtered phase velocity by

{\overset{true¯}{ε}}_{q} ((), boldr, t) {\overset{false\sim}{bold-italicv}}_{q} ((), boldr, t) = ∭ ε_{q} ((), boldr, t) v_{q} ((), boldr, t) G ((), boldr - boldx) normald boldr = \overset{ε_{q} ((), boldr, t) v_{q} ((), boldr, t)}{true}

where “−” is the volume‐averaged variable and “~” denotes the Favre‐averaged quantity.…”

Section: Cfd Model Developmentmentioning

confidence: 99%

ε_{g}^{'} \nabla \cdot σ_{g}^{'}

Section: Cfd Model Developmentmentioning

confidence: 99%

“…For modifications to stress terms, interested readers can refer to open reports 10,11,13,16,31,47,48 . Noting that the fluctuations in the SVF and the fluid phase pressure gradient (

ε_{g}^{'} \nabla \cdot σ_{g}^{'}

Section: Cfd Model Developmentmentioning

confidence: 99%

See 1 more Smart Citation

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

2020

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show abstract

“…A lot of efforts have been made to develop and validate mesoscopic (e.g., filtered model) TFM and macroscopic (e.g., averaged model) TFM . Heterogeneous drag development and validation are one of the most critical parts of coarse‐grid simulation and it is the focus of many previous studies .…”

Section: Introductionmentioning

confidence: 99%

“…Heterogeneous drag development and validation are one of the most critical parts of coarse‐grid simulation and it is the focus of many previous studies . According to our previous work, heterogeneous drag model can be divided into four types based on the derivation methods, for example, (1) derived from fine grid TFM simulation, (2) derived from fine grid CFD‐DEM model simulation, (3) derived from particle‐resolved direct numerical simulation, and (4) derived from mesoscale‐structure‐based method . In many previous studies, reasonably good predictions of the gas–solid flow behavior were reported by employing the standard TFM with only drag correction; other subgrid corrections, such as mesoscale stress, were assumed to be negligible and were not considered.…”

Section: Introductionmentioning

confidence: 99%

Assessment of mesoscale solid stress in coarse‐grid TFM simulation of Geldart A particles in all fluidization regimes

Gao

Rogers

2018

AIChE Journal

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This study focused on assessing the effect of mesoscale solid stress in the coarse grid two‐fluid model (TFM) simulation of gas–solid fluidized beds of Geldart Group A particles over a broad range of flow regimes, including bubbling, turbulent, fast, and pneumatic transport fluidization regimes. Particularly, the impact of mesoscale solid pressure, mesoscale solid viscosity, and mesoscale solid stress anisotropy were investigated by comparing six different coarse‐grid TFM settings. Compared with the available experimental data, it is found that both the kinetic theory‐based TFM with only drag correction and the filtered TFM can predict the flow behavior in all fluidization regimes. Mesoscale solid pressure and viscosity have the opposite impact on flow hydrodynamics; they compete and offset each other, which confirms the assumption employed in many previous studies that the mesoscale solid stress could be neglected in coarse‐grid TFM simulation. Published 2018. This article is a U.S. Government work and is in the public domain in the USA. AIChE J, 64: 3565–3581, 2018

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Validation study on spatially averaged two‐fluid model for gas–solid flows: I. A priori analysis of wall bounded flows

Schneiderbauer

2018

AIChE Journal

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In our prior study (Schneiderbauer, AIChE J, 2017;63(8):3544-3562), we presented a spatially averaged two-fluid model, where closure models for the unresolved terms were derived. These closures require constitutive relations for the turbulent kinetic energies (TKEs) of the gas and solids phase as well as for the sub-filter variance of the solids volume fraction (VVF). In this study, we have performed highly resolved TFM simulations of a set of three-dimensional wall dominated periodic channels. An a priori analysis shows that these closures are able to correctly predict the wall profiles of the sub-grid drag modification, the TKEs, the turbulent viscosities and the VVF without requiring special wall corrections. Solely the mixing lengths, which is required by the closures, has to be adapted in the vicinity of wall similar to single-phase turbulence; in particular, the minimum of the filter size and the distance to the wall should be used.

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Towards filtered drag force model for non-cohesive and cohesive particle-gas flows

Cited by 75 publications

References 75 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

Assessment of mesoscale solid stress in coarse‐grid TFM simulation of Geldart A particles in all fluidization regimes

Validation study on spatially averaged two‐fluid model for gas–solid flows: I. A priori analysis of wall bounded flows

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