1American Institute of Aeronautics and Astronautics
NUMERICAL ANALYSIS OF THREE-DIMENSIONAL FLOWS
INSIDE / OUTSIDE A SUBMERGEED AIR INLET UNDER MANEUVER
Weng Peifen+ and Ding Jue∗
Shanghai Institute of Applied Mathematics and Mechanics
Shanghai University, Shanghai 200072, PRC
Email:[email protected]
ABSTRACT
Three dimensional turbulent flows around an air
inlet of a cruise missile are studied numerically in the
current paper by using Reynolds-averaged Navier
-Stokes equations and RNG k- turbulence model in a
curvilinear coordinate system. Detailed results show the
aerodynamic characteristics with the flow distortion in
the duct at different missile flying gestures were
analyzed, which offers ways of modifying intake
performance, and provides a foundation of
comprehensive design on the missile and submerged air
intake for research workers.
1. INTRODUCTION
A kind of inlet, which is embedded in the body of
a missile, becomes to the fore with time going for the
requirements of both flow properties and stealthy
effects, but generally the flows are quite distorted in
this kind of inlet[1]. Morever, the situation is getting
worse in flow characteristics while the missile flies in
some high angle of attack or angle of sideslip. It is so
important to have a good matching between missile and
jet propulsion in aerodynamic design, and also it is
needed that numerical analysis on three dimensional
separated flows inside and outside the air intake are
done at different maneuvering situations.1
Many previous papers focused mainly on
aerodynamic characteristics inside intakes are well
documented[2,3]. In contrast, those papers are much
more scare concerning a comprehensive study on flow
performances for a missile together with its air intake.
1 Sponsored by National Teaching / Research Award Fund for Outstanding Young Teachers in Higher Education Institutionof MOE, and by Shanghai “DAWN” Project, PRC
The present paper gives the numerical investigations on
turbulent flows of missile/submerged air inlet at low or
high subsonic speed by CFD software. Flow
characteristics including total pressure recovery, flow
distortion index at intake exit, and the wall pressure
distribution at different flying gestures were analyzed
further.
2. MATHEMATICAL MODEL
Such airflows are assumed to be steady three
dimensional, and Reynolds time averaged Navier
-Stokes equations can be written in Cartesian tensor
form as:
Continuity equation 0=∂∂
j
j
x
uρ 1
Momentum equation
2)( ijij
i
jij
ji guux
u
xx
p
x
uu ζρρµρ −′′−∂
∂∂∂+∂
∂−=∂∂
≠=
=20
212 i
iiδ (2)
Where, pui , represent mean velocity components
(i=1,2,3) and average pressure respectively. µ is the
viscosity coefficient. The “Reynolds stresses”,
''jiuuρ− can be modeled by Boussinesq viscous
hypothesis to show the Reynolds stresses with the mean
velocity gradients. According to the authors’
computational practice, the Renormalization- group
(RNG) k- model will be utilized here, provide an
analytically-derived differential formula for effective
viscosity accounting for low Reynolds number effects,
so it can be applied to both low and high Reynolds
number flows. In addition, it particularly provides an
33rd AIAA Fluid Dynamics Conference and Exhibit23-26 June 2003, Orlando, Florida
AIAA 2003-4138
Copyright © 2003 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
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analytical formula for turbulent Prandtl numbers.
3. COMPUTATIONAL METHOD
Based on three dimensional Reynolds-averaged
Navier-Stokes equations and RNG k- turbulence
model, a developing flow at the entrance to square
cross-section, 90 bend of 2.3 radius ratio for turbulent
flow curved duct[4] will be studied firstly by the finite
control volume method and improved SIMPLE scheme
in order to verify whether mathematical model right. A
comparison between the computed results[5] and
experimental data[4] shows both are in a good
agreement, and it also suggests the turbulent flows
within the core region and near-wall region of duct
affected by duct curvature can be predicted accurately
by RNG k- model and two-layer zonal wall model.
The present computation will continue based on the
above results.
(a) Missile (b) Submerged air inlet
Fig.1 The sketch of a missile and its submerged air inlet
A sketch map of a cruise missile with its typical
submerged air intake is illustrated in Fig.1. The
geometry of intake is determined by many blowing
experiments, and the shape of the inner wall is designed
smoothly from the entrance to the exit to avoid possible
large separation, seeing Fig.1(b). For convenience of
study, the exits of both curved intake and missile
fuselage are placed at the same mathematical section,
and original point is set at the center of the exit section
of the missile fuselage. Moreover, the cruise missile is
laid horizontally to realize the change of flying gestures
by varying its flow direction. The angle of attack ( ) is
defined as the angle of projection in the x-y plane
between the airflow direction and the symmetrical axle
of the missile. Additionally, the angle of sideslip ( ) is
defined as angle of projection in the x-z plane between
the airflow direction and the symmetrical axle of the
missile. The cylinder region around the missile is
chosen as the present computational field.
