High Lift Aerofoils For Low Aspect Ratio Wings With Endplates
High Lift Aerofoils For Low Aspect Ratio Wings With Endplates
High Lift Aerofoils For Low Aspect Ratio Wings With Endplates
Abstract
High-lift multi-element airfoils for low-aspect ratio
wings with endplates find application in race car rear
wings used to generate high aerodynamic down force.
Airfoils for such applications must not only generate
maximum lift (to maximize the down force) but also
must satisfy several geometric constraints imposed by
the race rules. Induced effects arising as a result of the
low aspect ratio determine the operating angle of attack
at which the lift is to be maximized. This paper presents
some of the challenges involved in designing such airfoils
and briefly describes the design methodology adopted in
the current work. A parametric study using a baseline
two-element airfoil is then presented to illustrate some
of the unusual results obtained as a consequence of satisfying the geometric constraints while maximizing the
wing down force.
V
w
00
=
=
=
=
ai =
=
1
=
p =
bf
Introduction
Most airfoils for practical aircraft applications are
typically designed to achieve not only a desired aerodynamic performance but also satisfy certain geometric constraints. Examples are constraints on maximum
thickness (for structural considerations), enclosed area
(for fuel volume considerations) and trailing-edge geometry (for manufacturing considerations).
This paper describes a design methodology used in
the design of two-element airfoils subject to some rather
unusual constraints on the geometry. The objective was
to design high-lift airfoils for race car rear wings to maximize the down force. As is well known, 1 increasing the
aerodynamic down force increases the maximum lateral
acceleration capability of the race car, allowing increases
in cornering speeds. Geometric constraints on the airfoil imposed by the race rules, however, make this design
problem challenging.
The current approach has been to use a multipoint
inverse design code 2 for rapid and interactive design of
two-element airfoils with desired inviscid velocity distributions and then analyze candidate designs using more
computationally intensive viscous codes, in particular,
MSES, 3 FUN2D 4 and NSU2D. 5 The results from the
viscous codes were then used to provide feedback to the
designer to further refine the performance of the airfoils. A MATLAB-based graphical user interface (GUI)
was developed for interactively executing the various elements of the design code and for plotting the resulting airfoil along with the constraints on the geometry
Nomenclature
=chord
= flap-element chord
Cm = main-element chord
Ct
= total chord, Cm + CJ
C1 =airfoil lift coefficient, l/lpV 2 w
CL =wing lift coefficient, Lh,pV:;,w
g
= ratio of the gap to the total chord
h = height of the constraint box
l
= local "2D" lift per unit span
L = wing lift per unit span
V = local velocity vector at an airfoil section
c
cf
Box constraint
L---:/11
~w
v
3r-----~------~------~----~
2.5
2
...J
(.)
1.5
c.5
0.5
Airfoil C1
Wing CL
0
-20
-15
-
-10
<lj (deg)
cl
and wing
-5
c L with induced
3.---~--~----~--~--~---.
= 2.57
d
~ 1.5
;:
0.5
0~--~--~----~--~--~--~
0.5
1.5
2
airfoil C1
2.5
Ste 1
Use initial values of !l.v,E,m & Llv,E,f to generate
airfoils for the elements using PROFOIL
3
Effective wing aspect ratio = / 2.57
/
2.5
lnviscid
operating point
/
c.Y
:g
1.5
"(ii
Main airfoil
0.5
--0
-20
Ste 2
Scale and position airfoils according to
specified geometry
-10
-15
(l
=- <lj
airfoil
c==:--->
0
condition 1
(deg)
condition 2
While the GUI allowed rapid design of several candidate two-element airfoils with desired inviscid velocity distributions subject to geometric constraints,
more computationally intensive codes such as MSES, 3
FUN2D 4 and NSU2D 5 were used to obtain the viscous
behavior of these airfoils. In this paper, only the results
from FU::"J2D are presented.
(a)
2.5
v
1.5
0.5
(b) 2
Parametric Study
In this section, a three-part parametric study is presented to illustrate some of the unusual results obtained
as a consequence of satisfying the geometric constraints.
The two-element airfoil shown with the constraint box
c,
= 1.59
Fig. 7 Airfoil designed for high-lift (a) at high-lift condition without box constraint (b) operating with box
constraint.
-4
2.5
1.2
Q)
:::::l
1.1 ~
"0
Q)
Cl
1.0 .....
Q)
(ij
0.9
:::::l
Q)
.s>.c
0.7 -g
Q)
0.8
a:
Cl
....J
-~
(ij
-10
-11
-12
0.5
()
"0
"iii
1.5
>
c
0.6 E
.....
