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

Abstract

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...

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

“…In addition, we have developed a data loader program to transfer mesoscale solids stress data between the CFD solver and the ANN computing process in order to assess the prediction reliability and accuracy of the ANN‐based mesoscale solids stress model in realistic coarse‐grid simulations. The detailed coupling scheme can be found in our previous work 32 . Here, an example of the coarse‐grid results predicted by the coupled CFD‐DDM simulations is presented in Supporting Information.…”

“…In the establishment of the fTFM, correlations for mesoscale drag and mesoscale stresses are fitted as a function of some filtered quantities, the so‐called markers. Most of the previous studies have been focusing on heterogeneous drag closures, in some of which reasonable predictions are made by correcting the homogeneous drag model alone 13,15,16,18,20,28‐32 . But other studies 18,33 revealed that the mesoscale stresses, which are at least one order of magnitude larger than the microscale stresses, should not be ignored.…”

“…Machine learning (ML) methods such as eXtreme gradient boosting (Xgboost), 38 support vector machine (SVM), 39 random forest, 40 and artificial neural network (ANN) 41‐46 have been increasingly used in the field of chemical engineering. It was around since the 1940s, 47 but it was not until the last two decades that the ANN was applied to engineering (e.g., the filtered drag development using ANN 32,41,46 ). ANN is able to process big data and produce good predictions in the training step, which makes it a powerful data mining technique 41 .…”

Study of filtered interphase heat transfer using highly resolved CFD–DEM simulations

“…The filtering procedure adopted for microscopic TFM and CFD–DEM formulations is analogous as those in the literature 19,35,46 . The definition of the filtered particle phase volume fraction is as follows …”

Conventional anddata‐drivenmodeling of filtered drag, heat transfer, and reaction rate ingas–particleflows

“…However, the DDM does not require an understanding of the specific function relationship between the feature inputs and output, thus is more flexible in predicting the target variable 15 . Recently, the DDM has been demonstrated to be an effective way to model the mesoscale drag correction, 16–20 turbulence closures, 21 and flow parameters (e.g., solid hold‐up, solid flux) 22–24 . For instance, Jiang et al 16 applied the ANN to estimate the filtered HDC (fHDC) correction in gas–particle fluidization.…”