Coefficient Of Restitution Research Articles

The effect of relative humidity on deposition pattern in inertial impactors: The role of particle elasticity and surface attraction

The role of relative humidity on particle bounce in an inertial impactor was investigated through a program of experiments and particle trajectory simulations. Inertial impactors are devices used to obtain particle size distributions by passing particle-laden air through a nozzle and collecting particles having sufficient inertia on a flat surface placed directly below the nozzle. Herein monodisperse hygroscopic particles impacted the flat hydrophobic surface of a single stage inertial impactor while varying the relative humidity of the flow. The results show that a circular deposition pattern occurs when the relative humidity is high. When the relative humidity is low secondary deposits beyond the circular deposit also occur. Particle trajectory simulations were performed where particle/surface interactions were quantified via the Hamaker constant (A) and the loss of kinetic energy via the coefficient of restitution (e). In a first-of-its-kind approach, (A, e) were iteratively adjusted until prominent features of the particle deposits in the experiments and simulations agreed, thereby providing values of (A,e) for each relative humidity. The results show that the observed deposition behavior is due to (i) the increase with relative humidity of the repulsion between the hygroscopic particles and the hydrophobic surface, (ii) multiple bounces along the particle trajectory, and (iii) kinetic energy loss at each particle bounce.

Impact of composite soft-rigid elastic projectiles: A numerical study.

We study by numerical simulation the impact of a one-dimensional composite projectile, composed of two superposed homogeneous parts, on an infinitely rigid and massive wall. The coefficient of restitution and the contact time are systematically measured as functions of the contrasts of mass and stiffness between the two parts. For purely elastic parts, these quantities show complex trends associated with different dynamics of the deformation waves propagating inside the projectile. A significant portion of the initial kinetic energy can be trapped in the deformation modes: the coefficient of restitution is lowest, about 0.2, when there is a strong stiffness contrast between the two parts and the stiff and soft parts are at the leading and trailing edges of the projectile respectively. In this case, we highlight the presence of multiple bounces, whose number increases as the proportion of the soft part increases. Finally, viscoelastic parts can be implemented in the same numerical framework to successfully recover the results obtained in real composite projectile impact experiments [D'Angelo et al., Phys. Rev. E 103, 053005 (2021)2470-004510.1103/PhysRevE.103.053005].

Three-dimensional fully-Lagrangian DEM-SPH modeling of river ice interaction with control structures

Ice control structures (ICSs) play a vital role in preventing ice jams and safeguarding communities by either stabilizing ice cover or relocating jams upstream. Understanding and modeling the interaction between ice floes and these structures is crucial for assessing their effectiveness and optimizing their designs. However, simulating these complex multi-physics systems poses challenges for numerical techniques. In this paper, we introduce and evaluate a fully-Lagrangian mesh-free continuum-discrete model based on the Smoothed Particles Hydrodynamics (SPH) method and Discrete Element Method (DEM) for three-dimensional (3D) simulation of ice interactions with control structures. To validate and parameterize the numerical model, we conduct two sets of experiments using real and artificial ice materials: (1) dam-break wave-ice-structure interaction and (2) ice-ICS interaction in an open channel. By comparing numerical and experimental results we demonstrate the capability and relative accuracy of our model. Our findings indicate that real ice generally exhibits faster jam evolution and ice passage through the ICS compared to artificial ice. Moreover, we identify the Froude number and ice material type as important factors influencing jam formation, evolution, and ICS effectiveness. Through sensitivity analysis of material properties, we highlight the significant impact of friction and restitution coefficients.

Restitution coefficient of various particles based on acoustic technology

The restitution coefficient is used to characterize the energy loss in particle impact, which is an important parameter for discrete element simulation and mechanical system motion analysis. However, the restitution coefficient of many materials needs to be determined, and the key material properties affecting the restitution coefficient are still unclear. In this paper, the acoustic frequency sampling method was used to study the restitution coefficients of 10 representative particles. The effects of material density and specific strength on the restitution coefficient and the relationship between the restitution coefficient and the damping coefficient were investigated. The results show that the particle restitution coefficient is inversely proportional to the density except for aluminium. The relationship between particle restitution coefficient and specific strength is not significant.

