Computers & Fluids 102 (2014) 62–73
Contents lists available at ScienceDirect
Computers & Fluids
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p fl u i d
CFD simulation of confined non-premixed jet flames in rotary kilns
for gaseous fuels
H.F. Elattar a,b,⇑, Rayko Stanev c, Eckehard Specht d, A. Fouda e
a
Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, North Jeddah, 21589 Jeddah, Kingdom of Saudi Arabia
Mechanical Engineering Department, Faculty of Engineering, Benha University, Benha, 13511 Qalyubia, Egypt
c
University of Chemical Technology and Metallurgy – Sofia, 8 St. Kliment Ohridski Blvd., 1756 Sofia, Bulgaria
d
Institute of Fluid Dynamics and Thermodynamics, Otto von Guericke University Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany
e
Mechanical Power Engineering Department, Faculty of Engineering, Mansoura University, 35516 El-Mansoura, Egypt
b
a r t i c l e
i n f o
Article history:
Received 29 June 2013
Received in revised form 26 February 2014
Accepted 27 May 2014
Available online 25 June 2014
Keywords:
Confined jet
Non-premixed flame
Rotary kiln
CFD simulation
a b s t r a c t
In the present study, computational fluid dynamics (CFD) methodology is used to investigate the confined
non-premixed jet flames in rotary kilns. Simulations are performed using ANSYS-Fluent, a commercial
CFD package. A two-dimensional axisymmetric model is conducted to understand the main operational
and geometrical parameters of rotary kilns, which affect the flame behaviors, including the aerodynamics
and heat transfer. Three kinds of fuels are employed in this study; Methane (CH4), Carbon Monoxide (CO)
and Biogas (50% CH4 and 50% CO2). Confined jet flame length correlations are developed and presented in
terms of kiln operational and geometrical parameters. Previous 2-D simulation results of free jet flames
are used to select and validate the turbulence model, which applied in this study. The present simulation
results are compared with available experimental data and previous analytical results, which show satisfactory agreement.
Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Rotary kilns have been used successfully for many years in
industrial processes and have continuously improved over the century. It has applied to many applications such as calcinations of
limestone, cement industry, metallurgy and incineration of waste
materials. It is pyroprocessing devices, which used to raise the
temperature of materials (calcinations) to high values in a continuous method. In the pyroprocessing technique, materials are subjected to high temperatures (typically over 800 °C), hence a
chemical or physical change might be occurred [1]. Moreover, it
can be employed for many industrial processes such as incineration, mixing, roasting, cooling, humidification, sintering, melting,
gasification, dehydration and gas–solid reactions [2]. This is
because the rotary kilns are able to operate at high burning zone
temperature, for example; lime burning (1200 °C) [3], burning of
cement clinker (2000 °C) and calcinations of petroleum coke
(1100 °C) [4] and calcinations of aluminum oxide (1300 °C) [5,6].
⇑ Corresponding author at: Mechanical Engineering Department, Faculty of
Engineering, King Abdulaziz University, North Jeddah, 21589 Jeddah, Kingdom of
Saudi Arabia. Tel.: +966 501531215.
E-mail address: [email protected] (H.F. Elattar).
http://dx.doi.org/10.1016/j.compfluid.2014.05.033
0045-7930/Ó 2014 Elsevier Ltd. All rights reserved.
However, cement industry is considered one of the most common
applications of rotary kilns [7].
Another essential application of rotary kilns is the incineration
of waste materials [8]. It can handle a wide variety of feed materials with variable calorific value and burn the solid wastes at the
exit without any problems. Typically, hazardous waste incinerators
operate with relatively deep beds and have a secondary combustion chamber after rotary kiln to improve the heterogeneous combustion of wastes [9]. It used to gasify the waste tires or wood to
obtain activated carbon [10,11]. Furthermore, it used to clean up
soil that has been contaminated with hazardous chemicals in a
process called thermal desorption [12,13]. Consequently, rotary
kilns can be used for three purposes: heating, reacting and drying
of solid materials, and in many cases, they are used to achieve a
combination of these aims.
CFD simulation methods have been extensively employed to
investigate the rotary kilns design and its operational parameters
over several decades. In the design process of rotary kilns, there
are four important aspects should be considered from a process-engineering point of view. These aspects are heat transfer
from flame, material flow through the kiln, gas–solid mass transfer and reaction [14]. Rate of heat transfer from flame is considered one of the most important factors among the four aspects,
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H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
Nomenclatures
kiln diameter, m
air inlet diameter, m
fuel nozzle diameter, m
fuel nozzle mean mixture fraction
stoichiometric mean mixture fraction, fst = 1/(1 + L)
stoichiometric air to fuel mass ratio, kgair/kgfuel
overall confined jet flame length, m
kiln radius, m
air inlet radius, m
axial temperature, °C
air temperature, °C
fuel temperature, °C
mean axial velocity, m/s
axial velocity of the mixture/flame, m/s
since it has a vital effect on the performance of the rotary kilns.
The effective heat transfer rate from flame to solid materials
and flame pattern are strongly related to flame properties, which
in turn have great effect on the kiln efficiency. Moreover, flame
characteristics such as length, shape and intensity play a crucial
role in improving the operation efficiency of the kiln. Furthermore, it strongly affects the rate of heat transfer, hence the fuel
consumption, product quality, total reduced sulfur emissions,
nitrogen oxide emissions, and refractory life. On the other hand,
the flame pattern plays an essential role in the formation of
mid kiln rings, which have contradictory effect on the kiln efficiency and increase its maintenance cost. Moreover, other thermal phenomena might be happened and can restrict the
performance of the kilns such as; flame instability that may cause
a wide variation in gas temperatures, short bushy flame which
can damage the refractory lining, and lazy flame that might not
deliver an enough heat to complete the reaction. As a result, it
is important to optimize the flame characteristics such as shape
and length, which are significantly affected by operational parameters including fuel type and flow rate [15]. Consequently, controlling the kiln flame characteristics is not an easy task due to
the fluctuations in operating parameters that affect the kiln performance and its flame [16].
