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ASME Paper Title:
NUMERICAL INVESTIGATION OF EFFUSION COOLING AIR INFLUENCE ON THE CO EMISSIONS FOR A
SINGLE-SECTOR AERO-ENGINE MODEL COMBUSTOR
Authors:
Sandra Recio Balmaseda, Tim Jeremy Patrick Karpowski,Hendrik Nicolai, Philipp Koob, Max Greifenstein
Andreas Dreizler, Christian Hasse
ASME Journal Title:
Journal of Engineering for Gas Turbines and Power
Volume/Issue Volume 146, Issue 12
Date of Publication (VOR* Online) August 06, 2024
ASME Digital Collection URL:
https://asmedigitalcollection.asme.org/gasturbinespower/article/146/12/121014/1202035/Numerical-
Investigation-of-Effusion-Cooling-Air
DOI:
10.1115/1.4066159
*VOR (version of record) GTP-24-1302, ASME ©; CC-BY distribution license
*
GTP-24-1302
NUMERICAL INVESTIGATION OF EFFUSION COOLING AIR INFLUENCE ON THE CO EMISSIONS FOR A
SINGLE-SECTOR AERO-ENGINE MODEL COMBUSTOR
Sandra Recio Balmaseda †∗
Tim Jeremy Patrick Karpowski †
Hendrik Nicolai
Philipp Koob
Christian Hasse
Institute for Simulation of reactive Thermo-Fluid Systems
Technical University Darmstadt
Otto-Berndt-Straße 2,
64287 Darmstadt, Germany
e-mail: recio@stfs.tu-darmstadt.de
Max Greifenstein
Andreas Dreizler
Institute for Reactive Flows and Diagnostics
Technical University Darmstadt
Otto-Berndt-Straße 3,
64287 Darmstadt, Germany
ABSTRACT
Stricter aviation emissions regulations have led to the de-
sire for lean-premixed-vaporized combustors over rich-quench-
lean burners. While this operation mode is beneficial for reduc-
ing NOx and particulate emissions, the interaction of the flame
and hot exhaust gases with the cooling flow results in increased
CO emissions. Predicting CO in computational fluid dynam-
ics (CFD) simulations remains challenging. To assess current
model performance under practically relevant conditions, Large-
Eddy Simulation (LES) of a lab-scale effusion cooling test rig is
performed. Flamelet-based manifolds, in combination with the
Artificial Thickened Flame (ATF) approach, are utilized to model
the Turbulence-Chemistry Interaction (TCI) in the test-rig with
detailed chemical kinetics at reduced computational costs. Heat
losses are considered via exhaust gas recirculation (EGR). Local
transport effects in CO emissions are included through an addi-
tional transport equation. Additionally, a Conjugate Heat Trans-
fer (CHT) simulation is performed for good estimations of the
thermal boundary conditions. Extensive validation of this com-
prehensive model is conducted using the available experimental
dataset for the studied configuration. Subsequently, model sen-
sitivities for predicting CO are assessed, including the progress
variable definition and the formulation of the CO source term in
the corresponding transport equation. To investigate the flame
thickening influence in the calculated CO, an ATF-postprocessing
correction is further developed. Integrating multiple sophisti-
cated pollutant submodels and evaluating their sensitivity offers
†Joint first authors
∗Address all correspondence to this author
insights for future investigations into modeling CO emissions in
aero-engines and stationary gas turbines.
NOMENCLATURE
Latin Letters
𝑎, 𝑏 ATF correction factors
𝐶𝑝heat capacity at constant pressure
Eefficiency function
Fthickening factor
ℎenthalpy
˙𝑚mass flux
𝑝pressure
𝑆𝑐𝑡turbulent Schmidt number
𝑇temperature
𝑡time
𝑈velocity
𝑥(𝑖),𝑦,𝑧spacial coordinate
𝑋𝑖mole fraction
𝑌𝑐progress variable
𝑌𝑖mass fraction of species 𝑖
𝑍mixture fraction
𝑧𝑤distance over the effusion cooling wall
Greek Letters
𝜌density
𝜇𝑡turbulent viscosity
𝜆thermal conductivity
𝜑equivalence ratio
𝜙control variables
Ξwrinkling factor
1 GTP-24-1302; ASME ©; CC-BY distribution license
˙𝜔𝑖source term of species 𝑖
Ωflame sensor
Super- and subscripts
±split into production and destruction term
𝑡 𝑎𝑏𝑙 𝑒 table look-up quantity
𝑡𝑟 transported quantity
𝑐(ATF)-laminar post-correction
𝑐,𝑇 (ATF)-turbulence post-correction
Abbreviations
ATF Artificial Thickened Flame
CFD Computational Fluid Dynamics
CHT Conjugate Heat Transfer
EGR Exhaust Gas Recirculation
FCAI Flame-Cooling Air Interaction
FWI Flame-Wall Interaction
FPF Freely Propagating Flame
IRZ Inner Recirculation Zone
ISL Inner Shear Layer
LES Large Eddy Simulation
LPP Lean-Premixed-Vaporized
ORZ Outer Recirculation Zone
OSL Outer Shear Layer
RMS Root-Mean-Square
RQL Rich-Quench-Lean
TCI Turbulence Chemistry Interaction
1. INTRODUCTION
Air traffic, a critical source of pollutant emissions, has con-
tinued to grow in the past 30 years. It is expected to double
in size by the mid-2030s [1]. This scenario strongly contrasts
the emission goals declared in “Flightpath 2050" [2]. Substan-
tial improvements to the existing aero-engines are required to
achieve these goals. With this purpose, Computational Fluid
Dynamics (CFD) has become an indispensable tool in devel-
oping future aero-engine designs [3]. Nevertheless, simulating
aero-engine combustion chambers under realistic operating con-
ditions is challenging due to the intricate interplay of complex
combustion phenomena, including turbulence-chemistry interac-
tion (TCI), transient conditions, and effusion-cooled walls [4].
The difficulties extend to designing experimental setups for data
validation at high pressures and temperatures.
