Abstract
Bio-particulate matter includes grains, cereal crops, and biomass that are considered discrete materials with irregular size and shape. Although the flow of these particles can behave like a continuum fluid at times, their discontinuous behavior cannot be simulated with traditional continuum-based modeling. The Discrete Element Method (DEM), coupled with Computational Fluid Dynamics (CFD), is considered a promising numerical method that can model discrete particles by tracking the motion of each particle in fluid flow. DEM has been extensively used in the field of engineering, where its application is starting to achieve the popularity in agricultural processing. While CFD has been able to simulate the complex fluid flows with a quantitative and qualitative description of the temporal and spatial change of the flow field. This paper reviews the recent strategies and the existing applications of the CFD–DEM coupling approach in aerodynamic systems of bio-particles. It mainly represents four principal aspects: the definition of aerodynamic systems with its principals, modeling of particle motion including interaction forces of particle–particle and particle–fluid in the system, CFD–DEM coupling methodologies, and drag correlation models with theoretical developments, and the applications of aerodynamic systems related to the agricultural field. The existing published literature indicates that CFD–DEM is a promising approach to study the bio-particulate matter behavior immersed in fluid flow, and it could be benefiting from developing and optimizing the device's geometry and the operations. The main findings are discussed and summarized as a part of the review, where future developments and challenges are highlighted.
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1 Introduction
1.1 Bio-particulate Matter
Agriculture crops are the primary source of various bio-particulate matter include cereal grains, seeds, and biomass, which are differences in shape, size, density, and other physical characteristics. These materials, which are considered the primary bio-particulate matter in this investigation, are used as a raw material or grinded for energy (biomass) production or food to provide calories and protein resource for human and animal diet. It sometimes contains a heterogeneous mass of foreign materials such as sands, stones, sticks, chaff, glass fragments, weed, and other crop seeds. These contaminants are mainly introduced during harvesting and post-harvesting process [1]. Therefore, before being processed, separation and purification of cereal grains and seeds from impurities is an essential process in food processing and oilseed trading [2]. This process can be carried out by more technological procedures depending on their physio-mechanical characteristics. In this way, a part of impurities is cast away depending on their size (width, length, thickness); others are separated depending on their drag coefficient [3]. Given that the principle of separation and the type of impurities, a wide range of technical equipment and installations are used for carrying out the separation of impurities such as aerodynamic separators, screening devices, magnetic separators, vibrating separators, etc. [4]. Herein, the current work will focus only on the aerodynamic systems and processing used for bio-particles such as cereal grains and seeds.
1.2 Aerodynamic Principals
Generally, aerodynamic devices are commonly used in the separation process of bio-particulate matter. It can be defined as a process of using air generated by natural or mechanical fan to remove light, chaffy, and dusty materials out of the bio-particles. It is considered one of the critical methods which can be used lonely or usually in conjunction with another method to separate and clean various heterogeneous agricultural grain mixtures [5,6,7]. The advantages of this technique can be summarized in the following points: allow for cleaning and segregation of seeds particles simultaneously without changing the separation parameters, obtain the product without damage, no change in the physical and biological properties of the particles during the separation process, and characterized by a high efficiency without demand much power [8]. Found that the most effective factors to improve the quality of the aerodynamic system are: the aerodynamic properties of the particulate matter, feeding load ratio of granular flow, speed and angle of feed grain material, airflow properties, particles properties, and the system inlet geometry [9,10,11,12].
In this process, the aerodynamic properties of particles, such as their critical or terminal velocity and drag coefficient, are mainly used [7, 13]. The large the difference values of terminal velocities in the mixture component, the better and more efficient is the aerodynamic separation [14, 15]. Commonly, the aerodynamic systems can be classified into three significant aspects based on the direction of the air stream in the system: vertical, horizontal, and oblique.it can also classified depending on the conditions of the airflow or location of the fan in the system (vacuum, overpressure, and hybrid) [15, 16]. Herein, the value of the redistribution of product components between fractions should be taken into account to evaluate the quality of the aerodynamic separation process, mainly when the initial product is divided into three or more fractions [17].
The expediency of using forced air technology is determined by the presence in the initial material of components that differ from the main product by aerodynamic properties. If there are no such differences, other methods will be used. Up to 70% of the impurities in the original grain material that comes to post-harvest processing are separated from the main crop by aerodynamic characteristics [17]. The efficiency of any air-using machine depends on the weight and aerodynamic drag of the particles, which in turn affects their terminal velocity of fall [18]. Consequently, awareness of the aerodynamic properties seems necessary in the proper design of aerodynamic equipment. The drag coefficients of a wide range of bio-particles material have been measured experimentally by finding the suspension velocities of the particles in an airstream [19, 20]. To correlate the drag coefficient, the Reynolds number has been used by grouping the particles within the limits of a sphere and a cylinder shape [21]. The need to correlate the drag coefficient is the difference between the experiment and the calculated terminal velocity of grains. As mentioned above, the aerodynamic properties can be mainly described by two major aspects: critical or terminal velocity and drag coefficient [22]. The first parameter, which is considered the main representation of the aerodynamic properties of particles, can be mainly used as their distinguishing feature in such aerodynamic applications and optimizations [8, 20, 23]. Terminal velocity is the velocity of the vertical air stream which keeps the particle to be suspended in the air as a result of balancing their weight with the force of the air stream [24,25,26]. The values of this parameter are affected by some secondary parameters like density, shape, and cross-sectional area [22] that can be formulated according to Eq. (1) [27, 28]. The greater the particle mass, the greater the terminal velocity, and the larger the particle area, the lower the velocity.
where \(V_{T}\) is the terminal velocity, \(m_{i}\) is the mass of the particle, \(g\) is the gravity acceleration, \(k_{a}\) is the dimensionless coefficient of aerodynamic resistance, \(A_{i}\) is the projected or lifting area of the particle,\(d_{i}\) is the particle diameter, \(\rho_{i}\) and \(\rho_{a}\) are the particle and air density,\(C_{d}\) is the drag coefficient and can be calculated, as mentioned in Sect. 6. The drag coefficient is a dimensionless parameter of the particle that is used to quantify how easy or difficult it is for a particle to be entrained in the fluid flow [29]. It is related to the particle Reynolds number, which is given by Eq. (2)
where \(R_{{e_{i} }}\) is the particle Reynolds number and \(\mu_{a}\) is the dynamic viscosity of the air. Since the particle Reynolds number depends on terminal velocity, the calculation of terminal velocity is an iterative procedure. The following three flow regimes can be characterized based on particle Reynolds number: Stokes’ regime when \(R_{{e_{i} }}\) < 0.2, intermediate regime when 0.2 \(< R_{{e_{i} }} <\) 1000, and Newton regime when \(R_{{e_{i} }} >\) 1000 that will be described in detail in Sect. 6. Typically, the value of the drag coefficient \(C_{d}\) of spherical and cylindrical particles can be assumed 0.44 and 1.0, respectively, in the range of Reynolds number of \(R_{e}\) = 1000 to 200,000 [22, 30].
Experimentally, the suspension or terminal velocity of particles can be determined by the suspension apparatus test, and it can be slightly differing from experiment to another depending on the grain material and the study condition [24, 31,32,33,34].
When applying aerodynamic principles to cereal grain crops, a method for expressing the projected area of the particle must be chosen because of the irregular shape of the particles. So, in most cases, the particles are assumed to be spherical, where the diameter of the particle could be taken as the diameter of a sphere of the same volume as the original size. In cases where the volume of the object is difficult to evaluate, the geometric mean diameter is a good approximation of the diameter of the equivalent sphere, provided that the shape factor is close to unity [26]. Theoretically, the net force acting on a particle moving in a fluid is defined by the difference between the drag and the gravitational forces, as shown in Eq. (3) [21].
where \(F_{net}\) is the net force acting on the particle, \(V_{a}\) is the velocity of the air.
1.3 Modeling Representations
Nowadays, improving the design and the performance of harvesting and post-harvesting devices such as combine harvester, grain dryers, spouted bed, aerodynamic separators, etc. becomes an urgent necessity for industrial needs. Experimental studies, mathematical models, and computer simulations are essential tools to solve this problem. With the current increase of computing power and technology, computational simulations are showing high adaptability to simulate the multiphase flow accurately. Numerical models have been used with some relevant modifications in recent and previous studies to describe the particulates matter and gas flow field inside the aerodynamic systems [35,36,37,38,39,40,41,42].
Since the bulk bio-particulate matter mass introduced to the structure domain, it is considered discrete elements, where each particle is an element, having an interaction with neighboring elements. Discrete Element Method (DEM) is a common and powerful numerical simulation technique for predicting and modeling this discrete media flow basis on Newton’s laws of motion. The extensive usage of bio-particulate matter applications in industrial processing methods leads to several DEM articles development [43,44,45,46,47,48,49,50,51]. Computers with significant memories and a high-performance processor make it possible to simulate a large number of particles with a straight-forward approach. DEM can dynamically simulate each particle trajectory of dense phase flow by tracking its rotational and translational movement in the domain, taking into consideration the contact forces and the interaction couples of particle–particle and particle-boundary [35, 52, 53].
Practically, the particulate matters are introduced to the aerodynamic systems with air or gas flow; hence, it can be regarded as multiphase flow. Therefore, Computational Fluid Dynamics (CFD) models are mainly used to capture the air or fluid flow characteristics successfully with essential data in predicting the aerodynamic behavior [54,55,56,57]. For gas-particle flows, CFD multiphase models cannot be used to estimate the particulate matter phases; due to many restrictions happen when the dense flow is applied, those restrictions can be exceeded by coupling CFD with DEM [58]. This coupled process increases the computational time but enables a resolved particle–particle interaction combined with gas to solid and solid to gas modeled interactions as well.
1.4 Scope of this Work
In this decade, as illustrated in (Fig. 1), CFD–DEM coupling has become a hot research area for fluid-particles flow modeling, especially with the increase of computer technology progress and theoretical developments. However, previous reviews related to the bio-particulate matter field concentrated on DEM modeling [51, 59] or CFD technique [57] only; no reviews can be found on CFD–DEM coupling basics on modeling the bio-particulate matter in aerodynamic systems. However, these reviews did not concentrate on the force models related to fluid-particle interactions or the coupling ways between CFD and DEM for the bio-particulate matter. This paper is the first try aiming to provide a summary of the investigates based on computational simulations in the past two decades or so to open the way for the researcher to know the last working in these field. This information is important in the application of grain modeling in particle–fluid multiphase flows, and therefore, an extensive review is necessary.
Number of published works obtained from Science Direct using keywords: “CFD–DEM” (Accessed in December 2019)
The objective of this paper is to comprehensively review and collect the existing published research that used the coupling of CFD–DEM as a numerical technique for simulating the aerodynamic particulate systems related to the agricultural field. Firstly, this review summarizes the representations of the aerodynamic system in the agricultural process and industries, including some experimental works. Secondly, it represents the equations of particle motion and contacts force models between particles and interaction forces between particles and fluid in the aerodynamic systems as apart of DEM and CFD theories. Thirdly, drafts the CFD–DEM coupling ways, including theoretical developments and applications with a brief introduction of drag correlation models. Fourthly, introduces the applications of CFD–DEM modeling in aerodynamic systems and particle–fluid flow systems where the significant findings were discussed in some detail. Finally, the main challenges of CFD–DEM currently faces, and the exciting research topics for future studies are discussed. We conclude that CFD–DEM is an effective method for particle–fluid scale research in the aerodynamic systems related to the agriculture field. It also has a bright future as it offers a new way of understanding industrial processes and/or phenomena with practical particle shapes. However, there are still some aspects that are needed to be investigated in the future.
2 Theoretical Background of DEM
The DEM is considered one of the numerical modeling technique, which is first published by Cundall and Strack [60]. It is mainly developed to complement the finite element method to solve the complicated problems in engineering and applied science and investigating natural phenomena of granular flow of differently shaped particles that display sporadic conduct [61]. DEM simulations can also provide dynamic information which is extremely difficult or impossible to obtain by traditional experimentations, such as trajectories of, and transient forces acting on, individual particles, and analyze multiple, interacting, deformable, discontinuous, or fractured elements undergoing rotations and large displacements [59, 62]. With advanced computers, the simulations software reiterates the calculations million times during a second for each element of the system. Currently, the most advanced software and hardware allow simulations of processes with over a million particles, which facilitate the practicality of the DEM approach [63].
