Low-velocity collisions of particles with a dry or wet wall

Plastic and metal spheres were impacted at low velocities in the range 0.02–0.30 m/s with a quartz plate that was dry or covered with a thin oil layer. Collisions were performed with a specially designed device in the low-gravity environment provided by a KC-135 aircraft. A pendulum-based experimental set-up was also used to perform low-velocity collisions under normal gravity. The dry restitution coefficient (ratio of the rebound velocity and impact velocity) is found to decrease weakly with increasing approach velocity, as is the general case with materials exhibiting inelastic deformation. The wet restitution coefficient is zero below a critical velocity and then increases with the impact velocity before evening out to form a plateau. A simple model for the wet restitution coefficient, e_wet=e_dry(1−St_c/St), was found to adequately predict the restitution coefficient, as has been reported in earlier studies at higher impact velocities, where e_dry is the dry restitution coefficient, St is the Stokes number and St_c is the critical Stokes number below which no rebound occurs. Surface asperities are seen to cause more scatter in the data at low velocities than at high velocities. The data from pendulum experiments coincide with those collected in low gravity, thereby affirming their applicability for performing low-velocity collisions.     

Energy absorption during compression and impact of dry elastic-plastic spherical granules

The discrete modelling and understanding of the particle dynamics in fluidized bed apparatuses, mixers, mills and others are based on the knowledge about the physical properties of particles and their mechanical behaviour during slow, fast and repeated stressing. In this paper model parameters (modulus of elasticity, stiffness, yield pressure, restitution coefficient and strength) of spherical granules (γ-Al₂O₃, zeolites 4A and 13X, sodium benzoate) with different mechanical behaviour have been measured by single particle compression and impact tests. Starting with the elastic compression behaviour of granules as described by Hertz theory, a new contact model was developed to describe the force-displacement behaviour of elastic-plastic granules. The aim of this work is to understand the energy absorption during compression (slow stressing velocity of 0.02 mm/s) and impact (the impact velocity of 0.5–4.5 m/s) of granules. For all examined granules the estimated energy absorption during the impact is found to be far lower than that during compression. Moreover, the measured restitution coefficient is independent of the impact velocity in the examined range and independent of the load intensity by compression (i.e. maximum compressive load). In the case of repeated loading with a constant load amplitude, the granules show cyclic hardening with increasing restitution coefficient up to a certain saturation in the plastic deformation. A model was proposed to describe the increase of the contact stiffness with the number of cycles. When the load amplitude is subsequently increased, further plastic deformation takes place and the restitution coefficient strongly decreases.     

Experimental investigation of the coefficient of restitution of particles colliding with surfaces in air and water

The coefficient of restitution is a parameter used to describe the result of a collision between either two particles or a particle and a surface. The coefficient of restitution is a measure of the amount of kinetic energy dissipation during a collision. This work aimed to study the behavior of the coefficient of restitution based on the velocity of the impacting particle and the properties of the surface and/or particle involved in the collision. This goal was achieved by establishing an experimental system to measure the coefficient of restitution, conducting experiments, and determining dependence between parameters using analytical tools.To measure the coefficient of restitution correctly, based on a large data basis and wide ranges of properties and operating conditions, experiments were conducted on different surfaces and particulate materials with different collision angles and velocities. These experiments were conducted in different surroundings (air and liquid), which posed an important issue. For accurate prediction, after analyzing the results, a correlation was proposed to estimate the value of the coefficient of restitution depending on the mechanical properties of the particle and surface, angle and speed of the collision, and characteristics of the collision medium. Most of the tests for the wide range of properties and conditions were fit to the final correlation by ±30%.     

