American Institute of Aeronautics and Astronautics
OPTIMIZATION OF HIGH-SUBSONICBLENDED-WING-BODY CONFIGURATIONS
Abstract
A study explored the design of Blended-Wing-Body(BWB) aircraft at high subsonic speeds, pushing theBWB from 0.85 to 0.95 Mach number. The WingMultidisciplinary Optimization Design (WingMOD)code was calibrated to Navier-Stokes computationalfluid dynamics (CFD) data and then used to optimize aseries of BWB configurations to show performancetrends with increasing Mach number and range. AMach 0.93 configuration from WingMOD was furtherdeveloped and analyzed with CFD. Except thatpropulsion airframe interference was not assessed, theresults show that a Mach 0.93 BWB is feasiblealthough it pays a performance penalty relative to Mach0.85 designs. A Mach 0.90 BWB may be the bestsolution in terms of offering improved speed withminimal performance penalty.
Introduction
By integrating the functions of wing and fuselage, theBlended-Wing-Body (BWB) achieves a cleanaerodynamic and efficient structural design that offerstremendous potential for reduced fuel burn, weight, andcost (Refs. 1-3 and Fig. 1). With the announcement ofthe Sonic Cruiser, a 0.95 to 0.98 Mach numberconfiguration, Boeing expressed a new emphasis onincreased speed. While the BWB had previously beenstudied as a Mach 0.85 configuration, the new emphasismotivated a study to determine if the advantages of theBWB could be maintained at higher speeds.
A source for optimism was the fact that the BWB isnaturally area ruled. This can be seen by examining thearea distribution of the BWB, shown in Fig. 2, alongwith the area distributions of the minimum wave dragSears-Haack body and a conventional wing andfuselage airplane. The BWB area distribution is similar
* Engineer/Scientist Specialist† Principal Engineer/Scientist, Senior Member AIAA‡ Associate Technical Fellow, Associate Fellow AIAA
in shape to that of the Sear-Haack body, but shifted aft.By comparison, the conventional airplane has a verynon-smooth area distribution, making a sudden breakwhere the wing meets the fuselage. The wave drag of abody is defined by the equation
∫ ∫ −′′′′≈
1
0
1
00
1log)()(
2
1 ξξ
ξπ
dxdx
SxSq
D
This equation shows that wave drag varies with thesecond derivative of cross sectional area, thus breakslike those in the conventional airplane distributionwould result in higher wave drag than the BWB. When
Richard Gilmore* Sean Wakayama† Dino Roman‡
The Boeing Company The Boeing Company The Boeing CompanyLong Beach, CA 90807 Long Beach, CA 90807 Long Beach, CA 90807
Fig. 1 Blended-Wing-Body.
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ax A
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MD11
Fig. 2 Area distribution.
9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization4-6 September 2002, Atlanta, Georgia
American Institute of Aeronautics and Astronautics
conventional aircraft are designed to travel at highsubsonic or supersonic speeds, they often use an arearuled fuselage. This modification results in amanufacturing cost penalty associated with changingfrom a pressure vessel with constant cross section toone with varying cross section. Since the BWB isalready area ruled, there is no additional cost penaltyfor changing the character of the pressure vessel. Thissuggests the BWB may perform at lower cost than aconventional airplane at high subsonic speeds.
Approach
WingMOD Overview
The current study was performed using WingMOD, acode consisting of several intermediate level analysismodules tied to an optimizer. As described inRefs. 4-5, WingMOD models configurations with asimple vortex-lattice code and monocoque beamanalysis, coupled to give static aeroelastic loads. Themodel is trimmed at several flight conditions to obtainload and induced drag data. Profile and compressibilitydrag are evaluated at stations across the span of thewing with empirical relations using the lift coefficientsobtained from the vortex lattice code. Structural weightis calculated from the maximum elastic loadsencountered through a range of flight conditions,including maneuver, vertical gust, and lateral gust. Thestructure is sized by bending strength and bucklingstability considerations. Maximum lift is evaluatedusing a critical section method that declares the wing tobe at its maximum useable lift when any sectionreaches its maximum lift coefficient, which iscalculated from empirical data.
These analysis modules are linked to a non-lineargradient based optimizer. The optimizer is flexible andallows the user to designate any analysis input as adesign variable and any database variable as aconstraint. In typical wing planform optimizations, awide variety of constraints is applied. Hard constraintssuch as payload, range, and approach speed are appliedas well as design constraints like maximum runningloads and buffet characteristics. These designconstraints are put in place to assure that the optimizerdesigns a practical configuration that can be refinedlater by higher fidelity methods.
