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A01-16059

AIAA2001-0129Aerodynamic Design of A Medium SizeBlended-Wing-Body Airplane

IE. Pambagjo, K. Nakahashi, S. Obayashi and K. MatsushimaTohoku University, JAPAN

39th AIAA Aerospace SciencesMeeting & Exhibit

8-11 January 2001 / Reno, NVFor permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,

1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.


AIAA-2001-0129

AERODYNAMIC DESIGN OFA MEDIUM SIZE BLENDED-WING-BODY AIRPLANE

Tjoetjoek Eko Pambagjo*, Kazuhiro Nakahashi^ Shigeru Obayashi*, Kisa Matsushima§

Tohoku University, Aoba 01, Sendai 980-8579, Japan

Abstract

This paper presents the aerodynamic designprocess of a Blended-Wing-Body airplane for 200passengers. The wing is designed by usingTakanashi's inverse design method where the targetpressure distributions are specified by using theconstrained target pressure specification technique.RAPID methodology is utilized to obtain a smoothwing surface. This study shows that the combinationof those three design tools works well to design theBlended-Wing-Body airplane configuration.

Introduction

A concept of a Blended-Wing-Body (BWB)airplane was proposed by Liebeck, Page andRawdon^1 for next generation, very large sizetransports. The main advantage of the BWBconfiguration is that its wetted area is smaller than theone of the conventional airplane. The smaller wettedreduction theoretically results in a higher Lift to Dragratio. This wetted area reduction is achieved mainlybecause of the use of streamlined disk fuselage insteadof conventional cylindrical fuselage.

Reference [1] shows that BWB configurationis effective to increase the efficiency of very largeairplane (800 passengers). It is interesting toinvestigate whether the BWB configuration can beapplied to medium size airplane or not. Preferablefeatures of the BWB concept, such as shorter fuselagelength and lower wing loading are attractive for themedium size airplanes. The shorter fuselage lengthwill speed up the loading and unloading process. Itslower wing loading requires only simple high liftdevices, which will reduce the structure complexityand weight.

* Graduate Student, Department of Aeronautics and SpaceEngineering, Tohoku Universityf Professor, Department of Aeronautics and Space Engineering,Tohoku University, Associate Fellow AIAA1 Associate Professor, Institute of Fluid Science, Tohoku University,Member of AIAA§ Lecturer, Department of Aeronautics and Space Engineering,Tohoku University, Senior Member of AIAA

Copyright © 2001 by the American Institute of Aeronautics andAstronautics, Inc. All rights reserved

However, the design of such BWB airplanesbecomes more difficult as the size of the airplanedecreases. In the conventional airplane the primaryfunction of the wing is to produce the lift force. In theBWB configuration the wing has to carry the payloadand provides the necessary stability and control aswell as produce the lift. The fuselage has to create liftwithout much penalty on the drag. At the same timethe fuselage has to keep the cabin size comfortable forpassengers. Furthermore the blending from the thickfuselage into the thin outboard wing should berealized smoothly. These geometrical constrains of thefuselage make it more difficult to design medium sizeBWB airplanes.

Despite these difficulties, medium size BWBairplanes are attractive because of its aerodynamicefficiency. The main objective of the study is toinvestigate whether BWB concept can be applied to anairplane for 200 passengers or not. However, thepresent study focuses on the design process and themethodology for the medium-size BWB configuration.The emphasis is on the aerodynamic design processwhere the authors have been researching to overcomethe difficulties.

Aircraft configuration

In essence a BWB configuration airplane is aflying wing. For a wing alone aircraft configuration,the longitudinal stability requires that the center ofgravity should be located ahead of the aerodynamiccenter. This requirement can be achieved by utilizing asweptback wing. By increasing the sweep angle theaerodynamic center will move further aft and this willcreate a space ahead of the aerodynamic center. Thisspace can be used to carry the payload, which shiftsthe center of gravity more forward. This will increasethe stability by means of making the pitching momentmore positive.

Because the present study focuses on theaerodynamic methodology, the wing sizing isdetermined based on the observation of the wingsizing of the conventional airplane with the samepayload and range capability. We know that in realitywing sizing is determined based on severalrequirements such as, takeoff weight and speed andtakeoff field length. Basically the design of the wingwill be under several disciplines such as weight and

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balance, structure, aerodynamics, flight mechanicsetc.

In the present study the designed constraintsinclude cruise Mach number of 0.8, maximum takeoffweight of 100,000 kg, takeoff speed of 130 knot, andrange around 2000 nm.