In DEM modeling, particle–particle interaction is treated as a dynamic process and solved by the explicitly numerical scheme. The contact forces, rotations, momentum, and displacements of a stressed particle are described by tracking each contact of the individual particles [64]. The primary assumption in the DEM is that every discrete element has different boundaries that physically separate it from every other element in the analysis. During the element movement in the domain, the translating and rotating behavior equations are applied on an element-by-element separately and the elements contacting through boundary forces. The deformation resulting from the collision can then be decoupled from the mean motion and written as the sum of the bodies’ normal modes, which in turn gives a newly derived set of decoupled modal equations. These new equations are then solved by an explicit central difference scheme, where the final solution is obtained through modal superposition [59, 65].
Recently, the Discrete element method (DEM) application is gaining popularity in the harvest and postharvest processing of grain and highly utilized for many industrial processes, such as granular mixing, drying food, pharmaceutical industries, mining, and agricultural processing. The widely spread is because of its close and real characterization of actual conditions in predicting various processes [66]. Unlike the field of mining and the chemical industry, however, DEM is not widely applied in the agricultural processes because of various particle property issues arising from the biological origins of grain and food products.
In the agricultural industry, the DEM in agricultural and food processing applications have been considerably developed to describe; the flow in chutes and dryers [37, 67,68,69], the aerodynamic conveying systems [70, 71], the discharging silo [72], the transportation and compression of seeds [73], the dynamics discharge of particles in hoppers [74], the shaking separation of paddy and brown rice [75], the grain–straw separation screening in combine harvester [76, 77], the fluidization and spray drying of food powders [78], the grain transportation and aerodynamic separation [79], the grains segregation and seed motion in seed feeding device [80, 81], the screening separation of crop seeds [82, 83], and the mixing process in a bucket elevator [84]. DEM has also been useful in the modeling of interactions between soft materials: fruits such as grape [85], apple [86], or biomass [87]. A complete description and good over a review of the DEM can be found in much previous literature [51, 59, 65, 88, 89].
2.1 Approaches in DEM Modeling
In general, the granular dynamics modeling through DEM techniques can be classified into hard-sphere and soft-sphere approaches depending on the particle deformation during contact or collision [90]. The first concept of the “hard sphere” that comes to mind to simplify the collision modeling is to treat the particles as hard spheres; however, it is not necessary to describe the collision as entirely elastic. The word hard simply means that there is no interpenetration or deformation during the collision. In contrast, the word “soft” revolves around the deformation of spheres and the duration in contact. Figure 2 schematically indicates the main differences between these two modeling approaches [91, 92].
In the hard-sphere modeling approach, the effect of overlapping and deformation or interpenetration between particles during contact is assumed to be neglected [93]. So, this contact can be named as a non-smooth DEM where the particle's motion and the energy loss during a collision can be modeled through shock laws and the coefficients of restitution [94]. Collisions are also assumed to happen in a short time and may be assumed to be instantaneous; because the collision is limited between two particles only, one collision at a time, and does not consider multiple contacts [58]. So, different time steps will be applied, and the time step interval for the numerical solution varies with the time between each collision. Therefore, this approach is probably suited for rapid granular flow simulations, where the particulate material is partially or entirely fluidized [92].
In contrast to the soft-sphere approach, the overlapping at the contact points is allowed, and the contact forces between particles are strongly considered [62, 91]. Herein, it is essential in this approach to model the forces of elastic restitution and friction that happened during the collision of the particles [95]. Because of the nature of the iterative schemes used in the soft-sphere approach, it is susceptible to the time step. Therefore, the time step interval is assumed constant during simulation [93] and should be smaller than the duration of contact for stability considerations [96]. Usually, in most soft- sphere models, the duration of the contact is artificially increased by allowing softer interaction and hence reducing the required CPU time. The obtained deformation due to the collision can be considered similar to that occurs at the contacts among bio-particles. These deformations are used to calculate elastic, plastic, and frictional forces between particles [59]. Hence, this approach highly used in particulate mechanics models related to agricultural cereals and crops. The motion of particles in this approach is described through numerical integration of the Newtonian equations of motion. Apart from external forces acting on the system, the interparticle forces are of crucial importance to these models [38, 97]. The magnitude of the overlap can be related to the interparticle contact force, as discussed subsequently.
The significant advantage of soft-sphere models is that they can model the dense-phase bulk granular materials regarding the multiple particle contacts [98], which is essential when modeling quasi-static systems [62]. These models start by solving the equations governing the linear translation and rotational motions of particles [92]. While in hard-sphere models, the interaction forces are assumed to be impulsive, and hence the particle modeling strategy starts from the equations governing momentum exchanges [93].
However, hard-sphere approaches are computationally cheap, fast, and preferred for non-dense flow; it can give a limited description of the dense material’s response involving multiple simultaneous contacts [99]. Therefore, given the advantages of soft-sphere approaches mentioned above for describing the bulk material physics, where it is most commonly used in the grain and food processing industries, no further consideration of the hard-sphere algorithms is given in this study. Thus, soft-sphere modeling is called DEM (Discrete Element Method or Distinct Element Method) [100], which is the scope of this review.
2.2 Governing Equations of Motion
In soft-sphere DEM modeling, the motion of each particle can be tracked by calculating the contact forces and displacements using an explicit numerical scheme and a very small time step [60]. The particle movements can be divided into two parts: the translation motion calculated by the basic’s equations of Newton’s second law as shown in Eq. (4), and rotation motion described by Euler’s law as formulated in Eq. (5) [101,102,103]. In general, the spaces between the particles are filled with interstitial fluid, usually air in aerodynamic systems. When that fluid forces the particles, the effect of this interstitial fluid should be taken into account. Nevertheless, if the particles are considered to be large and heavy, they are exempt from the effects of the interstitial fluid [98, 104].
where \(m_{i}\) is the particle mass,\(x_{i}\) and \(\Phi_{i}\) are the position and the orientation in the space of particle \(i\), respectively,\(F_{ij}^{C}\) the total contact force, \(M_{ij}\) is the momentum acting on particle \(i\) by particle \(j\) or wall,\(f_{i}^{g}\) is the gravitational force, \(F_{i}^{f}\) is the fluid-particle interaction force on the particle \(i\), \(M_{rij}\) the momentum generated by rolling friction when the particle rotates in a fluid which will be represented in Sect. 5, \(F_{ik}^{nc}\) is a term of non- contact force acting on particle \(i\) by particle k or other sources, and \(I_{i}\) is the moment of inertia of particle \(i\), and \(T\) is the time.
The contact between two particles is not taken place at a single point but on a specific area, which can lead to making the particles slightly overlapping on the normal and tangential coordinates (n and t) [62]. Particle overlapping cannot be neglected because it can significantly affect the simulation result [105]. So, the total contact force acting on the particle at the contact plan can be analyzed on n and t coordinates which can be mathematically calculated according to Eq. (6). In addition, (Fig. 3) indicates a schematic illustration of the typical contact force vectors with overlapping and torques implicated in a soft-sphere DEM modeling.
where \(F_{ij}^{n}\) and \(F_{ij}^{t}\) are the normal and tangential contact forces on the particle \(i\) by contacting particle \(j\), respectively.
2.3 Modeling of Contact Force
In any granular flow, forces are mainly generated by interparticle contacts that can be mechanically described by how the particles “see” one another. The philosophy of DEM is to use rigid springs, acting both normal and tangentially to the contact plane to calculate the interparticle forces. Although DEM simulations are worked efficiently in predicting many processes in the agricultural industry, it requires a detailed understanding of the interactions between particles under various loads.
Precise values of physical and mechanical parameters of granular materials that have biological origins are considered critical parameters for modeling contact models of DEM [106]; due to the high moisture content of these particles, which makes the deformability to be high during contact [51]. As such, different contact models can be generated and developed based on elastic, viscous, plastic, dry friction, and adhesive interactions.
Usually, the main assumptions of the theoretical contact models are considered the particles to be isotropic and elastic, where the contact is completely smooth. It is a beyond contradiction that the bio-particulate matters are varied in geometry and shape. Most of them have a convex shape, while others are spherical in shape, but none of them are purely elastic bodies [51]. Therefore, the application and the development of contact models for biomaterials related to the agricultural field face many restrictions.
The contact forces in any DEM code consist of forces normal-to-contact plane and force tangent-to-contact plane. For spherical particles, the contact plane is perpendicular to the line that connects the centers of two spheres. For non-round particles, the methodology for determining a contact plane is more complicated. It can be determined by the closest points of two particles or the closest points of a particle and triangle or the two points with the maximum overlap distance in the case of a physical contact [107]. This chapter will introduce the standard contact models and the interaction properties, including coefficients of restitution, static and rolling friction, plastic or viscous damping, and adhesion used by investigators for the bio-particulate matter.
2.3.1 Normal Force Modeling
The primary requirements to model the normal contact force are that the force should have to be repulsive, and the model has to allow significant energy dissipation. For this purpose, several investigators developed many models to describe the behavior contact of the granular medium systems.
2.3.1.1 Hertzian Contact Model
Following the work of Hertz in the nineteenth century and the theory of elasticity [108, 109], the normal contact force is modeled by considering the response of two elastic spheres in contact over a small circular contact area. This model has been widely used to determine the modulus of elasticity for various agricultural grains that have a convex shape [110]. It is usually called as a Hertzian spring dashpot model where the normal contact force is modeled as the sum of an elastic force and a damping force. When considering the overlapping during contact, the model can be expressed mathematically in an incremental way, as shown in Eqs. (7, 8, and 9).
where \(E^{*}\) and \(R^{*}\) are Young's modulus equivalent and radius, \(E_{i} , E_{j}\), and \(\nu_{i} ,\nu_{j}\) are Young's moduli and Poisson's ratios of the two contacting spheres of radii \(R_{i} , R_{j}\),\(S^{n}\) is the normal overlapping, \(\eta\) is called a damping ratio, which is a dimensionless parameter related to the restitution coefficient that can be calculated as expressed in Eq. (10) [44, 111].
where \(\varepsilon\) is the coefficient of restitution defined by DEM user according to the studying case and \(m^{*}\) is the equivalent mass for the particles in contact and can be calculated according to Eq. (11).
2.3.1.2 Elastic–Plastic Contact Model
This model was first introduced by Walton and Braun [112] and named as a Hysteretic Linear Spring Model [113, 114]. This elastic–plastic or repulsive-dissipative normal contact model allows simulation of the plastic energy dissipation on contact without introducing the overhead of long simulation times. Besides, the energy dissipation is not considered the velocities of the neighboring particles and loading rate that makes the energy dissipation insensitive to other contacts. Furthermore, the coefficient of restitution is velocity independent, and it can be accurately modeled the compressible materials with correctly simulating the non-adhesive particles flow [35, 52, 53, 115]. The following equations starting from Eqs. (12–17) draw and describe mathematically one by one the linear hysteresis model used in DEM code [29, 107, 116,117,118]
where \(F_{i}^{n,T}\) and \(F_{i}^{{n,\left( {T - \Delta T} \right)}}\) are the normal elastic–plastic contact forces acting on the particle \(i\) at the current time \(T\) and at the previous time \(T - \Delta T\) respectively, where \(\Delta T\) is the timestep, \(\Delta S^{n}\) is the change in the overlapping during the time step, \(S^{n,T} , S^{n,T - \Delta T }\) are the normal overlap values at the current and at the previous time, respectively, \(K_{u}^{n}\) and \(K_{l}^{n}\) are the unloading and loading contact stiffnesses, respectively.
Note that the unloading force is limited by the value of \(0.001 K_{l}^{n} S^{n,T}\) to ensure that the normal force becomes zero with zero overlappings. A schematic sketch, as shown in (Fig. 4) can demonstrate the overlapping circle (A–C) of loading and unloading response due to the normal force effect where the hatched area is represented the energy dissipation during the particles contact. Besides,\(K_{l}^{n}\) and \(K_{u}^{n}\) are the slope of loading and unloading lines, respectively, and the plastic deformation only happens during the contact of the particles \(i\) and \(j\); after that, the residual deformation neglected.
The coefficient of restitution can be determined by the user, which represents the energy dissipation due to particle–particle or particle–wall contact; also, the loading and unloading stiffness represented in Eqs. (14 and 15) can be taken into account by considering the valve of Young’s modulus and the particle geometry.
whereas:
where \(E_{i}\) and \(E_{w}\) are Young’s modulus of particle and boundary, respectively, and \(Z\) is representing the particle size or geometry. This model should be applied to adequately selected individual cases of the behavior of dry and hard seeds with the elastic behavior in the normal direction, such as the application of discharging silo with rapeseeds and the aerodynamic systems of seeds and foreign materials separation [35, 72].
