Enhanced Emission Prediction Modeling and Analysis For Conceptual Design
Enhanced Emission Prediction Modeling and Analysis For Conceptual Design
Enhanced Emission Prediction Modeling and Analysis For Conceptual Design
2
Ldiff_axial LPZ_axial LSZ_axial LDZ_axial Ltr
r
m
3
3
r
i
3
3
r
i
3
4
L
r
m
3
m
r
i
3
m
r
o
3
m
m
r
o
3
9
L
r
o
3
4
31
32
33
34
39
40
31t
39t
0
Lm3m
Li3m
Lo3mm
3m
3mm
Lm33 Li33 Lo34 Li34L Lo39L L40
=
Ltotal_axial
25
of a dump diffuser. Off-design, the calculation keeps geometry the same (hence diffuser
efficiency) and iterates on exit total pressure to match diffuser efficiency.
Figure 21: Diagram of Diffuser Element
The user-provided inputs to the diffuser element are summarized in Table 4.
Table 4: Diffuser Element Inputs
rm31 Mean radius at HPC exit
Mach32 Mach number at diffuser exit
theta Diffuser passage half angle
alpha Combustor meanline angle
passage_number Number of diffuser splitter plates
sweet_spot Maximum aspect ratio for a flat-wall diffuser
Combustor Element
The Combustor element represents the assembly of the liner (primary, secondary and dilution
zones + transition duct) surrounded by a casing for annulus flow (secondary, dilution and cooling
air). A diagram of the Combustor element is presented in Figure 22 below.
rm
32
/rm
31
#passages
AR
max
P
S
=P
S32
-P
S31
Mach
32
rm
31
geometry
swirler
atomizer
2
26
Figure 22: Diagram of Combustor Element
Total pressure is assumed to be constant in the liner and in the annulus. The relative difference
between the annulus and liner total pressures is dPqP. Liner and casing cross-section areas are
also assumed constant. The liner dynamic pressure is considered negligible compared to the
liner total pressure. This hypothesis, together with the constant total pressure assumption in the
liner and casing yields a constant velocity for every jet flowing from the casing into the liner
(i.e., through the primary zone swirlers, secondary holes and dilution holes).
The Combustor element, as a parent element, is intended to facilitate transfer of variables
between the different objects constituting the combustor. The different zones (PZ, SZ, DZ) are
hence represented by subelements plugged into the Combustor element. Each subelement
calculates the airflow required for its associated zone, the geometry of the zone and exit flow
station properties. Any variable declared in the Combustor element is readable and writable by
any subelement plugged in. Specific calculations in the Combustor element are related to cooling
flow.
On design, pressure losses (dPqP) and either FAR or WFUEL (fuel weight flow) are specified by
the user, with the other of the two calculated as an output. Airflow sent to the primary zone
depends on the PZ equivalence ratio (eqratio_PZ, user input) and the global equivalence ratio
(eqratio_40). Airflow sent to the secondary zone is calculated such that total temperature does
not vary between the primary and secondary zones. Cooling flow is calculated depending on the
maximum temperature the liner can withstand (MaxTempLiner), the type of cooling used
(CoolMechanism_factor) and PZ & SZ total temperature. The remainder of air is dumped into
the dilution zone. It should be noted that while eqratio_PZ is greater than 1, the combustion
process is assumed to take place in stoichiometric conditions to compute the maximum possible
temperature for purposes of sizing the cooling flow. However, the airflow through the combustor
itself is calculated using the input value of eqratio_PZ .
Off design, the combustor pressure drop is assumed to be constant (dPqP). Again, either FAR or
WFUEL is specified. Primary zone airflow depends on the geometry (LINtoCASE_areaRatio),
assuming dPqQ is constant (also calculated on design). Secondary and dilution zones airflows
are calculated based on the geometry (using mass conservation). Cooling airflow is calculated as
the remainder of air.
W
fuel
/ FAR
W
fuel
/ FAR
dPqP
dPqP
geometry
T
max
liner
cooling factor
subelements outputs
subelements outputs
27
The user-supplied inputs required for the Combustor element are summarized in Table 5 below.
Table 5: Combustor Element Inputs
MaxTempLiner Maximum allowable liner temperature
CoolMechanism_factor Cooling mechanism factor
dPqP Burner pressure drop
switchBurn Burner mode; input either FAR or WFUEL
switchPower Power setting for use by regression model
injector_Ploss_design Injector pressure loss (percent)
FuelProperties Subelement
To simplify the user interface, all the fuel property data needed for calculations is handled in the
FuelProperties subelement. These parameters are used for the fuel droplet evaporation model
and/or are passed along to the CRN for use in the detailed chemical mechanism calculations.
The FuelProperties inputs are summarized in Table 6 below.
Table 6: Fuel Properties Subelement Inputs
fuel_density Fuel density in kg/m3
fuelTemp Fuel temperature in deg R
fuelFormula Fuel chemical formula, e.g. C12H23
numCarbon Number of carbon atoms in fuel formula
numHydrogen Number of hydrogen atoms in fuel formula
FuelDropletEvaporationModel Subelement
The purpose of the FuelDropletEvaporationModel subelement is to compute the ratio of fuel
vapor to total fuel. The fuel droplet evaporation model is described in Appendix A.
PZ Subelement
The PZ subelement represents the combustor primary zone. The purpose of the PZ subelement
computes the swirler number and geometry, the primary zone required air, PZ geometry, and PZ
exit temperature. A diagram of the PZ subelement is presented in Figure 23 below.
28
Figure 23: Diagram of PZ Subelement
An adiabatic flame temperature calculation is performed using the NPSS burn function (limited
to lean or stoichiometric mixtures depending on which NPSS ThermoPackage is selected). The
inputs are the combustion efficiency (ratio of fuel burned over fuel injected) and equivalence
ratio.
The swirlers are designed with the conditions that the swirl number be large enough (greater than
0.6) and that all the swirlers fit in the liner dome (checking both azimuthal and radial space
constraints). The swirler blade angle and number of nozzles are iterated on while hub radius and
discharge parameters are inputs.
The primary zone length is calculated as the length of the recirculation bubble (based on swirler
geometry and swirl number).
The user-supplied inputs required for the PZ subelement are summarized in Table 7
Table 7: PZ Subelement Inputs
sw_angle Swirler blades angle (desired value)
swirler_discharge_parameter Swirler discharge coefficient
r_hub Swirler hub radius
Wair_nozzletoWfuel Air/Fuel ratio of each fuel injector
eff_PZ PZ combustion efficiency
eqratio_PZ PZ equivalence ratio
mixer_PZ_vol_rat Mixer to PZ volume ratio
SZ Subelement
The SZ subelement represents the combustor secondary zone. A diagram of the SZ subelement
is presented in Figure 24 below.
blade angle
swirler C
d
r
hub
(W
fuel
/W
air
)
injector
ef f iciency
PZ
ef f iciency
PZ
eq. ratio
PZ
29
Figure 24: Diagram of SZ Subelement
On design, the amount of air to be added in the secondary zone through the secondary holes
(frac_SZ) is calculated such that total temperature remains unchanged from the PZ (iterates on
the fuel to air ratio). The number and diameter of the secondary zone dilution holes are
calculated using conservation laws (mass & momentum), together with the Boussinesq
assumption (density varies with temperature only) and empirical relationships (jet penetration as
a function of dynamic pressure ratios). Jet penetration over liner height is a user input in this
procedure. The SZ length and volume are fixed by the user when choosing the aspect ratio (SZ
length to liner height ratio).
The required user-supplied inputs for the SZ subelement are summarized in below.
Table 8: SZ Subelement Inputs
SZ_discharge_coeff SZ holes discharge coefficient
SZ_length_ratio SZ aspect ratio (length/liner height)
SZ_penetration_ratio SZ jets penetration ratio (Y
max
/liner height)
eff_SZ SZ combustion efficiency
DZ Subelement
The DZ subelement represents the combustor dilution zone. A diagram of the DZ subelement is
presented in Figure 25 below.
SZ C
d
(Y
max
/H
liner
)
SZ
efficiency
SZ
efficiency
SZ
geometry
L
SZ
/H
liner
combustor.int outputs
PZ outputs
combustor.int outputs
PZ outputs
30
Figure 25: Diagram of DZ Subelement
On design, the air flowing through the dilution holes is simply the remainder of air after flow
was partitioned between the cooling flow and the primary and secondary zones. In the dilution
zone the adiabatic flame temperature is calculated using the overall efficiency and equivalence
ratio of the entire burner, to be consistent with the NPSS cycle calculations using the standard
NPSS Burner element.
The number and diameter of the dilution holes are calculated similarly to the secondary zone, but
with unique values for the discharge coefficient and jet penetration ratio (both user inputs). As
in the secondary zone, the dilution zone length and volume are fixed with the aspect ratio of the
zone (user input). A transition duct is added to provide a good pattern factor at the HPT inlet (no
hot spots). The length of this duct is fixed with an aspect ratio variable. It is assumed that no
combustion occur in this zone, just mixing. The exit area is varied until the desired HPT inlet
Mach number (Mach40) is matched.
The required user-supplied inputs for the DZ subelement are summarized in Table 9 below.
Table 9: DZ Subelement Inputs
DZ_discharge_coeff DZ holes discharge coefficient
DZ_length_ratio DZ aspect ratio (length/liner height)
tr_length_ratio Transition duct aspect ratio (length/liner height)
DZ_penetration_ratio DZ jets penetration ratio (Y
max
/liner height)
eff_DZ DZ combustion efficiency
Mach40 HPT inlet Mach number
rm40 HPT inlet mean radius
CombPerfParams Subelement
The CombPerfParams subelement is provided for the user to calculate any additional
performance parameters of interest for the combustor which may not affect any of the combustor
sizing and flow partitioning calculations. Currently the element is used to compute the
unmixedness parameter from an empirical relationship [58]. The unmixedness parameter is
needed for the CRN.
DZ C
d
(Y
max
/H
liner
)
DZ
efficiency
DZ
efficiency
DZ
Mach40
L
DZ
/H
liner
rm40
31
CreateCHEMKI NI nputs Subelement
The CreateCHEMKINInputs subelement is provided to gather or compute the necessary
variables that are needed as inputs to the CHEMKIN model, such as the volumes of each of the
elementary reactors (PSRs and PFRs) used in the CRN. Many of the parameters computed in
this subelement are related to the unmixedness model, which is described in Appendix A.
4.2 Rich-Quench-Lean Combustor
The RQL 1D-Flow model is an extension of the 1D-Flow model of the SAC. An overview of
the RQL 1-D Flow Model is presented in Figure 26. The RQL 1-D Flow Model comprises the
Diffuser, the Rich Zone, the Mixing Zone, the Lean Zone, and the Dilution Zone. The Diffuser
and Dilution Zone are identical with those elements of the SAC model.
Figure 26: Overview of 1-D Flow Model for RQL Combustor
The following sections outline the major differences between the RQL model and the SAC
model. More details and equations may be found in Appendix C.
RZ Subelememt
An important point in computing the Rich zone properties is that, since the Rich zone
combustion occurs at conditions above stoichiometric, the normal GasTbl or AllFuel property
tables in NPSS are not appropriate. A higher fidelity combustion model, such as chemical
equilibrium analysis (CEA) is required to determine the flame temperature and flow properties at
Rich conditions. The CEA Package is based on the NASA Chemical Equilibrium Analysis
FORTRAN code that has been implemented in NPSS.
Rich zone
An additional feature is added to the Rich zone model which is the configuration option. Since
some of the validation cases are performed for the a tubular type RQL combustor, it became
necessary to include the tubular option (in addition to already available option of annular
configuration) to the Rich zone, Mixing zone, Lean zone and Dilution zone models. The major
difference between these two configurations is in the equation used to calculate the liner and
casing heights for each component.
0 2 4 6 8 10 12 14 16 18 20
8
10
12
14
16
18
20
22 RQL Combustor
Diffuser
RZ LZ DZ
Flow
Partitioning
CEA gas
properties
MZ
32
MZ Subelement
The Mixing zone is specific to the RQL combustor, where the annulus air must mix quickly with
the fuel rich hot gases coming out from the Rich zone section. Different mixing methods may be
used, but this research is limited to the Wall-Jet mixing method.
