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Contents lists available at ScienceDirect
Combustion and Flame
www.elsevier.com/locate/combustflame
Investigation of the effect of chemistry models on the numerical predictions
of the supersonic combustion of hydrogen
K. Kumaran, V. Babu
Department of Mechanical Engineering, Indian Institute of Technology, Madras, India 600 036
a r t i c l e i n f o a b s t r a c t
Article history:
Received 30 April 2008Received in revised form 7 January 2009
Accepted 17 January 2009
Available online 11 February 2009
Keywords:
Supersonic combustion
Numerical simulations
Supersonic reacting flow
Hydrogen detailed chemistry
Scramjet
In this numerical study, the influence of chemistry models on the predictions of supersonic combustion
in a model combustor is investigated. To this end, 3D, compressible, turbulent, reacting flow calculations
with a detailed chemistry model (with 37 reactions and 9 species) and the SpalartAllmaras turbulence
model have been carried out. These results are compared with earlier results obtained using single
step chemistry. Hydrogen is used as the fuel and three fuel injection schemes, namely, strut, staged
(i.e., strut and wall) and wall injection, are considered to evaluate the impact of the chemistry
models on the flow field predictions. Predictions of the mass fractions of major species, minor species,
dimensionless stagnation temperature, dimensionless static pressure rise and thrust percentage along the
combustor length are presented and discussed. Overall performance metrics such as mixing efficiency and
combustion efficiency are used to draw inferences on the nature (whether mixing- or kinetic-controlled)
and the completeness of the combustion process. The predicted values of the dimensionless wall static
pressure are compared with experimental data reported in the literature. The calculations show that
multi step chemistry predicts higher and more wide spread heat release than what is predicted by single
step chemistry. In addition, it is also shown that multi step chemistry predicts intricate details of the
combustion process such as the ignition distance and induction distance.
2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction
The emerging interest in hypersonic flights has motivated re-
search efforts towards developing a scramjet engine. Supersonic
combustion is the key enabling technology for sustained hyper-
sonic flights. In scramjet engines of current interest, the combustor
length is typically of the order of 1 m, and the residence time of
the mixture is of the order of milliseconds. This requires effec-
tive mixing and injection strategies from the combustor side and
high diffusivity and short ignition delay from the fuel side. Over
the years, hydrogen fuel has been preferred over hydrocarbon fu-
els due to its high mass diffusivity, wide flammability limits andminimum ignition energy. However, the low molecular weight of
hydrogen is a distinct disadvantage, since this increases the tank-
age requirement. Notwithstanding this, there have been numerous
investigations, both experimental and numerical, on the supersonic
combustion of hydrogen. A review of the literature on numerical
investigations that have utilised detailed chemistry for modelling
the combustion is presented next.
Jachimowski [1] developed a detailed mechanism for H2O2 re-
action to study the effect of chemical kinetics on supersonic com-
* Corresponding author.E-mail address: [email protected] (V. Babu).
bustion at high Mach numbers. The mechanism was validated with
shock tube and laminar flame studies reported in the literature. In
this study, three flight Mach numbers, namely 8, 16 and 25, were
considered. It was reported that for the Mach 8 condition, the ig-
nition delay was primarily controlled by chain branching and chain
propagation reactions. Recombination reactions were seen to have
a significant influence in the combustor section but not in the noz-
zle section. Further, it was illustrated that HO2 chemistry played an
important role in the reaction mechanism, and that the predictions
in the absence of HO2 chemistry were poor. It was also reported
that the rates of formation and consumption of HO2 reactions sig-
nificantly affected the prediction of heat release and in turn the
temperature in the combustor.
Sung et al. [2] experimentally studied the supersonic combus-
tion of hydrogen in a model combustor using parallel injection of
gaseous hydrogen into a supersonic vitiated airstream. The exper-
iments were conducted over a wide range of stagnation pressures
and temperatures. It was shown that the variation of ignitability
of the mixture with total pressure at constant total temperature
was similar to the classical homogeneous explosion limits of the
hydrogenoxygen system. This similarity highlighted the competi-
tion between chain branching and chain termination reactions and
in turn the inadequacy of the global reaction approximation to pre-
dict the ignition delay and heat release pattern.
0010-2180/$ see front matter 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
doi:10.1016/j.combustflame.2009.01.008
http://www.sciencedirect.com/http://www.elsevier.com/locate/combustflamemailto:[email protected]://dx.doi.org/10.1016/j.combustflame.2009.01.008http://dx.doi.org/10.1016/j.combustflame.2009.01.008mailto:[email protected]://www.elsevier.com/locate/combustflamehttp://www.sciencedirect.com/ -
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K. Kumaran, V. Babu / Combustion and Flame 156 (2009) 826841 827
Nomenclature
A cross-sectional area (m2)
F thrust (N)
mfuel,in mass flow rate of fuel (kg/s)
P static pressure (Pa)
P0,inlet inlet stagnation pressure (Pa)T0 local stagnation temperature (K)
T0,inlet inlet stagnation temperature (K)
u velocity along the x-direction (m/s)
H2 mass fraction of fuelH2O mass fraction of water vapours stoichiometric fuel mass fractionc combustion efficiency
m mixing efficiency kinematic viscosity (m2/s) mass density (kg/m3)wall wall shear stress (N/m
2)
Davidenko et al. [3] carried out a parametric study to investi-
gate the effect of uncertainties in experimental conditions and the
influence of modelling parameters on the supersonic combustion
of hydrogen. In their investigation, three reduced mechanisms and
one comprehensive mechanism were used. Predicted wall static
pressure, static temperature, OH species concentration and axial
velocity were compared with experimental data. It was reported
that reduced mechanisms were able to predict these quantities
reasonably well. However, it was also reported that reduced mech-anisms may not correctly predict ignition delay, and heat release
rate when the temperature of the mixing layer was not high
enough.
Recently, OConaire et al. [4] developed a detailed kinetic mech-
anism to simulate the combustion of H2O2 mixtures over a range
of pressure, temperature and equivalence ratios. They compared
their prediction of ignition delay, flame speed and concentration
profiles with experimental data reported in the literature. The
mechanism used in their study was very similar to the one pro-
posed by Stahl and Warnatz [5]. Based on a detailed sensitivity
study, the three body (HO2 formation from H and O2) reaction was
shown to be the most sensitive among the reactions. In addition,
they reported that the reactions involving H2O2 and HO2 must be
taken into account to successfully simulate a wide range of con-
ditions. All the above studies clearly underscore the importance of
detailed chemical kinetics to accurately predict the ignition delay
and heat release in supersonic combustion.
Rajasekaran and Babu [6] numerically investigated the super-
sonic combustion of hydrogen in a model combustor using a single
step chemistry model and the SpalartAllmaras one-equation tur-
bulence model [7]. In their study, the discrepancy between the
numerically predicted wall static pressure and the experimental
data was attributed to the over-prediction of mixing by the one
equation turbulence model and the inadequacy of the single step
chemistry model. Recently, Mitani and Kouchi [8] investigated the
effect of two chemistry models, namely, the thin-flame model and
the detailed chemistry model, on the numerical predictions of the
supersonic combustion of hydrogen in a scramjet combustor at
a Mach 6 flight condition. Their investigation revealed the dual-
mode operation of the combustor. Also, it was shown that a de-
tailed chemistry model was essential to make accurate predictions
in the mixing controlled regions, whereas the thin flame model
was adequate in the large diffusion flame zone.
Although the single step chemistry model is adequate for the
prediction of overall combustor performance, a detailed chemistry
model would provide additional information for improving and op-
timising the combustor design. In order to improve the combustor
design, intricate details of the reacting flow field, such as the inter-
mediate species distribution, formation and consumption of these
species and correlation with the heat release, pressure rise due to
combustion and thrust profile are needed, which are all difficult, if
not impossible to measure (except pressure rise). Numerical inves-
tigations with detailed chemistry model can provide insights intothese features of the combustion phenomena at high speeds.
Fig. 1. Perspective view of the model combustor [9].
2. Formulation and solution methodology
The model combustor considered here is the same as the one
studied experimentally by Tomioka et al. [9] and numerically by
Rajasekaran and Babu [6]. This is a staged supersonic combustor
with strut injectors for the first stage and wall mounted injec-
tors for the second stage. The staged supersonic combustor was
tested for Mach 2.5 vitiated airflow at a stagnation temperature
of 1500 K. With staged injection, the pressure rise from the first
stage combustion was isolated from the pressure rise due to the
second stage combustion, and an amount of fuel corresponding to
an overall equivalence ratio of more than unity could be injectedwithout causing separation in the inlet section. This allowed the
thrust to be doubled when compared with that of the first stage
injection alone. Hence, this design is very promising for use in full
scale supersonic combustors using hydrogen fuel.
