Interaction and Wall Corrections for the Slow Motion of Two Fluid or Solid Particles Parallel to the Axis of a Circular Cylinder through a Viscous Fluid

1980 ◽  
Vol 22 (5) ◽  
pp. 243-249 ◽  
Author(s):  
T. Greenstein
Keyword(s):  
Circular Cylinder ◽  
Solid Particle ◽  
Particle System ◽  
Slow Motion ◽  
Solid Particles ◽  
Spherical Particles ◽  
Cylinder Wall ◽  
Characteristic Distance ◽  
Direction Parallel ◽  
Drag Forces

Numerical values are provided which enable the drag force on the reference spherical fluid or solid particle, and the torque on the reference spherical solid particle, to be computed for the particular case when two spherical particles move in a direction parallel to their line of centres parallel to the axis of a circular cylinder. Results for this motion are also expressed in terms of the ratio of drag forces experienced by (1) the particle of arbitrary shape in a bounded, two particle system, and the particle in an unbounded, two particle system, and (2) the particle in a bounded, two particle system, and the particle moving alone with the same speed and orientation in the same, but unbounded, fluid. The computation furnishes the interaction and wall corrections correctly to the first-order in the ratios of characteristic particle dimension to characteristic distance of the particle from both another particle and from the cylinder wall. The axisymmetric problem was extended to the more general case where the two particles may be placed eccentrically within the cylinder and the torque was also computed. Furthermore, the two particles may be fluid droplets as well as solid particles.

Numerical Simulation of Fluid-Particle Flows: Geothermal Drilling Applications

1987 ◽  
Vol 109 (3) ◽  
pp. 324-331
Author(s):  
R. C. Givler ◽  
R. R. Mikatarian
Keyword(s):  
Flow Model ◽  
Mixture Theory ◽  
Solid Particles ◽  
Fluid Particle ◽  
Spherical Particles ◽  
Primary Concern ◽  
Drag Forces ◽  
Particle Flows ◽  
Geothermal Drilling ◽  
Interfacial Drag

In order to understand how a particulate plug may evolve within the flow of an essentially homogeneous suspension, we have developed a fluid-particle flow model. This theoretical model is based upon a monodisperse collection of rigid, spherical particles suspended in an incompressible, Newtonian liquid. Balance equations of mass and momentum are given for each phase within the context of a continuum mixture theory. The interactions between the phases are dominated by interfacial drag forces and unequilibrated pressure forces. The pressure associated with the solid particles is given by a phenomenological model based upon the flow dynamics. Of primary concern is the calculation of solid particle concentrations within a flow field to indicate the initiation of a particulate plug.

The acceleration of solid particles subjected to cavitation nucleation

2008 ◽  
Vol 610 ◽  
pp. 157-182 ◽  
Author(s):  
BRAM M. BORKENT ◽  
MANISH ARORA ◽  
CLAUS-DIETER OHL ◽  
NICO DE JONG ◽  
MICHEL VERSLUIS ◽  
...  
Keyword(s):  
High Speed ◽  
Pressure Pulse ◽  
Particle System ◽  
Volume Growth ◽  
Solid Particles ◽  
Spherical Particles ◽  
High Speed Photography ◽  
Neck Formation ◽  
Cavitation Inception ◽  
Nucleation Sites

The cavity–particle dynamics at cavitation inception on the surface of spherical particles suspended in water and exposed to a strong tensile stress wave is experimentally studied with high-speed photography. Particles, which serve as nucleation sites for cavitation bubbles, are set into a fast translatory motion during the explosive growth of the cavity. They reach velocities of ~40 ms−1 and even higher. When the volume growth of the cavity slows down, the particle detaches from the cavity through a process of neck-breaking, and the particle is shot away. The experimental observations are simulated with (i) a spherical cavity model and (ii) with an axisymmetric boundary element method (BEM). The input for both models is a pressure pulse, which is obtained from the observed radial cavity dynamics during an individual experiment. The model then allows us to calculate the resulting particle trajectory. The cavity shapes obtained from the BEM calculations compare well with the photographs until neck formation occurs. In several cases we observed inception at two or more locations on a single particle. Moreover, after collapse of the primary cavity, a second inception was often observed. Finally, an example is presented to demonstrate the potential application of the cavity–particle system as a particle cannon, e.g. in the context of drug delivery into tissue.

