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47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit
31 July - 03 August 2011, San Diego, California
AIAA 2011-5831
Numerical Analysis of a Model Scramjet Engine with Two
Intake Side Walls and a Cavity Flame-Holder
Hyo-Won Yeom1, Bong-Gyun Seo2, and Hong-Gye Sung3
Korea Aerospace University, Goyang Gyeonggi-do, South Korea, 412-791
A detailed 3D numerical simulation of the flow and H2-air mixing characteristics in a
model scramjet engine with two intake-sidewalls and a cavity flame-holder was conducted.
Turbulence closure was achieved by a model combining the low-Reynolds-number k-e twoequation model and Sarkar and Wilcox’s compressible turbulent correction model. The
governing equations were solved numerically by means of a finite-volume, preconditioned
flux-differencing scheme. Cases with and without intake side walls were considered. Intake
side walls were found to strongly affect the inlet flow structure, which became more complex
in the non-uniform flow field on the cross section perpendicular to the engine axis. The
complex and non-uniform flow affected the H2-air mixing pattern inside the combustion
chamber, unlike the pattern of the case without side walls. Mixing efficiency and fuel
propagation rate were evaluated for the two cases with and without side walls. To verify the
accuracy of the simulation, the computed wall pressure was compared with experimental
data.
Nomenclature
a1, a3, a5
Ck
Cε1, Cε2
Cμ
c
E
h
k
Mt
Mt0
H( )
hk
P
Pk
Ru
Tturb
t
u
x
Wk
Yk
a1 , a 2 , a
γ
δij
ec
3
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
model constant of damping factor
model constant of turbulent time scale
model constants of turbulent energy dissipation
model constant of turbulent viscosity
speed of sound
specific total energy
specific enthalpy
turbulent kinetic energy
turbulent Mach number
reference turbulent Mach number
Heaviside step function
specific enthalpy of species k
static pressure
production of kinetic energy
universal gas constant
turbulent time scale
time
velocity
spatial coordinate
molecular weight of species k
mass fraction of species k
model constants for compressible correction
specific heat ratio
Kronecker delta
compressible dissipation
1
Graduate Research Assistant, School of Aerospace and Mechanical Engineering, [email protected]
Graduate Research Assistant, School of Aerospace and Mechanical Engineering, [email protected]
3
Professor, School of Aerospace and Mechanical Engineering, [email protected], AIAA Associate Fellow
1
American Institute of Aeronautics and Astronautics
2
Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
es
m
mt
r
s k ,s e
t ij
= dissipation rate
= molecular viscosity
tk
= Kolmogorov time scale
= turbulent viscosity
= density
= model constants
= viscous stress tensor
Subscripts
i, j, k
= spatial coordinate index
Superscripts
%
˝
= time average
= Favre average
= fluctuation associated with mass-weighted mean
I. Introduction
O
ver the last several decades, a great deal of research on scramjet engines has been performed in several
countries, at a number of institutes and universities. The scramjet engine is currently being considered as an
appropriate option for several hypersonic applications, such as hypersonic missiles and reusable launch vehicles.
Most of the previous research has been experimental, but numerical studies are now on the rise and play an
important role in studying scramjet engine. Numerical efforts are particularly appropriate to scramjet engine studies
due to the complexity of the flow structures in supersonic and hypersonic vehicles, and the inherent limitations of
experimental study for detailed flow investigation. Most numerical studies, however, have treated either the inlet
flow, which is supersonic and/or hypersonic, or the combustor section, which contains fuel injection/mixing and
combustion. The interaction between the two sections has generally only been passively considered. Fuel
injection/mixing, ignition, flame-holding, and flame characteristics in the supersonic flow field have been studied
with a uniform inlet profile or no inlet effect. Many numerical studies have focused on supersonic combustion, fuelair mixing enhancement, injection type, and other specifics. The researchers expanded 2D intake simulation (no
variation in span-wise direction) to the inlet profile of 3D combustor simulation.1-3 This technique unfortunately
ignores the effects of disturbances caused by intake flow conditions, such as size/type of intake sidewall, or nonuniform turbulence boundary thickness.
