A Framework for Aerodynamic and Structural Optimization
in Conceptual Design
K. Amadori * and C. Jouannet †
Linköping University, Linköping, 581 83, Sweden
P. Krus ‡
Linköping University, Linköping, 581 83, Sweden
Aircraft design is an inherently multidisciplinary activity that requires different models
and tools for various aspects of the design. At Linköping University a novel design
framework is being developed to support the initial conceptual design phase of a new
aircraft. In this work main attention has been paid to wing design, with respect to
aerodynamic efficiency and loads, and to structural analysis. By linking together various
modules via a user-friendly interface based on a spreadsheet, the framework allows
multidisciplinary analysis and optimizations to be carried out. This paper will present the
framework, give an overview of its development status and give an indication on the future
work.
Nomenclature
CAD
cL
cdi
cm
MDF
MDS
SOA
SOAP
(t/c)
WSDL
=
=
=
=
=
=
=
=
=
=
Computer Aided Design
Lift coefficient at given angle of attack α
Induced drag coefficient at given angle of attack α
Pitching moment coefficient at given angle of attack α
CAD Datums Model
CAD Surfaces Model
Service Oriented Architecture
Simple Object Access Protocol
Thickness-to-chord ratio
Web Service Description Language
I.
Introduction
D
URING last years a research project at Linköping University has been aimed at developing a novel design
framework to be used from the very beginning of the conceptual design phase of new aircraft1,2,3. The
framework is intended to be a multidisciplinary optimization tool for defining and refining aircraft designs, with
respect to its aerodynamic, stability, weight, stability and control.
The conceptual design phase could take advantage of a novel methodology, that would not be based on
empirical or semi-empirical equations to estimate e.g. weights4, performances, costs and loads, but relay on
analytical models to a greater extent. The presented design framework is thought to meet also requirements of
modern complex product development. Many companies are located all over the world and are tightly involved in
several global partnerships, where modules of the product are designed and manufactured at different locations. This
is especially true in the aerospace and automotive industry where the end products are more or less assemblies of
subsystems from different suppliers. This implies that today’s product development is carried out in a distributed,
collaborative and competitive fashion and this forms a rather complex environment for the employment of modeling
and simulation technology. These aspects must therefore be supported by the modeling and simulation tools.
*
PhD Student, Department of Mechanical Engineering, [email protected], AIAA Student Member.
Postdoctoral fellow, Department of Mechanical Engineering, [email protected], AIAA Member.
‡
Professor, Department of Mechanical Engineering, Petter.Krus@ liu.se.
†
1
American Institute of Aeronautics and Astronautics
Previous work carried out by the research group at Linköping University has taken into consideration ways to
determine the weight of aircraft concepts by means of CAD tools5. Using a parametric three dimensional model of
the aircraft, it has been shown that the structural weight could be estimated with good precision while the high
degree of parameterization ensures that the model can cover a wide range of concepts.
Thanks to the experience gathered during the development of the framework, key requirements have been
pinpointed. Among them, the model’s flexibility, reliability and robustness are of highest importance and have been
key aspects during the development of each part of the framework modules.
A wing design study was chosen as test case for the presented work. The wing comprises both the external
surfaces to be aerodynamically analyzed and the wing-box design to be structurally analyzed. When compared with
examples of similar applications that can be found in the litterature6,7, the presented work shows a much higher
grade of design flexibility. In other wing structure design studies the designer is usually required to enter a structure
layout before the optimization can start. Then the system modifies thicknesses and maybe moves the structural
elements from their starting position. This work will instead demonstrate that it is possible to design concepts with a
much higher degree of freedom. The kind of structural analysis will get close to a topological optimization of a
general wing design. Thus it can be ensured that the solution obtained will be of a more general character.
Figure 1. The complete aircraft design framework
II.
The Wing Design Framework
The part of the design framework here presented is intended to be a tool that permits to optimize the design of
wings during the conceptual design phase. Several different aspects of the design and the wing plan-form can be
controlled. This includes the wing profiles at the end of each wing section and the structural layout. The complete
wing model will be explained in more detail in the following sections. As illustrated in Fig.1 the framework
comprises many modules that can be run independently or together with others. When running each module alone it
is possible to analyze the properties of one aspect at the time. The other modules will then work as support only; if
needed they can be substituted by simpler equations that may be less precise, but faster. In this way the number of
parameters to be optimized can be greatly reduced as well as the time required to complete the optimization. This
modularity of the framework allows for starting using it even if not all of the modules are completely developed and
ready to use. Only once one module is ready and validated it can be added to the framework and used together with
all the others.