2.3.1.3 Visco-Elastic Contact Model
The simple model to describe the Visco-elastic behavior of the particles is called a linear elastic, viscous model. The advantage of this model is that it takes less time and machine resources to process but provides less accurate results compared to the hysteretic linear spring model [107]. When Visco-elastic particles are in contact, the normal contact force is given by the sum of elastic repulsive force and a damping force proportional to the velocity as formulated in Eq. (18) [51, 119].
where \(C^{n}\) is the normal damping coefficient and defined as follows in Eq. (19).
where the relationship between the damping ratio and the restitution coefficient can be described in Eq. (20) [120]. In detail, (Fig. 5) describes the relationship between the damping ratio and restitution coefficient given by Eq. 19. The graph is showing the increase of damping ratio when the restitution coefficient decreased; because of the inverse relationship between the two parameters.
For soft biological materials such as apple, potato, and tomato, etc. in addition to the soft and high moisture content of seeds, Visco-elastic contact model is efficient and appropriate to predict the energy dissipation and the impact reaction [121, 122]. While for dry and hard seeds such as rapeseed, the Elastic–plastic contact model works well to estimate the contact and impact behavior [72].
2.3.2 Tangential Force Modeling
2.3.2.1 Linear Spring Coulomb Model
This model named by the Linear Elastic-frictional model; because of its elastic behavior before the friction commencement, and it can regenerate Coulomb frictional contact behavior for static and dynamic frictional values. During the tangential contact, the particle sliding plays a vital role in determining the total tangential contact force, where Eq. (21). can express this effect [29, 53, 118].
where \(F_{i}^{t,T}\) and \(F_{i}^{{t,\left( {T - \Delta T} \right)}}\) are the tangential contact forces at the current and previous time of the simulation, respectively,\(\Delta S^{t}\) is the change in the tangential overlapping during the time step, and \(\mu\) is the friction coefficient which can be defined as a static and dynamic coefficient (\(\mu_{s }\), \(\mu_{d}\)) depending on the tangential sliding contact, as shown in Eq. (22) [29, 117].
When the tangential force exceeds the limit of \(\mu_{s} F_{i}^{n,T}\) The sliding is considered to be taking place on the contact. Once that force falls below the value of this value, the contact is considered non-sliding again. This model applied effectively and shoe a high validity to separate jojoba seeds from its leaves using cyclonic separation process [35] and for vertical pneumatic separation of sugarcane bagasse particles [29].
2.3.2.2 Mindlin-Deresiewicz Model
This model is called the elastic-frictional contact model, which is first derived from the mathematical analytic of elastic spheres in contact under varying oblique forces [123]. It is mainly consisting of simple loading histories of varying normal and tangential forces and a minimal range of tangential displacement between the contacting spheres [124, 125]. The tangential force in this model is given by Eq. (23) [107]:
where \(s^{t}\) is the tangential relative displacement at the contact, \(\widehat{{n_{c} }}\) is the unit vector in the normal direction at the contact, \(\eta^{t}\) is the tangential damping ratio and is estimated using Eq. (24), \(s_{max}^{t}\) is the maximum relative tangential displacement at which particles begin to slide as can be formulated in Eq. (25), and \(\frac{d}{dT}S^{t}\) is the relative tangential velocity at the contact.
The Mindlin–Deresiewicz model does not work appropriately with rolling resistance models for non-spherical particles. Therefore, when the Mindlin-Deresiewicz model is selected with non-round particles, the rolling resistance must be neglected [107]. This model was improved to be suitable in simulating soybeans flowing down an inclined chute [68]. In this simulation, the soybeans (non-spherical particles) are represented by clusters of spheres to simplify contact detection, and the modeling showed a good agreement with the experimental data. The frictional contact model of spherical particles was also developed based on the Mindlin-Deresiewicz model to predict the particle–particle slip and the sliding of stainless steel beads, pea, and rapeseed [126].
2.4 Tangent Stiffness Model
Hertz-Mindlin contact model is usually used to represent the tangent stiffness model, which is applied in DEM applications as the primary law to calculate particle interaction forces in the tangent directions [44, 123, 125]. It is also named as a linear spring-dashpot model that includes springs, dashpots, and frictional sliders, as shown in (Fig. 6) [127]. This model combining Hertz's theory [109] to describe normal stiffness and Mindlin and Deresiewicz's theory [123] to describe tangential stiffness. These stiffnesses were calculated as mentioned in the above sections by assuming the presence of elastic springs and dashpots in the normal and tangential directions. The spring stiffness, dashpot coefficient, and friction sliders are expressed through Young’s modulus parameter, friction coefficient, and coefficient of restitution, respectively [39, 116, 128].
Hertz-Mindlin contact model with viscous damping and frictional slider in the tangential direction [35]
This model is applied intensively to model and predict the interaction of bio-particulate matter, including seeds and grains. The calibrations and validations showed high reliability of this model, which is presented a high prediction of the particle’s behavior. For an instant, simulating the motion of rice grain and short straw in air-and-screen cleaning device [39], simulating the flow of corn-shaped particles in spouted bed [40], simulating of rapeseed and wheat grain motion in seed feeding device [81], predicting the corn grain flow behavior in a commercial screw auger [129], simulating the motion of rice grain and rice straw in a variable-amplitude screen box [76], and optimizing the air-blowing maize precision seed-metering device [42], etc.
2.5 Adhesion Contact Model
In order to separate bodies in intimate contact; mechanical work must be expended to overcome the adhesive forces. They have appeared in beddings of biological materials that have an amount of moisture content, and its effect is shown in agglomeration of powders and small size particles that may create problems for storage and handling [130, 131]. In order to capture this behavior numerically, the normal repulsive force has to be supplemented by the attractive normal force to predict its flow characteristics accurately [107]. Adhesion between biological particles not only acts because of moisture content but van der Waals forces, electrostatic forces, or liquid bridges effects as well [132]. Liquid bridge force plays a vital role during modeling particles more significant than a fraction of millimeter-scale, which arises from the capillary pressure in the bulk of the liquid and the sum of the surface tension of the liquid [119, 133]. This force value depended on some significant aspects, such as space area between particles, the surface tension of the liquid, geometry and the volume of the bridge, and contact angle between the liquid and solid surface [134].
The most common and popular model for representing the adhesive behavior is developed by Johnson-Kendall-Roberts (JKR) [135]. This model introduces the effect of adhesion into the Hertzian contact model, where the contact area between two particles is slightly larger than the one predicted by the Hertzian theory. This surface energy term is added to the total energy of the system [107]. The normal JKR adhesive model force can be calculated according to Eq. (26) [107]:
where \(F_{{i_{adh} }}^{n,T}\) is the normal adhesive contact force at the current time, \(a\) is the separation distance of contact between particles or between a particle and a boundary, as shown in (Fig. 7), where it is related to the normal overlap using the expression introduced in Eq. (27) [51, 107]:
where \({\Gamma }\) is the surface energy and can be used to calculate the maximum liquid bridge tensile force that occurs between two particles as formulated in Eq. (28) [119]:
where \(P_{max}\) is the maximum liquid bridge tensile force since the effect of its behavior can be observed through the DEM simulation of the particle’s free-flowing and the discharge rate from hoppers of different inclinations [74, 136]. Another study was performed on agricultural material and reported that the maximum liquid bridge tensile force between wet rapeseeds is approximately tenfold of the seed weight, which means that cohesive behavior can occur in the case of some millimeters of particles’ size [51].
Schematic diagram of the liquid bridge force as a function of the separation distance between two particles [74]
The JKR model has a strong theoretical basis and is widely accepted for adhesive elastic sphere particles. Since the surface energy can be measured experimentally, this model could be used without calibration, in principle, for simulating perfect spheres [107].
On the other hand, when adhesion between particles is due to liquid bridge forces (big attraction between the polar molecules of water), another adhesive model was used, namely the constant adhesive force model [29, 127]. This model depends on two significant aspects: the minimum distance between particles or particles and a boundary before the adhesive forces applied and the force fraction expressed as a function of the particle gravity force. Hence, it means that since the force fraction reached 1, the adhesive force will be equal to the gravity force applied to the particle. In the case of contact between two particles of different masses, the smaller mass is considered for the calculation of gravitational force [107], as described in Eq. (29):
where \(f_{adh}\) and \(\delta_{adh}\) are the force fraction and the adhesive distance, respectively. Note that, when \(\Delta S^{n} \ge 0\) the particles start adhering to each other, but if \(\Delta S^{n} < 0\) the particles separate [127]. This model is applied effectively to represent the adhesion force of sugarcane bagasse particles during the pneumatic separation [29].
3 Modeling of Particles
The granular material is introduced in many fields of industries such as chemistry, agricultural processing, civil engineering, but their behavior is not yet well understood. Even though a pile of particles will behave like a porous solid, it will flow like a liquid if it is put on an inclined plane. Nevertheless, if it subjected to significant vibrations, it would have a gas-like behavior. These behaviors of granular solids were first described in an old proverb (ca. 98–55 B.C.) as “One can scoop up poppy seeds with a ladle as easily as if they were water and, when dipping the ladle, the seeds flow in a continuous stream” [95]. To model granular materials correctly, the shape is not only required but physical properties, which include size, density, moisture content, etc. should be taken into consideration and determined individually for each particular DEM modeling application as well [106].
Generally, realistic modeling of the particle shape in simulations plays an essential role in emulating real processes [137,138,139,140]. The Bio-granular materials, such as grain, seeds, tubers, and soft fruits have a considerable difference of shapes, from spherical (e.g., rapeseed), ellipsoidal (e.g., rice) and diamond with round (e.g., corn) or sharp-edged (e.g., buckwheat), to very complex, non-convex shapes of fruits and tubers [51]. The dimensions of these materials can vary from below an mm to tens of cm, which gives it a significant consideration during modeling. Although measuring the three dimensions: length, width, and thickness of the particles is very important for modeling, the roundness of edges and a ratio of the dimensions should also be determined especially to describe the complex shapes [106, 141].
Real particles are almost non-spherical, so they are rarely used in simulation studies due to difficulties in representing these shapes in simulations’ software [137]. Early, particles in DEM simulations were modeled as discs and spheres; because the direction of the normal contact forces is always toward the center, and the particles’ rotation is only affected by tangential contact forces [142]. Athanassiadis et al.[143] reported that the particle shape has a strong influence on the mechanical response and the interaction forces of granular material, particularly on stiffness and yielding parameters. They obtained this quote based on an experimental work carried out on fourteen particle geometries where all are in three dimensions (3-D) printed from the same material. The work includes several shapes, such as sphere, tetrahedron, cube, octahedron, dodecahedron, icosahedron truncated, tetrahedron, triangular bipyramid, tetrahedral frame, and jacks with arm length. Not only the particle size, shape, physical and mechanical properties are regarded as a big challenge for operating the DEM simulation modeling but the computing power, time-consuming, and the number of discrete particles in the system as well [59, 106, 143].
Complex shapes or non-spherical particles which are very common in the bio-particulate matter are often modeled on DEM as the multi-sphere approach [124, 137, 144, 145]. In this method, the particle shape is made by assembling a different number of spherical particles together, which in turn increases the computational speed and increasing the accuracy to determine the interaction between spheres [145]. The multi-sphere approach was ideally used to model the shape of bio-particles such as soybean [106, 124], corn [40], rice [146], wheat [69], pea, and bean [147]. The Accuracy of the particle behavior prediction is influenced by the number of sub-spheres combined. In the case of a small number of sub-spheres (\(\le 9\)), the particles interpreted as interlocked, if higher than that it may be simply classified as a decrease of roughness when the number of sub-spheres increases [148].
Advanced approaches were developed to model more complex particle shape in DEM using 3-D shapes, such as ellipsoidal [149,150,151], super-ellipsoid [152,153,154], sphero-cylinders and capsules [41, 155, 156], superquadric [157,158,159], bonded particles [160,161,162,163], polyhedral [35, 164, 165] and polygonal [166,167,168]. Applying these advanced approaches needs a precise determination of the contact point, and normal and tangential contact vectors [51, 169].
Table 1 summarized the developed particle shape models used for predicting the behavior of most common agricultural cereal grains. As presented, the multi-sphere approach is commonly used where the best number of spheres to represent a single grain, or a seed kernel has not been confirmed yet. This leakage is because of the complicated shape of agricultural grains, and the presence of the surface crease makes it challenging to develop a particle with identical shapes. So, the number of spheres should be approximated by trials depending on the computation time and prediction accuracy required.
