Coefficient Of Normal Restitution Research Articles

Euler-Lagrange model of particles circulation in a spout-fluid bed apparatus for dry coating

The main objective of the study was to develop a model describing the flow of particles (cores) in an apparatus operating within the range of the fast circulating dilute spout-fluid bed. The greatest emphasis was placed on the selection of appropriate description of the particle-wall interactions (impact model or fixed values of restitution coefficients). Its influence on the dispersed phase velocity in the draft tube and annulus of the apparatus was investigated. Results obtained from computer simulations were compared with our own experimental data. The use of equations calculating normal and tangential restitution coefficient resulted in a noticeable improvement in the accuracy of results only in the area of the draft tube in relation to the fixed restitution coefficient approach. It was found that the flow hydrodynamics and apparatus geometry favour computing of low restitution coefficients in the annular zone.

Динамическая модель упруго-пластического нормального столкновения сферических частиц при нелокальной пластичности

AbstractThe problem of normal collision of a spherical particle with a half-space is considered with allowance for nonlocal plastic deformation in the case where the strength limit depends on the contact radius, as well as for the strengthening effect in the deformed material. The dimensionless coefficient of normal velocity restitution has been calculated numerically as a function of the initial velocity of the spherical particle. The obtained data coincide well with experimental results available in the literature.

Anomalies in normal and oblique collision properties of spherical particles

Collision of particles either between themselves or with the wall, are typically characterized by normal and tangential coefficients of restitution, which depend on material and surface properties of the colliding objects. An accurate estimate of coefficients of restitution is of importance as it is one of input parameters in the discrete element simulations of a large system of particles. Often anomalies in the experimentally obtained values of the coefficients are reported in the literature. In the present work, both normal and tangential coefficients of restitution along with the surface and the local material properties are determined and compared with the predictions of the existing models. In certain cases, the experimentally obtained values agree fairly well with the values determined using the models while in some other cases anomalies in the experimental results are observed.

Experimental characterization of particle-wall interaction relevant to entrained-flow gasification of biomass

The present study addresses particle–wall interaction phenomena relevant to entrained-flow gasifiers. Two types of biomass have been investigated, i.e. wood chips and corn stover. The dynamics of char and ash particles as they are impacted onto a flat surface in cold and hot conditions has been characterized by means of high speed imaging and tracking. Particle–wall collisions were described in terms of normal, tangential and global coefficients of restitution as well as deposition efficiency. The influence of carbon conversion and impact velocity on the dynamical pattern of rebound and deposition has been investigated. The results indicate that, even at ambient conditions, some plastic deformation occurs during the impact. Experiments performed under hot conditions demonstrate that a drop of the coefficients of restitution takes place at high temperature, especially at low impact velocity, for both the tested biomasses. This feature can be explained by considering the change of mechanical properties of particles as the temperature increases, and the effect of the adhesion energy during the impact. Results highlighted that ash of wood chips is not prone to form a slag layer, while ash of corn stover extensively contributes to formation of ash deposits and melts under hot conditions. Results from experiments with corn stover indicate that char particles deposit onto the molten ash surface. The dissipation of momentum associated with particle impact promotes the establishment of a dense-dispersed phase in the near-wall zone of entrained-flow slagging gasifiers.

An impulse based model for spherical particle collisions with sliding and rolling

Particle impact behavior description is significant for dense multiphase flow simulation and particle deposition prediction. The paper presents a novel impulse based particle collision model considering sliding and rolling. The collision model includes three components, normal, tangential and adhesion model. Normal collision model is established to predict the normal coefficient of restitution (COR), contact area, total normal impulse etc., by dividing the collision process into three compression stages (elastic, elastic-plastic and fully plastic stages), and an elastic recovery stage. The tangential and angular velocities are calculated based on the normal impulse and the determination of sliding or rolling contact. It is verified that the direction of tangential relative velocity remains the same during the whole collision process, with the assumption that the deformation of the particles does not affect the tangential forces. The adhesion loss is only activated in the recovery stage using Dunn's model, which describes the adhesion force as an idealized line force acting on the contact radius. Several cases are tested to verify the proposed model, including low velocity normal impact of particle and wall, oblique impact of particle and wall with or without spin, sphere moving on a flat plate under gravity, and particle-particle collision. The results show that the proposed model is able to predict the experimental measurements with good accuracy and captures the essential physics of particle-particle and particle-wall impacts.