Investigation of Pounding between Two Adjacent Building Models with Experimental Methods

This study investigates the pounding phenomenon by shaking table experiments on two scaled building models. Representing the situation where the seismic gap is insufficient, two building models are adjacently positioned on the shaking table, and pounding was investigated for harmonic and strong ground motion excitations. Displacement and acceleration responses were obtained to observe the pounding effect experimentally from video and accelerometer recordings, respectively. The Kelvin-Voigt Model consisting of spring and damper was used for numerical pounding analysis. The most critical parameters of the Kelvin–Voigt model, which are the spring stiffness (ks) and the damping, are calculated according to the coefficient of restitution (r) and were investigated and compared with harmonic experimental results. The obtained parameters, compatible with the harmonic experiments, were used to examine structural behavior under earthquake effect for the case where the building models are positioned for an insufficient seismic gap. For comparison, numerous numerical simulations were realized using different spring stiffnesses and coefficients of restitution. The study shows that when the coefficient of restitution is taken as 0.2 or 0.4, and the ratio of spring stiffness to shear stiffness (ks/k) is 1 or 5, reasonable results in numerical earthquake simulations can be obtained.

Independent friction-restitution description of billiard ball collisions

The oblique impact of a cue ball moving on a horizontal surface with an arbitrary spin on an object ball at rest is described using the independent friction-restitution modeling of impact. The model yields theoretical expressions for the post-collision linear and angular velocities in terms of ‘constant’ coefficients of normal restitution, tangential restitution, and friction for both stick and slip regimes of impact. The model also predicts the post-impact velocities reached by the balls when, as a result of friction with the supporting surface, the pure rolling motion is established. Theoretical predictions are in satisfactory agreement with experimental data for collisions between regulation billiard balls, steel, brass, and rubber spheres.

Insights into protective performance of CoCrNi medium entropy alloy coating subjected to supersonic micro-ballistic impact

Medium- and high-entropy alloys (MEAs and HEAs) coatings have attracted increasing attention owing to their exceptional mechanical properties and potential applications in structures protective from supersonic microparticle impact. However, there are no experimental insights into their protective performance. In this study, we fabricated high-quality amorphous CoCrNi MEA coatings with a thickness of 4.5 μm on the rigid and flexible substrates through ion beam-assisted deposition. Based on nanoindentation and laser-induced supersonic microparticle impact experiments, the mechanical properties and protective performance of the CoCrNi MEA coating were characterized and compared with those of the aluminum and copper coating. The results show that the CoCrNi MEA coating exhibits a high hardness of 9.7 GPa and an elastic modulus of 146.8 GPa. Under the supersonic impact, the CoCrNi MEA coating shows high coefficient of restitution, low rebound-to-fracture transition velocity, and small impact-mode ratios. The impact-mode ratios of the CoCrNi MEA coating subjected to microparticles of different materials further indicate that the CoCrNi MEA coating can efficiently withstand the high-velocity impact of most metallic particles except tungsten ones. Our work provides direct experimental insights into the excellent impact resistance of CoCrNi MEA coatings, which holds a great promise for improving the reliability and durability of equipment subjected to high-speed collisions of solid particles entrained within the air such as ice and sand dust.

