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Particulate flows in a mixture of gas and liquid, i.e. gas–liquid–solid three-phase flows, are frequently encountered both in nature and industry. In such flows, complex interactions between multiple phases, i.e. particle–particle interactions, fluid–particle interactions and interfacial interactions (such as surface tension and particle wetting), play a crucial role. In literature, simulations of three-phase flows are sometimes performed by incorporating interface capturing methods (e.g. VOF method) into the CFD–DEM coupling model. However, it is practically impossible to perform large (industrial) scale simulation because of the high computational cost. One of the strategies often employed to reduce the computational cost in CFD–DEM is to upscale particle size, which is applied mainly to particle single-phase and fluid–solid two-phase flows. The present work is focused on the scaled-up particle model for gas–liquid–solid three-phase flows. The interaction forces between multiple phases are scaled using the general criteria derived from the continuum assumption of particulate flow. A colour function based interface-capturing method with improved interface smoothness is developed, and the diffusion based coarse graining is employed to ensure sufficient space resolution in CFD even when particle size is increased. It is shown that the model developed is capable of predicting the both particles and fluid behaviour in the original system.

In this work, a resolved CFD–DEM coupling model for the simulation of gas-liquid-solid flows is developed: the interface capturing method based on the colour function is employed for fluids (i.e. a gas and liquid) whilst Discrete Element Method (DEM) is used for particles. The Volume Penalisation (VP) method is adopted to consider the hydrodynamic interactions between fluids and particles along with the Immersed Free Surface (IFS) method, which artificially extends the gas-liquid interface into the interior of the particle to account for the wettability. The unique point of the proposed model is that the thickness of the gas-liquid interface can be controlled by using both interface compression and diffuse interface techniques simultaneously. From the simulation results, it is presented that the accurate evaluation of the surface tension force as well as the capillary force can be achieved by appropriately controlling the interface thickness. Moreover, the major two methods in the literature to calculate the capillary force are compared in this work. The validity of the proposed model is presented for both static and dynamic cases. The behaviour of two colliding particles with a dynamic liquid bridge is then simulated to demonstrate the applicability of the proposed model to a complex three-phase system.

A resolved CFD–DEM coupling model for the simulation of particulate flows is proposed in this work. The Volume Penalisation (VP) method, which is a family of the continuous forcing Immersed Boundary (IB) method, is employed to express the particle–fluid interaction. A smooth mask function is used to avoid sharp transition between the solid (particle) and fluid domains that may cause numerical oscillation with moving particles. Optimal permeability is employed to reduce the model error associated with the VP method. It is determined as a function of only the interface thickness and fluid kinematic viscosity. The proposed model is accurate, easy to implement with any discretisation scheme, and only requires small computational overhead for particle–fluid interaction. Several simulations are performed to test the validity of the proposed model in various systems, i.e. from dilute to relatively dense flows, and the results show good agreement with the exact solution or empirical correlation. It is found that the error can be scaled with the ratio between the gap and interface thickness. The proposed model is also applied to predict the relative viscosity of suspensions and the density segregation in fluidised beds.

K. Washino, E. L. Chan, T. Tsujimoto, et al. Development of resolved CFD–DEM coupling model for three-phase flows with non-spherical particles. Chemical Engineering Science 267, 118335 (2023); https://doi.org/10.1016/j.ces.2022.118335., In this work, a resolved CFD–DEM coupling model for gas–liquid-solid three-phase flows with non-spherical particles is developed where the shape of the particle is implicitly captured by a superquadric function. Both gas–liquid and fluid–solid interfaces are smoothly represented with a specified thickness so that the interface thicknesses and CFD cell size are independent of each other. Several sensitivity studies are carried out and criteria for mesh- and thickness-independent results are proposed. It is confirmed that the proposed model can properly predict the hydrodynamic and capillary forces acting on particles with a wide range of shapes and contact angles. Finally, the model proposed is applied to perform several virtual experiments of typical chemical engineering processes: a liquid–solid fluidised bed and bubbly flow with various particle shapes. It is found that particle shape can have a significant impact on the fluid-particle interactions and resultant particle movement, leading to segregation and preferential alignment.

Hu Y., Chan E.L., Tsuji T., et al. Geometric similarity on interparticle force evaluation for scaled-up DEM particles. Powder Technology, 404, 117483. https://doi.org/10.1016/j.powtec.2022.117483., The scaled-up particle model, which is also commonly known as the coarse grain model or discrete parcel model, is frequently used to reduce the computational cost in Discrete Element Method (DEM). In the direct force scaling approach, the forces acting on original particles are first estimated and then directly scaled to apply to scaled-up particles. It is therefore crucial to appropriately evaluate the variables of the original particles, e.g. overlap and separation distance, from the scaled-up particles particularly when estimating complex interparticle forces. The present work proposes the use of geometric similarity for the evaluation of the original particle overlap and separation distance. It is demonstrated that the proposed method can provide an almost identical stress-strain curve between the original and scaled-up particles during uniaxial compression of a packed particle bed, whilst the conventional method in the literature gives significant overestimation of the stress. In addition, the scaled-up particles can reasonably replicate the original velocity distributions of cohesive particles with both liquid bridge and JKR surface adhesion forces in a dynamic flow system (vertical mixer). The simulation results suggest that the method proposed can be applied to any type of interparticle forces. A scaling of time step limit is also derived theoretically and discussed.

