AN APPROACH TO THE DESIGN OF AIRFOILS WITH HIGH LIFT TO DRAG RATlOS BY DAVID ...

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AN APPROACH TO THE DESIGN
OF AIRFOILS WITH HIGH LIFT TO DRAG RATlOS
BY
DAVID WALTER ZINGG
TECHNISCHE HOGESCHOOL D[lFT -
LUCHTVAART- EN RUIMTEVAARTTECHNIEK
BIBLIOTHEEK
Kluyverweg 1 - DELFT
UTIAS TECHNICAL NOTE NO. 245
NOVEMBER, 1983 CN ISSN 0082-5263
AN APPROACH TO THE DESIGN
OF AIRFOILS WITH HIGH LIFT TO DRAG RATlOS
BY
DAVID WALTER ZINGG
SUBMITTED 1983
MARCH~
UTIAS TECHNICAL NOTE NO. 245
• NOVEMBER, 1983
CN ISSN 0082-5263
t
Summary
A procedure for the design of low-speed,
single-element airfoi1s with high lift to drag
ratios is presented. The pr ocedure uses an
inverse approach which proceeds from a set of
desiraó1e boundary 1ayer characteristics, which
are determined from the performance objectives,
to a velocity distribution and, fina11y, to an
airfoi1 shape. The boundary 1ayer shape factor,
whi ch is a measure of the nearness of the
boundary 1ayer to separation, is used to de fine
the boundary 1ayer characteristics in the upper
surface pressure recovery region. The turbulent
boundary 1ayer equations are solved in inverted
form to ca1cu1ate the velocity distribution
which corresponds to a shape factor variation.
The ve10cities on the upper surface prior to
pressure recovery are chosen to cause boundary
1ayer transition at a desired location. The
lower surface velocity distribution is se1ected
to satisfy the requirement that a c1osed, non
reentrant shapewhich meets the specified
structura1 requirements resu1ts. The design
procedure described can be uti1ized for the
design of high performance airfoi1s for a variety
of performance objectives, operating conditions,
and practical constraints.
Using this procedure, an airfoi1 has been
designed which achieves a lift to drag ratio of
180 at a lift coefficient of 1.2 and a Reyno1ds
number of one mi11ion. Through this design study,
a set of guide1ines for the design of a1rfoi1s
with high lift to drag ratios is estab11shed.
ii
AcknowTedg'ement s
The author wishes to thank Dr. G. W. Johnston of
the University of Toronto Institute for Aerospace Studies
for his supervision. In addition, the author is grateful
',.. to Mr. B. Egglestone of de Havilland Aircraft for his
advice and for the use of his computer programs.
iii
Ta'bleof Contents
Page
Summary ii
Acknow1edgements iii
List of Figures v
List of Symbols vi
• 1. Introduction 1
2. Basic Design Considerations 4
3. Design Procedure 6
4. Resu1ts and Discussion 23
5. Conclusions 35
6. References 39
Figures 42
Appendix A: Thwaites' Method for the
Laminar Boundary Layer Calculation 53
Appendix B: Inverse Turbulent Boundary
Layer Program 55
Appendix C: Program to Calculate the
Gradient of a Linear Velocity
Distribution to Give a Desired
Transition Point 57
Appendix D: Coordinates of Designed
Airfoil 58
't
iv
.
