evaluation of delta wing effects on the stealth ... · about radar cross section (rcs) and...

EVALUATION OF DELTA WING EFFECTS ON THESTEALTH-AERODYNAMIC FEATURES FORNON-CONVENTIONAL FIGHTER AIRCRAFT

Pedro David Bravo-Mosquera∗, Alvaro Martins Abdalla∗ , Fernando Martini Catalano∗∗ Department of Aeronautical Engineering, São Carlos Engineering School, University of São

Paulo, Brazil

Keywords: RCS, Delta wing, Wave drag, CFD

Abstract

Survivability and maneuverability have becomethe major design factors in the development offuture military aircraft with stealth ability. Theintake fully integrated into the fuselage com-bined with an S-duct diffuser provide line-of-sight blockage of the engine blades, satisfyingthe requirement of low signature, lightweightand low drag for the next generation of air-craft. This paper aims to provide an insightabout radar cross section (RCS) and aerodynam-ics of several delta platforms that would helpthe need and amount of RCS suppression to es-cape detection from surveillance radars and re-duce wave drag. The stealth characteristics weremodeled using POFACETS software, which en-abled the prediction of the RCS targets using tri-angular facets. The aerodynamic characteristicswere evaluated through the investigation of thewave drag phenomena of each delta platform, us-ing a linearized mathematical model to interceptthe aircraft cross sectional area regarding the an-gle of the Mach cone produced. These resultswere compared with computational fluid dynam-ics (CFD) simulations, which were performed us-ing Reynolds-Averaged-Navier-Stokes (RANS)equations, coupled with the Shear Stress Trans-port (SST) turbulence model. Results showedthat the stealth and aerodynamic characteristicsof a non-conventional fighter aircraft can be opti-mized through integration analysis processes.

1 General Introduction

The conception of non-conventional fighter air-craft with the aim of achieving a certain perfor-mance or operational improvement is undoubt-edly, one of the most important objectives ofthe aeronautical engineering. These improve-ments involve: drag reduction, radar cross sec-tion (RCS) reduction, noise reduction, shorten-ing of take-off and landing distances, increaseof aerodynamic efficiency, armament weight in-crease, among others. Therefore, the analy-sis of delta platforms effects on the stealth-aerodynamic characteristics are essential to up-grade the conceptual design of this kind of air-craft.

During the design of a fighter aircraft, thereare different techniques to reduce the RCS; themost common is by modeling the surface of theaircraft in such a way that radar waves be dis-persed away from radar receiver. However, its ex-ceptional form, manufactured by flat boards, areaerodynamically unstable [1]. For that reason, inthis work was considered another approach to air-craft design, which refers to the use of a thin air-foil and a tailless delta wing design, with a topmounted intake and single vector engine hiddenwithin the fuselage, highlighting a smooth com-bination of the external surfaces and improvingthe survivability and maneuverability aircraft ca-pabilities.

The delta platform study continues to be a

1

BRAVO-MOSQUERA, P. D. ABDALLA, A. CATALANO, F.

subject of interest for most aircraft designers, dueto its advantages of significant reduction in struc-tural weight, drag, and cost. The weight reduc-tion and drag over traditional aircraft is achievedby eliminating the empennage surface. There-fore, the cost reduction comes by virtue of theimproved lift to drag and consequently reducedfuel consumption [2].

This paper conducts studies of theoreticalmodels developed for the purpose of demonstrat-ing the importance of the shape in the RCS andwave drag of a non-conventional aircraft. Theconfigurations have the same airfoil, fuselagelength and intake location, however, five differ-ent delta platforms were designed in order to de-termine the configuration that best adjusts to themission constraints, performing an equilibriumbetween low RCS and aerodynamics.

2 Delta wing platforms

Delta wings suffer from some undesirable char-acteristics such as notably flow separation athigh angles of attack (swept wings have sim-ilar problems), and high drag at low speeds[3]. This originally limited them primarily tohigh-speed, high-altitude interceptor roles. Sincethen the delta design has been modified in dif-ferent ways to overcome some of these prob-lems. These include: Ogival delta wing, Stan-dard delta with LEX (Leading Edge Extensions),Compound delta wing, Canard delta wing, Dou-ble delta wing (Fig. 1).