Previously, the combination of flamelet-based tabulated
manifolds coupled with Large-Eddy Simulation (LES) showed
success in developing rich-quench-lean (RQL) burners [5–7].
To decrease NOxemissions through lower peak temperatures
and comply with the “Flightpath 2050" goals, it is advanta-
geous to change from RQL to a lean-premixed-vaporized (LPP)
concept [8]. However, LPP burners imply an increased de-
mand for effusion cooling due to the higher thermal loads on
the combustor walls [9, 10]. This affects the predictability of
the current manifold models, as the cooling flow interaction
with the flame is known to increase CO emissions [11] through
chemical quenching and mixing-enhanced processes with the ex-
haust gases. The process is dominated by dilution and higher mix-
ing with the cooling air when moving downstream with an incre-
ment of effusion cooling holes in the axial direction, provoking a
decline in CO concentrations and temperature. This was demon-
strated in recent experiments performed in an effusion-cooled
single-sector model gas turbine combustor [12–15]. The mea-
sured thermo-chemical states (characterized by CO mole fraction
and temperature) revealed a substantial influence of the effusion
cooling flow on the lean-flame chemistry.
Capturing all these processes in the simulation is challenging
due to the high sensitivity of CO to the local combustion regime
and heat losses. Generally, model extensions are required to
capture these combustion effects accurately [6, 16, 17], but their
combined utilization in effusion-cooled chambers is yet to be
performed.
In general, tabulated manifolds in the literature are based on
1D freely propagating flames (FPF) [18, 19]. Popp et al. [5, 6]
validated this standard tabulation approach for premixed and dif-
fusion flames in a multi-regime burner setup. The local combus-
tion regime effects combined with recirculation zones and their
influence on CO emissions were analyzed. It was found that the
premixed flamelet-based manifolds can correctly capture temper-
ature and major species trends. However, larger discrepancies are
reported for minor species such as CO, which is highly affected by
local transport processes. Solving an additional transport equa-
tion for CO [20] improved the results significantly compared to
direct lookup from the manifold, as also observed in [16, 21] in
more generic configurations.
In realistic configurations, heat loss effects must be ac-
counted for in the combustion chemistry, especially for the
prediction of minor species and pollutants such as CO. Thus,
improved manifolds, which consider enthalpy as a third table
dimension, are needed [16, 17]. The reason is the diffusion of
CO towards lower enthalpy levels. Heat losses can happen due
to flame quenching to the wall or due to mixing with cooling air.
Several authors have addressed numerically the influence of
heat losses due to cooled walls on the global flow field solution.
Ketelheun et al. [22] implemented enthalpy variation through
exhaust gas recirculation (EGR) in wall-enclosed flames. The
author could observe cooling effects not captured by the standard
manifolds and a better agreement in the main combustion zone
with the experimental data. However, wall heat transfer was
still underestimated. This flame quenching phenomenon was
addressed in more detail in academic flame-wall interaction
(FWI) configurations [16, 17, 21].
In the case of flame-cooling air interaction (FCAI), significantly
less work has been performed. According to Palulli et al. [23],
who studied FCAI in a generic configuration, depending on
the combustor geometry and combustion mode, both FWI and
FCAI can take place inside the combustor. While both lead
to an increase in exhaust CO emissions, depending on which
phenomenon dominates, there would be a predominance of
either quenching or mixing and dilution effects. The combustion
2 GTP-24-1302; ASME ©; CC-BY distribution license
modeling strategy would need to be adjusted accordingly [24]. At
higher cooling rates, the 𝑌𝐶 𝑂 −𝑇dependency could be properly
featured by 1D FPF solutions in an a-priori analysis [23, 24].
The previous studies offered an overview of the influence
of different parameters in generic FCAI scenarios. However, no
further numerical analysis was performed on the FCAI influence
on CO emissions and the modeling strategy required to capture
all these physical effects properly in closer-to-reality aero-engine
conditions. It is still unclear if the EGR extension for heat losses
in the flamelet manifold is enough to capture the combustion
chemistry in the FCAI zone or if the effect of surrounding non-
adiabatic walls is still significant and further model extensions,
e.g., flame quenching are required. In the experimental field, the
effusion-cooled single-sector gas turbine combustor previously
investigated by Hermann, Greifenstein et al. [12, 14, 25] is a
suitable configuration towards FCAI relevant-industry set-ups. It
provides accurate FCAI boundary conditions and comprehensive
validation data, both for the global flow field and thermo-chemical
states. Amerini et al. [26] simulated this combustor to assess
their loosely-coupled Conjugate Heat Transfer (CHT) approach
with tabulated chemistry for adiabatic flamelets. These authors
demonstrated that their modeling strategy was capable of cap-
turing the general flowfield characteristics. However, a detailed
numerical analysis of CO evolution, especially with the cooling
flow in the FCAI zone and its sensitivity to model extensions, has
not been performed yet.
The objective of this work is to assess the effect of cur-
rent CFD model capabilities for predicting the complex thermo-
chemical states during FCAI in a practically relevant aero-engine
scenario. The capabilities of the employed flamelet manifolds
to predict CO emissions evolution along the chamber are evalu-
ated. In particular, the use of EGR flamelet manifolds is validated
against the available detailed experimental measurements in an
FCAI-dominant scenario. In addition, improvements in mod-
eling strategies, namely a transport equation for CO, split and
linear correction of the CO source term within, and an ATF
post-processing correction, are validated with experimental data.
Their interaction with the progress variable definition, as well as
the benefits and shortcomings of the tested model extensions, are
highlighted.
The remainder of this work is structured as follows: first, the
experimental setup is introduced. Subsequently, the employed
combustion models and numerical set-up are presented. In the
results section, first, the simulations are compared to the exper-
imental data in terms of temperature and velocity, and then the
CO predictions are discussed. In the end, a conclusion is given.