There have been some studies that consider the effects of intake flow conditions which could affect flow
structure, fuel-air mixing enhancement, ignition, and supersonic combustion inside a combustor. Abdel-Salam4
conducted a numerical investigation of a Mach 2.5 dual-mode scramjet combustor. A three dimensional model of
the combustor configuration was used. The study was concerned with the effect of the inlet boundary layer in the
flow of a dual-mode combustor. They observed that the thickness of the boundary layer has strong effects on the
structure of the flow-field and the combustion characteristics. Kirchhartz5 conducted experiments in the T4 Stalker
Tube to assess the combustion of hydrogen injected directly into the boundary layer of a circular constant-area
supersonic combustion chamber (M > 4). The wall-boundary layer conditions at the fuel-injection station were
varied to study the effects on the ignition and combustion of the injected hydrogen. They reported that a thicker
boundary layer promotes combustion and is more effective for ignition.
Korkegi6 performed comparison of shock-induced flat plate ramp(2-D) and flat plate ramp with sidewall(3-D)
incipient turbulent separation. The skewed shock wave interacts with the sidewall turbulent boundary layer in
rectangular diffusers or inlets and leads to separation and possible flow breakdown. In a rectangular supersonic inlet,
the first oblique shock wave interacts with both the sidewall boundary layers and the corner flows. This can create
large, complex 3-D separation zone. Driscoll7 conducted experiments to quantify these flow separation patterns. For
the scramjet with and without intake side walls, shock-boundary interactions near the intake side walls make the
flow structure at the entrance of the combustor complex. Shock wave-turbulent boundary layer interaction near the
two intake side walls leads to deflection of the flow entering the inlet, and the flow structure becomes more complex.
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The inlet flow may be turned inwards due to the shock wave interaction with the turbulent boundary layer in the
inlet, which can lead to inlet flow separation.8 The production of swirl as the stream ribbons passes through the
interaction between the leading edge shock wave and the shock wave generated by the side wall.9 The effects of
sidewall compression in 3D scramjet inlet have also been studied.10,11 The side wall compression causes the ramp
shock to bend farther upward and if the location of the cowl lip is unchanged, more mass flow spillage will occur.11
The whole process from fuel injection to complete combustion in a scramjet engine is completed in a very short
time because the mean flow in a combustor is so fast in the supersonic regime. Mixing enhancement is one of the
most important factors to realize the scramjet. Flow patterns near the injectors and flame holder determine the
mixing efficiency. Therefore, a three dimensional numerical analysis was conducted to investigate the flow
structures and fuel-air mixing characteristics with and without intake side walls, in terms of flow patterns.
II. Geometry
The scramjet engine used for simulation in this work was designed by Korea Aerospace Research Institute
(KARI). The engine is composed of four major parts; intake ramp, wedge shaped cowl, intake sidewall, and
combustor with cavity flame-holder, as shown in Fig. 1. Four sonic injectors with injection angle of 45 deg. inject
H2 into the main stream. The engine has a width of 100 mm. A full description is presented by Kang et al. 12
a)
b)
c)
Figure 1. Schematic of model Scramjet engine[12].
III. Numerical Approach
The Favre averaged governing equations based on the conservation of mass, momentum, energy, and species
concentration for a compressible flow can be written as
¶r ¶r u% j
+
=0
¶t
¶x j
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(1)
(
)
¶r u%i ¶ ( r u%i u% j + pd ij ) ¶ t ij - r u ¢¢j ui¢¢
+
=
¶t
¶x j
¶x j
(2)
%
¶ u%it ij - r h¢¢ui¢¢ ¶q j
¶r E% ¶ ( r E + p ) u% j
+
=
¶t
¶x j
¶x j
¶x j
(3)
(
)
¶r Y%k ¶ r u% j Y%k
¶
+
=
¶t
¶x j
¶x j
(
)
(
)
æ
ö
¶Y%
çç r Dk k - r u ¢¢j Yk¢¢÷÷ , k = 1,..., N
¶x j
è
ø
(4)
For a multi-component mixture, pressure and specific total internal energy can be written as follows;
E = e+
N
ui ui
p
, e = h2
r
(5)
N
T
h = å Yk hk = å Yk æç Dhof , k + ò C p , k (T ¢ ) dT ¢ ö÷
T
ref
è
ø
k =1
k =1
(6)
N
Yk
k =1 Wk
p = r Ru T å
(7)
The governing equations are solved numerically with finite-volume formulation.