Based on reviewing the previous studies on this research area,
much crucial information about the flame length, gas temperature
distributions and flow visualization inside the rotary kilns, is still
not completely understood. Moreover, the effects of the inlet air
conditions, excess air number, air inlet diameter and radiation
effect on the flame characteristics are rarely investigated. Such
information and parameters are very important for efficient design
and operation of the rotary kilns. In a pace towards that object, a 2D simulation study of a confined non-premixed jet flame using gaseous fuels is performed. A large cylinder has a diameter of 2.6 m
and length of 20 m is proposed in the present study to investigate
the effect of kiln geometry and various operating parameters on
flame behaviors such as thermal distribution and flow visualization. The obtained findings are presented in form of centreline axial
velocity profiles, centreline temperature profiles and axial mean
mixture fraction profiles to estimate the flame length. In addition,
mean mixture fraction and temperature contours are shown to
visualize the flame shape. Such parameters are varied to regulate
the flame length, which controls the thermal processes and controls the product quality. Finally, useful design guidelines and
dimensionless correlations that characterize the flame length are
developed and presented.
uo
v
w
x
k
qo
qst
CH4
CO
CO2
H2
H2O
O
fuel velocity at the nozzle, m/s
mean radial velocity, m/s
mean tangential velocity, m/s
axial distance from burner, m
excess air number
fuel density, kg/m3
stoichiometric density (density of combustion gas at
stoichiometric mixture fraction), kg/m3
Methane
Carbon Monoxide
Carbon dioxide
Hydrogen
Water
Oxygen
2. Computational methodology
2.1. Turbulence model selection and validation
The flame simulation results that obtained from the present
CFD solver are compared and validated with published experimental data and analytical results. Fig. 1 shows a comparison between
the present numerical results obtained from different turbulence
models and analytical solution of axial velocity distribution for free
jet flame that presented by Jeschar and Alt [17], which show good
agreement. The figure explains the effect of the turbulence model
used in the present study on the accuracy of simulation results
when comparing with the analytical solution of axial velocity profile. As can be seen in Fig. 1, the realizable k-e turbulent model
gives the best agreement with the analytical solution among the
other employed turbulence models. Fig. 2 shows another comparable study that is performed between the present simulation results
and the experimental data [18] in terms of the axial mixture fraction. Similar to the results shown in Fig. 1, the realizable k–e turbulent model gives the best agreement with the experimental data
compared to the other turbulence models applied. Furthermore,
it can be seen in Fig. 2 that the Reynolds-Stress-Model (RSM) has
approximately the same behavior of realizable k–e model; how30
CH 4, free jet,
Tair= 20 oC, To= 20 oC
Analytical (R. Jeschar & R. Alt, 1997)
Numerical (K-ε, Standard)
Numerical (K-ε, RNG)
Numerical (K-ε, Realizable)
20
Numerical (K-ω, SST)
Numerical (RSM)
uo/u a
D
da,i
do
fo
fst
L
Lf
R
ra,i
Ta
Tair
To
u
ua
10
0
0
40
80
120
160
200
x/do
Fig. 1. Turbulence model comparisons and validation with analytical axial velocity
[17].
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H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
d o= 8 mm, dp= 140 mm,
u o= 42.2 m/s, up= 0.3 m/s, Tair= To= 300 K
Axial mixture fraction, f a
Num. (k- ε, standard)
0.8
Num. (k- ε, RNG)
Num. (k- ε, realizable)
Num. (k- ω, standard)
Num. (k- ω, SST)
Num. (RSM)
Exp. (Sandia, Meier et al., 2000)
Exp. (DLR, Meier et al., 2000)
0.6
0.4
0.2
0
0
40
80
120
x/do
Fig. 2. Turbulence model comparisons and validation with experimental axial
mixture fraction [18].
ever, it is not recommended for the present study since it needs
much computational time.
2.2. Numerical approach and assumptions
A CFD flow solver based on finite volume method (ANSYS-Fluent) is employed in the present study to solve the Reynolds Averaged Navier– Stokes (RANS) equations, species transport, energy
equation and radiation model. The flow is assumed as steady
and incompressible and the problem is dealt as axi-symmetry.
The walls assumed to be adiabatic and the wall type (construction) does not consider in the simulation (i.e. wall heat flux = 0,
internal emissivity = 1, and wall thickness = 0) and these assumptions lead to relative approximate results. Rotation speed, bed
percent fill and buoyancy has no significant effect on the flame
behaviors and its aerodynamics [19]. The steady-state continuity
equation of gas phase is stated in Eq. (1). Where the source term
Sm resulted from fuel injection. The components of velocity in a
three-dimensional coordinate system are represented by the
momentum equation that is given in Eq. (2). The terms in Eq.
(2) include pressure, turbulent shear stresses, gravitational force
(buoyancy effects), and the source terms.
@
ðqui Þ ¼ Sm
@xi
@
@p @ sij
ðqui uj Þ ¼ þ
þ q g i þ F i þ Sm
@xj
@xi @cj
lt @k
þ Gk þ Gb qe
ð3Þ
rk @xj
@
@
l @e
e2
e
pffiffiffiffiffi þ C 1e C 3e Gb ð4Þ
þ qC 1 Se qC 2
ðqeuj Þ ¼
lþ t
@xj
@xj
re @xj
k
k þ me
@
@
ðqkuj Þ ¼
@xj
@xj
1
ð1Þ
ð2Þ
A preliminarily study is conducted using different turbulence
models to select the appropriate model for the present study that
gives accurate results in compassion with the available experimental and analytical data. As stated in the previous part, the realizable
k–e turbulence model showed the best agreement with the experimental and analytical data available. The realizable k–e turbulence
model is derived from the instantaneous Navier–Stokes equations
[20], and the term ‘‘realizable’’ means that the model satisfies certain mathematical constraints on the Reynolds stresses and consistent with the physics of turbulent flows. The analytical derivation
of the realizable k–e turbulence model, its constants and additional
terms and functions in the transport equations for k and e are different from those in the standard k–e and RNG k–e models. The
transport equations for the realizable k–e model are given in Eqs.
(3) and (4).
lþ
As can be seen in Eqs. (3) and (4), Gk and Gb represent the generation
of turbulence kinetic energy due to the mean velocity gradients and
due to buoyancy respectively. C2 and C1e are constants and rk and re
are the turbulent Prandtl numbers for k and e. In the present kiln
simulation, the turbulent intensity for the air inlet is taken as 10%
and for the fuel inlet is 5%.
