Particle-wall Collisions Research Articles

Particle trajectories in pipe flow considering particle–wall collisions

Particle–wall collision behaviors have strong effects on confined particle-laden pipe flows, which are important in pneumatic conveying and pulverized coal combustion. In this paper, a numerical simulation of a pipe flow was conducted to analyze the effects of different initial conditions and particle–wall collision model parameters. The results show that a realistic collision model with coefficients provided by experiments can predict accurate particle exit velocity distributions. The effects of the initial motion of the particles diminish at the exit as long as the pipe length and the number of wall collisions are sufficient, and larger particles require the length to be longer. A simplified collision model with an arbitrary constant restitution coefficient e and a friction coefficient f leads to inaccurate results of the particle exit velocity probability density function, and using constant coefficients from data of a single collision angle will make the model ineffective. It is better to apply a normal distribution for e and a constant f if available collision data are limited, which gets reasonably accurate statistical results despite small distribution deviations.

Modeling of Ice Slurry Flow through Bend Pipe

In this work, CFD Eulerian multiphase model with KTGFis used to investigate the flow behaviour of the ice slurry in 90° elbow bend pipe. The present model considered the particle-particle collisions along with particle-wall collisions. In the modeling of ice slurry flow various interfacial forces viz. drag force, lift force and turbulence dispersion force are considered. The solid phase viscosity is calculated as a sum of kinetic and collision viscosity component and the turbulence in the ice slurry flow is modeled by the per phase k-model. Simulation has been performed at velocity of 1 m/s, concentration of 10% and particle size of 0.25 mm for the bend radius ratios (R/r) of 2, 2.98 and 5.6. Apart from that, effect of particle size, velocity and concentration on solid particle distribution has also been investigated. Results show that, secondary flow is generated similar to single phase flow which influences the velocity, particle distribution and pressure drop.

The behaviors of particle-wall collision for non-spherical particles: Modeling analysis

The particle-wall collision behaviors are important to gas-solid separation, a common process in the energy and chemical industries. To model such collisions in simulations, the impulsive equations involving the restitution and friction coefficients are commonly used, with a virtual wall to address the abnormal rebound behaviors for grazing impacts. In the present work, this model was analyzed and compared with experimental data of spherical and non-spherical particles. The results show that a restitution coefficient distribution is necessary to accurate model predictions, because of stochastic energy loss for large impact angles. The updated model is feasible for particle-wall collisions of non-spherical particles, with relative velocity errors up to 15% within the experimental conditions. Non-spherical particles' fitted model parameters are featured with smaller restitution coefficients, larger variations of restitution coefficients, larger friction coefficients and larger deviations of wall inclination angles, as the energy loss increases while the rebounding becomes more stochastic.

The behaviors of particle-wall collision for non-spherical particles: Experimental investigation

The particle-wall collision behavior for non-spherical particles has significant effects on gas-solid separation, which is important in mechanical, energy and other industries. Particle-wall collision experiments of spherical and non-spherical glass particles with polished and rough walls were conducted. The collision velocities were measured by high-speed photography, and the effects of particle sphericity and wall roughness were analyzed. The results show for large impact angles α1, the restitution coefficient e is independent of α1 and increases with increasing particle diameter. For the non-spherical particles or the rough wall, e increases when α1 is small and the friction coefficient f increases with decreasing α1. The non-spherical particles have smaller e, and larger f for small α1. The rough wall has smaller e for large α1 but greater dependence of e on α1, resulting in larger e instead for α1 → 20°. Under sliding condition, f increases with increasing wall roughness or decreasing particle diameter.