Theoretical study of the slow motion of a sphere and a fluid in a cylindrical tube

1968 ◽  
Vol 34 (4) ◽  
pp. 705-710 ◽  
Author(s):  
T. Greenstein ◽  
J. Happel
Keyword(s):  
Angular Velocity ◽  
Circular Cylinder ◽  
Spherical Particle ◽  
Cylindrical Tube ◽  
Slow Motion ◽  
Spherical Particles ◽  
Theoretical Treatment ◽  
Arbitrary Position ◽  
Small Spherical Particle ◽  
Neutrally Buoyant

The results of a theoretical treatment are presented for the slow flow of a viscous fluid through a circular cylinder within which a small spherical particle is confined. The sphere is situated in an arbitrary position within the cylinder, rotates with an arbitrary constant angular velocity and moves at constant velocity parallel to the wall. Approximate expressions are presented which give the frictional force, torque, and permanent pressure drop caused by the presence of this obstacle in the original Poiseuillian field of flow.An eccentricity function for the torque on a sphere in a circular cylinder was evaluated numerically. It can be used to predict the wall-effect for the torque as well as the angular velocity with which a ‘dense’ spherical particle will rotate. Expressions are presented which predict the angular velocity of ‘dense’ as well as neutrally buoyant hydrodynamically supported spherical particles.

Simulation of Impaction Between Liquid Droplet and Solid Particles Based on SPH Method

2014 ◽  
Author(s):  
Shuai Meng ◽  
Qian Wang ◽  
Rui Yang
Keyword(s):  
Surface Tension ◽  
Solid Particle ◽  
Liquid Droplet ◽  
Particle Interaction ◽  
Solid Particles ◽  
Seed Particle ◽  
Liquid Droplets ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Spray Granulation

The phenomenon of impaction between liquid droplets and solid particles is involved in many scientific problems and engineering applications, such as impaction between sprayed droplet and solid particles in limestone injection desulfurization system and the collision between a droplet of the liquid to be granulated and a seed particle in fluidized bed spray granulation process. There are a lot of factors affected this phenomenon: droplet and particle size, momentum of both liquid droplet and solid particles, materials, surface conditions of the solid particles and so on. However the experimental or numerical researches have been done mostly pay attention to Specific application or process, so the impaction phenomenon has not been through studied, for example how different factors affected the impaction process with its effect on different applications. This paper focuses on the basic issue of interaction between droplet and solid particles. Three main factors were considered: ratio of diameter between the droplet and solid particle, relative velocity and the surface tension (including the contact angle between droplet and solid particle). All the study is based on simulation using SPH (smoothed particle hydrodynamics) method, and the surface tension is simulated by particle-particle interaction.

A Model for the Effect of Velocity on Erosion of N80 Steel Tubing due to the Normal Impingement of Solid Particles

1992 ◽  
Vol 114 (1) ◽  
pp. 54-64 ◽  
Author(s):  
D. P. Chase ◽  
E. F. Rybicki ◽  
J. R. Shadley
Keyword(s):  
Solid Particle ◽  
Computational Study ◽  
Target Material ◽  
Target Surface ◽  
American Petroleum Institute ◽  
Solid Particles ◽  
Unknown Coefficient ◽  
Conservation Of Energy ◽  
Carrier Fluid ◽  
Erosion Behavior

As part of a combined experimental and computational study of erosion for gas and oil production conditions, a semi-empirical model has been developed to predict erosion ratio behaviors of metals due to solid particle impingement. One use of the model will be to reduce the total number of experiments needed to characterize erosion behavior. The model represents material property information associated with both the target material and the impinging particles, as well as impingement speed. Five different models are examined in terms of ability to predict erosion ratio behavior as a function of impingement speed. The model selected is based on a conservation of energy formulation and fracture mechanics considerations to predict the amount of material removed due to solid particle impingement. The resulting equation to predict the erosion ratio for a given particle size contains one unknown coefficient which is determined through comparison with experimental data. Illustrative examples are presented for data for two different sizes of glass bead solid particles in an oil carrier fluid impinging on an API (American Petroleum Institute) N80 grade steel target at an impingement angle 90 deg to the target surface. Using erosion data at one impingement speed to determine the unknown coefficient, the model was used to predict erosion behavior at a range of other speeds. Good agreement between the erosion ratio data and the values predicted by the model were found for two solid particle sizes. Recommendations for expanding the capabilities of the model are pointed out.

Raman-Microsampling Technique Applying Optical Levitation by Radiation Pressure

1984 ◽  
Vol 38 (1) ◽  
pp. 78-83 ◽  
Author(s):  
R. Thurn ◽  
W. Kiefer
Keyword(s):  
Radiation Pressure ◽  
Optical Potential ◽  
Solid Particles ◽  
Spherical Particles ◽  
Exciting Light ◽  
Potential Wells ◽  
Ion Laser ◽  
Optical Levitation ◽  
Argon Ion ◽  
Microprobe Technique

We report on a new Raman microprobe technique where micron-sized solid particles are trapped in stable optical potential wells using only the force of radiation pressure from a continuous gas laser. We demonstrate this technique with Raman spectra from spherical and non-spherical particles of sizes ranging between 10–30 μm. The particles are stably supported by a vertical directed focused TEM00-mode cw argon ion laser of ∼500 mW. The latter simultaneously serves as the exciting light source. Several suggestions for improvements of this technique are made.

scholarly journals Surface and subsurface contributions to the build-up of forces on bed particles

