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Heat and Mass Transfer

, Volume 52, Issue 12, pp 2635–2648 | Cite as

CFD modeling using PDF approach for investigating the flame length in rotary kilns

  • H. F. ElattarEmail author
  • E. Specht
  • A. Fouda
  • Abdullah S. Bin-Mahfouz
Original

Abstract

Numerical simulations using computational fluid dynamics (CFD) are performed to investigate the flame length characteristics in rotary kilns using probability density function (PDF) approach. A commercial CFD package (ANSYS-Fluent) is employed for this objective. A 2-D axisymmetric model is applied to study the effect of both operating and geometric parameters of rotary kiln on the characteristics of the flame length. Three types of gaseous fuel are used in the present work; methane (CH4), carbon monoxide (CO) and biogas (50 % CH4 + 50 % CO2). Preliminary comparison study of 2-D modeling outputs of free jet flames with available experimental data is carried out to choose and validate the proper turbulence model for the present numerical simulations. The results showed that the excess air number, diameter of kiln air entrance, radiation modeling consideration and fuel type have remarkable effects on the flame length characteristics. Numerical correlations for the rotary kiln flame length are presented in terms of the studied kiln operating and geometric parameters within acceptable error.

Keywords

Probability Density Function Biogas Mixture Fraction Rotary Kiln Flame Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Aa,i

Air entrance area (m2)

C2, C

Turbulence model constants

D

Diameter of kiln (m)

da,i

Air entrance diameter (m)

do

Fuel nozzle diameter (m)

dp

Primary air nozzle diameter (m)

f

Mixture fraction, f = ϕ/(ϕ + L)

fa

Axial mean mixture fraction

Fi

External body force (N)

fo

Fuel mean mixture fraction

fst

Stoichiometric mean mixture fraction, f st  = 1/(1 + L)

G

Incident radiation (W/m2)

gi

Gravitational acceleration (m/s2)

I

Turbulence intensity

k

Turbulent kinetic energy (m2/s2)

L

Stoichiometric air to fuel mass ratio (kgair/kgfuel)

Lf

Overall confined jet flame length (m)

p

Pressure (Pa)

qr

Radiation heat flux (w/m2)

R

Radius of kiln (m)

ra,i

Radius of air entrance (m)

ReDH

Reynolds number based on hydraulic diameter

T

Local temperature (K)

Ta

Axial temperature (K)

Tair

Air temperature (K)

To

Fuel temperature (K)

u

Mean axial velocity (m/s)

ua

Axial velocity of the mixture/flame (m/s)

ui, uj

Velocity components in x and y directions (m/s)

uo

Fuel velocity at the nozzle (m/s)

up

Primary air velocity at the nozzle (m/s)

v

Mean radial velocity (m/s)

w

Mean tangential velocity (m/s)

x

Axial distance from burner (m)

Zi

Mass fraction of species i

ε

Turbulent dissipation rate (m2/s3)

κ

Absorption coefficient (1/m)

λ

Excess air number

μ

Dynamic viscosity (Pa.s)

μt

Turbulent viscosity (kg/m.s)

ν

Kinematic viscosity (m2/s)

ρ

Density (kg/m3)

ρo

Density of fuel (kg/m3)

ρst

Stoichiometric density (density of combustion gas at stoichiometric mixture fraction) (kg/m3)

σ

Stefan-Boltzmann constant (5.669 × 10−8 W/m2K4)

σε

Turbulent Prandtl number for the turbulence kinetic energy dissipation rate

σk

Turbulent Prandtl number for the turbulence kinetic energy

σt

Turbulent Prandtl number, σ t  = μ t c p /k t  = 0.85

τi.j

Stress tensor (Pa)

ϕ

Equivalence ratio, ϕ = (air/fuel) stoichiometric /(air/fuel) actual

2-D

Two dimensional

3-D

Three dimensional

CFD

Computational fluid dynamics

CPU

Central processing unit

DLR

Deutschland fur Lüft und Raumfahrt (German Aerospace Center)

PDF

Probability density function

RANS

Reynolds averaged Navier–Stokes

RSM

Reynolds stress model

SWF

Standard wall functions

WSGGM

Weighted sum of gray gases model

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • H. F. Elattar
    • 1
    • 2
    Email author
  • E. Specht
    • 3
  • A. Fouda
    • 1
    • 4
  • Abdullah S. Bin-Mahfouz
    • 5
  1. 1.Mechanical Engineering Department, Faculty of EngineeringUniversity of JeddahJeddahKingdom of Saudi Arabia
  2. 2.Mechanical Engineering Department, Faculty of EngineeringBenha UniversityBenhaEgypt
  3. 3.Institute of Fluid Dynamics and ThermodynamicsOtto-von-Guericke-University of Magdeburg, Universitätsplatz 2MagdeburgGermany
  4. 4.Mechanical Power Engineering Department, Faculty of EngineeringMansoura UniversityEl-MansouraEgypt
  5. 5.Chemical Engineering Department, Faculty of EngineeringUniversity of JeddahJeddahKingdom of Saudi Arabia

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