aerodynamic considerations of blended wing body aircraft (transonico m=0.85)

8/9/2019 Aerodynamic considerations of blended wing body aircraft (transonico M=0.85)

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Progress in Aerospace Sciences 40 (2004) 321–343

Aerodynamic considerations of blended wing body aircraft

N. Qina,, A. Vavalleb, A. Le Moignea, M. Labanc, K. Hackettb, P. Weinerfeltd

aDepartment of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD, UK bFuture Systems Technology, QinetiQ Ltd., Bedford MK44 2FQ, UK

cNational Aerospace Laboratory, NLR, The NetherlandsdFuture Products, SAAB Aerospace, SE-581 88 Linko ping, Sweden

Abstract

In this paper, we present a progressive aerodynamic study of a blended wing body (BWB) configuration within a

European project, MOB (A computational design engine incorporating multi-disciplinary design and optimisation for

blended wing body configuration). The paper starts with an overview of various blended wing body aircraft design

projects in relation to their aerodynamic behaviour. After a theoretical assessment of the ideal aerodynamic

performance for the baseline configuration, viscous flow simulations were carried out to investigate the aerodynamic

performance of the baseline design. The effects of spanwise distribution on the BWB aircraft aerodynamic efficiency

were studied through an inverse twist design approach, combining both a low-fidelity panel method and a high-fidelity

Reynolds-averaged Navier–Stokes solution method. Following the inverse design studies, the BWB wing was mapped

to an aerofoil optimisation problem and the optimised aerofoil was projected back to the BWB wing to investigate

further performance improvement. Finally, three-dimensional aerodynamic surface optimisation of the BWB is carried

out based on both continuous and discrete adjoint approaches. A progressive improvement of the aerodynamicperformance is demonstrated for the given BWB planform and the design cruise condition.

r 2004 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

2. An overview of BWB projects and related aerodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

3. Baseline BWB model and an assessment of its aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

3.1. Geometry and flow conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

3.2. Ideal and low-fidelity drag calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

3.3. High-fidelity RANS solvers and grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

3.4. Grid sensitivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

3.5. Assessment of aerodynamic performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

ARTICLE IN PRESS

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0376-0421/$ - see front matterr 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.paerosci.2004.08.001

Corresponding author. Tel.: +44-114-222-7718; fax: +44-114-222-7890.

E-mail address: [email protected] (N. Qin).

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described in Refs. [8,9], which incorporates the aero-

dynamic modelling, structural analyses, flight dynamics

and aeroelasticity in the MDO design process.

2. An overview of BWB projects and related

aerodynamics

In a series of papers, Liebeck et al. [1,7,10] presented

work in the US in the late 1990s on the design studies of

the blended wing body aircraft as a potential candidate

for future large subsonic transport design. The project

involves Boeing, NASA and universities in the United

States (Stanford, South California, Florida and Clark-

Atlanta). For the 800 passenger Mach 0.85 design, the

configuration evolves from 106 m span and a trapezoidal

aspect ratio of 12 to 85 m span and a trapezoidal aspect

ratio of 10, indicating a significant difference in potential

aerodynamic performance. To compare with the existingfleet of large transport aircraft (Boeing 747 and Airbus

380), a 450 passenger BWB was also presented with the

span and the trapezoidal aspect ratio further reduced to

within the 80 m requirement and 7.55, respectively. The

BWB-450 was designed with a multi-disciplinary design

tool, WingMOD [11]. In comparison with the 800

passenger BWB design, the centre body chord to span

ratio is increased so that the maximum thickness to

chord ratio (on the centre body) is substantially reduced,

implying a potential improvement in transonic per-

formance. The authors conclude that a reduction of

about 30% fuel burn per seat can be achieved for both

BWB-800 and BWB-450 configurations in comparison

with the conventional designs (requiring 3 instead of

4 engines).

In order to gain confidence of the state-of-the-art

CFD simulations used for the BWB design assessment,

tests of the BWB configuration close to the full-scale

Reynolds number in NASA’s National Transonic

Facility were reported in Ref. [7]. Excellent agreements

between the wind tunnel measurements and the CFD

simulations were observed for lift, drag, pitching

moment as well as wing pressure distributions, confirm-

ing the reliability of the CFD tool used in the BWB

analysis and design. Wind tunnel test were alsoconducted within the MOB project by Carlsson and

Kuttenkeuler [12] for low speed aerodynamic and

aeroelastic data.

The work in the US attracted the interest of other

parties in the world. With support from BAE Systems

and Rolls Royce, a group of MSc students led by Dr.

Smith from Cranfield College of Aeronautics in the UK

designed their version of a BWB in 1998. In Ref. [2],

Smith presented the BWB design project, which is based

on a similar payload and performance as Airbus A380-

200 with over 650 passengers accommodated in three

classes. It is designed to be compatible with existing

airports and facilities, limiting the aircraft span to 80 m.

On the aerodynamic side, the author also suggested that

the BWB configuration is well suited for the application

of laminar flow technology to the engine nacelle and

potentially to the lifting surfaces. Successful implemen-

tation of the laminar flow technology implies potentially

substantial reduction in skin friction drag. In this

respect, one may refer to an earlier work by Denning,

et al. [13] who advocated the potential benefits of a semi-

integrated delta planform with laminar flow control

using distributed suction for profile drag reduction for

large aircraft design.

Bolsunovsky et al. [3] reported studies of a number of

blended wing body geometries from the point of view of

future large transport aircraft configuration design at

TsAGI in Russia with support from Airbus and Boeing.

In particular, a flying wing, a lifting body and an

integrated wing body were studied in comparison with

the conventional design. From the aerodynamic perfor-mance aspect, it is noticeable that all the proposed

designs have a significantly increased span (100 m) as

compared to other designs of about 80 m, which also

represent the capacity of most current airports. A

significant improvement in the aerodynamic perfor-

mance was promised for the new configurations with

the integrated wing body design performing best at

Mach 0.85 cruise.

Most BWB designs have used Mach 0.85 as a cruise

design point as this is consistent with current large

transport aircraft operation. Related to the sonic cruiser

concept, it is interesting to investigate the potential of

BWB configurations at nearer to the sonic condition. In

a recent paper, Roman et al. [14] studied the aero-

dynamic behaviour of a blended wing body aircraft at

high transonic speed and concluded that a Mach

number of 0.93 is feasible with a performance

penalty relative to Mach 0.85 designs. In particular,

a 10% reduction in ML/D was observed for the

design. Further increase in the cruise Mach number

results in a substantial rise in drag and makes the design

unfeasible.

Pambagjo et al. [15] carried out an aerodynamic

inverse design study of an even smaller version of the

BWB for 200 passengers (medium sized aircraft) cruisingat Mach 0.80. The span is 50m and the trapezoidal

aspect ratio is 7.7. A significant point to note is that the

wetted area for the BWB design was reckoned to be

higher than that of a conventional design for the

medium sized 200 seat aircraft. It is an indication that

not all BWB designs can exploit the originally claimed

saving in wetted surface area due to other constraints.

The targeted span loading distribution is an elliptic

distribution in the inverse design process. A lift drag

ratio of 18.87 at cruise has been achieved for the design

and the design is shock free at Mach 0.80. However, a

substantial negative pitching moment was present at the

ARTICLE IN PRESS

N. Qin et al. / Progress in Aerospace Sciences 40 (2004) 321–343 323



design condition, indicating a large trim drag in order to

balance the aircraft.