During a typical optimization, WingMOD analyzes 28conditions. Most conditions are subject to balance andtrim constraints. The objective function is takeoffweight. Thus a WingMOD designed configurationmeets the specified mission requirements (i.e. payloadand range), is trimmed and balanced, and is theminimum takeoff weight configuration for the mission(subject to the particular optimization setup).
A key advantage of using WingMOD is the ability tomake rapid trade studies on multiple configurations. Inthe current study, 28 design conditions were analyzedand 154 design variables were specified. For a 100 stepoptimization, this translates to roughly 20,000 functionevaluations, each including about 20 aerodynamiccalculations. WingMOD requires quick, intermediatefidelity analyses to explore such a large design space inonly four hours on an HP C-3000. The current studyalso included 1,091 constraints, of which 134 wereactive, meaning the system had 20 unconstraineddegrees of freedom.
Drag Calibration
In analyzing BWB configurations at Mach numbersgoing up to 0.95, there is concern that the simpleWingMOD models may not capture significanttransonic effects. This concern was addressed bycalibrating the WingMOD models to CFL3D Navier-Stokes CFD results for a number of BWBconfigurations, comparing calibrated WingMOD andCFD results, and performing CFD design and analysison the final WingMOD optimized configuration.
Figs. 3 and 4 show the WingMOD compressibility dragmodel. Compressibility drag is determined on a sectionby section basis. For each section, a thickness to chordratio and lift coefficient are evaluated perpendicular tothe effective sweep line, which is determined from asource-sink thickness model described in Ref. 6. Theseproperties are then input to a function represented inFig. 3 to determine the section crest-critical Machnumber (Mcc). Mcc is described as the freestream Machnumber at which the local flow at the crest of theairfoil, the location where the surface is tangent to thefreestream direction, becomes sonic.7 Once Mcc isdetermined, compressibility drag can be derived. Foreach section, compressibility drag is related to the ratioof freestream Mach number to crest-critical Machnumber, as shown in Fig. 4. The curve shown isrepresented by a spline that can be manipulated by theoptimizer during calibration.
To calibrate for the current study, a Mach 0.85 BWBconfiguration and two Mach 0.93 BWB configurationswere analyzed in both WingMOD and CFL3D. Tomatch WingMOD and CFD representations, WingMODspanloads were tailored to match CFD, and theconfigurations were analyzed without nacelles, pylons,or winglets. The WingMOD compressibility dragmodel was then adjusted, via the coefficients for thespline shown in Fig. 4, to minimize the error incompressibility drag over all three configurations.Procedures described in Ref. 8 for linking variableswere used to enable a simultaneous optimization over
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the three configurations to calibrate the compressibilitydrag model. Fig. 5 compares lift to drag ratio (L/D) forthe three configurations relative to the maximum L/D of
the Mach 0.85 configuration, analyzed both in CFD andin WingMOD after the calibration. WingMOD L/Dlevels are within 5% of CFD and show similar trends inCL. This is good agreement considering the WingMODaerodynamic analysis runs in a fraction of a second. Itis also possible that the less mature Mach 0.93 designswill improve relative to the Mach 0.85 design withfurther aerodynamic refinement in CFD, resulting inbetter agreement between WingMOD and CFD.
Results
A series of eight BWB configurations was optimized,covering Mach numbers of 0.85, 0.90, 0.93, and 0.95and ranges of 7,500 nm and 8,900 nm. Trends fromthese optimized configurations are shown here, alongwith more detailed information on critical constraints,balance considerations, and CFD analysis for the 0.93Mach, 7,500 nm configuration.
Critical Constraints
To understand what drives WingMOD to shape theplanform in a particular way, it is necessary to examinethe critical constraints driving the configuration. Fig. 6summarizes the critical constraints for the 7,500 nm,Mach 0.93 configuration. The setup of design variablesand constraints is similar to that described in Ref. 9.
Constraints to match design and desired payload arecritical. Payload height constraints are applied toensure the upper cabin is tall enough to fit passengers
Fig. 3 Crest critical Mach number as a function oft/c and cl.
1.0 1.1 1.2 1.3 1.4
M / Mcc
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mp
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ibili
ty D
rag
Fig. 4 Sectional compressibility drag curve.