The non-premixed combustion model and Probability Density
Function (PDF) are chosen for chemical reaction simulation. The
non-premixed modeling approach offers many benefits over the
finite rate formulation. This model allows intermediate (radical)
species prediction, dissociation effects, and rigorous turbulence–
chemistry coupling. The method is computationally efficient in
that it does not require the solution of a large number of species
transport equations. When the underlying assumptions are valid,
the non-premixed approach is preferred over the finite rate formulation. The non-premixed approach can be used only when the
reacting flow system meets several requirements. First, the flow
must be turbulent. Second, the reacting system includes a fuel
stream, an oxidant stream, and, optionally, a secondary stream
(another fuel or oxidant, or a non-reacting stream). Finally, the
chemical kinetics must be rapid so that the flow is near chemical
equilibrium [21].
Owing to the fluctuating properties of a turbulent mixing process, the Probability Density Function, PDF is a preferred method
for the cases containing combustion process and turbulent flow.
In this study b-PDF model is used because its better results for
the turbulent non-premixed reacting flow in comparing with different PDF models [22]. In b-PDF model the PDF is defined by
two parameters of mean scalar quantity and its variance. Due to
the difficulty in solving the transport equation for each species,
the mixture fraction, f in the presumed b-PDF is written in terms
of mass fraction of species i, Zi:
f ¼
Z i Z i;ox
Z i;fuel Z i;ox
ð5Þ
The subscripts ‘‘ox’’ and ‘‘fuel’’ denote the value at the oxidizer and
fuel stream inlets, respectively. It has a value of one (f = 1) in the
fuel stream, zero value (f = 0) in the oxidizer stream and it takes values between zero and one (f = 0–1) within the flow field.
The transport equations of mean mixture fraction, f and its variance, f 02 , are:
@ @
@
ðqf Þ þ
ðquj f Þ ¼
@t
@xj
@xj
lt @f
rt @xj
@
@ 02 @ qf þ
quj f 02 ¼
@t
@xj
@xj
!
ð6Þ
!
lt @f 02
@ f
þ C g lt
@xj
rt @xj
!2
e
C d q f 02 ð7Þ
k
where f 0 ¼ f f . The default values for the constants rt, Cg, and Cd
are 0.85, 2.86, and 2.0, respectively. The power of the mixture fraction modeling approach is that the chemistry is reduced to one conserved mixture fraction. Under the assumption of chemical
equilibrium, all thermochemical scalars (species fractions, density,
and temperature) are uniquely related to the mixture fraction.
The instantaneous values of mass fractions, density, and temperature depend solely on the instantaneous mixture fraction, f:
/i ¼ /i ðf Þ
/i ¼ /i ðf ; HÞ
ð8Þ
ð9Þ
In Eqs. (8) and (9), /i represents the instantaneous species mass
fraction, density, or temperature in the case of adiabatic and non-
H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
adiabatic systems, respectively and H is the instantaneous enthalpy.
The prediction of the turbulent reacting flow is concerned with prediction of the averaged values of fluctuating scalars which obtained
from Eqs. (6) and (7). How these averaged values are related to the
instantaneous values depends on the turbulence–chemistry interaction model. This relation is established by a PDF model as a
closure model when the non-premixed model is used. The Probability Density Function, written as p(f), can be thought of as the fraction of time that the fluid spends in the vicinity of the state f. The
method applies to mean values of species concentration and tem i,
perature. The mean mass fraction of species and temperature, /
can be computed as:
i ¼
/
Z
65
pðf Þ/i ðf Þdf
ð10Þ
The P-1 radiation model is used to calculate the flux of the radiation inside of the rotary kiln. It is the simplest case among of the
more general P–N radiation models that was derived based on the
expansion of the radiation intensity (I) into an orthogonal series of
spherical harmonics [23,24]. Moreover, the model the P-1 model
requires only a little demand of the Central Processing Unit
(CPU) demand and can be applied easily to various complicated
geometries. It is suitable for applications where the optical thickness (aL) is large, where a is the absorption coefficient and L is
the length scale of the domain. The absorption coefficient (a) can
be a function of local concentrations of H2O and CO2, path length
and total pressure. On the other hand, the Weighted-Sum-ofGray-Gases model (WSGGM) is chosen for calculating the variable
absorption coefficient as shown in Eq. (17).
pðf Þ/i ðf ; HÞdf
ð11Þ
rqr ¼ aG 4arT 4
1
0
i ¼
/
Z
1
ð17Þ
0
Eqs. (10) and (11) represent the mean mass fraction of species and
temperature in the case of adiabatic and non-adiabatic systems.
, can be comSimilarly, the mean time-averaged fluid density, q
puted as
1
¼
q
Z
1
0
pðf Þ
df
qðf Þ
where pðf Þ ¼ R
ð12Þ
f a1 ð1f Þb1
f a1 ð1f Þb1 df
; a and b are defined as follows:
"
#
f ð1 f Þ
a¼f
1
f 02
"
#
f ð1 f Þ
b ¼ ð1 f Þ
1
f 02
ð13Þ
ð14Þ
i in the non-adiabatic system thus requires soluDetermination of /
tion of the modeled transport equation for mean enthalpy, H:
@
k
ðqHÞ þ r ðq~
v HÞ ¼ r t rH
@t
cp
ð15Þ
The restrictions for non-premixed model are that the unique
dependence of /1 (species mass fractions, density, or temperature)
on f requires that the reacting system must meet the following
conditions: The chemical system must be of the diffusion type with
discrete fuel and oxidizer inlets. Moreover the Lewis number must
be unity. (This implies that the diffusion coefficients for all species
and enthalpy are equal, a good approximation in turbulent flow). In
addition to, when a single mixture fraction is used, the following
conditions must be met: Only one type of fuel is used, and multiple
fuel inlets may be included with the same composition; two or
more fuel inlets with different fuel composition are not allowed.
Only one type of oxidizer is involved. The oxidizer may consist of
a mixture of species, and the multiple oxidizer inlets may be
involved with the same composition. Two or more oxidizer inlets
with different compositions are not allowed. Finally, the flow must
be turbulent [21].