GPU-Accelerated Simulation of a Rotary Valve by the Discrete Element Method

The rotary valve is the most frequently used piece of equipment that is suitable for the controlled feeding or discharging of products in powdered or granular form. It is usually connected to silos, hoppers, pneumatic conveying systems, bag filters or cyclones. In this paper, a simulation study is presented on the discharge of solid particles from a silo through a rotary valve. The discrete element method (DEM), which accounts for collisions between particles and particle-wall collisions, was used to model and simulate the motion of individual particles. The diameter of the simulated silo was 0.2 m and a total of 245,000 particles were calculated. In the simulations, the effect of the geometric and operational parameters of the rotary valve on the mass outflow rate was investigated. The diameter of the rotary valve varied between 0.06 and 0.12 m and the rotational speed of the rotor was changed between 0.5 and 5 1 . The simulations showed that the mass outflow rate of the particles from the rotary valve changes periodically due to its rotary cell structure. Within the lower range of rotational speeds of the rotor, the mass outflow rate of particles changes linearly in correlation with the rotational speed. The identification of this linear section is important in terms of control as this would facilitate the implementation of control devices by applying well-established linear control algorithms. Adjacent to the linear section, the dependence of the average mass outflow rate on the rotational speed was found to be nonlinear. Within the upper range of examined rotational speeds for each diameter of the rotary valve, the mass outflow rate reaches a maximum then decreases. The simulations were performed using GPU hardware. The application of parallel programming was an essential aspect of the simulations and significantly decreased the calculation time of simulations. In the treatment of particle-wall contacts, a novel flat triangular-based geometric representation technique was used which allows the particle-wall contacts to be calculated more effectively and their treatment implemented more easily into the parallel programming code. Using the calculated particle positions, the particles were visualized to view the effect of the interactions between the particles and rotor blades on particle motion. The simulation results showed that the discrete element method is capable of determining the detailed flow patterns of particles through the rotary valve at various rotational speeds.

The critical sticking velocity of non-spherical graphite particles: A numerical study and validation

For high temperature gas-cooled reactors (HTGR), the accumulation of the micro-sized graphite dust in the primary loop is a major concern during a potential accident such as the water ingress and loss of coolant accidents. The critical sticking velocity and the restitution coefficient are important for estimating the deposition rate of graphite particles. However, as far as the authors know, the experimental data of the graphite particle–wall collision is limited. Besides, the traditional theoretical models based on approximately spherical particles are not applicable to disk-like graphite particles. In this study, we use the finite element method (FEM) to simulate the particle–wall collision process at a microcosmic scale. The surface adhesion is determined by the van der Waals force between the two contact surfaces. The viscoelastic damping behavior of the material is described by the Maxwell standard model. At lower incident velocities, the effect of the surface adhesion becomes more important, which not only directly contributes to the energy loss by the adhesion work but also indirectly contributes by increasing the strain rate near the interface. For spherical particles, the method shows a good agreement with the experimental data. Then the FEM model is extended to study wall collisions of micro-sized dike-like graphite particles and both the restitution coefficient curve and the critical sticking velocity are obtained. The results show that the critical sticking velocity increases with the decreases of the aspect ratio and the particle size. A correlation for predicting the critical sticking velocity of disk-like graphite particles is proposed. Our work could provide a realistic particle–wall model for predicting the graphite particle deposition rate using Eulerian-Lagrangian CFD method.

The effect of surface roughness on normal restitution coefficient, adhesion force and friction coefficient of the particle-wall collision

The normal restitution coefficient is an important parameter in particle deposition which is widely used in industrial fields. The normal restitution coefficient can be affected by many factors, and a typical factor is the surface roughness. Furthermore, a rough surface will influence the adhesion force and friction coefficient. The adhesion force and friction coefficient have effects on the normal restitution coefficient. However, the relationship between the normal restitution coefficient and the surface roughness has not been obtained. Therefore, an experimental study of microspheres impact on a rough surface is developed. The normal restitution coefficient decreases with the increasing surface roughness. The adhesion force is calculated by the Rabinovich model, and the results indicated that the adhesion force increases with the increasing surface roughness within the surface roughness range in this paper. Moreover, the adhesion energy and friction coefficient dissipation increase with the increasing surface roughness.