In this paper, the RCS of several planformshapes of delta wings are studied, when the plan-form has the same reference area, the same airfoilat a constant angle of Attack and wing dihedralangle at zero degrees. To ensure this, the AspectRatio (AR) and taper ratio (λ) are varied so thatall the examples have an equal area but are rep-resentative of the actual airplanes. It should benoted that conceptual 3D digital models are de-signed in SOLIDWORKS software.

The non-conventional fighter aircraft concep-tually designed for this article is a kind of oper-ational aircraft with a single seat, single vectorengine and dorsal intake configuration, since this

Fig. 1 Delta wing planform: (a) Ogival delta, (b)Standard delta with LEX, (c) Compound delta,(d) Canard delta, (e) Double delta.

configuration represents a low radar signature byintegrating the engine into the aircraft using anS-duct diffuser, which prevents direct radar line-of-sight to the engine face. (Table 1).

Table 1 Basic parameters of the conceptual design.Parameter ValueLength 14.6 mHeight 4.5 mMTOW 14000 kgEmpty weight 6600 kgWeapons weight 4000 kgRange 3000 kmService ceiling 16500 mWing loading 415 kg/m2

T/W ratio 0.92Engine Pratt & Whitney F100-229Main airfoil wing NACA64a204

More specific details are found in Bravo-Mosquera [4].

3 Radar cross section

The RCS is a measure of the ability of a targetto reflect radar energy, affecting the maximumrange at which this target is detected by a radarset [5]. Concerning monostatic radars, RCS canbe defined as the power scattered from a targetto a certain direction, when the target is illumi-

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EVALUATION OF DELTA WING EFFECTS ON THE STEALTH-AERODYNAMIC FEATURES FORNON-CONVENTIONAL FIGHTER AIRCRAFT

nated by electromagnetic radiation [6, 7]. There-fore, a larger value of this measure means highdetectability by radar. Summarizing into a singleterm, monostatic RCS, in terms of electric fieldis:

σ = limr→∞

4πr2 | ES |2

| EI |2(1)

where r is the distance between the target andthe radar, ES and EI are the scattered and incidentelectric fields, respectively.

The Eq. 1 is valid when the target is illumi-nated by a plane wave. It should be noted thatRCS values must be in square meters. However,due to the large range of values, it is usually givenin a decibel scale. The conversion of scales canbe presented as Eq. 2.

dBSm = 10log(

σ

1m2

)(2)

Radar cross section is a function of many fac-tors which include the target configuration and itsmaterial composition, frequency or wavelength,transmitter and receiver polarizations, and the tar-get aspect (angular orientation of the target) rela-tive to the radar [8].

3.1 POFACETS software application

The POFACETS code is a MATLAB applicationbased on the Physical Optics (PO) method to pre-dict the RCS targets (3D CAD models) using tri-angular facets [8].

PO is a high frequency approximation thatprovides adequate results for electrically largetargets, in the specular direction, by approximat-ing the induced surface currents. The PO currentsare integrated over the illuminated portions of thetarget to obtain the scattered far field, while set-ting the current to zero over the shadowed por-tions. Since the current is set to zero at theshadow boundary, the computed field values areinaccurate at wide angles and in the shadow re-gions. Furthermore, surface waves, multiple re-flections and edge diffractions are not taken intoaccount. However, the simplicity of this ap-proach ensures low computational overhead [9].

Table 2 No. of cells for the different delta wingplanform.

Delta wing Area [m2] No. of cells at 10 GHzOgival 34.27 13549LEX 34.12 13254Compound 34.10 12459Canard 34.01 11509Double 34.35 11492

In this paper, a two-step approach is proposedin order to predict the RCS for each configura-tion. Firstly, a 3D model of the targets are createdand refined according to available data, i.e. fuse-lage length, intake position and wing planform.Then, the POFACETS code is employed.

For any signature shape, the low observabilityof aircraft depends on the wavelength. Therefore,it is one of the factors that determine the area ofthe radar cross-section. This work only calculatesRCS considering high frequencies. The reasonof this is that radar operating in L-band (lowerfrequencies) produces wavelengths with compa-rable size to the aircraft itself and should exhibitscattering in the resonance region rather than theoptical region [10].

