UWE Bristol Engineering showcase 2015

Christopher Farndon
BEng Aerospace Design Engineering
Project Supervisor
Dr. Chris Toomer
Investigation, creation and validation of an inverse design code for twodimensional
aerofoils using MATLAB
Creation of MATLAB model
After completing a thorough literature
survey, it was decided that the most suitable
method of inverse design for this project was
the Modified Garabedian McFadden (MGM)
method. This approach uses coefficient of
pressure distributions to compute a residual
value between a target and initial Cp
distribution, with this driving an iteration
process which optimises an initial aerofoil
shape. The fundamental equation used to
compute the aerofoil change is:
AA δδδδ + BB ∂∂(δδδδ)
∂∂∂∂
− CC ∂∂2 δδδδ
∂∂xx 2
= CCCC tttttttttttt − CCCC iiiiiiiiiiiiii
This second order ordinary differential
equation can be solved using a central finite
difference method for δδδδ (the change in
aerofoil height) which can then be added to
the initial aerofoil to create a new shape
closer to the required aerofoil. This process
is repeated in an iterative loop until the Cp
residual is reduced to 0 (or a negligible value)
indicating the aerofoil has been optimised
correctly.
Tri-diagonal sparse matrix created to solve the fundamental equation
Validation
With an inverse design method (MGM) created in
MATLAB, this model was required to be validated to
ensure the process was producing accurate and
reliable results. This was done by comparing the
output produced by the MATLAB model against two
industrially established computational-fluid-dynamics
(CFD) software packages: ANSYS Workbench v15 and
Javafoil v2.23.
For the ANSYS analysis, a target aerofoil was created
in Solidworks, a computer-aided-design (CAD)
program and then imported into ANSYS. The results
of this and the Javafoil analysis can be seen above. It
can be seen that overall the MATLAB model matches
the general shape of both the ANSYS and Javafoil
solutions, providing
confirmation that the
inverse
design code created in
MATLAB was
implemented
correctly and was
producing dependable
and trustworthy
results.
Testing
The testing phase allowed the capabilities of the
developed MATLAB inverse design code to be
investigated. A variety of test series were
created; each assessing a different aspect of the
program’s functionality. The constants A, B and
C seen in the fundamental equation were
required to be determined experimentally, as
well as the optimal value of the Cp error. Once
these were determined, various tests were
performed to observe the MATLAB’s success at
transforming an initial aerofoil shape based on a
variety of key aerofoil design parameters:
camber, maximum thickness and the position of
the maximum thickness.
These tests were all passed with overwhelming
success, with the inverse design code efficiently
optimising the aerofoil shape to within an
acceptable level of accuracy for any change in
design criteria.
The testing phase continued on to assess the
MATLAB model’s ability to analyse viscous flows,
where it also successfully passed this, increasing
the flexibility and usefulness of the algorithm.
3D representation of change in aerofoil shape over time.
Project summary
The project attempted to gain an
understanding of inverse design methods
when applied to the aerospace industry, by
creating, validating and testing a working
model from first-principles.
Project Objectives
Overall project objectives:
• Create an inverse design code in MATLAB.
• Use computational-fluid-dynamics (CFD)
to validate the output of the inverse
design code .
• Devise and complete a comprehensive set
of test procedures to investigate the
program’s ability to successfully optimise
an aerofoil based on a variety of varying
design criteria.
Project Conclusion
An inverse design code was successfully
created in MATLAB, before being validated
and tested to confirm the program produced
accurate and reliable aerofoil shapes. The
developed program provided not only a
useful aerodynamic design tool, but also
served as an opportunity to observe the
concepts and principles associated with
inverse design first hand by creating a
working model first-hand.