The work described in this paper on the BWB is part

of a European Commission funded project (2000–2003)

entitled MOB—A computational design engine incorpor-

ating multidisciplinary design and optimisation for

Blended Wing Body configuration [8]. The aim of the

project is to develop a computational design engine

(CDE) i.e. an integrated suite of codes to perform the

multidisciplinary design and optimisation of an aircraft,

using the novel BWB configuration as the driving

scenario based on the Cranfield design [2]. The CDE

has been accessed from different sites across Europe to

enable aircraft designers and engineers from different

companies and organisations to work together on

cooperative design projects. A session at the recent 9th

AIAA/ISSMO Symposium on Multidisciplinary Analy-

sis and Optimisation in Atlanta was devoted to the

MOB project with presentations in all major aspects of the research including the CDE development [9,16], the

model generator based on ICAD [17], the aerodynamic

analyses and design performed on the BWB [18] as well

as the studies on aeroelasticity [12,19] and flight

mechanics [20] carried out on this geometry.

The present study is part of the aerodynamic analysis

and design work conducted within the MOB project. In

the following sections, we will present a progressive

study of the aerodynamic performance for the given

BWB planform and the design cruise condition as it

happened in the MOB project. It starts with the ideal

drag estimation and moves up to three-dimensional

aerodynamic surface optimisation.

From the above review, the primary argument for the

aerodynamic performance gain is based on the fact that

a blended wing body design will have a much lower

aircraft surface to its volume ratio. It was believed that,

conceptually, this should translate to a higher lift to drag

ratio. This implies that for a given volume, smaller

surface area should give smaller drag. However, the

surface area is only directly related to skin friction drag

and a substantial part of the drag comes from

the pressure drag, which includes lift-induced drag.

The current paper will pay some attention to the relative

contributions of the skin friction drag and the pressuredrag and minimising the latter through shape design and

optimisation.

3. Baseline BWB model and an assessment of its

aerodynamics

3.1. Geometry and flow conditions

In the present paper, the baseline BWB geometry is

defined in Ref. [21] for the MOB project, which is based

on a previous BWB design as described in Ref. [2]. The

half-model geometry is composed of the central body,

an inner wing and an outer wing to which a winglet is

attached. They are ‘‘blended’’ to form the BWB

geometry. The total span including the winglets is just

under 80m. For the present study, the propulsion

system and its integration with the BWB design is not

included, although its importance is fully appreciated.

The design conditions considered correspond to the

first segment of cruise as specified in Ref. [21]. Hence, to

balance the weight of the aircraft, the design C L is 0.41

based on the trapezoidal reference area of 842m2. All

the aerodynamic coefficients presented in this report are

based on this trapezoidal reference area. Unless other-

wise stated, the cruise flow conditions are specified as in

Table 1.

Fig. 1 shows an isometric view of the CAD model of

the aerodynamic surface provided by Delft University

[30] using an ICAD parametric model generator

program.The model is composed of two lifting bodies, which

are blended to form the BWB geometry:

a thick streamlined centre body, where the payload is

accommodated, from 0 to 13 m span,

a pair of inner wings, which hosts fuel tanks, from 13

to 23.5m in span,

an outer wing, from 23.5 to 38.75 m, to which a

winglet is attached.

Fig. 2 shows the planform of the BWB design,

indicating the dimensions of the aircraft in the spanwise

direction.

ARTICLE IN PRESS

Fig. 1. BWB baseline configuration: isometric view of the CAD

model.

Table 1

Cruise design condition

Mach number M ¼ 0:85

Reynolds number Re ¼ 5:41 106=m

Design lift coefficient C L ¼ 0:41

Altitude 11500 m

C.G. position X cg ¼ 29:3 m

N. Qin et al. / Progress in Aerospace Sciences 40 (2004) 321–343324



The total aircraft span is limited to just under 80 m,

adopted as a constraint to be compatible with existing

airport runways. The leading edge sweep angles are

swept back 63.81 for the centre body and 381 for the

outer wing, respectively. The aspect ratio of the aircraft

is AR=4.26. The trapezoidal wing area (842 m2) is taken

as the reference area for the aerodynamic coefficients

and the mean chord (C ref ¼ 12:3 m) is taken as reference

chord for the pitching moment coefficient and the lift

per unit of span definition. The length of the centre

chord is C ¼ 50:8 m: The wetted area is S wet ¼ 3079 m2:The reference trapezoidal wing including the winglet has

an aspect ratio of 7.6.

The CAD program separates the whole geometry into

wing trunks, whose external surface is defined by the

profile of the end sections and a set of intermediate

sections, which are then interpolated spanwise by means

of a B-spline. When only the two end sections define the

wing trunk, the associated surface is obtained by meansof a linear interpolation. The centre body consists of six

wing sections positioned at span stations: y ¼ 0:0; 1.0,

3.0, 6.0, 10.0, 13.0 m, respectively.

Fig. 3 shows the aerofoils for the centre body at y ¼ 0

and 13 m, respectively. The centre section has a front

positive camber of ðz=cÞmax ¼ 0:01 at x=c ¼ 0:21 which

is then reflexed at 60% chord with ðz=cÞmin ¼ 0:004 at

x=c ¼ 0:81: For the tailless BWB aircraft, the reflected

camber design is essential to provide the longitudinal

stability at the cruise condition as revealed later in the

aerodynamic assessment.

Moving spanwise from root outwards, both leading

edge positive curvature and trailing edge reflected

camber diminish at y ¼ 10:0 m; where the profile

becomes almost symmetric, which is maintained to the

outer section of the centre body ( y ¼ 13:0m).

Further out in the span, the inner and outer wing

sections are composed of aerofoils with aft camber

design for transonic performance (supercritical), which

are shown in the aerofoil sections at y ¼ 17:5m and

y ¼ 23:5m in Fig. 4.

The winglet surface is composed of a linear interpola-

tion of an NACA 0012 aerofoil between the relevant

root and tip sections.

A similar wing thickness distribution to that of

Liebeck et al. [1] is adopted, as shown in Fig. 5. The

spanwise thickness to chord ratio distribution is

averagely 17% on the centre body with a maximum of

18% at about 6 m span. The inner wing blends the thick

centre body with the thin outer wing (8%) with a largevariation in its thickness.

The twist distribution of the aircraft is shown in

Fig. 6, where a positive sign indicates a section pitching

upwards, rotating about the leading edge. It is notice-

able that the centre body and the outer wing are twisted

downwards with respect to the inner wing.

This completes the description of the baseline

geometry in relation to its aerodynamic shape. The

planform of the baseline is maintained throughout the

paper, while the detailed shape is redesigned progres-

sively as presented in the following sections.

ARTICLE IN PRESS

Fig. 2. BWB baseline configuration: planform.




due to non-linear compressibility and variation of the

skin friction from the flat plate values. The curves can beviewed as the upper limit for the given planform and

volume distribution and the actual performance of the

aircraft is much lower than the panel method curve, as

shown later.

