Energy and Power En gi neering, 2011, 3, 607-615
doi:10.4236/epe.2011.35076 Published Online November 2011 (http://www.SciRP.org/journal/epe)
RANS and LES Modeling of the GE10 Burner
Vladimir L. Zimont1, Vincent Moreu1, Valerio Battaglia1, Roberto Modi2
1CRS4, Science and Technology Park Polaris, Pula, Italy
2GE Oil & Gas Nuovo Pignone, Florence, Italy
Recieved April 28, 2011; revised May 29, 2011; acce p ted June 10, 2011
Abstract
The paper presents 1) the numerical results of RANS (Reynolds Averaging Navier-Stokes) simulations for
two versions of the premixed combustion GE10 burners: the old one with non-premixed and modified one
with swirled premixed pilot flames; and 2) the numerical results of joint RANS/LES (Large Eddy Simula-
tion) modelling of the ONERA model burner and a simplified GE10 combustor. The original joint
RANS/LES approach is based on using the Kolmogorov theory for modelling sub-grid turbulence and com-
bustion intensity and using RANS numerical results for closure the LES model equations. The main conclu-
sion is that developed joint RANS/LES approch is the efficient timesaving tool for simulations both the av-
erage and instantaneous fields of parameters in gas turbine and boiler burners with premixed combustion.
Keywords: Turbulent Premixed Combustion, Gas Turbine Burner, Joint RANS/LES Simulation
1. Introduction
The proposed work is devoted to lean premixed combus-
tion technology, which is nowadays well established
within industrial gas turbine industry in order to reduce
nitric oxides (NOx) emission. The main numerical mod-
eling tool for industrial gas turbine combustion is RANS
codes, which yield averaged fields and integral charac-
teristics of the flow. The main part of this presentation is
devoted to RANS simulations of two variants of the
GE10 gas turbine combustor, which include 1) simula-
tions of the premixed combustion in the chamber; 2)
simulations of the preliminary partial mixing of gas fuel
and air; 3) simulations of the non-premixed pilot flame
(old version GE10); 4) premixed pilot flame (new ver-
sion GE10); and 5) air jets cooling system of the cham-
ber. In conditions of industrial gas turbines, instanttane-
ous combustion takes place in non-laminar (microturbu-
lent) and strongly wrinkled sheets with small-scale
structure, which fundamentally cannot be resolved by
model RANS and LES equations. In the presented simu-
lations, we used our Turbulent Flame Closure (TFC)
model [1-3], where this fundamental problem of model-
ing (“challenge of turbulent combustion”) is resolved in
the context of the Kolmogorov hypothesis of statistical
equilibrium of small-scale turbulent structures general-
ized for the case of turbulent combustion. This model
was already used for RANS simulations of the gas tur-
bine combustion and these results where presented in
IGTACE, Florida, 1997 (97-GT-395) published in [4]
and JPGC, 2001 [5]. (This mode l is now implemented in
the commercial codes Fluent and CFX.)
RANS results are important but not sufficient as non-
stationary characteristics of the flow are also important
in gas turbine applications. In academicals works, an
attempt to replace RANS tool by LES one is ongoing.
We think that “LES instead of RANS” in industrial ap-
plication is untimely and we proposed in [6] a joint
RANS/LES approach where the mean fields are simu-
lated by the RANS tool while the corresponding non-
stationary fields are simulated by the LES one using for
modeling some information from the preceding RANS
simulation. The paper [6 ] contains numerical illustrations
of this approach concerning mainly “academic” flames.
We achieved agreement between RANS and LES sub-
problems by using in fact the same combustion models in
both sub-problems. In this paper, we present numerical
results in the context of the joint RANS/LES approach
for gas turbine com b us tors.
We found support to our approach in the invited lec-
ture [7]. In the conclusions, the authors write: “The fu-
ture tools for gas turbine designs will be based on classi-
cal Reynolds Averages codes to predict main flows but
will also rely on Large Eddy Simulation tools coupled to
acoustic codes” (in our example both RANS and LES
sub-problems were stated in incompressible formulation).

