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American Institute of Aeronautics and Astronautics Paper
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EFFECT OF SIDEWALL CONFIGURATIONS ON THE AERODYNAMIC
PERFORMANCE OF SUPERSONIC AIR-INTAKE
Y. Watanabe*, A. Murakami and H. Fujiwara National Aerospace
Laboratory
Tokyo, Japan
Abstract The effects of the sidewall variation on the
aerodynamic performance for a two dimensional external
compression supersonic air-intake were investigated by performing
both of wind tunnel tests and numerical simulations. It became
clear that one of the major disadvantages of the air-intake with a
larger sidewall is its comparatively poor pressure recovery and
skewed spatial distortion, both of which being caused by the
separation vortices induced by the interaction between the sidewall
boundary layer and the shock waves. It also became clear that
another disadvantage is its comparatively large spillage drag. On
the other hand, it turned out to have the advantage of
comparatively wide stable range in subcritical operation. The
reason for the wide stable range of the air-intake with a larger
sidewall was investigated in detail using both of the results of
the wind tunnel tests and numerical simulations.
Nomenclature A1 = area of throat A2 = area of exit Ac = capture
area at full flow condition B = width of stream tube Cd = drag
coefficient of intake drag Cdspillage = drag coefficient of
spillage drag Cdbleed = drag coefficient of bleed drag Cdcowl =
drag coefficient of cowl drag D = diameter of intake exit DC(60) =
circumferential distortion parameter DImax, DImin = distortion
index Hc = capture height at full flow condition H = capture height
Ht = height of stream line L = length of subsonic diffuser
MFRcapture = capture mass flow ratio MFRspillage = spillage mass
flow ratio p = pressure exit = pressure recovery at exit plane slit
= pressure recovery behind slit
throat = pressure recovery at intake throat
Introduction National Aerospace Laboratory of Japan is
promoting the development of two types of Scaled Supersonic
Experimental Airplanes (Non-powered Experimental Airplanes and
Jet-powered Experimental Airplanes), as well as conducting the
research on related technology. The propulsion system for the
experimental airplane must have enough net thrust to accelerate the
airplane up to the flight speed of M2.0. The air-intake plays a key
role on the propulsion in the supersonic flight, the air-intake
being required to have high aerodynamic performance such as low
total pressure loss, low spatial distortion, low external drag and
wide stable operational range. In order to satisfy such
requirements, each component constituting the air-intake, such as
the ramp for supersonic compression, the sidewall, the subsonic
diffuser and the bleed system, should be sophisticated
independently and moreover should be working altogether at the
highest performance.
In this study, special focus was paid on the design of the
sidewall configuration for the air-intake. The objective of this
study is to clarify the effect of the sidewall configuration on the
aerodynamic performance such as the pressure recovery, the spatial
distortion, flow stability characteristics and the external drag.
Both of the wind tunnel tests and numerical simulations of the
air-intake with four types of sidewalls were performed, the results
of which were compared to each other.
Configuration of Intake Figure 1 illustrates the schematic of
the
supersonic air-intake. The air-intake is a rectangular and
external compression air-intake with three shock system. The design
Mach number was 2.0. The total length and capture area was 1663mm
and 910cm2, respectively, to the scale of the air-intake
integrated
38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference &
Exhibit7-10 July 2002, Indianapolis, Indiana
AIAA 2002-3777
Copyright 2002 by the American Institute of Aeronautics and
Astronautics, Inc. All rights reserved.