3.2 Model description

Five aircraft of different delta wing shape aremodeled in SOLIDWORKS and discretized intriangular facet surfaces using the ACIS Solidsmodule of POFACETS. (see Fig. 2).

Table 2 lists the number of surface cells usedfor discretization for the surface area considered.

The main objective is to study the RCS mea-surements which aim to determine effective arearesponsible for backscatter when hit by a radarwave. In this way, some assumptions are re-quired. As the radar is only monostatic case,the target is involved with the high frequency (X-Band) range.

Based on the assumptions described above,the frequency bands chosen in this analysis fol-low the guidelines of the Federal Radar SpectrumRequirements [11].

On the polar coordinates of the RCS charac-

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Fig. 2a. Ogival delta.

Fig. 2b. Standard delta with LEX.

Fig. 2c. Compound delta.

Fig. 2d. Canard delta.

Fig. 2e. Double delta.

Fig. 2 Triangular facet surface scheme of deltawing planform.

teristics, the azimuth angle (Θ) is set between 0o

to 180o. The elevation angle (Φ) is set at 0o in or-der to nearby RCS analysis in front of the aircraft.It should be noted that no special materials wereused in the coating of the configurations, there-fore, materials application to reduce wavelengthis beyond the scope of this research.

4 Wave drag estimation

The wave drag of the configurations was calcu-lated based on the method proposed by Raymer[12]. This uses several empirical tools and takesinto account both, the wing and fuselage dimen-sions using a plane average method and Machcone method [13]. The following steps are fol-lowed to obtain the areas to calculate the wavedrag.

• Use Computer Aided-Design tools to cre-ate the configurations.

• Create Mach cone planes defined by its re-spective Mach angle.

• Intersect the geometry of the configura-tions with the Mach cone planes regardingthe direction of flight (Fig. 3).

Fig. 3 Mach cone plane intersection with aircraftgeometry.

• Normalize the obtained area by the inter-section of the configurations with the Machcone plane.

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• Create a point in the Z-direction in orderto obtain the profile of the area distributionat each section of the models, as shown inFig. 4.

Fig. 4 Effective Mach cone area distribution fordifferent Mach numbers ranging from 1 to 2.

• Calculate the wave drag coefficient (CDW )in relation to the area distribution obtained.

For preliminary wave drag analysis atMach ≥ 1.2, a correlation to the Sears-Haackbody wave drag is presented in Eq. 3.

CDW = EWD

[1−0.386(M−1.2)0.57

(1− πΛ0.77

LE100

)]· · ·

· · ·(

Dq

)Sears−Haack

(3)where EWD is defined by the correlation be-

tween the aircraft and the Sears-Haack bodywave drag; also known as empirical wave dragefficiency factor. ΛLE is the wing leading edgesweep angle, given in degrees, and (D/q)wave isthe minimum possible wave drag for any closed-end body of the same length and total volume,given by Eq. 4.(

Dq

)wave

=9π

2

(AMAX

l

)2

(4)

where AMAX is the maximum cross-sectionalarea, determined from the aircraft volume-distribution plot, and l is the overall aircraftlength.

Based on Hayes [15], the shock wave dragfor bodies immersed in transonic speeds only de-pends on the longitudinal area distribution of thesystem as a whole. Therefore, the Theodore von

Kármán formula for slender bodies of revolution(Eq. 5 ) was used for Mach between 0.8 to 1.2.

CDW =ρV 2

4π

∫ x0

−x0

∫ x0

−x0

S′′(x)S

′′(x1)Log|x− x1|dxdx1 (5)

where S(x) represents the cross-sectionalarea intercepted by a perpendicular plane to thefreestream, at a distance x from the tip of thebody.

5 CFD approach

CFD Simulations were carried out using thecommercial code ANSYS-FLUENT, whichsolves the compressible Reynolds-Average-Navier-Stokes (RANS) equations using a 2ndorder finite volume scheme. The solver uses theShear Stress Transport (SST) turbulence modelfor all of the simulations. For the computationaldomain, no-slip adiabatic wall boundary condi-tions are imposed on the solid walls. Specifiedinlet velocities are imposed at inlet boundaryregarding the flying Mach. The outlet conditionwas imposed with no pressure gradient and wallswere set as non-friction (ideal) walls.