3.3. High-fidelity RANS solvers and grid

In order to gain insight of the aerodynamic behaviour

of the baseline BWB geometry at the defined transonic

cruise condition, we have used both Cranfield high-

fidelity implicit multi-block Reynolds-averaged Navier–

Stokes solver, MERLIN, which employs an approx-

imate Riemann solver based on Osher’s flux difference

splitting for shock and boundary layer capturing

[26–29], and the NLR ENFLOW system, which

supports aeroelastic deformation and incorporates

pitching moment trim [9]. The Baldwin–Lomax alge-

braic turbulence model is used to close the Reynolds

averaged Navier–Stokes equations. In all the simula-

tions, the status of the boundary layer is assumed to be

turbulent, which is a reasonable assumption due to the

high Reynolds number and the high leading edge sweep

of the configuration, similar to most large transport

aircraft. The BWB geometries were input from the

ICAD model generator [30] into the grid generatorsused. Structured multi-block grids were generated

around the BWB geometry including the winglet.

Automatic three-dimensional grid deformation techni-

ques [9,31] were used in trimming the BWB aircraft

through the deflection of the trailing edge control

surfaces and in shape change in the three dimensional

surface optimisation.

3.4. Grid sensitivity

To gain some insight into how much grid stretching

was needed near the aircraft surface to obtain a good

prediction of the turbulent boundary layer and therefore

the aerodynamic coefficients, a grid sensitivity analysis

was carried out in the grid direction normal to the

surface. Five different grids were created and a CFD

analysis was performed on each of them to obtain the

aerodynamic coefficients. The first 4 grids have the same

number of points in the direction normal to the surface

i.e. 60 but a different stretching which leads to a range of

y+ from 40 to 1 on the aircraft surface. The number of

points for the fifth grid was doubled in the direction

normal to the surface, resulting in a total grid number of

1 million, much more costly to run.

From the RANS simulations, the total drag comes

from the integration of the pressure and the shear stress

around the whole geometry surface. The former acts

normal to the surface while the latter is a vector

tangential to the surface. It is therefore obvious that

the pressure drag defined above should include the

induced drag (also known as vortex drag) due to liftgeneration, the wave drag due to shock generation, and

the drag due to boundary layer displacement.

The results obtained with the different grids are

shown in Table 2. Most noticeable is the severe under-

prediction of the skin friction drag for grids without

enough resolution in the boundary layer (with first cell

distance yþmax ¼ 40 or 13). The skin friction converges

for yþmaxp5 as the grid is further clustered towards the

surface. On the other hand, for a given number of grid

points in the wall normal direction, stronger clustering

in the boundary layer implies less grid away from the

near wall region. To investigate this effect, a finer grid

solution is obtained, for which the resolution in the

normal direction outside the boundary layer is doubled,

while the first cell distance is kept to yþmax ¼ 1: It is

interesting to note that the skin friction becomes less

sensitive to grid density for the three cases for yþmaxp5:

3.5. Assessment of aerodynamic performance

A series of computations at different incidences for

M ¼ 0:85 were carried out in order to form a polar for

the baseline BWB configuration, as shown in Fig. 8. The

different flow conditions and the corresponding aero-

dynamic coefficients are presented in Table 3. Computa-tion at M ¼ 0:92 is also shown. The case at M ¼ 0:92

ARTICLE IN PRESS

Table 2

Grid sensitivity analysis M ¼ 0:85; a ¼ 3

J max yþmax C L C D total C Dpressure C D friction

60 40 0.336 0.0247 0.0244 0.00037

60 13 0.409 0.0285 0.0249 0.00365

60 5 0.414 0.0327 0.0250 0.00764

60 1 0.416 0.0330 0.0254 0.00763

120 1 0.421 0.0318 0.0241 0.00767

-10

-5

0

5

10

15

20

25

30

35

40

-0.1 0 0.1 0.2 0.3 0.4 0.5

CL

L / D

(L/D) ideal

(L/D) low fidelity

Fig. 7. BWB baseline: comparison between ideal and panel

method prediction of the aerodynamic efficiency.




was carried out in order to investigate the behaviour of

the aircraft at a speed nearer to the sonic speed outside

the design conditions (commonly required for certifica-

tion requirement).

From the results, one can note that the design lift at

M ¼ 0:85 is obtained at an incidence of about 31. The

total drag is composed of 77% pressure drag and 23%

skin friction drag. The rate of lift increase reduces with

the incidence while the rate of pressure drag increase

goes up. These opposite trends result in a peak lift drag

ratio at the design condition for the baseline BWB

geometry at an unsatisfactorily low value of 12.7.

Distributions of the spanwise local lift coefficient and

spanwise loading for the various incidences are plotted

in Figs. 9 and 10. Note that the winglet load is not

shown in the plots and the 100% span corresponds to

the junction between the outer wing and the winglet.

The distributions show that the outer wing is very

highly loaded, where the chord is much shorter than theinner wing and the centre body. At the design condition,

i.e. the 31 case, the local lift for the baseline geometry

peaks at about 80% of the span. On the other hand, the

local lift for the central body is comparatively much

lower than that on the outer wing.

The high demand on lift from the outer wing results in

shock formation on the upper surface of the outer wing,

which starts to appear at a ¼ 1:751: This shock gets

stronger as the incidence increases. At incidences higher

than 31, the outer wing can no longer sustain the high lift

and the lift on this portion of the wing stalls, as shown in

Figs. 9 and 10, due to shock induced flow separation

revealed from the flow field solutions at a ¼ 41 and 51.

Fig. 11 shows the pressure contours on the upper

surface of the baseline BWB at the design cruise

condition (M ¼ 0:85; a ¼ 31; C L ¼ 0:41). Also shown

are the pressure contours on both sides of the winglet.

A strong shock wave can be seen, extending from the

junction of the central body and the inner wing to

the outer wing tip. Although the central body has the

greatest thickness, no significant shock can be observed

on this part of the BWB due to the spanwise lift

distribution (relatively low local lift) and the three

dimensional effects of high leading edge sweep. A

trace of a shock-bifurcation is visible on the inner wing.

The outer wing experiences the strongest shock due tothe high local lift demand.

The shock wave extends to the inner side of the

winglet and a relatively weaker shock also forms on the

ARTICLE IN PRESS

Table 3

Lift and drag coefficients for baseline BWB

M a C L C D total C Dpressure C D friction

0.85 0 0.0144 0.01730 0.00937 0.007924

0.85 1.75 0.2305 0.02111 0.01326 0.007848

0.85 3 0.4136 0.03268 0.02504 0.007637

0.85 4 0.5229 0.04790 0.04045 0.007445

0.85 5 0.5690 0.06214 0.05483 0.007297

0.92 3 0.3761 0.06230 0.05483 0.007473

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.2 0.4 0.6 0.8 1

% of span

l o c a l C L

0°

1.75°

3°

4°

5°

0

Fig. 9. Spanwise local lift for baseline geometry.

0

0.07

0.06

0.05

0.04

0.03

0.02

0.01

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

CL

C D t o t a l

Fig. 8. Lift-drag polar for baseline geometry M ¼ 0:85:

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

% of span

C L l o c a l * c / c b a r

0°

1.75°

3°

4°

5°

Fig. 10. Spanwise loading for baseline geometry.




outer side of the winglet. Further flow separation is

observed on the inner side of the winglet surface.

