Using CAD-Tools and Aerodynamic Codes in a Distributed
Conceptual Design Framework
K. Amadori * and B. Johansson †
Linköping University, Linköping, 581 83, Sweden
P. Krus ‡
Linköping University, Linköping, 581 83, Sweden
Aircraft design is an inherently multi-disciplinary 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. Different modules are included, each one addressed to analyze and evaluate
different aspects of the airplane, such as its aerodynamics, its weight and structure, its sub
systems and its performances. All modules are easily accessible from a user-friendly
interface based on an Excel spreadsheet. The link between all modules is based on Service
Oriented Architecture (SOA) and allows both distribution and integration of all functions.
This paper will present the framework, give an overview of its development status and give
an indication on the future work.
Nomenclature
α
CAD
CFD
cL
cLα
cdi
cdiα
cm
cmα
c
MDF
MDS
SOA
SOAP
WSDL
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
Angle of attack
Computer Aided Design
Computational Fluid Dynamics
Lift coefficient at given angle of attack α
Lift coefficient as function of the angle of attack α
Induced drag coefficient at given angle of attack α
Induced drag coefficient as function of the angle of attack α
Pitching moment coefficient at given angle of attack α
Pitching moment coefficient as function of the angle of attack α
Chord length
CAD datums model
CAD surfaces model
Service Oriented Architecture
Simple Object Access Protocol
Web Service Description Language
I.
Introduction
T
HERE is a need to reduce the time-to-market for every new aircraft being developed. To be able to do so, new
and more efficient approaches to the design process need to be introduced. This is one of the reasons why
design optimization has seen a growing interest in the recent years. In particular, true Multi-Disciplinary
Optimization (MDO) has a great potential. Moreover, computers becoming constantly cheaper and more powerful,
and the increasing computational capacity is greatly welcome for MDO applications.
In particular, 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. weights1, performances, costs and loads, but relay on
analytical models to a greater extent. There are many examples of how MDO can be successfully adopted in the
*
PhD Student, Department of Mechanical Engineering, [email protected], AIAA Student Member.
PhD, Department of Mechanical Engineering, [email protected].
‡
Professor, Department of Mechanical Engineering, [email protected].
†
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American Institute of Aeronautics and Astronautics
early development phases of new aircrafts2-7. A field where it is felt that much work can still be done is in the
flexibility of the optimization tools, in order not to have a tool that is tailored for one specific type of aircraft only,
but can be adopted on a range of types as wide as possible.
With this in mind, a novel design framework is being developed at Linköping University that aims at being
flexible enough to permit the study of a variety of different types of airplanes and that includes modules that allows
for optimizing the design of all main sub-systems. Previous work has taken into consideration ways to determine the
weight of aircraft concepts by means of CAD tools8. 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.
Within the above mentioned framework, a module for the evaluation of aerodynamic performances has also been
developed9. Different concepts can be studied with help of panel code algorithms instead of relaying on semiempirical or statistical methods. A generic unmanned flying wing concept was used as a test case to examine the
aerodynamic goodness of the concept layout. Moreover the module was developed to enable the optimization of the
design parameters using different optimization algorithms.
The 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.
Both the utilization of a CAD system in combination with analytical design tools as well as with concepts for
distributed simulation will be described in this paper.
II.
CAD Tools and Aerodynamic Codes for Conceptual Design
The design of a new complex product, such as an aircraft, is a difficult task that involves many different teams
and departments, within or between companies. It happens often that each group decides to use its own tools to work
on their specific part of the project. This leads inevitably to a non optimal use of time due to the fact that many
operations are repeated several times or due to incompatibilities between some of the tools. One possible way to try
to reduce these inefficiencies is to standardize the tools used within the same project. It can be very useful to start
using a powerful CAD system from the very start of the design of a new aircraft, from its conceptual design. The
model generated during this phase would be the base for all future design work with no need for redoing what has
already been done. Moreover, the availability of a fairly detailed three dimensional CAD model of the airplane in
early design phases permits to carry out more precise estimation of crucial design properties. These are otherwise
traditionally calculated with semiempirical or statistical methods that
can loose accuracy in case of nonDesign Parameters
External Aircraft Shape
Aerodynamics
(CAD)
(PANAIR)
conventional concepts10. It is however
important that the model generation is
not time consuming, in order to allow
the design team to rapidly evaluate
Structure Optimization
concept layouts, instead of spending
precious time drawing them. Hence
the CAD model needs to be very
flexible so that it can cover a variant
FEM Analysis
Structural Layout
range as wide as possible. The answer
is a fully parametric CAD model that
requires the users only to insert a
limited set of input parameters to
display the wanted geometry. Here a
systematic
approach
for
Design Parameter Values
Optimization Algorithm
parametrization is used. In this way
the optimization can be given a high
degree of freedom to explore the
design space, using a limited set of Figure 1. The optimization loop scheme
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design parameters to control the design. The model shall include a reasonably detailed structure together with all
main sub-systems, such as fuel tanks, engine(s) and air intake(s), landing gears and payload. In the application
example presented in the following section, a fully parametric CAD model of an unmanned combat aircraft in a
flying wing configuration will be presented, which has been developed at Linköping University.