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M=0.85 Design in WingMOD
M=0.93 CFD Design in WingMOD
M=0.93 Early WingMOD Design in WingMOD
M=0.85 Design in CFD
M=0.93 CFD Design in CFD
M=0.93 Early WingMOD Design in CFD
Fig. 5 Comparison of CFD and WingMOD lift to drag ratios.
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and the lower cabin is tall enough to fit standardcontainers. Minimum lower deck containerizedpayload requirements result in a minimum side of cabinchord for the lower deck. Constraints force the payloadto sit between the spars. The lower deck payload isforced to lie forward of the gear and the lower deck isforced into a more usable convex shape. A constraintforces the rear spar to be straight.
On the outer wing, constraints keep the front spar areasonable distance away from the leading edge and therear spar a reasonable distance away from the controlsurfaces. For manufacturing purposes, the number ofleading and trailing edge breaks is reduced byconstraining the edges to be straight at variouslocations. Also for manufacturability, the spanwiseradius of curvature of the outer mold line is limited.
A maximum trailing edge closure angle constraint iscritical on the afterbody. Centerbody incidence, theamount of twist on the centerbody, is limited in order toallow for a level floor. Wing twist rate is limited toavoid a wing that rapidly twists back and forth. Toavoid unmodeled reductions in control surfaceeffectiveness, the maximum trailing edge sweep islimited.
In addition to these geometric constraints, manystructural constraints are critical. Maximum runningload, applied for manufacturability, is critical in thekink region of the wing. Wing skins are sized by loadsfrom several different conditions, with taxi bump, aftcenter of gravity (CG) maneuver, forward CGmaneuver, and lateral gust conditions critical.
The maximum lift on the stall critical section of thewing is critical for four different conditions. A stall
characteristic constraint is critical on the winglet.Buffet characteristic and leading edge shock constraintsare also critical. Local fuel volumes in tanks across thewing max out as the fuel distribution is adjusted forbalance purposes. Three constraints that restrict controlsurface movement are also critical.
Several other constraints are critical on the currentconfiguration. Range requirements must be met fortwo different missions. The severity of the pitchingmoment break at buffet is limited. Cruise angle ofattack is limited to 3.5 degrees and outer wing quarter-chord sweep is limited to 45 degrees. CG locations forseveral different conditions are tracked and required tolie within stability limits. While ballast can be used,this design hits zero ballast minimum limits. Fuelvolume is critical in two conditions. Load factor andpitching moment are constrained to trim the airplanefor aerodynamic conditions. Additionally, rollingmoment is constrained in conditions using ailerons.Landing approach speed is limited to 150 kn. Becauseof nonlinearities in the centerbody structural modelresulting from the coupling of column loads (from wingbending) and bending loads (from hydrostaticpressure), centerbody structural thicknesses aredesigned in the optimizer with correspondingconstraints on centerbody stresses. Finally, a constraintis used to maintain the thrust to takeoff weight ratio forthe purpose of engine sizing.
In all, the configuration was driven by 134 activeconstraints. With 154 design variables, the currentconfiguration had 20 unconstrained degrees offreedom.
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range (2)buffet pitching moment break (1)ferry cruise AOA (1)wing sweep (1)CG location (4)CG in limits (2)ballast weight (2)fuel volume (2)load factor (21)pitching moment (21)rolling moment (1)stall speed (1)centerbody stress (4)constant thrust to weight ratio (1)
number of active constraints (134)
critical section maximum lift (4)stall character (1)local fuel volume (7)buffet character (1)take-off climb trim deflection (1)load alleviation schedule (2)leading-edge shock (2)
American Institute of Aeronautics and Astronautics
Balance
WingMOD considers balance when designingconfigurations. Fig. 7a shows the baseline aircraft asanalyzed in WingMOD. The points in the plotrepresent CG locations for different conditions. Thedashed lines represent the control limits of the aircraft.Several of the CG locations fall outside the controllimits, indicating the aircraft is not balanced.
Fig. 7b shows how WingMOD is able to balance thisairplane using ballast. The addition of ballast increasesoperating empty weight (OEW) through increases in
structural weight in addition to the weight of the ballastitself. As the aircraft balances at more-aft CGlocations, L/D increases, improving fuel burn. Takeoffweight (TOW) then increases less than OEW as fuelburn improvement partially offsets the empty weightincrease.
By reshaping the planform, WingMOD is able to solvethe balance problem and reduce the weight of theaircraft at the same time. The balance diagram for theoptimized 0.93 Mach, 7,500 nm configuration is shownin Fig. 7c.