2. EXPERIMENTAL SETUP
A schematic of the studied burner, including the used coor-
dinate system, is shown in Fig. 1. The burner is enclosed in a
pressure vessel but still enables optical access from the top and the
sides of the burner through glass windows. Preheated air and nat-
ural gas are premixed in a plenum before a movable block swirler,
x
z
Effusion
cooling air
Flametube
Main
fuel
Oxidizer
Pressure vessel
Main
fuel
FIGURE 1: SCHEMATIC OF THE EXPERIMENTAL SETUP,
ADAPTED FROM [13].
which is based on the well-known TECFLAM design [27]. A
modular effusion plate is mounted at the bottom of the chamber.
All mass flows entering the combustor are individually condi-
tioned and controlled using thermal mass flow controllers. In
TABLE 1: INVESTIGATED OPERATING CONDITIONS FROM [13].
Name Symbol Main Cooling Unit
Mass flow ˙𝑚ox/eff 30 15 g/s
Temperature 𝑇ox/eff 623 623 K
Equivalence ratio 𝜑0.75 0 -
Operating pressure p 0.25 0.25 MPa
Swirl number S 0.7 - -
this study, the low swirl, high cooling, fully premixed condition
is investigated. The parameters of this operating condition are
summarized in Tab. 1. This operating condition features high CO
emissions and represents the highest FCAI interaction among the
measured operating conditions. As a consequence, mixing, dilu-
tion, and chemical quenching effects due to the interaction of the
flame and hot exhaust gases with the cooling air are expected to
dominate over heat loss and thermal quenching to the wall.
Particle Image Velocimetry (PIV) measurements were per-
formed in [25]. The measured velocities are recorded for an
equivalence ratio 𝜑=0.65. For the velocity comparison, a sim-
ulation with an adapted equivalence ratio is performed.
Gas phase temperature and CO mole fractions 𝑋𝐶 𝑂 mea-
surements of the studied operating condition are available for
𝜑=0.75 [14]. The temperature was measured with coher-
ent anti-Stokes Raman spectroscopy (CARS), while 𝑋𝐶 𝑂 was
measured with quantitative CO two-photon laser-induced fluo-
rescence (CO-LIF).
For the studied operating point, no measurements of the wall
temperatures exist. In Greifenstein et al. [12], measurements of
the effusion cooling plate temperature exist for 𝜑=0.65, which
only gives a qualitative comparison to the here studied condition,
𝜑=0.75.
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3. COMBUSTION MODEL
In the following, an overview of the employed modeling
strategies as well as model improvements for capturing CO accu-
rately, are outlined.
3.1 Standard flamelet-manifold methodology
The basis for the combustion model is the commonly em-
ployed flamelet-based tabulation method [18, 19].
In the first step, adiabatic freely propagating flamelets with
varying mixture fractions are computed with the flame solver
Cantera [28] using a unity Lewis number for all species. This
modeling approach has continued to be employed in CH4-air
turbulent flame works of relevance [6, 29, 30].
The chemical kinetics are modeled through the GRI-3.0 de-
tailed mechanism (53 species and 325 reactions) [31]. Subse-
quently, the calculated flamelets are parameterized by the mixture
fraction 𝑍and the progress variable 𝑌𝑐. For the tabulation, 200
points were set for the mixture fraction, keeping a refined resolu-
tion Δ𝑍=0.001 in the flammable range for this set-up, and 100
points for the progress variable. Two progress variable definitions
were considered: 𝑌𝑐, 1=CO2and 𝑌𝑐,2=CO2+H2O+CO.
3.2 Heat losses implementation in the manifolds
Standard flamelet-based manifolds are unable to represent
the high CO diffusion in the direction of decreasing enthalpy lev-
els from the adiabatic region [16]. Given that heat losses are
expected in the current FCAI configuration, it is necessary to
extend the tabulation strategy by including the enthalpy dimen-
sion. Due to the operating point considered with the highest
cooling mass flow rate, it is expected that mixing, dilution, and
chemical quenching effects due to the cooling flow influence dom-
inate over flame quenching to the wall. Under this presumption,
EGR flamelet manifolds would be suitable to model the set-up
physics [22, 32, 33]. They are generated from a series of inde-
pendent one-dimensional freely propagating flames with varying
enthalpy levels as proposed by Fiorina et al. [34].
Enthalpy reduction is achieved by exhaust gas recirculation, that
is, different amounts of cooled burned gases are added to the
inflow mixture of the flame [35, 36]. Additionally, the upper
enthalpy limit is expanded using one-dimensional freely propa-
gating flames with increased inflow temperatures.
In the range between 𝑍min and pure oxidizer (𝑍=0), the
thermo-chemical states from the last flammable mixture and pure
oxidizer are interpolated [22]. The simulation results are mapped
on a normalized state space Φ = Φtable (𝑍 , 𝐶𝑛, 𝐻𝑛), with the
normalized progress variable 𝐶𝑛and enthalpy 𝐻𝑛. The manifold
final dimensions are 200 ×100 ×100.
3.3 Local transport effects for CO
A CO-transport equation to account for the local transport
phenomena [20, 21] is implemented
𝜕𝜌𝑌CO
𝜕𝑡 +𝜕
𝜕𝑥𝑖
(𝜌𝑈𝑌CO )=𝜕
𝜕𝑥𝑖𝜆
𝐶𝑝
+𝜇𝑡
𝑆𝑐𝑡𝜕𝑌CO
𝜕𝑥𝑖
+˙𝜔CO (1)
with 𝜆the thermal conductivity, 𝐶𝑝the heat capacity at con-
stant pressure, 𝜇𝑡the turbulent viscosity, 𝑆𝑐𝑡=0.7the turbulent
Schmidt number and ˙𝜔𝐶 𝑂 the chemical source term. This allows
the CO mass fraction to evolve according to its own time scale,
considering possible perturbations due to the effect of transport
terms [5, 6]. The flamelet-based tabulation approach relies on
the fast-chemistry assumption. It is able to provide an accurate
prediction of the individual species trends as long as their time
scales are of smaller or the same order when compared to the
time scale of the selected progress variable. As discussed by
Popp et al. [6], complex flow and recirculation structures can
lead to discrepancies between the tabulated and transported CO
timescales. The introduction of an additional transport equation
for slowly reacting species was pioneered for NO formation by
Ihme and Pitsch [37] and Ketelheun et al. [38]. Derived from a
timescale analysis highlighting the relatively slow NO formation
compared to the flamelet lifetime, this concept was later applied
by Mueller et al. [39] to address slow polycyclic aromatic hy-
drocarbons (PAH) species for soot formation. The additional
transport equation for CO was implemented in the works of Gan-
ter et al. [21] and Han et al. [20] to enhance the representation of
CO formation by accounting for the local transport phenomena.