The framework can and is intended to be used for full design optimization. Figure 2 shows how the modules
involved in the wing optimization problem are linked to each other.
2
American Institute of Aeronautics and Astronautics
-
Dell Precision PW390
CPU : Intel® Core™Duo E6600, 2.40 GHz
2Gb of RAM
NVidia Quadro FX 3500
Windows XP 64bits
Design
Parameters
CAD
Optimization
Algorithm
Mass
Panel Code
Pressure
Distribution
Wing Geometry
The framework is built to allow for being
distributed1,3,8. That means that any module can
be placed on a dedicated computer and connected
to all the others through the Internet. Connections
are implemented using SOAP messages, as
explained in Ref.1. In this example, however, all
framework modules are run on the same machine.
The specifications are as follows:
Deformed
Geometry
Lift & Drag
Stresses
FEM
The design parameters are input through a
user-friendly Excel spreadsheet interface that is
shown in Fig.3. There are different areas
indicated by different colours, where selected
aspects of the wing design are governed. With Figure 2. The wing design optimization framework
reference to the figure below, the grey area
(“Wing Geometry Layout”) includes the parameters that determine the plan-form of each wing section and the
parameters that specify the shape of the wing profiles; in the green one (“Structural Layout”) are the parameters that
control type, number and placement of the structural element; finally in the light blue area (“Design Results”) the
results from the different modules are displayed.
Figure 3. The Excel interface of the wing design framework
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The framework can be used both for automatic optimization of a particular design as well as for exploring
different design alternatives interactively. In the first case the spreadsheet is coupled with an optimization algorithm
that acts on a set of input parameters or on all of them. Otherwise the designer is asked to enter by hand the
parameter values and to start the analysis.
III.
The Parametric CAD Model
The most important characteristic of the CAD model is to be highly flexible in order to be able to represent a
variety of designs as large as possible. Secondly the model must be robust and reliable, since there will not be a
specialist entering new parameters and supervising the update process. It is fundamental that the model does not
produce mathematical errors within its whole allowed design range.
A. The Model Structure
In order to guarantee a high degree of flexibility
and robustness, the CAD model must be built in a
proper way. Figure 4 shows the relational links
between the different elements of the model. The
input parameters described above govern directly
the “Datums Model” (MDF) and the “Surfaces
Model” (MDS). The MDF-model is a wireframe
model where all reference planes and lines, needed
to define the wing and its structure, are defined. It is
important to notice that all the structure components
in the CAD model depend on both the MDF-model
and MDS-model, that depend instead only on the
top level input parameters. The MDS surfaces
model contains all the external surfaces.
The structure is obtained by instanciating a
general structural element that is designed to adapt
itself, given the following parameters that are
specified in the MDF-model and MDS-model
(Fig.5):
-
The main direction along which to
develop the structural element
Two lines defining the start and end Figure 4. Relational links between the different elements in
the CAD model
point
Upper and lower surfaces between
which the element is adapted
This general element is used for all the structure
parts of the wing: longerones and ribs. The element
thicknesses are governed by individual parameters,
allowing for optimization of the structural design.
B. Wing Geometry Layout and Profiles
The wing is divided into three wing sections:
-
-
an inner wing section, supposed to be
the part of the wing hidden inside the
fuselage
a middle wing section
an outer wing section.
It is of course possible to divide the wing into more
Figure 5. The general structure element model
sections, but in the present study it was decided to
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set the number to three. Figure 6 shows the wing sections and their input parameters. With these parameters the
designer can set span, leading edge sweep, root chord length, tip chord length, dihedral angle and twist of each one
of the three wing sections.