A coefficient of restitution model for particle–surface collision of particles with a wide range of mechanical characteristics

The coefficient of restitution describes the energy dissipation resulting from particle-particle and particle–surface interactions in solid–fluid flows. The energy loss depends on the mechanical characteristics of the solid phase, therefore, to correctly predict the behavior of these systems it is necessary to use reliable coefficient values based on the properties of the particles. This paper investigated the energy dissipation in particle–surface collisions using 7 types of particles with a wide range of mechanical properties (Young's modulus between 1.38 × 10⁴ and 2.83 × 10⁹ Pa). Three empirical equations have been proposed to calculate the coefficient of restitution based on the impact velocity and the compressional wave velocity. The experimental results presented an inverse relation between the impact velocity and the coefficient of restitution. This effect was more pronounced for less elastic particles. The models presented an accurate fit to the experimental data and statistical analysis showed that the Power model presented the greater capacity to predict the coefficient of restitution from generic data. The experimental results showed the predominant effect of mechanical characteristics on the coefficient of restitution. In addition, the proposed equations are proved to be precise tools for predicting particle coefficients of restitution with a wide range of elasticity modulus at low velocities.     

Experimental study on electrostastic particle deposition from gas–solids two-phase flow based on tribo-electrification

Electrostastic particle deposition on a target embeded in a substrate under a locally applied voltage has been investigated experimentally based on the tribo-electrification of particles. Initially particles deposit mainly on the edge of the target because of the contact potential difference between substrate (poly(methyl methacrylate)) and target (brass). The thickness of particle layer formed by the deposited particles increases with time, but gradually saturates. Since then almost no additional particles deposit on the target. When high voltage is applied to the target, and orange peel phenomenon is observed on the surface of the particle layer. In the central region of the target, the particles under high particles. The larger the Coulombic force parameter K_E, the higher the effective deposition velocity is. The velocity increases dramatically for K_E 6 × 10⁻⁶ and 20 < St < 60. The larger Stokes number makes the coefficient of variation larger for the thickness of the particle layer, i. e. the deposition under higher Stokes number gives a less uniform deposition layer. However, for St < 10, particles deposit almost uniformly. For the deposition under a larger Coulombic force parameter, onset of the rebound and resuspension is suppressed, and the region with a uniform deposition layer is shifted to a higher Stockes number. It is also found that particles can successfully deposit on a non-conductive target of a dielectric substance through setting a grounded guard electrode around the target.     

Die wall friction and influence of some process parameters on friction in iron powder compaction

Abstract

The coefficient of friction is a system response parameter, which is affected by a number of parameters such as normal load and sliding distance. Experimental results describing the influence of these parameters are presented in this study. These parameters have a crucial role in the modelling of the compaction process and also provide an in depth understanding of the mechanism of friction in powder compaction. The powder surface characteristics change continuously during the pressing, making friction measurement quite difficult. An attempt has been made to identify and separate the powder behaviour during compaction. The experimental results show that the plastic deformation of the surface in contact with the die wall occurs at an early stage of the compacting. At densities above 5 g cm³ the plastic deformation is completed and the variation of the coefficient of friction is minimal. It has been observed that most changes of the powder surface occur at low densities. The nature of the friction has also been discussed.     

Rebound behaviour of spheres for plastic impacts

This paper presents a study on the rebound behaviour of spheres impacted normally against a target wall using finite element methods. The emphasis is on the prediction of the coefficient of restitution and the effects of material properties and impact velocities on the rebound behaviour of the sphere. Finite deformation during plastic impact is addressed. The finite element results show that, for impacts of small plastic deformation, the coefficient of restitution is mainly dependent on the ratio of the impact velocity V_i to the yield velocity V_y which is consistent with those predicted by the theory of impact mechanics; while for impacts of finite-plastic-deformation it is also dependent on the ratio of the representative Young's Modulus E^* to the yield stress Y. The FEA results suggest that for impacts of finite-plastic-deformation the coefficient of restitution can be approximated to be proportional to [(V_i/V_y)/(E^*/Y)]^−1/2.     