The validity of the lubrication force model on particles in the normal direction due to a pendular liquid bridge of power-law fluid based on the Reynolds lubrication theory is investigated by comparing it with Direct Numerical Simulation (DNS) results. It is found that the model can predict the force with less than 10% error when the dimensionless separation distance is smaller than 0.05. In the DNS results, a spike of the pressure at the edge of the bridge as well as a drop in pressure around the axis connecting the centres of the particles are observed on the particle surface. It is revealed that these phenomena are caused by the component of the viscous stress tensor which is neglected in the lubrication theory. A new closed-form solution of the lubrication force model is also proposed in this study which can be easily incorporated into the Discrete Element Method (DEM) framework.

In many powder handling processes, liquid is added and dispersed into bulk dry powder. To study these systems, simulations of wet particles with small amounts of liquid are often performed by incorporating liquid bridge forces consisting of capillary and viscous forces into Discrete Element Method (DEM) (Sakai and Koshizuka, 2009). One of the existing challenges in DEM is the high computational cost to perform industrial scale simulations with large number of particles. One of the strategies often employed to reduce computational cost is by scaling up particle size, also known as the coarse grain method, which have been applied in several studies for dry cohesionless or dry cohesive particles. In the present work, the “direct force scaling” coarse grain model (Sakai and Koshizuka, 2009; Sakai et al., 2012) is applied for a dense and dynamic system of wet particles with liquid bridge forces. A general scaling criteria is proposed for different types of DEM related forces based on force balances on a control volume: l 3 scaling for body forces and l 2 scaling for interaction forces, where l is the scaling factor of the coarse grain particle. The coarse grain model is validated for wet particles in a vertical mixer in terms of the bulk flow and mixing behaviour. It is shown that the coarse grain model with l 2 scaling of the liquid bridge forces can accurately predict the flow and mixing behaviour of the original wet particles.

In Discrete Element Method (DEM), the stiffness of particles is often reduced from the real material property to increase the time step and decrease the calculation cost. Although this approach is widely accepted for dry and relatively coarse particles where only contact force is dominant, it is recently reported that the powder behaviour changes drastically with reducing the particle stiffness when cohesion forces are exerted on the particles [1] , [2] . The present study generalises this problem to any type of attraction forces and provides a solution, which is named as the Reduced Particle Stiffness (RPS) scaling. The RPS scaling for both linear and non-linear contact models are developed based on the dimensionless equation of motion where additional attraction forces such as liquid bridge, cohesion and electrostatic forces are exerted on particles. It is proven that, using the RPS scaling, particles with reduced stiffness show similar sticking/rebound behaviour and the bulk velocity as those of the original (stiff) particles.

In this study, new models are proposed for hydrodynamic interaction forces acting on particles through a pendular liquid bridge. The liquid considered is a power-law fluid, and the tangential forces due to both translational and rotational motions of particles are independently modelled, which can be superposed as long as the Reynolds number is sufficiently small. The force models are derived by obtaining improved expressions for the pressure profile inside a liquid bridge which can be reduced to the solutions of the pressure equations based on the lubrication theory in the limiting cases. Direct Numerical Simulation (DNS) is also performed to provide reference data to compare. The forces obtained from the proposed model and DNS are in reasonable agreement compared to the model in the literature where significant overestimation can be seen especially when the power-law index is small. Furthermore, the models proposed are written in a closed-form and can be easily implemented in Discrete Element Method (DEM) for wet particle simulation in the future.

In wet powder handling processes, it is of paramount importance to accurately estimate the viscous force acting on particles. In the present work, the tangential viscous force models for a pendular liquid bridge used in Discrete Element Method (DEM) in literature are reviewed first, and then new models are proposed by modifying the Xu model (Xu et al., 2005) based on the numerical solution of the pressure equation derived from the lubrication theory. The results obtained from the proposed models are compared with those from Direct Numerical Simulation (DNS) to find that they show good agreement with each other when the separation distance is sufficiently small, i.e. when the lubrication approximation is valid. The validity and accuracy of the models in literature are also discussed.

In this work, Direct Numerical Simulations (DNS) of a pendular liquid bridge formed between two relatively moving particles are performed to evaluate the normal component of the viscous force exerted on the particles. The viscous force obtained are non-dimensionalised in order to clarify the parameters which can affect the dimensionless force. The DNS results are compared with the viscous force models in literature which are commonly used in DEM simulations. It is found that these models cannot be used with large inter-particle separation distance. A new and more accurate viscous force model is proposed from the DNS results which can be directly implemented in the DEM framework.