The length of the combustor in the x-direction is 895 mm and
the total width in the z-direction is 94.3 mm. The height of the
combustor in the y-direction is 51 mm and 120 mm at the inlet
and the exit respectively. In this work, all the calculations have
been carried out on a quarter geometry (top right quadrant in
Fig. 1), based on symmetry considerations. A perspective view of
the combustor is shown in Fig. 1. A sectional view of the combus-
tor is shown in Fig. 2.
A strut with a blunt leading edge (of 1 mm radius) and a 6 half wedge angle compression surface is located with the nose (de-
noted by A) at x = 43.8 mm. There is a shoulder on the strut(denoted by B in Fig. 2) where the wedge transitions to a straight
portion (denoted by BC in Fig. 2). There is also a step of height
2 mm at the shoulder as shown in Fig. 2. The top wall of the com-
bustor features a constant height inlet (isolator) section (denoted
by DE in Fig. 2) from x =239 mm to 0 mm. There is a step onthe wall (EF in Fig. 2) of height 2 mm coinciding with the step at
the strut shoulder. The height of the top wall remains constant un-
til x = 56 mm. This is followed by the divergent part (denoted byGH in Fig. 2) from x = 56 mm to 656 mm. The divergence angleis 3.1. The injection ports on the strut (8 mm downstream of B)and on the top wall of the diverging section are shown by vertical
lines. There are a total of 10 injectors on the strut (5 each on the
top and bottom side of the strut straight portion) and 8 injectors
on the diverging wall (4 each on the top and bottom wall). In thenumerical calculations, owing to symmetry considerations, the fuel
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828 K. Kumaran, V. Babu / Combustion and Flame 156 (2009) 826841
Fig. 2. Sectional view of the model combustor [9] on the vertical symmetry plane.
is injected only from two and a half ports on the strut and from
two ports on the top wall.
Vitiated air (with mass fractions of O2, H2O and N2 equal to
0.198, 0.139 and 0.663 respectively) enters the combustor at a
Mach number of 2.5, stagnation temperature of 1500 K and stag-
nation pressure of 1 MPa. Hydrogen fuel is injected from the strut
as well as wall injection ports depending on the type of injection
scheme. Three injection schemes, namely, strut, staged (i.e., strutand wall) and wall are studied in this work. In all these injection
schemes, the fuel is injected in the y-direction into the supersonic
vitiated airstream. The equivalence ratio is 0.4 for the strut in-
jection scheme and 1 for the staged (0.4, 0.6) and wall injection
schemes. In the simulations, three-dimensional, compressible and
turbulent Favre-averaged NavierStokes equations are solved along
with species conservation equations.
In the present work, calculations have been carried out us-
ing the one equation, SpalartAllmaras turbulence model. This
model [7] is a relatively simple and well established model for
aerospace applications. In this model, a separate transport equa-
tion for the turbulent kinematic viscosity, t, is solved. Defaultvalues have been used for the model constants, Cb1 = 0.1355,Cb2 = 0.622, Cv1 = 7.1, Cw2 = 0.3, Cw3 = 2.0 and = 0.4187. Theturbulent Schmidt number and Prandtl number have been taken to
be equal to 0.7 and 0.667 respectively.
A finite rate detailed chemistry model [5] has been used in the
present work. The detailed mechanism along with the Arrhenius
model constants is given in Table 1. The detailed mechanism con-
sists of 37 reactions and 9 species (H2O, H2, H, O2, O, OH, HO2,
H2O2 and N2). Third body efficiencies for the recombination reac-
tions have also been taken from Stahl and Warnatz [5]. The effect
of the turbulent fluctuations on the rate of reaction has been ne-
glected, based on the finding by Baurle [10] that this is largely
insignificant for this type of flow.
The mass diffusivity of the mixture is modelled using kinetic
theory with default values for the Lennard-Jones characteristic
length and energy parameter for the individual species. The vis-
cosity and Cp of the mixture have been evaluated using mass-
weighted mixing laws. For the individual species in the mixture
these properties have been evaluated using Sutherlands law and
fifth order polynomials in temperature respectively. All the calcu-
lations have been carried out using FLUENT [11].
2.1. Boundary conditions
At the combustor inlet where the flow is supersonic, the static
and stagnation pressure, stagnation temperature and species mass
fractions are specified. In addition, turbulence intensity (10%) and
hydraulic diameter have been specified. At the hydrogen inlet,
where the flow is sonic, the mass flow rate of hydrogen, static
pressure, total temperature and species mass fraction are specified.
At the combustor exit where the flow is supersonic, all the flowvariables including pressure are determined from the interior of
Table 1
Detailed H2O2 reaction mechanism [5].
S. No. Reactions Pre-exponential
factor
(cm/mol/s)
Activation
energy
(kJ/mol)
Temperature
exponent B
R(1) O2 +H OH+O 2.20 1014 70.30 0.00R(2) OH+O O2 +H 1.72 1013 3.52 0.00R(3) H2 +O OH+H 5.06 10
04
26.30 2.67R(4) OH+H H2 +O 2.22 1004 18.29 2.67R(5) H2 +OH H2O+H 1.00 1008 13.80 1.60R(6) H2O+H H2 +OH 4.31 1008 76.46 1.60R(7) OH+OH H2O+O 1.50 1009 0.42 1.14R(8) H2O+O OH+OH 1.47 1010 71.09 1.14R(9) H+H+M* H2 +M* 1.80 1018 0.00 1.00R( 10 ) H2 +M* H+H+M* 7.26 1018 436.82 1.00R( 11 ) H+OH+M* H2O+M* 2.20 1022 0.00 2.00R( 12) H2O+M* H+OH+M* 3.83 1023 499.48 2.00R( 13 ) O+O+M* O2 +M* 2.90 1017 0.00 1.00R( 14 ) O2 +M* O+O+M* 6.55 1018 495.58 1.00
Formation and consumption of HO2R( 15 ) H+O2 +M* HO2 +M* 2.30 1018 0.00 0.80R(16) HO2 +M* H+O2 +M* 3.19 1018 195.39 0.80R(17) HO2 +H OH+OH 1.50 1014 4.20 0.00R(18) OH
+OH
HO2
+H 1.50
1013 170.84 0.00
R(19) HO2 +H H2 +O2 2.50 1013 2.90 0.00R(20) H2 +O2 HO2 +H 7.27 1013 244.333 0.00R( 21 ) H O2 +H H2O+O 3.00 1013 7.20 0.00R(22) H2O+O HO2 +H 2.95 1013 244.51 0.00R( 23 ) H O2 +O OH+O2 1.80 1013 1.70 0.00R( 24) O H+O2 HO2 +O 2.30 1013 231.71 0.00R( 25 ) H O2 +OH H2O+O2 6.00 1013 0.00 0.00R(26) H2O+O2 HO2 +OH 7.52 1014 304.09 0.00
Formation and consumption of H2O2R( 27) H O2 +HO2 H2O2 +O2 2.50 1011 5.20 0.00R( 28 ) O H+OH+M* H2O2 +M* 3.25 1022 0.00 2.00R(29) H2O2 +M* OH+OH+M* 1.69 1024 202.29 2.00R(30) H2O2 +H H2 +HO2 1.70 1012 15.70 0.00R( 31) H2 +HO2 H2O2 +H 1.32 1012 83.59 0.00R(32) H2O2 +H H2O+OH 1.00 1013 15.00 0.00R(33) H2O
+OH
H2O2
+H 3.34
1012 312.19 0.00
R(34) H2O2 +O OH+HO2 2.80 1013 26.80 0.00R( 35 ) O H+HO2 H2O2 +O 9.51 1012 86.68 0.00R(36) H2O2 +OH H2O+HO2 5.40 1012 4.20 0.00R( 37 ) H2O+HO2 H2O2 +OH 1.50 1013 134.75 0.00
Third-body efficiencies
M*= 1.00H2 + 6.50H2O+ 0.40O2 + 0.40N2 + 1.00O+ 1.00H+ 1.00OH + 1.00HO2+ 1.00H2O2
M has equal efficiencies for all species
the domain by extrapolation. All the stationary surfaces have been
assumed to be adiabatic and standard wall functions have been
used.
