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47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition
5 - 8 January 2009, Orlando, Florida
AIAA 2009-645
Large Eddy Simulation of the Turbulent Flow Field in a
Swirl Stabilized Annular Combustor
Jong-Chan Kim1 and Hong-Gye Sung2
Korea Aerospace University, Goyang, Gyeonggi, 412-791, South Korea
Dai-Ki Min3
Korea Aerospace Research Institute, Daejeon, Chungnam, 305-333, South Korea
and
Vigor Yang4
Pennsylvania State University, University Park, PA16802, USA
Flow difference between reacting and non-reacting flow in a swirl stabilized annular
combustor is investigated using 3D Large Eddy Simulation with level-set flamelet turbulent
combustion model. The combustor of concern is the LM6000, lean premixed dry low-NOx
annular combustor, developed by GEAE. Boundary conditions are based on experimental
data. Strong vortex breakdown in main stream, vortex ring proceeding downstream, and the
turbulent structure periodically oscillating have been observed. Heat release as a result of
combustion drastically increases the dilatation of density in primary combustion zone so that
the main swirl stream behind of a swirl cup stretched further downstream along shear layer
than non-reacting flow. The oval shape of core flow in cross-section to flow direction, which
clearly observed in non-reacting case, tends to be circle shape, and small vorticities in wide
range of non-reacting flow disappears, but the size of iso-vorticity is stretched to flow
direction in reacting flow.
I. Introduction
Modern gas turbines are operating under lean-burn conditions to reduce NOx emissions and tend to be much
more compact with low surface-to-volume ratio.
The tight regulation of pollutant emissions in a limited volume of combustor has led engine researchers to
carefully investigate the detail mechanism of emission. Since the most effective way to reduce NOx emission is to
decrease the flame temperature (Zel’dovich et al.1), through such techniques as water injection into the flame zone,
staged combustion, catalytic combustion, and lean premixed/pre-vaporized (LPP) combustion have been suggested
and evaluated for their effectiveness (Lefebvre2). Among the low emission techniques, lean premixed (LPM)
combustion is probably the most promising combustion technology for practical engines at the present time. In LPM
combustion, the lean fuel and air are premixed upstream in the combustor to avoid chemical reaction at
stoichiometric condition to reduce the flame temperature. Consequently, thermal NOx is reduced. However, lean
premixed combustion may become unstable to small change of inlet condition or small perturbation in the
combustor, which may lead to excessive thermal loads and incomplete burning of fuel. By using swirl injector,
flame stability and mixing efficiency are improved in small volume of combustor due to the shorten flame length
with strong toroidal recirculation zone.
The annular combustor is attractive to fit producing the required power in small size and compact combustor
because several ignitions are distributed at the combustor head without any side wall among igniters. So, the more
detail understanding of the dynamic flow, mixing, and combustion characteristics in the annular combustor is very
1
Research Assistant, School of Aerospace and Mechanical Engineering.
Professor, School of Aerospace and Mechanical Engineering, AIAA Senior Member. [email protected]
3
Principle Research Engineer, Engine Department, KHP Development Division.
4
Professor, Department of Mechanical and Nuclear Engineering, Fellow AIAA.
1
American Institute of Aeronautics and Astronautics
2
Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
important to improve engine power and efficiency for developing the small size and high energetic combustor. A
comprehensive understanding of turbulent characteristics in the annular combustor is the motivation of this study.
The large eddy simulation (LES) techniques may be viewed as the next step in addressing fluid mechanics
problems where RANS failed to deliver accurate results and the computer power requirement of DNS for solving
engineering problems far exceeds our current computer capabilities. LES technique computes the contributions of
large energy carrying structures to mass, momentum, and energy transfer, with the effect of small-scale turbulence
modeled either analytically or empirically. They are most suited for the study of gas turbine combustion dynamics,
since the flow field of concern is highly unsteady and dominated by turbulence motions that can be adequately
resolved computationally. LES technique is widely used to investigate complex turbulent flow structures in complex
thermal flow, in practical engineering application fields.
In treatment of turbulent reacting flow within the context of LES, combustion models are needed on the subgrid
scale. Several approaches have been proposed for the treatment of premixed flames. These approaches can be
classified into two categories: flamelet and non-flamelet models. The level-set model is one of the flamelet models,
which attempts to model the premixed flame from a geometrical point of view. The level-set or G-equation
originally proposed by Williams3. Several models have been developed based on the G-equation. Kim et al.4
considered the level-set function as a progress variable(i.e., G=0 and 1 for the fresh unburnt and burnt gases,
respectively). This model is simple and easy to implement, but, as is pointed out, the numerical difficulties and grid
resolution may incorrectly broaden the flame. Peters5 proposed a transport equation for the level-set function treated
as a distance function within the context of RANS. This approach, along with a laminar flamelet library and a
presumed PDF method, offers a more realistic treatment of premixed turbulent flame dynamics. The level-set
approach has been explored by Peters5 and tested by Herrmann6 and Nisson and Bai7 within the context of RANS,
and tested by Y.Huang et al.8 and Safta et al.9 within the context of LES.
The purpose of this study is analyzing the turbulent flow structure of a LPM annular combustor with swirlers
(GEAE lean premixed dry low NOx LM6000) by applying three dimensional LES turbulent model combined with
level-set flamelet library approach to take account of turbulent combustion.
II. Theoretical and Numerical Formulation
A. Governing Equation
The governing equations based on the Favre-filtered conservation equations of mass, momentum and energy in
three dimensions can be written as:
  u j

