Energy and Power En gi neering, 2011, 3, 616-624
doi:10.4236/epe.2011.35077 Published Online November 2011 (http://www.SciRP.org/journal/epe)
Joint RANS/LES Modeling of Flameless Combustion
Vladimir L. Zimont, Valerio Battaglia
CRS4, Science and Technology Park Polaris, Pula, Italy
Recieved May 26, 201 1; revised July 15, 2011; accepted August 14, 2011
Abstract
We present our timesaving joint RANS/LES approach (we originally developed it for numerical simulations
of turbulent premixed combustion) to simulate flameless combustion with separate injection of gas fuel and
strong exhaust gas recirculation. It is based on successive RANS/LES numerical modeling where part of the
information (stationary average fields) is achieved by RANS simulations and part (instantaneous nonstation-
ary image of the process) by LES. The latter is performed using the RANS field of mean dissipation rate to
model the sub-grid turbulent viscosity in the context of the Kolmogorov theory of small-scale turbulence.
We analyze flameless combustion in the FLOX® combustor where we also simulate non-premixed flame
combustion used for preliminary heating of the combustor. Different regimes take place using different sys-
tems of air injection. We applied for both regimes the simple assumption of “mixed is burnt”. The main re-
sults are the following: 1) RANS simulations demonstrate for used two injection systems respectively more
compact flame and distributed flameless combustion; 2) There is agreement between RANS and correspond-
ing LES results: RANS and averaged LES profiles of the velocity and temperature are in reasonable agree-
ment; 3) LES modeling with Kolmogorov independent on time sub-grid viscosity reproduce instantaneous
image of the process including the vortex structures. Probably due to using an annular injector system for air
the instantaneous field of the temperature demonstrate significant irregularity in the beginning of the burner,
which in an animation looks like moving coherent structures; 4) In the joint RANS/LES approach the com-
puter time of the LES sub-problems is much shorter than classic LES modeling due to using time independ-
ent subgrid transport coefficients and avoiding long-continued simulations, which are necessary for average-
ing of instantaneous LES fields. Practically in our simulations time consuming of the LES sub-problem was
only several times lager then the RANS one and it makes this approach suitable for industrial applications.
Keywords: Flameless Combustion, Joint RANS/LES Modeling, FLOX Burner
1. Introduction
Combustion air preheating by flue gas heat recuperation
and using of a particular regime of diluted combustion
usually called in the literature “Flameless combustion ” or
“Flameless oxidation” is a promising technology for
saving fuel, reduction of the NOx emissions and avoi-
ding of unsteady combustion regimes [1-5].
Numerical simulations of the reacting flow inside an
industrial burner is a fundamental tool for the develop-
ment of new combustion systems that match the new
emission limitations and the efficiency targets, the fla-
meless combustion burner is one of the most promising
system for industrial combustors. For practical applica-
tions the modeling approaches is still based mainly on
the RANS formulation of the Navier-Stokes equations
and the same situation takes place in the flameless com-
bustion [1,6,7].
At the same time the RANS modeling presents some
intrinsic limitations in the analysis of the flow character-
istics as does not present the instantaneou s nonstationary
picture of the processes, the instantaneous structure of
the turbulent eddies and reaction zones and so on. It is a
reason why now in academic research there is a tendency
to replace stationary RANS simulation by nonstationary
LES tool. The latter has obvious fundamental advantage
of avoiding modeling of the large-scale processes. At the
same time LES arises fundamental and technical prob-
lems, which, in fact, renders replacing of RANS by LES
difficult or even practically impossible for numerical
simulations of industrial combustors with real geometry,
injection systems and so on.
The aim of this work was to propose our joint
RANS/LES approach for CFD simulations of the flame-