2.2. Convergence metrics
All the calculations are carried out until the global (overall)mass, momentum and energy balance is acceptable. For all the
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K. Kumaran, V. Babu / Combustion and Flame 156 (2009) 826841 829
Fig. 3. Illustration of the hybrid mesh showing the volumes meshed using hexahedral and tetrahedral cells. Refined regions are shown in grey.
results reported here, the difference in overall mass flow rate be-
tween the inlet(s) and the outlet is less than 3% of the injected fuel
mass flow rate (fuel mass flow rate rather than the inlet mass flow
rate is used since the former is two orders of magnitude less than
the latter). Furthermore, the difference in the mass flow rate of H
and O atoms between the inlet(s) and the outlet is less than 4%
and 0.25% with respect to the injected mass flow rate for H atom
and the inlet mass flow rate for the O atom respectively.Momentum balance can be checked by evaluating the left and
right hand sides of the expression
F=
(P+ u2)d Aoutlet
inlet
separately and then calculating the difference. The right hand side
of this expression is the impulse function. The left hand side is the
net force acting on the walls (pressure+viscous) in the x-direction.For all the results reported here, the difference between the left
and right hand side of the above expression is less than 5%. Also,
the overall energy balance is within 5% of the inlet total enthalpy.
2.3. Grid independence study
Numerical solutions to the problem outlined above but with-
out H2 injection were obtained initially on a mesh with 254658
tetrahedral cells [6]. This grid was then refined successively. First,
adaption based on gradients of static pressure was done, so that
the shocks could be captured accurately. Refinement near all the
no-slip surfaces was done next, so as to resolve the boundary lay-
ers well and to achieve wall y+ values as low as possible. Here,wall y+ is defined as ywallu/ , where ywall is the normal dis-tance of the first node from the wall and u =
wall/ is the
friction velocity. These refinements resulted in grids with 309220
and 362385 cells respectively. The maximum value of wall y+for the three grids were 228, 165 and 118 respectively. The grid
with 362385 cells was used for all the non-reacting flow calcula-
tions. For the reacting flow calculations with single step chemistry,
the grid was adapted further based on the gradients of reacting
species. After progressive refinement, a grid with 751690 cells was
taken as the final grid for all the calculations [6]. All the calcula-
tions in the present work with detailed chemistry have also been
carried out on this mesh. The details of the maximum and the
area-weighted values of wall y+ for the three injection schemesare given in Table 2. Except for some isolated spots in the vicinity
of the injection ports, wall y+ is generally between 40 and 100.Since the gradients of the species mass fractions are high in
the same regions, i.e., in the vicinity of the injection locations, in
both the single step and detailed chemistry predictions, it is rea-
sonable to assume that the gradient based adaption that has been
done earlier is adequate for the detailed chemistry calculations
also. Nevertheless, grid independence of the effect of chemistry
model has been established for one case, namely, the staged in-jection scheme.
Table 2
Wall y+ values for the detailed chemistry calculations on different grids.
Injection scheme No. of cells Wall y+
Max Avg
Strut injection 751690 144 71
Staged injection 751690 156 65
Staged injection (hybrid mesh) 1316000 136 65
Wall injection 751690 150 55
For this purpose, the entire computational domain has been
meshed in a completely different manner using a hybrid mesh
with hexahedral and tetrahedral cells, as illustrated in Fig. 3. It
can be seen that the volumes enclosing the injector ports have
been meshed with tetrahedral cells, to facilitate the meshing of
the circular injector faces. In the hybrid mesh, the spacing of the
hexahedral cells in the direction normal to the walls has been tai-
lored to achieve approximately the same values for wall y+ as thesolution obtained using the mesh with 751690 cells (Table 2). The
axial spacing of the mesh is fine in the regions 0 x 56 mm
and 180x 325 mm. These regions are shown shaded in Fig. 3.
This refinement strategy allows the gradient in the flow variables
near the strut, wall injection ports and also the separated flow re-gion upstream of the wall injection ports to be resolved better. The
number of tetrahedral cells in the volume surrounding the strut
and the wall injection ports is higher now by a factor of 4 and 6
respectively. The number of cells in the rest of the refined region
is higher by a factor of 3 and 2 upstream and downstream of the
wall injection ports respectively. Since the tetrahedral mesh is un-
structured, the required refinement near the no-slip surfaces and
in the interior of the flow domain has to be achieved by adjusting
the number and size of the cells. Refining the tetrahedral mesh ex-
cessively in one direction will result in highly skewed cells, which
are undesirable. In the present case, the volume-weighted equi-
angle skew of the tetrahedral mesh is 0.38.1 As a result, the total
number of cells in the hybrid mesh is 1316000. It is worth not-
ing that the change in the mesh topology from a pure tetrahedralmesh to a hybrid mesh in addition to the higher cell count results
in a more stringent test for the grid independence of the solution
than the customary increase in cell count alone.
Predictions of the single step and multi step chemistry cal-
culations obtained using the refined hybrid mesh are compared
against those on the tetrahedral mesh in Fig. 4. It can be seen
from this figure that the differences in the profiles of mass frac-
tions of the minor species between the two grids are negligible. On
the other hand, profiles of the dimensionless stagnation tempera-
ture on the two grids (with single step and multi step chemistry)
exhibit some difference. The most significant change is a down-
1 An equi-angle skew measure of 0 indicates a perfect tetrahedron and a value
of 1 denotes a degenerate one. In practice, skewness measure values below 0.6 are
usually acceptable.
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830 K. Kumaran, V. Babu / Combustion and Flame 156 (2009) 826841
Fig. 4. Variation of the mass fractions of the minor species and the dimensionless stagnation temperature on the present tetrahedral mesh and the refined hybrid mesh.
stream shift of the point of separation ahead of the wall injectors
by about 15 mm. However, the volume occupied by the separatedflow is approximately the same on both the grids. The change in
the dimensionless stagnation temperature is below 5% everywhere,
except in the region of separated flow, where it is 7%. For the com-
pressible, 3D, turbulent, reacting flow considered here, and keeping
in mind the change in the mesh topology and the increase in the
cell count, these changes can be safely said to be reasonable. More-
over, the difference between the predictions of the single step and
multi step chemistry model remain almost the same on the tetra-
hedral and the hybrid mesh, clearly demonstrating that inferences
on the effect of chemistry are grid independent.
3. Results and discussion
Results from the reacting flow calculations for each of the in-
jection scheme are presented and discussed next. Axial variation of
the mass fractions of major species (H2O, H2 and O2) and minor
species (H, O, OH, HO2 and H2O2), dimensionless stagnation tem-
perature, dimensionless static pressure rise and thrust percentage
are presented for each scheme. Area weighted averages of these
quantities at various x= constant planes have been plotted.The static pressure rise (P) is the difference in the static pres-
sure between the reacting flow and the cold flow (without fuel
injection). Thrust percentage is defined as the ratio of the differ-
ence in the impulse function between any x = constant plane andthe inlet to that between the outlet and the inlet.
3.1. Strut injection
Fig. 5 shows the axial variation of the mass fractions of the
major species for the strut injection scheme. In this scheme, fuel
is injected from the strut (equivalence ratio of 0.4) at x = 8 mmdownstream of B as shown in Fig. 2. The vitiated air entering the
combustor does not contain any H2 and so the mass fraction of H2is zero up to x 4 mm. The separated flow region downstream ofthe strut step results in the availability of H2 ahead of the injection
location. However, the H2 mass fraction peaks just downstream of
the injection location. Also, the marginal rise in H 2 mass fraction
downstream of the first peak at x 28 mm, where the strut ends(location C in Fig. 2), shows the availability of more H2 in the re-
circulation region downstream of the strut base. The mass fraction
of H2 beyond x 200 mm is almost zero. Almost 98% of the peakvalue of the H2 mass fraction is consumed within the combustor.
This can be attributed to the long residence time (due to the ax-ial location of the strut) and low mass flow rate of the fuel (due
Fig. 5. Variation of the mass fractions of the major species with single step [6] and
multi step chemistry models (strut injection scheme).
to the low equivalence ratio). Also, the mass fraction of H 2 at the
exit is the same in both the chemistry models.