For the higher speed case at M ¼ 0:92 the lift stalls

due to shock induced separation at a ¼ 31 as shown in

Table 3. At this Mach number, which could be

encountered during manoeuvres, the shock wave is very

strong and sits very close to the trailing edge on the

outer wing in a region where control devices are

situated.

From the above assessment of the aerodynamic

behaviour of the baseline geometry, it is revealed that

the strong shock wave on the outer wing and the

associated wave drag are crucial problems prohibiting

high aerodynamic performance. In addition, from a

structural point of view, the high outer wing loading also

results in a high bending moment, which requires

stronger and heavier structures. It is therefore desirable

to investigate the effects of shifting the aerodynamic

loading inboard on its aerodynamic performance.

4. Twist inverse design

4.1. Introduction

This section addresses the effects of the spanwise lift

distribution on aerodynamic performance for the fixed

BWB planform and the given thickness distribution.

Although the interaction of the lift distribution with the

wing bending moment and trim will also be discussed,

the discussion does not intend to cover the full multi-

disciplinary optimisation issues (see Refs. [8,9]).

The baseline BWB spanwise lift (load) design adopted

a near elliptic distribution for a large part of the wing

through twist variation, with the centre part of the BWB

(‘‘body’’) lightly loaded. This is typical of a lift

distribution for a conventional aircraft with a wing/

fuselage configuration. For such a design, a strong shock

wave is present on the outer wing due to the high local

lift at the design cruise condition at M ¼ 0:85; which

results in a high wave drag and unsatisfactory aero-

dynamic performance.

To alleviate the high wave drag at the cruise

condition, redistribution of the spanwise lift was studied

through a twist redesign for the given planform

and thickness distribution. A combination of low- and

high-fidelity aerodynamic models was used for the

study due to the efficiency of the low-fidelity model.

The low order aerodynamic model based on a panel

method was used for the inverse design of the spanwise

loading. The redesigned twist distributions were then

studied with the MERLIN solver to investigate the

wave drag reduction due to the new designs. The

spanwise loading from the high-fidelity model provesthe desirable shift of aerodynamic loading inboard. The

wave drag components were extracted from the RANS

solutions and a substantial reduction of the wave drag

is observed through the twist redesign at the cruise

condition.

4.2. A discussion of spanwise lift distribution

From the lifting line theory, an elliptic lift distribution

was proved to produce minimum induced drag for a

given lift and an aspect ratio. For a conventional

aircraft, an elliptic lift distribution is normally targeted

to minimise the induced drag produced by the wing.

However, if the whole aircraft is treated as an integrated

system, such an elliptic spanwise load distribution on the

wing is no longer the optimum for minimum induced

drag.

The spanwise load distribution is complicated by a

number of factors as presented by Jupp of Airbus at the

Royal Aeronautical Society in Ref. [32]. The effects of

the winglet and the tailplane were discussed, linking the

spanwise loading strongly with structural weight and

aircraft balancing in addition to wing aerodynamics.

For a blended wing body, it is essential to treat the

whole aircraft as an integrated system. Unlike theconventional aircraft, the spanwise distribution of a

BWB includes the centre body and the wing as a whole.

For a conventional aircraft, the body does not

contribute significantly to the lift generation. However,

for a well-designed BWB, the centre body should be an

intrinsic lift generating surface.

What is the best spanwise lift distribution for a BWB?

Obviously there is no simple answer to this question. A

practical solution will have to require multi-disciplinary

teams to work together in an interactive way. The MOB

team was working towards the development of such a

computational design for the optimal BWB design.

ARTICLE IN PRESS

WingletInner Outer

Fig. 11. Contour lines of pressure coefficient on the baseline

geometry, a ¼ 31; M ¼ 0:85:




4.3. Target spanwise loading distributions

From the aerodynamic assessment of the baseline

BWB, it is desirable to shift the span load inboard in

order to off-load the outer wing to reduce the shock

strength and the wave drag. Such a move should also

benefit from a reduced bending moment. For the current

planform geometry, this also implies a movement of the

aerodynamic centre forward. According to the centre of

gravity of the present design, this movement will result

in a reduced trim, as shown in the results later.

Three aerodynamic loadings are imposed on the BWB

apart from the winglet as target lift distributions at

cruise condition. They are (1) an elliptic distribution, (2)

an average of elliptic and triangular distributions and (3)

a triangular distribution, as shown in Fig. 12.

The related targets in terms of section lift coefficient

are shown in Fig. 13. As expected, there is a substantial

difference in the outer wing loading for the current BWBplanform with the elliptic and the triangular loading at

the two extremes.

4.4. Inverse twist design for specified span loading

From the baseline planform geometry without the

winglet, a configuration without twist was initially

derived. Panel method calculations for this untwisted

geometry was then carried out at a series of different

incidences. The local sections were then twisted to meet

the specified local lift coefficient from the above

calculations. The twist angles were derived at all thedesign sections and as a result a new span twist

distribution is obtained. Since the geometry is a full

three-dimensional geometry, the geometry with the new

twist distribution does not necessarily satisfy the

specified spanwise lift distribution when it is analysed

by the panel method. The discrepancies were then used

to derive a correction of the twist distribution. An

iterative procedure was set up to refine the twist

distribution until the specified spanwise loading dis-

tribution is satisfied by the panel solution for the giventwist distribution.

Fig. 14 plots the twist distributions obtained from the

above inverse design procedure in comparison with the

baseline geometry twist, where the positive sign has been

assumed for a downward twist rotating about the

leading edge in relation to the untwisted geometry.

In relation to the central body, all the three new

designs twist downwards with the maximum twist at the

tip of the outer wing.

The induced drag coefficients calculated for the low

speed condition are listed in Table 4. As expected, the

elliptic distribution gives the lowest induced drag among

the candidates for this condition.

4.5. RANS analyses of the new designs

The inversely designed new twist distributions are

then implemented in the RANS surface grid models.

Multi-block structured grids were generated for the new

geometries. Through running MERLIN for the new

geometries at a series of incidences, the design lift

condition can be simulated for each of the new

geometries.

The new spanwise loadings obtained with the RANS

calculations at the design M ¼ 0:85 and C L ¼ 0:41 areshown in Fig. 15, followed by the spanwise distribution

of the local lift coefficient in Fig. 16, in comparison with

the baseline geometry. It is important to note that the

RANS computations include the winglet, which is

indicated in the lift distributions towards the outer wing

tip.

In comparison, the baseline twist distribution has the

highest outer wing loading and the lowest central body

loading. In some way, this reflects a lift distribution of a

conventional aircraft, where the wing is designed with a

near elliptic loading and the central cylindrical body

does not carry much lift.

ARTICLE IN PRESS

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.2 0.4 0.6 0.8 1

y/b

C l

ellliptic

triangular

elliptic/triangular

Fig. 13. Target lift distributions.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.2 0.4 0.6 0.8 1y/b

C l * c / C r e f

elliptic

triangular

elliptic/triangular

Fig. 12. Target aerodynamic loadings.




4.6. Aerodynamic performance of the new twist designs

Table 5 shows the drag coefficients for the new twist

designs in comparison with the baseline geometry at the

design lift condition (C L ¼ 0:41) and the cruise speed

(M ¼ 0:85).