V. L. ZIMONT ET AL.617
less combustion. Originally this approach was aimed for
premixed flames [8,9] mainly applying to gas turbine
clean combustion [10]. Here we modify this approach for
simulation of the flameless combustion with separate
injection of gas fuel and air. We try to suggest an eco-
nomical tool for prediction of mean and instantaneous
fields by combining positive properties of both RANS
and LES approaches:
1) RANS is more economical in terms of computa-
tional resources and directly yields the required average
fields on sufficiently refined meshes. In this sub-problem
the large-scale turbulence is modeled statistically and we
use in our simulation the standard “” turbulence
model. For combustion modeling we assume infinitely
fast chemistry and use a presumed PDF function for the
passive concentration. Such approach is theoretically
justified for a stabilized flame combustion as well as for
stabile form of flameless oxidation (area C on the classi-
cal diagram of the stability limits for different combus-
tion modes, Figure 9, [1]) and we analyze only this op-
erating mode. A limit of this approach is that we cannot
describe the unstable mode when takes place lift off and
finally blow out of the flame when temperatures below
self-ignition [1] (area B of the diagram) as well as the
boundaries between the modes. In simulations we also
ignore the effect of radiation.
- 
2) In the LES sub-problem the large-scale structures of
the flow and the reaction zone are directly resolved, and
it is possible to analyze the subgrid smoothed instanta-
neous fields of the velo city, temperature, pressure and so
on as well as the location of the reaction sheet. The main
peculiarity of this approach is that LES modeling is
based on a previous RANS simulation namely the sub-
grid turbulence in LES is estimated by the Kolmogorov
theory of equilibrium small-scale turbulence using the
mean dissipation rate ε from the RANS simulation. In
this case the subgrid viscosity has no pulsations and the
time step can be significantly larger than at using tradi-
tional Smagorinsky model for subgrid turbulence.
It is significant that we do not need the time consum-
ing procedure of averaging of the LES results as the
mean fields follow directly from RANS simulations, and
it the larger time step makes the LES modeling more
friendly in comparison with known attempts to replace
RANS simulation with LES. Nevertheless for methodo-
logical purpose we compare in this paper the RANS and
averaged LES results to show the degree of agreement
between RANS and LES results.
All numerical results refers to the FLOX® burner.1 We
simulate not only the flameless combustion regime of
combustion but also the flame combustion one. The latter
is used at initial stage for heating of the burner, which is
necessary for realization of the flameless combustion.
Transition from the flame to the flameless combustion
regime is performed by changing of the air injection inlet.
The air is fed inside the burner through annular sections
coaxial to the fuel port. Flame combustion is generated
by an air inlet section around the fuel port. Shifting air
inlet to a section at a radial distance of 4 mm from the
fuel port, the inlet air mix with exhaust gas before mix-
ing with the fuel, generating flameless combustion; addi-
tional details about this burner is given in a following
section. Our simulation were performed in the context of
the commercial code Fluent so the RANS sub-problem
was simulated using the implemented equation for
non-premixed combustion. Additional equations for the
LES sub-problem where installed through the Fluent
subroutines.
2. The Basic Equations
Here we shortly describes the main equations of the
RANS and LES sub-problems and present data concern-
ing the numerical procedure: used numerical methods,
grids, computer system, time of simulations, used visu-
alization method for animations, which illustrate LES
results. We simulated the FLOX combustor with separate
injection of fuel and air, i.e. in fact both flame and flame-
less combustion regimes correspond to different realize-
tions of non-premixed combustion with exhaust gas re-
circulation. We assume in our simulations equilibrium
chemistry that is reasonable not only for stabilized flame,
but also for stable flameless combustion [1]. The second
simplification is that our modeling is based on using one
mixture fraction f, which is a conservative scalar quantity
that is characterized by instantaneous mixing.
The main idea of the joint RANS/LES approach is that
we combine RANS and LES 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 dissipation


,
x
t 
obtained from RANS to es-
timate the subgrid turbulence. The latter staged gives a
nonstationary image corresponding to the former statio-
nary one.
2.1. The RANS Sub-Problem
The Favre average equations in terms of
f
f

 

and


2
f
ffff 
 



are as follows:






tt

f
tuf  f

 


(1)






22
22
tt gtd
ft uf
f
CfCkf

 
 



 


 

(2)
1FLOX® is a registered trademark by WS GmbH, Renningen.