V. L. ZIMONT ET AL. 608
We notice that proposed in this paper approach was dis-
cussed at the ASME ATI Conference in Italy “Energy:
production, distribution and conservation” in May, 2006
and was submitted to the proceeding of the conference,
but it was not published in a journal. We use this joint
RANS/LES approach in our work with the industries and
hope that this publication would be useful for engineers
working in the field modeling of industrial combustion.
2. Principles of Modelling and the Equations
In this section we briefly describe a physical model of
premixed combustion at strong turbulence and fast
chemistry and present the equations used for both RANS
and LES simulations.
2.1. The Physical Model
In gas turbines, typical turbulent Reynolds numbers
RetuL


 are large and typical Damkohler numbers
tch
Da

  are moderately large. Here, tLu


 and
2
ch L
S   are the turbulent and chemical times,

is
the molecular heat conductivity and
L
S is the speed of
the normal laminar flame, these parameters being used in
the model as the physico-chemical characteristics of the
reactant. In this case, the speed
f
U and width
f

of
the thickened flamelets are controlled by the statistically
equilibrium small-scale turbulence and the chemical time
t

, and it results the following expressions [1-3]:
12 32
,.
f
Lf L
UuDaSL Da



  (1)
The flamelet broadening takes place at43 Re
Lt
L 

 ,
i.e. when the size of the minimal eddies

is less than
the laminar flame width
L

. At the same time, the thic-
kened flamelet sheet is strongly wrinkled by turbulence
when
f
L

 and hence the condition for this combus-
tion mechanism is the following [1-3]:
3232 43
1Re
t
DaDa   (2)
So the mod el is val id at and ;
these conditions are common for large-scale gas turbine
combustors. For weaker turbulence, common for small-
scale laboratory burners, instantaneous turbulent com-
bustion takes place in a wrinkled laminar flamelet sheet.
Real combustion takes place in transient flames with
increasing width. The reason is that the large-scale wrin-
kles of the flamelet sheet remain statistically in non-equi-
librium at real residence time in the combustor. So the
width is controlled by the turbulent diffusion coefficient
t quite similarly to the nonreacting mixing layer. At
the same time, the small-scale winkles can be assumed
statistically in equilibriu m and as they give the main con-
tribution in the dimensionless flamelet sheet area
23
Re(10-10 )
t1
10Da 
D


0,
F
Fthe turbulent flame velocity


0tf
UUFF is
controlled by large-scale turbulence parameters (in the
model, they are the r.m.s. velocity pulsation u

and the
integral scale ) and the chemical time
L
14
:
tt
UuDa 

[1-3].
2.2. RANS Equations of the TFC Premixed
Combustion Model
We analyze premixed flames adopting the flamelet for-
malism in terms of the progress variable c, using the
known bimodal approximation of the PDF p(c) where the
width of the thin instantaneous reaction zone is ignored.
In this case, we have the following expressions:





1
,,
11
1,
1,
uub
ub
iiu ib
c
TTc Tc
CC cCc
 

 





,
(3)
where , ,,
uu iu
TC

and , ,,
bb ib
TC

are the density,
temperature and species concentrations in unburned (re-
actants 0c

) and burned (equilibrium products 1c

)
gases.
The turbulent combustion front, moving with speed Ut
and having increasing brush width controlled by Dt, is
described by the following transport equations:


341212 14
(),
(),
tut
tLu
ct c
DcU ca
UuS Lb





 


 

u
(4)
where

is an empirical constant equal to 0.5


H
valid for all fuels tested in [8,9] (methane 4, ethane
26
, propane 38 and even for hydrogen 2).
Equations (4) are combined with the average hydrody-
namic equations and the “
CH
CH CH
-k

” model.
2.3. The LES Equations of the TFC Model
The main idea of our joint RANS/LES approach [6] is to
combine LES and RANS in a two-stage process. The
first step consists of the RANS simulation which yields
the averaged flow field; the second step entails LES us-
ing the mean turbulent dissipation rate (,)
x
t

 obtained
from RANS to estimate the subgrid turbulence u


and
subgrid flame speed

0tf. LES gives non-
stationary images of a RANS simulation.
UUFF

The model LES equation can be cast as follows:



ut
ct uc
DcUc


 