In addition to the shape, dimension and position of each section, it is also possible to modify the wing profiles at
the end of each of the sections through the Excel interface. They are defined using the formulation suggested by
Kulfan and Bussoletti in Ref.9:
⎛
n
⎞
(ξ )Upper = C (ψ ) ⋅ ⎜ ∑ Aui ⋅ Si (ψ ) ⎟ + ψ ⋅ ΔξUpper
⎝ i =1
(ξ ) Lower
ξ=
where:
z
c
⎛
⎞
= C (ψ ) ⋅ ⎜ ∑ Ali ⋅ Si (ψ ) ⎟ + ψ ⋅ Δξ Lower
⎝ i =1
⎠
(1)
is the non-dimensional airfoil ordinate;
z
is the profile coordinate along the z-axis;
x
ψ=
c
is the non-dimensional airfoil station;
x
is the profile coordinate along the x-axis;
C (ψ ) = ψ N1 ⋅ (1 − ψ )
Si (ψ )
⎠
n
N2
is the “class function”;
is the ith-term of the Bernstein polynomial of order n;
zuTE
is the non-dimensional upper surface trailing edge thickness ratio;
c
zl
= TE is the non-dimensional lower surface trailing edge thickness ratio;
c
ΔξUpper =
Δξ Lower
Ali, Aui, N1 and N2
are coefficients to be determined to obtain the wanted shape.
To improve ease-of-use, in the CAD model the above formulation was reworked in order to allow the wing profiles
being defined by more familiar inputs, rather than less practical coefficients. In addition to the root length, each
wing profile needs four parameters to be set:
-
thickness-to-chord ratio (t/c)
relative position of (t/c)MAX
maximum camber
maximum camber relative chord position.
Figure 6. The wing is divided in three sections, each one defined by separate parameters
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C. Wing Update Procedure
When new parameters have been entered and the designer or the optimization algorithm starts the update
procedure, a set of controls and actions are automatically carried out. They are here briefly explained:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
The system checks for any modifications in the wing plan-form, such as changed chord lengths, spans
or wing profile settings.
Comparison between the old and new number of structural elements, to determine if parts are going to
be deleted or added.
The start and end values for the already present ribs and spars are verified and updated if needed.
Thickness values for the already present ribs, spars and skins are verified and updated if needed.
Deletion or addition of new structural elements (ribs and spars).
Wing surface mesh update.
Mesh node coordinates are measured and stored.
PANAIR input file is written.
PANAIR aerodynamic analysis is started.
Results from PANAIR are retrieved from the output file.
FEM analysis model is updated with new structure mesh.
FEM analysis model is updated with new loads from aerodynamic analysis.
FEM analysis is started.
All relevant results are retrieved and presented in the Excel interface.
The time required for all operation to be completed depends of course from how many of the above steps that are
actually carried out and from how computationally heavy they are. For instance there is a big difference between
adding one rib only, compared to adding ten of them; or if for one or for all the already present elements the
thickness need to be modified. In Table 1 the time required to complete some typical operations are listed.
Type of Operation
Change rib layout case
Change 1 parameter value
Change 5 parameter values
Add 1 structural element
Add 5 structural elements
Delete 1 structural element
Delete 5 structural elements
PANAIR analysis
FEM analysis
Elapsed Time [sec]
31
31
75
19
30
20
28
13
~780
Tabel 1. Time required for typical operations
IV.
The Wing Structure Model
In the previous section it has been described how the structural elements are instantiated. Here, it will be
discussed what the design possibilities are, how the wing structure can be specified and how it is meshed prior to the
analysis to take place.
The structure modeled in the CAD tool consists only of the elements within the wing load carrying structure, the
so called wing-box. This is the part of the wing limited by the front and rear spars and by the root and tip ribs. The
whole structure is governed by the parameters located in the green field in the spreadsheet. Here it is possible to set
the number of ribs, the number of spars and the type of desired layout. As already explained, one fundamental
requirement for the model was maximum flexibility. Therefore, to permit the widest range of arrangements, it was
not desired to limit the ribs to start from the front spar and end on the rear one. By selecting the value of the
parameter “Rib Layout Case” it was possible to choose from the four arrangements shown in Fig.7. Please note that
the examples shown in the figure are obtained only by changing the value of the “Rib Layout Case” parameter.
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TIP CHORD
FRONT SPAR
REAR SPAR
ROOT CHORD
Case 0
Case 1
Case 2
Case 3
Figure 7. There are four different structural ribs layout arrangements. Changing only case it is possible to
obtain different rib layouts.
