Numerical investigation on the mixing mechanism in a cross-torus paddle mixer using the DEM-CFD method

Highlights

• Advanced DEM-CFD method is applied to investigate the mixing state in a cross-torus paddle mixer.

• Various operational parameters can significantly affect the mixing performance.

• Different mixing mechanisms can be identified using the probability distribution.

Abstract

Studies on powder mixing in industrial mixers are crucial for the improved criteria of mixing equipment design and optimization within various mixing unit operations. In the present study, a series of simulation for the powder mixing in an elaborately designed mixer, called a cross-torus paddle mixer, is conducted using the Advanced DEM-CFD method. The effects of various operational parameters on the mixing performance are analyzed and discussed in detail. Through these investigations, it is found that rotational speed, filling level, liquid viscosity, and paddle obliquity can significantly affect mixing performance. Owing to a much-enhanced convective motion of particles, a higher rotational speed exhibits a more efficient mixing process. Smaller number of particles inside the vessel shows the better mixing performance, which is attributed to an enhanced diffusive motion of particles. Decreasing the liquid viscosity or increasing the paddle obliquity can also result in a more efficient mixing in a diffusive dominant mode. By performing the simulation of mixing behavior in a mono-dispersed system, the present work provides significant evidence and novel insights to further understand the mixing mechanisms.

Introduction

Powder and particulate materials have been widely utilized in a variety of engineering fields such as food, pharmaceutical, chemical, mineral, and metallurgical engineering, in which the mixing and blending of powders is one of the most demanding unit operations to ensure the quality and performance of industrial products [[1], [2], [3], [4]]. Various types of industrial mixer are currently available with the purpose of achieving an efficient mixing under a specific industrial condition [5]. For instance, according to the features of mixing-driven structure, the industrial mixers can be broadly classified into mixers with rotating vessels (e.g., tumbling drum, V blender, double-cone blender, batch mixer etc.), and mixers with fixed vessels and rotating components (e.g., ribbon blender, paddle blender, ploughshare mixer etc.) [3]. According to the different predominant roles in mixing mechanisms, mixers can also be regrouped into convective, shear, and diffusive dominant mixers [6,7].

To analytically evaluate the granular dynamics, mixing, and segregation within various mixing unit operations, a series of experimental approaches are proposed such as particle sampling, visual tracking, particle image velocimetry, positron emission particle tracking, and magnetic resonance imaging [2,8]. However, those experimental tools may be expensive and intractable to obtain all the detailed information of particles within the powder mixing process [4,9,10]. Incidentally, even if the experiments can be performed successfully, development of theoretical models is impossible to predict mixing state in a mixer. This is because the theoretical solution does not exist in the powder system. In contrast, due to the improvement in advanced numerical models and computer hardware, numerical simulation provides us with a comparably more feasible way to perform the parametric studies and allow us to attain some insights into the optimization of device design and operating conditions [11]. The discrete element method (DEM), originally proposed by Cundall and Strack [12], has been widely applied to the modeling of granular and multiphase flows within a variety of industrial processes [13], such as pneumatic conveying [14,15], screw conveying [16,17], die filling [[18], [19], [20]], fluidized bed [11,[21], [22], [23], [24], [25], [26], [27]], and blending [[28], [29], [30], [31], [32], [33]]. Moreover, with an aim to deal with the modeling of complex shape boundary involved in a dense granular flow especially for the difficult procedures of particle-to-wall collisions, the DEM simulation coupled with the signed distance function (SDF) is currently developed [17], which has been validated in previous studies with a high adequacy as compared to the experiments [4,9,28]. As far as the modeling of arbitrary-shaped boundaries using the computational fluid dynamics (CFD), the immersed boundary method (IBM) has been recently introduced and developed [[34], [35], [36], [37], [38]], in which an arbitrary-shaped boundary can be easily modeled using the local-volume fraction of a solid object. A combination of the SDF and the IBM, referred to the Advanced DEM-CFD method [18,39], herein provides us with a desirable and adequate approach with a broad applicability to a variety of real industrial systems [40].

Over the past decades, to acquire a comprehensive understanding on the mixing features and mechanisms in industrial mixers [41], a large amount of research works including both experiments and simulations have been carried out. Typically, combined with operational conditions, particle properties, and mixer types, the mixing dynamics can exhibit different predominant modes along with all of three mechanisms (i.e., convective, diffusive, and shear mixing) to a higher or lower extent [42,43], which is accompanied by other abundant behaviors in terms of various flow patterns, segregations, avalanches etc. For instance, in a batch mixer such as in a rotating drum, different flow regimes (i.e., slipping, slumping, rolling, cascading, cataracting, and centrifuging) have been experimentally and numerically identified [44,45]. Moreover, for the mixing mechanism in such a mixer, the radial mixing is much stronger than axial mixing, thus, the predominant mixing mode is diffusion [9,43]. In a ribbon mixer, evidence shows that mixing in the axial direction is not as good as mixing in the perpendicular direction; thus, the predominant mixing mode is convection [4,46]. In a horizontal or vertical shaft mixer, it is verified that a high shearing force is exerted by the shear motion of mechanical blades to promise a high-efficient mixing process; hence, the predominant mode is shear [47]. Unfortunately, it should be pointed out that, despite of some achievements on the mechanism analysis of geometry-related properties as indicated above (e.g., batch mixer, ribbon mixer, and shaft mixer), an unambiguously scientific understanding especially for the effects of operational conditions remains limited. Consequently, the design and selection of an appropriate mixing equipment that is suitable for current industrial environments are still not straightforward [3]. Additionally, the mixing mechanism over a broad scope of operational and geometrical parameters has not yet been completely investigated and understood. Considering the critical importance of mixing mechanisms to determine the appropriate parameters to improve the mixing efficiency, it is necessary to provide a novel insight into the predominant mode related to the mixing performance as the change of various operating parameters (e.g., the effect of liquid viscosity, filling level etc.).

Focusing on the above aspects, in the present study, a series of simulations for powder mixing in an elaborately designed mixer, called a cross-torus paddle mixer, is conducted using the Advanced DEM-CFD method. The mixing vessel composed of a hemisphere and a coaxial cylinder remains stationary during the mixing process, inside which a torus paddle attached to a cross support can rotate along one extended rod of the cross support. In this mixer, optimization design, dominant parameters for mixing and mixing mechanism have not been investigated thus far. Hence, the paddle shape and mixing conditions are empirically decided by engineers. Moreover, in such a cross-torus paddle mixer, the mixing state is empirically known to be influenced by rotational speed, filing level, liquid viscosity, and paddle obliquity. Indeed, the liquid viscosity might influence the particle behavior in liquid, and hence effect of the viscosity on mixing state should be examined carefully. Therefore, in this study, the visualization and quantification of the mixing behavior in the cross-torus paddle mixer are discussed in detail over a broad scope of operational and geometrical parameters, i.e., paddle rotational speed, filling level, liquid viscosity, and paddle obliquity. In this study, probability density is newly proposed to examine the convective and diffusive motion during the mixing process in this mixer.

In this paper, the numerical modeling and boundary treatment of Advanced DEM-CFD method are concisely described in Section 2. Further, the simulation models including the geometry of mixer as well as the input parameters are discussed in detail in Section 3. Afterwards, the visualization and quantification of mixing processes regarding the effects of paddle rotational speed, filling level, liquid viscosity, and paddle obliquity are presented in 4.1 Mixing behavior for the reference case, 4.2 Parametric study of mixing state, respectively. By performing the simulation of mixing behavior in such a mono-dispersed system, the present work provides significant evidence and novel insights to further understand the mixing mechanisms.