Since vitiated air enters the combustor, a fractional amount of
H2O is present from the combustor inlet onwards (Fig. 5). The sud-
den increase in the mass fraction of H2O is due to combustion
of the fuel injected from the strut. The H2O mass fraction profile
peaks in the constant area section (from x = 28 to 56 mm) andthe peak value is higher with the multi step chemistry model than
with the single step chemistry model. This can be attributed to
more reaction pathways being available for the formation of H2Oin multi step chemistry. This difference in the mass fractions of
H2O and O2 between the single and multi step chemistry model
persists in the divergent section (x > 56 mm) until the combustor
exit. In both cases, the mass fractions of the major species do not
change significantly beyond x= 200 mm, showing that the kinetics(and the heat release) slows down in the diverging section beyond
this point. This is due to the fact that the static temperature de-
creases as the flow expands. This argument is corroborated by the
variation of stagnation temperature presented later. Trends in the
variation of the mass fraction of O2 are consistent with those of
H2O (i.e., any change in the mass fraction of H 2O is accompanied
by a commensurate change of the opposite kind in the O 2 mass
fraction).
Fig. 6 shows the variation of the mass fractions of the minorspecies along the combustor. A close-up view of the peaks is also
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K. Kumaran, V. Babu / Combustion and Flame 156 (2009) 826841 831
Fig. 6. Variation of the mass fractions of the minor species along the combustor. Entire combustor (left) and a close-up view (right) (strut injection scheme).
shown on the right. It can be seen from Fig. 6 (left) that, among
the radicals, OH mass fraction is the highest, starting just down-stream of the injection location. The mass fraction of OH reaches
a peak value at x 210 mm. This indicates that the chain branch-ing and chain propagating reactions that produce the OH radical
are active even in the diverging section. Beyond this axial location,
the OH mass fraction starts decreasing but it is not consumed com-
pletely even at the combustor exit. This indicates that the reactions
that consume the OH radical and the chain terminating reactions
are not dominant in this section. However, the peak values for all
the other radicals occur in the constant area section after the strut
base, where most of the heat release takes place. This is clearly
seen in the close-up view in Fig. 6.
The profiles of the mass fraction of O and H radicals follow
similar trends. Further, the profiles of HO2 and H2O2 show an in-
crease, a plateau and then a sharp decrease after x = 30 mm. Itcan be seen from the close-up view in Fig. 6 that the formationof HO2 and H2O2 occurs only after adequate amounts of OH, O
and H are formed. This trend is consistent with the formation re-
actions shown in Table 1. The induction distance is about 6 mm
for this injection scheme. Beyond this induction distance, the rates
of formation of HO2 and H2O2 increase sharply. The rates of con-
sumption of these species through the recombination reactions
also increase after a slight delay. The plateau region in the mass
fraction profiles of HO2 and H2O2 indicate that the rates of for-
mation and consumption of these species are the same. The sharp
decrease in the HO2 and H2O2 profile following the plateau region
indicates that the consumption of these species through chain ter-
mination is higher from this location onwards. These reactions are
accompanied by heat release and this is corroborated by the steep
rise in stagnation temperature at the same location. In contrast to
the OH and O radicals, 85% of the H radical that is produced is
consumed within the combustor, while HO2 and H2O2 are con-
sumed almost entirely. This implies that most of the consumption
reactions of HO2 and H2O2 involving the H radical are active in
the diverging section. In spite of the decrease in static tempera-
ture (and hence reaction rate) due to the expansion of the flow
in the diverging section, these reactions are active mainly due to
their low activation energy. From the above discussion on interme-
diate radicals it is evident that recombination reactions involving
the H radical are more active than those involving the OH and O
radical in the diverging section.
Stagnation temperature on any x = constant plane gives an ac-curate indication of the heat release, since any increase in stagna-
tion temperature has to be solely due to heat release from com-bustion. The axial variation of the dimensionless stagnation tem-
perature along the entire length of the combustor and a close-up
view of the peak are shown in Fig. 7. The stagnation temperatureprofile remains constant up to the strut shoulder (x= 0) and thenincreases in the region x= 0 to 8 mm (between B and the injectionlocation as shown in Fig. 2) due to the combustion in the separa-
tion region ahead of the injection location. The heat release in this
region is higher with single step chemistry and so the rise in stag-
nation temperature is more. This is clearly seen in Fig. 7 (right).
The stagnation temperature starts decreasing immediately after the
injection location. This is due to the mixing of the lower stagnation
temperature fuel stream with the main flow. It is important to note
that the dimensionless stagnation temperature goes below 1 only
marginally for the single step case owing to the higher heat re-
lease ahead of the injection location, in contrast to the multi step
case. Consequently, in the latter case, it takes a longer distance
for the dimensionless stagnation temperature to reattain the inletvalue of 1. However, the difference in the stagnation temperature
diminishes in the region 28 < x < 186 mm. This can be attributed
to the decreasing difference in the static temperature.
Furthermore, the stagnation temperature profile predicted by
multi step chemistry crosses over the single step chemistry profile
at x = 186 mm. The axial location of this cross-over is very closeto the axial location of the OH radical peak. This is an additional
indication of reactions being active in the diverging section. Also,
the stagnation temperature profile is very steep in the constant
area section (after the strut base) and levels off after x= 300 mmin the diverging section, indicating maximum heat release in the
former. This also implies that the heat release diminishes in the
diverging section due to the decrease in the reaction rates (owing
to the decrease in the static temperature), and so the stagnationtemperature increases very slowly due to residual heat release. The
above discussion clearly underscores the difference in the predic-
tions of heat release between single step and multi step chemistry,
though there is not much difference in the value of the stagnation
temperature between the two at the exit.
Axial variation of the dimensionless static pressure rise along
the entire length of the combustor and a close-up view are shown
in Fig. 8. The static pressure rise at any x= constant plane is non-dimensionalised using the inlet stagnation pressure. Since there is
no combustion in the isolator section, there is no pressure rise,
although the multi step prediction shows a slight decrease just
ahead of the strut nose. Downstream of the strut shoulder, P
starts increasing due to the combustion in the separation region
behind the strut step. The difference in the prediction of the staticpressure rise between the single step and the multi step chemistry
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Fig. 7. Variation of the dimensionless stagnation temperature with single step [6] and multi step chemistry models. Entire combustor (left) and a close-up view (right) (strut
injection scheme).
Fig. 8. Variation of the dimensionless static pressure rise along the combustor. Entire combustor (left) and a close-up view (right) (strut injection scheme).
model in the region x= 8 mm to 28 mm is due to less heat releaseand in turn lower static temperature with multi step chemistry.
The multi step chemistry calculations predict the P peak
value to be higher than that of the single step chemistry predic-
tion as seen in Fig. 8. Also, the prediction of the peak location is
slightly different between the chemistry models (i.e., at x 30 mmin the single step and at x 34 mm in the multi step chemistrymodel) in Fig. 8 (right). The axial shift in the peak locations in turn
can be inferred as the difference in the prediction of ignition delay
distance. This correlates well with the shift in the prediction of thelocation where the dimensionless stagnation temperature reattains
the inlet value with multi step chemistry. In addition, the static
pressure rise in this region with multi step chemistry is more than
that with single step chemistry, indicating more heat release. This
could be due to the fact that the recombination reactions, which
are accompanied by heat release, are more active in this region.
The decrease in static pressure rise is very steep in the region,
x = 56 mm to 78 mm, and further downstream the decrease isgradual.
Axial variation of the thrust percentage along the combustor is
shown in Fig. 9. The thrust is negative in the constant area isolator
section of the combustor essentially due to the deceleration of the
flow in this section. This drag force gradually increases from the
inlet to the strut nose location. From this location onwards, thedrag force increases steeply, since there is an additional pressure
Fig. 9. Variation of the thrust percentage along the combustor (strut injection
scheme).
drag on the strut compression surface. The drag force reaches a
maximum value at the strut shoulder, where the strut compression
surface has the maximum penetration into the flow. Downstream
of this location the flow accelerates through expansion fans gen-erated from the step on the top wall and on the strut shoulder.
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Fig. 10. Variation of the mass fractions of the major species with single step [6] and
multi step chemistry models (staged injection scheme).
This is indicated by the first steep increase in Fig. 9. Thrust per-
centage remains constant over the strut straight region (x = 0 to28 mm), where the fuel is injected and the heat release starts. The
sudden augmentation of thrust at x = 30 mm is due to more heatrelease in the constant area section downstream of the strut base.
This is seen as the second steep increase in Fig. 9. Following this,
the thrust increases continuously in the diverging section. As dis-
cussed earlier, though only residual heat is added to the flow in the
diverging section, the thrust increases continuously due to the ac-
celeration of the flow. This is consistent with the trends discussed
earlier for the dimensionless stagnation temperature and the static
pressure rise.
