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

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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.

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Abbreviations

A a,i :

Air entrance area (m2)

C 2 , C 1ε :

Turbulence model constants

D :

Diameter of kiln (m)

d a,i :

Air entrance diameter (m)

d o :

Fuel nozzle diameter (m)

d p :

Primary air nozzle diameter (m)

f :

Mixture fraction, f = ϕ/(ϕ + L)

f a :

Axial mean mixture fraction

F i :

External body force (N)

f o :

Fuel mean mixture fraction

f st :

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

G :

Incident radiation (W/m2)

g i :

Gravitational acceleration (m/s2)

I :

Turbulence intensity

k :

Turbulent kinetic energy (m2/s2)

L :

Stoichiometric air to fuel mass ratio (kgair/kgfuel)

L f :

Overall confined jet flame length (m)

p :

Pressure (Pa)

q r :

Radiation heat flux (w/m2)

R :

Radius of kiln (m)

r a,i :

Radius of air entrance (m)

Re DH :

Reynolds number based on hydraulic diameter

T :

Local temperature (K)

T a :

Axial temperature (K)

T air :

Air temperature (K)

T o :

Fuel temperature (K)

u :

Mean axial velocity (m/s)

u a :

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

u i , u j :

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

u o :

Fuel velocity at the nozzle (m/s)

u p :

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)

Z i :

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)

μ t :

Turbulent viscosity (kg/m.s)

ν :

Kinematic viscosity (m2/s)

ρ :

Density (kg/m3)

ρ o :

Density of fuel (kg/m3)

ρ st :

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

τ i.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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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, University of Jeddah, 21589, Jeddah, Kingdom of Saudi Arabia

    H. F. Elattar & A. Fouda

  2. Mechanical Engineering Department, Faculty of Engineering, Benha University, Benha, 13511, Qalyubia, Egypt

    H. F. Elattar

  3. Institute of Fluid Dynamics and Thermodynamics, Otto-von-Guericke-University of Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    E. Specht

  4. Mechanical Power Engineering Department, Faculty of Engineering, Mansoura University, 35516, El-Mansoura, Egypt

    A. Fouda

  5. Chemical Engineering Department, Faculty of Engineering, University of Jeddah, 21589, Jeddah, Kingdom of Saudi Arabia

    Abdullah S. Bin-Mahfouz

Authors
  1. H. F. Elattar
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  2. E. Specht
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  3. A. Fouda
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  4. Abdullah S. Bin-Mahfouz
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Correspondence to H. F. Elattar.

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Elattar, H.F., Specht, E., Fouda, A. et al. CFD modeling using PDF approach for investigating the flame length in rotary kilns. Heat Mass Transfer 52, 2635–2648 (2016). https://doi.org/10.1007/s00231-016-1768-7

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  • DOI: https://doi.org/10.1007/s00231-016-1768-7

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