L~&~bf F~gures
Fig. 1. Drag on a flat p1ate with different transition
points
=
Fig. 2. Velocity gradients for transition at x/c 0.7
Fig. 3. Shape factor variation on the NAGA 633-018
Fig. 4. Boundary 1ayer characteristics of Liebeck L1003
and Wortmann FX 74-GL6-140 airfoi1s
Fig. 5. Experimenta1 lift, drag, and pitching moment data
for Liebeck L1003 airfoi1
Fig. 6. Deve10pment of Rg and R for a constant velocity
gtr
6
distribution with Re = 2.0 X 10
Fig. 7. Fami1y of upper surface velocity distributions
Fig. 8. Variation of lift coefficient and lift to drag
ratio with recovery point 10cation
Fig. 9. NAGA 67-015 thickness form cambered to give design
=
upper surface velocity distribution with xr/c 0.7
0
Fig. 10. Velocity distribution on above section at ~ = 3
Fig. 11. Designed airfoi1 section
Fig. 12. Velocity distribution on designed section at
0
design incidence, ,~= 3.5
Fig. 13. Shape factor variation on designed section at
design incidence
Fig. 14. Momentum thickness on designed section at design
incidence
0
Fig. 15. Velocity distribution on designed section at ~= 1.0
Fig. 16. Ga1cu1ated lift, drag, and pitching moment 6
characteristics of the designed airfoi1 at Re = 10
= 0
Fig. 17. Velocity distribution on designed section at ~ 4
Fig. 18. Velocity distribution on Liebeck L1003 airfoi1
at design incidence
v
List Of Symbols
c chord length
drag coefficient
local skin friction coefficient
lift coefficient
.
, pitching moment coefficient about quarter-chord
pressure coefficient
.
H boundary layer shape factor, ~ ;9
1 parameter in Thwaites' method
LID lift to drag ratio
p pressure
Re chord Reynolds number
Reynolds number based on momentum thickness
Reynolds number based on streamwise distance
airfoil thickness
u streamwise velocity at outer edge of boundary layer
free-stream velocity
UQ()
x position of recovery point
r
angle-of-attack
boundary layer displacement thickness
parameter in Thwaites' method
kinematic viscosity
f density
'.
vi
ooundary layer momentum thickness
wall shear stress
SUb scripts
denotes a value at the start of the recovery region
i
te denotes a value at the trailing edge
tr denotes a value at the transition point or a
value required for transition
.'
vii
1. Introduction
The advent of high-speed computers and advanced
numerical methods has led to new possibi1ities in airfoi1
design. Prior to 1930, airfoi1 design was primari1y an
empirica1 process aided somewhat by potentia1 flow theory.
In the 1~30's, boundary 1ayer considerations were
qua1itative1y integrated into the design of "low-drag"
sections such as the NACA 6-series airfoi1s. Significant
improvements upon these sections were not achieved unti1
the late 1950's, when large computers became avai1ab1e.
Since that time, the performance of the NACA 6-series has
been consistent1y exceeded by sections such as the Wortmann
FX-series (Ref. 1).
The designer has at hand an extensive array
present~day
of numerical ca1cu1ation techniques. Singu1arity methods
are a general, accurate, and efficient way of performing
a potentia1 flow ca1cu1ation. Boundary 1ayer characteristics
can be accurate1y determined by a variety of techniques,
inc1uding integra1 and finite-difference methods (which
invo1ve some empiricism). Empirica1 corre1ations adequately
predict boundary 1ayer transition and separation. Fina1ly,
iterative schemes are avai1ab1e to combine potentia1 flow
and viscous solutions so the ana1ysis of ful1y attached
1
viscous flow about two-dimensional sections can be
performed.
The recent advances in airfoil design, however, are
primarily the result of a change in the fundamental
design approach from an iterative cut and try procedure
to a synthesis or inverse technique. The traditional
empirical approach consists of modifying an initial
shape by trial and error until given performance
objectives are achieved. The inverse approach, in
contrast, begins with a set of boundary layer characteristics
which are derived from the performance objectives. The
velocity distribution which results in these characteristics
is determined and, finally, the shape which produces this
velocity distribution is calculated. The airfoil section
shapes generated by such an inverse design approach, such
as the Liebeck high-lift sections (Ref. 2), are generally
unique and are not likely to be obtained using an
empirical approach.
This thesis describes an example of an inverse approach
applied to the design of an airfoil with a high lift to
drag ratio. As energy costs continue to rise, low fuel
consumption is becoming an increasingly high priority
in aircraft design and hence such sections are required.
In general, an airfoil design problem involves several
conflicting requirements and therefore the final solution
2