Sediment transport in high‐speed flows over a fixed bed: 2. Particle impacts and abrasion prediction

AbstractSingle bed load particle impacts were experimentally investigated in supercritical open channel flow over a fixed planar bed of low relative roughness height simulating high‐gradient non‐alluvial mountain streams as well as hydraulic structures. Particle impact characteristics (impact velocity, impact angle, Stokes number, restitution and dynamic friction coefficients) were determined for a wide range of hydraulic parameters and particle properties. Particle impact velocity scaled with the particle velocity, and the vertical particle impact velocity increased with excess transport stage. Particle impact and rebound angles were low and decreased with transport stage. Analysis of the particle impacts with the bed revealed almost no viscous damping effects with high normal restitution coefficients exceeding unity. The normal and resultant Stokes numbers were high and above critical thresholds for viscous damping. These results are attributed to the coherent turbulent structures near the wall region, i.e. bursting motion with ejection and sweep events responsible for turbulence generation and particle transport. The tangential restitution coefficients were slightly below unity and the dynamic friction coefficients were lower than for alluvial bed data, revealing that only a small amount of horizontal energy was transferred to the bed. The abrasion prediction model formed by Sklar and Dietrich in 2004 was revised based on the new equations on vertical impact velocity and hop length covering various bed configurations. The abrasion coefficient kv was found to be vary around kv ~ 105 for hard materials (tensile strength ft > 1 MPa), one order of magnitude lower than the value assumed so far for Sklar and Dietrich's model. Copyright © 2017 John Wiley & Sons, Ltd.

A size-dependent viscoelastic normal contact model for particle collision

Considering different energy dissipation mechanisms, many normal contact models have been proposed. However, the size effect and velocity effect of normal restitution coefficient (NRC) cannot always be accurately described. In addition, most of the normal contact models have unphysical tension stage for particles without adhesion during the simulation of particle collisions. Such problems limit the application of discrete element method (DEM) in particle dynamics. Given such limitations, the normal contact model proposed in the present work consists of a nonlinear Hertz spring and a size-dependent nonlinear dashpot, and the model parameters are determined by the NRC obtained in lab tests. Compared with other viscoelastic contact models, the current model can effectively alleviate the influence of unphysical tension force stage on the calculated results, satisfying the accuracy requirement of calculation, and accurately describe the size effect and velocity effect of the NRC of marble spheres at the same time. Besides, due to the viscous force, the contact time calculated by the current model is a little larger than the elastic contact time. The relationship between model parameters and particle size has been analyzed, which shows the law of K1 conforms to exponential decay law and the K2 conforms to hyperbolic tangent function.

Impact experiments of char and ash particles relevant to entrained-flow coal gasifiers

The present study addresses particle–wall interaction phenomena relevant to entrained-flow coal gasifiers. The dynamics of coal, char and ash particles as they are impacted onto a flat surface in cold and hot conditions and undergo momentum transfer and rebound, has been characterized by means of high speed imaging and tracking. Particle–wall collisions were described in terms of normal, tangential and global restitution coefficients. The influence of carbon conversion, impact velocity and surface properties and structure of the target on the dynamical pattern of rebound has been scrutinized. The results indicate that, even at ambient conditions, some plastic deformation occurs during the impact. The restitution coefficients decreased as temperature and carbon conversion increased. This feature was more pronounced at large carbon conversion, confirming the criticality of the char/slag transition to particle deposition on the wall. The dissipation of momentum associated with particle impact may promote the establishment of a dense-dispersed phase in the near-wall zone of entrained-flow slagging gasifiers.

Adhesive tangential impact without slip of a rigid sphere and a power‐law graded elastic half‐space

The JKR‐adhesive impact of a rigid sphere on a power‐law graded half space is studied analytically and numerically under the assumptions of elastic similarity, no‐slip and quasi‐stationarity. The coefficient of normal restitution is determined analytically. The tangential problem is solved by a numerical algorithm based on the Method of Dimensionality Reduction. The tangential coefficient of restitution is depending on only two properly chosen dimensionless parameters. Thereby the presence of only very weak adhesion severely changes the tangential restitution of the sphere.

