Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
222 In order to get an equivalent comparison, the 3D grid
elements are distributed in the same way as for the 2D grid. The inlet velocity profile for the pilot and burner is
positioned at the exit plane of the burner. Inlet turbulence parameters for
k and ε were either
estimated values, constant or linearized values based on measurements [16]. At the outlet, the surface
surrounding the co-flowing air and the surface opposite of the burner, a constant pressure is applied as boundary
condition. Material and process data used for the simulations are summarized in Table I. The equations are
solved using the ANSYS-FLUENT CFD package. The thermo physical data of FLUENT are used. To account
for detailed chemical kinetic the Gri-Mech 3.0 mechanism was implemented, considering 53 species
and 325 reactions [20].
For all simulations presented in this paper, a second order upwind scheme was used for the conservation
equation of momentum, turbulent kinetic energy, turbulent dissipation rate, mean mixture fraction and
mean mixture fraction variance. The Presto scheme was used for interpolation methods for pressure [13]. Simple
was chosen for the coupling between velocity and pressure [13].
V. Results and Discussions
In the present study, the stationary laminar flamelet approach is applied and the turbulence flow field for the
Sandia Flame D is predicted with the realizable k-
ε model in 2D case and RSM in a 3D case. The effect of
the assumption of isotropic turbulence predicted with the k-
ε model and the possibility of an anisotropic turbulence calculation with RSM as well as the change of
the empirical turbulence constant C
2
are studied. The effect of radiation is studied using the DTRM and the
DO radiation model. The results are compared to experimental data [15], [16].
In most cases, inlet values for k and
ε have to be estimated.
For the Sandia Flame D measurements of the turbulent kinetic energy profile at the burner exit inlet of
the simulation domain is available. A short study has been performed to show the effect
on the flame temperature with various turbulence inlet conditions. The conditions have been chosen as an
estimated value turbulent intensity of 10 , as a constant value mean value of k from the measured
profile and as a linearized profile of the measured turbulent kinetic energy.
The effect of different turbulence inlet boundary conditions is shown in Fig. 4.
Here, the temperature along the center line of the flame is compared. In the case of the estimated values,
the predicted temperature is farthest from the experimental data.
The constant value and linearized profile based on measurements show better agreement, mainly in the near
region of the burner. Both of them give similar results. In this simulation,
radiation was neglected and the realizable k-
ε was chosen as turbulence model.
500 1000
1500 2000
20 40
60 80
100 xd[-]
T em
p era
ture [
K ]
Experimental Data; C2 = 1.9 Estimated Value; C2 = 1.9
Constant Value; C2 = 1.9 Linearized Profile; C2 = 1.9
Fig. 4. Comparison of the axial temperature profiles with experimental data for different turbulence boundary conditions [15]. Here, x is the
axial distance from the burner nozzle and d is the diameter of the nozzle
Fig. 5. Predicted temperature field for the Sandia Flame D in 2D axisymmetric
It seems that a constant value for k and
ε as inlet condition is adequate, but it has to be selected carefully.
The predicted temperature field of the flame in 2D axisymmetric is shown in Fig. 5. A comparison of the
axial temperature is given in Fig. 6. Radiation is not considered in this case. Realizable
k- ε gives a slightly
lower maximum temperature than RSM. Measurements have shown anisotropic turbulence in
this flame [16]. The estimation, that the consideration of the known
anisotropic turbulence in this flame with the RSM model can reproduce the measured temperatures, was not
achieved. Both models, realizable k-
ε and RSM with standard turbulence constants, were not able to reproduce
the measurements exactly. The change of the proposed turbulence constant
C
2
for both turbulence models to a value of
C
2
= 1.8, produces a change in the axial
temperature curve as can be seen in Fig. 6. The value of
C
2
was recommended for the standard k-
ε model [15]. However, for the realizable
k- ε and RSM it seems to
have an important effect on a better prediction of turbulent non-premixed jet flames as well.
The change of the constant leads to a later increase of temperature. Realizable
k- ε and RSM with C
2
= 1.8
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
223 predict the measurement data better until the position
xd = 50. Subsequently, the decline of temperature is lower than in the experiment.
These results demonstrate that realizable k-
ε in 2D and RSM in 3D, with the turbulence constant
C
2
= 1.8, are able to predict the flame temperature more accurate as
using the standard turbulence constants.
