[American Institute of Aeronautics and Astronautics 22nd Applied Aerodynamics Conference and Exhibit - Providence, Rhode Island ()] 22nd Applied Aerodynamics Conference and Exhibit

American Institute of Aeronautics and Astronautics

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Numerical Simulation of Three-Dimensional Flows for Flush Inlet

Jin Gyu Lee* , Suk Young Jung† and Chang Soo Ahn‡ Agency for Defense Development, Daejeon, South Korea

Flush inlet, which has been chosen for modern air vehicles to take advantage of structure compactness and small RCS, gives rise to some aerodynamic problems such as flow separation and distortion due to vortices which deteriorate the performance of both inlet and engine. In this study, pressure recoveries at inlet exit plane were evaluated through numerical analyses of 3D turbulent flow for various inlet shapes and flight conditions. Inlet shape was controlled by changing ramp angle and width of throat, and effects of mass flow rate and angle of attack were investigated.

Nomenclature A = area Aj = flux jacobian formed from the derivatives of Fj with respect to Q c = sound speed Fj = inviscid flux vector Gj = viscous flux vector I = identity matrix

= mass flow rate Pt = total pressure Q = conservation vector Re = Reynolds number t = time variable ξj = curvilinear coordinates ∆t = time step ρ = density M = Mach number Subscripts throat = throat plane exit = aerodynamic interface plane(AIP) ∞ = freestream value ξ, η, ς = differentiation with respect to subscript Superscripts n = time level

I. Introduction NE of the important parameters carefully considered in design of inlet for a air vehicle is how to reduce the radar cross section. Having low observability characteristics, flush inlet has widely been applied some air

vehicles (for examples, the Harpoon missile) in some advanced countries. But it is difficult to find current research studies performed on this type of inlet mounted on the cylinder in the open literature1 although many research activities have been held on so-called NACA submerged inlets starting from early 1940s.2,3 However, this kind of inlet gives rise to some aerodynamic problems; flow separation and distortion due to vortices which deteriorate the performance of both inlet and engine. To achieve maximum engine performance, the duct of inlet has to maximize

* Senior Researcher, Aerodynamics Team, P.O.Box 35-3 Yuseong, Daejeon, 305-600, Korea, AIAA Member. † Senior Researcher, Aerodynamics Team, P.O.Box 35-3 Yuseong, Daejeon, 305-600, Korea, AIAA Member. ‡ Principle Researcher, Aerodynamics Team, P.O.Box 35-3 Yuseong, Daejeon, 305-600, Korea, AIAA Member.

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22nd Applied Aerodynamics Conference and Exhibit16 - 19 August 2004, Providence, Rhode Island

AIAA 2004-5190

Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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the total pressure recovery and minimize the flow distortion at the engine compressor (at the exit of inlet). Therefore, it is necessary to have a numerical investigation on the complex flows of flush inlet at high subsonic speed to evaluate the performance of the design shape in advance before experiment.

The objective of the present study is to investigate the effects of the parameters to performance of flush inlet by numerical simulation. Four parameters affecting the total pressure recovery at the exit of inlet are discussed: mass flow ratio, angle of attack, ramp angle and width of throat (throat aspect ratio).

II. Numerical Methods Three-dimensional turbulent flow was solved using an implicit, approximately factored scheme of Beam and

Warming for the full, compressible RANS equations. The governing equations can be formulated in the conservation law form in the transformed coordinates:

1Re

j j

j j

F GQt ξ ξ

∂ ∂∂ + =∂ ∂ ∂

The implicit, approximately factored scheme of Beam and Warming employed a central differencing and was

written in terms of finite-difference notations as:

( )1nI t A Q RHSξδ ∗∗+ ∆ ∆ =

( )2nI t A Q Qηδ ∗ ∗∗+ ∆ ∆ =∆

( )3n nI t A Q Qζδ ∗+ ∆ ∆ = ∆

1n n nQ Q Q+ = + ∆

The RHS vector was based on a central difference approximation to the governing partial differential equations. For all central difference algorithms, artificial viscosity based on the ideas of Jameson was added implicitly to damp the high-frequency errors. Flow field was assumed fully turbulent and the two-layer algebraic eddy viscosity model of Baldwin and Lomax4 was used in the present computations.