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American Institute of Aeronautics and Astronautics Paper
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into the experimental airplane. Figure 2 shows the cross
sectional view of the air-intake. The first ramp, shown as a red
area in the supersonic diffuser in Figure 1, consists of a wedge of
3 degrees and an isentropic compression surface of 5 degrees. The
second ramp, the green area in the supersonic diffuser in Figure 1,
is a variable wedge, the turning angle of which varies from 0 up to
12 degrees. The hinge point location of the movement of the second
ramp is shown Figure 2. The oblique shocks and compression waves
originating from the first and second ramps focus on the cowl lip
at the condition
Fig.1 Schematic of air-intake
Fig.2 Cross sectional view of air-intake ( Unit : mm )
Fig.3 Detail of supersonic diffuser
Fig.4 Schematic of experimental model
Fig.5 Experimental model installed in wind tunnel
Fig.6 Computational grid
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American Institute of Aeronautics and Astronautics Paper
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of the inlet Mach number 2.3. The diffuser ramp, shown as the
green area in the subsonic diffuser in Figure 1, is also of a
variable type, the turning angle of which is uniquely determined by
the position of the second ramp trailing edge. A wide slit is
located just downstream of the throat to suck the boundary layer
developing on the first and second ramps. Bleed mass flow ratio was
varied by changing the bleed exit area. The length-to-exit-diameter
ratio of the subsonic diffuser, L/D, was about 3.3. The variation
of the cross-sectional shape along the flow direction is shown in
the upper part of Figure 2, where it is shown that the shape
changes from rectangular to circular while the width D is always
constant along the flow direction. The area ratio of the subsonic
diffuser A2/A1 depends on the position of the two variable ramps,
which was equal to 2.05 at the condition that the turning angle of
the second ramp was 12 degrees.
Four kinds of sidewall configurations were tested shown in
Figure 3. The largest sidewall L1 covers most of the supersonic
diffuser, the edge line starting from the leading edge of the first
ramp. The smallest sidewall was referred to as S1, in which the
upstream half area of the sidewall was cut away. The edge line of
S1 starts from the corner of the second ramp. The edge line of the
sidewall L3 starts from the starting point of the isentropic
compression surface, while that of L4 starts from the ending point
of the isentropic surface.
Wind tunnel test Figure 4 shows the schematic of the
experimental model. It was a 19.2% scale model of the actual
air-intake used for the experimental airplane. The exit diameter of
the air-intake is 70mm. In the wind tunnel test, two kinds of
sidewall, S1 and L1, were tested. The bleed exit area was set 8
percents of the capture area, Ac. A flow plug was used to control
the mass flow ratio. A spatially high resolution measurement of the
total pressure distribution at the air-intake exit was performed by
means of rotatory pitot rakes. For steady pressure measurements,
three electrical scanners (PRESSURE SYSTEMS Inc.) were used, each
of which contains 64 pressure transducers. For unsteady pressure
measurements, high response pressure transducers (Kulite XCQ-062)
were used. The unsteady pressure transducers were set at the two
locations, one of which was near and inside the cowl lip and
another was at the center of the air-intake exit surface. Figure 5
shows the picture of the experimental model installed in the 1m1m
blowdown type supersonic wind tunnel of National Aerospace
Laboratory of
Japan. The wind tunnel tests were performed with the free stream
Mach numbers ranging from 1.5 to 2.0. The duration time of a blow
was 36 seconds. The color schlieren method and the oil flow
technique were applied to visualize the flow fields in and around
the supersonic diffuser.
The pressure recovery and the total pressure distortion were
obtained based on the results of the total pressure distribution
measurements. The pressure recovery is defined as,
= PPf / (1)
where Pf is the spatial average of the total pressure on the
air-intake exit surface while P is the total pressure of the free
stream. Two kinds of distortion parameter were used in this study,
one of which is the distortion index (D.I.) used for the guideline
to determine the engine operation limit. The maximum and minimum
values of the D.I. are defined as,
( )
= PPP f /D.I. maxmax (2)
( )
= PPP f /D.I. minmin (3)
where Pmax and Pmin are the maximum and minimum values of the
total pressure within the region of the air-intake exit surface
excluding the outer 1.5 percents region near the wall. Another
distortion parameter is the circumferential distortion parameter
DC(60) which is defined as,
( ) ff qPP /DC(60) 60= (4) where qf is the mean dynamic pressure
at the air-intake exit while P60 is the spatial average of the mean
total pressure obtained in the worst 60 degrees sector of the exit.