4 Theoretical Background of CFD
At present, Computational Fluid Dynamics (CFD) is frequently used in the simulation of the internal or external flow field of several fluid systems [184]. It is continued to expand the scope of application and offers new ways to solve practical engineering and agricultural problems. It can predict and provide a qualitative and sometimes even quantitative prediction of fluid flows via mathematical modeling (partial differential equations), numerical methods such as finite volume method, and software tools by solving the transport phenomena equations of mass, momentum, and energy [54, 185]. It has been widely used in industry to optimize processes, reduce the energy costs, create new designs without wasting resources by carrying out experiments, and predict fluid flow in several processes such as mixing, drying, separation, and fluidized bed granulators [186].
Usually, to drive the continuum flow pattern in the presence of a secondary particulate phase, the system domain is discretized in small grid cells where the volume-averaged Navier–Stokes–Equations governed the fluid phase motion [53, 102, 103, 187]. These 3-D governing Eqs. (30 and 31) are typically referred to as continuity and momentum conservation equations. Recently, the solution of these equations is solved computationally utilizing finite volume method in a CFD code, which can be written as:
where \(\alpha_{f}\) is the fluid volume fraction in each cell,\(\rho_{f}\) is the fluid density,\(v_{f}\) the average velocity of a fluid cell, \(p\) is the pressure shared by two phases, \(\tau_{f }\) is the viscous stress tensor, and \(F_{i}^{f}\) is the interaction force of the fluid on the particle \(i\).
The numerical settings of CFD should be selected appropriately to make the results more reliable. Therefore, a series of numerical calculations for aerodynamic systems were performed using different grid numbers and turbulence models [184]. The accuracy of the solution generally increases with an increase in cells in the region but using a smaller grid size to discretize the region results in longer computational time [186, 188]. Although the internal flow of most agricultural aerodynamic systems is considered a turbulent flow, it is an unfortunate fact to accept a single turbulence model to be generally used as a solver for all classes of problems. Numerically, the choice of turbulence model mainly depends on some parameters such as physics encompassed in the flow, established technique for a specific class of problem, level of accuracy required, the availability of computational resources, and the time available for the simulation [189].
Currently, the CFD technique with fast and advanced computational processing equipment makes the complex turbulent fluid systems possible to model. Furthermore, most commercial CFD software such as STAR-CCM + from CD-Adapco, COMSOL Multiphysics, SIMULIA PowerFlow, ANSYS Fluent, and other open or licensed sources software provide parallel computing options to speed up the computational processes. A large number of turbulence models starting by \(k - \varepsilon\) model and renormalization group RNG \(k - \varepsilon\) model to the more complicated as Reynolds stress models (RSM) can be applied smoothly in many CFD software codes. These models can provide a real velocity, pressure, and temperature profiles of the fluid over the given domain [54]. While it is impossible to state the best turbulent model for a specific application categorically, so in this section, we will draft a small brief about the most critical and popular turbulence models used in the aerodynamic systems related to the agricultural application.
4.1 Standard k − ε Model
The standard \(k - \epsilon\) model was firstly proposed by Launder and Spalding [190, 191], which is regarded as a semi-empirical model based on modeling transport equations for the turbulence kinetic energy (\(k\)) and its dissipation rate (\(\epsilon\)) as presented in Eqs. (32 and 33). Authenticity, validity, economy, and realism for a wide range of turbulent flows give an explanation of its popularity in industrial flow and heat transfer simulations. The assumption of driving this model is that the flow is fully turbulent with high-Reynolds-number, and the effects of molecular viscosity are negligible [29, 189].
where \(u_{f}\) is the average velocity component of fluid at the position \(x\), \(\mu_{f}\) is the turbulent fluid viscosity,\(G_{k}\) is the generation of turbulence kinetic energy due to the average velocity gradients, \(G_{b}\) is the generation of turbulence kinetic energy due to buoyancy, \(Y_{M}\) is the contribution of the fluctuating dilatation incompressible turbulence to the overall dissipation rate, \(\sigma_{k}\) and \(\sigma_{\epsilon }\) is the turbulent Prandtl numbers for \(k\) and \(\epsilon\), respectively, \(S_{k}\) and \(S_{\epsilon }\) are user-defined source terms, \(R_{\epsilon }\) represents the dissipation of swirl and rotational effect on turbulence, where \(C_{1}\), \(C_{2 }\), and \(C_{3 }\) are constants.
Although the standard \(k - \epsilon\) model considered famous and popular for modeling the full turbulence flow, it provides an inaccurate rate result for high internal velocity with high swirling and turbulence (anisotropic flow). These results make it useless and weak for modeling real-flow in the chaotic aerodynamic systems, mainly cyclone separators [35, 49, 54, 192, 193].
4.2 RNG k − ε Model
To overcome the shortages of the standard \(k - \epsilon\) model, the RNG-based \(k - \varepsilon\) model has been successfully developed. It is derived from the instantaneous Navier–Stokes equations of average mass and momentum conservation, using a mathematical technique, namely “Renormalization Group”(RNG) methods [194]. This method has some powerful features, such as the effect of swirl on turbulence, an additional term in the dissipation rate equation that significantly improves the accuracy for rapidly strained flows, an analytically derived differential formula for effective viscosity that accounts for low-Reynolds-number effects. These characteristics make the models more accurate and reliable for a broader category of flows than the standard \(k - \epsilon\) model [189, 195, 196]. Considering these refinements in the standard \(k - \epsilon\) model equations mentioned above, the model can be mathematically described well as formulated in Eqs. (34 and 35):
where \(\mu_{{f_{eff} }}\) is the fluid effective turbulent viscosity, \(\alpha_{k}\) and \(\alpha_{\epsilon }\) are the inverse Prandtl numbers for \(k\) and \(\epsilon\), respectively. For more details and the sufficient background theory about the RNG \(k - \varepsilon\) model, it can be found in the following biographies [197,198,199].
4.3 Reynolds Stress Model
The Reynolds Stress Model (RSM) is mainly constructed for the effects of streamline curvature, swirl, rotation, and rapid changes in strain rate in a more accurate way than one-equation and two-equation models [200, 201]. So, this model has more significant potential to give accurate predictions for complex flows, especially when the flow has heavy swirls and anisotropic turbulence inside aerodynamic systems such as cyclone devices [197, 202,203,204,205]. The algebraic transport equation of the Reynolds stress \(\rho u_{i}^{^{\prime}} u_{j}^{^{\prime}}\) tensor can be given in Eq. (36), while the description can be drafted in Eqs. (37–44) [206,207,208]:
where the first term from the left side is the local time derivative of Reynolds stress tensor, \(C_{ij}\) is the convection; \(D_{T,ij}\) is the turbulent diffusion, \(D_{L,ij}\) is the molecular diffusion, \(P_{ij}\) and \(G_{ij}\) are the stress and buoyancy production rate of \(\overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} }}\), respectively, \(\phi_{ij}\) is the pressure strain consists of three contributions to the pressure-strain correlation considered below, \(\epsilon_{ij}\) is the dissipation, \(F_{ij}\) is the production by system rotation, and \(S_{user}\) is the user-defined source term.Whereas:
where \(\phi_{ij,1}\) is the slow pressure-strain which representing a return to isotropy by purely turbulent interactions [209], \(\phi_{ij,2}\) is the rapid pressure-strain taking account of the return to isotropy by the interaction between the turbulence and the mean velocity gradients [201], and \(\phi_{ij,3}\) is the wall-reflection term which is responsible for the damping of the velocity fluctuation component close and perpendicular to the wall that is included by default in the Reynolds Stress Model. Each component of the pressure strain can be formulated as following Eqs. (45–47):
where \(n_{k}\) is the \(x_{k}\) component of the unit normal to the wall,\(d\) is the normal distance to the wall, and \(C_{1 } = \frac{{C_{\mu }^{3/4} }}{k}\). According to some applications, four terms can be neglected, such as the convection, the molecular diffusion, and the production by system rotation, where the buoyancy production can be equals zero for isothermal flow.
5 CFD–DEM Coupling
A CFD simulation has to be integrated with a DEM simulation to consider the effect of aerodynamic forces, which play an essential role in particle behavior. When a spherical particle is moving through the air, it is usually modeled by the sophisticated methodology of Maxey-Riley [210], which considers the flow field around the particle and the stresses obtained from the background flow. Several investigators such as Casas et al. [211], Ren et al. [40], and Sturm et al. [70] simplified these equations by combining the interaction of particle’s Collision forces, Drag force, Magnus lift force, Saffman lift force, and Gravitation force. So, the translation motion of a particle through the airflow field was governed by the force balance equation, as indicated in Eq. (48) [70]:
where \(F_{ij}^{C}\) contact forces due to particle–particle and particle–wall contacts and can be calculated as mentioned before in Eq. (3), \(F_{D}\) is the drag force resulting from particle–fluid interaction (fluid damping force), and can be calculated as mentioned before in Eq. (3), \(F_{M}\) is the Magnus lift force generated by the relative motion between the rotating particle and the air which can be mathematically expressed by Eq. (49) [211, 212]:
where \(v_{i}\) and \(\omega_{i}\) are the relative velocity and the relative rotational angular velocity between air and particle, respectively, and \(C_{LM}\) represented the Magnus lift coefficient due to the rotation of the particle and can be expressed by the empirical formula given by Eq. (50) [40, 212, 213]:
where \(\sigma\) is a non-dimensional spin parameter which represents the particle lift due to its rotation and can be calculated according to Eq. (51).
The Saffman lift force \(F_{S}\) which generated in the normal direction due to fluid shearing field around the spherical particle can be proposed by Eq. (52) [214,215,216,217]:
where \(C_{LM}\) represented the Saffman shear lift coefficient and can be calculated from Eq. (53) [81, 216]:
where \(\gamma\) is the ratio between transitional and rotational Reynolds number as defined in Eq. (54):
where \(Re_{sh}\) is the particle Reynolds number of shear flow and can be expressed by Eq. (55):
Note that the value of (\(F_{M} + F_{S} )\) is so-called the fluid-particle interaction force \(F_{i}^{f}\). The net gravitational force of the particle immersed in the fluid \(F_{gb}\) was defined as the difference between particle gravity and buoyancy, as indicated in Eq. (56):
Later, Guillermo et al. [211] concluded that the particle motion in an aerodynamic system could be numerically described through three non-dimensional groups by assuming the characteristics of length scale \(L_{s}\) and velocity scale \(U_{s}\) for the time scale. These non-dimensional groups as formulated in Eqs. (57–59) are mainly depended on the non-dimensional parameters such as spin parameter due to particle rotation \(\sigma\), Remolds number of particles \(Re_{i}\), particle Stokes number \(St_{i}\), and gravitational parameter.
where group \(\pi_{1}\) represents the drag forces over particle inertia, group \(\pi_{2}\) represents the Magnus lift forces over particle inertia, and group \(\pi_{3}\) represents the gravity over particle inertia.
Recently, the rotational motion of the particle in a flow field has been investigated considering the rolling friction when the particle rotates in a fluid that can be given by Eq. (60) [41, 104, 218, 219]:
where \(\omega_{ir}\) is the angular velocity of the particle relative to the fluid and \(C_{R}\) is the rotational resistance factor and can be calculated according to Eq. (61)
where \(Re_{r}\) is the rotational Reynolds number and can be defined in Eq. (62)
Casas et al. [211] also employed another reasonably approximated equation to describe the rotational motion of the spherical particle in the aerodynamic systems, as indicated in Eq. (63):
As mentioned before, Coupling Discrete Element Method (DEM) with Computational Fluid Dynamics (CFD) is considered a powerful and reliable technique for understanding the physical phenomenon of particle movement in the fluid flow field, resulting in optimizing and designing the granular matter systems [35, 58, 97]. The CFD–DEM coupling approach was firstly proposed by Tsuji et al. [44], and then followed and developed by many others [47, 93, 96].
Generally, the granular flow can be defined as a group of discrete solid, and whenever it interacts with itself or fluid flow, part of the energy will be lost [95]. The granular matter has a wide range of industrial applications and is frequently modeled by coupling CFD–DEM approach [220]. CFD code can provide an interface to generate a set of fluid flow data files, which can include air, water, and other gases and fluids; thus, DEM code characterized the granular matter existing in that fluid to predict its behavior. Figure 8 provides a basic scheme to understand the main algorithm of CFD–DEM coupling.