A. Numerical Method
The conservation equations for moderate and high Mach number flows are well coupled, and standard numerical
techniques perform adequately. In regions of low Mach number flows, however, the energy and momentum
equations are practically decoupled, and the system of conservation equations becomes stiff. Over the entire
scramjet flow path, the flow fields are governed by a wide variety of time scales (from subsonic flow in the cavity
flame-holder to hypersonic flow in main stream). Such a wide range of time scales causes an unacceptable
convergence problem. To overcome this problem, a two-step dual time-integration procedure is applied for flows at
all Mach numbers. First, a rescaled pressure term is used in the momentum equation in order to circumvent the
singular behavior of pressure at low Mach numbers. Second, a dual time-stepping integration procedure is
established.
The pseudo-time derivative may be chosen in order to optimize the convergence of the inner iterations by using
an appropriate preconditioning matrix that is tuned to rescale the eigenvalues to render the same order of magnitude,
so as to maximize convergence. To unify the conserved flux variables, a pseudo-time derivative of the form Γ∂Z/∂τ
can be added to the conservation equation.13 Since the pseudo-time derivative term disappears upon convergence, a
certain amount of liberty can be taken in choosing the variable Z. While dual time stepping and LU-SGS are applied
for second-order time integration, a control volume method is used to integrate inviscid fluxes represented by
AUSMPW+ and MUSCL as well as viscous fluxes represented by central difference. A multi-block feature using an
MPI library was used to speed up the calculation.
B. Turbulence Model and Compressibility Correction
The standard k-e model, which was proposed for high Reynolds number flows, is traditionally used with a wall
function and the variable y+ as a damping function. However, the flow situation with separation has singularity on
the wall because of y+. Thus, a low Reynolds number k-e model was developed for near-wall turbulence. Within
certain distances from the wall, all energetic large eddies will reduce to Kolmogorov eddies (i.e. the smallest eddies
in turbulence), and all the important wall parameters such as friction velocity, viscous length scale, and mean strain
rate at the wall can be characterized by the Kolmogorov micro scale.
Yang and Shih proposed a time-scale-based k-e model for the near-wall turbulence related to the Kolmogorov
time scale as its lower bound, so that the equation can be integrated to the wall. The advantages of this model are (a)
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no singularity at the wall, and (b) adaptability to separation flow, since Ry instead of y+ is used as the independent
variable in the damping function. Thus, the model could be applicable to more complex flows.14 The low Reynolds
number models have been designed to maintain the high Re formulation in the log-law region and further tuned to fit
measurements for the viscous and buffer layers. As the Mach number of a turbulent flow increases, the velocity
fields can no longer be assumed to be solenoidal. Turbulence modeling for compressible flow has to account for the
additional correlations involving both the fluctuating thermodynamic quantities and the fluctuating dilatation. The
interaction of a shock wave with a turbulent boundary layer leads to a significant increase in turbulence intensity and
shear stress across the shock15. To take account of the important features of the high-speed flow and shear layer over
the cavity, this study employed the compressible-dissipation and pressure-dilatation correction proposed by
Sarkar.15-18 Wilcox’s model18 is applied for wall-bounded flow. Not only did the Low Reynolds number k-e with
Sarkar’s model adequately predict the impinging point of the jet on the diffuser wall, but the separation point, as
compared with experimental data, also captured the dynamic motion near operational pressure.19,20 The Low
Reynolds number k-e with Wilcox’s model showed better accuracy than Sarkar’s model.21
The turbulent kinetic energy and its dissipation rate are calculated from the turbulence transport equations
written as follows:
¶r k ¶ ( r u% j k )
¶
+
=
¶t
¶x j
¶x j
ææ
m
çç ç m + t
s
k
èè
¶re s ¶ ( r u% j e s )
¶
+
=
¶t
¶x j
¶x j
ö ¶k
÷
ø ¶x j
ææ
m
çç ç m + t
se
èè
ö
÷÷ + Pk - r ( e s + e c ) + p ¢¢d ¢¢
ø
(8)
ö ( Ce 1 Pk - Ce 2 re s )
+L
÷÷ +
Tturb
ø
(9)
ö ¶e s
÷
ø ¶x j
where e c and p ¢¢d ¢¢ represent compressible-dissipation and pressure-dilatation, respectively, and
F ( M t ) = éë M t 2 - M t 0 2 ùû H ( M t - M t 0 )
e c = a1 F ( M t ) e s
p ¢¢d ¢¢ = -a 2 Pk F ( M t ) + a 3 re s F ( M t )
(10)
(11)
(12)
The turbulent Mach number is M t 2 = 2k / c 2 .
