Effective drag coefficient correlation for coarse coal particle fluidization in transitional flow regime

Highlights

• Coarse coal particle fluidization is investigated by experimental and numerical simulation approaches.

• An effective drag closure for coarse coal particle fluidization in the transitional flow regime is proposed.

• The accuracy of drag closure is validated by experimental data.

• The effects of particle density, particle size, and liquid velocity are investigated.

Abstract

Liquid–solid fluidized beds are widely used in industrial processes, such as polymerization, mineral processing, and water treatment. Among these processes, particle fluidization behaviors perform a significant function in determining heat and mass transfer performance. In this study, a large set of expansion experiments are performed to investigate the effects of the particle density, particle size, and liquid superficial velocity on bed expansion height and bed porosity. The drag coefficient is obtained based on experimental data. The relationship between drag coefficient and Reynolds number, Froude number and Stokes number is clarified, and an effective drag closure for coarse coal particle fluidization in the transitional flow regime is proposed. Then the developed drag coefficient correlation is incorporated into liquid–solid two-phase flow model to predict the bed expansion height. The output predictions agree well with the experimental data, ensuring the accuracy of the proposed drag closure.

Introduction

Liquid–solid fluidized beds have extensive applications in industrial production, such as polymerization, food processing, metallurgical processing, and wastewater treatment (Galvin et al., 2018; Jameson et al., 2020; Lu et al., 2016; Sowmeyan and Swaminathan, 2008; Trivedi et al., 2006; Zhu et al., 2000). Among these processes, high solid particle mixing rates, which are mainly controlled by the quality of particle fluidization, are inherently required to improve the interphase heat and mass transfer rate (Fosu et al., 2015; Zhu et al., 2000). Accordingly, to improve the performance of liquid–solid fluidized beds, an insight into the hydrodynamic characteristics of these systems is critical.

Over the last few decades, despite their wide application, liquid–solid systems have received limited attention compared with gas–solid systems, which usually have many heterogeneous flow structures (Xie et al., 2021; Zhu et al., 2016). In liquid–solid fluidized beds, however, a low solid–fluid density ratio can easily lead to particle entrainment, especially small and light particles; thus, severe heterogeneous fluidization seems improbable under normal operating conditions. In contrast, the homogeneous fluidization of liquid–solid fluidized beds has been frequently observed (Wang et al., 2010). Nevertheless, it should be noted that heterogeneous liquid–solid flow behaviors, such as particle clustering, bubbling, and velocity fluctuations, do occur (Chen and Zhu, 2008; Esteghamatian et al., 2017, 2018; Kasat et al., 2008; Kramer et al., 2020; Sardeshpande et al., 2009, 2010; Song et al., 2019a, 2019b). As early as 1995, heterogeneous fluidization in liquid–solid fluidization systems had been reported by Di Felice (1995). In these systems, the degree of heterogeneity has been attributed to the particle morphology, particle size distribution, and fluid–solid density ratio.

Generally, experimental and numerical simulation approaches have been used in previous studies to investigate the liquid–solid flow characteristics. Based on advanced experimental measurement techniques, such as particle image velocimetry (Reddy et al., 2013; Peng et al., 2014), electrical resistance tomography (Razzak et al., 2007, 2009, Razzak et al., 2010; Zbib et al., 2018a, 2018b), and laser Doppler anemometry (Mathiesen et al., 2000), the particle phase distributions can be visualized. The characterized particle concentration, particle velocity, and particle clusters can aid in clarifying the fluidization mechanism and provide guidance for optimizing fluidized beds. However, the experimental data may be extremely dependent on the specific experimental method. As a result, the experimentation cost usually hinders obtaining a variety of experimental data.

Recently, the modeling and simulation of liquid–solid fluidized beds have been performed through computational fluid dynamics (CFD) to investigate the hydrodynamic characteristics, particularly for the purpose of scaling up. Although experiments are still required to validate the CFD model, numerical simulations allow particle scale characterization. For liquid–solid fluidized beds, the typically reported numerical techniques can be classified into Eulerian and Lagrangian approaches according to the treatment of the solid phase. In particular, the computational fluid dynamics–discrete element method (CFD–DEM) can provide a detailed description of the particle scale information based on the analysis of forces acting on individual particles (Liu et al., 2017; Zhu et al., 2007). In the past few decades, various numerical simulations have been performed to investigate the hydrodynamic behaviors of liquid–solid fluidized beds under different flow regimes (Lettieri et al., 2006), to explore flow stability (Ghatage et al., 2014; Ramesh et al., 2018; Zbib et al., 2018a, 2018b), and to study the homogeneous and heterogeneous fluidization phenomena (Fan et al., 2010; Mazzei and Lettieri, 2008). Such qualitative and quantitative studies have also afforded considerable amounts of important basic data derived by investigating the effects of liquid superficial velocity, physical properties of solid particles and liquids, and the structure of fluidized beds (Cornelissen et al., 2007; Dadashi et al., 2014; Hua et al., 2020; Wang et al., 2012; Ye et al., 2017). Additionally, the importance of liquid–particle and particle–particle interactions has been confirmed by many researchers (Luo et al., 2019; Koerich et al.,2018; Wu and Yang, 2019; Xie and Luo, 2018; Yu et al., 2016). In terms of numerical simulation, it is necessary to choose the interphase force model carefully because it can considerably influence the two-phase flow behavior (Visuri et al., 2012). In transitional flow regimes, many interphase drag models are available; however, each has its own character and application scope.

This study aims to investigate the hydrodynamic behavior of a liquid–solid fluidized bed applied to coarse coal separation. The three-dimensional (3D) fluidized bed was operated in the intermediate flow regime, and the expansion experiments and CFD simulations were implemented considering different particle densities, particle sizes, and liquid velocities. Based on the measured experimental data, a drag relationship was developed; thereafter, the drag coefficient correlation was incorporated into liquid–solid two-phase flow model to predict the bed expansion height. To the best knowledge of the authors, the obtained experimental data and simulation results can improve the understanding of liquid–solid fluidized beds with coarse particles.