The first step of the design process is to specifythe required space to carry the payload. The requiredspace is based on the human measurement, which willaffect their comfort during the flight. The minimumheight at the corner of the passenger's cabin is set to 2meters, while the maximum height depends on theairfoil contour. These requirements result in thickairfoil for the inboard section. The maximumthickness reaches around 15% and it is located in thewing section that connects the passenger's cabin andcargo space. In this section the chord length is shorterthan the center chord length while the required cabinheight is the same, which results in thick airfoil. Therequired cabin floor area is 0.929 m2 area perpassenger includes volume required for eachpassenger's share of galley, lavatories. Weight perpassengers is 80 kg with luggage of 20 kg perpassenger. First the fuselage is design to meet thosespace requirements then the wing is added. The outerwing should have enough space to carry the fuel.Figure 1 shows the design result. Some of itsproperties are displayed in table 1.

many aircraft configurations. At seat pitch of 80 cmthe total passenger becomes 224. Two galleys and fourlavatories are located at the most aft position, whichgive clear forward view for the passengers. Reference2 describes the necessary methods to compute therequired spaces.

In conventional airplanes the payload iscarried inside the fuselage that basically does not orhas little contribution to the lift. In general fuselage isdesigned to be able to load and unload the payloadquickly. In the BWB airplane, payload is carried alsoinside the wing along with cargo and fuel. Passengerscabin and cargo bay are located in the inboard wingwhile the outboard wing is used to carry the fuel.

In comparison to the conventional airplane, thewetted area of the BWB configuration in the presentstudy might be higher. This shows one of thedifficulties of utilizing BWB concept for medium sizeairplanes that is to achieve the wetted area reduction.However, BWB configuration has shorter passenger'scabin that will speed up the loading and unloadingprocess.

Figure 1. Design configuration Figure 2. Design configuration in comparisonto conventional airplane

Wing span 50 mTotal Length 31 mWing Area (trap) 325 m2Wetted Area 1164 m2Aspect Ratio 7.7

Table 1. Configuration's properties

The layout consists of 8 eighteen-abreast seats,1 twelfth-abreast seats, 2 ten-abreast seats, 2six-abreast seats and 3 four-abreast seats. Thepassenger's seat pitch is set at 90 cm, which iscomparable to the business class or even first class in

Figure 2 shows the comparison between aBWB airplane and the typical conventional airplanewith the same payload. The designed BWB airplanewill have 2 engines at the aft center part of the wingalong with the vertical tails. However, in the presentstudy engines and vertical tails are not included in thedesign process.

Aerodynamic Design Tools

BWB configuration has thick inboard wing tocarry the payloads. One of the problems in designingthe BWB configuration airplane is to design theinboard wing. The difficulty is that the wing should

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meet the flow constraints and also provides thenecessary space to carry the passengers. One way tosolve this problem is utilizing the inverse designmethod. One of the most useful inverse design methodis the Takanashi's[3] inverse design method. To realizethe flow constraints and the space requirement, itrequires a method to specify the target pressuredistribution, which satisfies both requirements. Tosolve this problem a constrained target pressurespecification technique as proposed by Campbell[4] isutilized.

Other important requirement of the BWBconfiguration is the surface smoothness. The wingsurface between two known wing sections can becreated by linear lofting method. This is especiallytrue in the case of straight taper wing as commonlyused in the conventional airplanes. However thismethod will be more difficult to be implemented in theBWB configuration design, especially for the inboardwing design.

The BWB configuration has thick inboardwing and thin outboard wing. The blending of thickinboard wing into the thin outboard wing will be quitedifficult to be realized by the linear lofting method.Therefore another method of surface modeling isrequired to create smooth curved surface. Thecurved-surface modeling becomes more important forthe medium-size BWB airplane because of the abruptchange from the inboard to outboard wings.

In the present study the wing is design by usingTakanashi's inverse design method at several designlocations in span wise directions. The target pressuredistributions are specified by constrained targetpressure specification technique. To obtain betterresults in achieving the constraints the target pressuredistributions are modified iteratively during designcycle. After completing the inverse design cycleRAPID(Rapid Airplane Parametric Input Design)[5]

method creates the wing surface between the designedwing sections. RAPID method is applied only tocreate the fuselage surface. The outboard wing surfaceis specified by linear lofting method, because theoutboard wing is similar to the wing of conventionalairplanes. The following sections give briefdescription of the design tools used in this study.