In order to detect the buzz, the pressure fluctuation was
monitored, the pressure being measured through the high response
pressure transducers explained above. The mass flow through the
subsonic diffuser was calculated on the choked area of the flow
plug using both of the free stream total temperature and the total
pressure just upstream of the flow plug. The bleed mass flow was
calculated based on the total pressure and the static pressure at
the bleed exit.
Numerical simulation methods The steady, compressible,
Reynolds-averaged
Navier-Stokes equations were solved for the flow through the
supersonic air-intake. The turbulence viscosity was evaluated with
the low Reynolds number k-epsilon model developed by Myong and
Kasagi2. Spatial difference was evaluated by a third order upwind
biased Roe scheme3 with a TVD
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limiter of Chakravathy and Osher type4. For the time
advancement, an implicit method was adopted.
Figure 6 illustrates the computational grid in and around the
air-intake. The computational domain was decomposed into four
regions. The total number of grid points was 450,000. A straight
duct and a variable second throat was located downstream of the
air-intake to control the capture mass flow ratio corresponding to
the flow plug in the wind tunnel test. The internal flow through
the bleed chamber for boundary layer removal was also simulated.
The bleed chamber was connected to the main duct through the slit
located just downstream of the throat. The bleed exit area was 9
percents of the capture area Ac of the air-intake. Four kinds of
sidewall configuration shown in Figure 3 were investigated in the
present numerical simulations.
Results and Discussions Flow fields around the air-intake
Figures 7 and 8 show the flow fields through the air-intake with
the largest sidewall L1 obtained by performing the numerical
simulations with different mass flow ratio. The inlet Mach number
was 2.0. The operation conditions shown in Figure 7 and 8 are
nearly critical and subcritical, respectively. As is shown in
Figure 7(a), the oblique shock waves and the compression waves
cross the terminal shock wave above the cowl lip at critical
operation. Figure 7(b) shows that large longitudinal vortices were
induced in the subsonic diffuser. This is due to the shock boundary
layer interaction on the large sidewalls. These vortices still
remained in the subcritical operation shown in Figure 8(b). The
results of the smallest sidewall S1 with different mass flow ratios
are shown in Figures 9 and 10. Note that the mass flow ratio of the
flow shown in Figure 9 is nearly equal to that of the flow shown in
Figure 7. In the case with S1 sidewall at critical condition shown
in Figure.9(b), the vortices induced in the subsonic diffuser were
fairly small compared to the previous large sidewall case shown in
Figure 7(b). The reason for the difference lies on the thickness of
the sidewall boundary layer upstream of its interaction with the
shock waves. It can be easily estimated that the thickness of the
sidewall boundary layer on the large sidewall was larger than that
on the small sidewall one, which naturally resulted in the larger
longitudinal vortices downstream of the shock boundary layer
interaction as long as the strength of the shock waves is almost
the same. Figure 10 shows the flow field through the air-intake
with the smallest sidewall S1 in subcritical operation.
Note that the mass flow ratio of the flow shown in Figure 10 is
nearly equal to that of the flow shown in Figure 8. Although the
location of the terminal shock wave in the flow field shown in
Figure 10(a) is approximately the same as that in Figure 8(a),
there exists a clear difference between these two flows, especially
on the cowl side of the subsonic diffuser. In the case with the
small sidewall, Figure 10(b) shows the existence of the low total
pressure region on the cowl side of the diffuser, which turned out
to be caused by the shear layer ingestion, the shear layer
originating from the intersection point of the shock waves
(referred to as Triple point in the figures). On the other hand, in
the case with the large sidewall, no such low total pressure region
could be observed on the cowl side as is shown in Figure 8(b). The
reason of this difference will be explained later.
Figure 11 compares the oil flow pictures on the first and second
ramps for the air-intakes with S1 and L1 sidewalls. In the case
with S1 sidewall, streamlines on the first ramp are diverted
outside indicating that sideways spillage occurred, on the other
hand, streamlines are nearly straight in the case with the large
sidewall L1 indicating that the sideways spillage was negligible.