V. L. ZIMONT ET AL. 618
duces the computer time. The reason is that the rate-
of-strain tensor for the resolved scale ij has very
strong fluctuations in space and time and in some points
S



,t xt


is very small so in nonstationary LES numeri-
cal modelling the time step

 must be significantly
smaller than in the case of using Equation 4 as it is con-
trolled by minimal values of the sub-grid viscosity. In
accordance with our testing the computational time could
be five times shorter than the time requested by the clas-
sic Smagorinsky model.
with the following values of empirical constants:
0.85, 2.86,2.0
tgD
CC

.
In simulations we used a presumed PDF


pf
-

function. As a turbulence model we used the standard
“” one presented in the Fluent code. -

2.2. The LES Sub-Problem
As we mentioned above the main peculiarity of our LES
modelling is using for estimation of the subgrid turbu-
lence the Kolmogorov theory instead of traditional Sma-
gorinsky model. Assuming the existence of Kolmogorov
inertial spectrum

23 53
Ek C k 

 we can directly es-
timate the subgrid turbulent velocity and scale using

from a previous RANS simulation:
3. The Burner Configuration

 
13 13
1
1
11
d,
dd
uEkk
LkEkkEkk










,
 
(3)
We have simulated flame and flameless combustion in a
model FLOX® burner aimed for steel treatments or glass,
Figure 1. The fuel is natural gas and the nominal power
Qin is 13 kW. The burner has an inner chamber with a
radius of 0.02 m and a length of 0.41 m; the exhaust
gases flow in an outer coaxial tube with a diameter of
0.09 m and a length of 0.58 m. The operative pressure is
1 bar. The exhaust recirculation take place through three
windows in the inner tube. A sketch of the burner is
showed in Figure 1. In the operative mode the burner is
self-recuperative, the exhaust gases are used to preheat
the inlet air; this aspects is not directly simulated and air
inlet temperature is defined by previous experimental
analysis and set to 980 K. The injection system controls
the operative combustion mode of the burner that can be
switched from flame mode to flameless mode changing
inlet air ports. In fact flameless combustion depends on
the degree of exhaust gases recirculation that is con-
trolled by the configuration of air in let jets. The configu-
ration that we tested has the characteristics presented in
the Table 1, where air is the excess of air and e
R
k is
the recirculation factor

.
Rexhastfuel air
kmm m
and hence the subgrid turbulent transp ort coefficients are
equal to
13 13
.
tuL




 (4)
The field

x

 in Equation (4) was used from the
RANS simulation so the sub-grid transport coefficient
t

 depends only on coordinates

t
f
x 


t
and does
not depends on t. This stationary
x

 is used in the
non-stationary LES e q ua tion
 
 
tt
f
tu
f


 







f
. (5)
The sub-grid Favre average parameters in Equation 5
also calculated using the PDF -

function where corre-
sponding 2
f


 is estimated not from an sub-grid equa-
tion for the mixture fraction variance similar to Equation 4. Results of Numerical Simulations
2, but from an algebraic expression 22
var S
f
CL f

 


, Simulations were performed with the commercial code
Fluent 6.2 on a cluster of 8 processors. The computa-
tional domain is a 3D 120 degree angular sector with
periodic conditions at the lateral boundaries. Grid gen-
eration was made with Gambit and the final mesh has 1.5
M cells with hexahedral and tetrahedral elements.
where var and As we mentioned before,
using of Equation 4 for estimation of the sub-grid viscos-
ity instead of the Smagorinsky expression
0.5C.
S
L


12
22
tSij ij
CSS 
  [11] strongly re-

0.1
S
C

Figure 1. The sketch of the FLOX burner.

V. L. ZIMONT ET AL. 619
Table 1. Burner operative parameters.
Qin [kW] mFUEL [kg/s] eair [%] Aair in [mm2] kR [%]
10.42 2.67E–04 46 88 136
Special refinement has been necessary near the inlet jets
to resolve the strong velocity gradien ts in this region. As
explained in the description of Joint RANS/LES ap-
proach, the simulation results consist of stationary RANS
and unsteady LES.
4.1. RANS Simulations of Flame and Flameless
Combustion
The turbulent model for RANS is the classic “-