The main purpose of the MZ subelement is to determine the fraction of the air that should be
added to the hot gases to bring it from Rich regime to Lean regime. In the SAC model the flow
of the secondary zone is calculated based on the amount of increase in efficiency from PZ to SZ
zone with the gas temperature kept constant from PZ to SZ. In the RQL model, the amount of
flow that goes into the Mixing zone is based on the defined LZ equivalence ratio (in On-Design)
or the quench orifice size and pressure drop (in Off-Design).
The Mixing zone component is linked to the Rich zone component through the flow station
FS33. Similar to the Rich zone, the configuration may be Annular or Tubular. The cross
section area at the mixing zone is reduced by the user-defined factor MZtoPZ_areaRatio. The
number and size of the orifices at design condition is calculated and the maximum penetration is
determined using empirical relations.
For determining the Mixing zone exit temperature, the Burn function is not used. Assuming
the ideal case of the perfect mixing and absence of any reaction, the exit temperature of the
Mixing zone is simply the sum of the sensible enthalpies of air and core flows divided the total
flow. A more accurate exit temperature is determined later in the Chemical Reactor Network
model.
CreateCHEMKI NI nputs Subelement
The CreateCHEMKINInputs subelement collects and/or comptues all the inputs required by the
Chemical Reactor Network (CRN) model. The droplet SMD and evaporation modeling are the
same as for the SAC model, as are the Rich zone unmixedness and corresponding distribution of
equivalence ratio in the Rich zone.
The significant difference with the SAC model is the additional equations added to take into
account the unmixedness in the Mixing zone. A simplified model is developed to model the
macro-mixing and its quality in the mixing zone. The assumption for developing this model is
that the perfectly mixed model (zero unmixedness) will burn in the Lean zone right at the Lean
zone equivalence ratio (which is well below one). As the Mixing zone unmixedness increases
from zero to one, more and more of the mixture will burn at the unity equivalence ratio and the
rest will burn at an equivalence ratio that is determined by the remaining air and fuel. The
unmixedness value is an input from the Mixing zone object. A linear relationship is assumed
between the Mixing zone unmixedness value and the equivalence ration between the Lean zone
equivalence ratio and one.
Additional parameters are related to the PaSR (Partially Stirred Reactor) model. First is the
residence time of the Mixing zone, based on half the Mixing zone volume because the mixing
flow enters the zone at the halfway point. The PaSR simulation time should be long enough so
the solution of the PaSR reaches the steady state condition but not so long to make the simulation
very slow. It is defined to be 5 times the calculated residence time. Also, the time step of
33
statistical samples that is required in the Monte Carlo simulation in the PaSR is set to one tenth
of the Mixing zone residence time. The design inputs for the RQL 1-Df Flow Model are
summarized in Table 10.
Table 10: Inputs to RQL 1-D Flow Model
Component Inputs Units
D
i
f
f
u
s
e
r
Inlet Mean Radius in
Inlet Mach Number -
Exit Mach Number -
Half Angle -
Orientation Angle (guess) deg
Passage Number -
Sweet Spot -
B
U
R
N
E
R
dP_injector Psia
Fuel Density Kg/m3
dP/P -
T_liner_max R
Cooling Mechanism
Factor
-
T_fuel R
Configuration -
R
i
c
h
Z
o
n
e
Swirl Angle deg
Swirler Discharge
Coefficient
-
Swirler_hub in
W_nozzle_air/w_fuel -
Burning Efficiency -
Equivalence Ratio -
Vol_Mixer/Vol_RZ -
M
i
x
i
n
g
Z
o
n
e
Discharge Coefficient -
Length Ratio -
Area_MZ/Area_RZ -
Mixing Model -
Mixing Model Factor -
Mixing Mode -
Monte Carlo Sample
Number
-
L
e
a
n
Z
o
n
e
Burning Efficiency -
Equivalence Ratio -
Length Ratio -
D
i
l
u
t
i
o
n
Z
o
n
e
Burning Efficiency -
Discharge Coefficient -
Jet Penetration Ratio -
Transition Length Ratio -
Length Ratio -
Exit Mean Radius in
Exit Mach Number -
34
4.3 Lean-Burn Combustor
The Lean-Burn combustor considered in this study is intended to be representative of a GE Twin
Annular Premixing Swirler (TAPS) type of combustor. The TAPS combustor is characterized by
two co-annular swirling jets produced by a pilot and a main mixer [39]. The swirl in the pilot is
primarily responsible for the recirculation zone around the axis of the combustor. All the fuel of
the pilot injector and some of the main mixer, in the pilot/main interaction zone, are received by
this recirculation zone. The resulting high fuel-air ratio in this zone leads to long residence time
and high temperature which in turn give the necessary stability to the combustor. The remainder
of the fuel from the main injector travels along the border of the recirculation zone and is
consumed there [21], [33]. The pilot and main swirling jets are separated by a step height. This
allows for the fuel injected into the main burner to be thoroughly mixed before it is consumed by
the combustor flame downstream. This combustor utilizes an advanced fuel injection method to
optimize the fuel mixture for low emissions products while maintaining the system design
requirements. To ensure the combustor maintains a flame at both low and high power settings,
fuel injection occurs at multiple sites in the fuel injector assembly.
The TAPS fuel injection system is what allows the combustor to reduce the NOx produced.
There are two main sites of fuel injection; the first is the pilot injector. The pilot injector utilizes
a similar fuel injection method as the SAC model. A fuel injector is surrounded by two swilrers
that help to atomize the fuel. The second fuel injection site is referred to as the main mixer
which contains a swirler situated parallel to the incoming airflow and a fuel injector.
Figure 27: Overview of 1-D Flow Model for Lean-Burn Combustor
To create the 1-D Flow Model for the Lean-Burn combustor, the previously constructed SAC
model is used as a starting point. Several changes are made to the model in order to more closely
resemble the TAPS fuel injection method.
It is assumed that all of the air entering the combustor is used to create the lean conditions in the
primary zone. As a result, there is no remaining air to be introduced through secondary or
dilution zone jets (it is noted that there are still cooling holes). Therefore all of the calculations
35
in the SAC model that deal with air jets and jet hole sizing are omitted in the Lean-Burn
combustor model.
The most significant difference between the two combustor models is the fuel injection system.
The Lean-Burn injection system incorporates both a pilot injector and a main injector. The pilot
injector is sized the same as the SAC injector and the physical geometry of the main injector is
assumed to be a percentage of the pilot swirler size. This assumption is made because the main
injector swirlers are parallel to the flow and so do not affect the sizing of the primary zone.
In addition, fuel- and air-schedules were added to the model. These schedules change the
amount of fuel that enters the pilot injector and the main injector zones as a function of engine
power setting, from 100% fuel flow through the pilot at idle to 15% fuel flow through the pilot at
max power.
Other than the changes discussed above the 1-D Flow Model remained the same as the SAC
model. The same program structure was kept so that there was continuity between all of the
created advanced combustor models.
5 ModelCenter Integrated Environment
Due to the complexity of the CHEMKIN model, fileWrappers are provided to link the two codes
using ModelCenter. As described above, a special NPSS subelement called
CreateCHEMKINInputs was created to compile the inputs needed by CHEMKIN (and to convert
them to SI units) through a special viewOut file. An example screen-shot of the ModelCenter
environment created for the SAC model is shown in Figure 28.
36
Figure 28: ModelCenter Environment for SAC Combustor Model
In this example, each data point is run one at a time, and the user may either specify the inputs
via a DOE table or he may manually input the values in the window on the left-hand side of the
screen.
Figure 29 shows an example screen-shot ModelCenter environment created for the RQL model.
In this example, the process for running all four ICAO power settings to compute LTO emissions
has been completely automated, and so four instances of the model appear in the right-hand
window of the screen.
37
Figure 29: ModelCenter Environment for RQL Combustor Model
38
6 Validation Cases
Each combustor model (1-D Flow Model and CRN) was validated against published test data.
The SAC was validated against the GE Energy Efficiency Engine (E
3
) single-annular combustor
[5], the RQL was validated against a NASA HSR combustor [44], and the Lean-Burn combustor
was validated against an ONERA multi-point combustor [33]. The results are described in the
following sections.
SAC
Figure 30 presents a comparison of the E
3
model results to the data published in the E
3
report.
On the left, it may be seen that the EINOx is predicted very accurately. On the right, it may be
seen that the EICO matches at high power but the model under-predicts at lower power.
Figure 30: SAC Model Emissions Predictions vs. Validation Data
RQL
Several test conditions were reported in the HSR report; however only one condition included
emissions data (see Table 11). The EINOx and EICO were matched at this point. The other
conditions were evaluated and the trends were judged to be acceptable.
Table 11: HSR Combustor Test Results [44]
Test Conditions T3 (R)
P3
(psia)
FAR
Wa
(lb/s)
Wf
(lb/s)
EI NO
x
EI CO
Subsonic Cruise 1090 80 0.02 22.2 0.44 ? ?
Supersonic Cruise 1660 150 0.03 39.6 1.18 13.6 5-20
100% Thrust 1379 301 0.0329 79.2 2.6 ? ?
65% Thrust 1200 212 0.0248 39.6 0.98 ? ?
34% Thrust 1048 134 0.0187 38.4 0.72 ? ?
15% Thrust 906 82 0.0141 25.8 0.36 ? ?
5.8% Thrust 755 45 0.0113 ? ? ? ?
0
5
10
15
20
25
0.0 0.5 1.0 1.5
E
I
N
O
x
(
g
/
k
g
)
Fuel Flow (kg/sec)
E3 Report
E3 Model
0
5
10
15
20
25
30
0.0 0.5 1.0 1.5
E
I
C
O
(
g
/
k
g
)
Fuel Flow (kg/sec)
E3 Report
E3 Model
39
Lean-Burn
The Lean-Burn model predictions were compared to experimental measurements on the ONERA
multi-point combustor by Grisch et al.[21], and Matuszewski et al. [33]. NOx measurements
were reported at Idle and Takeoff conditions. These results were matched, as shown in Table 12.
Table 12: ONERA Multi-Point Combustor Results [21, 33]
P
(bar)
Inlet T
(K)
Airflow
(kg/sec)
Fuel Flow
(g/sec)
Overall
EI NOx
(Data)
EI NOx
(Model)
Idle 45 480 0.344 5.03 0.215 0.8 1.75
Takeoff 22 730 1.255 38.17 0.433 12.6 12.65
40
7 CFM56-class Baseline Cases
To create a meaningful demonstration of a parametric design space, it is desirable to compare the
three combustor types applied to the same engine cycle. The CFM56-7B27 engine cycle was
selected for this purpose, since an existing, validated NPSS model was already available. The
CFM56 engine model was developed previously as part of the FAA Environmental Design
Space (EDS) project; the required engine cycle values taken from EDS engine model run at
ICAO flight conditions and power settings are presented in Table 13. Geometry information
needed for the 1-D Flow Model was determined from a CFM56 engine cross-section drawing.
Table 13: CFM56-7B27 Engine Cycle Parameters
Cycle Parameter Unit Takeoff Climb Approach Idle
Pt3 psia 420.6 359.3 164.2 81.1
Tt3 R 1441 1375 1103 908.9
- 0.42 0.39 0.245 0.144
Wair lbm/sec 98.2 86.2 46.0 26.7
In the following Figures the baseline model for each combustor type (SAC, RQL, and Lean-Burn)
are compared to the ICAO data. In each case, all the ICAO data for applicable single-annular
CFM56-5 and CFM56-7 engines with the same combustor design was plotted, in order to give an
indication of the experimental error in the ICAO data.
Figure 31 shows a good match of the SAC baseline model to the ICAO NOx and CO emissions
index data for the family of CFM56 engines.
Figure 31: Comparison of SAC Model to CFM56 Baseline Data
Figure 32 presents the results for the RQL baseline model. In this case, the RQL 1-D Flow
Model was scaled up to the CFM56 engine operating conditions. Fixed geometry fuel
scheduling was assumed. Note that a 66% improvement in NOx is predicted; this is consistent
with estimates given in the published literature.