Collision dynamics of wet solids: Rebound and rotation

Knowledge about collision dynamics and energy dissipation during particle collision is fundamental for the description of particulate processes. However, such knowledge is still missing for particulate processes that involve liquids. Therefore, in this work rebound behavior of particles impacting normally or obliquely on a wet target plate is investigated experimentally via measuring the coefficient of restitution. In real processes, collisions are mostly associated with particle (initial) rotation, which makes the collision dynamics more complex than just translational energy dissipation. Thus, a focus of this work is on analysis of particle rotation and its influence on normal and tangential coefficient of restitution.The normal coefficient of restitution was found to be independent of particle initial rotation, but decreases strongly with application of a liquid layer. The tangential coefficient of restitution, on the contrary, is strongly dependent on initial rotation. Initial rotation in direction of rolling leads to an increase of translational tangential velocity, resulting from the conversion of rotational energy to kinetic energy in tangential direction. Accordingly, initial rotational velocity decreases after collision. During collisions without initial rotation, on the contrary, kinetic energy in tangential direction is converted to rotational energy due to friction.

Investigation of collisional parameters for rough spheres in fluidized beds

The effect of normal restitution coefficient and friction coefficient on the hydrodynamics of a dense bubbling solid-gas fluidized bed is investigated using a two fluid model (TFM) based on our kinetic theory of granular flow (KTGF) for rotating frictional particles. A comparison between TFM simulations using the present KTGF model, and a simpler KTGF model for rapid flows of slightly frictional, nearly elastic spheres derived by Jenkins and Zhang [1], is carried out. The simulation results reveal that both the coefficient of normal restitution and friction coefficient play an important role in the homogeneity of the bubbling bed. The particle friction has a strong effect on the solids flow patterns and distribution, while the normal restitution coefficient has a relatively small effect on both. The present model also predicts a larger amount of energy dissipation caused by the inclusion of particle friction. The present KTGF model leads to better agreement with detailed discrete particle model (DPM) simulation results for the axial particle velocity profiles and solids volume fraction distribution.

Experimental Investigations of the Superelastic Impact Performance of Nitinol 60

ABSTRACTNitinol 60 (NiTi60) is a nickel–titanium alloy that has a unique combination of properties such as high hardness, low elastic modulus, and superelasticity. Recent studies of static indentation tests on prestressed samples demonstrated a considerable load capacity increase, which led to the current experimental work. The coefficient of restitution (COR) is measured for two NiTi60 spheres of different diameters (0.635 and 1.270 cm). This work shows that mechanically stressing NiTi60 spheres enables them to achieve a normal COR greater than 0.9 when colliding with NiTi60 landing. This is one of the highest ever reported COR values for self-mated crystalline metal alloys at moderate impact velocities. Consequently, it is believed that this material may be a potential candidate for use in applications requiring highly resilient and wear-resistant metallic materials. A well-known analytical formulation for the coefficient of restitution is used to gain insight and to elucidate some of the COR results presented.

Method for Estimating Normal Contact Parameters in Collision Modeling Using Discontinuous Deformation Analysis

AbstractThis paper presents a contact parameter estimation method for collision modeling using discontinuous deformation analysis (DDA). Most DDA codes and discrete element method (DEM) codes use the viscoelastic contact model for contact-stress calculation. The contact parameters of the viscoelastic contact model, such as normal stiffness and damping constant, affect the computation results observably. Although the DDA method has been proposed for more than 20 years, the contact parameters in DDA modeling are still difficult to determine. In collision dynamics, the coefficient of restitution (COR) is considered the critical parameter for describing the changes of motion state after collision between two objects. In the proposed method, the normal COR is used for evaluating calculation results of rockfall modeling with three-dimensional DDA. The normal COR of the two-object model is obtained by tests or empirical methods. The relation curve of contact parameters and the normal COR is generated on the basi...

Modeling and simulation of particle–wall adhesion of aerosol particles in particle-laden turbulent flows

