The Trapped Vortex Combustor (TVC) is a challenging configuration where flame stabilization is achieved through the presence of a cavity. The present work describes an unsteady non-reacting and reacting annular TVC flow studied with Large-Eddy Simulation and Immersed Boundaries Method. The combustion model is based on tabulated chemistry associated with a presumed PDF. The effects of local strain rate and of heat losses are included in the modelling. The simulations are compared with experimental results and the performance of the modelling closures is discussed

DOMINGO, Pascale

MERLIN, Cindy

VERVISCH, Luc

I-Revues

20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
Large Eddy Simulation of a Trapped Vortex Combustor
C. Merlin, P. Domingo, L. Vervisch a
a. CORIA-CNRS INSA de Rouen, Campus du Madrillet, 76801 Saint Etienne du Rouvray cedex
Re´sume´ :
Le concept de Trapped Vortex Combustor repose sur une nouvelle architecture de chambre de combus-
tion ou` la stabilisation de la flamme est assure´e par la pre´sence d’une cavite´. Cette e´tude est consacre´e
a` la caracte´risation de l’e´coulement re´actif et non re´actif dans une chambre annulaire de type TVC a`
l’aide de simulations des grandes e´chelles (SGE) couple`es a` une me´thode de frontie`res immerge´es. La
prise en compte de la combustion est base´e sur une me´thode de tabulation de la chimie de´taille´e pour
des flammes de pre´me´lange, associe´e a` des fonctions de densite´ de probabilite´s pre´sume´es (PCM-FPI
pour Presumed Conditional Moments-Flame Prolongation of ILDM). Les re´sultats de ces simulations
sont confronte´s a` des re´sultats expe´rimentaux permettant ainsi l’e´valuation des diffe´rents mode`les et
l’explication du me´canisme de stabilisation.
Abstract :
The Trapped Vortex Combustor (TVC) is a challenging configuration where flame stabilization is
achieved through the presence of a cavity. The present work describes an unsteady non-reacting and
reacting annular TVC flow studied with Large-Eddy Simulation and Immersed Boundaries Method.
The combustion model is based on tabulated chemistry associated with a presumed PDF (PCM-FPI)
for premixed flames. The simulations are compared with experimental results and the performance of
the modeling closures is discussed along with the analysis of the stabilization mechanism.
Mots clefs : Large Eddy Simulation, Turbulent combustion modeling, Trapped Vortex
Combustor
1 Introduction
Combustion stability may be achieved with recirculation zones providing a continuous source of igni-
tion, through the mixing of hot products with the incoming air and fuel mixture. To generate these
recirculation zones, swirl vanes, bluff bodies and rearward facing steps are commonly used. As opposed
to conventional combustion systems which rely on swirl stabilization, the Trapped Vortex Combustor
(TVC) is a challenging configuration where flame stabilization is achieved through the presence of a
cavity. The flow is then trapped within a cavity where the reactants are mixed. This challenging confi-
guration provides high combustion efficiency, low emission and low pressure drop. Some experimental
and numerical studies have also been devoted to the effective use of cavities to suppress combustion
instability [13, 8, 10, 2]. Generally, a bluff body is located upstream to initiate shear layer instabilities
which are then trapped in the cavity region and provides a wake to help the flame stabilization.
The numerical study of a non rectangular configuration with a bluff body is possible in a non-structured
mesh solver. Another approach, retained in this paper, is to keep a structured mesh with the addition
of the immersed boundary concept. Immersed Boundary Methods employ cartesian meshes that do
not conform to the shape of the body in the flow and modify the governing equations to incorporate
the boundary conditions. First introduced by Peskin [14], IBMs involve either continuous or discrete
forcing approaches. Only discrete forcing approach preserves good performance at high Reynolds
number. A ghost-cell method (a discrete forcing approach) is used here with a sharp boundary and
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20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
with a modification of the computational stencil and an extrapolation scheme to deduce the state
variables in cells bordering the computational domain.
The present work describes an unsteady non-reacting and reacting annular TVC flow studied with
Large Eddy Simulation and compared to experimental measurements [3]. In the following sections, the
numerical method as well as the combustor configuration are briefly described. The cold flow properties
are first compared with their experimental counterparts to assess the ability of the immersed boundary
to deal with complex compressible flows. The flame dynamics is then investigated with a combustion
