Fluid velocity fluctuations in a collision of a sphere with a wall (original) (raw)
Related papers
Particle–wall collisions in a viscous fluid
Journal of Fluid Mechanics, 2001
This paper presents experimental measurements of the approach and rebound of a particle colliding with a wall in a viscous fluid. The particle's trajectory was controlled by setting the initial inclination angle of a pendulum immersed in a fluid. The resulting collisions were monitored using a high-speed video camera. The diameters of the particles ranged from 3 to 12 mm, and the ratio of the particle density to fluid density varied from 1.2 to 7.8. The experiments were performed using a thick glass or Lucite wall with different mixtures of glycerol and water. With these parameters, the Reynolds number defined using the velocity just prior to impact ranged from 10 to approximately 3000. A coefficient of restitution was defined from the ratio of the velocity just prior to and after impact.
Velocity measurements of vortex structures induced by sphere/wall interaction
Experiments in Fluids, 2022
This study experimentally investigates the vortex structure induced by sphere-wall collision and a falling sphere in a viscous liquid. The velocity fields of sphere-induced vortices were measured with refractive-index-matched materials and particle tracking velocimetry. The Reynolds number, based on the sphere diameter and the falling velocity, was in the range of 350-3200. The results revealed that the sphere-induced vortex ring was axisymmetric when the Reynolds number Re is ≤ 800. For the case of Re = 2000, the vortex structure developed into a non-symmetric flow after the sphere collided on the wall. Nonetheless, the influence of the Reynolds number on the vortex trajectory is insignificant. The moving speed of the primary vortex increases as the Reynolds number increases. In addition, the trajectories of free-falling spheres at a high Reynolds number of Re = 3200 deviate from a vertical straight line, owing to the non-axisymmetric flow field around the sphere. The experimental results presented in this work can be used to validate numerical schemes for solid/vortex interaction problems.
Dynamic behavior of collision of elastic spheres in viscous fluids
Powder Technology, 1999
The dynamic behavior of the collision of two elastic spheres in a stagnant viscous fluid is investigated in this study for particle Reynolds numbers ranging from 5 to 300. The interactive behavior of these particles is examined both experimentally and theoretically. Specifically, the trajectory and velocity of a moving particle in collinear and oblique collisions with a fixed particle are measured using a Ž . high speed video system and an Infinity lens. The lattice-Boltzmann LB simulation is conducted to obtain the detailed three-dimensional flow field and the forces around the particles during the course of collision. Furthermore, a mechanistic model is developed which Ž . Ž . Ž . accounts for four stages of collision processes, including: 1 immediately before the collision, 2 compression during the collision, 3 Ž . rebound during the collision, and 4 immediately after the collision. The LB simulation and experimental results lead to an empirical expression for the drag force on the particle during the close-range particle-particle interaction. This close-range interaction between two approaching particles is taken into account in the equation of motion of the particle. The pressure force and added mass force are derived, based on collisions in inviscid fluids, as a function of separation distance. Results of the LB simulation and prediction by the mechanistic model are in good agreement with the experimental results. The viscous effects on the compression and rebound processes of colliding particles with regard to the elasticity properties of the particle are examined. The studies are also conducted for simulation based on a hard sphere model, which is commonly used in accounting for the particle collision behavior in gas. The study concludes that the key to proper quantification of the particle collision characteristics in liquid is the ability to accurately predict the particle velocity upon contact. q 1999 Elsevier Science S.A. All rights reserved. 0032-5910r99r$ -see front matter q 1999 Elsevier Science S.A. All rights reserved.
Effect of fluid motions on finite spheres released in turbulent boundary layers
Journal of fluid mechanics, 2024
- to investigate the effect of turbulent fluid motions on the translation and rotation of lifting and wall-interacting spheres in boundary layers. Each sphere was released from rest in smooth-wall boundary layers with Re τ = 670 and 1300 (d + = 56 and 116, respectively) and allowed to propagate with the incoming fluid. Sphere and surrounding fluid motions were tracked simultaneously via three-dimensional particle tracking velocimetry and stereoscopic particle image velocimetry in streamwise-spanwise planes. Two-point correlations of sphere and fluid streamwise velocities yielded long positive regions associated with long fast-and slow-moving zones that approach and move over the spheres. The related spanwise correlations were shorter due to the shorter coherence length of spanwise fluid structures. In general, spheres lag the surrounding fluid. The less-dense lifting sphere had smaller particle Reynolds numbers varying from near zero up to 300. Its lift-offs coincided with oncoming fast-moving zones and fluid upwash. Wall friction initially retarded the acceleration of the denser sphere. Later, fluid torque associated with approaching high-velocity regions initiated forward rotation. The rotation, which was long-lived, induced sufficient Magnus lift to initiate repeated small lift-offs, reduce wall friction, and accelerate the sphere to higher sustained velocity. Particle Reynolds numbers remained above 200, and vortex shedding was omnipresent such that the spheres clearly altered the fluid motion. Spanwise fluid shear occasionally initiated wall-normal sphere rotation and relatively long-lasting Magnus side lift. Hence the finite sphere size contributed to multiple dynamical effects not present in point-particle models.