0
5
10
15
20
25
30
35
40
0.0 0.5 1.0 1.5 2.0
E
I
N
O
x
(
g
/
k
g
)
Fuel Flow (kg/sec)
ICAO Data
SAC Model
0
5
10
15
20
25
30
35
40
0.0 0.5 1.0 1.5 2.0
E
I
C
O
(
g
/
k
g
)
Fuel Flow (kg/sec)
ICAO Data
SAC Model
41
Figure 32: Comparison of RQL Model to CFM56 Baseline Data
The horizontal characteristic of the EINOx plot is of particular interest. The NOx production
appears to be independent of the engine power setting over a wide range. This may be explained
by the fact that the PZ equivalence ratios are greater than unity except in idle case. Since NOx
production increases with reaction temperature, and reaction temperature increases as the PZ
equivalence ratio is nearer to stoichiometric. Figure 33 shows that indeed the PZ reaches
stoichiometric conditions at Approach power.
Figure 33: Variation of Equivalence Ratio with Power Setting in RQL Combustor
For the Lean-Burn baseline model, Figure 34 shows 37% improvement in NOx, again consistent
with the published literature.
0
5
10
15
20
25
30
35
40
0.0 0.5 1.0 1.5 2.0
E
I
N
O
x
(
g
/
k
g
)
Fuel Flow (kg/sec)
ICAO Data
RQL Model
66%
0
10
20
30
40
50
60
70
0.0 0.5 1.0 1.5 2.0
E
I
C
O
(
g
/
k
g
)
Fuel Flow (kg/sec)
ICAO Data
RQL Model
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
E
q
u
i
v
a
l
e
n
c
e
R
a
t
i
o
Fuel Flow (kg/sec)
PZ
LZ
DZ
42
Figure 34: Comparison of Lean-Burn Model with CFM56 Baseline
Finally, one additional sanity check of the baseline models may be made to pusblished data
with known combustor types (ref. Mongia [38]) on an overall (NOx Dp/F00) basis. In Figure 35,
the SAC baseline model exactly coincides with the CFM56-7B27 engine at an OPR of around 29,
as expected. At the same OPR, the RQL baseline model gives the lowest Dp/Foo NOx and plots
very near a Talon X data point. Also the Lean-Burn model at the same OPR plots in the
neighborhood of a CFM56 TAPS data point. All in all, the baseline models are judged to be
good baseline points about which to build the regression models.
0
5
10
15
20
25
30
35
40
0.0 0.5 1.0 1.5 2.0
E
I
N
O
x
(
g
/
k
g
)
Fuel Flow (kg/sec)
ICAO Data
Lean-Burn Model
37%
0
5
10
15
20
25
30
35
40
0.0 0.5 1.0 1.5 2.0
E
I
C
O
(
g
/
k
g
)
Fuel Flow (kg/sec)
ICAO Data
Lean-Burn Model
43
Figure 35: Comparison of Combustor Models to Existing Engines
8 Regression Models
The time required to execute the CHEMKIN Chemical Reactor Network models may hinder a
comprehensive parametric analysis. This is especially true for the RQL combustor due to its use
of the Partially Stirred Reactor (PaSR). Thus it is desirable to replace the CRN with a regression
model. A regression model is not needed for the 1-D Flow Model because it runs quickly
enough, even though the CEA gas properties do slow down the RQL model calculations.
The general steps in creating the regression model are summarized below:
- Establish baseline (center-point) values and ranges for independent variables
- Create space-filling Latin hypercube DOE
o Approx. 15 independent variables based on CRN
o 3000 cases run for each of the four ICAO power settings
- Generate training data by executing the models in ModelCenter
- Fit models to responses using Neural Network
o EICO is transformed with log function
o Hold back some of the data for validation
The baseline points for each of the three regression models (SAC, RQL, and Lean-Burn) were
described in the previous section. In each case, the dependent variables (outputs) to be regressed
are the EINOx and EICO for each of the four ICAO power settings. The independent variables
depend upon the specific CRNs, and are summarized in previous sections.
0
10
20
30
40
50
60
70
80
90
20 25 30 35 40 45
N
O
x
D
p
/
F
0
0
OPR
CFM56-7B27 (SAC)
PW4090 (TALON)
PW4098(TALON I)
CF6-80C2B1(RQL)
PW6122A(TALONII)
Talon X
CFM56 TAPS
SAC Model
Lean-Burn Model
RQL Model
44
The Neural Network method was chosen to create the regression models due to the non-linear
nature of the problem. The goodness-of-fit was evaluated by examining the Model Fit Error
(MFE) and the Model Representation Error (MRE). 3600 data points were used to train the
Neural Networks, and 20% of the data was held back for evaluating the Model Representation
Error.
The Model Fit Error evaluates the regression model against the data that was used to train the
Neural Network; it indicates how well the regression model reproduces the training data. The
mean and the standard deviation of the error (residual) are computed and plotted. The mean
should be near zero. A histogram of the error distribution and a plot of the residuals vs. the
predicted data should indicate that the error is normally distributed, and the standard deviation
should be less than one. In addition, a plot of the predicted results vs. the training data should be
a straight line with a value of correlation coefficient R
2
near one.
The same criteria are applied to the Model Representation Error, which compares the regression
model to the data points which were not used for training the Neural Network. The Model
Representation Error indicates how well the regression models perform at points for which the
models must interpolate.
Figure 36: Goodness-of-Fit Results for Regression Model of SAC NOx
Takeoff
Climb Out
Approach
Idle
45
Figure 37: Goodness-of-Fit Results for Regression Model of RQL NOx
Takeoff
Climb Out
Approach
Idle
46
Figure 38: Goodness-of-Fit Results for Regression Model of RQL CO
Takeoff
Climb Out
Approach
Idle
47
Figure 39: Goodness-of-Fit Results for Regression Model of Lean-Burn NOx
Takeoff
Climb Out
Approach
Idle
48
Figure 40: Goodness-of-Fit Results for Regression Model of Lean-Burn CO
The goodness-of-fit results are presented in the Figures above. It may be seen that all the
regressions meet the criteria, although the Lean-Burn model displays a curious bi-modal
characteristic in the NOx prediction at idle (see Figure 39). The cause for this behavior could not
be verified, but it is believed to be related to the main- and pilot-zone equivalence ratios.
EmissionsNN Subelement
The regression models are incorporated into the NPSS models through a combustor subelement
called EmissionNN. This subelement contains the neural network equations for EINOx and
EICO for the four LTO cycle power settings. There is a different subelement for each of the
three combustor types.
9 Conclusions and Recommendations
The research presented herein has successfully developed and demonstrated an emissions
prediction capability for systems-level analysis during conceptual design. The new capability has
infused more physics-based effects into the emissions predictions, such as unmixedness, droplet
evaporation, rich burning, and lean burning. In addition, a library of NPSS elements has been
developed to model combustors in more detail, explicitly taking into account the diffuser, the
primary zone, the secondary or mixing zone, and the dilution zone. The new capability was
demonstrated for three types of combustors: a conventional single annular combustor, a Rich-
Takeoff
Climb Out
Approach
Idle
49
Quench-Lean type of advanced combustor, and a Lean-Burn type of advanced combustor. The
new NPSS elements allow parametric modeling of these types of combustors.
Recommendations for Future Research
1. While the resulting model did match well with the limited data available, it is difficult to
fully assess the model accuracy without more data. It is recommended that the model be
calibrated with real combustor data.
2. The Kollrack chemical mechanism described in Appendix xx was not intended for
emissions prediction. In particular, the Kollrack mechanism contains only the thermal
NOx mechanism which is dominant in conventional stoichiometric combustors. Other
NOx and CO production processes may be more important for rich and lean conditions.
Some of the limitations of the Kollrack mechanism may be reflected in the relatively poor
matches to EINOx and EICO for the advanced combustors at idle conditions. It is
recommended that additional reduced mechanisms be investigated. These mechanisms
should be tailored for emissions prediction with Jet-A and alternative fuels.
3. The fuel injector, swirler, and unmixedness models make use of empirical relationships
which were created for existing conventional combustors. Advanced combustors depend
upon advanced swirler configurations for improved atomization and mixing. A more
physics-based model of the fuel injection system would permit the effects of
atomizer/swirler design on fuel-air distribution (unmixedness) to be evaluated. It would
also permit improved flow partitioning and pressure loss variation with power.
4. The capability of the model should be increased to provide emissions predictions
throughout the engine operating envelope. This capability depends mostly on the ability
of the regression model to predict over a wide range of operating conditions.
5. Finally, the capability of the model should be extended to the use of alternative fuels
(biofuels) and for the prediction of other species (e.g., SOx, soot). These capabilities
depend upon having the appropriate chemical mechanisms and adequate models for other
related combustion processes.
10 Acknowledgements
This research was performed under NASA grant number NNX07AO08A. Several members of
the research team were supported by related FAA research programs. The research team would
like to thank Nan-Suey Liu and Dan Bulzan from NASA Glenn Research Center for the LDI
data, and John Crane of Georgia Tech for the SPRF data. The research team would also like to
thank Dr. Vigor Yang, chair of the Daniel Guggenheim School of Aerospace Engineering at
Georgia Tech, for his review of the project leading into the final year of research.
50
Appendix A: Combustion Theory
Appendix A provides relevant background information on aircraft gas turbine combustors and
combustion modeling.
Parts of the Combustor
A brief explanation of the combustor elements that are used in the component modeling
approach is provided here. Figure 41 illustrates the major parts of a typical gas turbine
combustor.
Figure 41: Parts of a Typical Gas Turbine Combustor
Diffuser
The purpose of the diffuser is to slow down the air flow coming from the compressor, to provide
smooth and well-distributed flow to the combustor core and annulus, and to increase the static
pressure with a minimum total pressure loss, flow distortion or swirl. Diffusers may have a flat
or curved wall, with gradual or sudden expansion, and single or multiple passages.
Atomizer
Fuel atomization and spray droplet size have important effects on combustor performance and
emission levels. When liquid fuel such as Jet-A is injected to the combustor core, the stream of
fuel forms droplets with various sizes through aerodynamic and hydraulic instabilities [10, 59].
The heat that exists in the vicinity of the droplets evaporates most of them quickly, but the size
of some of droplets is such that they enter the flame zone before they completely evaporate.
Existence of droplets in the flame region creates what is called a diffusion flame [51].
In contrast to the premixed flame, where the fuel and oxidizer (air) are mixed together before
burning, in the diffusion flame the fuel and air are separate and they encounter the flame from
opposite directions through the diffusion process. The flame front is located at a place between
the incoming air and fuel streams where the fuel to air ratio is stoichiometric and it always
produces the maximum flame temperature. Thus the existence of droplet burning and
consequentially the diffusion flame has a significant effect on the level of pollutants. While high
temperature diffusion flames can burn off Carbon Monoxide (CO) and Unburned Hydro Carbons
51
(UHC), at the same time they will enhance one of the NO
x
formation mechanisms and result in a
higher level of NOx emissions [48].
The droplet size distribution depends on many factors such as atomizer type, flow-field around
the fuel jet and upstream fuel line conditions (see Figure 42).
Figure 42: Example Droplet Size Distribution
It is convenient to work with mean droplet diameter instead of droplet distribution. Among many
different definitions available for mean diameter, the Sauter Mean Diameter or SMD is widely
used in combustion applications and is defined as the diameter of a droplet whose ratio of
volume to surface is the same as whole fuel spray. The SMD can be looked at as an average or
mean value diameter of all droplets that are present in the spray. Droplet models are usually
defined in term of the droplet SMD as a function of atomizer type. Lefebvre [28] and Mellor [37]
have provided droplet models for simplex and air blast atomizers.
Swirler
The other element that has a direct effect on the structure of the flame, emissions levels and
overall combustor efficiency is the swirler. The main purpose of the swirler is to impose a
tangential motion to the flow and create a flow recirculation that brings the hot gases back to the
flame front. This increases the flame stability and prevents flame blow-off. At the same time the
toroidal motion of the flow reduces the flame length [9]. The amount of swirling that a swirler
imposes to the flow is quantified by the Swirl number (S) which is shown in the equation below
[11].