A force–displacement relation based on the JKR theory for DEM simulations of adhesive particles

Studying the collective behavior of adhesive particles with the discrete element method (DEM) requires well-founded force–displacement relations (force models). While the Johnson–Kendall–Roberts (JKR) theory reliably predicts the dependence of the contact radius a on the force F, it has remained a challenge in this framework to obtain a straightforward force–displacement relation F(δ) with physically meaningful parameters to calculate the force F from the displacement δ. We derive a novel force–displacement relation from the JKR theory as a composition of functions F(δ)=(F∘a∘λ)(δ), with the intermediate functions contact radius a(λ) and effective adhesive contact radius λ(δ). We also analyze contact geometry errors in the Hertz and JKR models, derive the exact contact centroid to accurately calculate contact torques and relative tangential velocities, and propose a smoothed JKR model to avoid discontinuities in force and energy. We find that incorrect torques and relative tangential velocities are obtained when the stiffness quotient is neglected because it affects the exact location of the contact centroid. We also find that contact geometry errors can become non-negligible for nanoparticles due to their large relative contact size. In addition, we show from bouncing ball simulations that the JKR models with a nominal coefficient of restitution derived for the Hertz model result in higher damping and thus reduced actual coefficients of restitution. Our analysis serves as a foundation for contact-mechanics-based force models for DEM simulations of adhesive particles to investigate their collective behavior in the future.

Validation of a DEM Model for predicting grain damage in an industrial-scale handling system

An industrial-scale handling system with a flight conveyor, a screw conveyor, and a rethresher as the core components was designed and built to validate a previously developed discrete-element-method-based (DEM) grain impact damage model. Corn and soybean samples were processed by the system at three impeller speeds and two feed rates, and the amount of damage caused by handling was evaluated. DEM simulations with the impact damage model were performed for the same test conditions. The experimental results showed that grain damage increased with increasing impeller speed and decreasing feed rate, which aligned with the simulation predictions. The damage fraction values estimated by the simulation were larger than the experimental measurements when the original DEM input parameters were used. The mean absolute error between the simulation and experimental results was 0.14 for the corn tests and 0.05 for the soybean tests. This overprediction may be because the particle-geometry coefficient of restitution (PG COR) was measured at low impact speeds but impact speeds in the validation system is high. The simulation predictions can be significantly improved by decreasing the PG COR from 0.75 to 0.55 for the corn and from 0.6 to 0.4 for the soybeans. The mean absolute error between the simulation and experimental results decreased from 0.14 to 0.02 for the corn tests and from 0.05 to 0.01 for the soybean tests after the reduction of PG COR. In addition, the sensitivity analysis suggested that the Young's modulus and particle shape contribute only minor changes to the damage fraction and the location of the damage for the conditions examined.

Liquid metal droplets bouncing higher on thicker water layer

Liquid metal (LM) has gained increasing attention for a wide range of applications, such as flexible electronics, soft robots, and chip cooling devices, owing to its low melting temperature, good flexibility, and high electrical and thermal conductivity. In ambient conditions, LM is susceptible to the coverage of a thin oxide layer, resulting in unwanted adhesion with underlying substrates that undercuts its originally high mobility. Here, we discover an unusual phenomenon characterized by the complete rebound of LM droplets from the water layer with negligible adhesion. More counterintuitively, the restitution coefficient, defined as the ratio between the droplet velocities after and before impact, increases with water layer thickness. We reveal that the complete rebound of LM droplets originates from the trapping of a thinly low-viscosity water lubrication film that prevents droplet-solid contact with low viscous dissipation, and the restitution coefficient is modulated by the negative capillary pressure in the lubrication film as a result of the spontaneous spreading of water on the LM droplet. Our findings advance the fundamental understanding of complex fluids’ droplet dynamics and provide insights for fluid control.

Study on the feasibility of partial replacement of cement with IOT in extruded concrete roof tiles production