 ” tur-
bulence model with standard wall functions. The con-
vective scheme is second order upwind. The valu e of
and k

at the inlets derives by previous experimental
analysis. The burner was simulated in flame and flame-
less conditions. Figure 2 shows the temperature field
inside the burner for the both operative modes. It clearly
demonstrates that the flameless mode presents very
smooth temperature distribution compared to the flame
mode that produces a hot spot in the first part of the inner
tube. Figure 3 explains the reason of it: in the flame re-
gime the isosurface with average stoichiometric compo-
sition is concentrated near the beginning of the burner
while in the flameless regime this isosurface is more dis-
tributed along the chamber. Notice that relatively short
averaged stoichiometric contour in the case of the flame
mode is connected with large turbulent diffusion coeffi-
cient in this zone. At the same time dilution of air by
products strongly increases the stoichiometric coefficient
that results in very long averaged stoichiometrical con-
tour. Figure 4 demonstrates axial that results in very
long averaged stoichiometrical contour. Figure 4 dem-
onstrates axial qualitative behavior of the axis tempera-
ture for both combustion regimes which corresponds to
existing numerical simulations and experimental data
presented in [1]. We notice that due to assumption of
“mixed is burned” combustion in our simulations begins
in both regimes directly in the section of injectio n of fuel
and air. And only the intensity of combustion is different:
it is much lower in the case of flameless combustion in
comparison with the flame regime due to difference of
the injection systems. At the same time optical meas-
urements in [12] show that at the beginning of the burner
there is no detectable emission of the OH radical so
probably intensity of combustion in this zone is negligi-
ble that can be caused by influence of real chemical ki-
netics. We nevertheless think that the kinetic factor in the
case of stable form of flameless combustion as well as
for stabilized flame is not very significant in contrast to
intermediate unstable combustion [1]. It is clear that
boundary between these regimes as well as minimal fur-
nace temperature, which is necessary for combustion, are
controlled by both hydrodynamics and chemistry.
4.2. Comparison of RANS and Averaged LES
Numerical Results
For the LES sub-problem a second order centered
scheme was used for convective tem to reduce numerical
diffusion. The turbulence at inlets was reproduced creat-
ing signals coherent with the velocity fluctuation and
length scale given by experimental tests. The unsteady
Figure 2. Flameless (top) and flame (bottom) operative mode. Field of Temperature (K).

V. L. ZIMONT ET AL. 620
Figure 3. The stoichiometric isosurfaces.
Figure 4. Qualitative distributions of the axial.
formulation was second order implicit in time. In LES
sub-problem we concentrated in flameless mode to test
LES in this particular conditions.
Key moment of the joint RANS/LES approach is cor-
respondence of RANS and LES numerical results. We
can check it by comparison of RANS and averaged LES
results. For agreement between them, the turbulence
models in RANS and LES sub-problems must be con-
ceptually consistent as well as used in RANS simulations
PDF function


pf must be similar to it following
from LES in fact without modeling. Here we only notice
that used in the LES sub-problem Kolmogorov theory of
equilibrium small-scale turbulence [13] is also a basis of
used in the RANS sub-problem “” turbulence model
and the -

-

function is widely used as an acceptable ap-
proximation for


pf.
Temperature fields in Figure 5 demonstrate qualita-
tive agreement between RANS and averaged LES data
while Figures 6 and 7, which present RAN S and aver age
LES profiles of the axial speed and temperature, show
reasonable quantitative agreement between RANS and
LES results.
It is necessary to stress that in practical applications of
the joint RANS/LES approach time averaging of LES
results that needs long-continued simulations is not nec-
essary as the average fields follows directly from the
RANS simulations. We presented the comparison of the
RANS and average LES data only with a methodological
aim: to show reasonable agreement between RANS and
LES sub-problems.
4.3. LES Picture of the Flameless Combustion
LES data gives the opportunity to plot instantaneous
fields of the flow. We have used Tecplot to postprocess
LES data and produce the 2D and 3D pictures and also
animations, which give vivid image of the process.
Non-uniformity of the instantaneous field of the tempe-
rature at flameless combustion demonstrate Figures 8(a),
(b) and (c) where instantaneous 3D configurations of the
Figure 5. Top: RANS field of temperature. Bottom: averaged LES.

