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Inverse grading in granular flows
Published in G.N. Pande, S. Pietruszczak, H.F. Schweiger, Numerical Models in Geomechanics, 2020
M. A. Kern, W. J. Ammann, L. Vulliet
The model of granular flow presented here is a 3D extension of a 2D “hard disc model” of a granular flow of discs with bimodal size distribution , see (Nakagawa & Imaizumi 1992) or (Herrmann & Luding 1998). A box with length lx, width ly and infinite height contains spherical particles with a random radius distribution ri ∈ [rmin,rmax]. The particles can move freely subject only to gravitation until they collide with another particle or with the bottom of the box (see Fig. 1). The box is inclined by an angle ψ with respect to the horizontal and its bottom is “roughened” by a periodic function. Furthermore, the box has periodic boundary conditions in the sense that particles leaving the box through a wall enter the box through the opposite wall again. Particles in the vicinity of a wall can also interact with particles in the vicinity of the opposite wall. The individual particles’ mechanical properties are described by the longitudinal and transversal restitution coefficients e and b representing the inelastic behaviour of one single particle under collision and by the transversal Coulomb friction coefficient μ. The coefficient of restitution is defined as the ratio of longitudinal or tangential relative velocity after and before the collision of two particles. The interaction between the particles happens by instantaneous, binary collisions. This means that the interaction of two particles by exchange of momentum and spin is supposed to take place at one distinct time point.
Vehicle Accident Reconstruction Using Basic Energy Analysis Techniques
Published in Randall Noon, Introduction to Forensic Engineering, 2020
If a collision is purely elastic, the coefficient of restitution will be 1.0; if it is purely plastic, it will be 0. For moderate car velocities of about 25 mph, "e" will be approximately 0.2. For higher velocities, "e" will be equal to 0.05 to 0.1.
Impacts
Published in Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler, Instant Notes in Sport and Exercise Biomechanics, 2019
The coefficient of restitution (denoted by the symbol “e”) is a numeric value that reflects elasticity and describes how much of an object’s energy is lost to its deformation during a collision and what proportion remains to facilitate its rebound. Using the simple example of dropping a ball from a height Hdrop and observing it to rebound to a height Hrebound, the coefficient of restitution can be determined as: e=hreboundhdrop
A novel evaluation of shock absorption and adhesive strength under shear impact loading
Published in The Journal of Adhesion, 2021
First of all, shock absorption test standards and specifications are needed to address these questions. There have been several shock absorption measurement methods introduced. The first is the ball drop test (destructive, on top of glass).[7] Ball drop test is the most intuitive method because SAM is placed on top of the glass and the maximum ball drop height (when the glass breaks) shows the shock absorption capability with and without SAM. However, the deviation of the glass fracture toughness itself is too large, and it is impossible to obtain reliable data to make quantitative comparison. The second method is restitution coefficient measurement (nondestructive, standalone).[8] The coefficient of restitution, which can be denoted by e, corresponds the ratio of the final and initial relative velocity between two objects after they collide. With enough amount of SAM (over 1 mm thickness), restitution varies depending on whether SAM is present. However, minute changes cannot be seen due to low resolution of the restitution measurement in case of thin SAM (less than 1 mm thickness). Therefore, the impact response measurement was further suggested.[9,10] Especially, evaluating impact response using piezoelectric force sensor is appropriate for microscale SAM characterization.[11] Test preparation and data processing are classified for stable data acquisition since short-time dynamic response is very sensitive and it tends to deviate.
Characterization of soybeans and calibration of their DEM input parameters
Published in Particulate Science and Technology, 2021
Thiet Xuan Nguyen, Lu Minh Le, Thong Chung Nguyen, Nguyen Thi Hanh Nguyen, Tien-Thinh Le, Binh Thai Pham, Vuong Minh Le, Hai-Bang Ly
In order to relate the kinetic energy of two objects after collision, the coefficient of restitution was introduced as the ratio of the relative velocity after collision to the relative velocity before collision (Louge and Adams 2002; Weir and McGavin 2008). The coefficient of restitution is normally in the range of [0, 1] due to initial kinetic energy being lost to rotational energy, deformation and heat (Louge and Adams 2002; Hastie 2013). A coefficient of restitution of 1 exhibits a perfect elastic collision, whereas a perfect inelastic collision is characterized by a coefficient of 0 (Cross 1999). For agricultural granular materials, the restitution coefficients can be measured using grain-dropping tests (Gong, Zeng, and Qi 2019; LoCurto et al. 1997) or the double pendulum method (Hlosta et al. 2018). In this study, the coefficients of restitution between the soybeans themselves and between the soybeans and material surface were obtained by calibration using DEM simulation.
Simulation study of the effect of the restitution coefficient on interphase heat transfer processes and flow characteristics in a fluidized bed
Published in Numerical Heat Transfer, Part A: Applications, 2019
Hamada Mohamed Abdelmotalib, Ik–Tae Im
The collision of solid particles has a great effect on the operation of a fluidized bed reactor. This effect can be characterized using the particle–particle restitution coefficient. The value of the coefficient of restitution can range from zero for a fully inelastic collision to 1 for a fully elastic collision. The present study investigated the effect of the collision elasticity represented by the restitution coefficient on particle–particle and gas–particle heat transfer processes, as well as the relevant bed hydrodynamics. A 2D and a two-phase model of a fluidized bed reactor were used in our simulations study. Two different materials, sand particles and steel beads, were used as bed materials fluidized by air. We investigated the heat transfer between the bed materials and the fluidized gas, as well as the heat transfer between the solid particles. Increasing the collision elasticity resulted in increasing the bed pressure drop and decreasing the granular temperature, solid velocity, and collision frequency. The interphase heat transfer process, including interparticle and gas–particle heat transfer processes, decreased with increasing collision elasticity (i.e., with increasing the particle–particle coefficient of restitution). Sand particles showed better fluidization and heat transfer rates than the steel beads. The simulations results indicated that both the particle–particle and the gas–solid heat transfer processes strongly depended on the bed flow hydrodynamics, especially the void fraction and solid particles velocity.