To be able to obtain reasonable estimates of the aircraft’s structural weight, the CAD model needs to be linked to
an aerodynamic model. Here, the configuration described with the CAD tool is analyzed with two main purposes: to
gather information regarding aerodynamic efficiency and performance, and to calculate the pressure distribution on
the surface of the airplane. These pressure values can then be used to optimize the structure for each external
configuration, through iterated finite element analysis. The result of each one of these optimizations represents the
best structural layout that guarantees structural integrity for one given aircraft configuration (see Fig.1). The
coupling between CAD model and aerodynamic model can be designed in different ways. The simplest one is to
consider the pressure field around the aircraft as not dependant on the deformation of the structure due to the
aerodynamic loads. In this case, once the pressure field is known, the structure can be optimized using a constant
load set to obtain the smallest structural weight. If, on the other hand, it is decided to take into consideration the
aeroelastic couplings, the structural optimization must re-analyze the external surfaces every time a new deformed
structure is obtained.
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 speeds11. As pointed out by Amadori et. al.9, 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
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.
III.
The Parametric CAD model
As previously stated the CAD model needs to be very flexible, so that the model is able to represent a variety of
configurations as large as possible, without requiring designers to spend precious time at building new CAD models.
Obviously it is a time consuming task to build a highly flexible, fully parametric CAD model. And of course each
CAD model will have limits so that not all configurations can be represented through it. On the other hand each
model can be stored in a library of sort, where each type of basic configuration can be selected through a given
parameter. Each time a new CAD model is created it can be added to the library for future use.
A. Parametrization
For the test case adopted in this work the chosen basic configuration was a flying wing as described in Fig.2. The
main parameters used to define the geometry are:
1.
2.
3.
4.
5.
6.
Fuselage length at the centerline (CR)
Thickness-to-Chord ratio at the centerline (t/cR) (not shown in Fig.2)
Leading edge sweep angle (ΛLE)
Tip chord length (CT)
Thickness-to-Chord ratio at the tip (t/cT) (not shown in Fig.2)
Semi-span width (B)
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This may be felt as an unconventional way to
describe an aircraft wing geometry that usually is
described through a root chord length, quarterchord sweep angle and an aspect ratio. This type
of parametrization was not chosen mainly
because using the aspect ratio would have
required some parameters to be calculated before
being able to draw the aircraft, while the chosen
set directly describes the “raw” geometry. The
drawback is that a control has to be performed on
the input parameters to verify whether the relative
geometry is permitted or not12.
The wing profiles used to generate the upper
and lower external surfaces are described using
the formulation suggested by Kulfan and Figure 2. The basic flying wing configuration of the case
Bussoletti in Ref.13:
⎛
n
⎞
(ξ )Upper = C (ψ ) ⋅ ⎜ ∑ Aui ⋅ Si (ψ ) ⎟ + ψ ⋅ ΔξUpper
⎝ i =1
(ξ ) Lower
ξ=
where:
z
z
c
⎠
⎛
⎞
= C (ψ ) ⋅ ⎜ ∑ Ali ⋅ Si (ψ ) ⎟ + ψ ⋅ Δξ Lower
⎝ i =1
⎠
n
(1)
is the non-dimensional airfoil ordinate;
is the profile coordinate along the z-axis;
ψ=
x
c
x
is the non-dimensional airfoil station;
is the profile coordinate along the x-axis;
C (ψ ) = ψ N1 ⋅ (1 − ψ )
Si (ψ )
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.
This formulation presented a great improvement from the previously adopted NACA-4digits9, because it permits a
much larger range of shapes and profiles to be described by the same equations, simply varying some parameters.
The value to be assigned to the parameters Ali, Aui can not be decided intuitively. Thus, the order n of the Bernstein
polynomial was fixed to four and the parameters linked to other dimensions, the meaning of which was clearer.