Numerical study on erosion of a pipe bend with a vortex chamber

Abrasive erosion at bend is a common issue in gas–solid pneumatic system. Vortex chamber design is one of the specialized designs that offers promising prospect at reducing erosion. The performance of design is still relatively unknown in the literature. The aim of this work is to study the effect of basic erosion variables such as the flow Reynolds number, the particle Stokes number, and the vortex chamber size. The results show that the vortex chamber always reduces the erosion in comparison to the common radius bend, and it is more effective at higher Reynolds number. Increasing the chamber size reduces the erosion but the most significant reduction happens when the chamber size to the pipe diameter ratio is increased from 1 to 1.25. The chamber size influences the erosion differently at different Reynolds number. Trends describing these effects were obtained through trial-and-error approach. The particle Stokes number has nonunique effect on erosion. Increasing Stokes number through increasing Re increases the erosion while increasing Stokes number through decreasing Re_p decreases the erosion.     

Deformation microstructure and texture in hot worked aluminium alloys

Abstract

Three non-heat-treatable aluminium based materials (AA 1050, AA 1050+1%Mn, and AA 1050+1%Mg) were deformed by plane strain compression (strains of 0·5 to 2, strain rates of 0·25 to 25 s^?1) at elevated temperature (300 to 500°C). The resulting microstructures and textures were studied using optical and back scattered electron microscopy and neutron diffraction. Trends in the development of the deformation microstructure and texture with deformation parameters were noted. It was found that the amount of cube texture in the deformed material decreases as the strain increases. The Zener–Hollomon parameter is not suitable for describing the evolution of cube texture during hot deformation in AA 1050. The addition of 1%Mn or 1%Mg to AA 1050 has little effect on the trends of texture development during hot working. The subgrain size in these alloys decreases with increasing Zener–Hollomon parameter, but the strain has little effect. The misorientation between neighbouring subgrains appears to be approximately independent of deformation parameters in the range of deformation conditions studied.

MST/3472     

Sensitivity of numerical parameters on DEM predictions of sediment transport

The current work presents a sensitivity study of selected numerical parameters on the large-eddy simulation–discrete element method predictions of sediment transport in a unidirectional open turbulent channel. The sensitivity of the particle friction factor, restitution coefficient, and spring stiffness used in the soft sphere collision model is tested in the three regimes of sediment transport comprising of essentially no motion, bed load, and suspended load flow regimes. The simulations are run for 10?s using base values of the parameters of interest (reference calculation), then one parameter is changed at a time and the corresponding change in quantitative result is observed for the following 15?s where averaged results in the last 10?s are compared to the reference calculation. The sensitivity analysis shows that the underpredicted sediment transport in the suspended load regime can be bridged by moderately decreasing the friction factor of the particles from 0.6 to 0.25. The impact of the same change in bed load regime is not as significant. Both the coefficient of restitution and the particle stiffness show less significant to negligible impact as compared to the friction factor.     

Size dependence of the bulk modulus of Si nanocrystals

This study investigates the effect of size on bulk modulus and its related parameters, including melting temperature and mass density based on the ratio number of surface atoms to that of its internal. The equation of bulk modulus in the bulk state B(∞) is modified to include the related size-dependent parameters without any adjustable parameter, and is applied to Si nanocrystals. The bulk modulus B(r) decreases from 9.8?×?10¹⁰ N m² for the bulk state to 5.93?×?10¹⁰ N m² for a 5 nm diameter of Si nanoparticles. An inherent relation between bulk modulus and change of the lattice parameter in nanocrystals obtained from the variation in the surface to volume ratio, this leads to increase in the mean bond length. The effect of mass density and melting temperature on bulk modulus are also discussed. Calculated results for bulk modulus are verified by experimental as well as the available computer simulation data.     