Schematic diagram of CFD–DEM coupling technique
First, the granular flow was assigned by DEM code to set the properties of the particles where each particle placed into the grid cell. Second, the fluid flow field characteristics were set and resolved by the CFD algorithm to reach the convergence. Afterward, the velocity, pressure, density, and viscosity of the flow at each position in the computational domain are transferred to DEM code in order to generate the coupling interface to compute the forces acting on each particle. Thus, the CFD–DEM coupling interface took the particle translational and rotational motion data from the DEM solver and computed the volume fractions and momentum exchange in the mesh cell of CFD. Consequently, the CFD and DEM solvers entered into the cycles of the time steps until the simulation time ended.
Generally, there are three main methods for simulating the interaction between particles and the surrounding fluids, depending on the turbulence effect [58, 221]. The first method simulates how fluids change the flow of the particles with which they come into contact. In contrast, the second approach simulates how the fluid flow changes due to the particle movement. Thus, the particle movement is not affected by the flow, but the flow around the particle is affected by the presence of particles. The last one considers the fluid streamlines compressed between particles during the simulation. In this review, we give a little brief about these coupling techniques where a complete and very comprehensive review of different CFD–DEM approaches can be found in [62].
Figure 9 illustrates the different regimes of coupling techniques on a diagram using dimensionless coordinates considering the interaction between the particles and turbulence [221, 222]. Nowadays, various configurations of commercial or open-source software packages have been developed for CFD‐DEM coupling simulation, such as Rocky® (DEM package, can be coupled to Ansys Fluent®), EDEM® (DEM package can be coupled to Ansys Fluent®), PFC™ (DEM package with a built‐in fluid coupling package), SAMADII© (DEM for single and multiple GPUs), CFDEM® ( CFD‐DEM code in C + + ; OpenFOAM® for CFD and LIGGGGHTS for DEM), LIGGGHTS® ( DEM code in C + + on the LAMMPS platform), Yade (In C + + for DEM simulations), and MFIX‐DEM (CFD‐DEM code in FORTRAN for fluid‐solid flows).
In the flow regimes diagram, the terminology of symbols can be defined as: \(\alpha_{i}\) is the volume fraction of particles; [\(\alpha_{i} = \frac{{N \times Vol_{i} }}{Vol}\), \(N\) number of particles, \(Vol_{i}\) particle volume, \(Vol\) volume occupied by particles and fluid], \(T_{i}\) is the response time of particle; [ \(T_{i} = \frac{{\rho_{i} d_{i} }}{{18 \rho_{f} \upsilon_{f} }}\), \(\upsilon_{f}\) kinematic viscosity of the fluid], \(T_{K}\) is the Kolmogorov time scale; [\(T_{K}\) = \(\sqrt {\frac{{\upsilon_{f} }}{\varepsilon }}\)], \(T_{e}\) is the turnover time of large eddy; [\(T_{e} = {\raise0.7ex\hbox{$l$} \!\mathord{\left/ {\vphantom {l u}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$u$}}\), \(l\) length scale of the energy-containing eddies, \(u\) root mean square of fluid velocity].
5.1 One-Way Coupling
In the first interval of the flow regime, when the value of the particle volume fraction becomes very low (\(\alpha_{i} \le\) 10–6) the particles have infinitesimally effect on fluid turbulence, and the interaction between the particles and turbulence is named as one-way coupling. This phenomenon means that the distribution of the particles depends on the state of fluid turbulence and the momentum transfer from particles to turbulence. This phenomenon has an insignificant effect on the flow due to the low discrete particle concentrations. Consequently, the movement of the particle is only influenced by the fluid flow, where its velocity is considered to be the same as the surrounding fluid [221]. Numerically, the solution methodology starts with CFD calculations of the velocity and pressure distribution profiles generated by the fluid flow through the domain. Since the effect of the particles on the fluid is neglected, the only steady-state simulation needs to be performed [223]. At the end of CFD simulation, or once a steady state has reached the flow field, the CFD obtained data is then exported out and imported into DEM code. Thus, DEM calculates how the fluid flow would affect the particle flow by applying the external forces [35]. This method is particularly useful and ideally recommended in many investigations, especially for large particle separation process and unconfined homogeneous flows that has different densities of particles [186, 221, 224].
Potapov et al. [225] simulated the multiphase flow of gas and iron particles around the transfer chute using moving porosity technique with DEM Rocky® and CFD Ansys Fluent® one-way coupling. The authors mainly used this technique because of the relatively large and dense particles (+ 4 mm). The approving comparison of the model prediction against experimental results shows the validity of this model for the prediction of airflow around the industrial size of transfer chutes. Fonte et al. [53] flowed the strategy of one-way coupling of DEM Rocky® and CFD Ansys Fluent® to separate light from heavy particles in the wind-shifter device using different drag laws at a fixed value of airflow. Course particles with different geometries of paper (flat), stone (sphere), metal (rod), and wood (briquette), were used to determine the suitable drag low to use while simulating the separation process. The simulation showed that Ganser drag model [226] gives more accurate results because it considers the particle geometry.
Almeida et al. [29, 52] also used the one-way coupling method of DEM Rocky® and CFD Ansys Fluent® to put a theoretical algorism for separating the sugarcane bagasse into different groups of particles. Different air velocities through an aerodynamic conveying system were used considering the contact forces between particle–particle and particle–wall. The result showed that this coupling technique perfectly describes the separation process with reasonable accuracy. Since the main recommendation of this work is that the separation process will be more efficient and real when using coarse and large particles. El-Emam et al. [35] perfectly applied the above recommendations of DEM Rocky® and CFD Ansys Fluent® codes to simulate and optimize the separation process of real-particles of Jojoba seeds and its leaves. Five geometries of gas-cyclones were used, and the particle interaction was considered. The simulation can successfully predict the separation efficiency and the behavior of the particles that help to optimize the cyclone geometry and performance.
5.2 Two-Way Coupling
When the value of the particle volume fraction is located between 10–6 \(\le \alpha_{i} \le\) 10–3 and the particle loading volume is large enough to affect the turbulence structure, the term two-way coupling used. In this regime, the exchange of mass, momentum, and velocity information between the solid phase and the fluid phase occurred, where the meaningful feedback is noticed in turbulence damping due to buoyancy effects [186]. So, it can say that the particles are part of the fluid flow and will affect it in a two-way interaction. This phenomenon means that the particle movement is affected by the interaction with other particles and the fluid around it, while the flow is also affected by the particle presence. As described in (Fig. 9), at a specific value of particle volume fraction, when the diameters of the particles are small with the same material and fluid viscosity lowering (\(T_{i}\) is low), the surface area of the particulate phase increases resulting in increasing the dissipation rate of turbulence energy. On the other hand, increasing \(T_{i}\) for the same value of \(\alpha_{i}\) (inclined line), the particle Reynolds number increases, and the vortex shedding takes place resulting in promoting the turbulence energy production.
The simulation scheme used in this coupling technique is a transient state simulation that allows both solvers of CFD and DEM to run in a parallel way that can significantly decrease the simulation time [223]. This coupling methodology is suitable for dealing with a large number of particles through a CFD cell and not for dealing with particles larger than CFD cells. Therefore, it is recommended that the domain mesh size should be larger than the largest particle size through the simulated domain [58, 227]. The significant advantage of the two-way coupling simulation is that particle agglomeration can alter airflow trajectories and velocities and vice versa. Thus, the interaction between solids and gas is considerably closer to actual phenomena [29].
Zhong et al. [156] carried out a three-dimensional simulation of cylinder-shaped particles in a gas–solid fluidized bed using a two-way approach considering drag force, contact force, and gravitational force. The predictive behavior of particles and pressure drops at different superficial gas velocities were in good agreement with the experimental results. Ren et al. [40] study the flow behavior of corn-shaped particles in the cylindrical spouted bed with a conical base device using this coupling technique. The obtained results demonstrate that the coupling model methodology is valid and useful in describing the hydrodynamic behavior of the spouted bed.
Fonte et al. [53] set a fluidized bed simulation case to apply the two-way coupling technique of DEM Rocky® and CFD Ansys Fluent® using Huilin and Gidaspow drag law. The agreement between the pressure drop predicted by Ergun’s correlation and the pressure drop obtained in the simulation is relatively good until fluidization takes place, which states the capability of the fluid being affected by a reactive force. Devarampally [186] developed a two-way coupling of CFD–DEM using Simcenter STAR-CCM+ code for a top spray fluidized bed granulator to study the effects of inlet air flow rate, the temperature on the particle dynamics and the residence time in the spray zone. The developed model was able to predict the changes in particle velocities, temperatures, collision dynamics, and particle transfer from one compartment to the other as the inlet velocity and the temperature of the air changes. This model can be recommended to determine the agglomeration rates in a granulation process, develop hybrid CFD-DEM-PBM that describes the rate processes in granulation, and understand the effect of process parameters on the product quality attributes.
Carlos Varas et al. [101] employed a CFD–DEM two-way model to simulate the co-current gas-particle flow in a pseudo 2-D dilute flow riser. The model reasonably predicted the core-annulus flow and other hydrodynamic parameters such as cluster frequency, internal solids volume fraction, and aspect ratio that showed close agreement with experimental data. Baran et al. [155] applied a fully coupled CFD-DEM two-way approach to study the effect of particle shape on fluidization in a cylindrical fluidized bed using Simcenter STAR-CCM+ software. The observations are consistent with the similar simulation and experimental results reported in the literature [228, 229], which gives strong evidence for applying this technique to predict the dynamic behavior of different particles shape in the fluidized bed. Almeida et al. [29] simulated the dry bagasse separation in a pneumatic device using DEM Rocky® and CFD Ansys Fluent® coupling approach. The comparison with the experiment showed that the developed model predicted the particle separation phenomena with high accuracy.
5.3 Four-Way Coupling
Herein, the four-way coupling term is developed due to the interactions between particle-turbulence, particle–fluid-particle, particle–particle, and frictions of particles., In this case, the fluid streamlines between particles are compressed where the flow is considered to be dense [221]. This means the particle loading is very high and concentrated where the value of particle volume fraction is assumed to be higher than 10–3. Due to the complexities of flows in this regime, most experimental and numerical studies considered the flow to be dilute. As can be seen in (Fig. 9), the line which separates the two-way and four-way couplings are inclined as the particle–particle collision occurs at higher values of \(T_{i} /T_{e}\), thus transforming the two-way to four-way coupling technique. Note that, when particle volume fraction approaches to l, a total granular flow is presented in which there is no fluid will be obtained between particles. In this coupling approach, the simulation technique runs on a parallel implementation of CFD and DEM, which can significantly stimulate the two-phase fluid–solid phase.
Laín and Sommerfeld [230] predicted the behavior and the pressure drop in a particle-laden horizontal channel with rectangular cross-section by the Euler–Lagrange approach accounting for two-way and four-way coupling. Different diameters and mass loading ratios of particles were considered where the particle–wall interactions and inter-particle collisions have also been taken into account. The numerical simulation technique has reasonably reproduced the studied trends; however, the numerical predictions of wall-bounded flows cannot be appropriately applied when neglecting the wall roughness effects. Comparing the obtained data with the experiment result, it can be somewhat indicated that the considered model is appropriate to simulate aerodynamic conveying of spherical solid particles in a horizontal channel device with the dense flow. Kuang et al. [231] presented a 3-D numerical study of vertical aerodynamic conveying by combining a four-way CFD–DEM approach for dilute and dense gas–particles flow regimes. The numerical method can satisfactorily capture the key flow behaviors observed, such as particle flow pattern and gas pressure characteristics. In the dense-phase flow regime, the simulation results confirmed that the particle–particle and particle–wall force increases with the increase of the particle–fluid force, but in contrast for dilute-phase flow where it is small, if not negligible.
Sturm et al. [70] extended the previous simulation to also show the applicability of the presented simulation model to the different flow regimes: a dense vertical aerodynamic conveying system and dilute conveying in a horizontal-to-vertical pipe bend. To track the flow behavior, the Euler–Lagrange approach is presented, and an in-house soft sphere DEM code is coupled to Ansys Fluent®. It is shown that the different aerodynamic conveying regimes can be behaved well comparing to the experimental data. Traoré et al. [232] also derived a complete four-way coupling model of a gas–solid 3-D fluidized bed by taking into consideration particle–particle, fluid-particle, and particle–wall interactions. The simulation constructed on a high dense flow of 2.7 million particles in two different ways: pulsed jet and bubbly regime. The output data perfectly pointed out the existence of complex structures such as the worm-like shape one, similar to those that have already been described in other literature. Considering the above results, it is shown that a definite proof to use this coupling scheme for predicting sensitive phenomena in the large dense granular systems.
