jeong-yeol choi, fuhua ma and vigor yang- dynamics combustion characteristics in scramjet combustors...
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41st AIAA/ASME/SAE/ASEE Joint Propulsion
Conference & Exhibit 10 - 13 July 2005, Tucson, Arizona
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American Institute of Aeronautics and Astronautics
Dynamics Combustion Characteristics in ScramjetCombustors with Transverse Fuel Injection
Jeong-Yeol Choi*
Pusan National University, Pusan 609-735, Korea
and
Fuhua Ma, Vigor Yang
The Pennsylvania State University, University Park, PA 16802, U.S.A.
*Corresponding Author, Associate Professor, Department of Aerospace Engineering, [email protected]
Post-doctoral Research Fellow, Department of Mechanical Engineering, [email protected] Distinguished Professor, Department of Mechanical Engineering, [email protected]
Abstract
A comprehensive DES quality numerical analysis hasbeen carried out for reacting flows in constant-area and
divergent scramjet combustor configurations with and
without a cavity. Transverse injection of hydrogen is
considered over a broad range of injection pressure.
The corresponding equivalence ratio of the overall
fuel/air mixture ranges from 0.167 to 0.50. The work
features detailed resolution of the flow and flame
dynamics in the combustor, which was not typically
available in most of the previous studies. In particular,
the oscillatory flow characteristics are captured at a
scale sufficient to identify the underlying physical
mechanisms. Much of the flow unsteadiness is related
not only to the cavity, but also to the intrinsicunsteadiness in the flowfield. The interactions
between the unsteady flow and flame evolution may
cause a large excursion of flow oscillation. The roles
of the cavity, injection pressure, and heat release in
determining the flow dynamics are examined
systematically.
Introduction
The success of future high-speed air transportation will
be strongly dependent on the development of
hypersonic air-breathing propulsion engines.Although there exist many fundamental issues,
combustor represents one of the core technologies that
dictate the development of hypersonic propulsion
systems. At a hypersonic flight speed, the flow
entering the combustor should be maintained
supersonic to avoid the excessive heating and
dissociation of air. The residence time of the air in a
hypersonic engine is on the order of 1 ms for typical
flight conditions. The fuel must be injected, mixed
with air, and burned completely within such a short
time span.A number of studies have been carried out
worldwide and various concepts have been suggested
for scramjet combustor configurations to overcome the
limitations given by the short flow residence time.
Among the various injection schemes, transverse fuel
injection into a channel type of combustor appears to
be the simplest and has been used in several engine
programs, such as the Hyshot scramjet engine, an
international program leaded by the University of
Queensland [1]. For the enhancement of fuel/air
mixing and flame-holding, a cavity is often employed.
For example, the CIAM of Russia introduced cavities
into its engines [2] and U.S. Air Force also employedcavities in the supersonic combustion experiments [3].
From the aspect of fluid dynamics, transverse
injection of fluid into a supersonic cross flow and flow
unsteadiness associated with a cavity are of significant
interest topics due to their broad applications in many
engineering devices. Extensive efforts have been
applied to study these phenomena, and much of the
results have great relevance relevant to scramjet
combustors. Papamoschou and Hubbard[4] observed
the fluid dynamic instability of injector flow. Ben-
Yakar et al.[5] also observed essentially the same
unstable injection jet in their supersonic combustion
experiment and the showed that supersonic combustionis overlaid with the large eddy motions of the unstable
injection jet. The unsteady nature of transverse injector
flow has been first studied numerically by von Lavante
et al.[6] but its physical nature has been discussed less
importantly. A comprehensive study directly applied to
combustor dynamics, however, is rarely found. The
obstacles lie in the difficulties in conducting high-
fidelity experiments and numerical simulations to
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characterize the flow transients at time and length
scales sufficient to resolve the underlying mechanisms.
Choi et al.[7] has studies a two-dimensional
scramjet combustor configuration with transverse fuelinjection and a cavity flame holder with highly refined
computations. They found that RichtmyerMeshkov
shear layer instability or cavity-driven instability, those
are unavoidable in supersonic combustor,[8,9] triggers
the injector flow instability, and the disturbed injector
flow greatly enhanced the fuel/air mixing and
combustion. However, stabilized combustion has not
been observed and overall combustion characteristics
have not been justified. It is because of the constant-
area combustor configuration and ambiguously defined
combustor inlet. Thus, the present study attempts to
achieve improved understanding of the unsteady flow
and flame dynamics in a realistic scramjet combustorconfiguration employing a modified combustor
configuration and Reynolds averaging of the flow field.