The overall thrust predicted by the single and multi step calcu-
lation is 64.86 N and 71.57 N respectively. Thrust profiles predicted
by the two models are different in the heat release region. The
maximum value for the drag is predicted to be higher by the sin-gle step chemistry model. This is most likely due to the higher
static temperature predicted with the single step chemistry model.
The thrust profile is very important in combustor design since it
can be used to identify those parts of the combustor where thrust
generation can be enhanced to better distribute the thrust genera-
tion.
3.2. Staged injection
Fig. 10 shows the axial variation of the mass fractions of the
major species for the staged injection scheme. Here, in addition to
injection from the strut (equivalence ratio of 0.4), fuel is also in-
jected from the top wall (equivalence ratio of 0.6) at x
=296 mm.
This is seen as the two peaks in the mass fraction profile of H 2(one at x 10 mm and another at x 300 mm) both located justdownstream of the injection locations in Fig. 10.
The variation of the mass fractions of the major species in
the region x < 180 mm is the same as in the strut injection
scheme (Fig. 5) and so does not require any new discussion. For
x > 180 mm the mass fraction profiles are different due to the
heat addition in the diverging section. This heat addition in the
expanding and accelerating flow causes a flow separation ahead of
the wall injection location. Consequently, the mass fraction profile
of H2 starts increasing ahead of the injection location and peaks
just downstream. Although more fuel is injected from the wall, the
magnitude of the peak downstream of the wall injection is lower
than that of the strut injection. This can be attributed to rapid
consumption of fuel by the flow approaching at a higher statictemperature due to the heat addition in the strut region.
The peak value near the strut region in this scheme is the same
as that of the strut injection scheme owing to the same amount
of fuel being injected from the strut. Also, the peak values pre-
dicted by both the chemistry models are almost the same, as seen
in Fig. 10. However, the mass fraction of H2 at the exit predicted
with multi step chemistry is almost 50% less than that of the single
step chemistry prediction. This in turn implies that the prediction
of the fuel consumption within the combustor is different betweenthe chemistry models, in contrast to the strut injection scheme.
The amount of fuel consumed within the combustor with multi
step chemistry is higher than that of the single step chemistry.
This difference can be attributed to more reaction pathways be-
ing available for producing radicals through (chain initiation and
chain branching) reactions involving H2 in the diverging section,
which, in turn, is due to the higher static temperature of the flow
approaching the wall injection location. The amount of fuel leav-
ing the combustor is higher than that of the strut injection scheme
due to the short residence time of the fuel injected from the wall
(since the available combustor length is shorter) and the overall
higher mass flow rate of the fuel (since the equivalence ratio is
higher).
The mass fraction profiles of H2O and O2 are similar to the strutinjection scheme until x 230 mm. The combustion of fuel in theseparated region (over a length of approximately 60 mm) leads
to an additional increase in the mass fraction of H 2O and a com-
mensurate decrease in the mass fraction of O2 ahead of the wall
injection location. Similar to the strut injection scheme, here also
the mass fraction of H2O is predicted to be higher with multi step
chemistry in the diverging section. This difference persists until the
combustor exit for the same reason discussed earlier in the strut
injection scheme. Although the mass fraction of H2 at the com-
bustor exit is 50% lower with the multi step chemistry model, the
increase in the mass fraction of H2O with multi step chemistry is
only 6% at the combustor exit. This means that not all of the H2that is consumed is converted into H2O and so there is a consider-
able amount of intermediate species present at the combustor exit.Further, in the staged injection scheme the mass fraction of H2O at
the exit is higher than that of the strut injection scheme by 36%
and 31% with the multi step and the single step chemistry mod-
els respectively. This implies that more heat is released and in turn
considerable thrust augmentation can be expected in this injection
scheme.
Fig. 11 shows the variation of the mass fractions of the minor
species along the combustor. A close-up view is also shown on the
right. The mass fraction profiles of the intermediate radicals up to
x 236 mm are very similar to that of the strut injection scheme.The mass fraction profile of the OH radical starts increasing well
ahead of the wall injection location (due to combustion in the sep-
aration region) and reaches a peak value at x
406 mm. This in-
dicates that more chain initiation and chain propagation reactionsare active due to the higher static temperature in this region. The
OH radical is produced over a longer distance, which corroborates
well with the steep increase in the stagnation temperature which
is discussed later. The mass fractions of H, H2O2 and HO2 decrease
rather sharply beyond x= 100 mm indicating that the recombina-tion reactions that consume these species are very active in this
region. In particular, H2O2 and HO2 produced in the strut combus-
tion regions are consumed almost completely by x= 200 mm. Themass fractions of all these species increase sharply at x= 280 mmin the separation region ahead of the wall injection. This increase
is due both to the availability of more fuel from the wall injection
and the enhanced reactions rates of the chain branching reactions.
The latter aspect is a consequence of the higher static temperature
of the flow ahead of the wall injection location. For the same rea-son the profiles of HO2 and H2O2 show a rapid increase followed
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Fig. 11. Variation of the mass fractions of the minor species along the combustor. Entire combustor (left) and a close-up view (right) (staged injection scheme).
Fig. 12. Variation of the dimensionless stagnation temperature with single step [6] and multi step chemistry models. Entire combustor (left) and a close-up view (right)
(staged injection scheme).
by a rapid decrease without a plateau region in-between, as was
the case near the strut injection portion.
The steep decrease in the mass fractions of H, HO 2 and H2O2towards the end of the separation region show that the recom-
bination reactions are very active here. The O radical is neither
consumed nor produced much in this region. In this scheme, the
additional heat release through the recombination reactions results
in a higher static temperature in the diverging section than in the
strut injection scheme. Although the static temperature is higher,
the consumption reactions of HO2
and H2
O2
involving the H rad-
ical are still dominant over the reactions involving the O and OH
radical. This can be seen in Fig. 11. This indicates that most of the
OH and O radicals produced (i.e., about 85% and 67% of the maxi-
mum values) leave the combustor.
Axial variation of the dimensionless stagnation temperature
along the entire length of the combustor and a close-up view are
shown in Fig. 12. In the separation region (ahead of the wall in-
jection at x = 296 mm), the heat release predicted by multi stepchemistry is more than that of single step chemistry. This corre-
lates well with the steep decrease in the mass fractions of H, HO 2and H2O2 due to the recombination reactions in this region, which
are accompanied by the heat release. Further, the steep increase in
the stagnation temperature in the region (x 230 mm to 400 mm)correlates well with the continuous increase in the mass fraction
of the OH radical in the same region as seen in Fig. 11. In thisscheme, the decrease in the stagnation temperature due to the in-
jection of fuel at a lower stagnation temperature from the wall is
less than what was seen near the strut injection portion. This is
due to the higher stagnation temperature of the flow approaching
from the strut combustion region.
The single step chemistry calculations show that the rise in
stagnation temperature levels off after x= 500 mm indicating thatthe reaction rates have ceased and the flow is chemically frozen
beyond this location. The multi step chemistry calculations, on the
other hand, show the stagnation temperature to increase contin-
uously until the combustor exit, indicating residual heat release
from the recombination reactions. Mass fraction profiles of the O
and H radicals in Fig. 11 (left) show that, indeed, the recombina-
tion reactions involving these species are active in this region. This
is significant since the flow is undergoing expansion here, accom-
panied by a decrease in the static temperature, i.e., a reduction in
the rates of reactions and an increase in the velocity, i.e., reduc-
tion in the residence time. The difference in the predictions of the
stagnation temperature between the chemistry models increases
continuously from x 400 mm until the combustor exit. In thisregion, the multi step chemistry predictions are higher demon-
strating that the intermediate reactions are needed to predict the
heat release accurately. Moreover, the difference in the predicted
value of the stagnation temperature between the chemistry models
at the exit is about 3.6%. The above discussion clearly underscores
the inadequacy of the global reaction approximation for predictingthe heat release. The increase in the heat release due to wall in-
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Fig. 13. Variation of the dimensionless static pressure rise along the combustor. Entire combustor (left) and a close-up view (right) (staged injection scheme).
Fig. 14. Variation of the thrust percentage along the combustor (staged injection
scheme).
jection is about 22.5% and 18.6% with multi step and single step
chemistry respectively with a commensurate augmentation of the
thrust.
