CEAS 2015 paper no. 133 Page | 1
This work is licensed under the Creative Commons Attribution International License (CC BY). Copyright © 2015 by author(s).
Aerodynamic Validation of a Parametric Airfoil
Description
TITEL
Tomas Melin
Fluid and Mechatronic Systems, Department of Management and Engineering, Linköping University
Research Associate
Linköping, SE-581 83, Sweden
tomas.melin@liu.se
Roland Gårdhagen
Applied Thermodynamics & Fluid Mechanics, Department of Management and Engineering, Linköping
University
Assistant Professor
Linköping, SE-581 83, Sweden
roland.gardhagen@liu.se
ABSTRACT
This paper reports the aerodynamic validation of a parameterized modelling of wing profiles. The
parameterization uses 4 piece-wise C1 continuous cubic Bézier curves to model the wing profile envelope.
A large set of wing profiles were compared with respect to geometric and aerodynamic similarity between
parametric model and point cloud representation. In particular boundary layer properties such as
transition point position and drag coefficient; also the critical Mach number is compared between the two
sets of wing profile modelling in order to support the conclusion that the two methods of geometrical
representation are equivalent.
1 INTRODUCTION
A fundamental part of aircraft design involves wing airfoil design and optimization, establishing an outer
shape of the wing, which has good aerodynamic performance for the design mission, good internal
volume distribution for fuel and systems and which also serves as an efficient structural member
supporting the load of the weight of the aircraft.
There are different methods for airfoil modelling used, depending on where in the design loop
the work is done. In the conceptual phase a flat plate might suffice as wing profile model, while in later
stages the airfoil might be selected from a database or being modifications of database airfoils. One key
aspect of the data making up the airfoil is how it is stored. Several approaches to parameterization of
wing profiles can be found in the literature: Airfoils can be described by point clouds as done in most
airfoil libraries
[1]
or they could be described as mathematical functions as is the case with the NACA 4
digit libraries
[2][3]
and as the Joukowsky airfoils
[4].
A more modern representation method is the class
function/shape function transformation CST method
[5].
The wing profile representation method used for
this paper is the Bézier interpolation developed at Linköping University, described in
[6]
. The proposed
parameterization allows for a very compact wing profile data format, where the position of the control
points each is stored as a single digit number in a base 64 space. The entire profile can then be defined
as a 13 digit number, which in the same way as the NACA 4 digits profiles, have the name is the airfoil.
This paper elaborates on the validation work for the Bézier interpolation. A large number of
known wing profiles (1122) have been parameterized to test the validity of the interpolation method. The