Selecting for instance “Case 0”, the starting point for each rib will be the front spar, while the end-line will be
composed by the union of the rear spar with the root and tip chords. If “Case 1” is selected instead, the start-line will
be given by the union between the root chord and the front spar and the end-line by the union of tip chord and rear
spar. Similarly for “Case 2” and “Case 3”. The start and end points are placed according to the values indicated in
the “Start” and “End” columns in the green field of Fig.3. The numbers represents the relative distance from the line
starting point, where zero gives the line starting point and one gives the end point.
Each rib is then modeled having a simple rectangular cross-section. Thickness, starting and ending points are
defined by individual parameters. The thickness is constant over the whole rib. Spars are defined in a similar way.
The difference is only that there is the possibility to vary the thickness along the spar’s length. Three thicknesses are
defined: one at each extreme and one at the borderline between middle and outer wing section.
The skin panels are defined from the MDS-surfaces and inwards. The thickness in varying linearly along the
wing sections, and can be explicitly selected at the end of the middle and outer wing section by modifying the
parameter values in the corresponding spreadsheet interface fields.
One engine is also mounted under the wing. It is attached to one rib that is fitted with appropriate attachments.
The engine can be chosen from a list of ten different models, varying from the smaller FJ44-4A, mounted on Cessna
Citation CJ4, up to the larger GP7000, installed on Airbus A380. At the moment, th engine selection can not be done
through the spreadsheet interface, but requires the designer to actively modify one parameter in the CAD model
itself. Changing the engine will also change the loads applied to the wing structure deriving from the engine weight
and thrust.
The whole wing-box structure is meshed using the internal CATIA module “Advanced Meshing Tools”. So far it
has been possible to use only tetrahedral quadratic elements that tend to model structures to be stiffer than what they
really should be. This shortcoming can be addressed by the adoption of flat panel elements.
The loads that are applied to the structure are retrieved from the output file produced by PANAIR. In the
following section it will be explained how they are gathered and applied.
V.
The Aerodynamic Model
At the moment, the aerodynamic analysis tool adopted is a panel code, PANAIR. Panel codes are numerical
schemes for solving (the Prandtl-Glauert equation) for linear, inviscid, irrotational flow about aircraft flying at
subsonic or supersonic speeds10. As pointed out by Amadori et. al.3, panel codes are not as precise as modern CFDs
can be, but they have other advantages. Considering that during a conceptual design phase, the aircraft geometry and
its outer shape is not precisely defined and that the detail level is quite rough, it is clear that it can be unpractical and
not justified to use tools that have a much higher accuracy. Moreover CFDs requires the space around the studied
body to be accurately meshed, while for a panel code it is sufficient to approximate the aircraft’s outer surfaces with
proper rectangular panels. Therefore the meshing time required by a panel code is lower by several orders of
magnitude, compared to a CFD code. It should be kept in mind that, in this framework, PANAIR is used mainly to
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compare the effectiveness of different concepts with each other, rather than to gather exact and absolute figures of
their aerodynamic efficiency. When much powerful and faster computers will be available or if higher accuracy was
required, PANAIR could be substituted with other
solvers, thanks to the modular nature of the
framework.
The data that is gathered from the panel code
analysis are the wing lift coefficient (cL), its
induced drag coefficient (cDi), calculated using
Trefftz plane analysis, and the aerodynamic
forces and moments acting on the wing.
The upper and lower surfaces of the wing are
meshed with rectangular panels using an in-house
developed meshing application. This application
is based on a set of script-procedures that can be
activated from the spreadsheet interface and that
also handles all steps required for starting the
aerodynamic analysis. The surfaces are at first
split along the front and aft spars, as shown in
Fig.8. This is done to simplify the aerodynamic
loads retrieving operations. This is done because
PANAIR presents results for each surface Figure 8. The surface division prior to meshing
separately and then assembled for the whole
aircraft. Since the wing-box only is structurally analyzed, the air loads coming from the forward and aft surfaces are
then simply applied along the front and rear spars.
Another advantage of using a tailor made meshing tool is that the coordinates for each one of the meshing nodes
can be stored directly in the appropriate order for PANAIR to correctly interpret them. Thus data handling is in this
way simplified and speeded up.