To gain insight into the wave drag component, a

method from the ESDU data sheet [33] has been used to

extract the wave drag from the RANS flow field

solutions for the four different geometries. To calculate

the total wave drag of the BWB geometries and their

spanwise distributions, the program works on a series of wing sections along the span. For each wing section, it

needs as input the geometry of the section to be able to

calculate the curvature of the surface at the foot of the

shock wave, the pressure coefficient just ahead of

the shock, the chordwise location of the shock and the

leading and trailing edge sweep angles. As output the

method gives the local wave drag coefficient for each

wing section and integrates along the span to give the

total wave drag. This method does not include the

boundary layer effects on the local surface curvature but

should give reasonable estimates of the wave drag for

the geometries considered here. The wave drag coeffi-

cients are also listed in Table 5 and the spanwise wave

drag distributions are plotted in Fig. 17. A significant

reduction of the wave drag can be seen on the outer wing

for the new twist distributions. Note that, although all

the other drag coefficients include the whole BWB

geometry, the wave drag shown in Table 5 and Fig. 17

does not include the wave drag from the winglet. For all

the cases, 6 drag counts were calculated from the winglet

shocks on both sides.

Generally, all the three new twist distributions

substantially reduce the pressure drag partially due

to the wave drag reduction and partially due to the

induced drag reduction. As expected, the variation of skin friction with the span loading change is relatively

small.

The comparison shows that, among all the four

designs, the averaged elliptic/triangular distribution has

the minimum total drag and therefore the highest

aerodynamic efficiency, as shown in Fig. 18, the lift to

drag ratio being increased by 16% as compared with the

baseline geometry. The pressure drag reduction of 49

drag counts comes from reduction in both the wave drag

(23 drag counts) and the induced drag. Fig. 18 indicates

that the BWB operates around the drag rise point at the

design lift condition at C L ¼ 0:41:

ARTICLE IN PRESS

Table 4

Induced drag at M ¼ 0:3 and C L ¼ 0:23

Baseline Elliptic Average Triangular

C Di 0.00333 0.00268 0.00325 0.00470

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

% of span

C L l o c a l * c / c b a r

original configuration

triangular twist

elliptic twist

1/2(triangular+elliptic) twist

Fig. 15. Comparison of spanwise loading at design C L for

M ¼ 0:85:

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

% of span

l o c

a l C L


triangular twist

elliptic twist

1/2(triangular+elliptic) twist

Fig. 16. Comparison of spanwise local lift distribution at

design C L for M ¼ 0:85:-10

-8

-6

-4

-2

0

20 0.2 0.4 0.6 0.8 1

y/b

t w i s t a n g l e ( d e g . )

original

elliptic

elliptic/triangular

triangular

Fig. 14. Spanwise twist distributions for the baseline and

inverse designs.




Ideally, the elliptic loading should give the minimum

induced drag associated with lift generation if there is no

transonic shock on the wing, as shown in the panel

calculations. The wave drag counteracts this potential

benefit. On the other hand, the triangular distribution

has the least wave drag but the pressure drag is

higher than those from the elliptic and the averaged

distributions. This is believed to come from the

ARTICLE IN PRESS

0

0.002

0.012

0.014

0.016

0.018

0.004

0.006

0.008

0.01

0.02

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

% of span

l o c a l C D w a v e


1/2(triangular+elliptic)

triangular

elliptic

Fig. 17. Spanwise local wave drag distribution at design C L for M ¼ 0:85:

Table 5

Comparison of the performance of the three redesigned BWB geometries

Twist distribution C L C D total C Dpressure C D friction C Dwave L=D M max

Baseline 0.4136 0.03268 0.02504 0.00764 0.00407 12.66 1.43

Elliptic 0.4102 0.02837 0.02031 0.00806 0.00209 14.46 1.39

Averaged 0.4090 0.02783 0.02008 0.00774 0.00180 14.70 1.32

Triangular 0.4071 0.02866 0.02083 0.00783 0.00161 14.20 1.26

0.015

0.025

0.035

0.045

0.055

0.065

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

CL

C D t o t a l


triangular twist

elliptic twist

1/2(triangular+elliptic) tw ist

Fig. 18. Comparison of C D vs. C L at M ¼ 0:85:




induced drag penalty. Therefore, from an aerodynamic

performance point of view, the best spanwise

loading distribution should be a fine balance of

the induced drag and the wave drag at transonic

conditions.

Also listed in Table 5 is the maximum Mach number

just ahead of the shock wave on the BWB surface. It is

directly related to the wave drag for the corresponding

geometry. Note that for a well-designed transonic wing,

the maximum Mach number should normally be below

1.2, implying that there is still scope for further wave

drag reduction by optimising the sectional aerofoil

profiles.

4.7. Interaction with structure and trim

In Ref. [34], Iglesias and Mason concluded from their

study that the wing weight decreases nearly linearly with

reduced wing root bending moment, while the associatedinduced drag increases in a parabolic fashion. It is

therefore worthwhile to move away from the minimum

induced drag span loading with a small drag increase

(near the starting point of the parabolic curve) for a

substantial reduction in bending moment (weight) for

the best aircraft performance. Similar argument applies

in the present situation. When the structure is coupled to

the aerodynamics through the bending moment, the

triangular distribution, which implies less bending

moment, may well be a better choice for the BWB

design rather than the averaged elliptic/triangular

distribution. As compared with the baseline geometry,

all the new designs benefit from the structural point of

view with much reduced bending moments.

Fig. 19 shows the pitching moments about the centre

of gravity (29.3 m from the nose tip) for the BWB

designs. Without a tail plane, a BWB needs to be

trimmed by trailing edge devices to balance the aircraft.

An extra important gain from the averaged distribution

is that it requires the minimum trim at the design lift

condition, implying a small performance penalty due to

trim (trim drag).

5. BWB aerofoil profile optimisation

In the previous section, the inverse design variables

are the local twist angles at the chosen spanwise

locations and the wing aerofoil profiles are kept

unchanged. In the present section, the BWB aerofoil

profiles were optimised for further improvement of the

transonic aerodynamic performance. Similar to the twistinverse design, the profile optimisation does not change

the planform and spanwise volume distributions.

5.1. Mapping between 3D swept wings and 2D aerofoils

The three-dimensional geometry and flow conditions

were projected into local two-dimensional aerofoil

optimisation problems. The optimised profiles were then

implemented in the 3D geometry, which is checked with

3D RANS analyses.

The outer wing of the BWB geometry is a swept wing

with a leading edge sweep of 38.31 and a trailing edge

ARTICLE IN PRESS

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

-0.10 0.00 0.10 0.20 0.30 0.40 0.50 0.60

CL

C m y


new twist triangular

new twist elliptic

new twist 1/2(triangular+elliptic)

Fig. 19. Pitch moment about the centre of gravity.




sweep of 23.61. From

Lmean ¼ tan1ð0:5 tan LLE þ 0:5 tan LTEÞ: (2)

The mean sweep for the outer wing is 31.51. The line

of flight section cut of the BWB outer wing is projected

to a two dimensional aerofoil by

z

c2D

¼ z

c3D

1

cos Lmean

; (3)

where L is the mean sweep angle. Obviously, the

projected 2D aerofoil is thicker than the 3D aerofoil

defined by the line of flight section cut. The Mach

number is also projected according to the mean sweep

angle

M 2D ¼ M 3D cos Lmean: (4)

Therefore, the projected 2D Mach number is 0.725.

