Interaction of Solid Particles with a Tangle of Vortex Filaments in a Viscous Fluid

The results of thermal interactions between a solid particle and a fluid have two folds: the motion of fluid affects the heat transfer and energy balance of a particle; and the heat transfer from particles influences the fluid motion. When the temperature of a particle and its surrounding fluid is not the same, heat is transferred between the particle and the fluid. The heat flux influences the properties of the surrounding fluid and changes the dynamics of the sedimentation of the particle. To study the effect of non-isothermal flows to the motion of a particle, we have developed a Direct Numerical Simulation (DNS) method that is capable of solving both the momentum equation and heat transfer equation for the computation of thermal interaction between particles and fluid. This numerical method makes use of a finite difference method in combination with the Immersed Boundary (IB) method for treating the particulate phase. In particular, the IB concept has been extended to treat thermal boundary condition at the particle surface. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, which tracks particles, and a force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between particle and fluid. In this paper, the IB based DNS method has been applied to study the fluidization of 12,000 circular particles, the unsteady conduction of a sphere in a stagnant fluid, and the sedimentation of a non-isothermal sphere in a viscous fluid at different Grashof number. Our simulation results show that the sedimentation velocity of the particle depends strongly on the thermal interaction of particle and fluid due to the strong buoyancy force exerted on the particle.

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Simulation of Particle-Wall Collisions in a Viscous Fluid Using a Resolved Discrete Particle Method

ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C ◽

10.1115/fedsm-icnmm2010-30268 ◽

2010 ◽

Author(s):

Zhi-Gang Feng ◽

Efstathis E. Michaelides ◽

Shaolin Mao

Keyword(s):

Viscous Fluid ◽

Numerical Method ◽

Solid Wall ◽

Particle Method ◽

Solid Particles ◽

Force Density ◽

Model Parameters ◽

Discrete Particle ◽

Soft Sphere ◽

Discrete Particle Method

The process of particle-wall collisions is very important in understanding and determining the fluid-particle behavior, especially near walls. Detailed information on particle-wall collisions can provide insight on the formulation of appropriate boundary conditions of the particulate phases in two-fluid models. We have developed a three-dimensional Resolved Discrete Particle Method (RDPM) that is capable of meaningfully handling particle-wall collisions in a viscous fluid. This numerical method makes use of a Finite-Difference method in combination with the Immersed Boundary (IB) method for treating the particulate phase. A regular Eulerian grid is used to solve the modified momentum equations in the entire flow region. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, and a force density function is introduced to represent the momentum interactions between particle and fluid. We have used this numerical method to study both the central and oblique impact of a spherical particle with a wall in a viscous fluid. The particles are allowed to move in the fluid until they collide with the solid wall. The collision force on the particle is modeled by a soft-sphere collision scheme with a linear spring-dashpot system. The hydrodynamic force on the particle is solved directly from the RDPM. By following the trajectories of a particle, we investigate the effect of the collision model parameters to the dynamics of a particle close to the wall. We report in this paper the rebound velocity of the particle, the coefficient of restitution, and the particle slip velocity at the wall when a variety of different soft-sphere collision parameters are used.

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Channel Flow of a Mixture of Granular Materials and a Fluid

Volume 7A: Fluids Engineering Systems and Technologies ◽

10.1115/imece2013-65385 ◽

2013 ◽

Cited By ~ 2

Author(s):

Wei-Tao Wu ◽

Nadine Aubry ◽

Mehrdad Massoudi

Keyword(s):

Viscous Fluid ◽

Granular Materials ◽

Volume Fraction ◽

Three Dimensional ◽

Mixture Theory ◽

Solid Particles ◽

Two Component System ◽

Component System ◽

Coal Particles ◽

Two Component

In this paper, we consider the three dimensional flow of granular materials and a viscous fluid in a channel. We use Mixture Theory to treat this problem as a two-component system [1]: One component is the solid particles (granular materials), such as sand, coal particles or red blood cells; the solid particles are modeled as a generalized Reiner-Rivlin type fluid derived by Massoudi [2], which not only considers the effects of volume fraction but also has a viscosity which is shear rate dependent. The other component, the host fluid, is assumed to behave as a linear viscous fluid, such as water, oil or plasma. For the interaction forces, the effect of different hindrance functions for the drag force is studied; moreover a generalized form of the expression for the hindrance function is suggested. For studying this two-component system numerically, a three dimensional CFD solver based on OpenFOAM® has been developed. Applying this solver, a specific problem (blood flow) has been studied for which our numerical results and experimental data [3] show good agreement.