Theoretical Formulation and Numerical Treatment
Governing Equations
The flowfield is assumed to be two-dimensional for
computational efficiency, and can be described with the
conservation equations for a multi-component
chemically reactive system. The coupled form of the
species conservation, fluid dynamics, and turbulent
transport equations can be summarized in aconservative vector form as follows.
WGFGFQ vv +
+
=
+
+
yxyxt (1)
where the conservative variable vector, Q, convective
flux vectors, F and G, diffusion flux vectors, Fv and Gv,
and reaction source term W are defined in Eq. (2).
Details of the governing equations and thermo-physical
properties are described in Ref. 10.
2
2
+
=
+
=
=
v
kv
Hv
pv
uv
v
u
ku
Hu
uv
pu
u
k
e
v
u
iii
GFQ (2a)
=
=
=
s
s
w
y
yk
u
x
xk
u
k
i
k
y
yy
xy
d
ii
k
x
xy
xx
d
ii
0
0
0
WGF vv(2b)
where, i=1~N.
Numerical Methods
The governing equations were treated numericallyusing a finite volume approach. The convective fluxes
were formulated using Roe's FDS method derived for
multi-species reactive flows along with the MUSCL
approach utilizing a differentiable limiter function.
The spatial discretization strategy satisfies the TVD
conditions and features a high-resolution shock
capturing capability. The discretized equations were
temporally integrated using a second-order accurate
fully implicit method. A Newton sub-iteration method
was also used to preserve the time accuracy and
solution stability. Detailed descriptions of the
governing equations and numerical formulation are
documented in a previous work [11].
Chemistry Model and Turbulence Closure
The present analysis employs the GRI-Mech 3.0
chemical kinetics mechanism for hydrogen-air
combustion [12]. The mechanism consists of eight
reactive species (H, H2, O, O2, H2O, OH, H2O2 and
HO2) and twenty-five reaction steps. Nitrogen is
assumed as an inert gas because its oxidation process
only has a minor effect on the flame evolution in a
combustor. Turbulence closure is achieved by means
of Mentor's SST (Shear Stress Transport) model
derived from the k- two-equation formulation [13].
This model is the blending of the standard k- modelthat is suitable for a shear layer problem and the
Wilcox k- model that is suitable for wall turbulence
effect [14]. Baridna et al.[15] reported that the SST
model offers good prediction for mixing layers and jet
flows, and is less sensitive to initial values in numerical
simulations.
Code Verification
The overall approach has been validated against a
number of steady and unsteady flow problems
including shock-induced combustion oscillation. Good
agreement has been obtained with experimental data
[11,16,17]. In addition, numerical study was carried
out to validate the present turbulence modeling and to
justify the grid resolution for simulating transverse gas
injection across the supersonic flow over a flat plate.
The analysis simulates the experiment described in Ref.
[18] with a static pressure ratio of 10.29, for which
several numerical studies have been previously carried
out [19, 20]. In this case, choked nitrogen flow is
vertically injected through a 1-mm-wide slot locating
33 cm behind the leading edge into a supersonic
airflow with a Mach number of 3.75. The present
study used the same computational domain as that of
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Chenault and Beran [20]. Computations were carried
out for various combinations of grid systems having 71
to 351 points near the injection port in the streamwise
direction and 41 to 251 points clustered near the wall inthe transverse direction. Furthermore, a parametric
study was performed on the effects of numerical and
turbulence modeling parameters. The numerical
parameters were optimized to maintain numerical
stability and solution convergence. The turbulence
parameters of the SST model [13] have negligible
effects on the solutions for the grid systems employed
herein.
x/L
pw
/p
0.8 0.9 1.0 1.1 1.20.0
1.0
2.0
3.0
4.0Aso et. al., Experiment(1991)
Rizzetta (1992)
Chenault & Beran (1998)
141x101
211x151
281x201351x251
Fig. 1 Wall pressure distribution of the two-
dimensional transverse injection across the
supersonic flow over a flat plate.
Figure 1 compares the wall-pressure distributions
between the numerical and experimental results. A
coarse grid results in a longer separation distance ahead
of the injection port and cannot predict the pressure
picks near the injection port, although the solution
seems to better match the experimental result. The
281201 and 351251 grids have nearly identicalresults within 5% relative error range over the entire
wall. In comparison with previous results, the present
turbulence model predicts the same separation distance
and peak pressure as the k- model while maintaining
smooth pressure increase in the front separation region.Also, pressure variation behind the injector is more
closely predicted by the SST model. The 281201grid was then applied to the scramjet combustor
simulation. The minimum vertical spacing is y+ 5,and 21 grid points are employed in the injector port.