The Reynolds number is also scaled by the cosine of the

sweep angle.Further, the local lift coefficient on the outer wing

needs to be projected to the corresponding 2D data as

the optimisation constraint.

C L;2D ¼ C L;3D

cos2 Lmean

: (5)

5.2. Aerofoil camber optimisation with and without

pitching moment constraint

An aerofoil optimisation was carried out by QinetiQ

using the BVGK flow solver, coupling a full potential

transonic flow field solution with an integral boundary

layer solution, within QinetiQ’s optimisation package,

CODAS. A recursive quadratic programming,

RQPMIN, optimiser was used as the optimisation

algorithm. More details about the method can be found

in Ref. [35].

The local lift requirement was based on the twist

study of the previous section. For the given lift, the

drag is minimised with or without constraints on the

pitching moment. The design variables are the 6

camber parameters and the incidence. Since onlythe camber is optimised, the chordwise and spanwise

thickness distributions remain fixed during the optimisa-

tion process.

As mentioned earlier, the pitch moment constraint is

important for the trim requirement. Otherwise excessive

trim may be necessary, introducing large trim drag, as

for the baseline geometry shown in Fig. 19.

Fig. 20 shows the significant improvement of the

sectional L=D at the design condition through

the optimisation. Fig. 21 plots the baseline and the

optimised profiles in comparison. It clearly shows an

increased mean camber for the optimised profile (Fig. 22

compares the pitching moment for the original and

optimised sections).

5.3. Aerofoil profile optimisation with volume constraint

A further profile optimisation was carried out using

the MERLIN RANS solver coupled with a discrete

adjoint solver [36] to provide sensitivity derivatives. A

sequential quadratic programming (SQP) optimiser was

used. While the spanwise thickness distribution is fixed,

the chordwise thickness distributions can be changed

through the variation of the aerofoil upper and lower

surface shapes.

The initial shape is deformed by the addition of aperturbation that is defined by the design variables.

Deformations are limited to the normal direction. The

perturbation is defined by a Be ´ zier–Bernstein parame-

terisation. Sixteen parameters were used to describe the

aerofoil and one for the incidence. The baseline volume

per unit span is set as a lower constraint. For an efficient

optimisation, a multi-level approach (coarse grid Euler

and fine grid RANS) incorporating high-fidelity correc-

tion in the low-fidelity steps [37] has been implemented.

Fig. 23 compares the drag convergence for the

standard optimisation and the multi-level optimisation.

The latter shows a significant improvement in efficiency.

ARTICLE IN PRESS

0

20

40

60

80

100

120

140

0 0.2 0.4 0.6 0.8 1 1.2

CL

L / D

Original Section

Optimised Section at CL = 0.75

Optimised Section at CL = 0.75 with Cm constrained

Fig. 20. L=D versus C L for optimised BWB sections,

M ¼ 0:725:

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 0.2 0.4 0.6 0.8 1x/c

z / c

BWB baseline section

Optimised at CL = 0.75Optimised at CL = 0.75, CM constrained

Fig. 21. Comparison of original and optimised sections.




In total, a 20% increase in L=D is achieved through

twist inverse design and 2D aerofoil optimisation as

compared with the baseline configuration, which is a

significant improvement for the given planform and

thickness distribution BWB configuration.

6. 3D aerodynamic surface optimisation

In the previous section, the profiles are optimised in

2D and mapped back to 3D. As expected, the huge

benefit of the 2D aerofoil optimisation cannot be fully

carried forward in 3D. For example, the 2D optimisa-

tion managed to overcome most of the wave drag.

However, in the 3D realisation, this reduction is much

less significant due to the three-dimensional effects. To

take the fully 3D effects into account, 3D optimisation is

necessary, which is particularly important if the centre

body and the inner wing need to be optimised. 2Doptimisation has little use in these parts of the BWB

configuration due to the high sweep and the three

dimensionality of the geometry.

However, 3D aerodynamic optimisations using Euler

or Navier–Stokes simulations are very expensive due to

the large number of design variables in shape optimisa-

tion. For optimisation based on gradient search, the use

of adjoint methods is crucial for efficient calculation of

the sensitivity derivatives. Within the present project, the

BWB geometry was optimised at the cruise condition

using the Euler equation and adjoint methods to

generate the required sensitivity derivatives for gradi-

ent-based optimisers.

6.1. Twist and camber optimisation with pitching moment

constraint

The first 3D shape optimisation was carried out using

a continuous adjoint for the given BWB planform in the

MOB project using the optimisation system CADSOS at

SAAB Aerospace [38,39].

The twist and camber distributions of the baseline

wing (with the BWB centre body part fixed) were chosen

as the design variables. All calculations discussed in this

section were done for a cruising free stream Machnumber M ¼ 0:85 and a lift coefficient C L ¼ 0:3 for a

slightly different design case. The angle of attack was

adjusted during the calculations so that the prescribed

value on C L was kept. A typical optimisation run

consisted of 10–15 design cycles, which could be

performed over night at SAAB Aerospace.

A third-order polynomial was applied to describe the

twist and camber modifications of the wing. These

functions were combined with four functions (polyno-

mials) in the spanwise direction in order to get a smooth

modification along the wingspan. In total, 12 design

variables were used to control the wing shape. The

calculations were done on a grid consisting of 295,000

cells. Constraints were introduced on both the lift and

pitching moment. While the lift coefficient is constrained

to the design condition, the pitching moment is

constrained to the baseline value rather than the trim

condition presented later. As compared with the BWB

baseline, a drag reduction by 0.0022 or 19% was

obtained as can be seen in Fig. 27. The optimum was

reached after 8 design cycles. No further improvement

was obtained performing more design steps. The results

show that the constraints C L ¼ 0:3 and C

M ¼ 0:51 are

fulfilled. The angle of attack was increased by 0.51 from

2.01 to 2.51. This corresponds to a moderate global twist

modification of the whole configuration. The pressure

distribution over the baseline and optimised aircraft

shows the improved load distribution in the wing tip

area. The decreased suction at the tip results in a

lower load that is also of advantage from structural

point of view. The profile shapes of the baseline and

the optimised geometry at two span stations are

finally shown in Figs. 28 and 29. The results are

consistent with the twist inverse design carried out

earlier in the project.

6.2. 3D surface optimisation with trim constraint

In the second 3D optimisation, a full surface

optimisation with trim constraint was carried out. The

methodology used is a combination of a discrete adjoint

method with a variable-fidelity method for an efficient

optimisation [36]. Different from the 3D optimisation

described in the previous section, it uses the improved

geometry from the twist inverse design discussed in

Section 4 as the starting geometry. In particular, the

elliptic-triangular averaged design is chosen, reflecting

the design evolution in the MOB project.

ARTICLE IN PRESS

Fig. 27. Drag convergence history of the blended wing/body

optimisation.




The flow conditions for the optimisation are the sameas those presented in Section 3. At the design point, the

lift coefficient is required to be 0.41 based on the

trapezoidal area of 842 m2, which is used to non-

dimensionalise all the aerodynamic coefficients. The

pitching moment is calculated around the centre of

gravity situated 29.3 m behind the nose of the aircraft in

the plane of symmetry. The reference length used for the

pitching moment is the mean aerodynamic chord equal

to 12.3 m. A positive value of the pitching moment

corresponds to a nose up moment.