52
0 x
r G
G
S
|
=
(1)
where G
L
: Fuel (Jet-A) surface tension (N/m)
L
: Fuel (Jet-A) dynamic (absolute) viscosity (Poise, Pa.s)
m
L
: Fuel flow rate (Kg/s)
P
L
: Pressure drop across atomizer (Pa)
A
: Gas density (Kg/m3)
In order to find the amount of vaporized fuel in a given volume (mixer volume) before entering
into flame zone, following equation is derived from the droplet evaporation D
2
law and mass
conservation principle:
|
|
.
|
\
|
= |
.
|
\
|
=
|
|
.
|
\
|
=
n evaporatio
mixer
2
3
mixer
3
mixer
2
f
f
1
SMD
. K
1
SMD
. K SMD
m
m
total
vaporized
t
t t
t
(3)
K: Mean fuel evaporation constant
mixer
: Mixing characteristic time
evaporation
: Evaporation characteristic time
SMD: Droplet Sauter mean diameter
54
Evaporation time in mixer (
mixer
) is obtained from Equation (4):
Air
Air
mixer
m
V .
t =
(4)
The part of the fuel flow that remains in liquid form is considered to be burned at stoichiometric
ratio to resemble the diffusion flame; therefore an adequate amount of air will be assigned to
liquid fuel flow to make the equivalence ratio equal to one. The rest of the airflow and vaporized
fuel flow will be assumed to be mixed before ignition. The air and fuel mixture is not uniform in
the combustor and this non-uniformity should be modeled because it has a significant effect on
flame temperature and pollutant levels.
Non-Uniform Fuel and Air Mixture Model
To compensate for the non-uniformity and equivalence ratio dispersion that exist in the
combustor, the mixing parameter S, also known as the unmixedness degree, is used. The
unmixedness degree, as defined in Equation (5), determines the distribution of flow fraction over
an interval of equivalence ratio [22, 56].
o
= S (5)
: Standard deviation
: Mean equivalence ratio
As shown in Figure 44, there is one unique value of the unmixedness degree for each given mean
equivalence ratio which corresponds to various engine power settings.
Figure 44: Heywood Unmixedness Parameter [56]
Knowing the value for S and the mean equivalence ratio ( ), the value for the standard
deviation, is determined and the Gaussian (Normal) distribution of equivalence ratio is
obtained as in Equation (6).
55
2
2
2
) (
2
e
2
1
) ( f
o
to
=
(6)
It should be noted that each combustor model may have its own S- diagram which should be
obtained through experiment and tuning of the model to match the known data.
Idealized Chemical Reactors
Idealized chemical reactors are used to simplify combustion reaction calculations. The most
common types of reactors are the perfectly stirred reactor and the plug flow reactor. In this
research the partially stirred reactor is also considered.
Perfectly Stirred Reactor (PSR)
The perfectly stirred reactor (PSR) is an ideal reactor that neglects mixing processes in a reaction
[59]. In a combustion system, there exists a characteristic flow mixing time
flow
and a
characteristic chemical time
chem
. A non-dimensional parameter, the Damkohler number Da, can
be introduced to characterize this system:
chem
flow
Da
t
t
=
When Da 1, it suggests either the mixing rates are very high or the chemical reaction rates are
very slow, and the burning rate is almost completely dominated by the chemical kinetics of the
mixture and the mixing process can be ignored.
Inside a perfectly stirred reactor (PSR), it is assumed that the Damkohler number is essentially
zero and thus the mixture is considered perfectly stirred. Mixing has no effect on the system and
is neglected. This assumption allows for a large reduction in the complexity of the governing
equations.
Conservation Equations for the PSR
The conservation equations for the perfectly stirred reactor may be written as follows. The
control volume for the analysis is shown in following figure:
56
Figure 45: Diagram of a Perfectly Stirred Reactor [59]
Mass conservation for an arbitrary species i may be written as
out i in i i
m m m
, ,
' ' '
0 + =
where
' ' '
i
m is the rate of generation or destruction of mass of the i
th
species inside the control
volume,
and
in i
m
,
and
out i
m
,
are the mass flow of the i
th
species into and out of the control volume,
respectively.
The generation or destruction of a species is written as
i i i
MW m e =
' ' '
where
i
e is the net production rate of the i
th
species in mol/m and MWi is the molecular weight of
the i
th
species in kg/mol.
The mass flow of the i
th
species into the control volume is:
in i in i
Y m m
, ,
=
where Y
i,in
is initial mass fraction of i
th
species; and similarly, the mass flow out of the control
volume is
out i out i
Y m m
, ,
=
The conservation of energy for the PSR is:
) (
,in i out
h h m Q =
Also, Q
where hi is the specific enthalpy of the i
th
species, and
}
+ =
T
T
i p
o
i f i
ref
dT T c h T h ) ( ) (
, ,
where
o
i f
h
,
is the enthalpy of formation of the i
th
species and ) (
,
T c
i p
is specific heat of i
th
species
57
Plug Flow Reactor (PFR)
A plug flow reactor is an ideal reactor filled with ideal gas mixture, and assumes it has steady,
one-dimensional inviscid flow properties. It implies that there is no mixing in the axial direction
of PFR. The control volume for the conservation equations refers to following figure.
Figure 46: Diagram of a Plug Flow Reactor [59]
Conservation equations for PFR:
Conservation of Mass:
0
) (
=
dx
A u d
x
Conservation of Momentum:
0 = +
dx
du
u
dx
dp
x
x
Conservation of Species:
0 =
x
i i i
u
MW
dx
dY
e
Conservation of Energy:
0
1
)
1
(
1
2 2
= + =
=
n
i
i i i
p x p
x
p
x
MW h
c u dx
dA
A c
u
dx
d
c
u
dx
dT
e
Where is the mass density and
x
u is axial velocity of the mixture flow, while A is local cross
area of the PFR.
Partially Stirred Reactor (PaSR) [7]
When the turbulent mixing rate is not fast compared to chemical kinetics, the degree of mixing
can have a profound impact on the reactor characteristics. The PaSR focuses on the influence of
an unmixed state on the reactor properties. The mean thermo-chemical properties inside a PaSR
are assumed to be spatially homogeneous, but imperfectly mixed at the molecular level.
58
A PaSR addresses the interaction between chemical reactions and turbulence [8, 13]. It allows
fluid dynamics to control the extent of the molecular mixing and consequently the chemical
reactions, by means of an additional parameter: the scalar mixing time,
mix
t , which is
proportional to the turbulent eddy turnover time:
c
k
t
D mix
C =
C
D
is a constant for certain flow configuration, is turbulent kinetic energy and is turbulent
dissipation rate.
One of the crucial issues of modeling chemical reaction in turbulent flows is the chemical
closure problem. Due to the highly nonlinear dependence of chemical reactions on temperature,
using the mean temperature and mean species concentrations for calculations of mean chemical
reaction rates can cause significant errors. To avoid the closure problem associated with non-
linearities in the equations governing turbulent flow, a transport equation for the joint PDF of
flow variable scalars, ) , , ( t x P
|
, is introduced, irrespective of the complexity and nonlinearity of
the reaction mechanism.
To solve the PDF transport equation practical for general turbulent reactive flows with large
dimension, Pope
[43] developed a Monte Carlo algorithm. The dependent variable in the
simulation is represented by an N-member ensemble:
) ( ) ( ) 2 ( ) 1 (
,..., ,..., ,
N n
| | | |
Here each of the members of the ensemble is referred to as a particle. Each particle is ascribed
a unique number, 1nN, no ordering is implied. Operations are performed either on all particles
or particles selected at random. The ensemble average of any function ) (| Q is defined by
=
) (
N
n
n
Q
N
Q
1
) (
) (
1
) ( | |
In the limit of large N, Pope [43] showed that the ensemble average ) ( ) (| Q converges to the
corresponding density-weighted average, i.e.,
) ( ) (
~
) ( ) (
~
) ( | |
|
d P Q Q Q
}
= ) (
For the general multiple reactive scalars, the transport equation for the joint PDF in the PaSR is
derived by integrating the governing equation of the single-point joint scalar PDF over the
reactor volume. The resulting PDF transport equation for the PaSR is:
{ } { }
{ } ) , (
~
) , (
~
) , (
~ 1
) , (
~
) (
) , (
~
1 , 1
2
1
,
1
t P
t P t P t P S
t
t P
tot
tot
K
M
i
i
R
K
| c
t
| o|
| o | o
| | | o
o o
|
=
c c
c
+
c
c
=
c
c
= =
= =
The first two terms on the right hand side of the above equation represent the effects of chemical
reaction and the through-flow on the joint PDF, respectively. The last term represents the effect
of micro-scale mixing on the PDF, which requires the use of a finite rate mixing model. Two
widely used mixing models are employed as options in the current PaSR model: the modified
59
Curl's mixing model
[26] and the linear-mean-square-estimation (LMSE) model [18] their
mathematical formulas are listed below:
The modified Curl's mixing model:
{ }
}}
= =
Where
|
C is a constant parameter for the model.
The unmixedness is a parameter used to quantify the unmixed nature, which is bounded by 0 and
1, and represent completely segregated and perfectly mixed state, respectively.
The theoretical values of the unmixedness at the statistically stationary state for the two mixing
models are:
Modified Curl's model
mix res
s unmixednes
t t 3 / 1
1
+
=
LMSE (IEM) model
mix res
C
s unmixednes
t t
|
3 / 1
1
+
=
Reactor Equations
The PaSR consists of an adiabatic chamber having M steady flows inlet streams and one outlet.
The reactor pressure is assumed to be constant, no surface reaction. In order to represent the
evolution of the PDF properly by a stochastic scheme, PaSR addresses all problems in a transient
manner. The overall mass balance for the gas mixture inside the PaSR is
0
) (
1
= = =
=
M
i
o i
m m
dt
V d
dt
M d
60
where
i
m is the mass flow rate of the i
th
inlet and is the through-flow mass flow rate. The
average properties of the PaSR are obtained from the ensemble of particles inside the reactor.
Each particle is treated as an independent PSR and interacts with others only through the
molecular mixing process. Therefore, the conservation of energy and species is applied to an
individual particle rather than to the reactor.
{ }
) (
) (
1
,
) (
) (
1
n
n
k k
M
i
k kt i o
R o
n
k
W
Y Y m
m dt
dY
e
t
+ =
=
The energy equation for a particle is:
= = =
|
|
.
|
\
|
=
g g
k
k
n
p
n
n
k
n
k k
M
i
k
k
k k i k i i
R o
n
p
n
C
h W
h h Y m
m C dt
dT
1
) ( ) (
) ( ) (
1 1
, ,
) (
) (
) (
1
e
t
In the above equations, the angled bracket ( ) indicates the ensemble average that we use to
approximate the density-weighted average in the simulation. The average residence time of the
reactor,
R
t , is calculated as
o
R
m
V
t =
Stochastic Simulation
A time marching scheme with a time-step size of t A is used to solve
R
t and the stochastic
simulation is carried out by the following sequential procedures with N statistical particles:
First, we set the properties of these N
c
particles from the stochastic ensemble, the properties of
the inlet mixture. The number of correct particles in a time step is chosen as:
R c
t N N t / A =
Second, particles are chosen to mix with each other, with the modified Curl's mixing model,
N
m
= C
m
N t
mix
C
m
is a parameter for the modified Curl's model. If the IEM (LMSE) model is used, IEM
(LMSE) Equation is solved to determine the statistics over a period of t.
At last, we compute chemical kinetics for each particle by integrating the species and energy
equations over a period of t A .
These three procedures are repeated for the next time step until the end of the simulation time is
reached.
61
Chemical Kinetic Mechanisms
Although it is generally perceived that the reaction of fuel with air can be written as a single line
of chemical equation at which on the left there are reactants and at the right there are products
with coefficients to conserve the number of atoms at both sides; however, this is just overall
picture of what really happens and does not tell the whole story. This type of chemical equation
which is called the global reaction, gives the end products of chemical reaction without
mentioning intermediates steps. In fact, the creation of product molecules is not the direct result
of fuel and air molecules collision; it is more probable that there are many intermediate
molecular and atomic collisions and reactions that are responsible for forming the final product.
These reactions are called elementary reactions and they represent what really happens in
combustion process in molecular scale (Figure 47).
