ReviewReview and implementation of CFD-DEM applied to chemical process systems
Introduction
Multi-scale models for the simulation of chemical processes allow the investigation of multiphase flows in industrially relevant processes. Coupled computational fluid dynamics – discrete element method (CFD-DEM) is a multi-scale Eulerian-Lagrangian technique used for the simulation of systems that involve interaction of fluid and solid particles (Norouzi et al., 2016). Fig. 1 shows different modeling scales of fluid-solid systems (Norouzi et al., 2011). Following this notation, CFD-DEM treats the solid phase in micro scale and the fluid phase in meso scale. In process engineering, several systems, such as fluidized beds, spouted beds and pneumatic conveyors, are in this category. Consequently, CFD-DEM is a key model for simulation of such systems. The major drawback of using CFD-DEM is its high computational cost. This high computational cost limits the number of particles that can be simulated. This limit generally ranges from 105 on a workstation to 108 on high performance computers. In the recent years, with increasing the computational capacity of computers, application of CFD-DEM in chemical engineering (as well as other engineering fields) is increasing. Fig. 2 shows the number of Chemical Engineering publications since 2010 in which the word “CFD-DEM” has appeared in the title according to Web of Science (www.webofknowledge.com). The number of publications in this field is exponentially increasing.
Fig. 3 shows the schematics of a fluid-solid system considered in CFD-DEM simulations. The velocity vector of the fluid in each cell (red arrows inside red cells), wall (black line) and particles (gray spheres) can be observed in this figure. These fluid-solid flows appear in many multiphase systems such as fluidized and spouted beds which are frequently used for wide range of applications such as: performing chemical reactions (combustion, pyrolysis and gasification, to name a few), coating, granulation, mixing, drying, etc. (Rahimi and Azizi, 2011, Golshan et al., 2017b). This wide range of applications requires fundamental modifications of the CFD-DEM that are specific to each case. Consequently, various variants of CFD-DEM schemes have been developed by different groups of researchers.
The increasing trend in number of CFD-DEM simulations in process engineering and the wide range of CFD-DEM variants that are used for the simulation of fluid-solid systems in this field call for a review of applications and a modification of CFD-DEM models in chemical engineering. This problem is addressed in the present work. It should also be noted that this review is limited to cases where the particles are spherical. The modeling dynamics of non-sphercal particles by CFD-DEM is a vast field based on the shape of the particles with plenty of unknowns (Zhong et al., 2016a). Additionally, only the models using unresolved CFD-DEM approach, in which the fluid phase is studied in the meso-scale and the size of grids in the fluid phase are larger than the size of particles, are reviewed and discussed in this research, since in the resolved CFD-DEM, the number of particles are limited and not in the order of numbers in chemical engineering applications yet.
This article is divided in two sections: modeling methods (Section 2) and implementation of CFD-DEM (Section 3). The algorithms, modeling details and equations of unresolved CFD-DEM are presented in Section 2.1. Then, in 2.2 Heat transfer, 2.3 Mass transfer, the specificities related to the addition of heat and mass transfer sub-models to CFD-DEM are discussed. In Section 2.4, long-range forces, are introduced and details related to the implementation of these sub-models in the framework of CFD-DEM are discussed. The stability criteria of CFD-DEM simulations, as well as major advantages and drawbacks of CFD-DEM comparing to other modeling methods of multiphase flows conclude the modeling section. In the implementation part (Section 3), the implementation of the mentioned sub-models (heat and mass transport and long-range forces) in the framework of CFD-DEM is presented for the case of conventional fluid-solid contactors (including drying, coating, granulation, crystallization, mixing, chemical reactions such as combustion, gasification, pyrolysis, methanol to olefins, methanation, fluid catalytic cracking, ethylene polymerization and attrition of particles). By discussing the CFD-DEM modeling details of mentioned applications, some of the major researches for each application are also reviewed.
Section snippets
Equations and algorithms
In this section, the CFD-DEM governing equations and the solution procedures are first discussed. Then, the formulation and governing equations of each section of the algorithm are explained. Advantages and drawbacks of CFD-DEM are discussed and a few CFD-DEM codes are introduced. Since the majority of researches using CFD-DEM in the field of chemical engineering have been carried out using the unresolved approach and soft-sphere method, the scope is limited to this type of models.
Implementation of CFD-DEM in chemical engineering
In this section, the implementation of the models introduced in previous sections for the simulation of different processes in chemical engineering is reviewed. For this purpose, the sub-models for the simulation of each process are mentioned in a table and the models which are used in each sub-model in the simulations are introduced. Major findings and significant results of each work are also briefly described. The sub-models necessary for simulation of each process are shown in a figure and
Validation and verification issues
It is important to separate verification and validation of CFD-DEM models. In verification, which is performed for a new developed code, results of the programmed code of the model are compared with a problem with available analytical solution. These analytical solutions may be generated artificially using the method of manufactured solutions (Blais and Bertrand, 2015). Verification is performed once for a newly developed code and if the code passes the verification with high accuracy, there is
Conclusions and outlook
In this research, the unresolved CFD-DEM model, including governing equations and algorithm of the conventional CFD-DEM, was reviewed. Implementation of different sub-models, including heat transfer, mass transfer, long range forces (electrostatic, van der Waals, liquid bridge and solid bridge forces), was explained by introducing the equations and algorithm of each sub-model. In the second part of the paper, application of CFD-DEM models with the mentioned sub-models in simulation of chemical
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
Iran National Elites Foundation (INEF) is acknowledges for postdoctoral support extended to S. Golshan through the grant # BN096. The University of Tehran, Iran, is gratefully acknowledged for granting sabbatical leave to R. Sotudeh in 2020 at Polytechnique de Montreal.
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