(5)

V. L. ZIMONT ET AL. 609
lence model with wall functions. where the subgrid flame speed and subgrid transport co-
efficients are the following:
3.1. Premixing Channel



12
*121414
13 131343
(),
(), ().
tLu t
UAuSU La
ubD c







 
(6) This part is comprehensive of all the mixing channel up
to the combustion chamber inlet and goes upstream quite
before the system which controls the mass flow rate, as
shown in left. Taking into account the symmetries of the
problem, we have restricted the simulation to an angular
sector of 30 degrees. Inside this sector, there are two
half-winglet (lying on the cyclic boundaries), two fuel
nozzles and one openin g of the flow controller. We used
about 2 millions cells which was the maximum reasona-
bly acceptable for stationary computations with the
computational power a vailable.
Use of the Kolmogorov viscosity

, which in con-
trast to the commonly employed Smagorinsky model of
sub-grid tu rbulen ce does not dep end on time, makes LES
modeling more numerically favourable.
In our analysis, we paid special attention to the prob-
lem of consistency of the results of RANS and average
LES sub-problems, as it is a key point of the consistency
of joint RANS/LES approach. This correspondence is
based on using the same combustion model in both
sub-problems. A difference in the hydrodynamic p ictures
can be in the situation where “-k

” turbulence model is
not accurate. In the presented simulations it is not this
case.
When the flow controller is not fully open, it induces
some swirl component in the flow. For the open con-
figuration, the symmetry is higher and we could have
expected the flow to have a symmetrical pattern of 15
degrees opening. Nevertheless, as shown on Figures 1(b)-
(d), the numerical solution is very far away from the
symmetrical expectation, at least concerning the flow
investing the fuel nozzles. The winglet downstream has
the effect to strongly damp an eventual global swirl
component, but a departure of moderate strength from
the uniform axial velocity profile at the chamber en-
trance. Moreover, the fuel concentration also showed a
not so moderate dispersion, warning about an eventual
non-perfect mixing of the instantaneous fuel concentra-
tion. It is not yet known whether the discrepancy from a
symmetrical solution comes from numerical limitation or
is an indication that the symmetrical solution is really
unstable.
3. Burner Descriptions and Simulations
We present the result of RANS numerical simulations of
two versions on the NP GE10 gas turbine combustion
system, which use non-premixed and premixed pilot
flames. The examples presented not only refer to the
simulation of the combustor aerodynamics: the main and
pilot turbulent flames, cooling air jets and so on, but also
to the mixing process in the premixing channel and the
flow inside the premixed pilot burner. All the simulations
presented in this section have been performed with
StarCD (V.3.15) complemented with user subroutines.
Reynolds numbers are in the range 106 - 107 and the tur-
bulent flow has been simulated using the “- k

” turbu-
(a) (b) (c) (d)
Figure 1. (a): the mixing channel; (b) and (c): the pressure colored wall boundaries; (d) mixing coloured by the fuel concentration.

V. L. ZIMONT ET AL. 610
3.2. GE10 Burner with Non-Premixed Pilot
Flame
One forth of the combustion chamber has been simulated,
Figure 2. It includes 6 pilot burners at the chamber en-
trance and a variety of small secondary cold air inlet
disposed in rows and aimed at cooling the chamber wall.
It also includes one dilution air inlet close to the chamber
exit. The smallest inlet hole rows have been collectively
simulated as inlet annuli with the same mass flow rate.
The main flow inlet condition has been taken from the
mixing channel simulation with a cyclic replication to
obtain a 90 degree sector. The flame development is very
close to axial-symmetry. The small departures caused by
the main inlet condition and by the pilot burners do not
have large scale consequences. Intensive combustion takes
place in the relatively small part of the chamber. Figure
3 shows the mesh and 3D field of the temperature.
Chamber outlet
Numerical outlet
Cooling A
ir
Dilution Air
Pilot Fuel
Main Air Inlet
Fuel Inlet
Symetry Axis
Mixing HeadLiner
Lower part
Flame brush
(a) (b) (c)
Figure 2. (a): Sketch of the combustion chamber; (b): RANS simulations of the combustor GE10 colored by the temperature;
(c): the model source term with the flow streamlines and iso-contours of the progress variable.
(a) (b)
F
igure 3. (a): Mesh of the combustion chamber inlet and cap; (b): 3D isosurfaces of the temperature 1000-1400-1700-2000K.