The present study is concerned with the development of a computational model for predicting particle–wall adhesion (deposition) of aerosol particles in turbulent particle-laden flows. Particularly, the standard hard-sphere model is extended to include the adhesion during sticking or sliding particle–wall collisions. For both impact types the deposition condition of a particle on bounding walls is determined. The strategy of the proposed model is based on the momentum-based agglomeration model by Breuer and Almohammed (2015). The main advantage of the proposed model compared to the state-of-the-art in the literature is that the adhesive impulse is determined more reasonably taking the time intervals of the compression and the restitution phase into account. Furthermore, if the deposition condition is not satisfied, the treatment of the particle motion after the impact including adhesion depends on the particle–wall type (sticking or sliding). To examine the effect of the particle–wall adhesion, the developed model is first evaluated using simple test cases including oblique particle–wall collisions with friction. In the second step, the performance of the adhesion model is validated based on a horizontal turbulent channel flow against existing experimental data of Kvasnak et al. (1993) and numerical results by Fan and Ahmadi (1993)based on an energy-based deposition model. The predictions of the present model agree very well with the experiments and the numerical results chosen for the validation study as well as the empirical relation by Wood (1981). Third, the adhesion model is employed to investigate the influence of different simulation parameters (normal restitution coefficient for particle–wall collisions and particle diameter) on the particle–wall adhesion and deposition process in a vertical turbulent channel flow laden with a huge number of primary particles. The results show that the inclusion of the adhesion significantly reduces the number of particle–wall collisions, whereas the number of particle–particle collisions is only slightly reduced. Furthermore, the number of deposited particles is higher for small particles than for large particles, since the adhesive impulse is inversely proportional to the diameter of the primary particles. The proposed adhesion model is developed and tested in the context of large-eddy simulation, but it can also be applied in DNS or RANS predictions.

On the oblique collision of gaseous molecules with graphene nanosheets

In this paper, normal and tangential coefficients of restitution for gaseous molecules colliding with layerwise (single and few layers) graphene nanosheets were calculated using non-equilibrium molecular dynamics method. The normal and tangential coefficients of restitution depend on impact angle, velocity and landing position of projectiles. These parameters were evaluated computationally by implementation of several operations. Some differences were observed between proposed problem and macro-scale nature. The most notable difference was proportionality between the restitution coefficients and impact velocity, while in the case of macro-scale systems, they have inverse relation. Number of layers of graphene substrate does not contribute significantly to the normal and tangential coefficients of restitution. On the other hand, except for hydrogen, where its normal coefficient of restitution is approximately unity, the normal coefficient of restitution for other gasses increases as impact angle increases. Furthermore, tangential coefficients of restitution reduce with impact angle. These results can offer additional insights for further understanding the impact mechanisms and bombardment-related phenomena in low-dimensional materials. Presented results could be utilised to optimise some applied operations such as porosity generation via bombardment of layered nanostructures, gas detection process, thermal management and pressure sensor applications.

Influence of the liquid film thickness on the coefficient of restitution for wet particles.

The normal coefficient of restitution (COR) for a spherical particle bouncing on a wet plane is investigated experimentally and compared with a model characterizing the energy loss at impact. For fixed ratios of liquid film thickness δ to particle diameter D, the wet COR is always found to decay linearly with St^{-1}, where St, the Stokes number, measures the particle inertia with respect to the viscous force of the liquid. Such a dependence suggests a convenient way of predicting the wet COR with two fit parameters: a critical COR at infinitely large St and a critical St at zero COR. We characterize the dependence of the two parameters on δ/D and compare it with a model considering the energy loss from the inertia and the viscosity of the wetting liquid. This investigation suggests an analytical prediction of the COR for wet particles.

The coefficient of normal restitution for the Hertzian contact of two rough spheres colliding in a viscous fluid

We use previous theoretical results for the added mass, history and lubrication forces between two spheres colliding in a fluid with viscosity ν to investigate the effect of viscous dissipation on the coefficient of restitution during contact. We assume that the mechanical interaction is governed by Hertzian mechanical contact of small duration τ and that the minimum approach distance between particles is approximately equal to the height σ of surface micro-asperities. A non-dimensionalization of the equation of motion indicates that the contact dynamics is governed by two parameters – the ratio ϵ of the surface roughness σ and the sphere radius a, and a contact Stokes number defined as Stc=σ2/ντ. An asymptotic solution of the equation of motion in the limit of small ϵ/Stc is used to obtain an explicit expression for the coefficient of restitution during contact and the latter is compared with estimates based on numerical solutions of the non-linear equation of motion.

Experimental study of oblique impact of particles on wet surfaces

Granulation and agglomeration processes are characterized by intense particle–particle and particle–wall contacts. Furthermore, these collisions often happen in the presence of liquid layers due to liquid injection. Therefore the knowledge of micro-mechanics during wet collisions is fundamental for the exact description of such a process. In this work the collision behaviour of dry particles obliquely impacting a target plate covered by liquid layers is characterized by means of restitution coefficients. The coefficient of restitution describes the energy dissipation during an impact and is defined as the ratio of the velocities after and before impact. It is an important parameter for discrete element method (DEM) simulations and depends strongly on the collision parameters (such as collision velocity and angle), particle deformation behaviour (i.e. elastic or plastic) as well as on the properties of the injected liquid (viscosity, layer thickness). To investigate the influence of these parameters on the wet collision behaviour particle–wall impacts were recorded by two synchronized high-speed cameras allowing a three-dimensional analysis of the collision event. The focus of this work is to investigate the influence of liquid layer thickness, viscosity, surface tension and surface roughness on the normal and tangential coefficient of restitution.