Balance Diag ram
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igh
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(a) CFD Baseline
UnbalancedTOW: BaseOEW: Base
(b) Balanced CFD Baseline
Adds Aft BallastTOW: +2.1%OEW: +4.2%
(c) Optimized Configuration
Planform ReshapedTOW: -6.8%OEW: -5.5%
Fig. 7 WingMOD balance analysis.
7500 nm i
8900 nm i
M=0.85 M=0.90 M=0.93 M=0.95
Fig. 8 WingMOD optimized planforms.
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Mach Trends
The eight configurations optimized to evaluate speedtrends are shown in Fig. 8. The planforms were alloptimized with a common set of design variables andconstraints. Span was not varied and upper cabin areawas kept constant. Fig. 8 shows that there is very littleplanform change going from Mach 0.85 to Mach 0.90,for either range. Beyond Mach 0.90, however,WingMOD has visibly changed the configuration,primarily by adding chord to the outboard wing. Thekink region, a critical area for transonic drag, hasgrown the most chord. This area is critical because itsits next to the thick centerbody, which makes theeffective thickness of the kink region greater than theactual thickness.
The trend in takeoff weight with Mach number andrange is shown in Fig. 9, expressed as a percent changefrom a Mach 0.85, 7,500 nm configuration. Trends atboth ranges are similar. The variation of weight withMach number starts out relatively shallow, but becomesincreasingly steep as Mach number approaches 0.95.Because cost typically varies with weight, weight isoften used as a metric to determine the utility of adesign. The takeoff weight trend would indicate thatthe Mach 0.85 design is optimal; however, it does not
take into account the potential benefits of increasedspeed.
Trends in OEW and gross wing area that are similar tothe takeoff weight trend are shown in Figs. 10 and 11.
The trend in average cruise Mach number times lift todrag ratio (ML/D) is shown in Fig. 12, expressed as apercent change from a Mach 0.85, 7,500 nmconfiguration. The variation is not very large.Surprisingly, ML/D peaks at 0.90 Mach, a result ofspeed increasing faster than L/D decreases. This resultsuggests that aerodynamically, the 0.90 Machconfiguration may be optimal.
While ML/D is a good measure of aerodynamicperformance, it does not include the effect of increasingweight and specific fuel consumption (SFC) with Machnumber. To include these effects, a figure of meritcalled payload propulsive efficiency was created. Thisefficiency is defined as the product of Mach numberand payload divided by the product of drag and SFC.This metric differs from ML/D in that it replaces liftwith payload weight to avoid booking increasedstructural weight, which is captured in lift, as animprovement in the airplane. Payload propulsiveefficiency then captures trends in usefulness moreclosely than ML/D does. Fig. 13 shows that thepayload propulsive efficiency decreases monotonically
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Fig. 9 Takeoff weight trend.
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Fig. 10 Operating empty weight trend.
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Fig. 11 Gross area trend.
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Fig. 12 Mach number times lift to drag ratio trend.
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with Mach number over this range. The trend showsperformance penalties that begin small and getincreasingly worse with speed, similar to penalties intakeoff weight.
In both takeoff weight and propulsive efficiency, thedegradation in going from 0.85 to 0.90 Mach is lessthan 5%, while the speed increase is more than 5%.These results may indicate a favorable trade forselecting 0.90 over 0.85 Mach for the BWB. Favorableresults at 0.90 Mach in ML/D further suggest the BWBmight achieve its best performance at 0.90 Mach. Theemphasis on speed at Boeing, partially driven by the
consideration that increased utilization could producebetter economics, led to selection of a slightly higherspeed, 0.93 Mach, configuration for more study.
CFD Analysis
The 0.93 Mach, 7,500 nm, WingMOD-optimizeddesign was the basis for the BWB-6-250Bconfiguration shown in Fig. 14. From the WingMODdefinition of the configuration, a computer aided design(CAD) model was generated. The configuration wasdefined in more detail, with refinements to the wingloft.
CFD design and analysis using CFL3D coupled toCDISC inverse design was carried out on the BWB-6-250B. For simplicity, the isolated BWB wing wasconsidered without the added complications ofmodeling the winglet and nacelle and pylon. Whereasthe winglet has a fairly localized effect at the wing tip,the nacelle and pylon can have a more pronouncedeffect and would need to be integrated in the design atwhatever speed is deemed most appropriate from thisinitial study.