Figure 9. Results from FEM analysis of the wing-box structure
VI.
Optimization Problems
The presented models and framework can be used in different optimization scenarios, employing different
optimization tools. As for implementing optimization functionality, the most obvious is to use optimization software
available in the user application. For example, the commercial software Crystal Ball with the optimization toolbox
OptQuest has been evaluated. OptQuest incorporates Metaheuristics to guide its search algorithm11. It is capable of
handling a wide range of problems and is executed as an integrated module of Excel. Another plug-in Design
Analysis tools has been developed at Linköping University which includes sensitivity analysis, functional
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correlation, and support for both establishing and to carry out design optimization, Krus12. This can also be used
together with tools for statistical simulations for probabilistic design as in Mavris et al13. Excel also has support for
using web service technology and in this way models published as web services on other geographic locations can
be connected and used in the analysis and optimization. This has been done in other research projects carried out at
Linköping University1-3,14. For optimization both the so-called Complex-RF method and genetic algorithms have
been implemented and deployed. The Complex algorithm was originally presented by Box15, and is a non-gradient
method which is appropriate for problems where the objective function is defined by results from various
calculations or simulations and the derivative of the objective function cannot be defined. The algorithm was
improved by Krus et. al.16 to increase the probability of reaching a global optimum and has been used very
successfully over a wide range of problems and is characterized by simplicity and robustness.
By choosing the appropriate set of optimization variables among all the parameters that can be governed through
the Excel interface, a variety of engineering design problems could be solved. For instance one typical application
could be to minimize the wing weight and or drag, granting a given minimum lift force. The problem could be
approached with a fixed number of spars and ribs or with a variable number of them. In the second case of course
the solution would be more general, but at the cost of longer computing time. Also which geometry layout
parameters to include in the optimization problem can be freely selected.
VII.
Conclusions and Future Work
In this paper a framework for wing design and optimization has been presented. It is one part of a complete
aircraft design framework that is being developed at Linköping University. The whole framework is intended to
cover all the diverse parts and systems that an aircraft can be divided into: fuselage, wing, propulsion systems,
landing gears, subsystems, structures, and control system.
The framework itself is innovative in several ways. First of all, the design tools are based on real models rather
than historical data. Secondly, the modeling approach is an integration of several distributed domain specific models
which increases the possibilities to gain more reliable design information early in the design process without
revealing proprietary parts of the models. This is a very important aspect in real world design projects where several
distributed participants must efficiently cooperate while protecting restricted sensitive data.
The presented wing model is also innovative. It has been developed having its flexibility as a fundamental
requirement. Not only does it permit to modify and optimize a given wing design and one specified load carrying
structure, but it also allows to radically change the configuration and layout of the structure design. Not only the size
and relative position of structure elements can be changed, but also their number. If one rib is not required it will be
removed. This means that a more general design can be used for the optimization, while minimizing the designer’s
work load, since he/she will not be asked to enter a qualified structural proposal prior to starting the optimization.
Thus the resulting structural layout will not depend on how the wing-box is defined at the beginning of the
optimization. In this sense the proposed framework will work similarly to a topology optimization tool.
In order to verify the robustness and flexibility of the model a detailed analysis of the model has been carried
out. Now tests with optimization problems of increasing complexity will follow. The tests will be used to verify both
how precise results can be obtained and to evaluate the optimization performance. Even though if compared to
simpler applications often used in conceptual design phases, the presented tool will clearly require longer computing
time, the results obtained will be more detailed and reliable. The detail level of the obtained answers will also be far
more exhaustive than with classic tools. Moreover, since all elements are from the start modeled with CATIA, most
of the models can be directly reused in further design steps. All together this leads to reduced overall cost and time
for a project.
At the moment investigations are also done to verify the possibility to employ other aerodynamic codes, such as
ZOONAIR, ALIS or CFD codes like Edge (FFA) that will offer increased accuracy and flexibility. Thanks to the
modular structure of the framework, substituting one module is not compromising the functionality of the rest of
them, which ensures to be able to always use the most profitable tools available.
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American Institute of Aeronautics and Astronautics
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13
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14
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16
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