# Collisions in Particle-Laden Gas Flows

Aleksey Yur'evich Varaksin
Joint Institute for High Temperatures (JIHT) of the Russian Academy of Sciences, Izhorskaya Street, 13, Building 2, 125412, Moscow, Russia

## Description

The book is devoted to the problems of modeling turbulent gas flows carrying a dispersed impurity in the form of solid particles. Particular attention is directed to consideration of various collisional processes (particleâ€“particle, particleâ€“wall, particleâ€“body) occurring in heterogeneous flows.
With the use of a large file of experimental and numerical data, dimensionless criteria responsible for the presence and intensity of the indicated interactions have been suggested and verified. The characteristics of turbulent heterogeneous flows in channels (pipes), as well as near streamlined bodies and in boundary layers are considered in detail. The results of physical and mathematical modeling of particle-laden gas flows obtained in the last few years by both Russian and foreign research workers are described and analyzed.
The book is intended for research workers dealing with the study of the gas dynamics and heat and mass transfer of multiphase flows, as well as for teachers, post-graduates and students of universities.

368 pages, © 2013

## Table of Contents:

CHAPTER 1 CONCISE INFORMATION ON SINGLE-PHASE AND HETEROGENEOUS TURBULENT FLOWS

1.2. Equations of Single-Phase Turbulent Flows

1.2.2. Averaged equations

1.2.3. Fluctuation equations

1.2.4. Equations for the Reynolds stresses

1.2.5. Algebraic models of turbulence

1.2.6. One-parameter models of turbulence

1.2.7. Two-parameter models of turbulence

1.3. Main Characteristics of Single-Phase Turbulent Flows

1.3.1. Distribution of averaged velocity

1.3.2. Distribution of averaged fluctuation velocity

1.3.4. Energy spectrum of turbulence

1.3.5. Correlations in turbulent flows

1.3.6. Scales of turbulent flows

1.4. Characteristic Features of Investigation of Heterogeneous Flows

1.4.1. Specifi c features of mathematical and physical modeling of heterogeneous flows

1.4.2. Two basic classes of investigation of heterogeneous flows

1.5. Main Characteristics of Heterogeneous Flows

1.5.1. Times of relaxation of particles

1.5.2. Concentration of particles

1.5.3. Collisions of particles among themselves

1.5.4. Collisions of particles with channel walls

1.6. Classifi cation of Heterogeneous Turbulent Flows

1.6.1. Classifi cation by the volume concentration of particles

1.6.2. Classifi cation by the inertia of particles

CHAPTER 2 MATHEMATICAL AND PHYSICAL MODELING OF PARTICLE-LADEN GAS FLOWS

2.2. Principles of Mathematical Simulation of Solid Particle-Laden Gas Flows

2.2.2. Special features of simulation of different classes of heterogeneous flows

2.2.3. Description of motion of particles: Lagrangian approach

2.2.4. Description of motion of particles: Eulerian approach

2.2.5. Description of motion of gas carrying solid particles

2.2.6. Algorithm of the generalized computer model of heterogeneous flows

2.3. Principles of Physical Modeling of Solid Particle-Laden Gas Flows

2.3.2. Special features of experimental study of heterogeneous flows

2.3.3. Laser Doppler anemometry (LDA)

2.3.4. Special features of study of the behavior of solid particles

2.3.5. Special features of study of the effect of solid particles on gas flow

2.3.6. Possibilities and limitations of study of heavily dusted flows

2.3.7. Anemometry based on the images of particles (PIV)

2.3.8. Experimental apparatuses

CHAPTER 3 PARTICLE–PARTICLE INTERACTION

3.2. Theoretical Description of the Process of Particle Collision

3.3. Two Approaches in the Theory of Collisions of Particles

3.3.1. Collisions of particles: spherical formulation

3.3.2. Collisions of particles: cylindrical formulation

3.3.4. Collisions of particles in gravitational deposition

3.4. Collisions of Particles in Gravitational Deposition

3.4.1. Bidisperse particles: different sizes

3.4.2. Bidisperse particles: different densities

3.5. Collisions of Particles in a Turbulent Flow

3.5.1. Homogeneous isotropic turbulence

3.5.2. Influence of the shear of averaged gas velocity and gravity force

3.6. Influence of the Collisions of Particles on the Characteristics of a Heterogeneous Flow

3.6.1. Gravitational deposition (bidisperse particles)

3.6.2. Downward flow in a pipe (polydisperse particles)

3.6.3. Effect of the clusterization of particles

CHAPTER 4 PARTICLE-WALL INTERACTION

4.2. Physical Mechanisms of Sedimentation of Particles on a Wall

4.2.1. Sedimentation of particles under the gravity force

4.2.2. Influence of turbulent fluctuations on sedimentation of particles

4.2.3. Particle sedimentation in a shear gas flow

4.2.4. Dominating influence of the wall: evaluation of flow parameters

4.3. Change in the Behavior of Particles on Collision with a Wall

4.3.1. Relations for calculating the velocities of particles after collision

4.3.2. Velocity recovery and friction factors

4.4. Influence of Geometrical and Concentration Constraints on the Characteristics of a Heterogeneous Flow in Channels

4.4.1. Flows in horizontal channels

4.4.2. Flows in vertical channels

CHAPTER 5 PARTICLE-BODY INTERACTION

5.2. Sedimentation Factor

5.3. Physical Mechanisms Underlying the Increase in the Concentration of Particles during Flow Past Bodies

5.3.1. Retardation of particles near the surface of a body

5.3.2. Collisions of particles with the body surface

5.3.3. Collisions of incident and reflected particles among themselves

5.4. Influence of the Shape of a Body on the Characteristics of a Heterogeneous Flow

5.4.1. Flow past a sphere (potential case)

5.4.2. Flow past a sphere (viscous case)

5.4.3. Transverse flow past a cylinder (potential case)

5.4.4. Transverse flow past a cylinder (viscous case)

5.4.5. Longitudinal flow past a cylinder (hemispherical end)

5.4.6. Longitudinal flow past a cylinder (flat end)

5.4.7. Flow past flat wedges

5.4.8. Transverse flow past a plate

5.4.9. Flow past a blade cascade

5.5. Characteristics of a Heterogeneous Flow in a Boundary Layer

5.5.1. Characteristics of a laminar boundary layer

5.5.2. Influence of particles on the laminar-turbulent transition

5.5.3. Characteristics of a turbulent boundary layer