The use of mining waste (IOT) as supplementary materials for cement has the potential to significantly reduce carbon emissions, helping to mitigate the demand for natural resources and the impacts associated with their production.Concrete tiles have been gaining prominence in recent years due to practicality, aesthetics, weather resistance, attractive price, ease of fitting and useful life, however, there is no information in the literature about the effect of IOT as a pozzolanic material for partial replacement of Portland cement in these composites. Therefore, this study aims to expose the use of iron ore tailing (IOT) as a partial replacement for Portland cement in extruded concrete tiles in different proportions, qualifying and classifying them according to the marketing standards. The performance of concrete roof tiles using IOT was analyzed for bulk density, dry weight, apparent porosity, water absorption, wettability, breaking load, impact strength, coefficient of restitution, and thermal conductivity. In addition, microscopy and X-ray diffraction examined interactions between IOT particles and cementitious matrix at 28 days and after accelerated aging. Economic analyses regarding the effect of using IOT on the final cost of concrete roof tiles were also performed. The results showed that the concrete roof tiles produced with IOT presented suitable physical, mechanical, and thermal properties, highlighting the samples with 10% IOT as a replacement for cement, which proved superior to conventional tiles for the breaking load at 28 days, also presenting an average value reduction of 6.61% for porosity and 33.33% for wettability. All formulations were approved for breaking load according to the international marketing standard and may cut costs for companies producing cement roof tiles by up to 40%. In addition to reducing the potentially harmful waste in containment dams, IOT may lessen the demand for Portland cement and, consequently, CO2 emissions, producing more sustainable composites with significantly reduced manufacturing costs.

Experimental study on the fugitive characteristics of particles flow impacting inclined wall

The process of loading and unloading of bulk materials is common in industrial production, which is likely to cause dust pollution problems in the plant. In order to understand the dust generation mechanism of the material unloading process, this paper examines it through three processes. Firstly, we established an experimental model for the process of particle flow impacting on the wall. Secondly, the particle motion fugitive characteristics of the particles flow impacting the wall were tested using a high-speed camera. Finally, by processing the experimental data, the angle deviation ratio is pioneered to analyze the effect of wall angle on particle fugitive and the particle fugitive characteristics under different conditions. The results show that as the wall inclination angle increases, the angular deviation ratio is smaller, the total restitution coefficient of particles is larger, the fugitive contour tension angle is larger, and the outer particles fall further away; As the drop height increases, the farthest vertical distance of the fugitive contour from the impact surface is longer; As the outlet diameter increases, the particle impact velocity also increases. The research results can provide a theoretical basis for dust fugitive control during bulk material loading and unloading in industrial plants.

Seismic response reduction using a tuned pendulum pounding mass damper: Experimental verification of superior performance

The recent seismic events have underscored the importance of resilient designs in mitigating losses to life and property. While tuned mass dampers (TMDs) have demonstrated their effectiveness in reducing structural vibrations, they have limitations in safeguarding buildings against non-structural damage caused by earthquakes. Additionally, their efficacy can be overwhelmed in high-magnitude seismic events. This paper introduces a novel device, called the tuned pendulum pounding mass damper (PTMD), that adapts the TMD by introducing a pounding surface near its static equilibrium position. The hypothesis is that this modification will yield superior performance in earthquake mitigation. To test this hypothesis, we conducted a shake table experiment on a PTMD installed in a small-scale building model with a viscoelastic material to model the pounding effects. The study demonstrates that the PTMD's tuning frequency ratio can be analytically determined, although careful selection of the pounding stiffness and restitution coefficient is essential for optimal design. With a mass ratio of 1%, the PTMD significantly reduced the acceleration response. In comparison to the TMD, the PTMD exhibits greater robustness and effectiveness in reducing responses across a broader range of frequencies. Conversely, the TMD may amplify structural responses when detuned. The PTMD's exceptional capabilities position it as a promising candidate for shaping the future of infrastructure and contributing to seismic mitigation policies, thereby enhancing overall disaster resilience.

Impact of nanodroplets on cone-textured surfaces.

