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Unformatted text preview: AIAA 960058
A New Class of Airfoils with SlotSuction Farooq Saeed and Michael S. Selig
University of Illinois at UrbanaChampaign Urbana, IL 34th Aerospace Sciences
Meeting & Exhibit
January 1518, 1996 / Reno, NV For permission to copy or republish, contact the American Institute of Aeronautics and Astronautics
370 L'Enfant Promenade. S.W., Washington, 0.0. 20024 A NEW CLASS OF AIRFOILS WITH SLOTSUCTION Farooq Saeedl and Michael S. Selig‘ Department of Aeronautical and Astronautical Engineering
University of Illinois at Urbana—Champaign
Urbana, Illinois 61801 ABSTRACT In a recent paper by Saeed and Selig, a gener
alized method for the multipoint inverse design of
airfoils with slotsuction was proposed and success
fully implemented. The new inverse design method
for slotsuction airfoils, unlike earlier design meth
ods, not only addresses key issues particular to slot
suction airfoils but is also capable of multipoint de
sign. To illustrate the underlying principles of the
theory behind the new inverse design method for
slotsuction airfoils, the theory as applied in the de
sign of Joukowski airfoils with slotsuction is pre
sented along with a few examples. The examples
illustrate important differences and improvements
over the existing design methods. In light of these
developments, the more generalized method of Saeed
and Selig is used to design airfoils with slotsuction
for a variety of aircraft ~ ~ications, such as. thick
airfoils for allwing spamuaders, airfoils for maxi
mum lift, aud airfoils with extended length of lami
nar ﬂow. NOMENCLATURE b = location of the suctionslot, C = Re"‘9 c = airfoil chord C; = airfoil drag coefﬁcient C: = airfoil lift coefﬁcient 09 = slotsuction coefficient, Q, / Vooc d = location of the stagnation point down
stream of the suctionslot, C = Re“ D = airfoil drag f = front stagnation point, C = Re“ F,, F, = 1: and y components of force F(z), F (C ) = complex potential functions L = airfoil lift Mo = airfoil pitching moment R = circle radius Q, = suction strength t = rear stagnation point, C = Re“ Copyright © 1996 by Farooq Saeed and Michael
S. Selig. Published by the American Institute of
Aeronautics and Astronautics, Inc. with permission. t Graduate Research Assistant. Student Member AIAA.
1 Assistant Professor. Member AIAA. t /c = airfoil thickness to chord ratio
5 relative design velocity distribution
across the slotsuction segment V.» = freestream velocity z(¢), y(¢) = airfoil coordinates z = airfoilplane complex coordinate, a: + iy z" = trailingedge location in the z—plane a0], = the angle of attack for zerolift B = location of the suctionslot I‘ = circulation strength 6 = location of the stagnation point
downstream of the suctionslot e = trailingedge angle parameter C = initial circleplane complex coordinate,
E + in or Re“ C0 = a real constant I: = thickness control parameter 9) = camber control parameter,
2‘:  A p = ﬂuid density
INTRODUCTION The fact that large lift coefﬁcients can be obtained
from thick airfoils with active boundarylayer control
(suction and/or blowing) without separation has not
only been predicted through analytical models such
as those of Glauert"3 but has also been conﬁrmed
through numerous experimental studies."9 An in—
herent advantage of these airfoils is that large lift co
efﬁcients can be obtained as compared to the conven
tional airfoil conﬁgurations. Moreover, very thick
airfoils could also be designed that exhibit laminar
flow characteristics over a greater part of the sur—
face throughout a CLrange which is large enough to
completely cover the normal flight range, and which
are also thick enough to provide ample room for the
stowage of engines, passengers and other loads with
out the possibility of ﬂow separation. The possibilty for such efficient cruise perfor
mance and structural arrangements has revived
interestm'“ in advanced concept transport air
craft with active boundary layer control (suction
and/or blowing), such as the Goldschmied’s thick
wing spanloader allfreighter,m shown in Fig. 1, or
a more recent highlift system concept,11 Fig. 2, for
the CWing conﬁguration of the McDonnellDouglas Fig. 1 Layout10 of the modiﬁed GLAS II
31.5%thick laminarﬂaw airfoil with a 10.3 in
chord. Blended Wing Body concept, shown in Fig. 3. Ow—
ing to the renewed interest, it was felt necessary to
design a new class of airfoils that employ slotsuction
which could be used in the aircraft sizing studies to
examine the potential payoﬁ' for boundarylayer con
trol as applied to the advancedconcept wings. A common factor among the numerous aircraft
sizing studies, related to the design of the advanced
concept conﬁgurations with active active boundary
layer control, has been the use of the classical inverse
design approach of Glauertl'3 in the design of airfoil
sections that employ slotsuction. In a more recent
study,16 it was shown that Glauert’s airfoil did not
employ suction but a step drop in the velocity and,
therefore, on this basis a new inverse design method
for airfoils that employ slotsuction was proposed
and successfully implemented. The new method,16
which is bmed on conformal mapping, draws on the
theory of ﬁrst published by Epplerw'm and extended
by Selig and Maughmer.19 Unlike the existing inverse design methods“3 for
slotsuction airfoils, the new method16 not only ac
counts for the effect of true suction at the slot
location, i.e., the velocity increases in front of the
slot and decreases behind it,20 but it is also car
pable of multipoint design. This makes it a more
practical and versatile tool for the design of slot
suction airfoils. Moreover, unlike earlier methods,
the new method can address certain issues, for ex
ample, it can relate the amount of pressure recovery
with amount of suction and vice versa. In light of
the new developments, a need arose to reevaluate
the existing applications of earlier design methods
for slotsuction airfoils. Therefore, the main focus of
this paper is to reevaluate existing design concepts
as well as applications of slotsuction airfoils on the
basis of the new design method now available. In order to illustrate the underlying theoretical ba Fig. 2 HighLift system concepts11 for 18%
transonic Grifﬁth airfoils. Fig. 3 The McDonnellDouglas Blended
Wing Body (BWB) concept.11 sis of the new method for a generalized multipoint
inverse design of airfoils with slotsuction,14 the the
ory, as applied to the design of Joukowski airfoils
with slotsuction, is presented in the next section.