The geometry of a flush inlet mounted on a long ogive cylinder is shown in Figure 1 and this inlet is geometrically similar to NACA submerged inlets. The computational grids were generated using the commercial grid generation program CFD-GEOM. 5 As shown in Figure 2, the grid system included both the external and internal flow regions. The grid consists of approximately 630,000 grid points in 7 blocks, Table 1. The fifth and sixth modeled the duct of the flush inlet and the annular circular pipe of the last represented an entrance of engine compressor located downstream of the inlet. The external grid was fairly coarse and the mesh was packed to the solid wall and the distance to the first mesh point from the wall was controlled so that the y+ value at the leading edge of a inlet was equal to 0.01. Taking advantage of the x-y plane of symmetry, one half of the flow domain was analyzed.

Y

Z

X

Figure 1. Geometry of a flush inlet.


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Z X

Y

zone 7

zone 1 zone 2zone 3

zone 4

zone 5

zone 6

Figure 2. Flow domain for computational grid

Table 1. Computational grid

Block Region Grid points 1 External 88,218 2 External 88,218 3 External 62,361 4 External 16,400 5 Internal 93,480 6 Internal 150,100 7 Internal 135,564

Total 634,341

No slip condition was imposed at solid wall and characteristic boundary condition using Riemann invariant was applied at far-field. Mass flow rate at the exit of inlet was specified according to flow condition. All internal flow variables were initialized by setting them as values at throat plane which were analytically calculated using one-dimensional isentropic relationship.

The L2 residual as well as the back pressure at the exit of inlet were monitored for convergence. Approximately 20,000 iterations were required to acquire converged solution with a CFL number of 1.5. During the last 1,000 iterations, no appreciable change was observed in the flow field.

III. Results and Discussion In this paper, the performance of the flush inlet was described by total pressure recovery at the exit plane of inlet

with flow conditions such as mass flow ratio. Total pressure recovery (PR) was evaluated using area weighted averaging, which was defined as:

1PR texitt exit

P dAP A∞

= ∫

The ramp planform of a flush inlet in this study has the curved divergent shape which turned out to give the higher pressure recovery from previous investigations.2 Figure 3 shows the surface pressure distribution on the ramp.

Figure 3. Pressure coefficient contour (α=5.0o, MFR=0.87).


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The favorable pressure gradients at the forepart of inlet are helpful to induce flow into the flush inlet. The point to note is that pressure at divergent ramp walls varies more rapidly than one on the floor. This phenomenon is caused by roll-up vortices. As the flow moves further downstream, a pair of counter-rotating roll-up vortices emanate from the ramp walls due to a rapid change of pressures from favorable to adverse and enter the duct of inlet. Therefore, the flow in duct of a flush inlet is fully three-dimensional and involves interactions between the viscous effects and a pair of vortices, generated around ramp walls.

The effects of following parameters to performance of a flush inlet were investigated: 1) Mass flow ratio 2) Angle of attack 3) Ramp angle 4) Width of throat (throat aspect ratio).

A. Mass Flow Ratio Calculations were made over a range of mass flow ratio (MFR) for the flush inlet with ramp angle of 7.0o. Mass

flow ratio is defined as:

MFR

M throat throat

Amc A Aρ

∞

∞ ∞ ∞

= =×&

Figure 4 represents the computed pressure recoveries against various mass flow ratios. In general, the pressure

recovery was raised when the mass flow ratio was increased. But at higher mass flow ratio greater than 0.89, the adverse effect resulted from the interaction between the boundary layer and vortex. There are three important sources decreasing the pressure recovery: (1) the boundary layer on the ramp floor, (2) the boundary layer on the upper surface of the duct, and (3) the vortex cores. The trend shown in Figure 4 was caused by the location of vortex core moving away from the upper surface of the duct and then, the boundary layer growing near the upper surface. In Figure 5, the low velocity region in the boundary layer corresponded to low total pressure region. The effect of the boundary layer on the ramp floor was weak in this case because the downwash in vortex flow suppress boundary layer and made it thinner. With this information a detailed survey of variation of pressure losses at the exit of inlet according to mass flow ratio was carried out to optimize a flush inlet.