The last term on the right-hand side refers to the chemical
source term, which receives a special treatment [16, 19].
The value ˙𝜔table
CO looked up from the manifold is corrected
linearly to account for a changed transported CO mass fraction,
𝑌tr
CO, as compared to its local value at the manifold, 𝑌table
CO . The
total source term ˙𝜔CO is split into production and consumption
˙𝜔CO =˙𝜔+
CO +𝑌𝑡𝑟
CO ˙𝜔−
CO
𝑌𝑡 𝑎𝑏𝑙 𝑒
CO .(2)
3.4 Artificial Thickened Flame approach
The subgrid-scale turbulence-chemistry interaction (SGS-
TCI) closure is considered through the Artificial Thickened Flame
approach (ATF) as used in [40]. The ATF model is based on a
coordinate transformation that is applied to the scalar transport
equation to thicken the flame front and, as a consequence, make
it resolvable on coarse LES grids. For each control variable,
𝜙=[𝑍 , 𝑌𝑐, ℎ], the modified transport equation reads
𝜕𝜌𝜙
𝜕𝑡 +𝜕
𝜕𝑥𝑖
(𝜌𝑈𝜙)=𝜕
𝜕𝑥𝑖FE 𝜆
𝐶𝑝
+ (1−Ω)𝜇𝑡
𝑆𝑐𝑡𝜕𝜙
𝜕𝑥𝑖
+E
F
˙𝜔𝜙
(3)
with Fthe effective thickening factor, Ethe effective efficiency
function [41] , Ωthe flame sensor, and ˙𝜔𝜙the scalar source term.
In the context of ATF, a dynamic thickened flame approach with
grid-adaptive thickening following [42] is employed, in combi-
nation with the flame sensor definition Ω = 16[𝑌𝑐(𝑌𝑐−1)] 2[43].
In the flame front, 𝑛=5points is selected, which is validated
with 1D flame simulations at the corresponding operating condi-
tions. The efficiency function by Charlette et al. [41] with a static
constant 𝛽=0.5and a Kolmogorov constant 𝐶𝑘=1.5was used.
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3.5 CO post-processing correction for ATF
When performing ATF for the TCI closure, it is found that
species profiles such as CO are overestimated [30]. First, in
laminar flames, ATF thickens species profiles. This means that
the total mass of species is overpredicted. This is shown in
Fig. 2, where the mean flame brush was generated by shifting
10.000 1D flamelets assuming a uniform spatial distribution fol-
lowing [44], to mimic the impact on time-averaged flames. Here
< 𝑌𝐶𝑂 >marks the time-averaged thickened CO profile. Gruhlke
et al. [45] proposed a laminar flame thickening correction for the
time-averaged profiles of species mass fractions 𝑌𝑐
𝑘.
<
ˆ
𝑌𝑐
𝑘(𝑥∗)>=<
ˆ
𝑌𝑘(𝑥∗)/F(𝑥∗)>(4)
In turbulent flames, besides presenting the previous issue, the
thickening of the flame neglects the impact of sub-filter scale
flame wrinkling on the filtered chemical flame structure. As
discussed in [46], this leads to a 50 % underestimation of CO
peak under the given conditions as seen in Fig. 2 as < 𝑌 𝑐
𝐶𝑂 >.
Mercier et al. [47] proposed a correction based on manufactured
filtered wrinkled flamelets (FWF) to account for the impact of
subgrid-scale flame wrinkling on species production. In order to
incorporate it into the thickened flame framework, it is necessary
to correct the previous laminar correction 𝑌𝑐
𝑘with an empirical
wrinkling factor
ˆ
𝑌𝑐,𝑇
𝑘(𝑥∗)=
ˆ
𝑌𝑐
𝑘(𝑥∗) (𝑎Ξ+𝑏).(5)
The coefficients 𝑎and 𝑏can be estimated from FWF elements
as shown in [45]. As the current correction is empirical, the
values of Eq. (5) need to be evaluated for the selected progress
variables and studied operating conditions. In this study, the
values are determined to be 𝑎=0.816 and 𝑏=0.191 for 𝑌𝑐,1, and
𝑎=0.650 and 𝑏=0.375 for 𝑌𝑐,2, respectively. For more complex
partially premixed cases, the parameters could be included in the
flamelet table to account for the changing conditions. In Fig. 2, a
comparison between the original thickened profiles, the ones with
laminar correction, and the ones with turbulent correction applied
on the transported CO profiles is presented for both progress
variable definitions at the corresponding conditions.
As it can be noticed, 𝑌𝑐,2, used in the previous works [45, 47],
shows a better match with the unthickened flame solution in Fig. 2.
This might be due to the incorporation of CO in the progress vari-
able definition, which could favor 𝑌𝑐,2in this artificially generated
solution. However, in the coupled simulation, 𝑌𝑐,1provides a bet-
ter flame resolution, as well as a better alignment with the selected
flame sensor (see Fig. 3), thus both definitions are evaluated. To
the authors’ best knowledge, this is the first time a CO transport
equation is solved in conjunction with a three-dimensional table
including heat losses with ATF closure. Contrary to previous
works [30, 45], this correction is applied to the transported CO
instead of to the species tabulated values.
4. SOLVER AND NUMERICAL SETUP
In this section, the utilized solver and numerical setup are
presented. First, the setup for the fluid flow solver is described.
−10 0 10
x[mm]
0
1
2
3
<YCO >·103[-]
Yc,1
<YCO > < ˆ
YCO > < ˆ
Yc
CO > < ˆ
Yc,T
CO >
−10 0 10
x[mm]
Yc,2
FIGURE 2: AVERAGED PROFILES OF CO MASS FRACTION MIM-
ICKING THE FLAME BRUSH FOR THE PROGRESS VARIABLESYc,1
AND Yc,2.<Y
CO >(LAMINAR), <
ˆ
Y
CO >(THICKENED), <
ˆ
Yc
CO >
(THICKENED, LAMINAR CORRECTION), <
ˆ
Yc,T
CO >(THICKENED,
TURBULENT CORRECTION).