Issues on Turbulence and Chemistry
Present computational formulation constitutes an
unsteady Reynolds averaged Navier-Stokes analysis
(URANS), but showed highly refined combustion
characteristics overlaid with large eddy motions of
unstable injector flow, using a massive computational
grid for two-dimension.[7] These kinds of results were
comparable to the quality of DES (Detached Eddy
simulation), a seamless hybrid approach of LES andRANS, easily attainable by present SST turbulence
model by using local grid size instead of wall distance.
Another important issue is the closure problems for
the interaction of turbulence and chemistry in
supersonic conditions. Recently, there were many
attempts to address this issue using LES methods, PDF
approaches, and other combustion models extended
from subsonic combustion conditions. Although
much useful advances were achieved, the improvement
was insignificant in comparison with the results
obtained from laminar chemistry and experimental data,
as discussed by Mbus et al [21]. A careful review of
existing results, such as Norris and Edwards [22]suggests that the solution accuracy seems to be more
dependent on grid resolution than the modeling of
turbulence-chemistry interaction. In view of the lack of
reliable models for turbulence-chemistry interactions,
especially for supersonic flows, the effect of turbulence
on chemical reaction rate is ignored in the present work.
Highly refined turbulent flows were post-processed
by two kinds of time averaging techniques, Reynolds
average and discrete time average. Reynolds average is
a continuous time average of the flow variables at a
given location and its visualization result is equivalent
to the image taken with long-time exposure. The
discrete time average is an average of severalintermediate results within a given time frame, and its
image is equivalent to the averaged image of motion
pictures. Presently the continuous average was taken
for final 20,000 iterations of computation equivalent to
final 1.2 ms physical time period, and discrete average
was taken from 20 intermediate results among the same
time period.
Configuration of Scramjet Combustor
Combustor Configuration
The supersonic combustor considered in this study
is shown in Fig. 1. The channel type combustor of 10
cm height and 131 cm length is composed of transverse
fuel injection and a cavity. This combustor
configuration is quite similar to the Hyshot test model,
except for the cavity, in which a swallowing slot is
employed to remove the boundary layer from the inlet
and the combustor starts with a sharp nose [1]. A cavity
of 20 cm length and 5cm depth, having an aspect ratio,
L/D of 4.0, is employed at 20 cm downstream of the
injector. In the present computation, intake region was
also considered for the physical assessment of the
thermal choking condition,
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Operating Conditions
The incoming air flow to the combustor is set to
Mach number 3 at 600 K and 1.0 MPa. This combustor
inlet condition roughly corresponds to a flight Mach
number 5-6 at an altitude of 20 km, although the exact
condition depends on the inlet configuration. Gaseoushydrogen is injected vertically through a slot of 0.1 cm
width to the combustor through a choked nozzle. The
fuel temperature is set to 151 K. The injector exit
pressures are 0.5, 0.75, 1.0 and 1.5 Mpa, and the
overall equivalence ratios are from 0.167 to 0.5.
Combustor Conditions
A total of 800160 grids are used for the main-combustor flow passage, 5050 for inlet cowl and159161 grids for the cavity. The grids are clusteredaround the injector and the solid surfaces and the
injector. 54 grid points are included in the injector slot
and the minimum grid size near the wall is 70 m. All
the solid surfaces are assumed to be no-slip and
adiabatic, except for the upper boundary. For
convenience and reduction of the number of grid points
required to resolve the boundary layer, the upper
boundary is assumed to be a slip wall, which is
equivalent to the flow symmetric condition in the
present configuration. Extrapolation is used for the exit
boundary. Time step is set to 6 ns according to the
minimum grid size and the CFL number of 2.0. Four
sub-iterations are used at each time step. Fig. 2 is a
magnified plot of the computational grid around the
injector, cavity and the fore part of the combustor.
Summary of Results
Numerical simulations were carried out for 32 cases
of different configurations and fuel injection pressure
ratios: 1) divergent nozzle-type combustor and constant
area combustor, 2) with and without cavity, 3) reactingand non-reacting flows and 4) fuel injection pressure
ratios of 5.0, 7.5, 10.0 and 15.0. All the cases were run
for 12 ms starting from the initial condition, which is
longer than the typical test time of the ground based
experiments. The plots of the instantaneous flowfields
shown in the followings were taken at 12 ms, and
averaged images were taken from next 1.2 ms.
Figure 4 to 7 shows the instantaneous and averaged
results of reacting flows for different configurations
with dependency on fuel injection pressure. The images
are overlaid temperature and pressure contours to
account for the combustion and shock structures. Black
curve is the sonic line to show the flow choking. Fig. 8is the pressure histories of each case at reference
pressure probing point at x=59 cm along the bottom
wall, and Fig. 9 is its frequency spectrum obtained by
FFT (fast Fourier transform) analysis. Only 4 to 12 ms
time period was considered in FFT analysis to exculde
the transient effects at initial phase. In the following
only the overall characteristics will be discussed in this
paper since the detailed feature of unsteady combustion
was discussed in the previous paper.