B. Angle of Attack Figure 6 illustrates that the pressure recovery is raised by

Mass Flow Rate(M.F.R.)

Pressure

Recovery

0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00

α=1o

α=5o

Figure 4. Pressure recovery at the exit of inlet for each mass flow ratio

1.000.970.940.910.890.860.830.800.770.740.710.690.660.630.60

Total

Pressure

(Pt/Pt∞)

1.000.970.940.910.890.860.830.800.770.740.710.690.660.630.60

Total

Pressure

(Pt/Pt∞)

Figure 5. Comparison of total pressure distribution at the exit of inlet (MFR=0.89 [left-hand], 0.99 [right-hand]).

α(angle of attack)

Pressure

Recovery

-5.0 -2.5 0.0 2.5 5.0

Ramp Angle 0O, MFR=0.87

Figure 6. Pressure recovery at the exit of inlet for MFR=0.87.


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increasing the angle of attack. In practice, as the angle of attack increases, the flow can enter the flush inlet more easily and the boundary layer thickness on the cylinder surface near the entrance of inlet becomes thinner and the flow with relatively higher energy can be ingested into the inlet. These trends shown in Figure 7 can be.

In Figure 8, the low energy region seen at the exit of inlet gets fewer as the angle of attack increases, even if the streamline pattern at the exit of inlet are similar in all cases. These results suggest that if the ramp planforms of the flush inlet are identical, the angle of attack has few effects on the flow pattern such as the location of the vortex core.

Y

Z

X

1.000.960.930.890.860.820.790.750.710.680.640.610.570.540.50

Total Pressure(Pt/Pt∞)

(a) α = -5.0o

Y

Z

X

1.000.960.930.890.860.820.790.750.710.680.640.610.570.540.50


(b) α = 0.0o

Y

Z

X

1.000.960.930.890.860.820.790.750.710.680.640.610.570.540.50


(c) α = 5.0o

Figure 7. Total pressure contour (MFR=0.87)


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C. Ramp Angle The results given in Figure 9 were obtained from

computation with two flush inlet of which ramp angles are 0.0o and 7.0o, respectively and computation has MFR of 0.87. While increasing the ramp angles from 0.0o to 7.0o, the angle between the divergent walls as shown in Figure 10 of both cases set to be same as well as the shape of throat and cross-sectional area. There was only the geometrical change in ramp floor. From the calculated results, a ramp angle of 7.0o gave the higher pressure recovery over all angle of attack.

D. Width of Throat (Throat Aspect Ratio) The effect of varying the width of throat is given in Figures 11 and 12 for a constant ramp angle of 7.0o and

MFR of 0.89. The pressure recovery becomes higher as the throat gets wider while throat area is kept to be constant. Owing to extension of throat width, the divergent angle of ramp walls was increased and the height of throat became low. The vortex generated along ramp walls separated early and became stronger due to divergent angle increase. As the roll-up vortex moves downstream in the duct, the downwash of the vortex results in thinning the boundary layer

1.000.970.940.910.890.860.830.800.770.740.710.690.660.630.60

Total

Pressure

(Pt/Pt∞)

1.000.970.940.910.890.860.830.800.770.740.710.690.660.630.60

Total

Pressure

(Pt/Pt∞)

1.000.970.940.910.890.860.830.800.770.740.710.690.660.630.60

Total

Pressure

(Pt/Pt∞)

(a) α =-5.0o (b) α = 0.0o (c) α = 5.0o

Figure 8. Comparison of total pressure distribution and streamline at the exit of inlet (MFR=0.87).

