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:pfweng@mail.shu.edu.cn

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

5American Institute of Aeronautics and Astronautics

(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

Measurements of Developing Laminar and Turbulent

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.