The PRESTO and SIMPLE algorithms are employed in the present
study for pressure interpolation and pressure–velocity coupling,
respectively. The thermal properties of species are given as functions of temperature and standard atmospheric pressure
(1.013 105 Pa). The energy equation is stated in Eq. (16), which
is solved for enthalpy.
@
@
@h
þ Sh
ðqmi hÞ ¼
Ch
@xi
@xi
@xi
ð16Þ
The source term Sh in the energy equation includes combustion and
radiation heat transfer rates:
The term rqr can be directly substituted into the energy equation to calculate the heat sources due to radiation.
2.3. Geometry, grid generation and boundary conditions
Fig. 3 shows a schematic diagram for the confined non-premixed flame configurations, which used in the rotary kiln flame
simulation. This configuration is used to investigate the effects of
kiln geometry and various operating parameters on the flame aerodynamics and flame length. As shown in Fig. 3, a simple burner is
used with a variable air inlet area (Aa,i), which can be controlled by
changing air inlet diameter (da,i). The burner has 50 mm diameter
and its thermal power ranges from 0.69 to 1.97 MW according to
fuel type. The fuel flows with a uniform axial velocity of 30 m/s,
temperature of 20 °C and the excess air number (k) is changed from
1.1 to 2.5. The excess air number (k) can be defined as the ratio
between the actual feed air volume and the theoretical needed
(stoichiometric value), (e.g. k = 1.2 means that 20 percent more
than the required stoichiometric air is being used). In the present
study, three types of fuels are proposed; Methane (CH4), Carbon
Monoxide (CO) and Biogas (50% CH4 and 50% CO2), because they
have a wide range of stoichiometric air to fuel ratio. Fig. 4(a) and
(b) show the 2-D domain geometry and generated mesh of the
rotary kiln respectively. The full domain geometry is considered
as a symmetrical kiln (20 m length and 2.6 m diameter) to simulate
and investigate the effect of confinements on the flame behavior.
As shown in Fig. 4(a), half portion of the kiln has been taken for
the present simulation as a studied domain to reduce the computational cost. The mesh of the studied domain is generated by preprocessing package with 30,000 cells, structured and quadrilateral
mesh type. The mesh is controlled to be more dense near the burner, where the flame region exists. Moreover, the boundary conditions that implemented in the present study are illustrated in
Fig. 4(b).
2.4. Grid independence study
A number of 2-D meshes are generated with increasing the
number of cells to perform a grid independent study and to make
sure that the flame length converges as the mesh size increases.
Fig. 5 illustrates number of 2-D computational grids with different
number of cells ranging from 3000 to 100,000 cells that have been
tested for flame length convergence. As can be seen, the grids with
number of cells exceeding than 30,000 cells reveal a small variation
in flame length convergence less than 0.2%. Consequently, the grid
with 30,000 cells is recommended to use for accurate calculations.
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H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
Fig. 3. Schematic diagram of simulated rotary kiln.
Velocity inlet
Pressure outlet
Wall
Velocity inlet
Axi-symmetry
Fig. 4. 2-D domain of investigated rotary kiln flame model: (a) geometry and (b) mesh.
3. Results and discussion
3.1. Turbulence–chemistry interaction (PDF approach) shortcomings
In order to present the turbulence–chemistry interaction shortcomings, Figs. 6–8 show comparisons between the present simulation results of the confined jet flame with and without radiation
modeling and the experimental data of Kim [28]. Fig. 6 displays a
comparison between numerical simulation results with and without radiation modeling and experimental data of Kim et al. [28], at
Tair = Ta = 300 K do = 2.7 mm, and k = 6.17 for axial temperature versus axial mean mixture fraction. As shown in the figure, the
numerical results give good agreement with experimental data.
While, Fig. 7 presents the centreline axial mass fraction distribution of H2 and CO against mean mixture fraction for both simulation results and experimental data. As shown in the figure, the
numerical results have the same trend as the experimental results,
but with higher values than the experimental data. The discrepancies between the experimental data and simulation results are
attributed to the inherent simplified assumptions in the turbulence
and combustion models and due to the error in experimental measurements. Furthermore, a comparison between the experimental
data and simulation results of flame length at do = 2.7 mm and
4.4 mm at different fuel velocities is demonstrated in Fig. 8. As it
can be seen, the simulation results give satisfactory agreement
with experimental data. The discrepancies in the compared results
are due to the difference in definition of the flame length, numerical assumptions and experimental uncertainty.
In spite of the good overall agreement with the experimental data
[28], the shortcomings of the turbulence–chemistry interaction, PDF
approach are apparent. The model tends to underpredict for both
temperature and mean mixture fraction in axial locations along
the flame in case of radiation modeling and it gives perfect fit without radiation consideration. In case of radiation modeling, the model
predicts much lower for both temperature and mean mixture fraction around the flame end (i.e. around the stoichiometric mean mixture fraction value, fst = 0.055), otherwise it gives perfect predictions
(near the burner tip; down to fa = 0.3 and downstream the flame
end; up to fa = 0.03). Low temperatures are probably caused by overpredicting radiation heat transfer in the radiation model, P-1, and
67
H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
0.2
CH4, λ=1.3
without radiation
Tair= To= 20 oC
CH4, confined jet flame,
Tair= 300 K, To= 300 K, do=2.7 mm
0.16
Num. with radiation
Exp. (Kim et al., 2007)
mass fraction
Dimensionless flame length (L f /do)
200
180
0.12
CO
0.08
0.04
H2
0
0
0.2
0.4
0.6
0.8
1
Mixture fraction, f a
160
0
20000
40000
60000
80000
100000
Number of Cells
Fig. 7. Comparison of simulated and experimental data of centreline axial mass
fraction distribution for CO and H2 species versus mixture fraction using Methane
flame.
Fig. 5. Grid independence study for rotary kiln flame length.