Axial variation of the dimensionless static pressure rise along
the entire length of the combustor and a close-up view are shown
in Fig. 13. The steep rise just downstream of x 236 mm is dueto combustion in the separated region. In this region, multi step
chemistry predicts a higher static pressure than the single step
chemistry due to higher heat release. Downstream of this location
the static pressure decreases slightly and starts increasing imme-
diately afterwards. The location of the peak in the static pressurerise is just upstream (at x = 294 mm) of the injection location.The marginal rise in static pressure downstream of this peak at
x= 346 mm is due to residual heat release downstream of the in- jection location. The static pressure decreases steeply in the region
340 x 420 mm and more gradually further downstream. The
static pressure rise profile predicted with multi step chemistry is
slightly above the single step profile from the wall injection lo-
cation to the combustor exit. This implies that the higher heat
release predicted with multi step chemistry could have resulted
in reduced acceleration of the flow than the single step chemistry
case. Though the difference in the static pressure is marginal, this
can have a significant effect on the thrust predictions.
Axial variation of the thrust percentage along the combustor is
shown in Fig. 14. The thrust profile in the isolator and the strutportion, up to x 230 mm appears different in this figure from
Fig. 15. Variation of the mass fractions of major species with single step [6] and
multi step chemistry models (wall injection scheme).
the profile in Fig. 9 for the strut injection scheme. This is entirely
due to the fact that thrust percentage, not thrust itself is plotted.
The overall thrust generated in the staged injection scheme with
multi step and single step chemistry is 156.37 N and 149.45 N
respectively. Similar to the strut injection scheme, the thrust per-
centage predicted by both the chemistry models appear to be the
same close to the exit, though they are different in magnitude
by 4.63%. Further, the augmentation of thrust due to the wall in-
jection is 118.5% and 130.42% with the multi step and the single
step chemistry models respectively. It is important to note that the
higher thrust predicted by the single step chemistry model is dueto the inadequacy of the global reaction approximation to predict
the heat release accurately. Nevertheless, in this injection scheme
the thrust augmentation due to the wall injection is more than
100% of the strut injection scheme.
3.3. Wall injection
Fig. 15 shows the axial variation of the mass fractions of the
major species for the wall injection scheme. Here, the fuel is in-
jected only from the top wall (equivalence ratio of 1.0) at x =296 mm. Heat addition in the expanding and accelerating flow
in the diverging section causes flow separation ahead of the wall
injection location. Consequently, the mass fraction of H2 starts in-
creasing ahead of the wall injection location and peaks just down-stream. The magnitude of the peak in the wall injection scheme is
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Fig. 16. Variation of the mass fractions of the minor species along the combustor. Entire combustor (left) and a close-up view (right) (wall injection scheme).
higher than the staged injection scheme, since the entire amount
of fuel (corresponding to an equivalence ratio of 1) is now injected
from the wall. Also, the amount of fuel leaving the combustor inthe wall injection scheme is higher. This is due to the shorter
residence time of the fuel injected from the wall (since the avail-
able combustor length is shorter) and the higher amount of fuel
injected from the wall injectors. The amount of fuel leaving the
combustor is less with multi step chemistry than with single step
chemistry. This is clearly seen in Fig. 15. This in turn implies that
the prediction of the fuel consumption within the combustor is dif-
ferent between the chemistry models, which correlates well with
the mass fraction profiles of H2O which is discussed next.
In this injection scheme, since there is no combustion in the
strut region, the mass fractions of H2O and O2 remain almost con-
stant up to x 100 mm and the separation zone also extends farupstream than in the staged injection scheme. This causes a vari-
ation in mass fractions of H2O and O2 from x > 100 mm onwardsdue to combustion in the separation zone. This variation is seen to
be prominent with multi step chemistry owing to more reaction
pathways for the formation of H2O. For the same reason, the mass
fraction of H2O downstream of the injection location is predicted
to be higher with multi step chemistry and the mass fraction of
O2 is correspondingly lower. The difference in the mass fractions
of H2O and O2 between the chemistry models persists until the
combustor exit. In particular, the difference is quite pronounced
in the recirculation region (100 < x < 300 mm) ahead of the injec-
tion location. In this region, the mass fraction profile of H 2O shows
some interesting features. There is an initial increase followed by
a plateau and then another increase just before x = 300 mm. Theincrease abruptly becomes very steep just past x = 300 mm. Thissuggests that the formation of H
2O in the low speed recirculation
region is through a mechanism different from that downstream of
the fuel injection location. In addition, profiles of the mass frac-
tions of H2O, H2 and O2 gradually become flat beyond x 400 mmindicating that the chemical reactions are slowing down. This can
be attributed to the decreasing static temperature due to expan-
sion of the flow.
Fig. 16 shows the variation of the mass fractions of the mi-
nor species along the combustor. A close-up view of the peak is
also shown on the right. Due to the absence of combustion in the
strut region, minor species are not seen up to x 120 mm. Beyondthis point, minor species are present well ahead of the injection
location due to combustion in the separation zone. Among the rad-
icals, the mass fraction of OH is the highest and it is produced
over a longer distance with the peak occurring at x
390 mm.
Downstream of this peak, the OH radical is neither consumed norproduced much and an amount of OH almost equal to 95% of the
peak value leaves the combustor. This can be expected to have a
significant influence on the heat release and the combustion effi-
ciency predictions. Mass fractions of the O and H radicals peak justdownstream of the injection location and start decreasing rapidly
over the region where the OH radical is produced, i.e., between
x = 300 mm and 400 mm. Further downstream, consumption ofthe O radical is very minimal until the combustor exit and an
amount of O almost equal to 70% of the peak value leaves the
combustor. However, the H radical is consumed considerably in
this region, and approximately 55% of the peak value is consumed
within the combustor. It is important to note that the major part
of consumption of O and H radicals occurs before x 420 mm.The absence of HO2 and H2O2 in the low speed recirculation re-
gion (120 < x < 300 mm) suggests that the residence time is long
enough for the OH, O and H formation reactions to go almost to
completion. This, combined with the increase in the mass fraction
of H2O in this region (from Fig. 15) leads to the inference that re-actions R(5), R(7) and R(11) in Table 1 are the dominant reactions
here.
Mass fractions of the HO2 and H2O2 radicals peak just down-
stream of the injection location and remain almost constant for
a short distance and decrease sharply afterwards. This sharp de-
crease coincides with the increase in the mass fraction of the OH
radical. This indicates that the recombination reactions involving
the consumption of HO2 and H2O2, which are accompanied by
heat release, are active in this region. This corroborates well with
the steep increase in the stagnation temperature which is dis-
cussed later. Beyond x 400 mm, the mass fractions of OH andO radicals are almost constant and the decrease in the mass frac-
tion of H is only marginal (Fig. 16, left). This is in contrast to the
trends seen in the staged injection scheme in the same region
(Fig. 11, left). Trends in the mass fraction of HO2 in the wall in-
jection scheme are almost the same as those seen in the staged
injection scheme. However, the mass fraction of H 2O2 remains al-
most the same beyond x 400 mm in the wall injection scheme(Fig. 16, right), in contrast to the staged injection scheme, where it
decreases drastically (Fig. 11, right). Consequently, the residual heat
release in the wall injection scheme is less than that of the staged
injection scheme and the reduction in the static temperature due
to the expansion and acceleration of the flow in the diverging sec-
tion is more drastic. The small amount of HO2 and H2O2 radicals
and the low static temperature in this region prevents the con-
sumption of OH, O and H radicals by the recombination reactions.
Hence, higher mass fractions of radicals are seen to leave the com-
bustor in this injection scheme.
Axial variation of the dimensionless stagnation temperaturealong the entire length of the combustor and a close-up view are
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Fig. 17. Variation of the dimensionless stagnation temperature with single step [6] and multi step chemistry models. Entire combustor (left) and a close-up view (right) (wall
injection scheme).
Fig. 18. Variation of the dimensionless static pressure rise along the combustor. Entire combustor (left) and close-up view (right) (wall injection scheme).
shown in Fig. 17. Since there is no combustion in the strut region,
the stagnation temperature remains constant up to x 100 mm. Inthe separation region (ahead of the wall injection at x= 296 mm),the heat release with multi step chemistry is more than that of the
single step chemistry due to more reaction pathways for the for-
mation of H2O. This is consistent with the variation of the mass
fraction of H2O with multi step chemistry in this region (Fig. 15).
Further, the steep increase in the stagnation temperature in the
region x 300 to 400 mm correlates well with the continuousincrease in the mass fraction of the OH radical and the steep de-
crease in the mass fractions of HO2 and H2O2 in the same regionas seen in Fig. 16. Contrary to what was seen in the previous two
injection schemes, here, the mixing of the fuel stream at a lower
stagnation temperature with the main flow does not result in the
mixture stagnation temperature going below the inlet value. This
is because the stagnation temperature of the flow approaching the
injection location is higher due to the combustion and heat release
in the separation zone.