Multi-block structure mesh is generated byMeshing ANSYS ICEM-CFD software. Figure5 shows a detail view of the surface grids aroundthe configurations. A series of grid with increas-ing resolution is used to determine the grid sen-sitivity involved in the numerical study. The finalgrid of 5.8 million elements is adopted in the sub-sequent numerical analysis.

Fig. 5 Mesh structure for delta wing configura-tions: (a) Ogival delta, (b) Standard delta withLEX, (c) Compound delta, (d) Canard delta, (e)Double delta.

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6 Results and Discussion

In this section, results are divided in two subsec-tions. First, the RCS analysis is presented anddiscussed. Then, the analytic wave drag estima-tion is compared to CFD simulations.

6.1 Radar cross section

The monostatic RCS is computed, where trans-mitter and receiver are co-located. As mentionedabove, configurations are approximated by arraysof triangles (facets), and the scattered field ofeach triangle is computed as isolated. Multiplereflections, edge diffraction and surface wavesare not considered. All parameters are set to de-fault values, unless otherwise specified.

The RCS of the configurations was computedfor a radar transmitting at 10 GHz (X-Band), em-ulating a typical aircraft fire control radar. TheRCS pattern shown in the following figures cor-responds to polar plot of all RCS configurations,observed from the same level (Θ ranging from 0o

to 180o and Φ set at 0o).The configuration with lowest RCS signature

was the standard delta with LEX, with values be-tween -10 and 40 dBsm (see Fig. 6). In this polarplot, it is observed that the peaks occur in 0 and180 degrees with a signature of 40 dBsm. In thesame way, in the region between 100 and 120 de-grees, the RCS value was 10 dBsm. For otherregions, the RCS signature goes down to valuesclose to -10 dBsm.

On the other hand, the Double delta configu-ration presents its maximum peaks at 0 and 180degrees of around 55 dBsm and, in the region be-tween 100 and 120 degrees with value around 12dBsm. For other regions, the RCS signature goesdown to values close to 0.0 dBsm (see Fig. 7).

Finally, Ogival delta (8), Compound delta (9)and Canard delta (10) presented similar signa-tures, with peak values at 0 and 180 degrees ofaround 55 and 60 dBsm. Furthermore, for 20 and160 degrees, the average RCS signature was 20dBsm.

Since all configurations have the same fuse-lage, dorsal intake and vertical empennage, the

explanation of the RCS signature reduction forthe Standard delta with LEX and Double delta isdue to the planform of the configurations. Notethat Standard delta with LEX and Double deltahave different leading edges sweep, which en-hances survivability by the non-uniform fringesurfaces. By last, canards can potentially havepoor stealth characteristics due to their large andangular surfaces that tend to reflect radar signalsforwards.

Fig. 6 LEX configuration, RCS characteristic curve.

Fig. 7 Double configuration, RCS characteristiccurve.

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Fig. 8 Ogival configuration, RCS characteristiccurve.

Figure 11 shows the linear plot of the RCSanalysis, where are compared all the configura-tions tested. This figure allows to verify that forthis specific case, the standard delta with LEXwas the configuration with the lowest RCS signa-ture. However, for more accurately results, it isstill necessary to evaluate more azimuth and ele-vation angles on each configuration.

Table 3 summarizes the results obtained inthe RCS analysis.

Table 3 RCS signature results.Delta wing RCS min-max [dBsm]Ogival 20 - 55LEX -10 - 40Compound 20 - 60Canard 20 - 60Double 0 - 55

6.2 Wave drag estimation

In this section, the analytical wave drag calcu-lations are compared to CFD simulations. Fig-ure 12 shows the wave drag coefficient (CDW ) infunction of Mach number, between the analyti-cal model presented and the CFD simulation forthe five configurations evaluated. It was observedthat for Mach = 1, the analytical CDW were higher

Fig. 9 Compound configuration, RCS character-istic curve.

Fig. 10 Canard configuration, RCS characteristiccurve.