0.0 0.5 1.0
Normalized Yc[-]
0.0
0.5
1.0
Normalized ˙ωYc[-]
Yc,1
Ω ˙ωYc˙ωCO ˙ω+
CO ˙ω−
CO
0.0 0.5 1.0
Normalized Yc[-]
Yc,2
FIGURE 3: ALIGNMENT OF THE FLAME SENSOR [43] WITH THE
PROGRESS VARIABLES AND CO SOURCE TERMS.
Afterwards the employed CHT approach is shortly presented.
4.1 Fluid solver
LES of the effusion cooling test-rig is performed within an
OpenFOAM [48] in-house framework [6], using 2nd- order dis-
cretization in time and space and a pressure-based algorithm to
solve the Favre-filtered Navier-Stokes equations in the low Mach
number formulation. For brevity, the filtering operator ˜·is omitted
throughout, as only Favre-filtered quantities are discussed. The
non-resolved subgrid viscosity is modeled using the 𝜎-model by
Nicoud et al. [49] with a model constant of 𝐶𝜎=1.5. The LES
solver features tabulated chemistry (Sec. 3.1) with heat losses im-
plementation through EGR dimension (Sec. 3.2), coupled with
the ATF approach to model SGS-TCI (Sec. 3.4), and solves an
additional transport equation for CO to consider local transport
effects (Sec. 3.3). This transported CO quantity is further cor-
rected through an ATF post-processing correction (Sec. 3.5) that
considers the impact of flame thickening into the species pro-
files and flame wrinkling. An offline CHT approach outlined in
Sec. 4.2 is utilized to prescribe isothermal conditions to the fluid
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600 800 1000 1200 1400
T [K]
A
A
A-A
a) b)
FIGURE 4: a)TEMPERATURE DISTRIBUTION IN THE SOLID DO-
MAIN. b)GRID USED IN THE STUDY.
simulation. The isothermal conditions are shown by a cut through
the solid domain in Fig.4-a). At the inlets, the mass flows from
tab. 1, and a zero gradient condition for pressure are set. The
composition of the unburned mixture and pure air are set for the
main and cooling flow, respectively. At the outlet, a fixed back
pressure (0.25 MPa) and zero gradient for the other quantities are
set. The fluid domain is discretized with a hex-dominant grid
with 54 M, shown in Fig. 4-b). Local refinements have been in-
troduced to ensure the correct resolution of turbulent structures.
In the fluid, the maximum cell size is Δ𝑥=2 mm in the intake
section. In the swirler, it is refined to Δ𝑥=0.5 mm. The flame
zone and effusion cooling plate feature cells with Δ𝑥=0.25 mm.
This value was chosen to give a thickening factor F<10 with
𝑛=5in the flame front, which leads to values of F
max ≈7in the
simulation. Downstream, the grid size increases to Δ𝑥=0.5 mm.
It reaches Δ𝑥=1 mm close to the outlet.
This mesh is the result of a grid convergence study. A coarse
mesh with 4M cells showed flashback and generally a wrong flow
field. For an intermediate mesh with Δ𝑥=0.5 mm (24 M) in the
flame area and hence F
max ≈15, the global flowfield quantities,
such as temperature and velocity, were properly captured as they
are less sensitive to mesh resolution [50], but predictions on
CO emissions were unsatisfactory and needed of further mesh
refinements -results not included for the sake of brevity-. All
results shown are recorded on the fine grid with 54 M cells.
The timestep is dynamically adapted to limit the CFL number
to a maximum value of 0.8, which in the flame zone means
𝐶𝐹 𝐿max =0.3during the simulation, corresponding roughly to
a timestep of Δ𝑡=2.5·10−7s. Each fluid simulation took
approximately 0.5M core hours.
4.2 Conjugate Heat Transfer
The temperature conditions on the walls have a strong influ-
ence on flame stabilization, flame dynamics, and also possibly on
emissions such as CO due to the strong temperature dependency
of the CO source and sink terms [51, 52]. As temperature mea-
surements in optically inaccessible regions are not possible, CHT
simulations were performed.
An offline CHT approach is utilized here to give reasonable
wall temperature estimations in the entire burner [53].
The solid geometry is a simplification of the experimental
setup and is shown in Fig. 4-a), along with the final temperature
distribution.
Heat transfer and emissivity coefficients for the outer walls
are estimated from [12] and previous work on a gas turbine
combustor with optical access [54]. Material properties for the
solid [14] are assumed constant for a reference temperature of
1073 K, corresponding to the average temperature in the solid
around the chamber (see Fig. 4-a)) . The CHT was performed
with 𝑌𝑐,1. The simulation with 𝑌𝑐,2utilized the same wall tem-
peratures for comparability , but as seen in Fig. 7 and 8 there is
little impact of the 𝑌𝑐choice on the temperature.
The solid domain was discretized with 11 Mio. cells.
The solid simulations required to reach the steady tempera-
ture distribution amount to roughly 2000 core hours combined.
The fluid simulation is initially run with isothermal temper-
atures, and the heat flux from the walls is averaged for 15 ms.
Afterwards, the averaged heat flux is used as a Neumann bound-
ary condition to simulate the solid domain. This simulation is
run until a steady state is reached. The resulting temperature is
mapped to the fluid domain, which is rerun. After a few iterations,
a steady temperature is reached.
5. RESULTS AND DISCUSSION
In this section, the LES results for both progress variable defi-
nitions 𝑌𝑐,1=CO2and 𝑌𝑐, 2=CO2+H2O+CO are compared
against the experimental data. Before investigating the effect of
the different modeling extensions for predicting CO emissions,
the global features of the effusion cooling configurations are dis-
cussed and validated with the available experimental data.