The closure coefficients for the compressible corrections are:
a1 = 1.5 , a 2 = 0.4 , a 3 = 0.2 , M t 0 = 0.25
C. Computational Conditions and Computational Domain
The computational code is paralleled with a multi-block feature using an MPI library to speed up the
computation. The scramjet engine was simulated at an altitude of 31 km. The inlet conditions are: 1.040 kPa
pressure, temperature 224 K, and flight Mach number of 7.6. Figure 2 shows the computational domain and
boundary conditions of the engine. The computational domain consists of 11 blocks. The external zone with 5
blocks includes the intake ramp and intake sidewall. The internal zone consists of blocks 6 to 11. The external zone
has intake ramps and intake side walls which are set as wall boundary condition. In the case with no intake side
walls, the wall boundary is replaced with a symmetric boundary. The supersonic boundary was applied for the inlet
and outlet. The wall is assumed to be adiabatic. The sonic injector conditions are: total pressure of 263.8 kPa, total
temperature of 300 K, and overall equivalence ration of 0.11
The computation was performed in two parts -- part 1 (#1 to #6) and part 2 (#6 to #11) -- independently, to save
computational time and memory size. Block 6 was overlapped and used as the inlet boundary zone of part 2 to
preserve the accuracy and the consistency of the part2 calculation. Parts 1 and 2 have 1.2 million and 1.37 million
grid points, respectively. The block 6 consists of 338,100 grid points. Four sonic injectors are located in part 2. A
typical computational step is 10-7 sec. for the unsteady calculation.
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a)
b)
Figure 2. Computational multi-block domain and boundary condition:
a) boundary conditions and b) block arrangement
IV. Results
A. Flow Structure and Verification
Figure 3 shows the pressure distribution along the center line of the bottom wall for two cases: with two side
walls and without two side wall at the intake. In the overlapped zone, the pressure distribution of part 1 agrees well
with that of part 2. The experimental data were obtained for the case with intake side walls. The numerical data and
the experimental data are in fairly good agreement, except far down stream of the combustor. The pressure in the
combustor in the case with intake side
walls oscillates higher than the level of
pressure fluctuations in the case without
intake side walls because shock-wall and
shock-boundary interactions occur more
strongly and the compression of intake air
is much more non-uniform due to the side
walls. At the intake ramp, the pressure
distribution of the two cases is almost
identical because the effects of the intake
side walls at the center of the intake ramp
are weaker than that the effects near the
side walls. Figure 4 shows shock wave
patterns in the center x-z plan of the engine
with the intake side walls; a complex
combination of multiple shocks and
expansion waves originate from the
intake’s contraction and expansion. The
shock starting from cowl tip impinges and Figure 3. Pressure distribution along the center of the bottom
reflects on the bottom surface, impinges wall.
and reflects on the top wall, and impinges
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and reflects again until the compression wave propagates far down stream of the cavity. Figure 5 shows Mach
number distribution in cross section at the intake cowl tip for two cases. In the case of two intake side walls, the core
streams are observed at three locations: center, left, and right in the cross section, and the maximum Mach number is
located near the side walls. The flow is, however, very uniform in the y- direction in the case without intake side
walls. It should be noted that the side walls significantly affect the flow structure at the entrance of the combustor.
a)
b)
Figure 4. Shock wave system of model Scramjet engine with intake side walls.
a) With intake side walls
b) Without intake side walls
Figure 5. Mach number contour in Y-Z plane at the leading edge of cowl.
