Bubble-based EMMS mixture model applied to turbulent fluidization

Highlights

• Bubble based EMMS mixture model is suitable for simulation of turbulent fluidized beds.

• Partial slip wall boundary condition with EMMS model predicts better voidage profiles.

• The drag correction required for accurate simulation reduces with increasing Archimedes number.

Abstract

Turbulent fluidization is now widely recognized as a distinct flow regime and is commonly utilized in industrial fluidized-bed reactors. However, relatively fewer attempts have been made to rigorously model these systems in comparison to bubbling and circulating fluidized beds. In this work, we have rewritten the original bubble based EMMS model in the form of a mixture to apply it to turbulent fluidization. At microscale this mixture is composed of gas and particles whereas voids and gas-particle suspension make up this mixture at mesoscale level. Subsequently, all the system properties are then calculated in terms of mixture rather than individual phases. With the minimization of the objective function for the bubbling mixture, the set of equations is then solved numerically. The objective function, used to close the system of equations, is composed of the energy consumption rates required to suspend gas-particle suspension and the energy consumed due to the interaction between suspension and voids. The model is then applied to simulate gas–solid turbulent fluidized beds. Simulation results are encouraging as the model is able to predict the dense bottom and dilute top zones along the height of the bed. Comparison of results with experimental data and homogeneous drag model has been made for validation purposes.

Introduction

Gas–solid flows display heterogeneity over a wide range of spatial and temporal scales covering regimes from bubbling to pneumatic transport. Matheson et al. [1] were the first ones to show photographs of turbulent fluidization, which were significantly different from bubbling fluidization [2]. However, turbulent fluidization has only been widely recognized as a distinct flow regime for the past couple of decades, occurring between the bubbling and the high velocity fluidization regimes [3]. Extensive details about the identification and characterization of the turbulent fluidization regime can be found in published literature such as the work by Martin Rhodes [4] and John Grace [5].

Turbulent fluidization is widely used due to its vigorous gas–solid mixing, favorable bed-to-surface heat transfer, high solid hold-ups (typically 25–35% by volume), and limited axial mixing of gas [2]. It is considered to be a transition from the bubbling to the transport regime which occurs due to a change in the mechanism of bubble formation and breakage. Moving from bubbling to turbulent fluidization, the hydrodynamics of the bed change from a regime of bubble formation and coalescence dominant mechanism to a regime with breaking and gradual disappearance of the large bubbles [6]. In turbulent beds, a sigmoidal profile for the solid hold-up is generally observed. Therefore, turbulent fluidized bed is characterized by two different coexisting regions: a lower region where solids are the continuous phase and gas the dispersed phase and an upper region, where gas is the continuous phase and solids are dispersed [7].

Two major approaches have been followed in attempts to apply CFD modeling to gas–solid fluidized beds: Eulerian two-fluid models and Euler/Lagrangian models [8]. Euler/Lagrangian method, where fluid phase is described as a continuum fluid and a Lagrangian approach is implemented for solid particles, is generally limited due to limitation of computational resources [9]. In recent years due to increase in computational resources, there has been increased use of new emerging Euler/Lagrangian techniques such as discrete element method (DEM), the dense discrete phase model (DDPM) and multiphase particle-in-cell (MP-PIC) method [10], [11], [12], [13]. However, these techniques are still limited due to the size of the equipment they can handle and unavailability of reliable model for interparticle interactions. Therefore, the Eulerian modeling has become a preferred choice for simulation of large macroscopic systems. In this approach, the gas and solid phases are assumed to be fully interpenetrating continua [14]. This methodology has been adopted by several investigators to model turbulent fluidized beds [15], [16], [17], [18], [19]. This approach requires either fine-grid resolution of the flows or modification of simulation parameters to incorporate sub-grid structures [20], [21], [22], [23], [24]. Although there has been some progress towards accurate resolution of the sub-grid scale structures but to date no unified approach exists. In fact, some studies have reported that the Eulerian two-fluid models with the homogeneous drag model fails to capture typical features of gas–solid flows even with high resolutions [19], [25]. This requires large number of computational cells. Researchers have reported a dimensionless grid, l_r, defined as ratio of equivalent cell width to particle diameter size of 10 to 20 to achieve grid independent solutions using different homogeneous drag models [19], [26], [27]. Under such circumstances, the Eulerian two-fluid model may not be able to correctly reflect the effects of these sub-grid structures. Thus it may be difficult to reproduce the multi-scale nature of such heterogeneous flows unless their effects are considered in the constitutive closure laws governing these flows.

To consider the effects of these mesoscale structures, a practical approach is to modify the homogeneous correlation based drag coefficients and stresses etc. with structure-based entities in addition to the resolved parts of two-fluid simulations. In this context, in recent years there has been significant improvement. Some authors [28], [29], [30] have used empirical correlations or equivalent cluster diameters to modify the homogeneous drag force. Others have considered heterogeneity by modifying the drag coefficient through the cluster-based EMMS (energy-minimization multi-scale) approach [31], [32], [33]. Recently there has been attempt to model the bubbling bed heterogeneity by following the EMMS principle [34]. This bubble-based EMMS model has also been applied to simulate riser flow [35]. Although progress has been made, but a unified model is still far from available.

While many efforts have been dedicated to model and simulate bubbling and transport type systems such as risers of CFBs, turbulent fluidization has received relatively less attention in terms of modeling and simulation. An attempt by using the four zoned drag model approach to simulate turbulent fluidized bed has been made recently [16], [36]. Adopting a similar multi-zoned drag model, Gao et al. [18] simulated their turbulent fluidized bed in fair agreement with their experimental data. In another recent attempt, Hong et al. [37] extended the work of bubble based EMMS model of Shi et al. [34] by coupling the structure-dependent multi-fluid model (SFM) to model heterogeneous gas–solid flows including turbulent fluidization. These attempts reflect the interest of modelers in correct prediction of hydrodynamics of turbulent fluidized beds where the outlet solid flux is negligible.

The theme of the current work is the fact that the drag force and stresses in uniform gas–solid systems are significantly different from the real systems due to the existence of heterogeneous structures. These structures can be in the form of bubbles and/or clusters, depending upon the operating conditions. In this current work on turbulent fluidized bed modeling, we have followed this structure dependent drag model approach by considering the system to be in the form of a mixture at both micro- and mesoscale level. This model may be considered as an alternate representation of earlier work of Shi et al. [34] from our group. Details of the model formulations are presented in the next section. Then some discussion about the model results is made. Finally the modified drag from mixture formulation is used to simulate turbulent fluidized bed and the results are validated against available experimental data.