A mixed contact model for an immersed collision between two solid surfaces

Experimental evidence shows that the presence of an ambient liquid can greatly modify the collision process between two solid surfaces. Interactions between the solid surfaces and the surrounding liquid result in energy dissipation at the particle level, which leads to solid-liquid mixture rheology deviating from dry granular flow behaviour. The present work investigates how the surrounding liquid modifies the impact and rebound of solid spheres. Existing collision models use elastohydrodynamic lubrication (EHL) theory to address the surface deformation under the developing lubrication pressure, thereby coupling the motion of the liquid and solid. With EHL theory, idealized smooth particles are made to rebound from a lubrication film. Modified EHL models, however, allow particles to rebound from mutual contacts of surface asperities, assuming negligible liquid effects. In this work, a new contact mechanism, 'mixed contact', is formulated, which considers the interplay between the asperities and the interstitial liquid as part of a hybrid rebound scheme. A recovery factor is further proposed to characterize the additional energy loss due to asperity-liquid interactions. The resulting collision model is evaluated through comparisons with experimental data, exhibiting a better performance than the existing models. In addition to the three non-dimensional numbers that result from the EHL analysis--the wet coefficient of restitution, the particle Stokes number and the elasticity parameter--a fourth parameter is introduced to correlate particle impact momentum to the EHL deformation impulse. This generalized collision model covers a wide range of impact conditions and could be employed in numerical codes to simulate the bulk motion of solid particles with non-negligible liquid effects.     

Immersed-boundary/soft-sphere method for particle–particle-fluid interaction in a viscous flow: An OpenFOAM solver

We developed a stable OpenFOAM solver for Immersed Boundary Method based on direct forcing and regularized delta function. The soft-sphere model and a lubrication model were implemented to consider particle–particle collision in a viscous flow. We proposed a fluid–structure interaction (FSI) coupling method to accurately calculate the fluid forcing term and particle velocity. Our solver was validated for fixed and moving bodies, including rotation. The accuracy of various FSI schemes was evaluated in predicting the solid and fluid flow behavior in a viscous flow. It was demonstrated that neglecting or simplifying the fluid momentum change affects the accuracy of the solid velocity and fluid flow dynamic; for higher solid-to-fluid density ratios, a larger deviation was predicted. Furthermore, the FSI schemes highly influenced the behavior of the formed vortices.The solver was validated to predict the effective restitution coefficient of particles in a viscous flow as a function of the Stokes number. We also thoroughly analyzed the dynamic flow behavior of colliding particles through the pressure and velocity field and fluid force. This analysis helped us accurately determine the rebound velocity of particles in case of high Stokes numbers when the effect of viscous force is significant.     

Effect of base dissipation on the granular flow down an inclined plane

The effect of base dissipation on the granular flow down an inclined plane is examined by altering the coefficient of restitution between the moving and base particles in discrete element (DE) simulations. The interaction laws between two moving particles are kept fixed, and the coefficient of restitution (damping constant in the DE simulations) between the base and moving particles are altered to reduce dissipation, and inject energy from the base. The energy injection does result in an increase in the strain rate by up to an order of magnitude, and the temperature by up to two orders of magnitude at the base. However, the volume fraction, strain rate and temperature profiles in the bulk (above about 15 particle diameters from the base) are altered very little by the energy injection at the base. We also examine the variation of h _stop , the minimum height at the cessation of flow, with energy injection from the base. It is found that at a fixed angle of inclination, h _stop decreases as the energy dissipation at the base decreases.     

Entropy Generation for Flow and Heat Transfer of Sisko-Fluid Over an Exponentially Stretching Surface

In the present study, the effects of the magnetic field on the entropy generation during fluid flow and heat transfer of a Sisko-fluid over an exponentially stretching surface are considered. The similarity transformations are used to transfer the governing partial differential equations into a set of nonlinear-coupled ordinary differential equations. Runge-Kutta-Fehlberg method is used to solve the governing problem. The effects of magnetic field parameter M, local slip parameter λ, generalized Biot number γ, Sisko fluid material parameter A, Eckert number Ec, Prandtl number Pr and Brinkman number Br at two values of power law index on the velocity, temperature, local entropy generation number N_G and Bejan number Be are inspected. Moreover, the tabular forms for local skin friction coefficient and local Nusselt number under the effects of the physical parameters are exhibited. The current results are helpful in checking the entropy generation for Sisko-fluid. It is found that, an extra magnetic field parameter makes higher Lorentz force that suppresses the velocity. For shear thinning fluids (n < 1), the temperature dominates and the velocity rises. Local entropy generation number is more for larger generalized Biot number, magnetic field parameter and Brinkman number. The local skin friction coefficient increases as magnetic field parameter and material parameter are increase and it decreases as local slip parameter increases. The local Nusselt number decreases as magnetic field parameter, local slip parameter and Eckert number are increase, while it increases as material parameter, generalized Biot number and Prandtl number are increase.     