The computational boundary conditions are treated
as follows:
Inflow boundary condition: free-stream flow passes
through the whole missile at two given speeds.
(a) Ma∝=0.28, KT 293=∞ , 51001325.1 ×=∞P Pa.
(b) Ma∝=0.7, KT 293=∞ , 51001325.1 ×=∞P Pa
Outflow boundary condition: Neumann derivative
condition supposed, namely ∂ϕ/∂ξ=0
Where ϕ stands for the general parameters, and ξ is the
flow direction.
Wall boundary condition: the viscous non-slip condition
satisfied for viscous airflow
3American Institute of Aeronautics and Astronautics
0=u , 0=v , 0=w
and, 0=∂∂
n
T, 0=∂
∂n
p .
4. RESULTS AND DISCUSSIONS
4.1 Turbulent Flows Around Missile
The flow velocity isograms are given in Fig.2 at
the angle of attack of being 4°. It is shown that the
boundary layers with low aerodynamic energy exist on
the missile surface, result in much air with low energy
to flow into the submerged air intake so that the flow
properties are distorted. Fig.3 illustrates the velocity
isograms on y=0.0m cross section at Ma=0.28, β=20°revealing a non-symmetrical flow velocity distribution
affected by the free-stream flow. Computed results
show the free stream flow goes around the missile and
its curved intake fairly smoothly.
The secondary flows are quite large inside the
intake responsible for the duct curvature and the
transverse pressure gradient acting on the intake
cross-section. The characteristics of secondary motion
are given at different flying gestures. It can be found a
pair of vortices at the exit plane of intake is produced at
a certain angle of attack. Fig.4 shows the velocity
vector profile at intake exit while Ma=0.28 and α=4°.
In contrast, the secondary flow pattern at a certain β is
quite different from that at a certain α. With β rising up
to 4° or higher, a single vortex will appear at outlet of
intake with large flow separation in there.
(a) Ma=0.28 , 4°, 0° (b) Ma=0.7 , 4°, 0°Fig.2 Flow velocity isograms (y=0.0m cross section)
(Ma=0.28 , =0°, =20°)
Fig.3 Flow velocity isograms Fig.4 Secondary flow at duct exit
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4.2 Effects Of Maneuver On Flow Properties
(a) Variation of Angle of Attack ααααFig.5 gives total pressure recovery and flow
distortion index at the duct exit while the angle of
attack α changes from -20° to 30°. It is shown when αis within the range of -20° to 10°, the total pressure
recovery rises quickly (all above 0.98). Obviously the
airflow can enter into the submerged intake more easily
and smoothly as the angle of attack increases so that the
thickness of boundary layer around the missile near the
duct entry becomes thinner. More airflows with
relatively higher dynamic energy move into submerged
intake, cause the total pressure recovery higher. While
the angle of attack increases beyond 10°, total pressure
loses occur. Fig.5 also reveals flow field becomes worse
with the angle of attack being in a range of -20° to -8°.
However, when the angle of attack rises from 0° to 10°,
the flow distortion index decreases. Further observation
is the nonisotropic flow field is quite bad with the larger
angle of attack possibly for the airflow at the intake
entrance moves into the duct with much disturbance.
It can be concluded here that the aerodynamic
configuration of the missile and its submerged air
intake are basically rational, the flow parameters inside
the intake are good in general at Ma=0.28 and α=10°.
(a) ~ (b) DC~
Fig.5 Total pressure recovery and flow distortion index at exit (Ma=0.28)
(a) ~ (b) Dc~
Fig.6 Total pressure recovery and flow distortion index at exit (Ma=0.7)
In case of Ma=0.8, it can be found the flow
parameters are changed obviously while the angle of
attack α reaching about 7°. Fig.6 shows a relation
between total pressure recovery, flow distortion index
and angle of attack α. The later illustrates the index
rises firstly as the angle of attack is at near 7°, then falls
with α increases more.
Compared to those at low subsonic flow
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(Ma=0.28), the total pressure recovery is fairly small,
but distortion index is quite large for high subsonic flow
(Ma=0.7) in case of the same α and β.