Figure 47: Example of Elementary Reactions
Each elementary reaction can have forward or forward/reverse reaction. Each direction as is
shown in Figure 47 has forward and reverse reaction rates k
f
and k
r
which are used to find the
rate of production or destruction of species present in the reaction. For example the production
rate of CO in the above mechanism can be calculated as follows:
] H ][ CO [ k ] OH ][ CO [ k ] O ][ CO [ k ] O ][ CO [ k
dt
] CO [ d
2 r f 2 r 2 f
+ + =
The reaction rate constants are not constant but are functions of reaction temperature, usually
modeled as:
RT
E
n
e AT k
=
where the variables are the pre-exponential factor or frequency factor A, reaction order n and
activation energy E.
O NO O N
N NO N O
O OH O H
H CO OH CO
OH OH O H O
O CO O CO
f
r
f
r
f
r
f
r
f
r
f
r
k
k
2
k
k
2
k
k
2
2
k
k
k
k
2
2
k
k
2
+ +
+ +
+ +
+ +
+ +
+ +
62
Many species (i.e. CH, OH, HO
2
) that are present in elementary reaction are unstable and do not
exist in normal situations and do not last for a long time and will be destroyed or converted to
stable species. These species usually play an important role in the formation or destruction rate
of final product.
Combustion of a specific fuel with air has its own set of elementary reactions which is called the
Combustion Mechanism of that fuel. As the fuel molecule becomes more complex with higher
Carbon number, more intermediate species get involved in the process that increases the number
of elementary reactions and makes the combustion mechanism more complex; thus, it is hard to
model the complete combustion mechanism for these types of fuels. The solution is to lump the
couple of first initial elementary reactions that are responsible of breaking fuel molecule to
smaller ones (Pyrolysis process) into a few global chemical equations. In this approach, the
molecules that have available combustion mechanism are chosen as the smaller molecules to
make it possible to combine the pyrolysis global equations with known combustion mechanism
of smaller molecules to model the combustion mechanism of the fuel itself.
Besides the difficulty of modeling the combustion mechanism of pure fuels with high Carbon
number, there exists another problem associated with the fuels that are being used in industry.
Most of the hydrocarbon based fuels that are being used (including aviation fuels) are derivative
of petroleum and are mixture of different species. To make the matter worse, the percentage of
different species present in these fuels are not fixed and changes for different oil wells, refineries
or time of the year. For example, aviation fuels consist of more than 300 components which
makes it difficult (if not impossible) to model its physical or chemical properties. In order to
reduce the number of components to a manageable size (10 to 15), a surrogate model can be
created that mimics the same physical and chemical properties and distillate curve (Figure 48) of
the actual fuel as much as possible while its has much less components than the original fuel.
The surrogate model can be used in the modeling of the flow field or combustion inside
combustor Table 14 shows surrogate model of JP-4 that consists of 14 pure components.
Figure 48: Distillate Curve of JP-4 [60]
63
Table 14 : Surrogate model of JP-4 [60]
Compound
Class
Petroleum JP-4
vol%
Surrogate JP-4
vol%
Surrogate
Components
Paraffin 61.2 61.5 n-Hexane
n-Heptane
n-Octane
n-Nonane
n-Decane
n-Dodecane
n-Tetradecane
Monocycloparaffins 24.2 24.0 Cyclohexane
Methylcyclohexane
Cyclo-octane
Dicycloparaffins 4.9 5.0 Decalin
Alkyl benzenes 8.2 8.0 Toluene
Indans and Tetralins 1.1 1.0 Tetralin
Indenes and
Dihydronaphtalenes
0.0 0.0 -
Naphthalene 0.4 0.5 1-Methylnaphthalene
Total Paraffin 90.3 90.5
Total Aromatics 9.7 9.5
100% 100%
Although in such a surrogate model the number of components has been reduced dramatically,
considering the current computational ability, it is still difficult to model the combustion
mechanism for practical combustion analysis. Also there are not enough data about the reaction
path and reaction rates of hydrocarbon fuels with such a complex structure.
Since the major constituents of aviation fuel (namely JP-8 or Jet-A) are Paraffins and Aromatics;
it is possible to create a very simple model using a mixture of one Alkane and one aromatic that
exhibits the similar chemical structures. For Jet-A (C
12
H
23
), Lindstedt and Maurice [30, 34]
suggested using 89-mol% n-Decane (C
10
H
22
) representing Alkane and 11-mol% aromatic fuel.
The aromatic fuel can be Benzene (C
6
H
6
), Toluene (C
6
H
5
CH
3
), Ethyl-Benzene (C
6
H
5
C
2
H
5
) or
Ethyl-Benzene (C
6
H
5
C
2
H
5
) /Naphtalene (C
10
H
8
). Benzene is not a good choice for the aromatic
component since it does not give a good prediction of the aromatic concentration in the flame.
Any of the others might be selected for the aromatic based on the availability of data. [35]
To simplify the model even more, aviation fuel can be represented by the components that have
the highest percentage in the mixture and using its combustion mechanism. In the case of
aviation fuel C
10
H
22
or C
12
H
24
is often used. Another approach is to create the combustion
mechanism of the fuel using pyrolysis of a representative formula of aviation fuel (typically
C
12
H
23
). [41, 50]
64
Pollutant Formation Mechanisms
There are certain elementary reactions and reaction paths that are present in all hydrocarbon fuel
combustion mechanisms with little difference and they are responsible for the pollutant
formation. A brief description of each of these pollutant formation mechanisms follows:
Thermal NO Formation (Zeldovich) Mechanism[28]
The Thermal NOx mechanism is the main formation mechanism of NO and is produced by the
oxidation of atmospheric nitrogen in the high temperature region of the flame and in post flame
gases. Zeldovich proposed the following elementary reactions for it:
O+N
2
<==> NO+N
N+O
2
<==> NO+O
By adding the following reaction, the mechanism is called extended Zeldovich mechanism
N+OH <==> NO+H
Prompt NO Formation (Fenimore) Mechanism [28]
Particularly important in rich combustion, Prompt NO formation is related to the interaction of
atmospheric nitrogen with hydrocarbon radicals in the early stage of flame region which makes it
totally different from the Thermal formation mechanism. It was discovered by Fenimore when
studying the laminar premixed flame. Interaction of atomic nitrogen with HC radicals creates
amines and cyano compounds and they converted to some intermediate compounds that
ultimately will be turned into NO. Although the formation mechanism of Prompt NO is not as
simple as Thermal NO due to the presence of a high number of hydrocarbon radicals and
different reaction paths that depend on the combustion condition, the complexity can be reduced
by considering the HC radical as the main radical interacting with nitrogen and ignoring the
process that ends up to the formation of HC. The following reactions initiate the Prompt NO
formation mechanism:
CH+N
2
<==> HCN+N
C +N
2
<==> CN+N
After this point, the mechanism depends on the equivalence ratio. For equivalence values less
than 1.2, NO formation is based on following reaction [59].
HCN+O <==> NCO+H
NCO+H <==> NH+CO
NH+H <==> N+H
2
N+OH <==> NO+H
For higher equivalence ratios the mechanism becomes complex and its discussion is beyond the
scope of this report.
Nitrous Oxide (N
2
O) Intermediate Formation Mechanism
65
This mechanism is important in fuel-lean and low temperature conditions and consists of three
steps as follows. [59]
O+N
2
+M <==> N
2
O+M
H+N
2
O <==> NO+NH
O+N
2
O <==> NO+NO
Nitrogen Dioxide Formation Mechanism
A significant part of the NO that is produced by the above mentioned mechanisms is converted
to NO
2
in low temperature regions of combustion; hence, at the combustor exit there is a mixture
of NO and NO
2
which is called NOx. The reactions responsible for NO
2
formation or destruction
are given below:
NO+HO
2
<==> NO
2
+OH
NO
2
+H <==> NO+OH
NO
2
+O <==> NO+O
2
The first reaction, which is responsible for NO
2
production, is significant at low temperature
while next two reactions, responsible of NO
2
destruction, are significant at high temperature.
Carbon Monoxide (CO) Oxidation Mechanism
Unlike the NOx formation mechanisms, which do not produce a significant amount of heat and
can be separated from the other chemical reactions present in the combustor, CO oxidation is the
main source of heat release in combustion of hydrocarbon fuels. In simplified view,
hydrocarbon fuel combustion can be divided in two steps which are CO formation based on fuel
and air chemical interaction and CO oxidation to CO
2
in which the presence of water or
hydrogen significantly enhances the oxidation rate. The first step has a complex mechanism
which is fuel specific and sometimes not completely known to the researcher; however, the
second step is simple and can be modeled by the following reactions with water as a source of
hydrogen:
CO+O
2
==> CO
2
+O
O+H
2
O ==> OH=OH
CO+OH==> CO
2
+H
O
2
+H ==> OH+O
In the presence of hydrogen the following reactions also have to be considered:
O+H
2
==> OH+H
OH+H
2
==> H
2
O+H
Full Combustion Mechanisms
The calculation of many aspects of combustion, including performance and especially pollutant
emissions, requires a realistic representation of chemistry interactions to model the underlying
chemistry. Aviation fuels are comprised by complex mixtures of several hundreds of
hydrocarbons such as alkanes, cycloalkanes, aromatics, and cyclic compounds. Detailed
66
chemical-kinetic mechanisms describing the combustion process of many of these components
are not available, and thus detailed modeling of jet fuel remains as a real challenge. The study of
the combustion process of aviation fuels, however, requires a defined composition. An approach
to this problem is based on developing surrogates of these fuels. Surrogate fuels have been
proposed as blends of a limited number of hydrocarbons for which their detailed chemistry is
known. The blend components are determined to replicate the physical and chemical properties
of the combustion of the fuel of interest.
Unlike combustion of single molecule fuels such as hydrogen, methane, and propane for which
detailed mechanisms comprised of relatively small number of species and reactions are already
available [4, 25, 55], for aviation fuels detailed mechanisms of surrogates are few and they are
becoming increasingly complex, containing hundreds of species and thousands of elementary
reactions. The first aviation fuel surrogate was given by Schulz [54] who proposed a 12-
component mixture for JP-8. Other complex blends for aviation-type fuels were given by Dagaut
[15, 16], Lindstedt and Maurice [30], and Patterson [42]. A comprehensive review of surrogates,
experimental data, and kinetic schemes can be found in the survey by Dagaut and Cathonnet
[14]. More recent detailed surrogates were given by Luche et al. [31], and Honnet et al. [23].
Detailed chemical-kinetic mechanisms of surrogate fuel are essential to understand the
fundamental chemistry of the combustion process; however, their use is precluded by the high
computational cost. In order to address this problem, some simpler models have been developed.
For instance, a surrogate for kerosene TR0 composed of 89% n-decane, and 11% toluene, and
containing 167 reactions and 63 species was developed by Elliot et al [19]. More recently,
Strelkova et al [57] developed a surrogate for Jet A which is composed of 72.7 wt% decane, 9.1
wt% hexane, and 18.2 wt% benzene, involving 38 reactions and 24 species. These more
compact mechanisms are capable of reproducing reasonably results of more detailed
mechanisms. For instance, Figure 49 and Figure 50 show perfectly stirred reactor (PSR)
calculations for the Elliot and Strelkolva mechanisms. Calculations for a detailed mechanism by
Luche et al. [31] are also shown for comparison. The conditions of these calculations are those
corresponding to the CFM56-7B engine take-off condition, i.e., 429.27 Psi, and 1453.08 R. The
residence time is 2 ms and was chosen so that calculations were performed in the stable
combustion branch of the S curve. As shown by the temperature and CO profiles, good
agreement with the detailed mechanism was obtained. Although these mechanisms are more
affordable computationally, their main drawback is that they do not include NO chemistry, and
therefore are not suitable for emission predictions. Another approach to address affordability and
emissions is the use of mechanism reduction along with steady state approximation. This
approach was used by Lepinette et al. [29] to predict NO and CO emission for methane mixtures
for lean premixed combustion. Luche et al. [31] have also developed reduced mechanisms for
kerosene combustion using the aforementioned approach.
