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Environmental Modeling & Assessment

, Volume 16, Issue 3, pp 295–311 | Cite as

Extended Analytical Turbulent Diffusion Model for Particle Dispersion and Deposition in a Horizontal Pipe: Comparison with CFD Simulation

  • Alamgir Hossain
  • Jamal Naser
  • Monzur Imteaz
Article

Abstract

A 2D analytical turbulent diffusion model for particle dispersion and deposition at different heights along the pipe flow and circumferential deposition has been developed. This liquid–solid turbulent diffusion model presented in this paper has emanated from an existing gas–liquid turbulent diffusion model. This model can be used as a handy tool for quick estimation one and two-dimensional deposition fluxes of particles in water distribution networks. A comprehensive 3D numerical investigation has been carried out using multiphase mixture model available in “Fluent 6.2” to verify the above analytical model. Different particles sizes and densities were used for 3D numerical investigations. The deposition was studied as a function of particle diameter, density, and fluid velocity. The deposition of particles, along the periphery of the pipe wall and at different depths, was investigated. Both the models findings matched with qualitative phenomena such as deposition of heavier particles at the bottom of the pipe wall were higher at lower velocities and lower at higher velocities. The lighter particles were found mostly suspended with homogeneous distribution. Smaller particles were also suspended with marginal higher concentration near the bottom of the pipe wall. This marginal higher concentration of the smaller particles was found to be slightly pronounced for lower velocity. These analogies of particles are well discussed with the ratio between free-flight velocity and the gravitational settling velocity. Extended analytical model results were compared with the 3D computational fluid dynamics simulation results. Discrepancies in the model results were discussed.

Keywords

CFD simulation Free-flight velocity Horizontal flow Multiphase Particle deposition and turbulence diffusion 

Nomenclature

\( \vec{a} \)

Secondary-phase particle's acceleration

C+

Concentration of particles

Cf

Friction coefficient

D

Pipe diameter

Df

Fluid diffusivity

Dp

Particle diffusion coefficient

dp

Diameter of the particles of secondary phase

\( \vec{F} \)

Body force

fdrag

Drag function

k

Proportional constant

kD

Constant

kn

Eigenvalues

L

Length scale

l

Particle mean free path

mT

Mass transfer

n

Number of phases

P

Peclet number

RD

Deposition flux

Re

Entrainment flux of the particles

Re*

Reynolds number based on the friction velocity

Ref

Fluid Reynolds number

S

Stokes number

t0

Initial time

TL

Integral flow time scale

TP

Particle integral time scale

U

Velocity scale

u*

The friction velocity

v

Free-flight velocity

\( {\vec{v}_{{{\rm{dr,k}}}}} \)

Drift velocity for secondary phase

Vf

Pipe average fluid velocity

\( v_{\rm{f}}^{\prime } \)

Fluctuating velocity

vg

Gravitational settling velocity of the particle

\( {\vec{v}_{\rm{m}}} \)

Mass-averaged velocity of the mixture

\( {\vec{v}_{\rm{qp}}} \)

Relative velocity

\( \left\langle {v\prime_{\rm{p}}^2} \right\rangle \)

Particle’s mean square velocity

λK

Kolmogorov length scale

ρm

Mixture density

ρp

Densities of the particle

αk

Volume fraction of phase

ε

Kinetic energy dissipation

ϕ

Angle around the pipe circumference

γcross

Crossing trajectories coefficient

γinert

Inertial coefficient

λ

Free-flight/diffusion ratio

μm

Viscosity of the mixture

νf

Kinematic viscosity

ρf

Densities of the fluid

τp

Particle relaxation time

τqp

Particulate relaxation time

τs

Wall shear stress

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Faculty of Engineering and Industrial SciencesSwinburne University of TechnologyMelbourneAustralia

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