This is simply due to the effect of the large solid sidewall
preventing the flow from going outside. Pressure recovery
Figure 12 shows the pressure recovery plotted as a function of
the mass flow ratio obtained in the numerical simulations for four
sidewall configurations. The wind tunnel test result for only S1
sidewall case is also plotted in the same figure. The mass flow
ratio is defined by the ratio of the mass flow going through the
throat to the captured mass flow. The inlet Mach number was 2.0.
The numerical result for S1 sidewall agrees fairly well with the
corresponding wind tunnel test result. The results of the numerical
simulations with different sidewalls show a large difference of the
recovery. The pressure recovery for L4 sidewall is nearly equal to
that for S1. On the other hand, both of the recoveries for the
sidewalls L1 and L3 are clearly smaller than that for S1.
In the cases of the larger sidewalls, L1 and L3, the sidewall
boundary layer became too thick, due to the shock boundary layer
interaction, to be sucked into the bleed chamber completely, which
resulted in the appearance of the large longitudinal vortices
finally causing the reduction of the pressure recovery.
It was interesting that the pressure recovery for the larger
sidewall cases, L1 and L3, increased with
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(a) Cross sectional view of Mach number contour
(b) Total pressure distribution in subsonic diffuser
Fig.7 Flow field around L1 air-intake in critical
operation at M 2.0; MFRcapture = 0.830
(a) Cross sectional view of Mach number contour
(b) Total pressure distribution in subsonic diffuser
Fig.8 Flow field around L1 air-intake in subcritical
operation at M 2.0; MFRcapture = 0.795
(a) Cross sectional view of Mach number contour
(b) Total pressure distribution in subsonic diffuser
Fig.9 Flow field around S1 air-intake in critical
operation at M 2.0; MFRcapture = 0.833
(a) Cross sectional view of Mach number contour
(b) Total pressure distribution in subsonic diffuser
Fig.10 Flow field around S1 air-intake in subcritical
operation at M 2.0; MFRcapture = 0.793
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the reduction of the mass flow ratio (MFR) in the subcritical
operation with the MFR lower than about 0.82 shown in Figure 12.
This was not the case with the simulations with the smaller
sidewalls where the pressure recovery was nearly constant except
the state of buzz. The increase in the recovery for the larger
sidewall cases in the subcritical operation can be explained as
follows; the pressure in the bleed chamber became higher as the MFR
was reduced until the flow went into the state of buzz. This
pressure rise had an effect to increase the bleed mass flow as long
as the bleed exit area was fixed. As the results, the bleed chamber
was able to suck more boundary layer than before which improved the
pressure recovery. Figure 13 shows the pressure recoveries at the
throat and at the location just downstream of the slit for bleed
for the case with the sidewall L1. The former corresponds to the
recovery just before the boundary layer bleed, while the latter
corresponds to the recovery after the bleed. The figure shows that
the recovery after the bleed increased with the decrease in the MFR
even though the recovery before the bleed decreased with the
decrease in the MFR. This clearly indicates that the pressure
recovery was improved due to the increase in the bleed of the
boundary layer.
Similar investigation was performed for the inlet Mach number
1.7. Figure 14 shows the pressure recovery vs the MFR. The
sensitivity of the size of the side wall to the pressure recovery
is much less compared to the M2.0 cases just because the shock
waves amplifying the boundary layer thickness became weaker. Figure
15 shows the total pressure distribution for the air-intake with L1
sidewall, which corresponds to Figures 7(b) and 8(b) for M2.0
cases. The longitudinal vortices actually became small even in the
case with the largest sidewall at the inlet Mach number 1.7.