B. Effect of Intake side walls on flow structure
To demonstrate the effects of intake side
walls, the flow structure near the intake side
walls and at the entrance of the combustor is
shown in Figs. 6 and 7. Shock/boundary-layer
and shock-shock interactions occur at the
intake side walls. The ramp shocks from the
intake ramps claw at the boundary layer of the
intake side walls. The ramp shocks deflect the
flow and change the shape of the boundary
layer. In Fig. 7, only one shock starting from
the first ramp occurs in IP 1 plane, but two
shocks from the first and the second ramps
appear in IP 2 and IP 3 planes at 0.02 m and
0.08m downstream of the leading edge of the
second ramp, respectively. SBI 1 and SBI 2
Figure 6. Intake flow structure with two intake side walls.
are caused by the interaction between ramp
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shock and boundary layer of sidewall. SBI 1 and SBI 2 mean shock-boundary interactions caused by the first ramp
shock and the second ramp shock, respectively. The flow distortion with helical motion from side wall to center may
be intuitively expected from the motion of SBI 1 and SBI 2 as shown in Fig. 7. The flow deflection caused by the
interaction between the shock and the turbulent boundary layer makes the intake flow structure more complex and
the shock-shock interactions affect flow deflection. As shown in Figs. 5, 6, and 7, the inlet with intake side walls has
helical flow induced by the deflected flow at intake side walls. Mach number increases up to about 4.0 near both
side walls because of the helical flow, which develops from side wall to center region as some of the flow along the
side walls moves toward the center of the combustor.
a) IP 1 (at X=0.3 m)
b) IP 2 (at X = 0. 44 m)
c) IP 3 (at X = 0. 49 m)
Figure 7. Mach contour at three Y-Z planes in the intake. a) IP1: 0.3m, b) IP2: 0.02m c) IP3:0.0.8 m
downstream of the leading edge of the second ramp.
a) With intake side walls
b) Without intake side walls
Figure 8. Mach number iso-surface and stream-lines at the entrance of combustor.
Figure 8 represents streamlines at the entrance of the combustor. In the case of no intake side wall, the flow
deflected toward the center of the duct recovers towards the axial direction before the injector location. However, in
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the case with intake side walls, the deflected flow from both side walls recovers after passing the cavity flameholder behind the injectors and penetrates into the center of the combustor.
a) With intake side walls
b) Without intake side walls
Figure 9. Intake shock structure at combustor entrance.
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a) With intake side walls
b) without intake side walls
Figure 10. Shock-boundary interactions on the half cross section, from center to side wall, at
entrance of combustor: white color represents sonic velocity. Shock-boundary interaction is dashed
red lines and sonic line is presented by white line. The each Y-Z planes is shown in Fig. 9.
Figure 9 shows the gradient density inside the combustor for the two cases. The flow patterns in the combustor
with the side walls are much more complicated. Several shocks starting from the inlet cowl corners and the side
walls are deflected toward the center region of the combustor, which corrupts the flow structure as shown the cross
section IP7. Figure 10 shows density gradient in Y-Z planes, through IP4 to IP8 representing upstream of cavity,
enlarged to examine shock-boundary interaction on the walls. The curved cowl shock reflects from the side and the
top walls(IP4 and IP5) and impinges the bottom walls, which produces large separation flow at IP 7 and IP 8. Thus it
may be expected that the side walls will affect the fuel-air mixing structure in the combustor. The details of the
mixing characteristics are discussed in section C.
a) With intake side walls
b) Without intake side walls
Figure 11. Pressure distribution inside combustor.
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Figure 11 shows pressure distribution at the bottom wall of the combustor. Reflected shock-wall (or boundary
layer) interaction leads to pressure increase in the interaction region. In the case without intake side walls, pressure
distribution is a uniform band at the bottom wall. In the case with the intake side walls, the reflected shock impinges
more strongly near the side walls and at the center of the lower wall. The pattern of the flow structure is transformed
by the effect of the intake side walls. In the case without intake side walls, a higher level of pressure fluctuations
along the bottom wall is observed. The quasi-uniform shock structure forces the pressure distribution into a band
shape. In the case with the intake side walls, the deflected flow from the intake side walls disperses the flow
structures and contribute to an increase in a local pressure inside the combustor.