A two-way coupled Euler-Lagrange method for simulating multiphase flows with discontinuous Galerkin schemes on arbitrary curved elements

In this work, we develop a Lagrangian point-particle method to support high-speed dusty flow simulations with discontinuous Galerkin schemes. The carrier fluid is treated in an Eulerian frame through the solution of the compressible Navier-Stokes equations. Particle search and localization is based on the geometric mapping of mesh elements to a reference element and is applicable to arbitrary unstructured, curved, multidimensional grids. High-order interpolation is used to calculate the gas state at a given particle position, and the back-coupling of particles to the carrier fluid is carried out via a simple, effective procedure. Furthermore, we discuss difficulties associated with accounting for particle-wall collisions on curved, high-aspect-ratio elements. We develop a methodology that appropriately handles such collisions and accurately computes post-collision particle trajectories. We first apply the Euler-Lagrange method to one-way coupled tests and show the benefit of using curved instead of straight-sided elements for dealing with particle-wall collisions. We proceed by considering more complex multiphase test cases with two-way coupling, namely dusty flows over a flat plate and through a converging-diverging nozzle. Our final test case consists of hypersonic dusty flow over a sphere in which the target quantity is dust-induced surface heating augmentation at the stagnation point. Quantitative comparisons with experiments are provided.

A large eddy simulation study of cyclones: The effect of sub-models on efficiency and erosion prediction

In this study, first, the effect of different state-of-the-art dispersion and particle-wall collision models on the efficiency and erosion prediction are investigated. Second, the influence of particle size on the erosion pattern is explored. These assessments require reliable sub-model inputs, e.g. velocity statistics, which are provided through a large eddy simulation. The results reveal that a dispersion model for cyclone applications should account for the effect of anisotropic normal and shear Reynolds stresses and the “drift correction”. Furthermore, the erosion inside a cyclone can have four critical zones based on the particle size. It is also proven that the accurate prediction of erosion pattern necessitates the inclusion of the Saffman and Magnus lift forces on particles and realistic variable restitution coefficients in the particle-wall collision model. Finally, wall roughness increases the erosion rate of large particles through the combined impact of the “shadow effect” and energetic inner vortex on particles.

Direct numerical simulation of viscous incompressible flow with spherical particles in the flat channel

The paper deals with numerical simulation of 3D fluid flow with relatively large spherical particles in the flat channel. The simulation is performed using the previously developed SIMPLE based immersed boundary method. The collision model, describing particle-particle and particle-wall collisions, complements the numerical method. This model prevents particle overlapping and takes into account the complicated fluid flow in the space between the particles. The computed flow rates decrease significantly with increasing the particle concentration. It is shown that the value of the particle diameter has a small influence on the flow rate. The flow rate can be approximated using the value of effective viscosity computed by Maron – Peirce formula with the use of extremely high packing concentration. Particles are moving faster than the mixture, and the difference increases with increasing concentration.

Numerical Prediction of the Short-Term Trajectory of Microplastic Particles in Laizhou Bay

Microplastic particles are easily captured by microorganisms and enter the food chain, which poses a threat to ecological health. These particles are abundant in coastal areas because of the influence of anthropic activities and the interaction between the sea and land. Although much research on microplastics has been done, predicting the transportation of microplastic particles in coastal zones is still a challenge. In this paper, the trajectories of microplastic particles released from four river mouths around Laizhou Bay are investigated using the lattice Boltzmann method coupled with the Lagrangian particle-tracking method, involving inter-particle and particle-wall collisions. The trajectories of particles released from four river mouths are recorded within 30 days.

PTV experiments and DEM simulations of the coefficient of restitution for irregular particles impacting on horizontal substrates

For systems of particles with irregular shapes, the collisions between particles and between particles and walls are highly complex and strongly related to the contact geometry. In this work, the collision behavior between irregular maltodextrin particles (with a characteristic size of approximately 100 μm) and horizontal substrates was experimentally measured by an improved particle tracking velocimetry (PTV), which simultaneously reconstructed the trajectories of many particles during the process of free fall and rebound. In addition, the measurement data were compared with DEM simulations using the multi-sphere model and the superquadric model, regarding the distributions of total and normal coefficients of restitution and corresponding relationships with the rotational speed after collision and the absolute difference of incidence angle and rebound angle. Compared to the superquadric model, the multi-sphere model well predicts the macroscopic particle-wall collision behaviors of irregular non-convex particles.