0
0.5
s
<S
0.4
500
q.
shows the convergence of the airfoil C1 and residual after 500 iterations (in this case, for the baseline airfoil
at an angle of attack of -12 deg relative to the x-axis).
For a typical case, a three-level multi-grid analysis was
performed, with approximately 50,000 nodes for level
1, approximately 20,000 nodes for level 2, and approximately 10,000 nodes for level 3. Typical run times for
500 iterations were approximately 40 min on a Cray C90
for a solution at a single angle of attack.
2.5
(c)
(a)
0.5
Airfoil B (Baseline)
y
0.2 deg
Airfoil C
5.4 deg
Fig. 11 The airfoils and inviscid velocity distributions resulting from (a) 1
1 = 5.4 deg.
2.2
--2
1.8
o-- -o- .
...I
(.)
/ B
g' 1.6
-~
/ A
1.4
/
/
/
/
1.2
/
1
-15
-10
-5
10
y (deg)
Fig. 12 Effect of 1 on wing C L.
ctfem
(b)
(a)
jf
0.95
~ -10
::.
0 0.9
t5
i::S
(J)
.!:
.m 0.85
C)
(ij
B /
0.8
-15
a.
0 -20
0.75
-25L--~--~-~-~~~~
0.7L---~----~----~----~----~
-15
~
(J)
(.)
(,/)
-5 r-----.-------.---c-""'""/-
-10
-5
0
y (deg)
10
-1 5
-1 0
-5
10
y (deg)
2.5
(c)
(b)
(a)
v
1.5
0.5
Airfoil A
c1 /cm = 0.25
Airfoil B (Baseline)
c1 /em= 0.30
Airfoil C
c1 /em= 0.35
Fig. 14 The airfoils and inviscid velocity distributions resulting from (a) CJICm = 0.25, (b) cJicm = 0.30 and (c)
CJ I em = 0.35.
This study demonstrates that while the inviscid design tool is good for rapidly generating candidate airfoils, there is clearly a need for viscous analysis codes to
select design parameters that maximize the lift.
monotonically increasing trend for the wing C L with decreasing cf I em. The reason for this behavior can be understood by observing that, in this study, the flap angle
OJ increases with decreasing values of cJiem. The inviscid analyses are driving the design to a configuration
where the two-element airfoil nearly "crawls" along the
top and right-hand edges of the constraint box. For very
high values of bf, however, the flow begins to separate.
resulting in an optimum value of c f I Cm below which the
wing C L decreases because of separation resulting from
the high flap deflections.
2.2
65
60
55
50
1.8
/o--
.....
(.)
~ 1.6
-~
of
-O--
45
40
35
a'
30
1.4
25
0.2
0.25
0.3
Ct
1.2
0.35
/em
0.4
0.45
1L---~----~----~----~--~
0.2
0.25
0.3
0.35
0.4
0.45
2.5
(a)
v
1.5
0.5
Airfoil A
gap=30%
Airfoil B
gap=50%
Airfoil C (Baseline)
gap= 100%
Fig. 17 The airfoils resulting from (a) gap= 30%, (b) gap= 50% and (c) gap= 100% of the gap of the baseline
airfoil.
gap was obtained.
Figure 17a-c shows the baseline airfoil having g =
.0.02, and two airfoils with gap values of 50% and 30%
of the gap of the baseline airfoil. The variation in the
wing C L with gap from both inviscid and viscous computations is shown in Fig. 18. As can be expected. the
2.2 r---...----.------.------,
A
---<
c
1.8
o-
...J
()
C)
c: 1.6
...0-
--- - - -
Acknowledgments
The support of the Ford Motor Company is gratefully
acknowledged. Also, Dimitri :\Iavriplis (Scientic Simulations) and Chun-Keet Song (University of Illinois) are
thanked for their efforts in running the N avier-Stokes
code NSU2D, the results of which were not presented in
this paper yet nevertheless supported the conclusions of
this work.
---<
-~
1.4
1.2
---
References
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:\1., "Design and Optimization Method
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Feb. 1993.
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Jan. 1993
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6
Anonymous, 1997 CART Rule Book, Championship
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12
Liebeck. R.. ''Subsonic Airfoil Design," in Applied Computational Aerodynamics. P.A. Henne (Ed.),
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13
Selig, :\LS. and Guglielmo, J .J., "High-Lift Low
Reynolds Number Airfoil Design," Journal of Aircraft,
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1
1L---~--~--~--~
20
40
60
80
gap /gap of baseline (%)
100