5.1 Temperature and velocity fields
In Fig.5, the time-averaged velocity and temperature, CO
mass-fraction, and normalized mixture fraction fields on the cen-
ter slice of the lower half of the combustor are shown. The v-
shaped flame stabilizes near the swirler exit, and its lower branch
interacts with the first holes of the effusion cooling plate. Four
distinct zones of interaction can be identified: the inner recircula-
tion zone (IRZ), the inner shear layer (ISL), the outer shear layer
(OSL), and the outer recirculation zone (ORZ).
Regarding the OSL and ORZ and as noted from the 𝑍con-
tour, there is an increased penetration depth, leading to an en-
hanced chemical interaction between the cooling air and the recir-
culated hot products[13]. Downstream, the process is dominated
by dilution with increased cooling flow through the additional
effusion cooling holes. This results in a decrease in tempera-
ture in the axial direction close to the wall. The 50 % dilution
isoline illustrates that a full cooling film is only developed after
the fourth effusion cooling hole. The hot combustion products
6 GTP-24-1302; ASME ©; CC-BY distribution license
IRZ
ORZ
ISL
OSL
5mm
25m
m
50mm
15mm
<Zn>[-]
<YCO>[-]
5mm
25mm
50mm
15mm
a)
b)
c)
d)
FIGURE 5: TIME AVERAGED VELOCITY, TEMPERATURE, TRANSPORTED CO MASS FRACTION AND NORMALIZED MIXTURE FRACTION
FIELDS. FLOW STRUCTURES MARKED IN BLACK OVER THE VELOCITY FIELD. WHITE LINES MARK THE POSITION OF VERTICAL LINE
COMPARISONS. 50% DILUTION ISOLINE SHOWN OVER ZnIN WHITE. INSTANTANEOUS FISOLINES PLOTTED OVER Zn.
interact with the incoming cooling flow between the second and
fourth effusion cooling holes.
The IRZ features higher temperatures than the ORZ due to
the heat-loss effects on the wall through chemical quenching and
effusion cooling flow recirculation for the ORZ. The OSL shows
a strong mixing with the cooling flow and the possible influence
of the boundary condition at the cooling plate, which explains its
lower temperatures compared to the ISL.
In the following, the simulation results are compared against
the available experimental data at vertical lines indicated in
Fig. 5-b . Both 𝑌𝑐,1and 𝑌𝑐 ,2show nearly identical mean profiles
for the average velocity and temperature field. Thus, only results
for 𝑌𝑐,1are discussed for brevity.
For a qualitative comparison of the flow field, the mean
and Root-Mean-Square (RMS), of axial and radial velocity are
compared in Fig. 6 at different axial distances from the swirler
exit (𝑥∈ [5,15,15]mm) to the PIV data [25]. The PIV data
was recorded for a lower equivalence ratio (𝜑=0.65 [25]), which
was accounted for by the simulations used for this comparison.
The simulation features a higher peak at 𝑥=15 mm. The peak
in axial and radial velocities is slightly shifted inwards. RMS
profiles match well for both axial and radial velocities, indicating
that turbulent fluctuations are accurately captured by the LES.
In Fig.7, the time-averaged temperature profiles are com-
pared along the axial direction of the combustion chamber. The
experimental data was recorded for the same operating point [13],
so they are directly comparable.
At 𝑥=5 mm, simulation and measurement are in good agree-
ment. The low-temperature peak at 𝑧=−20 mm, coincident with
the fresh gases injection, as well as the rise in temperature in
the ISL and OSL, are well predicted. At the following profiles
at 𝑥=15 mm and 𝑥=25 mm, the simulations show higher
temperatures in the main flow jet region, indicating faster fuel
consumption in the simulation compared to the experiment. At
𝑥=50 mm, the profiles are again in good agreement. This is
the axial position at which the main flow starts to impinge on the
cooling jets.
In Fig.8, the time-averaged horizontal temperature profiles at
different heights over the effusion cooling plate 𝑧𝑤are compared
against the experimental data.
The general shape of the temperature profile and level of the
experimental measurement are reproduced by the simulations.
However, especially at 𝑧𝑤=1.5 mm, the individual effusion
cooling jets are visible as regions of lower temperature. This
suggests that the jet penetration lengths around the effusion cool-
ing area are slightly overestimated by the simulation. This might
be caused by different factors: uncertainties in the experimentally
estimated cooling flow temperature or mass flows, overestimation
of the numerical wall temperatures in the effusion holes, or over-
estimated boundary layer sizes in the holes leading to higher
velocity peaks. At 𝑧𝑤=3 mm, the jets coming from the second
and third effusion cooling hole are also apparent.
From the previous comparisons, it can be noted that the
choice of 𝑌𝑐definition has little impact on the general flow field.
Both simulations give identical predictions for both flow-field and
temperature distributions in the primary zone and the FCAI area.
5.2 CO formation during FCAI
While the global flow field is well predicted regardless of
𝑌𝑐choice, it is unclear if the same holds for CO predictions.
Furthermore, the effect of the split formulation in ˙𝜔CO (Sec. 3.3) is
analyzed for 𝑌𝑐,1and 𝑌𝑐, 2. Lastly, the ATF correction (Sec. 3.5)
is evaluated in a close-to-reality effusion cooling chamber.
In Fig. 9, the CO profiles on the vertical lines marked in
Fig. 5-d are presented. Both the direct table lookup of ˙𝜔𝑡 𝑎 𝑏𝑙𝑒
𝐶𝑂
and the split into production and destruction terms from Eq. (2)
is shown. At first, the effect of the ATF correction is discussed
for the split-based formulation (right column). As the investi-
gated vertical lines (𝑥∈ [5,15,25]mm) intersect with the flame
and thus thickened regions (see Fig. 5-d, instantaneous isolines
of F), average transported CO profiles are overpredicted for
both 𝑌𝑐definitions (black and grey) at all positions. Applying
the ATF-post-correction for transported CO from (5) results in
near identical profiles for both simulations at all positions. Sim-
7 GTP-24-1302; ASME ©; CC-BY distribution license
RMSRMSMEAN MEAN
FIGURE 6: MEAN AND RMS AXIAL (LEFT) AND RADIAL (RIGHT)
VELOCITY PROFILES.
ulations and experimental data agree well for 𝑥=25 mm. At
𝑥=15 mm, the simulations result in too low CO values. The
peak in CO is also shifted towards the lower wall due to the over-
estimation of ORZ temperature. At 𝑥=5 mm, the peaks are
over-predicting CO, which might be caused by an altered flame
anchoring behavior. Regardless of the chosen progress variable
and correction, the CO values in the IRZ are underpredicted, due
to long residence times and the recirculation from the top wall,
where thermal quenching is dominant. To summarize, the ATF
correction works well if applied to transported CO values at el-
evated pressures, which holds not just for 𝑌𝑐,2for which it was
originally developed at atmospheric conditions [45], but also for
𝑌𝑐,1.