0
t
x j
(1)
sgs
 ui  (  ui u j  p ij )  ( ij   ij )


t
x j
x j
(2)
E ((E  p)ui ) 


u jij  qi  Hisgs ijsgs
t
xi
xi


(3)
Where i, j are the spatial coordinate index.  ij and qi are the viscous stress tensor and heat flux, respectively.
The unresolved subgrid scale(sgs) closure terms are given by:
 ijsgs  (  ui u j   ui u j )
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(4)
  )  ( pu  pu )
H isgs  (  Eui   Eu
i
i
i
(5)
 ijsgs  (u j ij  u jij )
(6)
The sgs shear stress is modeled using the compressible version of the Smagrinsky model suggested by
Erlebacher et al.10



 ijsgs  2 t   Sij 
Skk  ij  2 sgs
   k  ij
3  3
(7)
where Sij is the rate of strain tensor,
1  u u j 
Sij   i 

2  x j xi 
(8)
 t  CR ( D ) 2 (2 Sij Sij )1/ 2
(9)
k sgs  C I ( D ) 2 (2 Sij Sij )
(10)
where the dimensionless constants, CR and CI represent the compressible Smagorinsky constants. They are
determined empirically. The Van-driest damping function, D , is used to take into account for the inhomogeneties
near the wall.
D  1  exp(1  ( y  )3 / 263 )
where
(11)
y   u / and u is friction velocity.
The sgs energy flux,
H isgs , is modeled as
H isgs   
The sgs viscous work term,
 t  h
u j 1 k sgs 
 u j



Prt  xi
xi 2 xi 
(12)
 ij , is neglected due to its small contribution to the total energy equation. 11
The filtered total energy can be modeled as:
T
p u 2
E     C p (T ')dT '  k  k sgs
Tref
 2
where  
N
 Y h
k 1
k
0
f ,k
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(13)
B. Level-Set Equation for Premixed Turbulent Flame
A scalar-field G equation describing the evolution of a thin flame front can be written as.
 G
    uG   S L  G
t
(14)
The laminar flame velocity S L for an idealized planar configuration depends on pressure, temperature, and
mixture equivalent ratio3.
From a scalar field G equation, the Favre filtered G equation is modeled by a level-set equation:
 G
    u G    Dt k G   ST G
t
(15)
The SGS turbulent flame velocity ST modeled as12:
n