160
2500
CH 4, confined jet flame,
Tair= 300 K, T o= 300 K
Num. without radiation
CH 4, confined jet flame,
Tair = 300 K, T o= 300 K, d o=2.7 mm
Num. without radiation
Num. with radiation
Exp. (Kim et al., 2007)
Num. with radiation
Flame length, L f (cm)
2000
Ta (K)
1500
1000
120
Exp. (Kim et al., 2007)
do= 4.4 mm
80
do= 2.7 mm
40
500
0
0
0
0.2
0.4
0.6
Mixture fraction, f
0.8
1
a
Fig. 6. Comparisons of simulated and experimental data of centreline axial
temperature versus mixture fraction with and without radiation modeling using
Methane flame.
low mean mixture fraction may be due to the shortcoming of turbulence–chemistry interaction model, PDF approach by underpredicting the mixing in the system at high temperatures (around the flame
end). Furthermore the model tends to overpredict the mass fractions
of CO and H2 against mean mixture fraction in axial locations along
the flame, where the model predicts much higher CO and H2. This
may be caused by the model may be underpredicting the mixing
in the system along the flame. In addition to the flame length is overpredicted by the model, where the model predicts much higher
flame length at higher fuel nozzle diameter (do = 4.4 mm) and gives
perfect fit with experimental data at smaller fuel nozzle diameter
(do = 2.7 mm). This may be attributed to the turbulence–chemistry
interaction model shortcomings which cannot predict the mixing
process in the system perfectly with higher fuel nozzle diameter
(i.e. lower jet momentum).
3.2. Effect of excess air number (k)
Fig. 9 explains the effect of excess air number (k) that varies
from 1 to 2.5 on the dimensionless inverted axial velocity profiles
20
24
28
32
Fuel velocity, u o (m/s)
Fig. 8. Comparison of simulated and experimental data of flame length versus fuel
velocity at different fuel nozzle diameter using Methane fuel with and without
radiation modeling.
(uo/ua) using CH4 fuel. As shown in Fig. 9, the axial velocity decays
along the flame axis and this trend is similar for all the investigated
values of the excess air number and for all the selected fuel gases.
Moreover, the excess air number has a considerable effect on the
axial velocity profiles, since the axial velocity increases with
increasing the excess air number for all the selected type of fuels.
This is due to the fact that the air axial velocity increases with
increasing the excess air number. This effect does not appear in
the entrance region of the kiln, however; it might be reasonable
behavior in fully developed region. In addition to that, the flame
confinement has a significant effect on the flame axial velocity profiles comparing with free jet profiles. This is because the confined
flame axial velocity is controlled by axial air velocity according
to the value of the excess air number.
Fig. 10 shows the velocity vectors colored by temperature values to explain the effect of excess air number on the outer recirculation zone size for confined Methane jet flame. As shown in the
figure, the recirculation appears at excess air numbers of 1 and
1.1 and after that, the recirculation diminishes with increasing
the excess air number. This can be attributed to that the low excess
air number has an ambient air momentum less than what the jet
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H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
40
CH 4, confined jet flame,
without radiation,T air=20 oC,
u o= 30 m/s, T o=20 oC
λ= 1
da,i/D= 1
λ= 1.1
30
λ= 1.3
λ= 1.5
λ= 1.7
uo/ua
λ= 2.0
λ= 2.3
20
λ= 2.5
free jet
10
0
0
100
200
300
400
x/do
[K]
Fig. 9. Influence of excess air number on inverted dimensionless axial velocity
profiles along the flame using Methane fuel.
The effect of excess air number on the centreline axial temperature compared with free jet flame for CH4 fuel is shown in Fig. 11.
As it can be seen, the excess air number has a significant effect on
the axial temperature profiles, since the higher the excess air number, the lower the peak flame temperature and product combustion gas temperature. This effect appears after x/do 170. The
figure explains that the temperature profile approaches to free
jet profile with increasing the excess air number. This trend is
the same for all the selected fuel gases, since the mixing temperature between fuel and air decreases with increasing the excess air
number, hence; a drop in the combustion gas temperature can be
obtained.
Fig. 12 illustrates the effect of excess air number on dimensionless inverted axial mixture fraction (fo/fa) profiles for Methane fuel.
As shown in the figure, the flame length decreases with increasing
the excess air number and it becomes the same as in free jet at
k = 2.5. This is due to that, the higher the excess air number, the
higher amount of oxidizer, hence; the combustion process will be
completed in small volume and consequently in short distance.
The same result has been concluded by Yang and Blasiak [26]. This
means that the flame length reaches to the smallest possible value
at the highest excess air number, and this effect is the same for all
the studied fuels (e.g., for CH4 fuel the flame length shortens by
about 7% with increasing the excess air number (k) from 1.3 to 2.5).
3.3. Effect of air inlet diameter (da,i/D)
o
Tair= 20 C
da,i/D= 1
λ= 1.0
CH4
o
To= 20 C
uo= 30 m/s
λ= 1.1
λ= 1.3
Fig. 10. Influence of excess air number on recirculation zones presented by velocity
vectors colored by temperature along the flame using Methane fuel.
2000
da,i/D= 1
1600
1200
The effects of dimensionless air inlet diameter (da,i/D) on the
axial velocity (ua) and centreline axial temperature (Ta) profiles
at different excess air numbers of 1.3, 1.7, and 2.3 using Methane
fuel are shown in Figs. 13 and 14 respectively. Fig. 13 explains that
the axial velocity decreases along the jet flame axis for all the studied values of the air inlet diameter and excess air number. However, at smallest values of air inlet diameter (da,i/D = 0.06 and
0.1), the axial velocity increases for awhile, then decreases again
along the jet axis. The possible explanation for this behavior is that
the axial air velocity around the jet is much higher than the fuel jet
velocity. As a result, the axial air affects the fuel jet velocity by
increasing the centreline axial velocity distribution until it reaches
to the maximum value at x/do 25 and 10 for da,i/D = 0.06 and 0.1,
respectively, then the velocity decreases along the jet flame axis.