Using CDISC, the camber was adjusted to achieve asmooth chordwise and spanwise pressure distribution,limit shock strength, and achieve a center of pressurecorresponding to the CG location from WingMOD.
Fig. 14 BWB 6-250B Configuration.
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7500 nmi
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Fig. 13 Payload propulsive efficiency trend.
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Fig. 15 shows the pressure distribution for theconfiguration. There is a very weak inboard shock wellahead of the engine inlet location with a somewhat
more pronounced outboard shock with a tendency todouble shock near the wing tip. The double shocktendency is typical of sections that are under loaded.The same techniques used thus far can be used to tailorthe spanload and airfoils to address this double shock,though judging from the L/D level, there does not seemto be a significant penalty associated with thischaracteristic at the tip.
Fig. 16 compares the L/D of the BWB-6-250B to theL/D of the BWB-5-250 at a few Mach numbers, a morerefined configuration designed and analyzed at 0.85Mach. At 0.93 Mach the peak L/D for theBWB-6-250B is about 15% lower than the peak L/D forthe BWB-5-250. This is expected: besides being at alower Mach number, the BWB-5-250 was originallydesigned for 8,900 nm range, thus placing moreimportance on cruise performance.
Fig. 16 also shows that L/D decreases rapidly as Machnumber increases from 0.93 to 0.95, indicating theconfiguration is at or near its drag divergence Machnumber.
This is demonstrated in Fig. 17. The BWB-6-250B wasanalyzed in CFD at several different Mach numbersfrom 0.50 to 0.95. The slope of the compressibilitydrag versus Mach number curve increases rapidlybeyond 0.93 Mach. Using a standard method, the drag
Fig. 16 Lift to drag ratios for the BWB-5-250 and BWB-6-250B
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divergence Mach number was determined to be 0.932.This is slightly higher than the cruise Mach number, anindication that the configuration was well designed forthis speed.
Fig. 16 also compares the L/D for the BWB-6-250B asanalyzed both in WingMOD and in CFD. The plotshows good agreement; however, the WingMODanalysis includes an increment for nacelle and pylondrag, and it includes winglets, thus the wing alone L/Dfrom WingMOD may not agree as well with CFDresults.
The nacelle inlets would most likely be located on theinboard part of the wing, on the upper surface aft of85% chord. As seen from the pressures, the inlet wouldlie in a slightly accelerated flowfield well aft of theinboard wing shock.The CFD analysis of the BWB-6-250B indicates that itachieves an L/D level similar to that obtained withWingMOD analysis. This simple wing alone CFDanalysis indicates that aerodynamically, the BWB-6-250B works at Mach 0.93.
Conclusions
This study evaluated performance trends for BWBconfigurations designed for Mach numbers from 0.85to 0.95. The WingMOD multidisciplinary optimizationtool was used to develop and analyze eight BWBconfigurations to show trends with increasing Machnumber. Takeoff weight increases with speed, withvery little penalty for going Mach 0.90 but fairlysubstantial penalty for going Mach 0.95. ML/Dactually peaks at Mach 0.90. That, coupled with theminimal takeoff weight increase, suggests that Mach0.90 may be an ideal cruise speed for a BWB.
Consideration of economic benefits from increasedutilization led to selection of a slightly faster BWB forstudy. The Mach 0.93, 7,500 nm design fromWingMOD became the basis for the BWB-6-250Bconfiguration, which was analyzed with standardanalyses including CFD. CFD design and analysis of
the BWB-6-250B wing indicated that it achievedreasonable L/D and a drag divergence Mach numberjust beyond 0.93. Although additional CFD work isneeded to quantify drag stemming from propulsionairframe interference, the work done so far indicatesgood potential for creating a BWB that performs well atMach 0.93.
Acknowledgement
The authors gratefully acknowledge the contributionsof the BWB team, especially the following individualswho contributed supporting data or provided guidancefor the study described in this paper: Jennifer Whitlock,Dharmendra Patel, Antonio Gonzales, Ronald Fox,Ronald Kawai, Blaine Rawdon, John Allen, RaquelGirvin, Derrell Brown, and Robert Liebeck.
References
[1] Liebeck, R. H., “Design of the Blended-Wing-Body Subsonic Transport,” 2002 Wright BrothersLecture, AIAA Paper 2002-0002, Jan. 2002.
[2] Liebeck, R. H., Page, M. A., Rawdon, B. K.,“Blended-Wing-Body Subsonic CommercialTransport,” AIAA Paper 98-0438, Jan. 1998.
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