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A Three-Dimensional Resolved Discrete Particle Method for Studying Particle-Wall Collision in a Viscous Fluid

Journal of Fluids Engineering ◽

10.1115/1.4002432 ◽

2010 ◽

Vol 132 (9) ◽

Cited By ~ 8

Author(s):

Zhi-Gang Feng ◽

Efstathios E. Michaelides ◽

Shaolin Mao

Keyword(s):

Viscous Fluid ◽

Solid Wall ◽

Three Dimensional ◽

Particle Method ◽

Solid Particles ◽

Immersed Boundary ◽

Model Parameters ◽

Discrete Particle ◽

Collision Force ◽

Discrete Particle Method

Particle collisions with the walls are very important in understanding the fluid-particle behavior near the walls and determining the boundary conditions of the particulate phases in two-fluid models. In this paper, we examine the velocity characteristics of several types of particles near solid walls by applying a resolved discrete particle method (RDPM), which also uses the immersed boundary approach to model the solid particles. We assume that the particles are spherical with an initial velocity that is prescribed. The particles are allowed to traverse part of the viscous fluid until they collide with the solid wall. The collision force on the particle is modeled by a soft-sphere collision scheme with a linear spring-dashpot system. The hydrodynamic force on the particle is solved directly from the RDPM. By following the trajectories of several particles, we investigate the effect of the collision model parameters to the dynamics of particle close to the wall. We report here the rebound velocity of the particle, the coefficient of restitution, and the particle slip velocity at the wall as functions of the collision parameters.

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Interaction of a sound wave with solid particles in a viscous fluid

Soviet Applied Mechanics ◽

10.1007/bf01362659 ◽

1983 ◽

Vol 19 (11) ◽

pp. 1013-1020

Author(s):

A. P. Zhuk

Keyword(s):

Viscous Fluid ◽

Sound Wave ◽

Solid Particles

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Vortex dynamics of viscous fluid flows. Part 1. Two-dimensional flows

Journal of Fluid Mechanics ◽

10.1017/s0022112094002478 ◽

1994 ◽

Vol 276 ◽

pp. 81-111 ◽

Cited By ~ 5

Author(s):

N. N. Ostrikov ◽

E. M. Zhmulin

Keyword(s):

Viscous Fluid ◽

Vortex Dynamics ◽

Slip Condition ◽

Regular Component ◽

Two Dimensional ◽

Stochastic Motion ◽

Vortex Filaments ◽

Boundary Velocity ◽

Macro Scale ◽

Micro Level

The method of product integration is applied to the vortex dynamics of two-dimensional incompressible viscous media. In the cases of both unbounded and bounded flows under the no-slip boundary condition, the analytic solutions of the Cauchy problem are obtained for the Helmholtz equation in the form of linear and nonlinear product integrals. The application of product integrals allows the generalization in a natural way of the vortex dynamics concept to the case of viscous flows. However, this new approach requires the reconsideration of some traditional notions of vortex dynamics. Two lengthscales are introduced in the form of a micro- and a macro-scale. Elementary ‘vortex objects’ are defined as two types of singular vortex filaments with equal but opposite intensities. The vorticity is considered as the macro-value proportional to the concentration of elementary vortex filaments inhabiting the micro-level. The vortex motion of a viscous medium is represented as the stochastic motion of an infinite set of elementary vortex filaments on the micro-level governed by the stochastic differential equations, where the stochastic velocity component of every filament simulates the viscous diffusion of vorticity, and the regular component is the macro-value induced according to the Biot–Savart law and simulates the convective transfer of vorticity.In flows with boundaries, the production of elementary vortex filaments at the boundary is introduced to satisfy the no-slip condition. This phenomenon is described by the application of the generalized Markov processes theory. The integral equation for the production intensity of elementary vortex filaments is derived and solved using the no-slip condition reformulated in terms of vorticity. Additional conditions on this intensity are determined to avoid the many-valuedness of the pressure in a multi-connected flow domain. This intensity depends on the vorticity in the flow and the boundary velocity at every time instant, together with boundary acceleration.As a result, the successive and accurate application of the product-integral method allows the study of vortex dynamics in a viscous fluid according to the concepts of Helmholtz and Kelvin.

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