(b) Variation of Angle of Sideslip ββββHere flow properties inside submerged air intake at
Ma=0.28, α=0°, but β changed from 1° to 30°, are
shown numerically. Fig.7 shows total pressure recovery
at the duct exit at different angle of sideslip. It can be
found the coefficient reaches 0.988 when β is about 10°,
mainly caused by the free-stream airflow comes into the
entry of the curved duct fairly easily at β= 1° to 10°.
With an increase of β, the coming airflow will produce
the flow separation near the bottom wall of the entry
with large energy loss, thus total pressure recovery will
have a drop, moreover, the flow distortion firstly rises
then falls as β changes from 0° to 30°. The flow field in
the inlet is quite distorted by this separated low energy
flows, see Fig.7(b). Detailed results give that the
airflow with low energy caused by flow separation
moves to another position with non-uniform
distribution for β inferior to 20°. With the larger βrising from 20° to 30°, the larger separated flow occurs
responsible for transverse pressure gradient at the
cross-section.
(a) ~ (b) Dc~
Fig.7 Total pressure recovery and flow distortion index at exit (Ma=0.28)
It can be known from Fig.7 the parameters vary
flatly within β ranges from 1° to 10°. However, as βincreases more than 10°, the parameters change quickly.
It is drawn β is limited to be lower than 10° is quite
good for engine running. Compared to those for
variation of the angle of attack, the change of β has
more influence on flow properties in curved air intake.
(Ma=0.28, =1°, =0°) (Ma=0.7, =1°, =0°)
Fig.8 Wall pressure distribution Fig.9 Wall pressure distribution
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4.3 Wall Pressure Distribution Inside Air Inlet
(a) Effect of Angle of Attack ααααFig.8 shows the pressure distribution along the
intake sidewall at α=1°, β=0°. It is shown the pressure
at the outer wall with a larger curvature radius is higher
than that at the inner wall with a smaller radius
attributed mainly to centrifugal action away from the
inner to the outer. No evidently separated phenomena
occur inside the duct under the above condition.
Considering high subsonic flow (Ma=0.7), Fig.9 shows
the pressure distribution quite different from that in
Fig.8. Pressure gradients along the intake wall in the
longitudinal direction are larger.
(Ma=0.28, =20°, =0°)
Fig.10 Wall pressure distribution Fig.11 Flow velocity Vectors near intake
(b) Effect of Angle of Sideslip ββββThe pressure distribution along submerged intake
wall at Ma=0.28, α=0°, β=20° is illustrated in Fig.10,
also changes flatly near the exit towards the inner wall
for flow separation there, see Fig.11 for the flow
velocity vectors in longitudinal direction.
5. CONCLUSIONS
(a) Twin vortices with counter-rotation occur at the
intake outlet while the missile flies at different angle of
attack. But a single swirl finally appears at the larger
angle of sideslip more than 4°. Angle of sideslip has
more effects than the angle of attack on flow properties
inside the curved duct for both low and high subsonic
flow situations. Additionally aerodynamic character-
ristics at the intake exit change slowly for low subsonic
flow while the angles of sideslip range from 1° to 10°.
(b) No obvious separated flow exists when the angle of
attack is both in -20° to 30° for low subsonic flow and
in 1° to 10° for high subsonic flow. However, flow
separation happens while the angle of sideslip increases
up to 20° so that the flows inside the submerged inlet
become worse.
(c) Appropriate angle of attack and sideslip lie in the
range of 1° and 10°.
REFERENCES
1.Guo Rongwei, Liu Shaoyong, “Design of Submerged
Inlet.”J. of Nanjing Univ. of Aero. & Astro., 2001,33(1):
8~12.
2.Yang Ai-ling, Guo Rongwei, “ Numerical Simulation
of the Flow of Two-dimensional Submerged Air
Intake.” Acta Aeronautica Et Astronautica Sinica, 1999,
20(5): 450~454.
3.Weng Peifen, Guo Rongwei. “Numerical Simulation
of Two-dimensional Separated Flow in Arbitrary
Curved Duct.” J. of Shanghai Jiaotong University,
1993,27(4): 14~18.
4.Taylor A M K P, Whitelaw J H, Yianneskis M.
“Curved Ducts with Strong Secondary Motion: Velocity
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Flow.” J. of Fluids Engineering, 1982, 104: 350-359.
5.Ding Jue, Weng Peifen. “A Study on Theoretical
Models and Flow Characteristics for the Flowfield in
90°°°° Duct.” Chinese Journal of Computational
Mechanics (to be published), 2003.