The flow solution at the design C L is calculated using

MERLIN for the new starting geometry based on the

study in Section 4. The resulting aerodynamic coeffi-

cients for the starting geometry are given in Table 6.

These are reference coefficients to which optimisations

results will be compared. Note that the wave drag here

and for the optimised BWBs presented in the remaining

of this section only accounts for the drag generated by

the wing and fuselage shock wave(s). The winglet wave

drag is not included.

Despite the twist redesign, a strong shock wave is still

present, that extends from the outer wing up to thefuselage. Strong compressibility effects are also present

in the wing-winglet junction region.

The BWB geometry is parameterised by 16 aerofoil

sections from the symmetry plane (geometry root) to the

tip of the outer wing, to which the winglet is attached.

Except the tip aerofoil (16th section), which is fixed in

shape, the other 15 wing section aerofoils are para-

meterised using 17 design variables each. The 17 design

variables at each wing section come from 8 active Be ´ zier

parameters for the upper surface, 8 for the lower surface

and 1 for the twist increment of that section (or local

incidence). The outer wing tip section is only allowed to

twist to avoid complication at the junction with the

winglet. The winglet geometry is fixed, rotating with the

outer wing. It is understood that the winglet design can

have a significant effect on the aerodynamic perfor-

mance but its optimisation is not a trivial problem. It is

regarded as a sub-optimisation problem and will not be

discussed in this paper.

In total, the above surface geometrical parameterisa-

tion results in 256 active design variables (15 17+1).

They are scaled in such a way so that an increment of 1

in any of the design variable produces a displacement of

2% of the chord of the corresponding aerofoil section.

The optimisation problem is set to minimise the dragat a given lift while maintaining the internal volume per

unit span of each aerofoil section. An additional

constraint on the pitching moment is included for

balancing the aircraft (trim). This can be written as

minimise C D

subject to C LX0:41

ðC mÞ2pð0:001Þ2

V 0 i pV i p2V 0 i ; i ¼ 1; . . . ; 15:

The constraint on the pitching moment implies a

trimmed design at the cruise condition, necessary due to

ARTICLE IN PRESS

Fig. 28. Twist and camber of the original and optimised wing

at 60% of the wingspan.

Fig. 29. Twist and camber of the original and optimised wing

at 80% of the wingspan.

Table 6

Aerodynamic coefficients for the baseline BWB geometry at the

design C L

C L C D total C Dpressure C D friction C Dwave L=D C m

0.4101 0.02855 0.01885 0.00969 0.00101 14.37 0.07360




the tailless nature of the BWB. Large deflection of the

control surfaces situated along the trailing edge will

induce a large associated trim drag. Calculations carried

out during the MOB project for the baseline BWB

geometry indicated a large trim drag penalty, i.e. the

penalty generated by the necessary deflection of the

control surfaces to trim or balance the aircraft. Hence, it

is important that the BWB shape is trimmed naturally or

requires very small control surface deflections during the

cruise. However, this constraint can limit the potential

improvements in L=D: It is obvious that a more realistic

optimisation with the trim constraint should also include

the effect of the propulsion system, although it is not

considered in this project.

The optimisation of the BWB in this section employs

the variable-fidelity method and the optimisation

problem is transformed into a corrected-low-fidelity

optimisation [36,37]. Additional linear constraints are

added for the interior volume and for the constraint ontrim.

The flow and adjoint solutions employed in the

optimisation of the BWB are required to converge to 5

orders or to the pre-specified maximum iteration

numbers, 5000 and 3000, respectively. The optimisation

starts from converged flow and adjoint solutions

calculated on the starting geometry and the computation

for each new design restarts from previous solutions to

save computing time.

The merit function Fhi employed in the variable-

fidelity method is given by

Fhi ¼ C D

dC D

db0

þ 10

ðC L 0:41Þ2

dC L

db0

2 þ 10

C 2m

dC 2m

db0

þ 10X15

i ¼1

ðV i V 0 i Þ2

dV 0 i

db0

2 : ð6Þ

Note that the function C 2m and its gradient are used

directly rather than C m and its gradient. The denomi-

nators are the initial gradients of the target function and

the constraints for normalisation.

The optimisation based on the Euler solution and itsadjoint solver is carried out using the method described

starting from the inverse design geometry. Note that the

initial design has a fairly large nose down pitching

moment.

The aerodynamic coefficients of the optimised shape

are shown in Table 7. It is pleasing to note that the

optimised shape reduced the drag (pressure drag) further

while decreasing substantially the pitching moment to

nearly trimmed condition. An L=D of 23.67 is reached

with a very low pitching moment as compared with the

starting geometry. This compares favourably to the lift

to drag ratio of 24.16 obtained by an optimisation

without constraint on C m; which has a pitching moment

40 times higher. This optimisation brings an 18%

pressure drag improvement (39 drag counts).

The alleviation of the shock wave on the upper surface

of the BWB geometry is shown in the chordwise pressure

distributions in Fig. 30. The shock wave has been

eliminated on most of the wing surface, as shown at

stations Z ¼ 0:4 and 0.71. The pressure distribution also

shows that the shock wave remains near the wing tip dueto the strong interaction with the winglet.

On the centre body (fuselage), the reflected camber

is increased with negative lift at the rear portion of

the sections (root section and station at Z ¼ 0:17).

This is clearly a result of the trim constraint to balance

the nose down pitch moment generated by the BWB

wing.

The shape deformations shown in Fig. 31 also explain

how the improved aerodynamics is achieved. On the

centre body, the profile is pitched downwards slightly

while maintaining the reflected camber. Except the two

profiles near the wing tip, all optimised profiles indicate

a movement of the maximum thickness backwards. The

rear part of the sections is thickened by transferring

some volume from the lower surface near the leading

edge region to the rear of the aerofoil on the upper

surface, reducing the leading edge radius in the process.

A slight increase of nose-up twist (pitching up) can also

be observed on the wing. The two outer wing sections

near the tip are substantially modified with a large

reduction of the rear camber, which is believed to be due

to the result of the local interaction between the wing

and the winglet. One can also observe a movement of the

maximum thickness forwards for this part of the wing.

From an optimisation point of view, the Euleroptimisation with constraint on C m proves to be

satisfactory, meeting both targets on drag reduction

and trim.

6.3. Comparison of the 3D optimised shape with previous

design shapes

In the previous section, the optimisation is based on

the solution of the Euler equations and the correspond-

ing adjoint equations. A large drag reduction has been

achieved, more importantly, along with the trim

constraint. As we can see from the paper, the spanwise

ARTICLE IN PRESS

Table 7

Inviscid aerodynamic coefficients of the Euler optimised BWB

with constraint on C m

C L C D L=D C m

Initial 0.4101 0.02125 19.30 0.08973

Optimised 0.4088 0.01727 23.67 0.00292




lift distribution and wave drag are the two key

aerodynamic factors influencing the BWB performance.

Therefore, an Euler optimisation should be meaningful

in the present context. Whether the drag reduction with

the trim constraint can be carried forward to the BWB in

the viscous flow can be confirmed by solving the RANS

equations.Table 8 shows the viscous results on the inviscid

optimised shape in the previous section. Compared with

the starting geometry, the wave drag has been well

reduced while the skin friction drag slightly increases.