67
Figure 49: Reactor temperature calculations for a single PSR
Figure 50: CO molar fraction calculations for a single PSR
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
1800
1900
2000
2100
2200
2300
2400
2500
2600
2700
2800
Equivalence Ratio
T
e
m
p
e
r
a
t
u
r
e
(
K
)
Luche
Elliot
Strelkova
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Equivalence Ratio
C
O
m
o
l
a
r
f
r
a
c
t
i
o
n
Luche
Elliot
Strelkova
68
Reduced Mechanisms
Similar to computational fluid dynamics in which the use of detailed mechanism is prohibited
due to the computational overhead, early stages of design requires a high number of evaluations
of the design tools that make the use of detailed chemistry unaffordable. Therefore, a tradeoff
between accuracy and affordability is needed. A few of the more commonly encountered
reduced mechanisms for Jet fuel are described below:
Kollrack Mechanism
The Kollrack mechanism is the simplest of the mechanisms considered. A 30-step mechanism
created by Reiner Kollrack in 1976 for combustion of Jet-A fuel is a mixture of different
hydrocarbons with the Carbon to Hydrogen ratio of 12/23 or the representative formula of
C
12
H
23
. [32] It consists of 21 species and 30 reactions and includes the production of UHC,
NOx and CO (Table 15). The first two steps are not elementary reactions but are global reactions
representative of a great number of complex elementary reactions in the pyrolysis of the fuel
molecules to smaller molecules. In this mechanism, the reaction rate coefficient is defined as:
T
T
N B
activation
e T 10 k
= (SI units: Kmole, m
3
, k, s)
Thus in order to use the mechanism in CHEMKIN format, the first term (10
B
) must be
considered as the pre-exponential factor A.
Table 15: Kollrack combustion Mechanism of Jet-A [32]
REACTION B N T
REACTION
C
12
H
23
+O
2
=> 5C
2
H
4
+C
2
H
3
+O
2
4.48 1.5 7900
C
12
H
23
+OH => 6C
2
H
4
+O 7.3 1.0 4500
C
2
H
4
+H => C
2
H
3
+H
2
10.48 0.0 9500
H+H+M => H
2
+M 12.30 -1.0 0.0
O+O+M => O
2
+M 11.0 -1.0 0.0
H+OH+M => H2O+M 13.85 -1.0 0.0
H+O
2
=> OH+O 11.35 0.0 8400
O+H
2
=> OH+H 10.24 0.0 4730
CO+OH => CO
2
+H -14.75 7.0 -7000
H+H
2
O => OH+H
2
10.92 0.0 10050
CH
3
+O
2
=> CH
2
O+OH 9.0 0.0 4000
HO
2
+M => H+O
2
+M 12.32 0.0 23000
HO
2
+H => OH+OH 9.89 0.0 950
CH
2
O+OH => H
2
O+HCO 10.90 0.0 2120
O+H
2
O => OH+OH 10.76 0.0 9000
N
2
+O => NO+N 9.00 0.0 25000
N+O
2
=> NO+O 5.00 1.0 2000
N+OH => NO+H 9.00 0.0 0.0
HCO+O
2
=> HO
2
+CO 10.48 0.0 7000
HCO+OH => H
2
O+CO 10.30 0.0 0.0
C
2
H4+OH => C
2
H
3
+H
2
O 9.78 0.0 1750
CH
2
O+HO
2
=> HCO+OH+OH 9.0 0.0 4500
C
2
H
2
+HO
2
=> HCO+CH
2
O 9.30 0.0 5500
C
2
H
3
+O
2
=> C2H
2
+HO
2
9.23 0.0 5000
NO+HO
2
=> NO
2
+OH 3.00 1.0 0.0
C
2
H
4
+O => CH
3
+HCO 9.93 0.0 1500
C
2
H
4
+HO
2
=> CH
3
+HCO+OH 9.90 0.0 5000
H
2
+CH
3
=> CH
4
+H 7.0 -1.5 7140
C
2
H
2
+OH => CH
3
+CO 8.2 0.0 2500
CH
3
+O => CH
2
O+H 11.11 0.0 1000
69
n-Decane Mechanism
In some publications the average carbon number of aviation fuels is assumed to be close to 10;
consequently it is concluded that n-Decane and aviation fuels might have similar combustion
characteristics and mechanism. Also a mixture of some aromatics and n-Decane has chemical
characteristics close to Kerosene. But a complete and detailed mechanism of n-Decane is not
entirely known, so it is modeled based on the observed n-Heptane pyrolysis and H-atom
abstraction. [30] This mechanism appears capable of predicting the formation and destruction of
benzene and aromatics in flames, which is essential for predicting soot formation and pollutant
prediction in combustion. The published mechanism [30] consists of 193 species and 1085
elementary reactions.
n-Dodecane Mechanism
The n-Dodecane mechanism was used by L. Q. Maurice [30] and consists of 177 chemical
species and 1138 elementary reactions. It contains sub-mechanism of molecules up to C
12
and
aromatics. Also the Nitrogen sub-mechanism consists of 3 main NOx formation mechanism of
Zeldovich (thermal), Fenimore (prompt) and N
2
O as well as NO and NO
2
chemistry.
Examination of Kollrack Mechanism
In the present work, the chosen kinetic mechanism is the one given by Kollrack [27, 49]. This
mechanism was developed for C
12
H
23
/air combustion and involves the breakdown of the fuel
molecule in two-stages. The NO chemistry includes thermal NO by the extended Zeldovich
reactions, and prompt NO by the superquilibrium of oxygen molecules. It is composed of 21
species and 30 chemical reactions.
Figure 51 through Figure 53 show comparisons between the Kollrack and Luche mechanisms for
PSR calculations. The conditions for the reactor are those for take-off as described above.
Temperature, CO, and NO molar fraction are plotted as a function of residence time for
stochiometric mixtures. It can be noticed that the Kollrack mechanism under-predicts
temperature for small residence times; however, for residence times greater than 0.5ms the
values show good agreement with those given by the Luche mechanism. Similarly, CO is under-
predicted for small residence times. The agreement, however, is better for values greater than 1
ms. Unlike temperature and CO, NO is certainly under-predicted by almost half over the entire
range of residence time.
70
Figure 51: Reactor Temperature
Figure 52: CO molar fraction
0.25 0.5 0.75 1 1.25 1.5 1.75 2
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
Residence time (ms)
T
e
m
p
e
r
a
t
u
r
e
(
K
)
Luche
Kollrack
0.25 0.5 0.75 1 1.25 1.5 1.75 2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Residence time (ms)
C
O
m
o
l
a
r
f
r
a
c
t
i
o
n
Luche
Kollrack
71
Figure 53: NO molar fraction
The behavior of the Kollrack mechanism with equivalence ratio was investigated and it is shown
in Figure 54 through Figure 56. The residence time of the reactor was set to 2ms to ensure
calculations at the stable combustion branch, and the conditions are the same as in the previous
figures. The temperature was found to agree well in the considered range. The CO also shows
good agreement; however, the CO prediction departs at equivalence ratio of 1.2 and thus CO
values are likely to be under-predicted for richer mixtures. The NO is under-predicted for
intermediate values, the agreement, however, is better for lean and rich mixtures.
Figure 54: Reactor temperature
0.25 0.5 0.75 1 1.25 1.5 1.75 2
0
1
2
3
4
5
x 10
-3
Residence time (ms)
N
O
m
o
l
a
r
f
r
a
c
t
i
o
n
Luche
Kollrack
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
1800
1900
2000
2100
2200
2300
2400
2500
2600
2700
2800
Equivalence Ratio
T
e
m
p
e
r
a
t
u
r
e
(
K
)
Luche
Kollrack
72
Figure 55: CO molar fraction
Figure 56: NO molar fraction
The above comparisons have shown that the Kollrack mechanism was found to give reasonable
agreement for temperature as well as major species. Accurate prediction of emissions, however,
depends on the conditions. For instance, at small residence times the mechanism is likely to fail
due to the lack of chemical step for ignition. The under-prediction of NO suggests the
importance of other paths for NO production that are not included in the Kollrack mechanism. In
spite of this drawback, the Kollrack mechanism is chosen due to its balance between
computational cost and accuracy.
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Equivalence Ratio
C
O
m
o
l
a
r
f
r
a
c
t
i
o
n
Luche
Kollrack
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0
1
2
3
4
5
x 10
-3
Equivalence Ratio
N
O
m
o
l
a
r
f
r
a
c
t
i
o
n
Luche
Kollrack
73
Appendix B: Equations for SAC Model
Appendix B contains a list of flowcharts giving the logic of the on-design procedure of each
element of the NPSS code for the SAC model and the calculations derived for the geometry.
74
- Set Pt32
- Adiabatic compression:
,32
=
,31
- Mach32 fixed by user
- Diffuser efficiency: =
32
31
32
31
=
Calculate flat-wall diffuser geometry
>
32
31
32
31
= ,
=
- Set Pt32
- Adiabatic compression:
,32
=
,31
- Mach32 fixed by user
Calculate dump diffuser geometry
passage_number Number of passages
Passage half-angle
Mach32 Mach number station 32
sweet_spot Max aspect ratio for
flat_wall diffuser
Comp1 output
User input
User inputs
Diffuser.int
75
32
=
32
switchBurn
=?
Burner equivalence ratio
,
=
,32
,
=
,
1
Constant pressure in annulus & liner
32
Pressure loss coefficient
32
=
=
32
-
,
=
,
-
,
=
,
+
Jet to reference momentum ratio
Hence all jets have same velocity
Execute S_PZ
Execute S_SZ
Execute S_DZ
Execute S_EmissionsNN
=
,
,32
1
Cooling fraction
Hyp: cooling flow does
not participate in
combustion, dumped in
DZ even though not
physically true
User inputs
Combustor.int
User inputs
Burner pressure
drop
Maximum liner
temperature
Cooling
mechanism
factor
Burner fuel to
air ratio/fuel
flow rate
Diffuser.in output
User input
S_PZ output
76
,
=
Adiabatic flame temperature, using NPSS burn function
PZ flow fraction
32
=
32,
32
= 1
32,
32
2
3
1
3
- Liner to casing area ratio to maximize jet
penetration (using momentum ratios)
- Constant , h
L
and r
m
from 32 to 39
with
32,
32
= 1
=
2
,32
32
,
=
,
=
cos
2
1
2
2
32
,
2
+
1
2
1
2
32,
2
=
2
3
tan
3
1
< 0
swirl < 0.6
>
,32
+ 1
+ 1
= 2
=
32
Equivalence ratio PZ
Efficiency PZ
Swirler hub radius
Mixer to PZ volume
Swirler discharge coef.
Diffuser output
Combustor output
User input
S_PZ output
User inputs
PZ.int
77
Set
,
=
Adiabatic flame temperature using NPSS burn function
,
=
,
32
32
=
1
32
=
sin
2
= 1
,
= 1.15
32
32
1
sin
,
=
,
,33
,33
,
=
4
32
,
2
32
- mass conservation:
- Boussinesq assumption:
32
=
,32
,
=
1
+ mass cons.
- Conservation of momentum :
- Regression (Lefebvre) :
- Using assumed jet penetration ratio:
- Using mass conservation:
33,
33,
User inputs
SZ.int
,33
SZ jets penetration ratio
Efficiency SZ
33,
SZ aspect ratio
,
SZ holes discharge coef.
78
= 1
32
Mass conservation
,40
=
Adiabatic flame temperature using NPSS burn function
32
=
32
=
sin
2
= 1
,
= 1.15
32
32
1
sin
,
=
,
,34
,34
,
=
4
32
,
2
32
- mass conservation:
- Boussinesq assumption:
32
=
,32
,
=
1
+ mass cons.
- Conservation of momentum :
- Regression (Lefebvre) :
- Using assumed jet penetration ratio:
- Using mass conservation:
34,
34,
34,
34,
+
1
2
+
40
40
=
40
,
,40
,
,
,
32
,34
DZ jets penetration ratio
Efficiency DZ
34,
DZ aspect ratio
,
DZ holes discharge coef.