Molecular dynamics simulations have been performed to study the dynamics of nanodroplets impacting on a flat superhydrophobic surface and surfaces covered with nanocone structures. We present a panorama of nanodroplet behaviors for a wide range of impact velocities and different cone geometrics, and develop a model to predict whether a nanodroplet impacting onto cone-textured surfaces will touch the underlying substrate during impact. The advantages and disadvantages of applying nanocone structures to the solid surface are revealed by the investigations into restitution coefficient and contact time. The effects of nanocone structures on droplet bouncing dynamics are probed using momentum analysis rather than conventional energy analysis. We further demonstrate that a single Weber number is inadequate for unifying the dynamics of macroscale and nanoscale droplets on cone-textured surfaces, and propose a combined dimensionless number to address it. The extensive findings of this study carry noteworthy implications for engineering applications, such as nanoprinting and nanomedicine on functional patterned surfaces, providing fundamental support for these technologies.

Scaling laws for the contact time of impacting nanodroplets: From hydrophobic to superhydrophobic surfaces

Nanodroplet impacts have attracted significant attention, while the effect of surface wettability on contact time is evaluated poorly. Utilizing molecular dynamics simulations, the current work with a special focus on the contact time studies nanodroplets impacting solid surfaces in a wide range of static contact angles (θ0 = 105°–175°) and the Weber number (We = 0.1–200). The complete trends in contact time and restitution coefficient with surface wettability are analyzed and reported for the first time. For surfaces with θ0 > 160°, four different regimes are identified for the contact time and restitution coefficient as a function of the Weber number. For surfaces with 110° < θ0 < 160°, the fourth regime is not observed. The restitution coefficient is employed to analyze the contact time of distinct rebound patterns in the individual wettability range. Intriguingly, surface wettability has a remarkable influence on the contact time of nanodroplets even for superhydrophobic surfaces. The main reason for the difference between the macroscale and nanoscale is attributed to the significantly enhanced viscous effect and interfacial effect of the nanoscale impact. Considering the different effects of surface wettability on spreading and retraction dynamics, the theoretical models for the maximum spreading factor, spreading velocity, and retraction velocity are established. Finally, scaling laws of the spreading time τspr ∼ (R0/Vi)We2/3Re−1/3 and retraction time τret ∼ (R0/Vi)We2/3Re−1/3(1 − cos θ0)−1/2 are proposed. An excellent agreement with both the current data sources and the results in the literature verifies the universality of the current scaling law from hydrophobic to superhydrophobic surfaces.

CFD Simulation of Wet Spouted Fluidized Bed using Two-fluid Model with Variable Restitution Coefficient and Diameter

CFD Simulation of Wet Spouted Fluidized Bed using Two-fluid Model with Variable Restitution Coefficient and Diameter

Evaluating gas-driven flow mechanics of non-spherical powders for directed energy deposition

The size and shape of metal powder particles play a central role in the performance and utility of directed energy deposition (DED) based metal additive manufacturing processes. Given their significant economic advantage, unconventional non-spherical metal powders have recently emerged as a potential, economically viable, alternative for use as DED feedstock. In this work, we investigate the mechanics of carrier-gas driven powder flows for non-spherical metal powders using coupled experiments and numerical simulations. The experiments are performed on a custom-built DED system that allows us to individually vary both gas and powder flows systematically. By suitably adjusting the flow conditions to ensure equal mass flow rates, we show that non-spherical powders compare favorably against gas atomized spherical particles vis-á-vis final concentration distribution and flow mechanics. The differences between these two types of powder particles are quantified with flat, angled and curved substrate geometries, allowing predictions for many practical deposition situations. The simulations use a two-way discrete phase model and predict best (perfectly elastic) and worst (perfectly inelastic) case concentrations on the substrate by varying the particle restitution coefficient. Our results suggest suitable process modifications (gas flow rate, feed rate, axis traverse speed) to facilitate the use of non-spherical powders alongside conventional spherical powders in DED processes.

