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Semi-analytical modeling of non-premixed counterflow combustion of metal dust

  • Seyed Amir Hossein Madani
  • Mehdi Bidabadi
  • Nafiseh Mohammadian Aftah
  • Abolfazl Afzalabadi
Article
  • 12 Downloads

Abstract

In this study, a semi-analytical model is developed for non-premixed combustion of metal dusts in counterflow configuration. Combustion domain is divided into three separate zones, each of which possesses corresponding mass and energy conservation equations as well as boundary and jump conditions. Metal dust, assumed to be aluminum, undergoes an Arrhenius-type reaction with oxidizer, when it is heated enough to reach the ignition temperature. Dimensionless forms of conservation equations are derived and utilized to elucidate the combustion characteristics. The effects of oxidizer Lewis number and fuel mass concentration on the flame position and temperature are discussed thoroughly. In addition, temperature distribution of the whole domain is calculated by numerically solving the system of partial differential equations. In order to track particles through combustion domain, Lagrangian equations of motion are solved either mathematically or numerically, considering thermophoretic, weight, buoyancy and drag forces. The effects of thermophoretic force on the particle path are investigated, and the deviation of particle from carrier neutral gas direction is obtained. The results showed a great agreement with the data reported in the literature highlighting the fact that the presented model is an efficient one to accurately model the non-premixed counterflow combustion of metal dust.

Keywords

Non-premixed combustion Aluminum dust cloud Mathematical modeling Counterflow configuration Thermophoresis effect Particle tracking 

List of symbols

a

Strain rate (s−1)

Ca

Gas heat capacity (J kg−1 K−1)

CD

Drag coefficient

Cp

Particle heat capacity (J kg−1 K−1)

\(\bar{C}\)

Mean thermal velocity of gaseous molecules (m s−1)

DO

Oxidizer diffusion coefficient (m2 s−1)

dp

Particle diameter (m)

DT

Thermal diffusion coefficient (m2 s−1)

Ea

Activation energy (J)

FB

Buoyancy force (N)

FD

Drag force (N)

FG

Gravity force (N)

FT

Thermophoretic force (N)

Kn

Knudsen number

Le

Lewis number

mp

Particle mass (kg)

np

Number of particles per unit volume (m−3)

Q

Heat released per unit mass of fuel (J kg−1)

R

Universal gas constant (J mol−1 K−1)

T

Temperature (K)

Ta

Dimensionless activation energy

u

Velocity in x-direction (m s−1)

U

Particle velocity (m s−1)

v

Velocity in y-direction (m s−1)

Vb

Burning velocity (m s−1)

WF

Molecular weight of fuel (kg mol−1)

xf

Initiation point of flame

YO

Oxidizer mass fraction

Ys

Solid fuel mass fraction

\(Y_{{{\text{s}} - \infty }}\)

Primary mass fraction of solid fuel

Greek symbols

μ

Viscosity (Pa s)

λ

Particle mean free path (m)

θ

Dimensionless temperature

ϑ

Stoichiometric mass ratio

ρ

Density (kg m−3)

Subscripts

o

Oxidizer

s

Solid fuel

ig

Ignition

p

Particle

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Seyed Amir Hossein Madani
    • 1
  • Mehdi Bidabadi
    • 1
  • Nafiseh Mohammadian Aftah
    • 2
  • Abolfazl Afzalabadi
    • 1
  1. 1.School of Mechanical EngineeringIran University of Science and Technology (IUST)Narmak, TehranIran
  2. 2.Faculty of New Sciences and TechnologiesUniversity of TehranTehranIran

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