Both the chemistry models show a steep increase in the stag-
nation temperature up to x 400 mm, beyond which the increaseis gradual until the combustor exit. This indicates that as the ki-
netics slows down in this part of the combustor, the heat release
diminishes. As discussed earlier, the residual heat release due to
the recombination reactions is less than that of the other two in-
jection schemes, which can be seen in the marginal increase inthe stagnation temperature with the multi step chemistry model.
Although the overall equivalence ratio is the same between the
staged and the wall injection schemes, the amount of heat re-
leased in the latter scheme is much lower. This is evident from
the magnitude of the dimensionless stagnation temperature at the
exit between Figs. 12 and 17. This will have a significant effect on
the overall thrust generation.
Axial variation of the dimensionless static pressure rise along
the entire length of the combustor and a close-up view are shown
in Fig. 18. The steep static pressure rise just downstream of x 100 mm is due to combustion in the separated region. In this re-
gion, the multi step chemistry model predicts a higher peak valuethan the single step chemistry model due to higher heat release.
The static pressure rise near the injection location (x= 296 mm) isseen to be higher with single step chemistry, whereas with multi
step chemistry, two pressure peaks of almost equal magnitude are
predicted in close proximity (one at x 270 mm and another atx 296 mm). This is clearly seen in Fig. 18 (right). This is in con-trast to the staged injection scheme, where the pressure peak pre-
dicted by both the chemistry models are of the same magnitude.
Moreover, the predictions with the multi step chemistry model in
the wall injection scheme indicate the heat release to be more
wide spread. The magnitudes of the pressure peaks in the wall
injection scheme are seen to be lower than those of the staged in-
jection scheme. This can be attributed to the lower heat release
in this injection scheme as discussed earlier. The marginal rise inthe static pressure downstream of the peak correlates well with
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Fig. 19. Variation of the thrust percentage along the combustor (wall injection
scheme).
the location of the OH radical peak in Fig. 16. Beyond x
=400 mm,
the static pressure decreases continuously and the predictions bythe two chemistry models are almost the same. This further sub-
stantiates the fact that the amount of residual heat release is only
marginal in this injection scheme.
Axial variation of the thrust percentage along the combustor is
shown in Fig. 19. In the wall injection scheme, the thrust percent-
age profile between the chemistry models is very similar, except in
the strut region. The overall thrust generated in this scheme with
the multi step and the single step chemistry models is 115.79 N
and 113.77 N respectively. In contrast to the other two injection
schemes, where the thrust predicted by the chemistry models are
considerably different, in this injection scheme, they are almost the
same as seen in Fig. 19. This can be attributed to the shorter resi-
dence time of the injected fuel and to the lower static temperature
of the approaching flow. Although, the overall equivalence ratio isthe same in the staged and the wall injection schemes, the thrust
generated is smaller in the latter scheme by about 25%. This in
turn clearly underscores the importance of staged combustion.
3.4. Overall performance metrics
In this section, two metrics for assessing the overall perfor-
mance of the combustor, namely, the mixing efficiency and the
combustion efficiency, are discussed. The desired objectives in a
supersonic combustor are proper mixing of the fuel and air, com-
plete combustion of the fuel and minimal loss of stagnation pres-
sure. The combustion efficiency indicates the completeness of the
combustion and regions of heat release. In addition, by correlat-
ing it with the mixing efficiency, inferences on whether the heat
release is mixing- or kinetically-controlled can be drawn.
3.4.1. Mixing efficiency
Following Baurle et al. [12] the mixing efficiency at an x= con-stant section can be defined as
m =
xRu d Ax mfuel,in
.
The denominator represents the total amount of fuel injected up-
stream of this section. The quantity R in the numerator is givenas [12]
R =H2 , H2 s,s
1H21s , H2 > s.
Fig. 20. Variation of mixing efficiency for different injection schemes [6].
The mixing efficiency at an axial location of the combustor is thus
an indication of how much of the fuel is likely to burn under sto-
ichiometric conditions. The variation of the mixing efficiency for
the three injection schemes (based on the non-reacting flow calcu-
lations) is given in Fig. 20. In all the three cases, a steep increase
in the mixing efficiency can be seen downstream of the injector, as
the fuel mixes rapidly with the main flow. In the case of the strut
injection scheme, the mixing efficiency levels off after x= 150 mmand attains a maximum value of almost 100%. Of the three injec-
tion schemes, the strut injection scheme shows the highest mixing
efficiency due to the lowest equivalence ratio (= 0.4) and also dueto the combustor length (almost 700 mm) available for mixing.
The staged injection scheme shows an identical trend for mixing
efficiency until x 250 mm. The mixing efficiency then decreasessharply before the wall injection ports due to extra fuel being
available in the separated flow region ahead of the wall injec-
tion ports. The mixing efficiency increases again and levels off to a
value of 85% around x= 500 mm. The wall injection scheme showsthe poorest performance of the three injection schemes with a
maximum value of 60% for the mixing efficiency, which means that
only 60% of the fuel is likely to burn under stoichiometric con-
dition. Although the equivalence ratio is the same for the staged
and wall injection schemes, mixing is poor in the latter primarily
due to two reasons: (a) the entire amount of fuel corresponding
to an equivalence ratio of unity is injected from the wall injec-
tion ports and (b) the combustor length available for mixing is
shorter.
3.4.2. Combustion efficiency
Combustion efficiency is one of the key performance metrics
used to evaluate a combustor. In this section, for each injection
scheme, the combustion efficiency from the multi step and the
single step chemistry calculations [6] are compared. Combustion
efficiency is calculated based on the amount of fuel that is con-
sumed completely. However, in the multi step chemistry model,
since H2 can be formed in the intermediate reactions, the amount
of fuel consumed has to be calculated from the amount of H2O
formed. It must also be kept in mind that some of amount of H 2O
is already present in the incoming vitiated air. Thus, on a given
x= constant plane, the combustion efficiency is given as [12]
c =
19H2Ou d A
xinlet
x mfuel,in.
The multiplicative constant in the numerator accounts for the fact
that 1 kmol (18 kg) of H2O is produced from the combustion of
1 kmol (2 kg) of fuel.
The variation of combustion efficiency for all the three injectionschemes is shown in Fig. 21. Since the multi step chemistry model
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Fig. 21. Variation of combustion efficiency for different injection schemes with sin-
gle step [6] and multi step chemistry models.
predicts higher heat release than the single step model, combus-
tion efficiency is also predicted to be higher by the former. The
strut injection scheme shows the highest combustion efficiency
(around 85%) at the combustor exit due to lower equivalence ratio
and longer residence time, which allows the fuel to burn com-
pletely. In the staged injection scheme, the combustion efficiency
in the strut region is the same as in the strut injection scheme. The
slight increase in combustion efficiency ahead of the wall injec-
tion location (x= 296 mm) is due to combustion in the separationzone. The sudden drop in the combustion efficiency following this
is due to the availability of the extra fuel injected from the wall
injection ports. The multi step chemistry model predicts the com-
bustion efficiency at the combustor exit to be 85% which is about
12% more than the value predicted by the single step chemistry
model.
The combustion efficiency is the lowest in the wall injection
scheme. Though the overall equivalence ratio is the same in the
staged and the wall injection schemes, the combustion efficiency is
lower in the latter scheme, primarily due to the shorter residence
time and also due to the injection of the entire amount of fuel
corresponding to an equivalence ratio of 1 from the wall injection
ports. In the staged injection scheme, the amount of fuel injected
from the wall injection ports corresponds to an equivalence ratio
of 0.6. The shorter residence time is itself due to a combination of
two facts: (a) the remaining combustor length available for com-
bustion is shorter and (b) the Mach number of the flow and hence
the axial velocity in the core section of the combustor is higher.
The second fact is due to the absence of any heat addition in the
strut region and the attendant deceleration of the flow. Notwith-
standing this, a considerable amount of heat release still takesplace in the divergent part of the combustor downstream of the
wall injection location.
In general, for all the injection schemes and for both chem-
istry models, the combustion efficiency (and the heat release)
increases sharply immediately downstream of the fuel injection
location followed by a gradual increase. In the region of sharp in-
crease (0 x 100 mm for the first two injection schemes and
300 x 375 mm for the wall injection scheme), the combus-
tion efficiency curves obtained using the single step and multi
step chemistry models lie on top of each other, clearly indicat-
ing that chemistry does not play a role here. It follows then that
the heat release in this region is mixing controlled. This is fur-
ther corroborated by the corresponding mixing efficiency curves
in Fig. 20, which show a rapid increase in the mixing in thisregion. Beyond this region, the combustion efficiency curves cal-
Fig. 22. Comparison of dimensionless wall static pressure for strut injection scheme
with experimental data [9].
culated using the different chemistry models deviate from each
other, showing that the heat release is now kinetically controlled.
