Investigation of the Effect of Chemistry Models on the Numerical Predictions of the Supersonic Combustion of Hydrogen

8/8/2019 Investigation of the Effect of Chemistry Models on the Numerical Predictions of the Supersonic Combustion of Hydr

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Combustion and Flame 156 (2009) 826841

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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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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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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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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


7/16


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.


8/16


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


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


9/16


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-


10/16


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.



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 injection 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.


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


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


11/16


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


12/16


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.



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


13/16


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.


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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Documents

Investigation of the Effect of Chemistry Models on the Numerical Predictions of the Supersonic Combustion of Hydrogen