Moreover, the air inlet diameter has a sensible effect on the axial
velocity profiles, whereas the axial velocity profiles shifted up with
decreasing the air inlet diameter until the flow reaches to fully
Ta (oC)
CH4, confined jet flame,
without radiation,Tair=20 oC,
uo= 30 m/s, To=20 oC
30
CH 4, confined jet flame,
without radiation,Tair =20 oC,
u o= 30 m/s, To=20 oC
free jet
λ= 1
800
λ= 1.1
λ= 1.3
λ= 2.5
λ= 1.5
λ= 2.3
λ= 1.7
400
λ= 2.0
20
λ= 2.0
λ= 1.7
λ= 2.3
100
200
λ= 1.3
fo/fa
0
0
fo/fst (CH4)
λ= 1.5
λ= 2.5
free jet
300
λ= 1.1
λ= 1
400
x/do
10
Fig. 11. Influence of excess air number on axial temperature profiles along the
flame using Methane flame.
can entrain, hence; the recirculation is commenced. However, at
high excess air number, the ambient air momentum is higher
enough to fulfil the requirements for entrainment, hence; the jet
will expand to attach the wall without recirculation. These results
are matched successfully with that explained by Curtet [25].
da,i/D= 1
0
0
50
100
150
200
250
x/do
Fig. 12. Influence of excess air number on inverted dimensionless axial mean
mixture fraction profiles along the flame using Methane fuel.
69
H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
2000
3
CH4, confined jet flame,
without radiation, Tair= 20 oC,
uo= 30 m/s, To= 20 oC
da,i/D= 0.06
λ= 1.3
1600
da,i/D= 0.1
da,i/D= 0.2
2
Ta (oC)
da,i/D= 0.4
ua/uo
da,i/D= 0.5
da,i/D= 0.6
da,i/D= 0.7
1200
CH 4, confined jet flame,
without radiation, Tair= 20 oC,
u o= 30 m/s, To= 20 oC
da,i/D= 0.06
800
da,i/D= 0.1
da,i/D= 0.8
1
da,i/D= 0.2
da,i/D= 0.9
da,i/D= 0.4
da,i/D= 0.5
da,i/D= 1.0
400
da,i/D= 0.6
da,i/D= 0.7
da,i/D= 0.8
da,i/D= 0.9
λ= 1.3
da,i/D= 1.0
0
0
0
0
100
200
300
100
400
200
300
400
x/do
x/do
2000
λ= 1.7
3
CH4, confined jet flame,
without radiation, Tair= 20 oC,
uo= 30 m/s, To= 20 oC
da,i/D= 0.06
1600
da,i/D= 0.1
Ta (oC)
da,i/D= 0.2
2
da,i/D= 0.4
ua/uo
da,i/D= 0.5
1200
CH 4, confined jet flame,
without radiation, Tair= 20 oC,
u o= 30 m/s, To= 20 oC
da,i/D= 0.06
800
da,i/D= 0.6
da,i/D= 0.1
da,i/D= 0.7
da,i/D= 0.2
da,i/D= 0.4
da,i/D= 0.8
1
da,i/D= 0.5
400
da,i/D= 0.9
da,i/D= 0.6
da,i/D= 0.7
da,i/D= 1.0
da,i/D= 0.8
da,i/D= 0.9
da,i/D= 1.0
0
λ= 1.7
0
100
200
300
400
x/do
0
0
100
200
300
400
2000
x/do
λ= 2.3
3
1600
Ta (oC)
CH4, confined jet flame,
without radiation, Tair= 20 oC,
uo= 30 m/s, To= 20 oC
da,i/D= 0.06
da,i/D= 0.1
2
da,i/D= 0.2
1200
CH 4, confined jet flame,
without radiation, Tair= 20 oC,
u o= 30 m/s, To= 20 oC
da,i/D= 0.06
800
da,i/D= 0.4
da,i/D= 0.1
ua/uo
da,i/D= 0.5
da,i/D= 0.2
da,i/D= 0.4
da,i/D= 0.6
da,i/D= 0.5
400
da,i/D= 0.7
da,i/D= 0.6
da,i/D= 0.7
da,i/D= 0.8
1
da,i/D= 0.8
da,i/D= 0.9
da,i/D= 0.9
da,i/D= 1.0
da,i/D= 1.0
0
0
λ= 2.3
100
200
300
200
300
400
x/do
0
0
100
400
Fig. 14. Influence of dimensionless air inlet diameter on axial temperature profiles
along the flame at different excess air number using Methane fuel.
x/do
Fig. 13. Influence of dimensionless air inlet diameter on dimensionless axial
velocity profiles along the flame at different excess air number using Methane fuel.
developed flow at x/do 200, then the effect of air inlet diameter
diminishes. This is because the axial air velocity increases with
decreasing the air inlet diameter, hence; the centreline axial velocity profile increases.
As shown in Fig. 14, the axial temperature distribution and peak
flame temperature increase and shift to right with increasing the
air inlet diameter. This behavior is the same for the studied values
of excess air numbers. This can be attributed to the increasing
length of recirculation eddies with decreasing the air inlet diameter that in turns improve the mixing process between air and fuel.
Consequently, the shorter flame can be obtained and the peak
flame temperature is shifted to the burner tip and vice versa. The
70
H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
[K]
25
o
T air= 20 C
λ= 1.3
20
λ= 2.3
CH4
fo/fst (CH4)
uo= 30 m/s
da,i/D= 0.1
CH4, confined jet flame,
without radiation, Tair= 20 oC,
uo= 30 m/s, To= 20 oC
da,i/D= 0.06
fo/fa
15
da,i/D= 0.4
da,i/D= 0.1
da,i/D= 0.2
10
da,i/D= 0.4
da,i/D= 0.6
da,i/D= 0.5
da,i/D= 0.6
5
da,i/D= 0.8
da,i/D= 0.7
da,i/D= 0.8
da,i/D= 0.9
da,i/D= 1.0
0
da,i/D= 1.0
0
Fig. 15. Influence of dimensionless air inlet diameter at k = 2.3 on recirculation
zones presented by velocity vectors colored by temperature using Methane fuel.
100
200
300
400
x/do
Fig. 17. Influence of dimensionless air inlet diameter on inverted dimensionless
axial mean mixture fraction profiles along the flame using Methane fuel at k = 1.3.
is presented in Fig. 17 in order to calculate the flame length using
Methane (CH4) fuel at k = 1.3. As shown in the figure, the flame
length increases with increasing the air inlet diameter and vice
versa. This is due to the axial air velocity and length of recirculation
eddy increase with decreasing air inlet diameter. However,
increasing the air velocity and length of recirculation eddy improve
the mixing process between air and fuel, which result in decreasing
the flame length. Moreover, the changing of dimensionless air inlet
diameter (da,i/D) from 0.06 to 0.4 has a considerable effect on the
flame length, otherwise it has negligible effect. For instance, the
flame length increases by about 180% with increasing the value
of da,i/D from 0.06 to 0.4 and by nearly 6% with increasing the value
of da,i/D from 0.4 to 1 at the same value of excess air number
(k = 1.3).