Inverse design method and target pressurespecification technique

Figure 3 shows the general illustration of theinverse design process. In essence the inverse designprocess consist of two primary processes, which areindependent of each other. One is the analysis process,which consists of grid generation and flow simulation,and the other is the design process itself. The flowsimulation solves differential equations, whichdescribes physical phenomena. Any flow simulationcan be utilized. With this arrangement the existingflow analysis still can be utilized, and when there is a

new and more powerful flow analysis becomingavailable then only the flow analysis part need to beupgraded. It is also possibility to utilize wind tunnel asthe flow analysis. The design part consists of thesolutions of inverse problem and the smoothingalgorithms as required.

i Input:v initial geometry

analysis process_!

grid generation

j Solution of Navier |I Stokes equations j

i 1. solution of inverse !/ \i Target pressure^| equation ^Kconverged^n distnbutlon |2. smoothing algonthms ; ! \^ ? // ^ ________,.

design process

Output: I1. design geometry i2. flowfield solution '

Figure 3. Schematic diagram of the inversedesign process

The first step of the inverse design process is todesign the target pressure distribution based on therequired aerodynamic performance. The pressuredifference between the initial and the target forms aninput of the inversely formulated transonic smallperturbation equations. The solutions of the equationsprovide the geometry's correction A/, which are usedto modify the initial geometry to form a new geometry.The flow solutions of this new shape may be obtainedby applying the Navier-Stokes equations. If, afterhaving checked the convergence, the designrequirements are not satisfied, the design cycle isrepeated with the new geometry as the replaced initialgeometry. The process is repeated until the pressuredifferent is minimized.

One of the most useful inverse methodalgorithms is the one developed by Dr. Takanashi[3],which uses the inversely formulated transonic smallperturbation equation. This algorithm findsgeometrical correction value to reduce the differencebetween the target pressure distribution and thecomputed pressure distribution of a given airfoil. Heformulated the inverse design problem to obtaingeometry correction by solving integral equations.These integral equations are the mathematical modelof the relation between the aerodynamic geometry andpressure distribution.

The formulation starts with the smalldisturbance approximation. Next introduces variableA, which represents the different between two states ofthe flowfield. After applying the Prandtl-Glauert



transformation the basic equations become : distribution is divided into several regions bounded byseveral control points as shown in figure 4.

d_dx'

,P

where A: = (p + OA/* and / is thesurface geometry of the wing. '+' and '-' representupper and lower surface respectively. The integralequation is obtained by applying the Green's theoremto equation (1). After performing integral by parts andapplying the divergence theorem to equation (1) yields

X,y,z)=~ f f

where :

Cp

CP'

\ x/c

O U.S. control points

O L.S. control points

Figure 4. Control points definitions

The location of the control points and theirpressure levels are obtained by using two approaches,empirical estimation approach and control pointfitting approach. In empirical estimation approach thecontrols points are developed by using empiricallyderived equations. Control point fitting approach isvery useful to design target pressure distribution basedon the existing airfoil, so the aimed of this approach isto modify the existing pressure distribution. In thecontrol point fitting approach the control pointsinitially are fitted into the existing pressuredistribution and then the pressure level at controlpoints are modified by using equations as used inempirical estimation approach.

To solve the volume integral finite part integralis adopted. Furthermore improper integral and integralby part will be required to solve equation (2). Therelation between the aerodynamic geometry andpressure distribution can be obtained by doing furthercalculus with equation (2). Differentiating both side ofequation (2) with respect to x and z respectively andtake the limit z —> 0 will get A^ and A^z

respectively. In fact AC is associated with A^. and

A/ is associated with A^z . A/* is the geometrycorrections which are used to modify the airfoil shape.

The specification of the target pressure is themost common problem of utilizing the inverse designmethod as practical design tool. The generation of thetarget pressure distribution is based on the requiredaerodynamic performance. However other disciplinein aircraft design may pose additional requirementsthat are usually translated into geometry requirementssuch as the maximum thickness and local thickness.To translate the geometry constraints into pressuredistribution, a method has been developed byCampbell[4]. In this method the pressure distribution isspecified using control points. The pressure

r Input:1̂ initial geometry

analysis process

Initial Target

Solution of NavierI Stokes equations

1. solution of inverse

2. smoothing algorithmserged

^Output :

1. design geometry2. flowficld solution

Figure 5. Schematic inverse design process withautomated target pressure specification

The integrated inverse design processcombined with automated target pressurespecification is shown in figure 5. In this processevery 5-design cycle the current airfoil properties are



compared with the constraints. When the requirementsare not met, the target pressure is modified. Themodification of the control point locations isperformed using perturbation form of the equationsused in the empirical estimation approach.