Modeling and simulation of agglomeration in turbulent particle-laden flows: A comparison between energy-based and momentum-based agglomeration models

In the present work, the particle agglomeration in shear flows is investigated in the framework of a hard-sphere model with deterministic collision detection employing two different modeling approaches: the energy-based and the momentum-based agglomeration models. The former is further improved concerning the agglomeration conditions. Moreover, the application area of both models is extended towards fully three-dimensional turbulent flows applying the large-eddy simulation technique. Here, the particles are assumed to be rigid, dry and electrostatically neutral and hence only the cohesion due to the van-der-Waals forces is considered. First, the energy-based and the momentum-based agglomeration models are successfully validated based on theoretical results using an existing laminar test case. The numerical results are found to be in close agreement with the theory. Then, both agglomeration approaches are used to investigate the dynamic process of the particle agglomeration in a vertical fully developed turbulent channel flow. A detailed comparison of the results obtained using both agglomeration models is reported. Additionally, the performance of both techniques is examined under the influence of varying normal restitution coefficients of the inter-particle collisions. Furthermore, the influence of the inclusion of three sub-models (the feedback effect of the particles on the fluid, the lift forces and the subgrid-scale model for the particles) on the agglomeration process is studied. The results show that a significantly lower agglomeration rate is observed if the sub-models are considered. Next, the agglomeration models are applied to evaluate the effect of the diameter of the primary particles and the wall roughness on the agglomeration behavior. The reduction of the diameter of the particles leads to a stronger cohesive impulse and hence to a higher agglomeration rate. The wall roughness enhances the particle–particle collisions and slightly increases the number of agglomeration processes leading to higher agglomeration rates. The comparative study clearly indicates that both models predict similar trends of the physical behavior of the agglomeration process, but their results deviate slightly from each other. The most important reasons for the differences observed between the numerical results of both models are discussed. Based on the advantages and drawbacks of both models highlighted in this study, it can be concluded that owing to the reduced necessity of empirical parameters and the slightly more accurate results the momentum-based agglomeration model is superior to the energy-based model.

Calibration and validation of rockfall modelling at regional scale: application along a roadway in Mallorca (Spain) and organization of its management

The Tramuntana range, in the northwestern sector of the island of Mallorca (Balearic Islands, Spain), is frequently affected by rockfalls which have caused significant damage, mainly along the road network. In this work, we present the procedure we have applied to calibrate and validate rockfall modelling in this region, using 103 cases of the available detailed rockfall inventory (630 rockfall events collected since the eighteenth century). We have exploited STONE (Guzzetti et al. 2002), a GIS-based rockfall simulation software which computes 2D and 3D rockfall trajectories starting from a DTM and maps of the dynamic rolling friction coefficient and of the normal and tangential energy restitution coefficients. The appropriate identification of these parameters determines the accuracy of the simulation. To calibrate them, we have selected 40 rockfalls along the range which include a wide variety of outcropping lithologies. Coefficients values have been changed in numerous attempts in order to select those where the extent and shape of the simulation matched the field mapping. Best results were summarized with the average statistical values for each parameter and for each geotechnical unit, determining that mode values represent more precisely the data. Initially, for the validation stage, 10 well-known rockfalls exploited in the calibration phase have been selected. Confidence tests have been applied to their modelling results taking into account not only the success but also the mistakes. The best accuracy is obtained when the rockfall has a preferential trajectory and worse results when the rockfall follows two or more trajectories. Additionally, the greater the rockfall runout length, the less precise the simulation is. We have further validated the calibrated parameters along the Ma-road (111 km), the main transportation corridor in the range, using 63 rockfall events that occurred during the past 18 years along the road. Of the rockfalls where source areas were properly identified, 81.5 % are well represented by STONE modelling, as the travel paths and the depositional areas are successfully ascertained. Results of the analysis have been used by the Road Maintenance Service of Mallorca to assess hazard and risk posed by rockfall at regional scale to design the road management plan.