Fig. 6. Comparison of the axial temperature profiles with experimental data [15]. Here, x is the axial distance from the burner nozzle and d is
the diameter of the nozzle
The reason for the effect of changing the turbulence constant
C
2
is shown in Fig. 7. The simulations using the standard turbulence parameters over-predict the turbulent
kinetic energy in the flame center. A decrease of C
2
in both cases decreases the maximum of the curve. Also a
slight shift to the right can be observed. C
2
is a factor for a sink in the turbulence dissipation equation. A decrease
of that factor leads to a lower reduction of dissipation and a faster reduction of turbulent kinetic energy. Thus,
C
2
is the amount of lost rotational energy due to friction. The mixing of fuel and oxidizer is strongly coupled
with turbulence. The lower turbulence decreases the mixing of methane and air. Therefore, the consumption
of methane is slower. Representatively, the distribution of mass fraction of methane along the centerline is
shown in Fig. 8. The results of all simulations which has been performed show a faster decrease of methane mass
fractions in comparison to the measurements. The fastest consumption of methane occurs with the predictions by
the use of the standard values for
C
2
= 1.9 and C
2
= 1.92 for realizable
k- ε or RSM, respectively. The complete
methane concentration is consumed at the position xd = 40. The experimental data and the simulations with
C
2
= 1.8 show the total consumption at the position of xd = 50.
The radial profiles of temperature at the position xd = 45 have the same tendency as the axial profiles. By
changing the turbulence constant, the predicted curves agree better with the measurement data Fig. 9.
However, the accordance is less than that for the axial profiles. The calculations predict a later temperature
decay along the radial position
xd = 45. In case of C
2
= 1.8 the decline is the same as that for the
measurements. In contrast, the predicted curves with standard values for the turbulence constants, the decrease
in temperature is lower. It has to be mentioned that due to the axial shifted
temperature peak Fig. 6, the predicted temperature at the axis is lower than experimental data show at this
position. To account for radiation, two models have been
evaluated. The Discrete Transfer Radiation Model DTRM and
the Discrete Ordinates Model DO. In this evaluation the 2D axisymmetrical domain together with the
realizable turbulence model are used. To achieve accurate results with the DTRM model a
high number of rays in Phi and Theta direction are necessary.
20 40
60 80
20 40
60 80
100 T
u rb
ki ne
ti c
en er
g y
[m ²
s² ]
xd [-]
Experimental Data 2D realizable k-epsilon, C2 = 1.9
2D realizable k-epsilon, C2 = 1.8 3D RSM, C2 = 1.92
3D RSM, C2 = 1.8
Fig. 7. Axial turbulent kinetic energy profiles compared with experimental data [16]. Here, x is the axial distance from the burner
nozzle and d is the diameter of the nozzle
0.00 0.05
0.10 0.15
10 20
30 40
50 60
CH
4
M as
s F ra
ct ion
[-]
xd [-]
Experimental Data 2D realizable k-epsilon, C2 = 1.9
2D realizable k-epsilon, C2 = 1.8 3D RSM, C2 = 1.92
3D RSM, C2 = 1.8
Fig. 8. Axial methane mass fraction compared with experimental data [15]. Here, x is the axial distance from the burner nozzle and d is the
diameter of the nozzle
500 1000
1500 2000
2 4
6 8
10 T
em p
er at
u re
[ K
]
rd [-]
Experimental Data 2D realizable k-epsilon, C2 = 1.9
2D realizable k-epsilon, C2 = 1.8 3D RSM, C2 = 1.92
3D RSM, C2 = 1.8
Fig. 9. Radial temperature profiles at xd = 45 compared with experimental data [15]. Here, r is the distance in radial direction and d
is the diameter of the burner nozzle
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
224 This leads to long computation times. In Fig. 10 a
coordinate system for the DTRM model is shown. At each radiating face, rays are fired at discrete values of the
polar and azimuthal angles. The standard values, 2 for the Phi angle and 1 ray in Theta direction, given in the
FLUENT Software, are not recommended. This configuration is not accurate enough and causes an
overpredicted heat release from the flame as can be seen in Fig. 11.
Fig. 10. Ray defined by the polar and azimuthal angle for the DTRM [13]
500 1000
1500 2000
20 40
60 80
100 xd [-]
T em
p er
at u
re [
K ]
Experimental Data Phi = 2; Theta = 1
Phi = 30; Theta = 4 Phi = 60; Theta = 8
Fig. 11. Axial temperature profile for different amounts of rays in Phi and Theta direction using the DTRM model compared with
experimental data [15]. Here, x is the axial distance from the burner nozzle and d is the diameter of the nozzle
The optimal result has been reached with 60 rays in Phi and 8 rays in Theta direction. With this configuration
the minimal deviation from the measurements was achieved.
The same study has been performed using the DO model. Here, already good results can be achieved with
15 rays in Phi direction and 8 rays in Theta direction. The DTRM model and the DO model give similar
results, but for the DO model fewer rays are necessary. Although the DO model is more complex and more
computational intensive, due to less rays the DO model results in a faster calculation in this study. The
comparison of the axial temperature profiles using the DTRM and the DO model are shown in Fig. 12. Due to
radiation a higher heat release after the maximum temperature is given.
VI. Conclusion