The mixing efficiency curves in Fig. 20 show that the mixing effi-
ciency has levelled off in this region suggesting that mixing does
not play a role any longer, corroborating the inference drawn from
the combustion efficiency curves. Within this kinetically controlled
region itself, it can be seen from Fig. 21 that there is a consider-
able amount of heat release, in the region 100 x 300 mm for
the strut injection scheme, x > 500 mm for the staged injection
scheme and x > 375 mm for the wall injection scheme. The de-
crease in the slope of the combustion efficiency curves in Fig. 21 in
the kinetically controlled region indicates that the amount of heat
released diminishes with increasing distance along the combustor,as discussed earlier. The combustion efficiency levels off beyond
x = 300 mm for the strut injection scheme and x = 500 mm forthe staged injection scheme (single step chemistry model), show-
ing that the heat released in this part of the combustor is almost
zero. This, in turn, indicates that reactions have ceased and the
species mass fractions are frozen.
All the above results clearly highlight the inadequacy of the
global reaction approximation in the combustion efficiency calcu-
lations. Furthermore, though the combustion efficiency is not the
maximum in the staged injection scheme, the augmentation of
thrust that is possible highlights the importance of staged combus-
tion. The strut injection scheme has higher combustion efficiency
but the thrust that can be generated is limited, since excessive heat
release in the strut region can result in an inlet interaction. On theother hand, the wall injection scheme can produce higher thrust,
but does so at a lower combustion efficiency. The staged injection
scheme is a good alternative to strut or wall injection alone. Thus,
it is clear that a better trade off between thrust augmentation and
combustion efficiency can be achieved through staged combustion.
3.5. Comparison with experimental data
In this section, numerically predicted dimensionless static pres-
sure on the combustor top wall is compared with the experimental
data reported by Tomioka et al. [9]. The influence of the chemistry
model is demonstrated by comparing the predictions of the single
step [6] and the multi step chemistry models with the experimen-
tal data for all the injection schemes.
It is clear from Fig. 22 that the predictions of both the singlestep and the multi step chemistry model are good (within 5% of
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Fig. 23. Comparison of dimensionless wall static pressure for staged injection
scheme with experimental data [9].
the experimental data) upstream of the strut shoulder (x < 0 mm),
where there are no reactions and in the region x > 125 mm. The
largest difference in the predictions between the chemistry mod-
els is seen in the heat release region in the proximity of the strut,
i.e., 0 < x < 125 mm. Both the models predict the location of the
first peak well (in between two measurement locations) but the
peak values are likely over-predicted by both the chemistry mod-
els. This is due to the over-prediction of the mixing and in turn
the heat release by the SpalartAllmaras model. However, the heat
release and hence the pressure rise spans over a longer distance
with the multi step chemistry model, owing to the availability of
more reaction pathways as discussed in earlier sections. The sec-
ond peak in the pressure profile is predicted better by the singlestep chemistry model.
The variation of the static pressure along the combustor top
wall for the staged injection scheme is shown in Fig. 23. In this
scheme also, the static pressure peak in the strut region is pre-
dicted well by both the chemistry models, and the peak values
predicted by both the chemistry models are almost the same. Fur-
ther, in the region 239 < x < 225 mm the pressure profiles arevery similar to those of the strut injection scheme. The static pres-
sure rise ahead of the wall injection location (x = 296 mm) isdue to the combustion in the separated region. Here, the multi
step chemistry model predicts a higher peak value than the sin-
gle step chemistry model due to the higher heat release predicted
by the former model. The static pressure rise downstream of the
wall injection location is predicted to be higher with the multi
step chemistry model. However, in this scheme also, the peak val-
ues are over-predicted by both the chemistry models. The modest
peak further downstream is better predicted by multi step chem-
istry. Beyond x = 350 mm, the static pressure predictions by boththe chemistry models are within 5% of the experimental data.
The variation of static pressure along the combustor top wall
for the wall injection scheme is shown in Fig. 24. Trends predicted
from both the models are within 5% of the experimental data for
x < 50 mm. Beyond x = 140 mm and almost up to the wall in-jection location, there is flow separation on the top and side wall
of the combustor. This is the region where the predictions by the
chemistry models exhibit the maximum difference between each
other and also maximum departure from the experimental val-
ues. In the separated region, the multi step predictions are higher
than the single step predictions for the same reason as mentionedearlier. One reason for the disagreement in this region could be
Fig. 24. Comparison of dimensionless wall static pressure for wall injection scheme
with experimental data [9].
the unsteadiness of the separated flow. Another reason could be
the inadequacy of the SpalartAllmaras model to accurately pre-
dict massively separated flows. Numerical predictions show heat
release to be taking place from the wall injection location to about
x = 350 mm, and both the chemistry models predict almost thesame value for the pressure peak. However, both the chemistry
models over-predict the static pressure rise near the wall injec-
tion location. It should also be noted that the spacing between the
pressure taps in the experiment is such that the predicted pressure
peak occurs in between two pressure taps.
4. Conclusions
Results from the numerical simulations of the supersonic com-
bustion of H2 in a model combustor with three different fuel injec-
tion schemes were presented. The main objective of the study was
to investigate the effect of the chemistry model on the predictions.
Accordingly, a detailed chemistry model with 37 reactions and 9
species was used and the results from these calculations were
compared with those obtained using single step chemistry [6]. It
was shown that the consumption of fuel within the combustor is
higher when using the multi step chemistry model. Consequently
the predicted value of the mass fractions of major species, like H 2O
was consistently higher with the multi step chemistry model in all
the injection schemes. Profiles of minor species such as OH, H, O,
H2O2 and HO2 were used to infer the ignition distance, the induc-
tion distance and the heat release distance. Intricate details of the
heat release were brought out through profiles of stagnation tem-
perature. Correlations between the intermediate species profiles
and stagnation temperature profiles were identified, which helped
in delineating the heat release regions inside the combustor. Fur-
thermore, plots of static pressure rise due to combustion as well as
the thrust profile were used to establish the connection between
the heat release and thrust generation, which is of paramount im-
portance to the designer. It is worth noting that such details have
hitherto not been reported in the literature.
Numerically predicted variations of the mixing efficiency and
combustion efficiency along the combustor length for the differ-
ent injection schemes were used to obtain insights on the nature
of the heat release mechanism, i.e., whether it is mixing controlled
or kinetically controlled. The multi step chemistry model, showed
higher heat release in the mixing controlled and in the kineticallycontrolled regions than the single step chemistry model, though
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there was not much difference in the exit value of stagnation tem-
perature between the two. Also, the residual heat release through
the recombination reactions was predicted to be higher with the
multi step chemistry model. The average static pressure rise plot
presented here revealed the flow and combustion phenomena in-
side the combustor in more detail than what can be inferred from
the customary wall static pressure measurements alone. The multi
step chemistry model predicted a more wide spread heat releaseand pressure rise compared to the single step model predictions.
Most importantly, the higher heat release with the multi step
chemistry model led to a commensurate augmentation in thrust
and higher combustion efficiency in all the injection schemes. Also,
the staged injection scheme, which showed a better trade off be-
tween thrust augmentation and combustion efficiency, and was
identified as a better alternative to the strut and the wall injec-
tion schemes.
The wall static pressure is the most commonly measured quan-
tity in supersonic combustion experiments. The predictions of the
wall static pressure by the multi step and the single step chem-
istry models were almost the same except for the peak values.
In addition, the overall thrust, which is an important performance
parameter for the designer was also predicted well by the singlestep chemistry model in comparison with the multi step chem-
istry model. Thus, the single step chemistry model is capable of
predicting the overall performance parameters with considerably
less computational cost. However, the prediction of the myriad de-
tails of the heat release/ignition delay, which offer insights into the
combustion process, demands a comprehensive chemistry model
as demonstrated in this work.
Acknowledgments
The authors would like to thank Dr. Panneerselvam and Dr.
Ramanujachari of Defence Research and Development Lab, Hyder-
abad, India for providing financial support for this work through a
grant. The authors gratefully acknowledge the insightful comments
and suggestions given by the reviewers.
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