C. Effects of Intake Side Walls with Fuel Injection
There is a general perception that fuel injection, ignition, and combustion are closely associated with boundary
layer conditions on the wall. Although the mean flow inside a supersonic combustor may not be at a high enough
temperature for ignition or combustion, the aerodynamic heating on the wall upstream of the injector is able to
supply enough heat energy for ignition. Some of the heated flow on the wall enters into the cavity and forms
recirculation zones.
Figure 12 shows iso-surfaces of H2 mass fraction near the cavity flame-holder. The fuel cores are quickly
bended downstream after being injected perpendicularly into the cross stream and then gradually mixed with the air.
Figure 13 shows iso-surfaces of H2 mass fraction and stream-lines zoomed at the cavity flame-holder. The rotation
in the case with sidewalls is more active and constrains the fuel’s upper section and then allows the fuel’s bottom
section to expand. The rotation direction in case with no side walls is opposite to that of the side wall case. Figure 14
shows fuel mixing. Fuel mass fraction is represented by iso-surfaces at 0.05 and 0.001. Stream-line with temperature
legend is nearby bottom wall. Some of the hot flow on the wall enters into the cavity and forms a recirculation flow.
The revolving flows split the cavity flow into several zones. Each fuel stream which penetrates the cavity is isolated
from other fuel streams due to the flow deflection at the intake side walls. The direction of the recirculating flow is
represented by arrows. Each pair of the four fuel streams downstream of the cavity flame-holder is merged until,
finally the four streams become two streams, because the streams injected by injectors #1 and #4 are bent by the
deflected flow on the side walls. In the case without side walls, the fuel streams flow side by side without being
merged. The revolving flow in the cavity moves toward the side walls.
Figure 15 shows stream-line and fuel mass fraction in the cavity. The mass fraction for the two cases is not very
different, but the flow pattern is somewhat different because a rotation ring in the cavity forms in the case with side
walls. The flow pattern may be due to the inwards rotational direction, as shown in Fig. 13.
a) With intake side walls
b) Without intake side walls
Figure 12. Iso-surfaces of H2 mass fraction near cavity flame-holder.
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a) With intake side walls
b) Without intake side walls
Figure 13. Iso-surface of H2 mass fraction and stream-lines at cavity flame-holder.
a) With intake side walls
b) Without intake side walls
Figure 14. H2 injection and mixing enhancement
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a) Locations of the X-Z planes
b) With intake side walls
c) Without intake side walls
Figure 15. H2 mass fraction and stream-lines in X-Z planes at the cavity flame-holder.
Figure 16 shows temperature contour and fuel mass fraction pattern inside the cavity and downstream of the
cavity. The locations of the y-z plane are 4.5 mm and 59 mm downstream of the leading edge of the cavity. As
shown in Fig. 14a, fuel spreads toward the center of the cavity because two of the fuel streams injected by injectors
#1 and #4 are bent by the flow deflected from the side walls. In contrast, in the case without intake side walls, the
two fuel streams injected by injectors #2 and #3 spread toward the side walls. At the plane 59 mm downstream of
the leading edge of the cavity flame-holder, all four fuel streams have semicircle shapes. In the case with intake side
walls, however, the fuel streams are combined.
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a)
With intake side wall
b) Without intake side wall
Figure 16. Temperature contour and H2 mass fraction contour lines at the middle of the
cavity (top) and 50 mm downstream of the end of the cavity (bottom).
After fuel injection, the flow structure inside the combustor undergoes transitions. Figure 17(a) shows a history
of the pressure changes in the combustor, including the cavity flame-holder. Both with intake side walls and without
intake side walls, the pressure increases and impinging points move upstream at the same time. The flow right
behind the cavity flame-holder in particular suffers more severe flow structure changes. In the case without intake
side walls, it takes about 0.5 msec to rearrange the flow structure, but about 0.8 msec in the case with intake side
walls. The difference is caused by the pattern of the fuel-air mixing and the effects of intake side walls. With intake
side walls, it takes longer for the fuel to be spread because the deflected flow from the intake side walls disperses the
flow structure.