Mach40
Mach number at station 40
rm
40
Mean radius at station 40
34,
Transition duct aspect ratio
Diffuser output
Combustor output
User input
S_PZ output
S_SZ output
User inputs
DZ.int
79
,32
=
,31
31
32
32
31
32
=
31
+ 2
tan
sin
,32
,31
1
=
31
2
+ 4
,31
tan
sin
31
32
31
1 +
,31
tan
sin
,32
=
1
2
,31
+
1
4
sin
tan
1
31
32
=
32
2
,32
,32
=
,32
32
2
cos
,32
=
,32
+
32
2
cos
,32
,31
sin
,32
=
cos +
31
2
sin
,32
=
,32
+
32
2
sin
,32
=
,32
32
2
sin
3
=
32
,3
=
,32
3
=
3,
=
32
,3
=
,3,
=
,32
,3
=
,3,
=
,32
,
=
,3
=
,32
,3
=
,3,
=
,32
,3
=
,3,
=
,32
AR_diff < sweet_spot ?
,31
=
,31
+
31
2
1 cos
,31
=
,31
,31
=
,31
+
31
1 cos
31
=
31
31
= 2
,31
31
,31
31
2
sin
Dump
Start
no
yes
Combustor
Geometry calculations
Note : in these flowcharts,
tilted stations FS31t and
FS39t and denoted with a
prime for easier reading
80
2
=
,31
+ sin
2
+
2
32
sin
,32
=
1
2
,31
+ sin
3
+
2
32
=
32
2
,32
=
32
3
: =
,32
=
,32
32
2
cos
,32
=
,32
+
32
2
cos
,32
=
cos +
31
2
sin
,32
=
,32
+
32
2
sin
,32
=
,32
32
2
sin
3
= _
31
1,
=
31
2
+ 4
,31
tan
sin
31
31
1 +
,31
tan
sin
,3
=
1
2
,31
+
1
4
sin
tan
1
31
3
=
3
2
,3
,3
=
,3
3
2
cos
,3
=
,3
+
3
2
cos
,
=
,3
,31
sin
,3
=
,
cos +
31
2
sin
,3
=
,3
+
3
2
sin
,3
=
,3
3
2
sin
3,
=
32
2
,3
,3,
=
,3
3,
2
cos
,3,
=
,3
+
3,
2
cos
,3,
=
,3
+
3,
2
sin
,3,
=
,3
3,
2
sin
Dump
: =
,32
=
,31
+ sin
32
=
32
2
,32
=
32
3
Combustor
,32
=
,31
31
31
3
=
31
+ 2
tan
sin
,3
,31
81
39
39
,
=
,
+
,
+
,
+
,
+
,40,
=
,39
40
=
40
2
,40,
,40
=
,40,
40
2
,40
=
,40,
+
40
2
39
=
39,
,39
=
,39
+
39,
2
1 cos
,39
=
,39
,39
=
,39
39
39
= 2
,39
39
39,
39
2
sin
,
=
39,
+
39,
39
=
33
=
34
=
32
=
32
32/33/34/39,
=
32/33/34/39
/
=
33/34,
33/34,
,33/34/39
=
,32/33/34
+
//
sin
33/34/39
=
33/34/39
2
,33/34/39
,33/34/39
=
,33/34/39
33/34/39
2
cos
,33/34/39
=
,33/34/39
+
33/34/39
2
cos
,33/34/39,
=
,33/34/39
33/34/39,
2
cos
,33/34/39
=
,33/34/39
+
33/34/39,
2
cos
//39,
=
//
cos
,33/34/39
=
//,
+
33/34/39,
2
sin
,33/34/39
=
//,
33/34/39,
2
sin
,33/34/39,
=
//,
+
33/34/39,
2
sin
,33/34/39,
=
//,
33/34/39,
2
sin
//
=
//
Start
Modify
Combustor
no
yes
Hyp: constant annulus &
liner areas in combustor
=
,40,
,40
,40
< 0.01 ?
82
Appendix C: Equations for RQL Model
Appendix C describes the equations used in each element of the NPSS code for the RQL model
where they differ from those used by the SAC model.
Mixing and Dilution Zone Hole Sizing
The sizes of the Mixing and Dilution zone holes are important in order to have adequate mixing,
to achieve the required temperature profile and to achieve the correct jet penetration. Small
diameters provide jets with low momentum that are unable to penetrate deep enough into the
Mixing and Dilution zones to mix well with the hot gases. Large diameters, on the other hand
may result in too much jet penetration, leading to uneven temperature distribution.
Equation (1) shows the relationship between the orifice area and flow coefficient and the total
mass flow. The mass density and total pressure drop are assumed to be the same for all the
orifices.
ref ref i D
n
i
t i D t
n
i
i D
t
t
n
i
i D i
n
i
ref
A V A c P A c P A c
P
A c V m A A
A
E E E E
= = = = =
= = = = 1 1 1 1
. 2 . 2
2
(1)
Unlike in the SAC, the RQL combustor may use variable geometry; therefore the assumption of
constant pressure drop coefficient (total pressure drop over dynamic pressure, dP/Q) cannot be
used, because the pressure drop coefficient is a function of the size of the orifices. From
Equation (2) one can obtain the pressure drop coefficient to be as follows:
2
2
1
2
2
1
|
|
|
.
|
\
|
+ + +
=
|
|
|
|
|
.
|
\
|
= =
=
cool D DZ D MZ D sw D
ref
i D
n
i
ref
ref
tot tot
A c A c A c A c
A
A c
A
V
P
Q
P
cool DZ MZ SW
E
A A
(2)
The above equation shows that changing the swirler area in the variable geometry RQL
combustor would change the pressure drop coefficient. After finding the pressure drop
coefficient at a given power setting, the amount of flow that passes through the orifices of
interest can be determined using the following equation:
Q
P
A
A c
m
m
frac
tot
ref
Orifices D
ref
jet
jet
A
= =
(3)
Atomizer and Swirler
To improve atomization in the RQL combustor an integrated high shear swirler may be used.
However, for simplicity, in this report the conventional pressure-swirl Simplex atomizer with
single axial swirler will be used. The following equation may be used to determine the amount of
the flow that passes through the swirler to the Rich zone at a given power setting.
83
2
2
.
sec
2
liner
inj
sw
sw
t
swirler
A
n
A
K
P
m
|
.
|
\
|
=
o
u
A
(4)
The total pressure drop is calculated from the pressure drop from equation (2). The variable is
the swirler area coefficient used when the variable geometry swirler area is used and n
inj
is the
number of injectors.
Rich Zone
The Rich zone component is almost the same as the Primary zone component for the SAC
model. In the RQL, after determining the pressure drop coefficient and consequently the
absolute burner pressure drop, the amount of the flow that goes to the Rich zone is determined
using equation (4).
An additional feature is added to the Rich zone model which is the configuration option. Since
some of the validation cases are performed for the a tubular type RQL combustor, it became
necessary to include the tubular option (in addition to already available option of annular
configuration) to the Rich zone, Mixing zone, Lean zone and Dilution zone models. The major
difference between these two configurations is in the equation used to calculate the liner and
casing heights for each component (Equations 5 and 6).
.
mean
sectiob cross
annular
r 2
Area
H
t
=
(5)
t
Section Cross
tubular
Area 4
H =
(6)
Mixing Zone
The Mixing zone is specific to the RQL combustor, where the annulus air should mix quickly
with the fuel rich hot gases coming out from the rich zone section. As described previously, there
are different mixing methods, but this research is limited to the use of the wall-jet mixing
method.
The first thing to be determined is the fraction of the air that should be added to the hot gases to
bring it from the rich regime to the lean regime. At design condition (Take-Off or Super-Sonic
cruise) this fraction is determined from the Lean equivalence ratio:
swirler inj
LZ st
fuel
ref
MZ
m . n -
far
m
m
m
.
= (7)
At off-design conditions, the fraction is obtained from a different formula based on the quench
orifices size and pressure drop that is provided later in this sub-section.
After obtaining the amount of air needed for quenching, the next step is to design the quench
orifices and determine their number and size. The design of the quench orifice is very important
as it will determined the quality of mixing and speed of quenching the rich zone hot gases. In the
84
wall-jet method, the number of the quench orifices for the can or tubular type configuration is
shown in the equation below [28, 52]:
C
J
n
2 t
=
(8)
where n is the optimum number of quenching orifices, J is the momentum flux ratio and C is an
empirical constant (equal to 2.5 for the tubular configuration). The orifices are of circular shape.
The momentum flux ratio is determined similar to the method described for the conventional
SAC combustor.
For an annular configuration the optimum distance between orifices (S) is found by [28, 52].
J
C
H
S
=
(9)
where H is the mixing zone height. The empirical constant (C) is 1.25 for in-line orifices
configuration and 5 for staggered orifices configuration.
The following equation provides the maximum amount of penetration in the mixing zone in
presence of multiple jets [52].
jet core
core
j
m m
m
J
d
Y
+
= 25 . 1
max
(10)
It should be noted that the wall-jet method results in larger mixing jets and lower efficiency in
the mixing process. That is, the size of the large energy-containing eddies are bigger than those
more advanced mixing concepts, in which case eddies with a larger range of size and turn-over
time can create local areas of mixture with stoichiometric fuel- air ratio that create high levels of
thermal NO
x
. In other words, the poor quality of macro-mixing contributes to local
stoichiometric burning.
Another important aspect of mixing in the mixing zone is the micro-mixing. After mixing of the
quench air with core gases in macro-scales, the quality of the micro-mixing determines the flame
temperature and emission levels. If one wants to model the whole macro and micro mixing
process, then the turbulent modeling and chemical kinetic/flow interaction modeling is inevitable
which is outside of the scope of the current research. To simplify the model, a characteristic
mixing time is defined as the following equation.
MZ MZ
3
MZ
mix
m
H
.
t =
(11)
To assess the mixing quality in the Mixing zone, an unmixedness parameter is defined as [8]:
( ) f f
f f
s unmixednes
~
~ ~
1
' ' ' '
=
(12)
85
The unmixedness value ranges between 0 and 1, zero representing perfect mixing (where
residence time is much longer than the mixing time) and one represents segregated mixture (very
long mixing time).
The following equation relates the unmixedness to mixing time (
mix
) and residence time(
res
) [8].
mix res
C
s unmixednes
t t
|
+
=
1
1
(13)
where C
\
|
=
o
u (14)
Having the values from the on-design Rich zone model and given the swirler area
multiplier () from a user-specified swirler area change schedule, one can determine the effective
area of the swirler at any given off-design condition. Having the pressure drop coefficient
calculated at off-design condition, the burner pressure drop is determined and then all objects are
executed to determine the zone temperature, flow fractions and flow station properties.
Mixing Zone Off-Design
The Mixing zone component is linked to the Rich zone component through the flow station
FS33. Similar to the Rich zone, the configuration may be Annular or Tubular. The cross
section area at the mixing zone is reduced by the user-defined factor MZtoPZ_areaRatio. The
number and size of the orifices at design condition is calculated using equations (8) and (9) and
the maximum penetration is determined using equation (10). At Off-Design condition, the
amount of the flow going through the mixing orifices is determined by the equations below.
MZ MZ
jet
2
jet orifices MZ
tot
MZ
.V 4.Area
.V .D . n
m
m
t
_
=
(15)
Q
P
V V
ref jet
A
=
(16)
For determining the Mixing zone exit temperature, the Burn function is not used. Assuming
the ideal case of the perfect mixing and absence of any reaction, the exit temperature of the
Mixing zone is simply the sum of the sensible enthalpies of air and core flows divided the total
flow (Equation 17). The more accurate exit temperature will be determined later in the Chemical
Reactor Network model.
RZ MZ
RZ t core sens RZ ref t air sens MZ
MZ t
m m
T h m T h m
T
+
+
=
) ( . ) ( .
(17)
Finally parameters related to the PaSR (Partially Stirred Reactor) model are calculated: the
residence time of the Mixing zone:
86
MZ MZ
MZ
residence MZ
V Area
Vol
.
2
= t
(18)
In equation (18), the volume is divided by two because the mixing flow is assumed to enter the
MZ at the half-way point of the Mixing zone. The simulation time should be long enough so the
solution of the PaSR reaches the steady state condition but not so long as to make the simulation
very slow. It is defined to be 5 times of the residence time:
residence MZ simulation MZ
t t . 5 =
(19)
The mixing time in the Mixing zone and corresponding unmixedness value are determined using
Equations (11) and (12). The time step of statistical samples that is required in the Monte Carlo
simulation in the PaSR is set to one tenth of the Mixing zone residence time:
10
residence MZ
MZ MCS
dt
t
=
(20)
CreateCHEMKI NI nputs Object
The significant difference in the CreateCHEMKINInputs object relative to the SAC model is the
additional equation to take into account the unmixedness in the Mixing zone. A simplified model
is developed to model the macro-mixing and its quality in the mixing zone. The micro-mixing
model is accounted for in the PaSR reactor of the CRN model.