6 Drag Correlation Models
During the run of CFD–DEM coupling in an aerodynamic system, the drag correlation model shows vital importance besides pressure gradient forces, especially for describing and dealing with the interaction between particle shape and concentration and the surrounding fluid [139, 233, 234]. For successful coupling, it is crucial to choose a suitable drag correlation model [53]. There are several drag correlation models developed and available in the literature. Most of them are mainly dependent on the Reynolds number, where others need other properties, such as fluid volume fraction and particle sphericity. Here, in this review, we will concentrate the attention on the most common correlations that can be used in modeling bio-particles based on the flow regimes. The attempts by investigators and the developments for models listed in Table 2 illustrate the applicability of this approach.
7 Applications
To model the granular flow in the agricultural aerodynamic systems, various mathematical and numerical models include theoretical approaches, differential equations of motion, incremental technique, and computer programming were used. For instance, by MATLAB modeling, Adewumi [79] started to simulate the flow of cowpea grains through the transport and separation process in a horizontal airstream. He developed a 2-D Modeling using the aerodynamic principles of drag and gravitational forces to provide a clear vision about the air-particle dynamics in such a system. The obtained results showed the ability to construct the separation, cleaning, sorting, grading, and density classification processes in one machine. Recently, with the increase of agricultural industry applications concurrently with the high power of computer technology, CFD–DEM coupling approach is frequently used to model, predict the behavior, and provide the solutions of the air-particle flow problems [80, 246].
7.1 Air-Screening System
The process of separation and cleaning grain materials from impurities such as spikelet, leaves, straw remnants, husks, and small weed seeds, etc. is essential in agricultural grains production. In modern harvesting machines such as combine harvesters, the separation and cleaning processing are mainly implemented by air-screening or air-sieving systems [247]. In such a system, the modeling process can be numerically described as a complex system of two-phase flow. One phase is the airflow generated by a centrifugal fan, and the other is solid particles dispersed in the system by the airflow [248]. As mentioned before, the effect of air velocity has significant influence in such a separation process that the airflow entrains the light particles due to the aerodynamic drag force. At the same time, the heavy ones are mainly separated by the force of gravity and the inertia of sieves.
Numerically, Li et al. [39] carried out a 3-D coupled of CFD–DEM approach in an air-and-screen cleaning unit to study and analyze the influence of inlet airflow velocity on rice grain and short straw taking into consideration the longitudinal velocity, vertical height, and cleaning loss. The rice grains were modeled as a spheroid particle, and the short straws introduced as a cylinder shape. The particle materials were modeled and generated in EDEM software and allowed to fall on an inclined vibrating screen. A Eulerian–Eulerian model was used in simulating the airflow using Ansys Fluent® as a part of a coupling, where the Hertz-Mindlin contact model was applied to simulate particle–particle and particle-screen (wall) collisions. The simulation results reported that the length of the screen could be shortened if material straws and foreign materials are not too much since the higher the inlet airflow velocity, the faster the backward velocity of the materials on the screen surface and the more the cleaning loss. This work is extended by Li et al. [249] to simulate the effects of throughput and operating parameters on cleaning performance in the same device. Ansys Fluent®, as an auxiliary investigation software, was used to analyze the movement behavior of the internal airflow. The standard \(k - \epsilon\) turbulence model is proposed for this simulation study to describe the real-physical processes at the different airflow velocities above and below the vibrating screen. The results as described in (Fig. 10a,b) showed that the fan speed have a great effect on cleaning performance by affecting the overall airflow velocities in the cleaning device where the throughput has a sharp effect on grain impurity ratio.
Polynomial diagram of (a) throughput and (b) fan speed with cleaning performance [249]
Furthermore, Lenaerts et al. [77] modeled the separation chamber in the combine harvester through a cubic box to predict the separation profile of the grain-straw using DEM simulations. The grains were assumed to be spherical, while the straw particles are modeled as a segmented hollow cylinder that can be bent in all directions using DEMeter + + software. The main prediction is that separation speed is influenced by particle properties, but the main effects can be related to straw coverage and grain diameter. Ma et al. [76] developed another variable-amplitude screen box to analyze the traditional reciprocating screen in the combine harvester. The particles used in their study were divided into two groups: rice grain and rice straw that are modeled as ellipsoidal and cylindrical, respectively, by a multi-sphere approach. Based on the Hertz-Mindlin contact model in EDEM software, the simulation showed that the variable-amplitude screen could make the particles at the front of the screen be quickly thrown up and moved back but could not favor their segregation and separation at the screen front.
On the other hand, [250] studied the grain behavior in an inertia separation chamber of the combine harvester based on CFD–DEM simulation. The grains were modeled as ellipsoidal, while the straw modeled as cylindrical shape through the multi-sphere approach. The \(k - \epsilon\) turbulence model was used in Ansys Fluent® software to reach the convergence state of the airflow while the Euler-Lagrangian method in EDEM code was applied to model the particles. The simulations showed that the grains were effectively separated from the short straw through the airflow. Besides, the performance of separating and cleaning grains was improved with the increase of airflow velocity. However, turbulence and pressure drop were severely increased at the end of the separation chamber.
Yuan et al. [218] investigated the screening process of rice-threshed mixture components (grains, shriveled grains, and short stalks) through a cylindrical sieve device using CFD–DEM coupling. The influence of inlet airflow velocity, the diameter of, and the rotating speed of the cylindrical sieve on the separation process was studied. First, the particles were scanned by a 3-D laser scanning system then, modeled by multi-balls fast filling method (API) in EDEM software and allowed to move smoothly through the cylinder sieve. The particle phase is considered to be in a continuous quasi-fluid phase and solved through the average Navier–Stokes equation, where the airflow was simulated through the existing Eulerian–Eulerian model in the Ansys Fluent® code. To track the separation process (Fig. 11), visualized the simulation of particle trajectories with the time though the device, where the yellow, green, and blue colors represent grains, shriveled grains, and short stalks, respectively. The numerical simulation showed an increase in the screening efficiency tendency when the cylindrical sieve diameter increased. At the same time, the rotating speed has a significant effect on the average axial velocity of the short stalks, screening loss rate, and screening efficiency. Figure 12 showed the mass distribution in every collect area (from 1 to 5) as a relation of inlet airflow velocity, cylindrical sieve diameter, and its rotational speed.
The particle trajectories of the rice-threshed mixture during the simulation process [218]
The mass distribution of the grain during the screening process [218]
As shown in the investigations, the technique and the methodology of the numerical simulations used for modeling the air-screening systems can provide a useful reference for predicting the flow behavior and solving the separation problems of biomaterials. Because CFD–DEM coupling models had a reasonable predict comparing to the experimental results in the above investigations, it is strongly recommended to be used for improving and optimizing the design of air-screening devices in the combined harvesters.
7.2 Seed-Metering Device
Precision agriculture made agricultural production and agricultural management more accurate and useful [251]. Precision seeding is an essential part of precision agriculture, which has always attracted the attention of researchers [252]. It can be defined as the placement of single seeds in the soil at the desired plant spacing [253]. The Seed-metering device considers the main component of the planter machine to represent adequate seeding performance. Although there are various types of seed-metering devices, each with unique individual working principles, aerodynamic seed-metering devices are used more widely because of their high accuracy, preservation of seed integrity and fitness for high-speed operation [254, 255]. Recently, the numerical simulation approach has effectively applied for modeling the air-seeds flow in the aerodynamic seed-metering devices to promote effectiveness and performance.
For instance, Dandan et al. [256] applied the coupling method of CFD–DEM to simulate the effect of different air nozzle installation positions on the working performance of inside-filling air-blowing precision seed metering device. They concluded that CFD–DEM simulation could detect and predict the maize seed movement behavior in a single seed meter. Han et al. [42] extended their work to simulate and optimize the air-maize flow in the same device using the same numerical methodology. The effects of positions, width, and average arc length of the lateral hole were studied in terms of the gas field and seed movement. The maize particles were regarded as a hard-sphere model and created by EDEM software using the bonded particle model (BPM) technique, which allows the particles treated as a soft sphere model. While the standard \(k - \epsilon\) two-equation turbulence model was used to solve the gas phase and the Eulerian two-fluid coupling approach was applied.
According to the numerical simulations, the seed motion behavior of the seed-cleaning process can be correctly predicted, as illustrated in (Fig. 13). The simulation results also indicated that the area of the lateral hole seriously affected the movement and airflow field of seeds in the hole. When the position is lower, the optimized lateral hole, which has a width of 1.5 mm and an average arc length of 10 mm, had an excellent working performance, with less pressure loss, superior drag force, and differential pressure. The performance of the optimized seed-metering device in the experiments reached 93% when the working pressure was above 5.5 kPa with a working speed lower than 10 km.h−1.
Seed motion behavior of the seed-cleaning process [42]
Lei et al. [81] studied and analyzed the effects of the throat’s structure, airflow inlet velocity, and seed feed rate in seed feeding device (pneumatic Venturi tube) in terms of air and seed behavior using CFD–DEM coupling approach. This feeding device is usually used in the pneumatic seeding planter machine. Rapeseed and wheat were used and modeled as spheres and multi-sphere, respectively, using EDEM software. Hertz-Mindlin model was chosen as particle modeling while the gas-phase was solved with the standard \(k - \epsilon\) two equations turbulence model. The coupling interface was implemented by the Lagrangian coupling method. Simulation results showed that the throat’s area and airflow inlet velocity mainly affected airflow outlet velocity, while seed movement was slightly affected by throat length and seed feed rate. The increase in the throat area resulted in a decrease in seed’s velocity and pressure loss in a certain range. When the inlet air velocity increased, resultant force and seed velocity developed. Figure 14a,b showed the simulation flow patterns of rapeseed and wheat seed at the designed air velocities. It can be concluded that the appropriate airflow inlet velocity was 16–20 m.s−1 and 20–24 m.s−1 for rapeseed and wheat, respectively.
Flow patterns of (a) rapeseed and (b) wheat seed at different air velocity [81]
Although Venturi tube was widely used in industry, limited numerical studies are available in the literature, especially for particle motion in aerodynamic seeding systems. Lei et al. [257] extended their study to characterize the rapeseed and wheat migration trajectory and predict the distribution behavior of a pneumatic distribution head in the air-assisted centralized seed-metering device (Planter). The streamlined angle, the radius of baseline, outlet diameter of streamlined angle, lid angle, and installation location in the distribution head were the main parameters to investigate in this study. The particles were regarded as a hard-sphere model where the Hertz-Mindlin (no-slip) model was applied as the particle contact model, and the seed feed rating was adjusted by EDEM software. The rapeseeds were modeled as the spherical shape where the wheat seeds were generated as ellipsoidal shape by a multi-sphere approach. To model the turbulence in the airflow, the standard \(k - \epsilon\) turbulence model and the airflow velocity were set in the Ansys Fluent® software. Simulation results first predicted the variation coefficient of seeds distribution in the head. With the increase of streamlined angle from 10° to 50°, the variation decreased initially and then increased for an inlet diameter of 20 mm and an airflow velocity of 20 m.s−1. Also, when the radius of baseline was less than 20 mm, the air pressure loss and resultant seed force visibly increased.
Furthermore, the resultant seed force and resultant velocity increased with the increase of airflow velocity. Second, as showed in (Fig. 15a), the distribution of the seed was more uniform when the streamlined angle is 60°, the radius of the baseline is 40 mm, and the lid angle is 120°. Also, the distribution uniformity and power consumption improved at the airflow velocity of 20–24 m.s−1 for rapeseed and 24–28 m.s−1 for wheat of different seed feed rates, as illustrated in (Fig. 15b).
Snapshots of wheat and rapeseeds simulation in the distribution head [257]
The obtained result approved that the CFD–DEM coupling approach is a reliable and feasible tool for simulating the physical phenomenon of seed movement in the airflow field. Also, It can help improve distribution uniformity, explain the seed distribution mechanism, assist the performance, and optimizing the design of air blowing seed devices.
7.3 Drying Systems
Drying technology is widely applied in agriculture to preserve large mass flows of food grains, seeds, kernels, and other macroscopic particulate matter after harvesting in farms [258, 259]. For continuous drying, which is common in the industry, mixed-flow or cross-flow dryers (MFDs) are widely used [260]. The moisture is removed from the grain by forced dry air convection through the grain bed using air ducts installed in the bed, in order to prevent microbial activity and spoilage.