 u  
ST  S L 1  C   

 S L  

(16)
where u is the SGS turbulent velocity fluctuation, which is assumed to be
u  2.03 (  ( 2u )) 13. The
constants C and n can be specified as 2.0 and 0.7 respectively. 14
Equation(15) is valid only at the flame front. Since the distance function property of G is not preserved by the
level-set equation, this condition needs to be enforced through a re-initialization procedure. For this purpose, several
  1 and render the level-set function a signed distance.
methods have been proposed to enforce the condition G
The method developed by Sussman15 and Russo16 with a narrow banding strategy is used here. This procedure
involves solving the following equation to steady state:
G
 sgn(G 0 )(1  G ),

G (x, 0)  G 0 (x)
(17)
where sgn(G 0 ) is the sign function. The steady solution satisfies the condition of G  1 and has the same
zero-level as G 0 .
With the assumption that mean turbulent flame is an ensemble average or local volume average of different
laminar flamelets that fluctuate randomly around the mean flame position in the normal direction under the effect of
turbulence, the mean chemical composition of a premixed turbulent flame can be obtained using a presumed PDF
method along with a resolved flamelet structure. To this end, the probability of finding the instantaneous flame front
at a given position and instant needs to be presumed. A reasonable choice appears to be a Gaussian distribution.
As mentioned before, the filtered G equation is valid only for the flame front, but the entire flow-field. A re-
  1 , can be applied away from the flame and renders G a distance function normal to
initialized condition, G
the flame surface. Once G is defined, the turbulent flame thickness
lF ,t , which measures the flame front
fluctuations in the normal direction, can be defined as:
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 
lF ,t  G 2
where
G 
2
1/ 2
G G0
1/ 2
(18)
G G0
is a conditional variance evaluated at the flame front G  G0 . Note that the flame thickness
can only be defined at the flame surface. Then a Gaussian shaped PDF can be obtained:
P(G; x, t ) 
1
 2 (G ) 
1/ 2
2
0

 G  G (x, t )
exp  

2(G2 )0


2




(19)
Here the effect of strain on the flame structure and orientation between the instantaneous and mean flame
surfaces are not included.
The averaged mass fraction of species i can be calculated by