model based on detailed tabulated chemistry associated with a presumed PDF (PCM-FPI).
2 Combustor configuration and computational details
As shown in Fig.1, the cylindrical combustion chamber consists of a 22 mm long cavity. Cavity flows
are often categorized depending on the length to depth ratio L/D. The experiment includes a deep
cavity of lenght-to-depth ratio of L/D=0.8. Flame holders (rods immerged in the main flow) are added
to enhance the mixing of the burnt gases with the main flow in the wake region and to improve the
main flame stability. The methane and air mixture is perfectly premixed upstream of the burner
entrance. Fuel and air are also injected on the forward and afterward faces of the cavity to reinforce
the stable vortex generated by the main flow over the cavity. The main air mass flow rate is 20g/s. The
air mass flowrate is 0.7 g/s for the mixture entering the cavity and 1g/s for the after body air injector.
Experiments were conducted on this new TVC combustor [3]. The Particles Image Velocimetry (PIV)
and Laser Doppler Velocimetry (LDV) methods were used to measure the velocity fields for the cold
flow. Reactive conditions measurements are still in progress.
φ = 0.85
Premixed air + CH4
Premixed air + CH4
φ = 3
Air
Figure 1 – 1/4 sector TVC geometry
The governing equations considered are the unsteady Navier-Stokes equations for a viscous compres-
sible flow. Computations are performed with a parallel solver based on a fourth-order finite volume
scheme for cartesian grids. To avoid the appearance of spurious reflections at the open boundaries, the
three-dimensional Navier-Stokes characteristic boundary conditions are used to describe non-reflective
boundary conditions [11]. The annular TVC is investigated using Immersed Boundaries Methods. The
approach employs a ghost-cell method [5, 9, 1] for imposing the boundary conditions on the immersed
boundaries. Image points are expressed resorting to bilinear or trillinear interpolations. The immer-
sed boundary conditions are described by a Neumann condition for pressure (∂P/∂n = 0, where n
is the direction normal to the immersed surface) and Dirichlet for the no-slip conditions. The wall
temperature is calculated by using an adiabatic hypothesis.
Many studies are dedicated to the study of cavities of parallepipedic shape [7]. There is neverthe-
less a lack of study with more complex geometry (axisymmetric cavity) where optical diagnostics
are challenging. To evaluate the accuracy of the present solver and especially the boundary layers
reconstruction with immersed boundaries, a transonic cavity of parallelepiped shape was investigated
for which measurements are available [6]. The simulations performed [12] accurately reproduce the
flow features (velocity fields and pressure spectra). Various LES investigations were conducted with
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20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
different subgrid scale strategies. The implicit LES (MiLES approach) leads to the best agreement
with experimental data. According to this subgrid scale modeling comparison, turbulence is addressed
in the present study with the MiLES technique.
The combustion model is based on detailed tabulated chemistry associated with a presumed PDF
(PCM-FPI model [4]). This method relies on the tabulation of chemistry based on laminar premixed
flames at different equivalence ratios. The species mass fraction and the reaction rates are then ex-
pressed with first and second order moment of two variables : the progress of reaction Yc and the
mixture fraction Z, which stands for the equivalence ratio of a flamelet. The SGS flame properties
are modeled with a probability density function (PDF) presumed with a beta-shape. To describe the
progress variable and the mixture fraction on the near wall region, the aforementioned IBM formalism
is used with a Dirichlet like condition for the progress variable on the wall (zero progress variable is
assigned) and Neumann like conditions for the Z variable. For the methane-air combustion, the che-
mical table has been generated from a collection of freely propagating premixed flamelets computed
with the PREMIX software and the detailed GRI-3.0 mechanism.
To reduce computational expense, simulations are performed over a sector spanning 1/4th of the
domain with the use of axisymmetric boundary conditions. A mesh of 13 millions of cells is then used
among them 63% are fluids and others immersed boundaries.
3 Results and discussion
3.1 Cold flow results
-3 0 3 6 9 12
<ux> (m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=2mm
-3 0 3 6 9 12
<ux> (m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=6mm
-3 0 3 6 9 12
<ux> (m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=10mm
-3 0 3 6 9 12