They were the following:
-
maximum camber
maximum camber chord position
maximum thickness
maximum thickness chord position
airfoil nose radius
boat tail angle13
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B. The Model Structure
In order to guarantee a high degree of
flexibility, the CAD model must be built in a
correct way. Figure 3 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 aircraft 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
together with the surfaces defining the air
intake, the exhaust gases outlet, the engine bay
and the payload bay (see Fig.3). These surfaces
are required to specify the limits within which
the general structural element is defined. The
structure is obtained instancing a general
structural element that is designed to adapt
itself, given the following parameters that are Figure 3. Relationships between elements in the CAD model
specified in the MDF-model and MDS-model
(Fig.4):
-
The main direction along which to develop the structural element
Two lines defining the start and end point
Upper and lower surface between which the element is adapted
Eventual surfaces defining cutouts.
This general element is used for all the
structure parts of the aircraft: frames, beams
and ribs. Widths and wall thicknesses of each
element are governed by individual parameters,
allowing for optimization of the structural
design. For the test case presented in this work,
the structure layout is only permitted to
“morph” changing the distance between the
elements, and it is not allowed to add or remove
any structural item. This functionality is though
planned to be added in the near future. In Fig.4,
it can be seen that the elements have a “C”section and have also a reinforcement web
made of vertical ribs. So far only the distance
between the ribs (and thus their number) can be
Figure 4. The general structure element model
varied, but in the future it will be also possible
to optimize their disposition and direction.
IV.
Distributed Design Framework
As described above, the design task involves several more than one design tools, which needs to be connected.
Moreover, as described in the introduction, product development today often also implies collaboration and
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distribution. In order to address these issues in this work, an implementation has been created using the Modelith
framework which is developed within the research group14. The Modelith framework is based on Web Service
Technology and implements as so-called Service Oriented Architecture (SOA)15. This architecture is based a set of
standards for distributed computing developed by World Wide Web Consortium which enables distribution and
integration of tools at the same time.
The interconnected modules communicate using standardized messages formatted according to the SOAP
standard (Simple Object Access Protocol). These messages include the transmitted data and instructions for which
method to invoke on the connected service. Each module is also described using WSDL (Web Service Description
Language). This description provides enough information to automatically create the computational interface
between the modules. These standards and general technical aspects of the computational framework are not
described in depth in this paper, rather, an overview of the framework and the implementation using the tools
presented in this paper is given. See Ref.14 and Ref.15 for a more detailed and technical description.
The main advantage using web service standards to communicate between models and tools is that it gives a lot
of new possibilities to integrate the models. First of all, the different models could be located at an arbitrary
computer at the Internet and be accessed from any other computer. This gives multidimensional possibilities in how
the models are combined. For example, it makes it possible to execute computationally heavy models on high
performance computers while other models and clients can be run on ordinary desktop computers, laptops or
handhelds.
Secondly, the web service models, due to the standardized interface, are very easy to access from other tools. In
this work, for example, a design client is implemented in a regular spreadsheet with a small module of encapsulated
Visual Basic code. This means that everything that is necessary to access the simulation models is available in the
spreadsheet and can be distributed without any other required software. The flexibility in combining models and
tools implies tremendous possibilities in achieving design automation using for example design optimization.
In the next section, an application example is given that illustrates an implementation of the Modelith framework
for aircraft design.
V.
Application Example
In the presented work, the CAD-model and the Aerodynamic model, described in the previous section, have been
integrated using the Modelith framework according to the illustration in Fig.5.
Spreadsheet model
Obj. function
Optimizer
Control
variables
Aerodynamic model
Geometrical
parameters
Mission
parameters
Subsystem
parameters
Cruise 2
Fuel system
Electric power
system
Cooling
system
Actuation
system
Loiter
Landing
Cruise 1
Payload Drop
Take Off
Parametric CAD model
Mission model
Subsystem models
Figure 5: The Modelith framework configured for conceptual aircraft design. Inputs and outputs
are here managed using an Excel spreadsheet.
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As an application example the conceptual design of an unmanned air vehicle (UAV) was chosen as test case for
the design framework implementing the tools and methods presented in this paper. The modules included so far are:
•
•
•
•
•
Three-dimensional modeling tool (CATIA V5)
Aerodynamic evaluation (PANAIR)
Mission simulation (MatLab)
Subsystem sizing models (Excel/VBA)
Optimizer (Complex algorithm and Crystal Ball/OptQuest)
For the first module listed, the same set of six parameters used when developing the aerodynamic calculation
module presented in Ref.9 was adopted to create a CAD model of the outer surfaces of the aircraft (Fig.6). A set of
Visual Basic scripts were then created to enable the system to change the parameter values of the model and update
it from outside CATIA V5.