Yi (x, t )   Yi (G, t ) P(G, x, t )dG

(20)
However, in order to obtain a presumed PDF, information about the flame thickness or the G variance is needed.
The filtered flame thickness lF ,t is determined by the fluctuation of laminar flamelets under the effects of
unresolved small-scale turbulence. The turbulent flame thickness, can be computed via a transport equation or
simply modeled based on dimensional analysis. Here, the approach by Y.Huang et al.8 is adopted:
lF ,t  C0   lF
(21)
where C0 ( 1) is an empirical constant. The model suffers from a major limitation that the effects of smallscale motions on flame thickness are totally represented by the filter width, a situation rather remote from reality.
C. Numerical Schemes
The governing equations are solved numerically by means of a finite-volume approach. This method allows for
the treatment of arbitrary geometry. The spatial discretization employs a second order central-differencing scheme in
generalized coordinates. Temporal discretization is obtained using a second step Runge-Kutta integration scheme. A
multi-block technique is used to facilitate the implementation of parallel computation with message passing
interfaces at the domain boundaries11.
III. Computational Condition
The present study employs the LM6000 lean premixed swirl-stabilized annular combustor due to the available
experimental and previous research data. The LM6000 device involves a co-axial dual swirl (swirl/counter swirl)
configuration; it is being developed as operational hardware by GEAE for gas turbine applications and used to test
computational modeling capabilities in lean premixed turbulent combustion regime.
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102mm
3mm
Figure 1. Schematic of boundary condition and grid system4.
Figure 1 shows a schematic of the LM6000 combustor: a swirling injector with a diameter of 34mm and two
secondary air inlet slots. The swirl number S is about 0.56. Operating conditions are P0=6atm, T=640K, and
equivalence ratio of methane-air 0.56. The mean axial velocity based on inlet diameter is 110m/s 4. The fuel/air
mixture is assumed to be perfectly premixed before entering the combustor. Coarse grid and fine grid are tested
here; each total grid points are 2.3x106 and
Figure 2. Swirl inlet velocity profile17.
4.1x106 and the computational domain is
divided into 62 blocks and 88 blocks,
respectively. Each block is assigned to each
processor.
The specific inlet velocity profile for this
study is shown in Figure 2, based on
experimental
data
from
a
practical
swirl/counter-swirl combustor configuration.
This initial velocity conditions involve a peak
tangential velocity component located farther
away from the axis and a more moderate radial
gradient of the axial velocity. The maximum
value of tangential velocity is slightly greater
than the maximum value of axial velocity.
IV. Results and Discussions
A. Characteristics of Reacting and Non-reacting Flow in a Rectangular Combustor
Figure 3 and 4 show the instantaneous vorticity magnitude contours in the plane perpendicular to flow axis at
different locations downstream from the inlet plane in both cases of coarse and fine grid, respectively. Three
important characteristics of swirling flow are visualized: diversity, processing but decreasing strength of vortex, and
vortex breakdown. The strong vortex breakdown occurs at the shear layer of main swirling flow. Large scale eddies
dissipate at the wall as well as downstream of main flow. It is noted that a typically tilted oval-shaped vortex ring is
observed downstream of the inlet, which is the unique flow characteristics of annular combustor with counter
swirlers. In case of fine grid, smaller scale eddies are observed than coarse grid case but the overall flow structures
are very similar which was described in section C below in this paper.
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Figure 3. Instantaneous vorticity magnitude contours Figure 4. Instantaneous vorticity magnitude contours
of non-reacting flow in fine grid.
of non-reacting flow in coarse grid.
Figure 5. Instantaneous vorticity magnitude contours of reacting flow.
Figure 5 shows vorticity magnitude contours of reacting flow. The shear layer at the swirl inlet is more clearly
observed in reacting flow than non-reacting flow(Figure 4). Also, the vortex strength of the non-reacting flow at the
corner recirculation zone weakens while the vortex at the center recirculation zone becomes intense. The vortex
structure with same vorticity magnitude tends to be enlarged and stretched to flow direction in compared with nonreacting flow.
Figure 6 shows the streamlines over averaged vorticity magnitude contours. The corner recirculation zone and
central toroidal recirculation zone are clearly observed. This is a typical phenomenon in swirling flows which is
occurred at approximately swirl number 0.6.
Figure 7 shows pressure fluctuation in both the non-reacting and reacting flow at 6mm downstream of swirl inlet.
The swirl flow in confined geometry produces acoustic pressure oscillation in periodic. The oscillatory frequency of