Spatial distortion index
Figure 16 shows a diagram of the maximum and minimum distortion
indices at the inlet Mach number of 2.0 obtained in the numerical
simulations. In all cases except in supercritical operation the
distortion indices were within the range of 7.5% which is one of
the requirements of the operation of the engine used for the
experimental airplane. Comparison of the distortion indices with
different sidewalls shows a clear tendency that the distortion was
larger with larger sidewalls. This is due to the large longitudinal
vortices induced by the shock boundary layer interaction explained
above. The circumferential distortion parameter DC(60) is shown in
Figure 17, where the flows with the four
Fig.11 Oil flow picture on ramp at M 2.0
Fig.12 Variation of pressure recovery against capture
mass flow ratio at M 2.0
Fig.13 Pressure recovery at throat and behind slit of
air-intake at M 2.0
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different sidewalls can be divided into two groups, one was the
air-intakes with the smaller sidewall, S1 and L4, and another with
the larger sidewall, L1 and L3. The former shows a clear reduction
of DC(60) near critical and subcritical range and shows rapid
increase in DC(60) when the shear layer was ingested into the
diffuser, while the latter shows that DC(60) kept nearly constant
at high value at any MFR. Figure 18 shows the circumferential
distortion index diagram in the case of the inlet Mach number of
1.7. The sensitivity of the size of the side wall to DC(60) was
weaker compared to the M2.0 cases although it shows DC(60) a rapid
increase with the ingestion of the shear layer for the cases with
the smaller sidewalls shows. Instability of the intake flow
Instability of an air-intake flow, which is often described as a
time distortion, is also an important characteristic of an
air-intake, which directly related to the stable operation margin
of an engine. In subcritical operation below a certain value of the
mass flow ratio, there might to be occurred serious shock wave
oscillation phenomena well known as buzz. Figure 19 shows the
schlieren photographs taken in the wind tunnel tests with the
sidewalls L1 and S1 both of which operating at supercritical
conditions. The chocked exit area controlled by the flow plug was
almost the same for the two cases. The similar photographs at
subcritical conditions are shown in Figure 20. At supercritical
conditions shown in Figure 19, shock system was stable in both
cases. At the subcritical condition shown in Figure 20, flow field
in the air-intake with L1 was still stable, while in the air-intake
with S1, the oscillation of the terminal shock wave occurred.
Further reducing the mass flow ratio, both of the flow fields went
into the state shown in the schlieren photographs of Figure 21.
Significant shock oscillations were observed in both cases. Figure
22 shows the root mean square values of the pressure fluctuation
measured near the cowl lip in the subsonic diffuser. As is shown in
the figure, the unsteady flow characteristics of the air-intake
with S1 sidewall is different especially in the operation condition
with the spillage mass flow ratio ranging from about 0.14 to 0.23
in which the flow with the sidewall S1 showed a higher level of
oscillation compared to the flow with L1 sidewall.
The ingestion of the shear layer is one of the important factors
of the occurrence of flow instability. The instability of this type
is referred to as Ferri instability5. Although the ingestion of the
shear layer is not a sufficient condition for the
occurrence of buzz6, it is a useful criterion to determine the
safety limit of the air-intake operation. Figure 23 illustrates the
streamlines of the flow through a supersonic air-intake. The height
Hc indicates the height of the cowl lip while the height
Fig.14 Variation of pressure recovery against capture
mass flow ratio at M 1.7
Fig.15 Total pressure distribution in L1 air-intake
at M 1.7; MFRcapture = 0.797
Fig.16 Variation of distortion index against capture
mass flow ratio at M 2.0
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Fig.17 Variation of circumferential distortion
parameter against capture mass flow ratio at M 2.0
Fig.18 Variation of circumferential distortion
parameter against capture mass flow ratio at M 1.7
Fig.19 Schlieren photos in supercritical operation at
M 2.0
Fig.20 Schlieren photos in subcritical operation at
M 2.0
Fig.21 Schlieren photos of buzz in subcritical
operation at M 2.0
Fig.22 R.M.S. value of pressure fluctuation at M 2.0
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H indicates the capture height and the height Ht indicates the
height of the streamline passing through the intersection point
between the second ramp shock and the terminal shock waves,
respectively. The shear layer is ingested into the subsonic
diffuser when Ht is smaller than H. The relations between the
heights Ht and H at the inlet Mach numbers 2.0 and 1.7 were shown
in Figures 24 and 25, respectively. Both of the heights Ht and
Hdecreased as the spillage mass flow ratio increased. The capture
height H was larger in the cases of smaller sidewall
configurations, while the height Ht was smaller in the cases of
smaller sidewall configurations. The minimum mass flow ratio
without the ingestion of the shear layer was thereby dependent on
the sidewall configuration. Assuming that buzz always occurs when
the shear layer is ingested, the subcritical stability margin
measured by the mass flow ratio increases by about 3 percents when
the S1 sidewall is replaced by L1 at the inlet Mach number of 2.0.