Parameter Calibration and Optimization of a Discrete Element Model of Plug Seedling Pots Based on a Collision Impact Force

To improve the accuracy of simulation parameters used in discrete element simulation tests for the transplanting operation of the transplanting machine and to facilitate further optimization of crucial components of the transplanting machine, in this paper, the discrete element model of 50-hole plug seedling pots was calibrated and optimized based on the collision impact force between the plug seedling pot and the steel plate measured by a flexible film network tactile pressure sensor. Basic tests determined the contact parameters of the pot, and the initial parameters were screened for significance using the Plackett–Burman test. The pot-steel static friction coefficient, the pot-pot collision restitution coefficient, and the bond radius significantly affected the simulated collision impact force between the pot and the steel plate. According to the relative error value of the impact force between the pot and the steel plate as the evaluation index, the steepest climbing test was carried out on three significant parameters to optimize their value range. Based on the Box–Behnken test, a second-order regression model of the impact force and significant parameters regulating the interaction between the pot and the steel plate was established, where the target impact force between the pot and the steel plate was 11.78 N. The optimal parameter combination is obtained by optimizing the significance parameters: the static friction coefficient between the pot and steel is 0.790, the collision restitution coefficient between the pot and the pot is 0.325, and the bond radius is 1.542 mm. The test results show that the relative error between the actual and simulation tests is only 0.084%. The calibrated parameters of the discrete element model of plug seedling pots are accurate and reliable. The research results presented here can provide a reference for the subsequent transplanting operation simulation of the transplanter.

Cohesive collisions of particles in liquid media studied by CFD-DEM, video tracking, and Positron Emission Particle Tracking

This paper investigates the cohesive collision of ice in an oil phase at temperatures ranging from −15.7 °C to −0.3 °C. The new information on the coefficient of restitution (COR) was obtained using three different velocity measurement methods: high-speed experimental video recording, Positron Emission Particle Tracking (PEPT), and numerical simulations. A new type of PEPT tracer was developed for the experiments. The COR values were in the interval 0.57...0.82, with a maximum at around −10 °C. The CFD-DEM coupled approach was applied to reproduce experiments with an ice particle drop and its collision with an inclined ice surface in a decane. The particle–wall interaction is modeled using commercial software, considering particle cohesion, particle size, and shape. CFD-DEM predicted the COR with an average deviation ∼10% from the experimental data. The numerical model’s results agree with the experiments, demonstrating that the CFD-DEM method is suitable for describing multiphase cohesive interactions.

Calibration of Ramie Stalk Contact Parameters Based on the Discrete Element Method

To obtain the physical parameters and contact parameters of ramie stalk decorticating simulation, the structural dimensions, density, moisture content, elastic modulus, and contact parameters of the ramie stalk were measured in this study based on the phloem and xylem of the ramie stalk. The physical stacking angles of the phloem and xylem were measured by the cylinder lift method and the extraction of the partition method, respectively. The contact parameters between the xylem and phloem of the ramie stalk were directly calibrated. Additionally, the contact parameters of the phloem–phloem, phloem–Q235A steel, xylem–xylem, and xylem–Q235A steel were used as calibration objects, and the simulated stacking angle was used as the evaluation index. Then, the Plackett–Burman test was designed to screen for the parameters which were significantly affecting the simulated stacking angle. Furthermore, the steepest ascent test determined the optimal range of values for two significant parameters of the phloem and three significant parameters of the xylem. Based on the central composite design, the second-order regression equations between the significant parameters of the phloem and xylem and the stacking angle were established, respectively. The physical stacking angles of 37.93° for phloem and 27.17° for xylem were the target values to obtain the optimal parameter group. The results showed that the restitution, static, and rolling friction coefficients between the xylem and phloem were 0.60, 0.53, and 0.021, respectively. The static and rolling friction coefficients between the phloem and phloem were 0.41 and 0.056, respectively. The rolling friction coefficient between the xylem and Q235A steel was 0.033, and the static and rolling friction coefficients between the xylem and xylem were 0.44 and 0.016, respectively. The verification test showed that the relative error values were less than 2.11%, which further indicated that the modeling method and parameter calibration of the ramie stalk phloem and xylem models were accurate and reliable. They can be used for the subsequent calibration simulation tests of ramie stalk bonding parameters and ramie stalk decorticating simulations.