Powder Technology, 2010
Experimental results were obtained on the steady settling of spheres in quiescent media in a range of cylindrical tubes to ascertain the wall effects over a relatively wide range of Reynolds number values. For practical considerations, the retardation effect is important when the ratio of the particle diameter to the tube diameter (λ) is higher than about 0.05. A new empirical correlation is presented which covers a Reynolds number range Re = 53-15,100 and a particle to tube diameter ratio λ b 0.88. The absolute mean deviation between the experimental data and the presented correlation was 1.9%. The well-known correlations of Newton, Munroe and Di Felice agree with the presented data reasonably well. For steady settling of spheres in a counter-current water flow, the slip velocity remains practically the same as in quiescent media. However, for rising spheres in a co-current water flow, the slip velocity decreases with increasing co-current water velocity, i.e., the wall factor decreases with increasing co-current water velocity. Consequently, the drag coefficient for rising particles in co-current water flow increases with increasing water velocity.
Flow around spheres by dissipative particle dynamics
Physics of Fluids, 2006
The dissipative particle dynamics ͑DPD͒ method is used to study the flow behavior past a sphere. The sphere is represented by frozen DPD particles while the surrounding fluids are modeled by simple DPD particles ͑representing a Newtonian fluid͒. For the surface of the sphere, the conventional model without special treatment and the model with specular reflection boundary condition proposed by Revenga et al. ͓Comput. Phys. Commun. 121-122, 309 ͑1999͔͒ are compared. Various computational domains, in which the sphere is held stationary at the center, are investigated to gage the effects of periodic conditions and walls for Reynolds number ͑Re͒ = 0.5 and 50. Two types of flow conditions, uniform flow and shear flow are considered, respectively, to study the drag force and torque acting on the stationary sphere. It is found that the calculated drag force imposed on the sphere based on the model with specular reflection is slightly lower than the conventional model without special treatment. With the conventional model the drag force acting on the sphere is in better agreement with experimental correlation obtained by Brown and Lawler ͓J. Environ. Eng. 129, 222 ͑2003͔͒ for the case of larger radius up to Re of about 5. The computed torque also approaches the analytical Stokes value when ReϽ 1. For a force-free and torque-free sphere, its motion in the flow is captured by solving the translational and rotational equations of motion. The effects of different DPD parameters ͑a, ␥, and ͒ on the drag force and torque are studied. It shows that the dissipative coefficient ͑␥͒ mainly affects the drag force and torque, while random and conservative coefficient have little influence on them. Furthermore the settling of a single sphere in square tube is investigated, in which the wall effect is considered. Good agreement is found with the experiments of Miyamura et al. ͓Int. J. Multiphase Flow 7, 31 ͑1981͔͒ and lattice-Boltzmann simulation results of Aidun et al. ͓J. Fluid Mech. 373, 287 ͑1998͔͒.
Collisional dynamics of macroscopic particles in a viscous fluid
2003
This thesis presents experimental measurements of the approach and rebound of a particle colliding with a wall in a viscous fluid. Steel, glass, nylon, and Delrin particles were used, with diameters ranging from 3 to 12 mm. The experiments were performed using a thick Zerodur or Lucite wall with various mixtures of glycerol and water. Normal and tangential coefficients of restitution were defined from the ratios of the respective velocity components at the point of contact just prior to and after impact. These coefficients account for losses due to lubrication effects and inelasticity. The experiments clearly show that the rebound velocity depends strongly on the impact Stokes number and weakly on the elastic properties of the materials. Below a Stokes number of approximately 10, no rebound of the particle occurs. Above a Stokes number of approximately 500, the normal coefficient of restitution asymptotically approaches the value for a dry collision. The data collapse onto a single ...
The influence of walls on the motion of a sphere in non-Newtonian liquids
Rheologica Acta, 1983
The influence of the contained wall on the drag of a sphere moving through a non-Newtonian fluid is analysed in this work separately for the low Reynolds number and the high Reynolds number regions. In the former, we make use of the two-concentric-sphere model. It is predicted that the wall effect will decrease with the increase of the shear-thinning anomaly and this is in a reasonable agreement with the available experimental data and correlations. The wall effect in the high Reynolds number region is analysed in this work using the cell model (used to study the motion of an assemblage of solid spheres) and the predictions are in satisfactory agreement with the available empirical correlation for non-Newtonian fluids.
Chemical Engineering Science, 2006
A generalized description of the rebound of spherical drops or solid spheres over a wall is proposed using two parameters: a coefficient of restitution that compares the velocity of restitution to the velocity before impact and the contact time with the wall. During the bouncing, the incident kinetic energy is transferred into deformation energy (stored on the surface for the case of liquid drops or in the bulk for the case of solid particles) and then restored into kinetic energy allowing the particle to leave or not the wall. The corresponding criteria is given by the Stokes number that compares the inertia of the particle (added mass included) and the viscous force exerted on the particle during the drainage of the film formed between the particle and the wall. The general behavior of the coefficient of restitution observed in many experiments can be modelled for solid spheres as well as spherical drops by the use of a unique simple correlation depending on this Stokes number. For solid particles, the contact time with the wall in viscous flows is found to be of the same order as that predicted by the Hertzian theory; hence, the contact with the wall can be described as a discontinuity in the particle motion. On the other hand, for liquid drops, the contact time is significant and of the same order as other characteristic time scales of the particle motion. Therefore, to properly describe the rebound process, both a restitution coefficient and a contact time must be considered. Finally, a simple model is proposed and its predictions are compared with experiments performed for millimetric toluene drops in water. ᭧