acoustic wave, vortex ring, flame fluctuation, and so on will be analyzed using data processing techniques. The
oscillations must be controlled because the resulting vibration can reduce the lifetime of the engine. The period of
oscillation of reacting flow is shorter than that of the non-reacting flow, which resultant from the sonic speed
increased by combustion.
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Figure 6. Averaged vorticity magnitude contours of coarse and fine grid.
Figure 8 shows a three dimensional view of iso-surfaces
of instantaneous vorticity at ω=36,000s-1 over a typical
periodic cycle. The swirl structures grow and breakdown to
axial distance. The somewhat organized structures are
620
highly stretched toward azimuthal direction near the
breakdown region. The small size vorticities moving from
the vortex core to top- and bottom-wall collide on the walls
and are squashed to flow direction on the walls, but the
600
vorticities moving to the right- and left-surface smoothly
dissipate because the left- and right-surface are fluid
boundaries.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
In case of reaction, heat release affects on temperature
Time (ms)
and density distribution which changes velocity magnitude
Figure 7. Pressure fluctuations of bothe non- and flow structure as well as.
reacting and reacting flow.
640
Pressure (kPa)
Non-reacting
Reacting
(a)
 =0
(b)
 = 45
(c)
 = 90
(e)
 = 180
(f)
 = 225
(g)
 = 270
Figure 8. Temporal evolution of iso-vorticity surface at ω=36,000s
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(d)
 = 135
(h)
 = 315
-1
Figure 9. Temperature and density contour of reacting flow
Figure 9 shows temperature and density contours of reacting flow. Fuel –air mixture gas from swirl inlet reacts
on both surfaces, called bifurcated flame, so that temperature rapidly increases near the flame surface, inducing large
volume expansion and re-distribution of velocity fields as specifically explained below.
Figure 10 represents absolute velocity magnitude of both non-reacting and reacting flow. The velocity of fuel-air
mixture in reacting flow strongly expands along swirl shear layer and even contacts on the top- and bottom-wall
surface. The volume expansion of combustion gas surrounding the fuel-air mixture prevents the processing of the
mixture’s axial velocity, turns the flow stream direction, and finally stretches the mixture velocity to shear layer.
Both of axial and radial velocities of reacting flow strongly develop as the same reasons above. However the
(a) Non-reacting flow
(b) Reacting flow
Figure 10. Absolute velocity magnitude of non-reacting and reacting case (m/s)
(a) Axial velocity
(b) Radial velocity
(c) Tangential velocity
Figure 11. Axial, radial, tangential velocity contours; Left : Non-reacting, Right : Reacting
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tangential velocity of reacting flow somewhat becomes mild because of the conservation of momentum in three
dimensions (Fig. 11).
Figure 12 shows instantaneous iso-vorticity surface. The main-stream vorticity magnitude of the reacting field is
smaller than that of non-reacting but the vortex sizes becomes enlarged because of the dilatation of combustion gas
and its increased viscosity.
(a) Non-reacting, ω=31,000-1
(b) Reacting, ω=25,000-1
Figure 12. Instantaneous iso-vorticity surface
B. Flow Structure of Real Annular Combustor
The turbulent flow structures in a geometrically equivalent annular combustor, i.e. real shape combustor, have
been numerically simulated to investigate the interactions among multi-injectors. It has the same cross-sectional area
as the rectangular shape combustor, and
involves the same inflow and other
boundary condition data as shown in
Fig. 13.
Figure 14 shows the instantaneous
iso-vorticity field in annular combustor
with muti-injectors. In general overview,
the mean flow fields of a real shape
combustor are similar as the rectangular
model combustor. However, the strong
vortex breakdown occurs along the
impinging surfaces of two neighbor
counter injectors so that the oscillatory
pressure propagates inside of the
Figure 13. The geometrically equivalent model annular combustor
combustor. The data analysis will be
continued.
C. Comparison with Experimental Data and Previous Research
The three directional velocities such as axial, radial, and tangential velocities are compared with experimental
data and previous researcher’s results to validate this study. In Fig.15, the solid lines are the result of the current
studies while the symbols and the dashed lines are experimental data and the results of previous research
respectively. In case of reacting flow, the axial velocity increases at approximately 35mm downstream to the axis
due to the flow expansion through the flame surface, which is in good agreement with experimental data and
previous research. The flow distributions of real annular shape are not much different from rectangular shape results.
The simulation results are in good agreement with experimental data.