The effect of radiation simulation on the mean mixture fraction
and temperature contours of Methane jet flame at k = 1.3 is
depicted in Fig. 18(a) and (b) respectively. As can be seen, radiation
modeling has a considerable effect on the flame length, where the
[K]
[K]
strength and size of those recirculation eddies will affect both
the stability and combustion length of the turbulent diffusion
flame [25]. Fig. 15 displays the velocity vectors colored by temperature to show the effect of air inlet diameter on the outer recirculation zones for Methane jet flame. As shown in the figure, the
length of recirculation decreases with increasing air inlet diameter;
this is because of the axial air velocity decreases with increasing
the air inlet area at the same excess air number. In addition to that,
the closed part at the air inlet helps the recirculation eddies to
occurs behind it. The effect of the air inlet diameter (da,i) on the
temperature contours is presented in Fig. 16. The figure explains
that the peak flame temperature increases and shifts to right with
increasing air inlet diameter. This trend is the same for the studied
values of excess air numbers. This can be attributed to the increase
of recirculation length increases with decreasing the air inlet diameter, which improves the mixing process between air and fuel,
hence completing the combustion process in short distance.
On the other hand, the effect of air inlet diameter (da,i) on the
inverted dimensionless axial mean mixture fraction (fo/fa) profiles
λ= 2.3
CH4
uo= 30 m/s
o
T air= 20 C
CH4
λ= 2.3
Without radiation
da,i/D= 0.06
(a)
With radiation
da,i/D= 0.1
da,i/D= 0.2
CH4
λ= 1.3
Without radiation
(b)
With radiation
da,i/D= 0.4
da,i/D= 0.5
Fig. 16. Influence of dimensionless air inlet diameter on temperature contours
using Methane fuel at k = 2.3.
Fig. 18. Influence of radiation modeling at Tair = To = 20 °C, uo = 30 m/s, and da,i/D = 1
on: (a) temperature contours along the Methane flame at k = 2.3 and (b) mean
mixture fraction contours along the Methane flame at k = 1.3.
H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
2500
da,i/D=1
2000
CO
CH4
Ta (oC)
1500
Biogas
1000
confined jet flame,
without radiation, λ= 2.3
Tair = 20 oC, u o= 30 m/s, T o= 20 oC
CH 4
500
Biogas
CO
(a)
0
0
40
80
120
160
200
x/do
25
confined jet flame,
without radiation, λ= 2.3
Tair= 20 oC, uo= 30 m/s, T o= 20 oC
20
da,i/D=1
fo/fs(CH4)
CH4
fo/fa
15
Biogas
10
CO
fo/fs(Biogas)
5
fo/fs(CO)
(b)
0
0
40
80
120
160
200
71
by Elattar [27], the flame length does not depend on the fuel velocity, therefore a comparison between CH4, Biogas, and CO is performed at constant fuel velocity of 30 m/s and fuel temperature
of 20 °C in order to investigate the flame lengths of gaseous fuels.
Fig. 19(a)–(c), explain the effect of different types of fuels on
axial temperature profiles, inverted axial mean mixture fraction
profiles at excess air number of k = 2.3, and the dimensionless flame
length versus excess air number, respectively. Fig. 19(a) shows a
comparison of axial temperature profiles for CH4, Biogas, and CO
at uo = 30 m/s, Tair = To = 20 °C, da,i/D = 1, and without considering
the radiation modeling. The figure shows that the Carbon Monoxide
fuel (CO) has the highest peak flame temperature of about 1950 °C
at x/do 41, Biogas fuel has the lowest peak flame temperature of
about 1550 °C at x/do 73, while, Methane fuel (CH4) has intermediate peak flame temperature of about 1800 °C at x/do 174. These
results are approximately the same as in free jet flame simulation at
20 °C air temperature, this due to the high value of excess air number, which closes the case from free jet case [27]. On the other hand,
Fig. 19(b), illustrates the inverted dimensionless axial mean mixture fraction profiles along the flame, in order to calculate the flame
length for the same gases at the same previous conditions. As displayed in the figure, CH4 has the longest flame length, CO has the
shortest flame length, and Biogas is in between of them and these
results are similar to the free jet simulation results [27]. This can
be attributed to the higher the fuel heating value, the longer the
flame length. In other words the lower the fuel stoichiometric mean
mixture fraction (fst), the longer the flame length, and vice versa.
That means the flame should be spread to reach to its stoichiometric mean mixture fraction to end its length. Furthermore, the
results of dimensionless flame length of CH4, Biogas, and CO fuels
at fuel velocity of 30 m/s, air temperature of 20 °C and dimensionless air inlet diameter of da,i/D = 1, without radiation modeling are
presented in Fig. 19(c). As can be seen in the figure, CH4 fuel has
the longest flame length, then Biogas and finally the CO fuel. Moreover, the results explain that the excess air number in the range
from 1.1 to 1.5 has a considerable effect on the flame length; otherwise, it has approximately no effect.
x/do
4. Prediction of flame length correlations
25
da,i/D=1
Confined jet flame, without radiation,
Tair= 20 oC, u o= 30 m/s, T o= 20 oC
(L f/do) fst
20
15
CO
Biogas
10
Lf
¼ 18:24k0:23 ð1 þ LÞ0:83
do
CH4
5
dai/D= 1
(c)
0
1
1.2
Fig. 20(a)–(d) show different predicted correlations of the confined flame length in relation with kiln geometry and various operating parameters that employed in the present study. Fig. 20(a)
shows the derived dimensionless form of the confined flame length
in terms of excess air number and air demand (mass basis) as
follows:
1.4
1.6
1.8
2
2.2
2.4
λ
Fig. 19. Influence of fuel type on: (a) centreline axial temperature profiles, (b)
inverted dimensionless axial mean mixture fraction, and (c) flame length trends
with excess air number.
flame length shortens by about 15% for k = 1.3. This value of reduction in confined jet flame is much higher than the reduction in
flame length of free jet Methane flame, which was about 4% at
20 °C air temperature [27]. As stated by many authors and proved
ð18Þ
Eq. (18) is formulated for the data in the following ranges:
2.46 6 L 6 17.3, 1.1 6 k 6 2.5, and da,i/D = 1 at Tair = To = 20 °C,
and. The correlation can predict 100% of the simulation results
within error of ±13%. Therefore, the correlation shows that the
flame length is directly proportional to air demand and reversely
proportional to excess air number. Moreover, it can be seen that,
the confined flame length is higher than the free jet flame length.