V. L. ZIMONT ET AL. 611
3.3. GE10 Combustor with Premixed Pilot
Flame
To lower to NOx formation, GE decided to test a variant
of the combustor where the 24 non-premixed pilot burn-
ers were replaced by 4 bigger but essentially premixed
pilot burners. This procedure allowed having less fuel
burnt in stochiometric condition. The pilot burner has
been numerically tested in stand-alone condition. Figure
4, left, shows the fuel concentration that remains high
only on a very narrow central region in exit of the burner.
In Figure 4, centre, we see how the flame develops on an
axial plane. Figure 4, right, show the n ew pilot burn er as
been numerically tested inserted in the combustion
chamber cap. The global reacting flow field is somehow
disturbed by the presence of the new pilot, Figure 5, and,
obviously, is not any more close to axial-symmetrical.
Mainly, the recirculation region is heavily perturbed as it
is shown on Figure 6, left and centre. The interaction of
the hotter pilot flame with the colder main flame can be
appreciated in Figure 6, right.
4. Joint RANS/LES Modelling of Turbulent
Premixed Gas Turbine Combustion
To understand the non- statio nary features of the flow, we
performed a LES analysis of the burner. We used our
Joint RANS/LES approach [6] that strongly shortens the
LES analysis. The simulations were performed using the
Fluent package, a finite volume code which gives the
possibility to customize the models implemented. It has a
second order centered scheme fit to LES simulations
which require low dissipative numerical schemes.
In the next paragraphs, we present the validation of
this approach for a standard test case and then we show
results of the LES for a simplified geometry of the GE
burner previously described, not considering pilot system
and cooling jets.
4.1. The ONERA Standard Burner
To validate the Joint RANS/LES approach, we used a
standard test case known as the Moreau (ONERA)
burner [10]. It consists in a rectangular section burner
with the flame stabilized by a burned gas flow. The fuel
is a methane-air mixture with equivalence ratio equal to
0.84. The flow structures is mainly 2D due to the high
aspect ratio of the cross section, so it is possible to per-
form 2D simulations without losing accuracy in the re-
sults. In this test case, LES simulations are very sensitive
to inlet boundaries conditions for turbulence; in the pre-
sent work, we introduced a disturbance in the average
inlet velocity derived by the amplitude and length of the
upstream flow turbulent characteristics reported in [10].
The results of both RA NS and LES approac hes, Figure
7, show that the turbulent premixed flame has increasing
brush widt h and at the sam e time nearly co nstant speed, as
it can be seen by the practically constant angle with re-
spect to the main flow. In the figure measured in the ex-
periment mean temperature T and velocity U, and the
turbulent param eters (the rms fl uctuation of the velocity u'
and the integral scale L) have indexes “u” and “b” that
refer correspondingly to the flows of the unburned and
burned gases at the entrance of the burner. The upper
graph represents a result of the RANS simulation of the
progress variable : five isolines and two profiles in the
sections x = 0.1 and x = 0.5. The lower graph represent
the LES results: five isolines of the i nstantaneous progress
variable and following from averaging of the LES result
mean profiles for x = 0.1 and x = 0.5 and isolines of
the mean progress variables.
c

c

The isolines, which directly follow from LES model-
ing, clearly show the instantaneous stru cture of the flame
with the effects of the large scale vortices that convoluted
Figure 4. Left: premixed pilot burner with 2 coaxial swirling flows, coloured by the fuel concentration, the external flow ar-
rives already mixed in the burning region and only the central part keeps a high fuel concentration; center: pilot burner
flame with streamlines coloured by temperature; right: the computational mesh of the combustion chamber cap with the
ilot burner inserted. p