Mixed convection of micropolar fluids along a vertical wavy surface

Summary This paper presents numerical results for the steady-state mixed convection in micropolar fluids along a vertical wavy surface. The problem has been formulated by a simple trnasposition theorem, and the spline alternating-direction implicit method has been applied to solve the governing momentum, angular momentum and energy equations. The influence of the micropolar parameters (R and ), the amplitude-wave length ratio and the Gr/Re² number on the skin-friction coefficient and Nusselt number have been studied. Results demonstrate that the skin friction coefficient and local Nusselt number consist of a mixture of two harmonics in micropolar fluids and in Newtonian fluids. As the vortex viscosity parameter (R) increases, the heat transfer rate decreases but the skin friction increases. In addition, when the spin gradient viscosity parameter () increases, the heat transfer rate and the skin friction decreases. However, the heat transfer rate of a micropolar fluid is smaller than a Newtonian fluid, but the skin friction of a micropolar fluid is larger than a Newtonian fluid under all circumstances.     

The validity of Weibull estimators

The parameters of the two-parametric Weibull distribution, the Weibull modulus and the scale parameter, were estimated by using not only analytical means but also Monte-Carlo simulations. The precision of the measurement of both parameters, i.e. their variation coefficient, has been calculated. It is shown that the variation coefficient of the scale parameter is dependent on the number of experiments, M, which were performed, and on the Weibull modulus itself, whereas the variation coefficient of the Weibull modulus is only dependent on M. Furthermore, the correctly interpreted results show that each single measurement gives the statistically correct Weibull parameters and the biasing arises only from the method of adding single measurements to obtain a mean value. Thus, in practice, when only one set of experiments for further evaluation is available, there is no need for adjustment factors.     

Direct measurement of particle–particle interaction using micro particle interaction analyzer (MPIA)

Direct particle–particle contact force measurement was successfully conducted for realistic parameter determination to support discrete element method (DEM) simulation by using a newly developed force measurement of micro particle interaction analyzer (MPIA). In this system particle-to-particle distance and deformation can be controlled by nanometer accuracy. The system can be used for measuring not only short-distance deformation but also long-distance deformation that was validated by both elastic contact and liquid bridge interaction including rupture distance, respectively. Then, the system was applied to obtain plastic normal deformation characteristics such as coefficients of restitution of the spherical granules at low loading force less than 0.5 mN. Granules were prepared from two-stage pressure swing granulation (PSG) technique in a fluidized bed.     

Effects of specularity and particle-particle restitution coefficients on the recirculation characteristics of dispersed gas-particle flows through a sudden expansion

We numerically investigate the effects of restitution and specularity coefficients on the characteristics of dispersed gas-particle flows through a sudden expansion. The studies are carried out using an indigenous finite volume flow solver in a collocated framework with two-fluid model. Parametric studies are performed to gain insights into the differences in recirculation patterns that arise due to variations in restitution and specularity coefficients. The simulations show that particle-particle interactions, quantified by restitution coefficient (e) have a greater impact on recirculation characteristics than particle-wall interactions, which are quantified by specularity coefficient ($?$). Studies reveal that the recirculation lengths tend to decrease as particle collisions become more elastic (as e tends to unity) while they increase, as the value of $?$ increases. However, the changes in recirculation length are very gradual and less pronounced when only particle-wall interactions are considered as compared to particle-particle interactions. From the range of parametric variations studied in this work, the maximum recirculation length has been found when the value of $?$ is maximum and that of e is minimum.