The assumption for developing this model is that the perfectly mixed model (zero unmixedness)
will burn in the Lean zone at the Lean zone equivalence ratio (which is well below one). As the
Mixing zone unmixedness increases from zero to one, more and more of the mixture will burn at
the unity equivalence ratio and the rest will burn at an equivalence ratio that is determined by the
reamining air and fuel. The unmixedness value is an input from the Mixing zone object. A linear
relationship is assumed between the Mixing zone unmixedness value and the equivalence ratio.
The result is the equation which is shown below:
RZ
st MZ LZ st
fuel
mixed - un MZ
m
far s unmixednes far far
m
m
+
=
) 1 ).( (
(21)
mixed - un MZ MZ mixed MZ
m m m =
(22)
87
References
1. Allaire, D.L., A Physics-Based Emissions Model for Aircraft Gas Turbine Combustors, Masters
Thesis, Massachusetts Institute of Technology, May 2006
2. Andreini & Facchini, Gas Turbines Design and Off-Design Performance Analysis with Emissions
Evaluation, Journal of Engineering for Gas Turbines & Power 126:83-91 (2004)
3. Bae, J.H. and C.T. Avedisian, Jet fuel droplet combustion with and without the convection, in
37th Intersociety Energy Conversion Engineering Conference (IECEC). 2002, IECEC:
Washington, WA, USA.
4. Balakrihnan, G., and Williams, F.A., Turbulent Combustion Regimes for Hypersonic Propulsion
Employing Hydrogen-Air Diffusion Flames, Journal of Propulsion and Power, Vol. 10, No. 3,
1993, pp. 434-436.
5. Burrus, D., Sabla, P.E., and Bahr, D.W., Energy Efficient Engine Component Development and
Integration Single-Annular Combustor Technology Report, NASA CR-159685, June 1980
6. Cai, Jeng & Tacina, The Structure of a Swirl-Stabilized Reacting Spray Issued from an Axial
Swirler, AIAA paper 2005-1424
7. Chemkin software 4.1.1, Theory Manual, Chapter 9, 2007
8. Chen, J., Stochastic modeling of partially stirred reactors. Combustion Science and Technology,
1997. 122(1): p. 63-94.
9. Chen, R.H. The role of the recirculation vortex in improving fuel-air mixing within swirling
flames. in Symposium(International) on Combustion, 22 nd. 1988. Seattle, WA: The Combustion
Institute.
10. Chigier, N., Energy, combustion, and environment. 1981: McGraw-Hill Companies.
11. Chigier, N.A. and J.M. Beer. Velocity and static-pressure distributions in swirling air jets issuing
from annular and divergent nozzles. in ASME Meeting FE-8, May 18-21 1964. 1964. New York,
NY, United States: American Society of Mechanical Engineers (ASME).
12. Coordinating Research Council, Handbook of Aviation Fuel Properties. 1983, Society of
Automotive Engineers (SAE): Atlanta, Ga. p. 113.
13. Correa, S.M., Turbulence-chemistry interactions in the intermediate regime of premixed
combustion, Combustion and Flame, Vol. 93, Issues 1-2, Pp 41-60 (April 1993)e
14. Dagaut, P., and Cathonnet, M., The ignition, oxidation and combustion of kerosene: A review of
experimental and kinetic modeling, Progress in Energy and Combustion Science, Vol.32, 2006,
pp. 48-92.
15. Dagaut, P., Reuillon, Cathonnet, M. , and Voisin, D., High Pressure Oxidation of Normal
Decane and Kerosene in dilute from low to high temperature, Journal of Chemical Physics.,
Vol. 92, 1995, pp. 47-76.
16. Dagaut, P., Reuillon, M., Boettner, J.-C., and Cathonnet, M. , Kerosene Combustion at
Pressures up to 40 atm.: Experimental Study and Detailed Chemical Kinetic Modeling,
Proceedings of the Combustion Institute., Vol. 25, 1994, pp. 919-926.
17. Dodds, W., Twin Annular Premixing Swirler (TAPS) Combustor, The Roaring 20th Aviation
Noise & Air Quality Symposium, 2005
18. Dopazo, C., Probability density function approach for a turbulent axisymmetric heated jet
Centerline evolution Physics of Fluids, vol.18, pp397 (1975).
19. Elliot, L., Ingham, D.B., Kyne, A.G., N.S. Mera, Pourkashanian, M., and Wilson, C.W.,A novel
approach to mechanism reduction optimization for aviation fuel/air reaction mechanism using a
genetic algorithm, Proceedings of ASME Turbo Expo 2004, June 14-17, 2004.
20. Gogineni, S., et al., Combustion Air Jet Influence on Primary Zone Characteristics for Gas
Turbine Combustors. Journal of Propulsion and Power, 2002. 18(2): p. 407-416.
21. Grisch, F., Orain, M., Rossow, B., Jourdanneau, E., and Guin, C., Simultaneous Equivalence
Ratio and Flame Structure Measurements in Multipoint Injector Using PLIF, AIAA 2008-4868.
88
22. Heywood, J.B. and T. Mikus, Parameter Controlling Nitric Oxide Emissions from Gas Turbine
Combustors, in AGARD Propulsion and Energetic Panel 41st Meeting on Atmospheric Pollution
by Aircraft Engines. 1973: London, England.
23. Honnet, S., Seshadri, K., Niemann, U., and Peters, N.,A surrogate fuel for kerosene,
Proceedings of the Combustion Institute, Vol.32, 2009, pp. 485-492.
24. http://commons.wikimedia.org/wiki/File:Combustor_diagram_airflow.png
25. Jachimowski, C.J., An Analytical study of the Hydrogen-Air Reaction Mechanism with
Application to Scramjet Combustion , NASA TP-2791, 1988.
26. Janicka, J., Kolbe, W. and Kollmann,W., Journal of Non-equilibrium Thermodynamics 4:47-
(1979).
27. Kollrack, R., Model calculations of the combustion product distribution in the primary zone of a
gas turbine combustor, ASME Winter Annual Meeting, Paper No. 76-WA/GT, 1976.
28. Lefebvre, A.H., Gas Turbine Combustion. 2 ed. 1999, Philadelphia, PA: Taylor & Francis.
29. Lepinette, A., Linan, A., and Lazaro, B., Reduced kinetics and coupling functions for
calculating CO and NO emissions in gas-turbine combustion, Combustion Science and
Technology, Vol. 177, 2005, pp. 907-931.
30. Lindstedt, R. P. and Maurice, L. Q., A Detailed Chemical-Kinetic Model for Aviation Fuels,
AIAA Journal of Propulsion and Power, Vol. 16, No. 2, 2000, p. 187.
31. Luche, J., Reuillon, M., Boettner, J.-C., and Cathonnet, M., Reduction of large detailed kinetic
mechanism: Application to kerosene/air combustion, Combustion Science and Technology, Vol.
176, 2004, pp. 1935-1963.
32. Mattingly, J. D. et al., Aircraft Engine Design, AIAA Education Series. New York, 1987.
33. Matuszewski, L., Dupoirieux, F., Guin, C., and Grisch, F., Numerical calculation of the NO
formation in a multi-point combustion chamber and results of the associated validation
experiments,, ONERA. Same as 6!
34. Maurice, L. Q. et al., Emissions from Combustion of Hydrocarbons in a Well-Stirred Reactor,
AIAA 99-1038, 1999.
35. Mawid, M. A. and Park, T. W., Development of a Detailed Chemical Kinetic Mechanism for
Combustion of JP-7 Fuel, AIAA-2003-4939, 39th AIAA/ASME/SAE Joint Propulsion
Conference and Exhibit, Hutsville, Alabama, July 2003
36. McKinney, R.G., et al., The Pratt & Whitney TALON X Low Emissions Combustor:
Revolutionary Results with Evolutionary Technology,2007
37. Mellor, A.M., Design of Modern Turbine Combustors. 1990, San Diego, CA: Academic Press.
38. Mongia, H., GE Aviation Low Emissions Combustion Technology Evolution, AIAA, 2008
39. Mongia, H., TAPS A 4th Generation Propulsion Combustor Technology for Low Emissions,
AIAA 2003-2657
40. Mongia, H.C., Aero-thermal design and analysis of gas turbine combustion systems - Current
status and future direction in 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and
Exhibit, . 1998, AIAA: Cleveland, OH.
41. Montgomery, C. J. et al. Reduced Chemical kinetic Mechanism for Hydrocarbon Fuels, AIAA
Journal of Propulsion and Power, Vol. 18, No. 1, 2002, p. 192.
42. Patterson, P.M., Kyne, A.G., Pourkashanian, M., Williams, A., and Wilson, C.W., Combustion
of Kerosene in Counterflow Diffusion Flames, Journal of Propulsion and Power, Vol.16, 2000,
pp. 453-460.
43. Pope,S.B., Combustion Science and Technology 25:159-174 (1981)
44. Pratt & Whitney and General Electric, Critical Propulsion Components Volume 2: Combustor,
NASA CR-2005-213584, 2005
45. Rizk & Mongia, Emissions Predictions of Different Gas Turbine Combustors, AIAA 94-0118
46. Rizk & Mongia, Semianalytical Correlations for NOx, CO, and UHC Emissions, Journal of
Engineering for Gas Turbines & Power 115:612-19 (1993)
47. Rizk & Mongia, Three-Dimensional NOx Model for Rich/Lean Combustion, AIAA 93-0251
89
48. Rizk, N.K. et al, Predictions of Nox Formation Under Combined Droplet and Partially Premixed
Reaction of Diffusion Flame Combustors, Journal of Engineering for Gas Turbines and Power,
Vol. 124, January 2002, pp. 31-38
49. Roberts, R., Aceto, L.D., Kollrack, R., Texeira, D.P., and Bonnell, J.M., An analytical model for
nitric oxide formation in a gas turbine combustor, AIAA journal, Vol. 19, No. 6. 1972, pp. 820-
826.
50. Roberts, Richard. et al, An Analytical Model for Nitric oxide formation in a gas turbine
combustor, AIAA Journal, Vol. 10, No. 6, June 1972, pp 820-826
51. Rosfjord, T.J., Aviation-fuel property effects on combustion. 1984, NASA Center.
52. Samuelson, S., Rich Burn, Quick-Mix, Lean Burn (RQL) Combustor, in The Gas Turbine
Handbook, National Energy Technology Laboratory, Editor. 2006, U.S. Department of Energy,
Office of Fossil Energy.
53. Sazhin, S.S., et al., Models for droplet transient heating: effects on droplet evaporation, ignition,
and break-up. Int J Thermal Science, 2005. 44: p. 610622.
54. Schulz, W., ACS petrol. Chem. Div. Preprints 37 (2), 1991, pp. 383-392.
55. Smith, G.P., et al, GRI mech 3.0, http://www.me.berkeley.edu/gri_mech/
56. Smith, R., et al., Advanced Low Emissions Subsonic Combustor Study. 1998, NASA Center:
Glenn Research Center.
57. Strelkova, M.I., Kirilov, I.A., Potapkin, B.V., Safonov, A.A., Sukhanov, L.P., Umanskiy, S.Ya,
Deminsky, M.A., Dean, A.J., Varatharajan, B., and Tentner, A.M., Detailed and reduced
mechanism of jet A combustion at high temperatures, Combustion science and technology, Vol.
180, 2008, pp. 1788-1802.
58. Sturgess, G.J., et al, Emissions Reduction Technologies for Military Gas Turbine Engines, AIAA
Journal of Propulsion and Power, Vol. 21, No. 2, March-April 2005
59. Turns, S.R., An introduction to combustion. 2 ed. 1996, New York: McGraw-Hill
60. Wood, McDonell, Development and Application of a Surrogate Distillate Fuel, AIAA Journal
of P&P, Vol4 (5), pp399, 1989