V. L. ZIMONT ET AL. 612
perature are not available to verify the accuracy of the
fluctuations resulting from the simulations, but observed
agreement between R ANS and a verage LE S data is a clue
of the reliability of the instantaneous data.
Figure 5. Field of equivalence ratio Φ with stream lines in a
section of the burner.
The lower graph in Figure 7 represent also a linear
distribution of a passive concentration z in the entrance
section x = 0, which was used in the simulations as a
boundary condition, and following from averaging of the
LES results the mean profilesin the section x = 0.1 and
x = 0.5. Performed in [6] comparative analysis of the
LES data for the progress variableand the passive con-
centrations z showed that in the flame the mean flux of
the passive concentration z is gradient, while the mean
flux of the progress variable c is predominantly counter-
gradient: it is gradient in the beginning of the flame and
then becomes counter-gradient in the main part of the
flame. The reason is that the flux of the passive concen-
z

c
and stretched the isosurfaces inside the flame. Compari-
son of the mean isolines and the profiles of the progress
variables simulated directly by the RANS simulation and
by averaging of the LES data (the uppe r a nd lower gra phs
in Figure 7) are similar. Figure 8 shows that the mean
profiles of the progress variable and the velocity, which
follow from the RANS and LES approaches, are close and
they are in reasonable agreement with the experimental
data from [10]. Measurements of r.m.s. velocity or tem-
Figure 6. Left: combustion chamber surface temperature. Centre: global flow temperature in the combustion chamber, trace
effects of the pilot burner, the cooling inlet rows and the dilution hole can be appreciated. Right: flow temperature and
streamlines on the plane containing the chamber and the pilot burner axes.
Inlet:
T
u
= 600K
U
u
= 60 m/s
T
b
= 2200 K
U
b
= 120 m/s
RANS
X(m) 1
0.50
0
0.1
y(m)
U
b
c = 0.1
c = 0.3
c = 0.5
c = 0.7
c = 0.95
0c

0.1
c

0.5
c 
y(m)
(a)
CH
4
+air

= 0.8
u
U = 8 m/s
L
u
= 5.4 mm
b
U
= 23 m/s
L
b
= 1.6 mm
LES
X(m)
1
0.5
0
0
0.1
0.1
c

0.5
c

y(m)
0.1
z

0
z

(b)
Figure 7. Average and instantaneous field of progress variable (a): RANS simulation, (b) corresponding LES.

V. L. ZIMONT ET AL.613
Figure 8. Comparison of axial velocity (left) and temperature (right) with experimental data.
tration is controlled only by turbulent diffusion, while the
flux of the progress variable is controlled by turbulence
and the gasdynamic mechanism: different pressure-dri-
ven acceleration in the flame of relatively heavy reac-
tants and light products. The balance between turbulent
and gasdynamic mechanisms controls observed in the
premixed flame transition from gradient to counter-gra-
dient flux of the reacting c. It is to remark that LES de-
scribe this transition without any additional model [6]. In
the RANS version of the TFC model we overcame this
problem by including of the gasdynamic contribution in
the model chemical source [2]. So the transport term in
Equation (4) is controlled only by gradient turbulent dif-
fusion and hence there is no need to model in practical
simulation the counter-gradient transport phenomenon.
4.2. Simplified Version of the GE10 Combustor
To test the Joint RANS/LES approach, we performed
LES of a simplified geometry of the first version of the
GE burner previously described (the cooling jets and the
pilot system were not meshed). We used Fluent code and
simulated a 60˚ degree section of the burner applying
periodic boundary condition at the lateral sections. LES
average shows good agreement with RANS data. The
non-stationary images of the flow field give an idea of
the effects of large scale vortices on the flame displace-
ments.
In Figure 9(a) RANS and instantaneous LES progress
variable are overlapping on a section of the burner to
show the convolu tion of the instantaneous reactin g zone,
which travels and is stretched by vortex shedding from
the geometrical step. Figure 9(b) clearly shows the tur-
bulent structure originated at the inlet step and how they
evolve along the flow. LES gives the possibility to un-
derstand the trend of variation of the flame shape chang-
ing operative conditions and boundary conditions. It is
possible to create 3D visualizations to see the effects of
the vortex structures in the circumferential direction as
shown in Figure 10. Our joint RANS/LES approach,
obviously, does not exclude the possibility to use LES
modeling, that is independent on the RANS one and
based on using common now Smagorinsky model of the
sub-grid viscosity. In this connection, we would like to
mention the paper [11], which is devoted to the com-
parison of predictions of the premixed flame anchoring
in the double cone gas turbine burner using independent
RANS and LES approaches based on our TFC combus-
tion model. We notice only that our joint RANS/LES
approach permits to reduce significantly computation
time of LES.
5. Conclusions
The presented results consist of two parts:
1) Comprehensive (wherever possible) RANS nume-
rical simulations of aerodynamic systems of two versions
of the GE10 gas turbine combustor (with nonpremixed
and swirled premixed pilot flames): cold mixing cham-
bers of the combustor and the premixed pilot burner,
aerodynamic of the main and pilot flames together with
an actual system of air cooling jets.
2) Numerical illustrations of our original joint RANS/
LES approach applied to the gas turbine combustion
(using the standard model situation and a simplified ver-
sion of the GE10 combustor), which can be an effective
and economical tool for the analysis of both stationary
mean and nonstationary fields of parameters.
All simulations where performed in the context of the
TFC combustion model, which, in particular yielded
reasonable agreement between RANS and LES sub-
problems.
Our general conclusion is that RANS simulations re-