Keppler et al. [67] analyzed the influence of different constructional modifications of air duct shape and wall friction on the velocity distribution difference of wheat particle within the MFD module through the EDEM code package. Two types of modified air duct shapes were used: wedge and circular ducts, as shown in (Fig. 16a,b). The particles were modeled by a multi-sphere approach as a clump of three spheres, where the Hertz-Mindlin (no-slip) contact model was used to model the interaction forces. The simulation data represented substantial velocity differences when using the circular air ducts, so it is not appropriate in wheat drying usage. Also, significant velocities difference observed depending on particle place in the module. While, the near-wall is much lower than in the middle, as shown in (Fig. 16c,d). So, using smooth structure materials lead to decreasing the particle–wall friction ratio resulting in more even velocities distribution. By this, it would be easy to get an excellent homogeneous drying for the particles.
Simulated velocity differences around the different air ducts (right): a wedge duct, b circular duct, c velocity distribution of the wheat (red higher, blue lower velocities), and (d) velocity differences from the dryer wall [67]
To avoid extra drying costs and improve the product quality, Weigler et al. [69] evaluated the traditional designs of MFDs employing CFD–DEM to discover design imperfection. The dryer geometry and different air duct arrangements (horizontal and diagonal) were studied. Wheat particles were chosen and modeled in two geometries as an ellipsoidal clump and spherical by Particle Flow Code (DEM-PFC 2-D) software to compare the particle flow simulation. The airflow domain was discretized by generating a finite volume grid employing the software ANSYS ICEM. Then, the airflow was regarded as a turbulence flow and modeled by ANSYS CFX® software using the two-equation shear stress transport (SST) model. The simulation data successfully captured the particle-air flow distribution inside the dryer, comparing to the experimental result. It was found that the drying is not perfect in the traditional mixed-flow dryers because of air duct arrangements, the appearance of dead zones in airflow, and irregular distribution of airflow due to the wall frictions. In this context, appropriate air duct arrangements should be fixed to adjust the higher and lower air velocities in the middle part and near to sidewalls of the dryer, respectively. Consequently, the current authors recommended a new dryer model to adjust the airflow distribution; consequently the particle flow velocities that the sidewalls of the dryer should be inclined, and the half air ducts should be removed.
So, Weigler et al. [261] worked in the previous recommended model to develop a new geometry of MFDs that results in the homogeneous particle drying, higher energy efficiency, and increase product quality. The wheat flow was tracked by the different grain colors through a transparent sidewall using DEM-PFC2-D. Based on the experiments and numerical simulation observations, the new design meets most requirements of the particles drying.
On the other hand, Weigler and Mellmann [258] discovered without airflow the dry wheat kernels behavior through the traditional MFD of Weigler et al. [69] using DEM-PFC2-D where the results were compared with the experiments. A multi-sphere approach shaped the wheat kernels as an ellipsoidal clump and its flow behavior compared to the spherical shape. Alternately, the particles were colored black and blue to observe the mass flow behavior in the 2-D view, as shown in (Fig. 17a–d). As illustrated, the DEM model based on the ellipsoidal particle can effectively predict the real-grain flow behavior that the colored grain layer in the experiment showed the same profile as in the numerical simulation. In contrast, when spherical particles were used, the bed angle that was typically formed under the air ducts did not appear.
Particles flow patterns in MFD: a particles after DEM gravitational generation, b DEM sphere particles, c DEM ellipsoidal clamp, d experimental result [258]
The simulation findings which are entirely agreed with the experimental results promoted the main flow features of particle flow: the higher flow velocities were through the center of the dryer and had lower friction effects than those flowing through the regions near the dryer walls. These particles traveled with lower vertical velocities due to the higher frictional effects, which made the grains have different residence times in the dryer. This phenomenon leads to a non-uniform moisture distribution at the dryer outlet. Consequently, developing a new design that can adequately evanesce the difference in residence time of the particles is still need. Moreover, the main recommendation is that the 2-D DEM model does not accurately predict the absolute values of the grain mass flow pattern and velocity. Therefore, a three-dimensional simulation should be applied for dryer modeling.
Hence, Khatchatourian et al. [37] carried out the first trial to develop a 3-D model of soya beans flow applying DEM-Yade software package to predict the behavior and motion of particles during the discharging process in MFDs. The particles were modeled as a 3-D single spherical geometry considering the physical properties. An experiment was carried out to validate the simulation data that showed a satisfactory agreement between their results, as shown in (Fig. 18a).
a comparison of soya bean discharge for simulation (left frame) and experiment (right frame) at discharging hole 20 mm, and (b) velocity field distribution [37]
By Applying the method of colored particles for continuous flow in the MFD, the differences of soya bean velocities successfully observed. Near the wall regions, seed velocities were lower than in the center, as illustrated in (Fig. 18b). Thus, the seed velocity field is nonuniform, leading to different residence times of the particles. This result is typically agreed with the previous investigation, as mentioned above. The current authors suggested thoughtfully combining the mass and heat transfer model with the air-particle flow for better simulation results that lead to optimizing the flow in the dryers.
As a result of that, Scaar et al. [262] extended the work on the developed MFD model recommended by Weigler et al. [69] using the heat and mass transfer models. Their study aims to predict the airflow distribution and investigate the effect of air duct arrangements. Based on 3-D CFD ANSYS CFX® code, two different bed materials were used: wheat and rapeseed and considered as a porous medium. The turbulence of fluid flow is modeled by an eddy viscosity approach using SST (Shear Stress Transport) \(k - \omega\) model. The numerical observations were validated by experimental data which showed that the air duct arrangement has a strong influence on the airflow distribution. In addition, the horizontal air duct arrangement showed more homogeneous airflow pattern as compared to the diagonal one. Furthermore, the numerical model well calculated the influence of the bed material with its different particle characteristics which gives a good support to use this model in future investigations.
On the other hand, Azmir et al. [263] established an in-house CFD–DEM drying model for food grains considering the shrinkage characteristics to investigate the influence of inlet air temperature and velocity on drying process in the fluidized bed. Wheat particles with spherical shape are considered as a model grain where a 2-D CFD–3-D DEM are coupled by assuming only one control volume in the thickness direction, and the source in the bed thickness direction is negligible. Hot air (100º–180º) is used to dry the grains at a given velocity (1.2–2 m s−1), which is introduced from the two corners of the bed. The developed drying model can successfully predict the overall particle shrinkage rate and the diameter of each particle during drying the simulation time, as shown in (Fig. 19a,b). At the studied range of air velocity, the particle shrinkage rate increases significantly with the increase of inlet air temperature but increases slightly with increasing inlet air velocity.
a Snapshot of particle size change throughout the drying process, b effect of inlet air velocity on particle size reduction [263]
Azmir et al. [264] continued their research to study the influence of the grain properties such as size, density, and initial moisture content on the drying process using the same methodology of CFD–DEM coupling. Millet particles were mainly used and compared with the five same genera that all of them modeled in shape as spherical particles. Three different inlet air temperatures (50, 150, and 200 °C) are set to predict the effect of different heat transfer modes. The numerical simulations proved that the convection and conduction heat transfer has a significant influence on drying, while the contribution of the radiation mode has a negligible effect. With decreasing the grain size, the drying rate exponentially increases while the size distribution and the uniformity of moisture content decreases. Besides, decreasing the initial moisture content leads to low drying rate and make the moisture content to be homogeneous. Finally, increasing grain density occurs at a lower drying rate with longer drying time and a lower uniformity of moisture content.
A sequel, the main advantage of using computational modeling, especially CFD–DEM coupling techniques in grain drying, is the ability to study the grain and air velocity distribution through the dryer sections, which affected by geometrical modifications. Based on the previous results, the coupling approach with mass and heat transfer models will be beneficial in a realistic-industrial scale because understanding grain behavior within the dryer allows analysis of drying without requiring an expensive prototype.
7.4 Pneumatic Separation Systems
The separation process is widely used in process engineering, for example, to obtain more homogeneous fractions of material in terms of size or even in chemical characteristics. Nowadays, studies have been conducted with the simulation of fluidization of mineral particles and medicines for equipment development and process improvement. However, with the bio-particulate matter field, it still has little studies.
Almeida et al. [52] established a new computational model to separate the sugarcane bagasse particles pneumatically by a riser device based on CFD Ansys Fluent® and DEM Rocky® tools. One-way coupling was used referred to as the Lagrangian–Eulerian method, while the linear hysteresis model was applied to model the interaction forces between particles and boundaries. For air turbulence flow, \(k - \epsilon\) turbulent model was chosen. The particles were classified into seven groups based on its characteristics and aspect ratio: group 1 as pith (fine particles), groups 2, 3, and 4 as fibers (coarse particles), and groups 5, 6, and 7 as the rind (coarse particles). The fiber and the rind particles are modeled as cylinders using Rocky® software. The pith particles will be neglected in simulation; because the air will entrain all of them due to the chosen velocities; besides, a lot of computational power and time will be consumed, making the simulations insignificant.
The chosen air velocities were set at 2.0 m s−1 and 3.5 m s−1 based on the calculated terminal velocities of the particles. During the simulation process, the particle mass distributions at the top and the bottom of the riser device with different air velocities are analyzed and visualized, as shown in (Fig. 20a,b). As a result of these data, it can be proved that the coarse particles can be easily tracked during separation even though the particles have a similar property.
a particle mass distributions, b snapshot during the simulation at the bottom and top of the riser device with different air velocities [52]
The current authors continued their investigation using one-way, and two-way coupling approaches for dry and wet particles to put a theoretical basis and understand the separation phenomena resulting in developing and improving the separation equipment used for that process [29]. The same methodology of the particle modeling was followed from the previous study. The mass distribution of dry and wet bagasse collected at the top and bottom outlets of the riser at different air velocities form the two coupling approaches provided the right prediction and showed high feasibility of the separation process comparing to the experiment result. The utilized parameters and the obtained results of this simulation give a confidant for these coupling models to be extended in several processes such as drying, pyrolysis, fluidization, and gasification. It will also result in studying and developing the ideal configurations of these devices.
In this context, El-Emam et al. [35] also applied the one-way coupling approach of CFD Ansys Fluent® and DEM Rocky® codes to observe the separation behavior of Jojoba seeds from its leaves using cyclone separator. The highly curved streamlines and the chaotic turbulence of the continuum airflow in the cyclone separator were modeled through RNG \(k - \epsilon\) turbulent model. The particles were modeled in shape as a sphere and custom polyhedron for the seeds and leaves, respectively. Also, the interaction forces of particle–particle and particle-boundary in the normal and tangential directions were modeled by the Hysteretic linear spring model and Linear spring coulomb limit model, respectively. Four geometrical modifications of the cyclone inlet height were used compared to the original one to optimize the performance. First, to make sure that the modeling methodology is correct, the performance validation of the original model has been carried out that showed a good between the numerical and the experimental data as shown in (Fig. 21a). Second, by tracking the number of separated seeds and the bottom of the cyclones and counting the number of leaves dragged by air at the top outlet numerically, the performance of the cyclone can be obtained as shown in (Fig. 21b).
a validation of the original model, b optimized cyclones performance, and (c) snapshot of particle separation at the end of the simulation time [35]
As illustrated in (Fig. 21c), the snapshots discovered the disadvantages of the original cyclone that a considerable number of leaves concentrated in the top portion of the cyclone lead to decreasing the performance. So, by modifying the cyclone inlet height, the performance significantly improved by increasing the separation efficiency, cleaning efficiency, and effectiveness. This data was useful for considering cyclone (2) as the most suitable modified and optimized design geometry for harvesting jojoba seeds with the lowest operation cost and highest performance.
8 Challenges and Future Issues
Considerable efforts mentioned above have proved that CFD–DEM coupling is a high-potential method to investigate the bio-particulate matter by capturing its behavior characteristics in the aerodynamic systems. However, since these systems are significantly varied and complex, there are still a significant shortage and many problems in terms of determining accuracy, efficiency, and appropriate model of CFD–DEM coupling for simulations. Insufficient understanding and description of the interaction between the particle–particle, particle–fluid, and particle-boundaries give misunderstanding of the way of CFD–DEM coupling resulting in impairing the simulation modeling. Additionally, due to the limitation of computational resources and complex shape structures of grains, most of the current CFD–DEM simulations for bio-particles are a little far from being perfect enough to deal with real-particulate systems in nature or industry accurately. Besides, it is still focusing on laboratory-scale systems. On the other hand, developing an advanced process for understanding and determining contact models of irregular shapes of grains opens up the possibility of computing particle behavior (translation and rotation) in 3-D modulation and hence of obtaining high-resolution impact.