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Figure 14. Flow interaction between injectors
120
Reacting Fine
Non-reacting Fine
Annular Non-reacting
Non-reacting (Ref.4)
Reacting (Ref.4)
Reacting-Exp
100
80
Reacting Fine
Non-reacting Fine
Annular Non-reacting
Non-reacting (Ref.4)
Reacting (Ref.4)
Reacting-Exp
100
80
U (m/s)
U (m/s)
60
60
40
40
20
20
0
0
-20
-20
0
20
40
60
80
100
120
140
-60
160
-40
-20
0
20
40
60
Y (mm)
X (mm)
(a) Axial velocity along the x-axis
(b) Axial velocity along the y-axis
150
Reacting Fine
Non-reacting Fine
Annular Non-reacting
Non-reacting (Ref.4)
Reacting (Ref.4)
Reacting-Exp
40
50
Ut (m/s)
20
Ur (m/s)
Reacting Fine
Non-reacting Fine
Annular Non-reacting
Reacting (Ref.4)
Non-reacting (Ref.4)
Reacting-Exp
100
0
0
-50
-20
-100
-40
-150
-60
-40
-20
0
20
40
60
-40
-30
-20
-10
(c) Radial velocity along the y-axis
0
10
20
30
40
Z (mm)
Y (mm)
(d) Tangential velocity along the z-axis
Figure 15. Comparison of the velocities of real shape with experimental data and previous research4
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V. Conclusion
Non-reacting and reacting turbulent flow characteristics of a lean-premixed swirl stabilized annular combustor
have been investigated by LES turbulent model, combined with flamelet library approach to take account of
turbulent combustion. MPI parallel computation technique has been applied to simulate very complex and massive
calculation within computation time for engineering application.
On the swirl number 0.56, in case of non-reacting flow, the strong vortex breakdown was observed at the shear
layer around the main flow field which weakens as swirling down to the axial axis. Both central and corner
recirculation zones are clearly observed. As the main flow field is expanded by a counter swirl, the flow pattern is
reconfigured from O-shape to Oval shape in the area influenced by neighbor counter-swirler. This oval shape and its
unique characteristics of annular combustor with a counter swirler, cannot be observed with a can-type combustor.
In case of chemical reaction, the main stream velocity near the inlet and exit velocity of the combustor was
increased by the dilatation effect induced by combustion. Corner recirculation velocity of the reacting flow was
smaller than that of the non-reacting flow, but central recirculation velocity of the reacting flow was larger than that
of the non-reacting flow. The shear layer boundary near the swirl inlet was more clearly observed in comparison
with non-reacting case.
In both the non-reacting and reacting flow, the turbulent structures oscillate periodically in confined annular
combustor. The strong periodic vortex ring may be the source of combustion oscillation. However, the oscillation
period in reacting flow is shorter than that of non-reacting flow because of more faster sonic velocity in reaction
flow.
The real shape combustor has been simulated in order to investigate the interactions among multi-injectors. The
mean flow fields of real shape combustor are very similar to the rectangular model combustor. However, the
turbulent structures were not compared with the experimental data due to the lack of information available from
previous researches. However, vortex breakdown is clearly observed along the impinging surface of counter swirl
injectors which are located left and right of its center.
In resultant, most of the results of the present study are in good agreement with experimental data and previous
researches.
Acknowledgments
This study has been supported by the KARI under KHP Dual-Use Component Development Program funded by
the Ministry of Knowledge Economy, Republic of Korea and TERA TEC for the supports of TERA CLUSTER
resources.
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2
Lefebvre, A.H., “The Role of Fuel Preparation in Low-emission Combustion,” ASME J.Eng Gas Turbines Power, Vol.117,
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3
Williams, F.A., Combustion Theory, Addison-Wesley Publishing Company, 1985
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Kim, W.W., Menon, S., Mongia, H.C., "Large-Eddy Simulation of a Gas Turbine Combustor Flow," Combust. Sci. and
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5
Peters, N., Turbulent Combustion, Cambridge University Press, 2000
6
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Thesis, RWTH, 2000
7
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8
Huang, Y., Sung, H.G., Hsieh, S.Y., Yang, V., “Large Eddy Simulation of Combustion Dynamics of Lean-Premixed SwirlStabilized Combustor,” Journal of Propulsion and Power, 2003, Vol. 19, No. 5.
9
Safta, C., Alabi, K., Ladeinde, F., Cai, X., Kiel, B. and Sekar, B., “Level-set Flamelet/Large-Eddy Simulation of a Premixed
Augmentor Flame Holder,” AIAA Meeting Paper, AIAA 2006-0156
10
Erlebacher, G., Hussani, M.Y., Speziale, C.G., Zang, T.A., “Torward the Large Eddy Simulation of Compressible
Turbulent Flows,” Journal of Fluid Mechanics, Vol.238, pp.155-158, 1992
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