Surface modeling method

In this study to achieve smooth wing surfacethe wing surface is developed by utilizing RAPIDmethodology. RAPID methodology generates thesmooth surfaces by solving the fourth orderdifferential equation. By using the PDE solution,(0 < £ < 1) x (0 <T] < 1) in computational space istransformed into Euclidean space surfaceX = (x(£,ii),yy;,ri),z(t;,Tj)). The transformations areachieved by solving fourth order partial deferentialequation :

x = o (3)

General periodic solution of the PDE isobtained by letting (o < £ < 1 )-»(o < £ < 2;r ) •The solution of the equation (3) is in the form ofFourier series :

X($9 77) = A, + (An

where :

4) =

4, = anle

K£) + Bn (17) s

(5)

constants obtained by the boundary condition imposedat 77 = 0 and 77 = 1 . The coefficients A0, An and Bn areobtained be applying Fourier Series. After thesecoefficients are computed by using Fourier seriesdefinitions at the boundary then the constant vectorcomponents an4 and bnl, bn2, bn3, bn4

can be obtained by solving the simultaneous linearequations.

The boundary conditions of the equations are :

Dirichlet condition :

Neumann condition :

= D0(Q

= N0(£)

These boundary conditions are :

8rj

5^:

~dn

where x(%, rj), y(£ rj) and z(£ TJ) are the coordinate ofthe wing section relative to the measurementcoordinate axes. X is the jc-coordinate the airfoilrelative to trailing edge (o < x < chord lenght). Thedefinition of section starts from the trailing edge. Thevalue of X has value 0 at the trailing edge andmoving anti clockwise back to trailing edge. Givenbasic wing section, the outer boundary is taken as77 = 0 , while the inner boundary has the value of77 = 1 . jc(£) can be obtained by utilizing therelation :

, where C is the airfoil chord

a. S0 and S} equal to 0

b. S0 = 0.3 and 57 = 0.12

Figure 6. Effect of design parameters S on thesurface shape


S is design parameter, which affects thetransition between the two boundaries. Figure 6 givesan example of the effect of the choice of designparameters S.


the fuselage surface. To create the surfaces, thefuselage is divided into three areas bounded by fourwing sections. The RAPID method is utilized to createthe surface in each area. The parameter S is chosen bytry and error until the desired shape is obtained. Figure7 shows the 3D views of the BWB airplane created byutilizing RAPID method.

Design Result

The author would like to focus on the result ofthe inboard wing design because inboard wing designis much more difficult than outboard wing. Theinboard wing is created using four wing sections atseveral design locations. Those design locations are at0%, 12%, 24% and 40% semi span. At those locationsthe wing sections are obtained by using Takanashi'sinverse design method, then the RAPID methodgenerates the wing surfaces. The target pressuredistribution has been defined based on the designrequirement. For example here are the geometryrequirement of the inboard wing, which can carry thepayload and the pressure load distribution.

The outboard wing is designed also by utilizingthe inverse design method with the main purpose tohave elliptical span loading distribution and to obtainenough space to carry the fuel. The surfaces arecreated by linear lofting method. Although thefuselage and the outboard wing are designedsimultaneously, it is observed that the processconverges faster in the outboard wing. When therequired space to carry the fuel is satisfied, then theoutboard wing is fixed. From that point the process iscontinued only to design the fuselage. This approachis done to reduce the problem with the target pressurespecification in the inboard section. The main purposeof the present study is to design the inboard part asthin as possible without too much penalty on the spacerequirement. The thin wing section in the inboardwing will lead to lower drag.

Figure 7. BWB configuration created by usingRAPID methodology

In this study this method is applied to design

Figure 8. Computational grid



a. 0% semispan

b. 12% semispan

c. 24% semispan

Q- o.oo I _ - _ .p - -*- - -Target

d. 40% semispan

Figure 9. Results of inverse design process.

Initially the target pressure distributions aredeveloped using the control point fitting approach andduring the design process the target pressuredistributions are modified iteratively to meet theconstraints. NASA supercritical airfoil[7] is chosen asthe initial airfoil. The constraint here is limited on themaximum thickness requirement at each designlocations, which are determined based on the spacerequirement. At this phase constraint target pressurespecification technique[4] is very useful. It helpsconstructing the required target pressure distributionthat leads to the desired requirements. Howevermanual adjustment usually is still required.

To evaluate the aerodynamic performance ofthe wing, the Navier-Stokes equations were solvedusing C-H type mesh contains 191x50x49 grid pointsshown in figure 8. The boundary layer on the airfoilwas assumed to be fully turbulent where theBaldwin-Lomax turbulence model is used. TheNavier-Stokes solver[6] adopted the LU-SGS methodfor the time integration and the right hand side issolved by 3rd order upwind scheme. The flowconditions is set at free stream Mach number 0.8,angle of attack at 0 deg., and the Reynolds Number is107.