Monostatic Angle, θ [Deg]

0 50 100 150

RC

S [

dB

sm]

-20

0

20

40

60

80Ogival

LEX

Compound

Canard

Double

Fig. 11 Comparison of linear plot, RCS charac-teristic curves.

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than CFD. However, for Mach > 1, the analyticalCD were reduced considerably.

These results are likely a product of the im-precision of the analytical calculations to eval-uate wave drag coefficients in transonic veloc-ities. Nevertheless, the CFD wave drag valueswere higher for supersonic velocities, mainly dueto the CFD simulations allowed to create condi-tions closer to reality, at which not only the crosssection is considered, whereas also the compress-ibility effects. Meanwhile, it was observed thatboth curves presented the same behavior, wherethe average margin of error for the five configu-rations in the six velocities evaluated was 1.93%,which allowed to conclude that the analyticalmodel developed were reliable.

The analytical wave drag comparison for thefive configurations tested are depicted in Fig. 13.It is evident that the Ogival delta configurationpresents a reduced wave drag coefficient at Mach= 1. However, for Mach = 2, the wave drag coef-ficient is increased. This result is a consequenceof the relative increase of the cross-sectional areaof the Ogival configuration with the Mach coneplane. LEX and Compound configurations arethe models with the lowest wave drag at all eval-uated velocities. However, Canard and Doubledelta configurations presented the highest wavedrag values.

Finally, similar results were obtained in thenumerical wave drag comparison for the five con-figurations (see. Fig. 14).

7 Conclusions

In the present research, the stealth and aerody-namic characteristics of five delta wing configu-rations in the same aircraft geometry were ana-lyzed.

The main results suggested that stealth-aerodynamic characteristics of the non-conventional fighter aircraft can be based onthe analysis process of the integration of stealthaircraft conceptual design and aerodynamicanalysis.

The RCS calculations presented adequate re-sults for preliminary stealth studies. However,

Mach number 1 1.2 1.4 1.6 1.8 2

CD

W

0.01

0.02

0.03

0.04

0.05Analytical

Numerical

Fig. 12a. Ogival delta.

Mach number 1 1.2 1.4 1.6 1.8 2

CD

W

0.01

0.02

0.03

0.04

0.05Analytical

Numerical

Fig. 12b. Standard delta with LEX.

Mach number 1 1.2 1.4 1.6 1.8 2

CD

W

0.01

0.02

0.03

0.04

0.05Analytical

Numerical

Fig. 12c. Compound delta.

Mach number 1 1.2 1.4 1.6 1.8 2

CD

W

0.01

0.02

0.03

0.04

0.05Analytical

Numerical

Fig. 12d. Canard delta.

Mach number 1 1.2 1.4 1.6 1.8 2

CD

W

0.02

0.04

0.06Analytical

Numerical

Fig. 12e. Double delta.

Fig. 12 Wave drag coefficient comparison, ana-lytical and numerical methods.

Mach number

1 1.2 1.4 1.6 1.8 2

CD

W

0

0.02

0.04

0.06 Ogival

LEX

Compound

Canard

Double

Fig. 13 CDW Vs Mach number, analytical calcu-lations.

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Mach number

1 1.2 1.4 1.6 1.8 2

CD

W

0.01

0.02

0.03

0.04

0.05Ogival

LEX

Compound

Canard

Double

Fig. 14 CDW Vs Mach number, numerical simu-lations.

more azimuth and elevation angles are still nec-essary for a detailed analysis of the presenteddesigns. On the other hand, the aerodynamicanalysis has been successfully used to evaluatethe aerodynamic drag of transonic and supersonicvelocities.

In short, following the obtained results, theStandard delta wing with LEX was the config-uration with the lowest RCS signature. Like-wise, this configuration presented adequate aero-dynamic characteristics when comparing the an-alytical and numerical models.

Acknowledgments

The authors express their gratitude to MariaLuisa Bambozzi de Oliveira and Roberto GilAnnes da Silva, members of the evaluation Juryof the masters degree dissertation of Bravo-Mosquera P. D.

The authors are thankful to CAPES (Coorde-nação de Aperfeiçoamento de Pessoal de NívelSuperior) for the scholarship granted.

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8 Contact Author Email Address

mailto: [email protected]

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