Figures 17 (b), (c) and (d) represent local equivalence ratio at specific locations in the combustor. At the location
closest to the injector (Fig.17 (b)), the local equivalence ratio is distributed over 1 in several locations in the y-z
plane and decreases downstream of injector. The fuel injected from injectors near the side walls spreads toward the
combustor center and forms a relatively narrower fuel region with high equivalence ratio. It seems more rapidly
mixed with the air stream in case with side walls
To quantify the level of mixing, mixing efficiency is considered. This efficiency is defined using the following
formulation.
hmix ( x) =
ò rY ua dA
ò rY udA
H2
(13)
H2
Where ρ is density, YH is mass fraction of hydrogen, u is the velocity component normal to the area dA . The
2
parameter a is decided by local equivalence ratio. If the ratio is less than 1, a has a value of 1. If not, the value is
given the reciprocal of the local equivalence ratio.22 This means that if the local equivalence ratio is less than 1, the
mixing is regarded as completed. Also, the mixing does not occur when the equivalence ratio is much larger than 1.
Figure 18 (a) represents histories of the efficiencies for both cases. The efficiency transition takes place quickly. At
0.1 ms, the efficiency is rapidly rising behind the injector and reaching 1, but it drops to 0 in the middle of the
combustor. This means that the fuel has not yet reached the exit of the combustor. After 0.2 ms, the fuel is observed
from the injection point to combustor exit. Although the location where the mixing efficiency reaches 1 is moved
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downstream, it keeps its value far downstream. The fuel mass maximum fraction decreases from 1 to an almost
negligible value in a short range due to fuel lean injection (0.11)
a) History of pressure distribution
b) 30mm downstream of cavity center
c) 80 mm downstream of cavity center
d) 130 mm downstream of cavity center
Figure 17. History of pressure distribution along the center line of the bottom wall and local equivalence
ratio distribution along span-wise direction at specific location of x. H: height from bottom wall.
a)
b)
Figure 18. History of a) mixing efficiency and b) maximum hydrogen mass fraction through combustor
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V. Conclusion
A 3D numerical simulation with fuel injection was conducted in order to illuminate the flow characteristics and
H2-air mixing characteristics in a model scramjet engine with two intake-sidewalls and a cavity flame-holder. Cases
with and without sidewalls were studied; flow patterns for the two cases were found to be quite difference. The flow
deflections caused by shock formation and shock/boundary interaction at the intake side walls influence the flow
structure over the entire flow path from intake to combustion. The computed wall pressure was compared with the
experimental data obtained with the intake side walls. The pressure distribution along the center-line of the bottom
wall agrees well with that of experimental data taken in the same combustor.
Shock-boundary layer and shock-shock interactions are generated on the intake side walls. The ramp shocks
occurring at the intake ramps claw at the boundary layer of the intake side walls. Because of this, the ramp shocks
deflect the flow and the boundary layer shape. The deflected flow makes the intake flow structure more complex and
produces helical flow at the inlet. In the case without intake side walls, a higher level of pressure fluctuations along
the bottom wall is observed in the combustor. Without intake side walls, quasi-uniform shock structure induces
pressure distribution with band shapes, but the flow deflected from the intake side walls disperses the flow structure
with three local peaks. Thus the increase in local pressure inside the combustor is caused partially by the reflected
shock.
In the case with intake side walls, it takes more time for the fuel to spread out in the combustor. The helical flow
bends the two fuel streams injected from injectors #1 and #4 near the side walls toward the center of the chamber
and recovers behind the cavity flame-holder. The pattern and direction of revolving flow inside the cavity flameholder are transformed. In the case of intake side walls, it is observed that each stream of fuel which penetrates the
cavity is isolated from other fuel streams.
For the fuel mixing efficiency transition, at 0.1 ms the efficiency is rapidly rising behind injector and reaching 1,
but it drops to 0 in the middle of the combustor. After 0.2 ms, the fuel mixing efficiency reaches 1 and keeps the
value far downstream. The fuel mass maximum fraction decreases from 1 to an almost negligible value in short
range due to very low fuel lean injection.
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