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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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
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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
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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.
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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.
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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.
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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:
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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.
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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
original configuration
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.
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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
original configuration
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
original configuration
triangular twist
elliptic twist
1/2(triangular+elliptic) tw ist
Fig. 18. Comparison of C D vs. C L at M ¼ 0:85:
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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
original configuration
new twist triangular
new twist elliptic
new twist 1/2(triangular+elliptic)
Fig. 19. Pitch moment about the centre of gravity.
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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.
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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.
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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
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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
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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
ARTICLE IN PRESS
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:
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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.
ARTICLE IN PRESS
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
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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.
ARTICLE IN PRESS
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
1/2(triangular+elliptic)
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
1/2(triangular+elliptic)
triangular
elliptic
2D optimised camber
2D optimised profile
3D shape optimised
Fig. 33. Wave drag along the span.
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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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