A. Three-Dimensional Modeling Tool (CATIA V5)
Within the framework described in this paper, the model is used at the moment only to measure the following
entities:
-
wetted area (Swet)
reference area (Sref)
structure weight (WST)
position of the center of gravity (xG, yG, zG)
principal moment of inertia
Work is being carried out to be able to use the same model also for structural validation through finite element
analysis and for directly creating the input file needed by the panel code (more on that can be found in the paragraph
“PANAIR” here below). Figure 6 shows the complete model with all the details that have been included so far.
Previous work carried out by the group has led to the definition of a parametric model of landing gears that will also
be included.
Figure 6. The complete CAD model of the test case aircraft
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B. PANAIR
The aircraft parametrization used for the CAD model and described in the previous chapter, is again used to
generate a mesh where the outer surface is approximated with rectangular elements. This grid is then used by the
panel code algorithm PANAIR to calculate basic aerodynamic coefficients for a given mission section. The
parameters that are required for an analysis to be carried out are angle of attack, yaw angle, air speed and altitude.
Outputs of this module are lift coefficients cL and cLα, induced drag coefficients cdi and cdiα, pitching moment
coefficients cm and cmα. PANAIR returns also the pressure values and speed vectors in each node of the mesh that is
input. This information will be used as a load case for the finite element analysis of the airframe structure. At the
moment, two separate geometry models are created. One is the previously described CAD model; the other one is
created in MatLab and contains only the mesh of the outer surfaces and is used as input for the panel code. As soon
as the connecting module between CATIA and PANAIR will be ready, this duplicity will not be necessary and the
mesh will be generated directly from the CAD model and sent to PANAIR. This function will also permit to analyze
the aerodynamics of deformed bodies, obtained from finite element analyses, enabling structural optimization with
respect to aeroelastic couplings.
The aerodynamic module of the framework is governed by MatLab algorithms. Modifications were made
compared to the scheme presented in Ref.9. The reason is that more modules of the framework have been developed
and do not need to be simulated by simple handbook equations. There is a function called Opt_Panair.m that is the
one that acts as an interface between the framework and PANAIR. Another function, Input_Panair.m, creates the
input text file with the proper formatting that PANAIR requires to run an analysis of the present aircraft
configuration. Once the analysis is completed and the output result file is ready, Opt_Panair.m scans it and retrieves
the data needed for calculating the objective function value.
C. Mission Simulation Module
The third module used in this test case is the mission simulation module. This is a MatLab algorithm that
calculates, using the outputs from the previous modules, whether the aircraft concept is capable of flying a given
mission or not. At the moment the module is based on very simple equations, like the Breguet equation and the
sizing equation presented by Reymer in Ref.16. This module also performs other controls on the aircraft. It
calculates the static stability and static margin using the knowledge of the center of gravity and the aerodynamic
center from the previous two modules. It also verifies that the total lift force is sufficient for the airplane to fly as
required.
As described in the following section, the core of the framework is an Excel spreadsheet where the user shall
insert the inputs needed and where all results coming from the different modules are displayed. There is total
freedom to select which module to use. It can be chosen to calculate only aerodynamic data for a certain concept
using only the dedicated module. Otherwise it can be necessary to carry out an optimization of the input parameters
with respect to a set of requirements. One typical optimization problem is to minimize the take-off weight required
in order to be able to fly a given mission, carrying a predefined payload and flying at desired speed and height. This
is the same kind of problem that has been addressed in Ref.9. Excel offers a range of built-in features that can be
employed for solving optimization problems.
D. Onboard System Models
To be able to predict the weight of the complete aircraft, it is important to enable estimation of the weight of the
onboard systems. For smaller aircraft such as UAVs, the onboard systems tend to represent a higher percentage of
the total weight compared to regular aircraft types. Typical for UAVs is also that conventional technologies such as
central hydraulic system and cooling system are replaced with new technologies such as electrically powered
systems. This means that historical data and trends for onboard system weight will not give valid results.
In previous studies conducted by the authors, models for so-called MEA-systems (More Electric Aircraft) have
been developed, see Ref.17. These models include for example estimations of weight, cost and required power and
have been connected to the framework presented in this paper. The MEA models include the following systems:
• Cooling System. Includes characteristics for compressor, heat exchanger, etc. The weight, cost and required
electrical power is computed from required cooling power and technology selection.
• Actuation System. An electro-mechanical or electro-hydraulic actuation system including electric motor and
mechanical or hydraulic system. The module computes weight, cost and required electrical power from required
performance and selected technology.
• Fuel System. Includes fuel tanks, electric motor, fuel pumps and piping. Computes weight and required
electrical power.