α(angle of attack)

Pressure

Recovery

-5.0 -2.5 0.0 2.5 5.0



Figure 9. Pressure recovery for each ramp angle (MFR=0.87).

7O

0O

Ramp Angle0o

7o

(a) profile of ramp floor (b) profile of ramp planform

Figure 10. Geometrical change with ramp angle


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on the ramp floor. And this interaction between them is stronger when the distance between vortex and boundary layer is narrower. Also increasing width of throat, the shape of throat is closer to a square entry section which is more suitable to the diffuser. Therefore, the extension of throat width is necessary for maximum pressure recovery.

The effects of parameters to performance of flush inlet

are summarized in Figure 13. Comparisons of pressure recovery for several configurations provide useful information to determine the geometrical parameters of flush inlet. The aspect ratio of throat and the ramp angle are seen to be important because they strongly affect interference strength between the boundary layer on ramp floor and a pair of vortices from divergent ramp walls.

IV. Conclusion In present paper, effects on the performance of flush inlet were investigated numerically. The conclusions from

these analyses are as follows.

Width Ratio(Wthroat/Wexit)

Pressure

Recovery

0.75 0.80 0.85 0.90 0.95 1.00 1.05

α=1o

α=5o

Figure 11. Pressure recovery at the exit of inlet for each width ratio (wthroat/wexit)

1.000.970.940.910.890.860.830.800.770.740.710.690.660.630.60

Total

Pressure

(Pt/Pt∞)

1.000.970.940.910.890.860.830.800.770.740.710.690.660.630.60

Total

Pressure

(Pt/Pt∞)

1.000.970.940.910.890.860.830.800.770.740.710.690.660.630.60

Total

Pressure

(Pt/Pt∞)

1.000.970.940.910.890.860.830.800.770.740.710.690.660.630.60

Total

Pressure

(Pt/Pt∞)

(a) wthroat /wexit = 0.79 (b) wthroat /wexit = 0.87 (c) wthroat /wexit = 0.95 (d) wthroat /wexit = 1.00

Figure 12. Comparison of total pressure distribution at the exit of inlet (MFR=0.89)

Divergent ramp walls angle

Height of throat

Throat aspect ratio Ramp angle

Mass flow across ramp walls

Strength of vortex

Separation length on ramp floor

Improvement of internal

momentum transfer

Total pressure recovery

Divergent ramp walls angle

Height of throat

Throat aspect ratio Ramp angle

Mass flow across ramp walls

Strength of vortex

Separation length on ramp floor

Improvement of internal

momentum transfer

Total pressure recovery

Figure 13. Schematic diagram of interference in flush inlet’s performance


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The throat aspect ratio was found to be a parameter to design the shape of flush inlet. Extending the width of throat had the same effects with increasing divergence angle of the ramp walls. Vortex early separated from ramp walls resulted in thinning boundary layer on the ramp floor so that the flow having higher energy was delivered to the exit cross section of inlet.

Comparison between the calculated and experimental data is necessary to verify the computational study.

Acknowledgments The CFD effort of this work was prepared under missile aerodynamic branch, ADD. Dr. S. K. Hong provided

valuable assistances.

References 1Taskinoglu, E., and Knight, D., “Numerical Analysis of Submerged Inlets,” AIAA Meeting Paper 2002-3147, 2002. 2Sacks, A. H., and Spreiter, J. R., “Theoretical Investigation of Submerged Inlets at Low Speed,” NACA TN-2323, 1951. 3Mossman, E. A., and Randall, L. M., “An Experimental Investigation of the Design Variables for NACA Submerged Duct

Entrances,” NACA RM-A7I30, 1948. 4Baldwin, B. S., and Lomax, H., “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA

Meeting Paper 78-257, 1978. 5CFD Research Corporation, Huntsville, AL, CFD-GEOM User’s Manual, 2002.

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[American Institute of Aeronautics and Astronautics 22nd Applied Aerodynamics Conference and Exhibit - Providence, Rhode Island ()] 22nd Applied Aerodynamics Conference and Exhibit