2018 ◽  
Vol 851 ◽  
pp. 558-572 ◽  
Author(s):  
Alessandro Leonardi ◽  
D. Pokrajac ◽  
F. Roman ◽  
F. Zanello ◽  
V. Armenio
Keyword(s):  
Mutual Influence ◽  
Subsurface Flow ◽  
Porous Wall ◽  
Industrial Applications ◽  
Solid Particles ◽  
Free Flow ◽  
Spherical Particles ◽  
Large Eddy ◽  
Lift Forces ◽  
Surface And Subsurface Flow

In nature and in many industrial applications, the boundary of a channel flow is made of solid particles which form a porous wall, so that there is a mutual influence between the free flow and the subsurface flow developing inside the pores. While the influence of the porous wall on the free flow has been well studied, less well characterized is the subsurface flow, due to the practical difficulties in gathering information in the small spaces given by the pores. It is also not clear whether the subsurface flow can host turbulent events able to contribute significantly to the build-up of forces on the particles, potentially leading to their dislodgement. Through large eddy simulations, we investigate the interface between a free flow and a bed composed of spherical particles in a cubic arrangement. The communication between surface and subsurface flow is in this case enhanced, with relatively strong turbulent events happening also inside the pores. After comparing the simulation results with a previous experimental work from a similar setting, the forces experienced by the boundary particles are analysed. While it remains true that the lift forces are largely dependent on the structure of the free flow, turbulence inside the pores can also give a significant contribution. Pressure inside the pores is weakly correlated to the pressure in the free flow, and strong peaks above and below a particle can happen independently. Ignoring the porous layer below the particle from the computations leads then in this case to an underestimation of the lift forces.

Direct Simulation of Electrorheological Suspensions

2001 ◽  
Author(s):  
Aijun Wang ◽  
Pushpendra Singh ◽  
Nadine Aubry
Keyword(s):  
Electric Field ◽  
Stokes Equations ◽  
Hydrodynamic Force ◽  
Particle System ◽  
Electrostatic Force ◽  
Body Motion ◽  
Three Dimensions ◽  
Spherical Particles ◽  
Point Dipole ◽  
Direct Simulation

Abstract A new distributed multiplier/fictitious (DLM) domain method is developed for direct simulation of electrorheological (ER) suspensions subjected to spatially uniform electrical fields. The method is implemented both in two and three dimensions. The fluid-particle system is treated implicitly using the combined weak formulation described in [1,2]. The governing Navier-Stokes equations for the fluid are solved everywhere, including the interior of the particles. The flow inside the particles is forced to be a rigid body motion by a distribution of Lagrange multipliers. The electrostatic force acting on the polarized spherical particles is modeled based on the point-dipole approximation. Using our code we have studied the time evolution of particle-scale structures of ER suspensions in channels subjected to the pressure driven flow. In our study, the flow direction is perpendicular to that of the electric field. Simulations show that when the hydrodynamic force is zero, or very small compared to the electrostatic force, the particles form chains that are aligned approximately parallel to the direction of electric field. But, when the magnitude of hydrodynamic force is comparable to that of the electrostatic force the particle chains orient at an angle with the direction of the electric field. The angle between the particle chain and the direction of the electric field depends on the relative strengths of the hydrodynamic and electrostatic forces.

Modeling evaluation on solid-liquid mixing characteristics in a dislocated guide impeller stirred tank

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Deyin Gu ◽  
Fenghui Zhao ◽  
Xingmin Wang ◽  
Zuohua Liu
Keyword(s):  
Power Consumption ◽  
Solid Particle ◽  
Particle Diameter ◽  
Solid Particles ◽  
Stirred Tank ◽  
Mixing Process ◽  
Solid Holdup ◽  
Aperture Ratio ◽  
Liquid Mixing ◽  
Solid Liquid

Abstract The solid-liquid mixing characteristics in a stirred tank with pitched blade impellers, dislocated impellers, and dislocated guide impellers were investigated through using CFD simulation. The effects of impeller speed, impeller type, aperture ratio, aperture length, solid particle diameter and initial solid holdup on the homogeneity degree in the solid-liquid mixing process were investigated. As expected, the solid particle suspension quality was increased with an increase in impeller speed. The dislocated impeller could reduce the accumulation of solid particles and improve the cloud height compared with pitched blade impeller under the same power consumption. The dislocated guide impeller could enhance the solid particles suspension quality on the basis of dislocated impeller, and the optimum aperture ratio and aperture length of dislocated guide impeller were 12.25% and 7 mm, respectively, in the solid-liquid mixing process. Smaller solid particle diameter and lower initial solid holdup led to higher homogeneity degree of solid-liquid mixing system. The dislocated guide impeller could increase solid particle integrated velocity and enhance turbulent intensity of solid-liquid two-phase compared with pitched blade impeller and dislocated impeller under the same power consumption.

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