In the case of M1.7 it increases by 7 percents.
Figures 26 and 27 show the stream tubes going into the subsonic
diffuser in the cases of L1 and S1 sidewalls, respectively. The
inlet Mach number was 2.0. The cross sectional area of the captured
flow at the infinite upstream, which is approximated by the product
of B and H, was almost the same in both
Fig.23 Definition of height of stream line
Fig.24 Variation of heights of stream line against
spillage mass flow ratio at M 2.0
of the cases because the spillage (or equivalently captured)
mass flow ratio was almost the same. In the case of L1 sidewall
air-intake, the sideways spillage mass flow was much smaller than
the mass flow of the subsonic spillage escaping upward over the
cowl lip. On the other hand, in the case of S1
Fig.25 Variation of heights of stream line against
spillage mass flow ratio at M 1.7
Fig.26 Shape of capture stream tube of L1 air-intake
at M 2.0; MFRcapture = 0.795
Fig.27 Shape of capture stream tube of S1 air-intake
at M 2.0; MFRcapture = 0.793
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sidewall air-intake, the ratio of the sideways spillage mass
flow to the total spillage mass flow is larger compared to the
air-intake with L1 sidewall. The increase in the sideways spillage
made the width of the stream tube B smaller causing the increase in
the capture height H as long as the captured mass flow or the
product of B and H was constant. The height H for S1 sidewall
air-intake thereby became higher than that of L1 which explains the
difference of S1 and L1 in Figure 24.
The sideways spillage, in addition, exhibits the influence on
the local Mach number distribution. The expansion waves generated
by the sideways spillage propagated inside of the supersonic
diffuser for spanwise direction. The flow upstream of the second
ramp shock was accelerated by the expansion waves making the shock
angle of the second ramp shock, shown in Figure 23, smaller. As a
result, the intersection point between the second ramp shock and
the terminal shock shifted lower. This made the difference larger
in the height Ht with the sidewall configuration shown in Figure 24
and 25. External drag of the air-intake
Figure 28 shows the air-intake total drag coefficient and its
three components, a spillage drag, a bleed drag and a cowl drag,
for the S1 and L1 sidewall air-intakes. The total drag of L1
sidewall air-intake was larger than that of S1 sidewall air-intake
mainly because the spillage drag was different, while the other two
components were almost the same.
Spillage drag is determined by the integral of the pressure on
the surface covering the capture stream tube. Figure 29 illustrates
the top view of the pressure distribution on the surface of the
capture stream tube. The upper half of Figure 29 shows the result
of L1 sidewall air-intake while the lower half shows the result of
S1 sidewall air-intake. It is
Fig.28 Drag coefficient of air-intake at M 2.0
clearly shown that the high pressure area in the case of L1
air-intake pushing the internal flow downstream to increase the
drag is wider than that of the a ir - in take with S1 s idewal l .