<ux> (m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=14mm
-6 -3 0 3 6 9 12
<ux> (m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=18mm
Figure 2 – Radial profiles of mean axial velocity behind a rod at different streamwise locations.
Symbol : Measurements. Solid line : LES.
The comparison between the experimental measurements [3] and the LES are done in a plane located
behind a rod and in a plane between two rods. The mean and fluctuating axial velocity profiles
behind rods at different longitudinal locations are shown in Fig. 2 and in Fig. 3, respectively. A fair
agreement is observed implying that the main features of the flow are reproduced by the LES. The flow
seems uniform across the entire span. Compared to the parallelepiped cavity from the previous section
investigated by Forestier et al. [6], the measurements are much more difficult in the actual set-up and
we may advance that the uncertainties are thus more important. This may partially explain the slight
disagreement found at certain locations between LES and experiment especially in the vicinity of the
rods or in the bottom of the cavity. The structure of the flow with the Q-criterion is is shown in Fig. 4.
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20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
The presence of a double vortex structure is highlighted.
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2
ux'(m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=2mm
0 0.6 1.2 1.8 2.4 3 3.6
ux'(m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=6mm
0 0.8 1.6 2.4 3.2 4
ux'(m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=10mm
0 0.6 1.2 1.8 2.4 3 3.6
ux'(m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=14mm
0 0.6 1.2 1.8 2.4 3 3.6
ux'(m/s)
-20
-15
-10
-5
0
5
10
r (
mm
)
x=18mm
Figure 3 – Radial profiles of fluctuating axial velocity behind a rod at different streamwise locations.
Symbol : Measurements. Solid line : LES.
Figure 4 – Iso-surfaces of Q-criterion
3.2 Burning flow simulation
The flame structure is shown in Fig. 5 with the iso-surfaces of progress variable. The flame is trapped
into the cavity. The injection of air and fuel directly into the cavity provides a stable recirculation zone.
The temperature and mixture fraction maps in Fig. 6 reveal that most of the combustion process occurs
within the fuel-rich cavity region. The cavity air-injection provides an efficient turbulent mixing of the
reactants and compensates the lack of oxidizer which may result from a low fluid exchange between the
main lean flow and the cavity region. Hence, the cavity seems to be an interesting option for fuel-lean
burning.
4 Conclusions
Unsteady compressible simulations have been conducted on a TVC combustor for the non-reacting
and reacting flows. The essential features of the cold flow are recovered. This demonstrates the ability
of LES-IBM to describe complex variable density flows. Concerning the combustion modeling, the
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20e`me Congre`s Franc¸ais de Me´canique Besanc¸on, 29 aouˆt au 2 septembre 2011
Figure 5 – Iso-surfaces of progress variable Yc = 0.2 colored by temperature
Figure 6 – Maps of the instantaneous resolved temperature (left) and of the resolved mixture fraction
with the iso-line of stoechiometric mixture fraction (right).
detailed chemistry approach based on the PCM-FPI model was investigated. The FPI method is
based on the assumption that the flamelets are laminar and unstrained. To take into account the
aerodynamic strain in the PCM-FPI method, a model to account for the effects of local strain rate
will be tested [15]. As flame stabilisation is achieved in a TVC combustor by a cavity which controls
the recirculation of the burnt gases, a third model including heat loss and dilution by burnt products
will also be implemented [16].
Future work will focus on the description of the trapped vortex complex mechanisms depending on
various parameters (structural and aerodynamic) and the comparison with further experimental data
which are in progress. On a domain reduced of one fourth, only structures with fourfold symmetry
or multiples can be supported. To verify that the assumption that one fourth sector is sufficient, a
complete simulation of the combustor will be performed with an unstructured code.
5 Acknowledgments
The investigations presented in this paper have been done as a part of the European research project
TECC-AE - FP7 (Technologies Enhancement for Clean Combustion in Aero-Engines), Grant No.
2010-020152. Computing resources were provided by GENCI, IDRIS-CNRS and CRIHAN.
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Large Eddy simulation of a trapped Vortex combustor

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Large Eddy simulation of a trapped Vortex combustor

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