Overall, the drag is reduced by a further 26 drag counts

i.e. 9%, achieved while reducing the pitching moment 18

times in magnitude at the same time. From the original

L=D at 12.67 with a large pitching moment to the final

15.8 with a near zero pitching moment, a substantial

improvement (25% for L=D) of the aerodynamic

performance has been made through aerodynamic

design for the given BWB planform and given thickness

distribution. It is expected that further significant

improvement requires planform (e.g. sweep and chord)

and thickness (t=c) changes, which necessitates the

consideration of multi-disciplinary issues in an MDO

design environment. An initial attempt is reported in

Ref. [9].

The resulting spanwise lift distribution and loadingare plotted in Fig. 32 in comparison with the other

designs. It is noticeable that there is a dip in lift near the

wing tip for the optimised design due to the local

interaction. There is also a redistribution of lift on the

fuselage, a move from the centre part to the outboard of

the fuselage in comparison with the starting design. On

the wing the spanwise lift distribution of the 3D

optimised BWB shape is closest to the inversely designed

averaged elliptic/triangular distribution, which proves

the validity of the inverse twist design in Section 4.

Fig. 33 shows that the progressive improvement

presented in the paper is associated with the progressive

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Fig. 30. Chordwise C p distributions for the Euler optimised BWB with constraint on C m: Euler calculations: (a) root section; (b) 4th

master section at Z ¼ 0:17; (c) 8th master section at Z ¼ 0:40; (d) 12th master section at Z ¼ 0:71; (e) 14th master section at Z ¼ 0:93;

(f) 15th master section at Z ¼ 0:98:




reduction in the wave drag for the cruise condition. The

final 3D shape optimisation exhibits the minimum

wave drag along the BWB wing. However, a careful

study of Table 8 indicates that among the total

drag reduction of 29 drag counts only 8 comes from

the wave drag reduction. This indicates the importance

of shape optimisation for both wave drag and non-

wave drag reduction in the pressure drag consideration.

It is also interesting to compare the proportion of

the pressure drag to the skin friction drag. For the

baseline geometry shown in Table 5, the ratio is 77:23

while the final optimised geometry it becomes 62:38.

This indicates two important issues: (1) for BWB careful

design to minimise the pressure drag is crucial as it

dominates the total drag due to the lower surface to

volume ratio; (2) the pressure drag dominance can be

reduced through design by improving the overall

performance. In contrast, for conventional transport

aircraft, the friction drag counts for about 50% of the

total drag.

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Fig. 31. Shape modification of some master sections for the Euler optimised BWB with constraint on C m: Euler calculations: (a) root

section; (b) 4th master section at Z ¼ 0:17; (c) 8th master section at Z ¼ 0:40; (d) 12th master section at Z ¼ 0:71; (e) 14th master section

at Z ¼ 0:93; (f) 15th master section at Z ¼ 0:98:

Table 8

Navier–Stokes check of the Euler optimised BWB with constraint on C m

C L C D total C D pressure C D friction C Dwave L=D C m

Initial reference 0.4101 0.02855 0.01885 0.00969 0.00101 14.37 0.07360

Optimised 0.4100 0.02595 0.01592 0.01003 0.00023 15.80 0.00401




7. Conclusions

The progressive aerodynamic study of the blended

wing body configuration highlights the importance of

wave drag, span loading distribution, aerofoil section

design and the three dimensional shaping for BWB

performance. The potential benefits of the novel BWB

configuration design can only be realised through

careful considerations of these factors in the

design process. At the design transonic cruise and

lift (weight) condition for the BWB configuration

studied, wave drag has been found to be a significantfactor affecting performance. Twist inverse design,

aerofoil profile design and three-dimensional surface

design carried out in the project can all alleviate the

wave drag problem in the design but with varying

effectiveness.

For a given planform and fixed aerofoil sections, the

twist inverse design can improve the aerodynamic

performance effectively by manipulating the spanwise

loading distribution from our understanding of transo-

nic aerodynamics. Although the triangular distribution

gives the most wave drag reduction, the averaged

elliptic/triangular distribution provides the best aero-

dynamic performance measured by the L=D ratio or the

total drag at the design cruise condition. This is believed

to be due to the less induced drag for the averaged

elliptic/triangular distribution as compared to the

triangular distribution.

The 2D aerofoil optimisation has further improved

the design through the mapping between the 2D aerofoil

and the 3D swept wing. However, the significant drag

reduction in the 2D optimisation cannot be fully realised

when implemented in the 3D shape.

In the three-dimensional surface optimisation, both

the spanwise twist distribution and the aerofoil profiles

at key stations along the span are variables in the design

process. The large number of design variables necessi-

tates the development of an efficient optimisation

methodology. The optimisation is able to find an even

better solution to the given design problem, including

the trim condition as a constraint.

Concluding from the study, due to the importance of shock wave for transonic flight, it was found that the

optimal spanwise lift distribution for best aerodynamic

performance should be a fine balance of the vortex

induced drag due to lift and the wave drag due to the

shock wave formation at transonic speeds. For the

integrated BWB shape, the elliptic distribution should

no longer be the target for minimum drag design. Since

the aerofoil profile design can have a significant effect on

shock alleviation, it is therefore essential that the

spanwise loading design is considered along with the

aerofoil profile design. In addition, the constraint on

trim has a strong effect on how these two distributions

are determined.

The study also reveals that for the BWB design the

pressure drag is playing a much more important role in

the total drag as compared with the conventional

designs due the intrinsic nature of the lower surface

to volume ratio for BWB shape. It is therefore

more rewarding to minimise the pressure drag before

skin-friction drag reduction techniques, such as laminar

flow control, are considered.

The current study is limited to aerodynamic and trim

considerations for a given planform design. For the

whole BWB aircraft performance optimisation with

targets such as maximum range or minimum directoperational cost, the aerodynamic performance (L=D) is

a key contributor in the target function. However, the

design needs to be further balanced with a number of

other disciplines, including structural weight through the

bending moment, aeroelasticity (flutter boundary),

integration of propulsion and flight stability and

controllability. For example, on the structural side,

moving away from the elliptic towards the triangular

distribution will reduce the wing bending moment

and therefore the structural weight. This emphasises

the importance of multi-disciplinary consideration in

design.

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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

% of span

C L l o

c a l * c / c b a r

baseline


triangular

elliptic

2D optimised camber

2D optimised profile

3D shape optimised

Fig. 32. Spanwise lift distribution comparison.

0

0.018

0.0160.014

0.012

0.02

0.008

0.006

0.004

0.002

0.01

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

% of span

l o c a l C D w a v e

baseline


triangular

elliptic

2D optimised camber

2D optimised profile

3D shape optimised

Fig. 33. Wave drag along the span.




Acknowledgements

The work reported in this paper was funded by the

European Union under contract G4RD-CT1999-0172

entitled MOB: A Computational Design Engine Incor-

porating Multi-Disciplinary Design and Optimisation

for Blended Wing Body Configuration. The first three

authors acknowledge the support from staff at Cranfield

University during the project and, in particular, they

would like to thank Professor Alan Morris, the

coordinator of the project for useful discussion.

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aerodynamic considerations of blended wing body aircraft (transonico m=0.85)

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