Another interpretation of the difference of the total spillage drag
with different sidewalls can be written as follows. The sideways
spillage flow is mainly supersonic because it goes through only
oblique
Fig.29 Pressure distribution on capture stream tube
Fig.30 Operational range at M 2.0
Fig.31 Operational range at M 1.7
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shock waves. In contrast, the spillage flow escaping upward over
the cowl lip is subsonic because it is decelerated and compressed
going through both of the oblique and terminal shock waves. This
compression caused larger drag per unit mass flow of the subsonic
spillage compared to the sideways supersonic spillage. The larger
portion of the subsonic spillage than the supersonic spillage in
the case of L1 sidewall air-intake was one of the main reasons for
the larger total spillage drag. Engine matching
It is usual that the occurrence of the ingestion of the shear
layer determines the low MFR operation criterion, while the spatial
distortion determines the higher MFR operation criterion. In
accordance with these criteria the data points in Figure 12 without
the stable operation range were eliminated and only the points
within the stable operation range were re-plotted in Figure 30.
There was no supercritical operation margin in the case of L1 and
L3 sidewall air-intakes. The air-intake with no supercritical
margin must be operated at subciritical condition with additional
spillage drag. The pressure recoveries of the air-intakes with the
larger sidewalls, L1 and L3, were worse than those of the smaller
sidewalls, S1 and L4. Using an air-intake with large spillage drag
and low pressure recovery causes the aggravation of the net thrust
of propulsion system. As the results, S1 or L4 sidewall
configurations were better in the present study at the condition
for the Mach number of 2.0.
Similar consideration was done for M1.7. Figure 31 shows that
there was no subcritical operation margin in the case of S1
air-intake at the inlet Mach number of 1.7. Subcritical operational
margins were wider in the case of the larger sidewall
configurations, L3 and L4, however, there was no operation margin
at supercritical condition either.
Conclusion In this study, the effects of the sidewall
configurations on the aerodynamic performance of the rectangular
external compression air-intake were investigated experimentally
and numerically at two Mach numbers of 1.7 and 2.0.
In the case with the large sidewall, the interaction of the
shock waves with the sidewall boundary layer induced the
longitudinal vortices in the subsonic diffuser, which caused
serious pressure loss especially at Mach number 2.0. The pressure
recovery and the distortion indices were aggravated by the
longitudinal vortices especially at higher
capture mass flow ratio in the case with the large
sidewalls.
The shear layer originating from the intersection point of the
oblique and terminal shock waves was ingested into the air-intake
in subcritical operation below a certain value of the mass flow
ratio. The minimum mass flow ratio without the shear layer
ingestion was higher for the air-intake with the smaller sidewall.
The stable operation margin in subcritical condition was reduced
more by the shear layer ingestion in the case of the smaller
sidewall.
The external drag was larger in the cases with the larger
sidewalls due to the influence of the relatively high ratio of the
subsonic spillage compared to the sideways supersonic spillage.
In short, at the inlet Mach number 2.0, the air-intake with the
smaller sidewalls have the advantage of high pressure recovery, low
distortion and low external drag, while the air-intake with the
larger sidewalls have the advantage of their wide range of safety
operation range in subciritical condition. At the inlet Mach number
1.7, the differences in the pressure recovery and distortion were
smaller compared to M2.0 because the interaction of the sidewall
boundary layer and the shock waves was softened in the case of M1.7
compared to M2.0.
References 1. Seddon, J. and Goldsmith, E.L., Intake
Aerodynamics, AIAA Education Series ISBN 0-93040-03-7, 1985.
2. Myong, H.K. and Kasagi, N., A new approach to the improvement
of k-epsilon turbulence model for wall-bounded shear flow, JSME
International Journal of Fluid Engineering, Vol. 109, 1990,
pp.156-160.
3. Roe, P.L., Approximates Riemann Solvers, Parameter Vectors
and Difference Schemes, Journal of Computational Physics, Vol.43,
1981, pp.357-372.
4. Chakravarthy, S.R. and Osher, S., A new class of high
accuracy TVD schemes for hyperbolic conservation laws, AIAA paper
85-0243, 1985.
5. Ferri. A. and Nucci, L.M., The origin of aerodynamic
instability of supersonic inlets at subcritical conditions, NACA,
RM L50 K30, 1951.
6. Fujiwara, H., Murakami, A. and Watanabe, Y., Numerical
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compression intakes, AIAA paper 2002-2740, 2002.
UmbertoHighlight