Figure 9 shows the results of the inverse designprocess at several design locations. It shows that ingeneral the design processes converge to the specifiedtarget pressure distribution. However there are smalldifferences near the leading edge and trailing edge.Figure 10 shows the three airfoils at the designlocation in the fuselage. The passenger's cabin isdesign inside those three airfoils. In this figure thepassenger's cabin is represented by the rectangle. Thisfigure shows that the geometry constrains to obtain thepassenger's cabin are achieved.

Figure 10. Passenger's cabin

Figure 11 shows the pressure contours on bothof upper and lower wing surface, which show that atthe design condition shockwave does not presenteither on the upper or lower wing surface. This isconfirmed by observing the pressure distribution atseveral design locations as shown in figure 12.

Although the current result shows that lift todrag ratio is 18.87, further improvement may stillpossible to increase the efficiency. This also indicatesthat from aerodynamic point of view medium sizeBWB configuration airplanes have comparableperformance with the conventional airplanes.



To reduce the pitching moment, this aft loading shouldbe reduced. Small pitching moment is preferablebecause it will require only a small deflection of theelevator to trim out the airplane during the flight,which reduces the trim drag.

a. Pressure contour of upper wing surfacea. 0% semispan

b. Pressure contour of lower wing surface

Figure 11. Pressure Contour

Future Study

The design tools described in this study havesuccessfully designed the medium BWB airplane.However, the present results indicate that there aresome problems to be settled.

To avoid the presence of the shockwave theouter wing use airfoils that has the typicalcharacteristic of the supercritical airfoil171, which alsogives the most contribution to the lift. Unfortunatelysupercritical airfoil also produces too negativepitching moment due to its aft loading. Pitchingmoment is one of the important requirements for thestability and control especially for BWB configurationwhere horizontal stabilizer does not presence. It isrequired that the pitching moment should be smallenough.

To reduce this effect, the inboard wing shouldhave pitching moment as small as possible. Figure 9shows that the airfoils still have too much aft loading.

b. 12% semispan

c. 24% semispan

Figure 12. Pressure distribution at design locations

Other improvement can be achieved byoptimization of the span loading distribution. Figure13 shows that the span loading for the current design isstill far from elliptical distribution. It is well knownthat elliptical distribution leads to minimum induceddrag. Improving the span loading requires lift

8American Institute of Aeronautics and Astronautics


reduction in the inboard wing. The lift reduction in theinboard wing might be achieved by reducing the aftloading. So, by reducing the aft loading of the inboardwing reduces the pitching moment and can improvesthe span loading distribution.

0.12

0.10

^ 0.08o73 0.06llO 0.04

0.02

0.000.00 0.20 0.40 0.60 0.80 1.00

y/b

Figure 13. Span loading distribution

Conclusion

Aerodynamic design of BWB airplane for 200passengers has been performed by using inversedesign method. The combination of Takanshi'sinverse design method, constrained target pressurespecification technique and RAPID method provide auseful design system for BWB configuration airplane.The RAPID method forms a good tool for generatingwing surface. It has more flexibility to createtransition from one boundary to the other boundary.Constrained target pressure specification technique asproposed by Campbell is very useful to be used in theinverse design process, which works well togetherwith Takanshi's inverse design method. For BWBconfiguration performances improvement by means ofdrag reduction is achieved by reducing the wave dragand thickness reduction.

References

[1]. R.H. Liebeck, M.A. Page and B.K. Rawdon,'Blended Wing Body Subsonic CommercialTransport', AIAA 98-0438, 1998.

[2]. Torenbeek E., 'Synthesis of subsonic AirplaneDesign', Kluwer Academic Publishers, 1999.

[3]. Susumu. Takanashi, 'Iterative Three DimensionalTransonic Wing Design Using Integral Equations',Journal of Aircraft, Vol. 22, No. 8, August 1985,pp. 655-660.

[4]. Richard L. Campbell, 'An Approach toConstrained Aerodynamic Design withApplication to Airfoils', NASA TP-3260,

November 1992.[5]. Robert E. Smith, Malcolm I. G. Bloor, Michael J.

Wilson, Almuttil M. Thomas, 'Rapid AirplaneParametric Input Design (RAPID)', AIAA95-1687-CP, 1995.

[6]. Shigeru Obayashi and Guru P. Guruswamy,'Convergence Acceleration of an AeroelasticNavier-Stokes Solver', AIAA Paper 94-2268,1994.

[1]. Charles D. Harris, 'NASA Supercritical Airfoil, AMatrix of Family-Related Airfoils', NASATP-2969, March 1990.


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