V. L. ZIMONT ET AL. 614
(a)
(b)
Figure 9. 2D visualization of middle-section. (a): Contour lines of progress variable (from 0.1 to 0.9 step 0.2) for RANS
(brown) and instantaneous LES (blue); (b); (b) iso-surfaces of LES and the field of the vorticity.
Figure 10. 3D visualization. Two isosurfaces of the progress variable (left) and the field of the vorticity (right).
main a necessary (but not sufficient) tool for practical
numerical analysis of the gas turbine premixed combus- tion and the joint RANS/LES approach can be a useful tool for investigation of non-stationary characteristics of

V. L. ZIMONT ET AL.615
the flow, including unsteady combustion regimes. It
seems that complete replacement of the RANS tool by
the LES one is untimely at least for gas turbine applica-
tions.
6. References
[1] V. L. Zimont, “A Theory of Turbulent Pre mixed Combus-
tion at High Reynolds Numbers,” Combustion, Explosion,
and Shock Waves, Vol. 15, No. 3, 1979, pp. 305-311.
doi:10.1007/BF00785062
[2] V. L. Zimont, “Gas Premixed Combustion at High Tur-
bulence. Turbulent Flame Closure Combustion Model,”
Experimental Thermal and Fluent Science, Vol. 21, No.
1-3, 2000, pp. 179-186.
doi:10.1016/S0894-1777(99)00069-2
[3] V. Zimont, “Kolmogorov’s Legacy and Turbulent Pre-
Mixed Combustion Modelling,” In: W. J. Carey, Ed., New
Developments in Combustion Research, Nova Science
Publishers, New York, 2006, pp. 1-93.
[4] V. Zimont, W. Polifke, M. Bettelini and W. Weisenstein,
“An Efficient Computational Model for Premixed Turbu-
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Turbulent Flame Speed Closure,” Journal of Engineering
for Gas Turbines and Power (Transactions of the ASME),
Vol. 120, No. 3, 1998, pp. 526-532.
doi:10.1115/1.2818178
[5] V. Biagioli, L. Zimont and K. J. Sy ed “Modelling and Nu-
merical Simulation of Turbulent Combustion in DLE
Burners Based on a Turbulent Flame Speed Approach,”
International Joint Power Generation Conference, New
Orleans, 4-7 June 2001, pp. 1-14.
[6] V. L. Zimont and V. Battaglia, “Joint RANS/LES Ap-
proach to Premixed Flame Modelling in the Context of
the TFC Combustion Model, Flow, Turbulence and Com-
bustion”, Vol. 77, No. 1-4, 2006, pp. 305-331.
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