Now the effects of the ˙𝜔𝐶𝑂 treatment are discussed for both
𝑌𝑐definitions. Only the turbulent corrected profiles are discussed
for brevity. As mentioned before, the split-based formulation
(right column) results in good agreement between 𝑌𝑐, 1and 𝑌𝑐,2.
Without the split formulation 𝑌𝑐 ,1gives similar results as with the
split formulation. For 𝑌𝑐 ,2using ˙𝜔𝑡 𝑎 𝑏𝑙𝑒
𝐶𝑂 directly results in severe
underpredictions at both 𝑥=15 mm ,and 𝑥=25 mm, although
the general shape is roughly captured. The drastic improvement of
𝑌𝑐,2and the minor differences for 𝑌𝑐, 1with the split formulation
can be explained by the CO-source terms in Fig. 3. For 𝑌𝑐,2, the
1000
2000
T[K]
x= 5 mm x= 15 mm
−40 −20 0
z[mm]
1000
2000
T[K]
x= 25 mm
−40 −20 0
z[mm]
x= 50 mm
Exp. Yc,1Yc,2
FIGURE 7: MEAN TEMPERATURE PROFILES ALONG THE AXIAL
DIRECTION.
negative peak in ˙𝜔CO is in a very narrow region of 𝑌𝑐∈ [0.9,1],
which is not well resolved by the table. Splitting this term into
production ˙𝜔+
CO and destruction ˙𝜔−
CO terms widens these profiles
and removes the zero crossing making the profiles better resolved
by the table. For 𝑌𝑐 ,1, all three CO source terms are smooth and
span a much wider 𝑌𝑐range. Furthermore, they are better aligned
with ˙𝜔𝑌𝑐. Thus 𝑌𝑐,1results in better performance without the
split-based formulation. Similar results might be obtainable with
a refined table for 𝑌𝑐, 2, but these are more costly and harder to
construct for a wide enthalpy and mixture fraction range.
In Fig. 10, the time-averaged CO mole fraction profiles are
plotted for different wall distances 𝑧𝑤over the cooling plate and
compared with the experimental data for both progress variables
and with and without the split formulation of ˙𝜔𝐶 𝑂 . As the flame
and thus thickening effects do not appear close to the wall (Fig.5-
d) ), there is no need for the CO-ATF post-processing correction.
Especially at 𝑧𝑤=1.5 mm, the influence of the ISL, OSL, and
ORZ on CO emissions can be observed in the experimental pro-
files. At 𝑥=30 mm, the first cooling jet flow penetrates and
interacts with the ORZ and OSL, leading to an increased chem-
ical quenching of the late CO oxidation branch and to the first
maximum of 𝑋CO in the measured profile. Further downstream,
there is a minimum of 𝑋CO next to the second cooling hole po-
sition, with the influence of more diluted ISL and OSL with an
increase in cooling rate flow. From this point, 𝑋CO increases
linearly, which is caused by the convective transport of exhaust
products from the ISL towards the cooling liner. A maximum is
reached at 𝑥≈65 mm, coinciding with the fourth cooling hole lo-
cation. Subsequently, 𝑋CO continually decreases monotonically
due to the development of a continuous cooling film and enhanced
dilution fromthis axial position (see 50 % dilution line in Fig. 5).
When analyzing the differences between both 𝑌𝑐definitions
8 GTP-24-1302; ASME ©; CC-BY distribution license
40 60 80 100 120
1000
2000
T[K]
zw= 1.5mm
40 45 50 55 60
x[mm]
1000
2000
T[K]
zw= 3.0mm
Exp. Yc,1Yc,2
FIGURE 8: HORIZONTAL TEMPERATURE PROFILES AT DIFFER-
ENT HEIGHTS zwOVER THE EFFUSION COOLING PLATE.
0
5
10
XCO ·103[−]
˙ωCO = ˙ωtable
CO
x= 5 mm ˙ωC O = ˙ω+
CO +Ytr
CO ( ˙ω−
CO /Y table
CO )
x= 5 mm
0
5
10
XCO ·103[−]
x= 15 mm x= 15 mm
−40 −20 0
z[mm]
0
5
10
XCO ·103[−]
x= 25 mm
−40 −20 0
z[mm]
x= 25 mm
Exp. Yc,1Yc,2Yc,T
c,1Yc,T
c,2
FIGURE 9: MEAN CO PROFILES IN AXIAL DIRECTION WITH
(RIGHT) AND WITHOUT (LEFT) SOURCE TERM SPLITTING FOR
˙
ωCO, EQ. (2).
without the split of ˙𝜔CO, similar results are observed as in the
vertical lines. Due to the bad resolution of the source term for
40 60 80 100 120
0
1
2
XCO ·103[-]
zw= 1.5mm
40 45 50 55 60
x[mm]
0
1
2
XCO ·103[-]
zw= 3.0mm
Exp. Yc,1Y±
c,1Yc,2Y±
c,2Xtable
CO
FIGURE 10: HORIZONTAL CO PROFILES AT DIFFERENT HEIGHTS
zwOVER THE EFFUSION COOLING PLATE.