Discrete element method (DEM) has been applied to simulate particulate flows with wet particles by taking into account the liquid bonding forces between particles. However, there is only limited work available in literature which applies DEM to simulate wet particles with highly viscous liquid. In this paper, the currently used DEM framework is assessed and the limitations are revealed for simulations of wet particles with highly viscous liquid in terms of the time step required for stable simulations, i.e. the time step decreases with increasing liquid viscosity. Semi-empirical time step criteria based on the viscous force decay time are proposed which determine the stable time step limit for given simulation conditions.

In high shear granulation, the rotating impeller blades impart forces on the granules which are subsequently transmitted throughout the bed through inter-granule collisions. These affect the granule growth behaviour in several ways — the granules could deform, consolidate and/or break under stress. In this paper, the blade-granule bed normal stress in a cylindrical, vertical axis high shear granulator is characterised using Discrete Element Method (DEM) simulations. The simulations are compared and validated with the measured blade-bed stress and bed surface velocities from our previous studies [1,2]. The blade-bed stresses were previously measured using a novel, custom-built telemetric impeller pressure sensor system. Following experimental validation for impeller speeds up to 350 rpm, higher impeller speeds up to 700 rpm or Fr = 3.88 are simulated to include flow regimes that can occur in most commercial granulators. Parameter study of particle properties, impeller geometries and granulator scales is also carried out. In our previous work, a blade-bed stress equation based on the blade and granule bed inertial forces with a correction factor, B 1 = K 1 1 v rel to account for bed fluidisation with increasing impeller speed, was proposed and validated with a range of dry granules [1]. Here, an improved correction factor, B 2 = K 2 1 F r rel 0.5 2 h w D 0.3 θ − 0.5 is introduced to account for different granulator scales, blade widths and blade angles, with a fitted constant K2.

In high shear granulation, various dimensionless or dimensioned parameter groups such as constant Froude number, tip speed, relative swept volume and specific energy input are commonly used as scale-up criteria, in order to maintain the powder bed internal flow or stress field across scales. One major challenge is obtaining the internal flow and stress field through experimentation given the lack of precise measurement techniques. Hence, this work employs DEM (discrete element method) simulations to study the internal flow patterns and behaviour of different scale batch, horizontal high shear mixers. The simulations provide a deeper understanding of the interaction of scale, impeller speed and fill level on the flow field, and show that the particle velocity is correlated with the relative swept volume in these mixers. It shows that the relative particle velocity is correlated, independent of scale, to the relative swept volume per rotation and highlights its values as a parameter for understanding and comparing mixer behaviour. The work also demonstrates the importance of the particle size chosen for the simulation as well as the tool-wall gap in the mixer, and highlights its importance as we interpret DEM results.

For high shear granulators, the rotating impeller blades exert forces on the granules, which are subsequently transmitted throughout the granule bed through inter-granule collisions. The effect of these collisional stresses on the granule growth behaviour is varied; as the granules could deform, consolidate and/or break under stress. This paper focuses on the normal stress between the blade and the granule bed in a cylindrical high shear granulator, which was directly measured using a custom-built telemetric impeller pressure sensor system. The stresses, evaluated at different operating conditions (impeller speed) and granule bed attributes (bed load, granule size and granule/particle type) were also fitted to a stress model derived based on the inertial force transferred from the blade to a continuous, cohesionless granule bed block. For the granule bed velocity and height parameters required in the model, the surface velocity of the bed at the sensor region and the bed height near at the wall, measured by high speed imaging, were used. A surface velocity corrected blade–granule bed stress model to account for the use of surface velocity and the effect of different flow regimes enabled much improved prediction of the stress for all types of dry granule beds used in this study. The effects of some individual granule/particle properties such as size, shape and strength on the stress were also negligible provided that the bulk flow behaviour is similar.

The behavior of dry, steady-state granule beds in each identified flow regime, i.e., frictional, toroidal, and fluidized, in a vertical-axis cylindrical high-shear granulator is studied. The granule bed behavior is discussed in terms of the blade-granule bed interactions and bed surface behavior. The blade-granule bed stress was measured with a custom-built telemetric impeller pressure sensor system and simulated with the discrete element method, while the bed surface velocity and height were studied by high-speed imaging and particle imaging velocimetry. The simulations reasonably predicted the average blade-granule bed stresses. The variability, i.e., fluctuation amplitude and periodicity, and trends of the average values differed in each flow regime. Frequencies of the periodic bed surface velocity and height fluctuations changed from single blade pass frequency to two blade passes frequency and finally a loss in periodicity across the flow regimes. Periodic fluctuations of the blade-bed stress were only observed in the fluidized regime until a certain impeller speed or Froude number was reached. These frequencies were slightly higher than one impeller rotation (three blade passes).