Microstructuring of steel surfaces via cold spraying with 316L particles for studying the particle-wall collision behavior

The surface morphology can have a significant influence on the contact behavior during particle collisions with surfaces. This work focuses on the design of surfaces to study the dynamic interactions between particles and component surfaces. Within this study two different methods with particle-substrate collisions were used. A cold spray method utilised for surface coating was adapted to generate different nub structures by applying single spherical stainless steel particles (316L) in the size range of 1–8 μm on stainless steel substrates (316Ti). Euler-Lagrange Computational Fluid Dynamics simulations of the spray process were performed to obtain impact velocities and temperatures of the particles. In cold spray experiments, different nub concentrations on the surface were generated by varying the spraying time. Measurements with Scanning Force Microscopy show a significant increase of the roughness with increasing spraying time. Collisions of polystyrene particles on the produced surfaces were observed by two high-speed cameras. A strong effect of the surface roughness on the coefficient of restitution during the particle collisions were obtained. These results can be used to create surfaces with a certain energy dissipation in future studies.

A numerical study on adhesive collision between a micro-sized particle and a wall

The theoretical study for the wall collision of small adhesive non-spherical particles is challenging due to the irregular shape. In this work we present a new numerical model to study the micro-sized particle-wall collision. The adhesion force is directly incorporated based on the Hamaker theory, which helps to achieve the shape-independence. The simulation not only agrees well with the JKR model for spherical cases but also naturally reproduces the adhesion-related phenomena such as the “jump-on” and “pull-off” events. Besides, the viscoelasticity is closely related to the local strain and strain rate. The results show that the restitution coefficient curves obtained by the simulation agree well with the classic experimental data over a wide range of incident velocity, particle size and material properties. Owing to the complete shape-independence of the sub-particle models, the present FEM model has the full capability to extend to the wall collision of complex-shaped non-spherical adhesive particles.

Computation of pressure drop and heat transfer in gas-solid suspension with small sized particles in a horizontal pipe

The present work deals with the investigation of the gas-solid flow in a horizontal pipe using the Eulerian-Eulerian modeling approach for a particle size range of at solid volume fractions of 0.001 and 0.10 which is missing in the existing literature. An extensive study has been performed to investigate the effect of the particle-wall collision and particle-particle collision, solid volume fraction, particle size and inlet slip ratio on two-phase pressure drop and Nusselt number. The effect of the collisions is found to be prominent only at higher solid volume fraction (10%). Under the particle size considered in the present study, interestingly, the pressure drop shows completely opposite trend under two different solid volume fraction situations which has not been reported in earlier studies due to the consideration of relatively large-sized particles. On the other hand, the Nusselt number gets reduced with an increase in the particle size. The effect of the inter-particle collision is found to affect the pressure drop significantly under the current operating conditions. Both the pressure drop and Nusselt number increases with an increase in the solid volume fraction. Similarly, an increase in the inlet slip ratio increases the Nusselt number, whereas it reduces the pressure drop.

A collision model for DNS with ellipsoidal particles in viscous fluid

The article proposes an algorithm to model the collision between arbitrary ellipsoids in viscous fluid. It is composed of several steps, each improving upon the standard procedure employed in the current literature. First, an efficient contact detection algorithm is presented. Then, the semi-implicit Immersed Boundary Method of Tschisgale et al. (2018) is enhanced by the collision forces using the hard-sphere approach, so that the resulting model accounts for fluid forces throughout the entire collision process. Additionally, a new lubrication model is proposed that applies a constant lubrication force in the region where hydrodynamic forces are not resolved by the spatial grid. The new collision model is validated against benchmark test cases of particle wall collisions with excellent agreement. Furthermore, the collision of an ellipsoidal particle with a wall is investigated. The normal restitution coefficient in the case of ellipsoidal particles does not solely depend upon the Stokes number as in the case of spherical particles but is also a function of its shape, and the orientation before the collision. Using the new model, the effect of these parameters on the rebound trajectory is studied. It is found that the maximum normal restitution coefficient decreases significantly as the flatness of the particle increases. Also, the coefficient of restitution depends on the particle orientation, a tendency increasing with particle flatness.

Application of the two-fluid model to prediction of sediment transport in turbulent open channel flow

The two-fluid model (TFM) formulation was used to predict the liquid and sediment transport in an open channel flow for dilute concentrations. A low-Reynolds-number k–ε model was used to represent the turbulence in the liquid phase; it included the effect of the sediment particles on the turbulence field. The particle-wall interactions were implemented using the boundary condition of Johnson and Jackson (1987), which resulted in a finite value for the sediment velocity at the bottom wall. The values of the specularity coefficient and coefficient of restitution for the particle-wall collisions were specified. Overall, the TFM prediction for the liquid velocity, sediment concentration, and turbulent statistics agreed well with two different experimental test cases by Lyn (1987). A key parameter for determining the sediment phase transport was the granular temperature, the level of which was set by the value of the specularity coefficient at the wall. In the context of the TFM, the presence of the sediment particles was found to enhance the wall shear stress of the liquid phase.