In Fig. 4, the computational results for divergent
nozzle configuration without cavity, the flow is nearly
undisturbed and close to steady state. It is though that
the present grid resolution is not enough to capture theflow instability and eddy motions for this flow
conditions. It is also considered that RANS may not
sufficient to account for the supersonic fuel-air mixing.
The eddy motions are captured for large injection
pressure of 10.0 and 15.0. Averaged results for these
cases are quite different to that of undisturbed low
injection pressure cases by showing greatly enhanced
fuel-air mixing and combustion.
The averaged field shows that most of the
combustor is maintained at supersonic condition, and
there is a significant delay in active combustion. The
active combustion begins roughly at 80 cm from cowl
Fig. 2 Scramjet combustor configuration
H2 10cm14cm5cm20cm
20cm131cm
no-slip adiabatic
sli wall
supersonic exit
x = 59cm, reference pressure probing point
Air
Fig. 2 Magnified plot of computational grid around
the injector and the fore part of combustor.
H2
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(a) Instantaneous Field
(b) Averaged Field of Discrete Frames
(c) Continuously Averaged Field
Fig. 4 Nozzle configuration without cavity
(a) Instantaneous Field
(b) Averaged Field of Discrete Frames
(c) Continuously Averaged Field
Fig. 5 Nozzle configuration with cavity
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(a) Instantaneous Field
(b) Averaged Field of Discrete Frames
(c) Continuously Averaged Field
Fig. 6 Channel configuration without cavity
(a) Instantaneous Field
(b) Averaged Field of Discrete Frames
(c) Continuously Averaged Field
Fig. 7 Channel configuration with cavity
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Fi . 8 Bottom wall ressure histories at x=59cm
Fig. 9 Frequency spectrum of bottom wall pressure at x=59cm
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lip for injection pressure ratio of 10.0 and 50 cm for
injection pressure ratio of 15.0. Both cases showed the
unsteady but stabilized combustion. However, pressure
build-up for the case of 10.0 was insignificant butpressure at reference probing point was maintained at
about 0.3MPa for the case of 15.0. It is considered
combustion efficiency would be low for these cases,
especially for the case of 10.0.
In Fig. 5, flow is disturbed for all injection pressure
ratios due to the presence of cavity, and pressure
histories in Fig. 8 also show higher levels than the
cases of same flow conditions without cavity. Thus
combustion is considered to be enhanced greatly.
Especially at pressure ratio 15.0, the active combustion
region is anchored over the cavity where flow is
choked locally.
Fig. 6 and 7 show the results of the constant areachannel type combustors with and without cavity.
Except for the low injection pressure ratio case of 5.0,
where unsteady but stabilized combustion is observed,
pressure is continuously build-up due to the heat
addition in constant area combustor. Although there is
a certain amount of time delay, the cases of injection
pressure ratio of 7.5 also showed the pressure build-up.
Therefore, most of the cases go eventually to thermal
choking condition, though there are time differences.
For the cases of injection pressure of 10.0, detached
bow shocks are shown ahead of the cowl lip, and the
bow shock ran against the inflow boundary.
The role of cavity, enhancing the combustion, isalso observed in these results. For low injection
pressure conditions, where combustion is stabilized, the
pressure level is higher for the case with cavity.
However, the cavity makes little differences for the
higher injection pressure condition except the time
difference in thermal choking.
To account for the turbulence frequencies that
dominate the unsteady combustion phenomena, FFT
analysis is carried out and plotted in Fig. 9. For the
cases of divergent nozzle type combustor, two
dominant frequencies are observed at around 2 kHz and
10 kHz for the cases without cavity, and one more
dominant frequency at 5 kHz for the cases with cavity.
The frequency of 5 kHz is considered as the second
mode of cavity oscillation, as predicted by Rossiters
semi empirical formula in the previous works. For the
cases of constant area combustor, very low frequencies
are dominant. Major oscillation frequencies are spread
over 2 to 10 kHz bad, but they are mixed-up and are
not easily identified, due to its transient nature of
continuous pressure build-up.
Conclusion
The reacting flow dynamics in a scramjet combustor
was studied by means of a comprehensive numerical
analysis. The present results show a wide range of
phenomena resulting from the combustor area effects,
the interactions among the injector flows, shock waves,shear layers, and oscillating cavity flows. The overall
results were also discussed by means of time averaging
the unsteady flow fields. Further analyses are expected
from these results to clarify and quantify the overall
combustion characteristics.
Acknowledgements
For the present study, the first author was
sponsored by Agency for Defense Development and
National Research Laboratory program of Korea
Science and Engineering Foundation. The supports areacknowledged greatly.
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