𝑌𝑐,2CO is severely underpredicted. For 𝑌𝑐,1, a better agreement
is observed, but the profiles are not captured. Furthermore, at
𝑧𝑤=1.5 mm, the individual cooling jets are visible as minima in
XCO concentration. When analyzing the split formulation ˙𝜔±
CO,
both 𝑌𝑐simulations result in very low CO predictions. This is
due to the linear scaling of the destruction term in (2). Close to
the wall, the transported CO is one to two orders of magnitudes
larger than the tabulated value. Thus, the destruction term is
overestimated, resulting in the CO𝑡 𝑟 𝑎𝑛𝑠 to be very close to the
tabulated CO𝑡 𝑎𝑏𝑙 𝑒 values, which are indicated as the black dotted
line in the plots. Thus close to the wall, the split formulation
no longer works as transported and tabulated CO values diverge
radically in these regions.
In general, the CO modeling becomes more challenging
closer to the effusion plate than in less dilution-affected areas.
The reasons are the stronger interactions of mixing, heat losses,
and chemical reactions. Besides, there may be an overlap with
heat loss-induced flame quenching with the wall, especially be-
fore the fourth hole and cooling film formation, which might
require more advanced chemistry tabulation techniques [21]. Ad-
ditionally, the high temperatures in some parts of the cooling plate
(≈1300 K) are above the auto-ignition temperature, which could
affect the CO predictions from flamelet-manifold models in gen-
eral and would equally require more advanced models. The strong
transport effects furthermore limit the applicability of previous
corrections, such as the linear scaled destruction term, due to the
large discrepancy between the tabulated and transported states.
6. CONCLUSIONS
In the present study, a practically relevant effusion-cooled
single-sector model gas turbine combustor was investigated by
using a LES-ATF approach coupled with tabulated chemistry
based on premixed flamelets. Temperature boundary conditions
9 GTP-24-1302; ASME ©; CC-BY distribution license
were computed via CHT. Model sensitivities to the progress vari-
able definition, the split and linear correction of the CO source
term in an additional transport equation for CO, and a CO post-
processing correction for ATF were thoroughly assessed.
This work demonstrates the capabilities of LES coupled with
premixed tabulated chemistry to accurately model global effects
in a laboratory-scale configuration. Temperature and velocity
profiles were well captured.
Regarding the CO modeling sensitivities following conclu-
sions are drawn:
•Two different progress variable definitions were considered,
𝑌𝑐,1=CO2and 𝑌𝑐, 2=CO2+H2O+CO. In the primary
zone, 𝑌𝑐,1showed a better performance than 𝑌𝑐,2when ˙𝜔CO
is read from the table.
•The split and linear correction in ˙𝜔𝐶 𝑂 effectively reconciled
the difference between 𝑌𝑐, 1and 𝑌𝑐,2, notably improving
𝑌𝑐,2predictions. The split’s benefits are linked to enhanced
resolution of production and destruction terms in the 𝑌𝑐 ,2
table, whereas 𝑌𝑐 ,1displays broader source term profiles
regardless of the splitting method. In the FCAI region, the
linear scaling of the destruction term results in profiles closer
to tabulated values for both 𝑌𝑐definitions. Thus, the tested
split shows minor influence compared to tabulated values
near walls when combined with EGR tables, as transported
CO deviates significantly from tabulated values.
•The CO-ATF post-processing correction successfully re-
duced the overestimation in numerical predictions and
aligned further the simulation and experimental data.
•Integrating EGR effects into the flamelet tables holds the
potential to enhance accuracy in the FCAI region. Despite a
reasonable agreement between experimental and numerical
thermo-chemical states (CO-T), addressing near-wall issues
could benefit from recently advanced manifolds with flame-
quenching effects and considerations of mixing, dilution
phenomena [32, 33], along with extensions to high wall
temperatures encountered in gas turbine combustors.
This thorough evaluation of submodels underscores the sig-
nificance of meticulous model selection, as the overall modeling
error is influenced by the weakest link. These insights can guide
future studies on modeling CO emissions in aero-engines and
stationary gas turbines.
ACKNOWLEDGMENT
The authors kindly acknowledge financial support through
the Federal Ministry of Education and Research under the Fed-
eral Aeronautical Research Program (LuFo VI, Call 1). The au-
thors gratefully acknowledge the funding by the aforementioned
institution, the ongoing support of Ruud Eggels and Max Staufer
from Rolls-Royce Deutschland, and the computing time provided
to them on the high-performance computer Lichtenberg at the
NHR Centers NHR4CES at TU Darmstadt. This is funded by
the Federal Ministry of Education and Research, and the state
governments participating on the basis of the resolutions of the
GWK for national high-performance computing at universities.
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LIST OF TABLES
Tab. 1 Investigated operating conditions from [13].
LIST OF FIGURES
Fig. 1 Schematic of the experimental set-up, adapted
from [13].
Fig. 2 Averaged profiles of CO mass fraction mimicking the
flame brush for the progress variables 𝑌𝑐,1and 𝑌𝑐,2.< 𝑌CO >
(laminar), <
ˆ
𝑌CO >(thickened), <
ˆ
𝑌𝑐
CO >(thickened, laminar
correction), <
ˆ
𝑌𝑐,𝑇
CO >(thickened, turbulent correction).
Fig. 3 Alignment of the flame sensor [43] with the progress
variables and CO source terms.
Fig. 4 𝑎)Temperature distribution in the solid domain. 𝑏)
Grid used in the study.
Fig. 5 Time averaged velocity, temperature, transported
CO mass fraction and normalized mixture fraction fields. Flow
structures marked in black over the velocity field. White lines
mark the position of vertical line comparisons. 50 % dilution
isoline shown over 𝑍𝑛in white. Instantaneous Fisolines plotted
over 𝑍𝑛.
Fig. 6 Mean and RMS axial (left) and radial (right) velocity
profiles.
Fig. 7 Mean temperature profiles along the axial direction.
Fig. 8 Horizontal temperature profiles at different heights
𝑧𝑤over the effusion cooling plate.
Fig. 9 Mean CO profiles in axial direction with (right) and
without (left) source term splitting for ˙𝜔CO, eq. (2).
Fig. 10 Horizontal CO profiles at different heights 𝑧𝑤over
the effusion cooling plate.
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