Macro-scale effects over filtered and residual stresses in gas-solid riser flows

Mouallem, Joseph; Niaki, Seyed Reza Amini; Chavez‐Cussy, Norman; Milioli, Christian C.; Milioli, Fernando Eduardo

doi:10.1016/j.ces.2018.09.054

Cited by 15 publications

(19 citation statements)

References 26 publications

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“…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}^{'}

) 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.…”

Section: Cfd Model Developmentmentioning

confidence: 99%

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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ε_{g}^{'} \nabla \cdot σ_{g}^{'}

Section: Cfd Model Developmentmentioning

confidence: 99%

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

2020

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“…For the sake of clarity and objectivity, results are presented here only in a limited extent. Among the independent variables the less influencing is 〈 ϕ s 〉, whose effects were already treated in previous analyses for the current dilute flow conditions . Owing to this, results are presented here for 〈 ϕ s 〉 = 0.15 only.…”

Section: Resultsmentioning

confidence: 99%

“…Even though not quite conclusive, Figure a,b also suggest that at sufficiently high values, both

k_{s} / v_{t}^{2}

and 〈Re g 〉/〈Re g 〉 susp stop having significant effects over H , as asymptotic behaviors arise. A discussion on flow homogeneity relevant to the current results can be found in Mouallem et al…”

Section: Resultsmentioning

confidence: 99%

“…While it is acknowledged that a more comprehensive study on suitability and correctness of markers is still missing, this work advances on this matter by adding a third marker to the analysis. This is done in addition to the accountancy of meso‐scale effects, which were already proven to considerably affect any HRS derived filtered parameter . It must be noted that most of the previously cited related literature trusts only on low velocity gas–solid fluidized suspensions for drawing the concerning analyses.…”

Section: The Marker Issuementioning

confidence: 99%

“…All the current simulations were performed with the MFIX code, and most of the concerning setup is described in Mouallem et al It suffices here to emphasize the main points as well as some new features. A 16 cm × 16 cm 2D computational domain was considered with periodic boundaries in all directions, under a grid mesh of 1.25 mm × 1.25 mm.…”

Section: Simulations Set Upmentioning

confidence: 99%

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Some accuracy related aspects in two‐fluid hydrodynamic sub‐grid modeling of gas–solid riser flows

et al. 2019

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Sub-grid closures for filtered two-fluid models (fTFM) useful in large scale simulations of riser flows can be derived from highly resolved simulations (HRS) with microscopic two-fluid modeling (mTFM). Accurate sub-grid closures require accurate mTFM formulations as well as accurate correlation of relevant filtered parameters to suitable independent variables. This article deals with both of those issues. The accuracy of mTFM is touched by assessing the impact of gas sub-grid turbulence over HRS filtered predictions. A gas turbulence alike effect is artificially inserted by means of a stochastic forcing procedure implemented in the physical space over the momentum conservation equation of the gas phase. The correlation issue is touched by introducing a three-filtered variable correlation analysis (three-marker analysis) performed under a variety of different macro-scale conditions typical or risers. While the more elaborated correlation procedure clearly improved accuracy, accounting for gas subgrid turbulence had no significant impact over predictions.

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On the effects of the flow macro‐scale over sub‐grid modelling in dense gas–solid fluidized flows

et al. 2022

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Multiscale modelling of gas–particle fluidized flows is frequently approached by means of sub‐grid modelling, which provides constitutive closures for filtered formulations applied to large scale simulations. A widely practiced procedure for the derivation of sub‐grid models consists of filtering over predictions from highly resolved simulations under two‐fluid modelling. The present work is intended as a contribution in this field by providing new supporting evidence for the enhancement of sub‐grid closure models. Most of the efforts in the area have been directed to providing sub‐grid models dependent on meso‐scale filtered effects alone, and under low gas Reynolds number suspension conditions. In this work, macro‐scale conditions are added to the analysis thereby accounting for flow topology, particularly for dense gas–solid fluidized flows. Two macro‐scale variables are considered in the simulations, namely the domain average solid volume fraction and the domain average gas Reynolds number. So, in addition to the usual meso‐scale filtered markers, relevant filtered parameters are also related to those macro‐scale conditions. The filtered parameters of interest here are the effective interphase drag coefficient and filtered and residual stresses in both of the phases. Various domain average solid volume fractions and domain average gas Reynolds numbers were enforced, thereby providing for a variety of macro‐scale dense conditions. It was found that both these macro‐scale parameters considerably affect the meso‐scale and the resulting filtered parameters of dense gas–solid flows, even though this occurs in a milder way when compared to results for dilute flow conditions available in the literature.

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Macro-scale effects over filtered and residual stresses in gas-solid riser flows

Cited by 15 publications

References 26 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

Some accuracy related aspects in two‐fluid hydrodynamic sub‐grid modeling of gas–solid riser flows

On the effects of the flow macro‐scale over sub‐grid modelling in dense gas–solid fluidized flows

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