V. L. ZIMONT ET AL.621
Figure 6. Comparison between RANS and averaged LES profile of axial-velocity. RANS: , LES: +.
Figure 7. Comparison between RANS and averaged LES profile of temperature. RANS: , LES: +.
isotherms with the temperatures ,
and are presented: we see that gas with T =
1700 K concentrates near the wall in the back part of the
burner. At the same time gas with is pre-
sented in all inner tube while the pots with
mainly in the first part of the inner tube of the burner.
T = 1700 K1900 K
2100 KT = 1900 K T = 2100 K

V. L. ZIMONT ET AL. 622
(a)
(b)
(c)
Figure 8. Instantaneous field of temperature. (a) T = 1700 K;
(b) T = 1900 K; (c) T = 2100 K.
One instantaneous 2D image of simultaneous fields of
temperature and pressure gradient from the animation is
reproduced in Figure 9. We see from the field of the
temperature that there is some kind of wrinkled sheet
with higher temperature. The field of the pressure gradi-
ent demonstrates the vortexes structures. From the an-
imations we clearly see that fluctuations in space and
time of this sheet are controlled by turbulent eddies
moving with the flow. 3D animation of the isotherm
(one picture is shown in Figure 10 clearly
demonstrates that this isotherm consists in separate pie-
ces, which decrease in size and disappear moving along
inner tube of the burner.
T = 2200 K
These instantaneous pictures demonstrate significant
non-uniformity of instantaneous temperature. Known
experiments also demonstrate large non-uniformity, for
example, in an instantaneous profile of the temperature
presented in [12] the difference between maximal and
minimal temperature T600 K

. Instantaneous non-
uniformity of the temperature field especially at first part
of burner strongly depends on the used injector system. It
is obvious that peculiarities of instantaneous non-uni-
formity of the temperature, which have limiting effect on
Figure 9. Instantaneous field of temperature and gradient pressure on a 2D section.

V. L. ZIMONT ET AL. 623
Figure 10. 3D instantaneous surface with the temperature T
= 2200 K from the 3D animation.
the averaged fields, could strongly affect on NOx pro-
duction. So optimization of the injector system in the
context of the pollution problem is significant. We think
that this optimization would be more effective using nu-
merical data of the LES sub-problem. non-uniformity of
the temperature field especially at first part of burner
strongly depends on the used injector system. It is obvi-
ous that peculiarities of instantaneous non-uniformity of
the temperature, which have limiting effect on the aver-
aged fields, could strongly affect on NOx production. So
optimization of the injector system in the context of the
pollution problem is significant. We think that this opti-
mization would be more effective using numerical data
of the LES sub-problem.
5. Conclusions
1) We present the original timesaving joint RANS/LES
approach to simulate flameless combustion with separate
injection of gas fuel and strong exhaust gas recirculation.
It is based on successive RANS and LES numerical
modeling where some part of the information (stationary
average fields) is achieved by RANS simulations and
another part (instantaneous nonstationary image of the
process) by LES. The latter is performed using the
RANS field of the mean dissipation rate, which is used
for modeling of the subgrid turbulence and subgrid vis-
cosity in the context of the Kolmogorov theory of equi-
librium small-scale turbulen ce.
2) Timesaving is achieved 1) due to use of the subgrid
turbulent transport coefficient from the Kolmogorov the-
ory of small-scale turbulence instead of the traditionally
used Smagorinsky model (and it results in the possibility
to increase the time step in our LES approximately five
times) and 2) due to avoiding time averaging of LES data,
which need long-continued simulations, which are ine-
vitable in an approach “LES instead of RANS”. In our
RANS/LES approach ratio of necessary times for RANS
and LES sub-problems in practical application could be
the same order of magnit ude (practically ~1 - 5).
3) For validation of our approach we performed long-
continued large eddy simulations. Presented time aver-
aged LES data and RANS results are in reasonable agree-
ment.
4) Though RANS results for the flameless regime
demonstrate distributed combustion with smooth profiles
of the temperature and velocity, corresponding instanta-
neous LES fields show significant nonuniformity of the
temperature and clear documented large-scale eddies
especially at initial part of the burner. As these tempera-
ture surges can be significant for NOx emission the
burner and especially the injection system need optimi-
zation. We think that using for this optimization the re-
sults of the LES sub-problem could be more effective in
comparison with using of the RANS one.
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