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•
Electric Power System. Includes batteries, generators, wiring etc. This module includes algorithms for how cost
and weight of the electric power system depends on selected technology and parameters such as frequency and
voltage level.
E. Design Optimization
Engineering design in general involves design iterations which to a large extent can be automated using an
optimization algorithm and a simulation model, as illustrated in Fig.7. In general, this is today a rather well
established procedure in engineering design. The approach presented here however adds a new dimension to the
typical approach in the sense that the involved tools and models are executed in a distributed fashion using the webservice interfaces described above.
The presented framework includes a module for optimization which has a rather generic and simple interface
accessible from the spreadsheet. From an optimization perspective, the model structure and localization don’t have
so large effect but it is important that the algorithm is robust, flexible and applicable to a wide range of problems.
1. Implemented Optimization Algorithms
Different approaches to implement
optimization functionality are possible. The
Objective function
most obvious is to use optimization
f1 (x ), f 2 (x ),..., f k (x )
software available in the user application.
Responses
Performance
For example, the commercial software
measures
Crystal Ball with the optimization toolbox
OptQuest has been evaluated. OptQuest
incorporates Metaheuristics to guide its
search algorithm18. It is capable of
handling a wide range of problems and is
executed as an integrated module of Excel.
Optimization
Another solution has also been
Simulation model
developed
where
the
optimization
algorithm is implemented as a Web service Distributed
modules
using the same type of interface as the
simulation modules described above. The
Design variables
advantage using this approach is that the
optimization
algorithm
can
be Figure 7. Principle of design optimization using distributed models
implemented in a wide range of
applications supporting the web service
interface regardless of location, platform or software implementation. This way, the models and the optimizer can be
connected and executed in a rather straightforward way.
For the remote optimization algorithm, the so-called Complex-RF method has been implemented and deployed
as a web service. The algorithm was originally presented by Box19, 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.20 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.
2. Optimization Procedure
The following procedure is required in order to perform an optimization (see also Fig.5 and Fig.7).
Step 1.The problem is formalized and set up in the user application. This means that the objective function and
optimization constraints are defined here. The optimizer is called with the initial optimization settings and
waits for response from the optimizer.
Step 2.The optimizer generates design parameter values, sends these back to the user application, and waits for an
updated evaluation of objective function and constraints.
Step 3.The user application calls the different simulation modules to evaluate the proposed design parameters.
Step 4.The distributed modules are evaluated and the responses are returned to the user application.
Step 5.The objective function is computed and the constraints are evaluated by the user application and the objective
function value is sent to the optimizer.
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Step 6.Return to Step 2 until optimization has converged.
If the system of connected models becomes large, the sequencing of the connected modules will be rather
demanding. Then, it is necessary that the process if formalized through an executable process description. Such
functionality is available in the Modelith framework and is described in Ref.14.
VI.
Conclusions
In this paper, a novel framework for aircraft conceptual design including both CAD-tools and aerodynamic
codes in a distributed framework has been presented. The framework is being developed at Linköping University
and once completed it will offer designers a collection of modules dedicated to evaluate different aspects of the
aircraft concept: its aerodynamics, its structure and weight and its on-board systems. The framework also includes
design tools such as design optimization.
The presented framework is innovative in several ways. First of all, the design tools are based on real models
rather than historical data where the fully parametric CAD models as well as aerodynamic codes have high
importance already from the conceptual design stage. 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 model. This is a very important aspect in real world
design projects where several distributed participants must efficiently cooperate while protecting restricted sensitive
data.
The user interface to the framework is a straightforward Excel spreadsheet where only the important design
parameters are needed to have a complete description of the whole system. This means that modules for Excel, for
different analysis can be used in the framework. The Excel workbook can then be connected to all the modules in
the framework via the Internet and can reach them from wherever in the world. The large computing power required
by the modules can be left on dedicated powerful stationary computers, while an easy-to-carry portable one can be
brought to meetings or on a trip.
The development of the framework is an ongoing activity with continuous improvements and extensions. As it
has already been pointed out, work is currently being carried out for linking the panel code PANAIR directly to the
CAD model. This will eliminate the need for a second geometrical model from which to derive the mesh. More
important it will enable optimizing the internal structure with respect to aeroelastic couplings. Another major area of
improvement is represented by the Mission Simulation Model where simple equations and methods are still
employed.
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8
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9
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10
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11
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12
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10
American Institute of Aeronautics and Astronautics
13
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14
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15
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16
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17
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18
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19
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20
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11
American Institute of Aeronautics and Astronautics