A multi-physics peridynamics-DEM-IB-CLBM framework for the prediction of erosive impact of solid particles in viscous fluids

In this paper, a new fully-resolved framework capable of capturing the fundamental physics of particle–fluid interactions, the collision of particles with solid surfaces, and the resulting damage is proposed. A coupled DEM-IB-CLBM, consisting of a discrete element method (DEM), an immersed boundary (IB) method, and a cascaded lattice Boltzmann method (CLBM), is used to fully resolve the interaction of the particles with the surrounding viscous fluid. The peridynamics theory is then implemented and used to predict the impact damage to the target material. This framework is validated by comparing the trajectory of a particle–wall collision event in a viscous fluid with the previous results in the literature. Furthermore, the variation of the restitution coefficient with the impact velocity is in a good agreement with the available experimental results. The influence of multiple impacts and the resulting surface damage on the fluid dynamics of the system is investigated. It is demonstrated that the method correctly predicts the expected effects of multiple collisions and impact angle variations on the surface damage.

Effect of secondary flow on gas-solid flow regimes in lifting elbows

The influence of the elbow lifting angle, airflow velocity and solid mass flow rate on particle flow regimes in lifting elbows has been characterized by an Euler-Lagrange four-way coupling method. The computational fluid dynamics (CFD) and discrete element method (DEM) were used for modeling in this paper. The effect of particle-wall collisions on particle motion was considered by adopting a modified Hertz-Mindlin (no slip) model. An orthogonal design method, to significantly reduce the number of the schemes, was used in this paper to discriminate the significant effects of three independent variables on pressure drops in the lifting elbow. The effect of the secondary flow on pressure drops, volume fractions and solid concentrations is discussed in the results section. The results indicated that the pressure drop increased gradually with increasing airflow velocity and solid mass flow rate; however, there was an optimal lifting angle at which the pressure drop was the smallest. For a 90° elbow, the maximum collision region of the particles on the inner wall of the elbow depended only on the ratio of the radius of curvature to the diameter of the pipe and was independent of the airflow velocity and particle concentration.

Four-way coupling of particle-wall and colloidal particle-particle interactions in direct absorption solar collectors

A novel model based on the Eulerian-Lagrangian approach was introduced in order to capture the physics of particle-fluid, particle-wall, and colloidal particle-particle interactions through four-way coupling in low-flux nanofluid-based direct absorption solar collectors (DASCs). This was accomplished by means of a computationally efficient particle-particle-interaction detection algorithm implemented within the frame of an in-house fluid-particle coupling algorithm that allowed for the simultaneous evolution of the carrier and particulate phases. The optical, thermal, and dispersion effects of particle-wall and colloidal particle-particle interactions were investigated over a range of particle volume fractions ϕp and flow Reynolds numbers (Re). It was found that the outcome of a particle-wall collision is either particle deposition or rebound, depending on the balance between kinetic energy of the incoming particle and particle-wall van der Waals potential energy. Brownian motion was established to be the main deposition mechanism for nanoparticles in the boundary layer. As Re decreased, Brownian motion of nanoparticles dominated over convection, which led to higher deposition rates. Deposited particles were found to cause greater attenuation of solar radiation near the collector upper surface, especially in the visible region of the solar spectrum. Whereas in the infrared region, radiation attenuation became less sensitive to particle deposition. The drop in collector efficiency when particles are allowed to deposit relative to the case when particles are not allowed to deposit was highest for low Re and ϕp. Yet, regardless of Re, an increase in particle surface potential led to a better dispersion of nanoparticles. Furthermore, colloidal interparticle interactions were found to have a negligible effect on collector performance. The results highlight the important effects of particle deposition and non-uniform particle distribution on the performance of DASC systems, which cannot be captured using conventional single-phase models.