Another dimensionless formula for the confined flame length in
terms of stoichiometric mean mixture fraction, fuel density, stoichiometric density (density of combustion gas at stoichiometric
mixture fraction) and excess air number is presented in
Fig. 20(b). The predicted formula is derived in the same way of
Eq. (1) as follows:
0:5 Lf
5:5 qo
1
¼
fst qst
do
k0:23
ð19Þ
72
H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
300
300
Confined jet flame, without radiation,
Tair= 20 oC, uo= 30 m/s, To= 20 oC
Confined jet flame, without radiation,
Tair= 20 oC, uo= 30 m/s, To= 20 oC
da,i/D=1
λ= 1.1
λ= 1.1
λ= 1.3
200
λ= 1.3
200
λ= 1.7
CH4
λ= 2
λ= 1.5
λ= 1.7
L f/do
λ= 1.5
L f /do
da,i/D=1
Numerical correlation
Numerical correlation
λ= 2.3
CH4
λ= 2
λ= 2.3
λ= 2.5
λ= 2.5
100
18.24*λ
-0.23
(1+L)
100
0.83
(5.5/fst)(ρο/ρst)1/2(1/λ0.23)
Biogas
Biogas
CO
(a)
CO
(b)
0
0
0
4
8
0
12
10
20
30
40
50
(1/fst )(ρ ο/ρst )1/2(1/λ 0.23)
λ -0.23 (1+L) 0.83
300
300
Confined jet flame, without radiation,
Tair= 20 oC, uo= 30 m/s, To= 20 oC
Confined jet flame, without radiation,
Tair= 20 oC, uo= 30 m/s, To= 20 oC
Numerical correlation
Numerical correlation
Numerical data
Numerical data
200
19.7 λ-0.23*(1+L)0.8*(da,i/D)0.06
L f/do
L f/do
200
CH4
100
1/2 −0.23
(5.5/fst)(ρο/ρst) λ
0.06
(da,i/D)
CH4
100
Biogas
Biogas
(c)
CO
(d)
CO
0
0
0
2
4
6
8
10
λ -0.23 (1+L) 0.8(da,i /D)0.06
0
10
20
1/2 −0.23
(1/fst )(ρ ο/ρ st ) λ
30
(d a,i /D)
40
0.06
Fig. 20. Prediction of dimensionless confined non-premixed flame length correlations in terms of: (a) L, k, (b) fst, qo, qst, k, (c) L, k, da,i/D, and (d) fst, qo, qst, k, and da,i/D.
Eq. (19) is formulated for the data in the following ranges:
0.055 6 fst 6 0.289, 1.1 6 k 6 2.5, da,i/D = 1 at Tair = To = 20 °C and.
The correlation can predict 100% of the numerical results within
error of ±8%. As a result, the flame length is reversely proportional
to both excess air number and stoichiometric mean mixture fraction. On the other hand, Fig. 20(c) illustrates a correlation of the
dimensionless flame length in terms of excess air number, air
demand (mass basis), air inlet diameter and kiln diameter, which
is derives as follows:
0:06
Lf
da;i
¼ 19:7k0:23 ð1 þ LÞ0:8
do
D
ð20Þ
Eq. (20) is correlated for the data in the following ranges:
2.46 6 L 6 17.3, 1.3 6 k 6 2.5 and 0.4 6 da,i/D 6 1 at, Tair = To = 20 °C.
This correlation can predict 83% of the numerical results within error
of ±11%. Correlation 3 is a modified shape from Eq. (1) where, the
effect of air inlet diameter is introduced in the correlation. Finally,
Fig. 20(d), shows a modified correlation from the formula demonstrated in Fig. 20(b) by introducing the effect of the air inlet
diameter, which is formulated as follows:
0:5 0:06
Lf
5:5 qo
1
da;i
¼
0:23
fst qst
do
D
k
ð21Þ
Eq. (21) is correlated for the data in the following ranges:
0.055 6 fst 6 0.289, 1.3 6 k 6 0.4 and 0.4 6 da,i/D 6 1 at Tair =
To = 20 °C. This correlation can predict 98% of the numerical results
within error of ±11%.
5. Conclusions
CFD simulation with Realizable k–e turbulence model is
employed in the present work to investigate the geometrical and
operational parameters of rotary kiln on the confined nonpremixed jet flames. Realizable k–e turbulent model is chosen as
the best turbulence model fit with analytical and experimental
results for non-premixed jet flames simulation in rotary kilns.
The simulation results show that the rotary kiln flame length and
peak flame temperature have strongly affected by fuel, excess air
number, air inlet diameter, air inlet temperature, and radiation
modeling.
Four general dimensionless correlations of the confined jet
flame length in terms of the rotary kiln geometry and its operating
parameters that investigated in the present study are developed.
These correlations can predict the simulation results within
acceptable errors. Moreover, it can be seen that the confined flame
length is directly proportional to air demand and air inlet area and
reversely proportional to both the excess air number and stoichiometric mean mixture fraction. In addition, the confined flame
length is higher than the free jet flame length.
There are shortcomings of the turbulence–chemistry interaction model, PDF approach are apparent in spite of the overall
agreement with experimental data. The model tends to underpredict for both temperature and mean mixture fraction, and overpredict the mass fractions of CO and H2 against mean mixture fraction
in axial locations along the flame. Furthermore the model overpredicts the flame length at higher fuel nozzle diameter.
H.F. Elattar et al. / Computers & Fluids 102 (2014) 62–73
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