As indicated above, many models have been used for describing bio-particle shapes and perceiving particle contacts. However, each of these models has its advantages and disadvantages regarding the accuracy, flexibility, numerical stability, and efficiency, considerable challenges still exist in the bio-particles flow models especially when applying in the real world. Usually, to compute the contact force of the non-spherical grains, which are common, models that are initially constructed for the ideal spherical particles are directly used. As indicated, the last decade introduced new and advanced models, namely bounded particle model and software such as Rocky®, for simulating the irregular particles by its true and real shape. By this methodology, the simulations proved to be useful for different modeling problems in the agricultural process. Therefore, to find out and develop more efficient, accurate, and trustable models to represent different particle shapes and detect their contact forces is still one of the urgent needs and most interesting areas to focus on in the near future. As mentioned in this review, since the current CFD–DEM coupling methods can be briefly divided into three categories: namely one-way, two-way, four-way, most of the research related to agricultural field concentrate on one-way only, while other ways are neglected which are considered more precise and accurate for representing real contacts.
One of the main bottlenecks faces CFD–DEM simulation is the massive computational cost when simulating intensive particulate systems, particularly the multiphase flow system. With typical PC hardware or workstation, three-dimensional CFD–DEM simulations are usually limited to systems with limited particle numbers, since in realistic systems, the number of particles often exceeded millions of particles. With recent developments in computer technology, parallel computing has shown great potential in accelerating computer simulations using multi-core CPU and GPU (Graphics Processing Unit). To date, using CPU and GPU platforms in the coupling CFD–DEM algorithm is still new technology compared to the traditional CPU that needs adequate development to reduce the time-consuming, especially when simulating agricultural crop grains.
Another significant problem still poses a severe challenge is simulating large ranges in grain shapes and sizes in some aerodynamic systems; also, the presence of the smallest particles in large systems requires an efficient treatment to model and simulate. Overall, modeling the bio-particulate matter process in disperse systems is a particularly open area of research that is very important for understanding agricultural processes such as precise planting, harvesting, post-harvesting, industrial, and agrophysical systems. At the same time, until now, little investigations have been done on these systems. However, the vital evaluating factors such as the validity, accuracy, speed, and versatility of the numerical technique need to be improved in the near future.
9 Summary and Conclusions
Existing literature that used CFD–DEM coupling approach to simulate aerodynamic granular systems, limited to bio-particulate matter, has been reviewed. Usually, the soft-sphere approach of DEM was commonly used to develop these grain simulations process. The advantage of soft sphere models was their capability to represent multiple particle contacts, which are of importance when modeling bulk grain systems. Particle models varied with the type of grain. For near-spherical grains such as soybean and rapeseed, single-sphere particle models predicted particle behavior with high accuracy. For non-spherical grains such as rice, wheat, and corn, particle, multi-sphere approach was used, resulting in increasing the simulation time and computational cost. That is because of the higher number of contact points requiring force and deformation calculation at each contact point. To avoid this excess computation time problem, most researchers have used single-sphere models and had reasonable success in predictions.
Depending on the software used in the simulation case, both linear and nonlinear Hertz-Mindlin contact models have been used effectively to study the aerodynamic operations such as separation and cleaning of crop grains. In general, coupling DEM with CFD has adequately simulated the separation of air-grain flow and recommended for better predictions. Although this coupling has been increasingly used to study particle processes, it has not been widely applied in agricultural grains. The considerable variation in grains characteristics such as size, shape, surface roughness, density, friction coefficients, composition, and other factors could be limiting the use of CFD–DEM. Computational cost also limits CFD–DEM application; specifically, most of the cereal crops are smaller, which need long computation time for simulation. The development of precision particle models could help spur the adoption of this numerical modeling concept and optimize process and equipment design in the grain handling and processing industry.
To date, up to the authors’ investigating and searching, few studies have been made on the gas–solid flow in aerodynamic separation devices employing CFD–DEM approach. One-way coupling approach is a proper technique for predicting the behavior of macroscopic particles, where it commonly applied in agriculture systems that consume less power for simulation. In contrast, two-way and four-way are commonly used in describing the particles flow in fluidized bed related to chemical or pharmaceutical field. However, limited research used these techniques in agriculture, but it still a big gap for simulation in many aerodynamic systems related to the agriculture field. Future developments for this coupling include implementation of non-drag laws, thermal fluid-particle coupling, and mass exchange between fluid and particles should be considered.
Finally, research effort should also focus on seeking far more efficient methods for multi-phase and multi-physics problems, which are often complexly coupled together. The comparison between simulations and real experimental results showed that the CFD-DEM model is predictive and can be extended to several aerodynamic processes related to the agricultural field. Using this coupling technique and simulation methods will make it possible to improve the aerodynamic systems of agricultural machines without high costs and efforts. The obtained characteristics from the above investigations can seriously provide a basis for developing and optimizing the structural and technological parameters of the aerodynamic systems of agricultural machines.
Abbreviations
- \(A_{i}\) :
-
Projected area of particle
- \(a\) :
-
Separation radius between particles
- \(C_{d}\) :
-
Drag coefficient
- \(C_{ij}\) :
-
Convection
- \(D_{T,ij}\) :
-
Turbulent diffusion
- \(D_{L,ij}\) :
-
Molecular diffusion
- \(D\) :
-
Domain diameter
- \(d\) :
-
Normal distance to the wall
- \(d_{i}\) :
-
Particle diameter
- \(d_{{i_{vol} }}\) :
-
Particle diameter with the same volume of the actual one
- \(E_{i}\) :
-
Young’s modulus of particle
- \(E_{w}\) :
-
Young’s modulus of wall boundary
- \(F_{net}\) :
-
Net force acting on a particle
- \(F_{ij}^{C}\) :
-
Total contact force acting on a particle
- \(F_{i}^{f}\) :
-
Fluid-particle interaction force
- \(F_{ij}^{n}\) :
-
Normal contact force on a particle
- \(F_{ij}^{t}\) :
-
Tangential contact force on a particle
- \(F_{i}^{t,T}\) :
-
Tangential contact force at current time
- \(F_{i}^{{t,\left( {T - \Delta T} \right)}}\) :
-
Tangential contact force at previous time
- \(F_{i}^{n,T}\) :
-
Normal contact force at current time
- \(F_{i}^{{n,\left( {T - \Delta T} \right)}}\) :
-
Normal contact force at previous time
- \(F_{{i_{adh} }}^{n,T}\) :
-
Normal adhesive force at current time
- \(F_{ij}\) :
-
Force production by system rotation
- \(F_{i}^{f}\) :
-
Interaction force of the fluid on particle
- \(f_{i}^{g}\) :
-
Gravity force
- \(f_{adh}\) :
-
Adhesive force fraction
- \(G_{k}\) :
-
Kinetic energy generation due to the velocity
- \(G_{b}\) :
-
Kinetic energy generation due to buoyancy
- \(G_{ij}\) :
-
Buoyancy production rate of \(\overline{{u_{i}^{\prime } u_{j}^{\prime } }}\)
- \(g\) :
-
Gravity acceleration
- \(T_{K}\) :
-
Kolmogorov time scale
- \(T_{e}\) :
-
Turnover time of large eddy
- \(T\) :
-
Time
- \(u\) :
-
Root mean square of fluid velocity
- \(u_{f}\) :
-
Average velocity component of fluid
- \(V_{a}\) :
-
Air velocity
- \(V_{T}\) :
-
Terminal velocity
- \(V_{f}\) :
-
Average velocity of the fluid
- \(V_{i}\) and \(V_{j}\) :
-
Particles velocity before interaction
- \(V_{i}^{^{\prime}}\) and \(V_{j}^{^{\prime}}\) :
-
Particles velocity after interaction
- \(Vol_{i}\) :
-
Particle volume
- \(Vol\) :
-
Volume occupied by particles and fluid
- \(Y_{M}\) :
-
Dilatation contribution over dissipation rate
- \(Z\) :
-
Particle size or geometry
- \(\phi_{ij,1}\) :
-
Slow pressure-strain
- \(\phi_{ij,2}\) :
-
Rapid pressure-strain
- \(\phi_{ij,3}\) :
-
Wall-reflection term
- \(\phi_{ij}\) :
-
Pressure strain
- \(\emptyset_{i}\) :
-
Particle sphericity
- \(\eta\) :
-
Damping ratio
- \(\eta^{t}\) :
-
Tangential damping ratio
- \(K_{1}\) :
-
Stokes’ shape factor
- \(K_{2}\) :
-
Newton’s shape factor
- \(k_{a}\) :
-
Coefficient of aerodynamic resistance
- \(K_{u}^{n}\) :
-
Unloading contact stiffnesses
- \(K_{l}^{n}\) :
-
Loading contact stiffnesses
- \(l\) :
-
Length scale of the energy-containing eddies
- \(m^{*}\) :
-
Equivalent mass of particles
- \(m_{i} \,\,{\text{and}}\,\, m_{j}\) :
-
Mass of particles \(i\,\, {\text{and}}\,\, j\)
- \(N\) :
-
Number of particles
- \(n_{k}\) :
-
Component of \(x_{k}\) normal to the wall
- \(\widehat{{n_{c} }}\) :
-
Unit vector in the normal direction
- \(n\,\,{\text{and}} \,\, t\) :
-
Normal and tangential coordinates
- \(p\) :
-
Pressure shared by two phases
- \(P_{max}\) :
-
Maximum liquid bridge tensile force
- \(P_{ij}\) :
-
Stress production rate of \(\overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} }}\)
- \(R_{{e_{i} }}\) :
-
Particle Reynolds number
- \(R_{\epsilon }\) :
-
Dissipation of swirl and rotational effect
- \(R_{e}\) :
-
Reynolds number
- \(R_{i}\,\, {\text{and}}\,\, R_{j}\) :
-
Radii of particles \(i\,\, {\text{and}}\,\, j\)
- \(s_{max}^{t}\) :
-
Maximum relative tangential displacement
- \(s^{t}\) :
-
Tangential relative displacement at contact
- \(S^{n}\) :
-
Normal overlapping
- \(\Delta S^{n}\) :
-
Change in the normal overlapping
- \(\Delta S^{t}\) :
-
Change in the tangential overlapping
- \(S^{n,T}\) :
-
Normal overlap value at the current time
- \(S^{n,T - \Delta T }\) :
-
Normal overlap value at the previous time
- \(S_{k}\) and \(S_{\epsilon }\) :
-
Constant source terms for user-defined
- \(S_{user}\) :
-
Constant source term for user-defined
- \(\Delta T\) :
-
Timestep
- \(T_{i}\) :
-
Response time of particle
- \(\rho_{f}\) :
-
Fluid density
- \(\rho_{f} \overline{{u_{i}^{^{\prime}} u_{j}^{^{\prime}} }}\) :
-
Reynolds stress tensor
- \(\rho_{a}\) :
-
Air density
- \(\rho_{i}\) :
-
Particle density
- \(\mu_{f}\) :
-
Fluid turbulent viscosity
- \(\mu_{t}\) :
-
Turbulent viscosity
- \(\mu\) :
-
Friction coefficient
- \(\mu_{a}\) :
-
Dynamic viscosity of the air
- \(\mu_{{f_{eff} }}\) :
-
Effective turbulent viscosity of a fluid
- \(\alpha_{f}\) :
-
Fluid volume fraction
- \(\alpha_{k}\) and \(\alpha_{\epsilon }\) :
-
Inverse effective Prandtl number for \(k\) and \(\epsilon\)
- \(\alpha_{i}\) :
-
Particle volume fraction of
- \(\varepsilon\) :
-
Coefficient of restitution
- \(\sigma_{k}\) and \(\sigma_{\epsilon }\) :
-
Turbulent Prandtl numbers for \(k\) and \(\epsilon\)
- \({\Gamma }\) :
-
Surface energy
- \(\epsilon_{ij}\) :
-
Dissipation
- \(\delta_{adh}\) :
-
Adhesive distance
- \(\tau_{f }\) :
-
Viscous stress tensor
- \(\upsilon_{f}\) :
-
Kinematic viscosity of the fluid
- \(\frac{d}{dT}S^{t}\) :
-
Relative tangential velocity at the contact
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 52079058 and 51979138), Nature Science Foundation for Excellent Young Scholars of Jiangsu Province (Grant No. BK20190101), National Key Research and Development Project (Grant No. 2020YFC1512404).
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El-Emam, M.A., Zhou, L., Shi, W. et al. Theories and Applications of CFD–DEM Coupling Approach for Granular Flow: A Review. Arch Computat Methods Eng 28, 4979–5020 (2021). https://doi.org/10.1007/s11831-021-09568-9
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DOI: https://doi.org/10.1007/s11831-021-09568-9