In the later sections, the more generalized multipoint
inverse design of airfoils with slot~suction is applied
in the design of airbils for various applications, such
as, thick airfoils for allwing spanloaders, airfoils for
maximum lift, and airfoils with extended lengths of
laminar ﬂow, to name a few. JOUKOWSKI AIRFOILS WITH
SLOTSUCTION Theory The ﬂow in the Cplane is modeled by the pres
ence of a uniform ﬂow of unit velocity at an angle
of attack a, a. vortex of strength I‘ at the origin and
a point sink of strength Q.(Q, < 0). The sink is
placed at C = b in the ﬂow ﬁeld so that when a cir
cle of radius R centered at the origin is added to the
ﬂow, using the MilneThomson circle theorem,”1 it
falls on the boundary of the circle at C = b = Re“. The complex potential for the ﬂow ﬁeld with the
circle added is given by 2
F(C) = e"" + slag;— Q: 32  .I‘
+'2—1r (T—b)+t2—Ilnc (l) + gm“ — b) and where l":41rRsin(a A)Q, cot(ﬁ 2 A) (2)
is the circulation strength required to satisfy the
Kutta condition by ﬁling the rear stagnation point
at C = t = Re“. Since a stagnation point must exist downstream of
the suction slot, say, at C = d = Re“ on the circle,
imposing this condition requires that . A — ,6 . ﬂ — 6 A  6
Q. — 81rRsm( 2 )sin( 2 )cos(a—T)
(3)
The front stagnation point is then located at C =
f: Re” where7 = 1r+2a+ﬁ—6—A and the
complex velocity is given by a02)(lz><l2)"(x%)e~ which on the circle C = Re“ becomes 77:" Ln: “4"?) “(g6) WE") cos(————¢  ﬂ 3 6 + A  a) fwd/2) (5) To obtain the flow about a Joukowski airfoil in the
zplane, the ﬂow about the circle in the Cplane is
mapped via the Joukowski tranformation, z = z(C).
The ﬂow about the Joukowski airfoil in the zplane
is then determined from the following relation E = (dF/dchny.
dz My. “(dz/dam.» In order to resolve the singularity at the trailing
edge stagnation point, since Eq. (6) becomes inde
terminate there, L’Hospital rule is applied to Eq. (6)
which yields the following result. (6) lim £—lsin(A6) A—ﬂ
zz..dz ‘ R 2 c“ 2 sin (lgZ) £4” (7) Ailfoil Lift, Drag and Moment The forces and the pitching moment acting on
the airfoil are determined from the Blasius relations,
which are Mo = gm” . (3—9224 (9) where Cl is any closed curve that encircles the air
foil. The resulting airfoil lift and drag components
of the forces are L = pI‘, D = —pQ, (10a,b)
which in coefficient form are
C: = 2r/C, 04 = —2Q,/c (110,5) Substituting Eqs. (2) and (3) into the above yields C; = Eggsmw— A) 2—Q'cot(ﬁ’\) (12) c 2
Ca = 16:}: sin(ﬁ;’\) sin(ﬁ;6) moor1%!)
(13) where c is the airfoil chord. As mentioned in Ref. 16,
the liftcurve slope is still nominally 21', with suction
Q, providing an oﬁ'set to the lift coefﬁcient. More
over, an expression for the angle of attack for zero
lift on can be obtained from Eq. (12) by setting 01
equal to zero. It is given by _ . 1 Q: g "‘ ’\
am, _ A+sin [—41]; cot( 2 )] (14)
It shows that the angle of attack for zerolift an], not
only depends on the amount of suction Q. but also
on the location of the suction slot ﬂ. the location of
the trailingvedge stagnation point A, and the radius
R. Using the deﬁnition of the slot—suction coefﬁcient,
Cq and comparing it with Eq. (11b) yields the result C4 = —2qu (14) Since Q, < 0 corresponds to suction, the analy
sis indicates that suction not only results in an in—
creased lift coeﬁicient due to the increased circula
tion around the airfoil, but *0 results in a positive
value for the drag coefﬁcient purely due to suction. The exprwsion for the pitching moment about the
origin of the zplane (positive clockwise) is given by Mo = 2pQ.{Rsin(a — H) + C. sin(a  x)} — pC.{Q, sin(a — It) + I‘cos(a — 06)}
pm. (15) I + 2rpsin 2a — Implementation The results from the theory were implemented in
a computer program. In the program, the angle of
attack a and the suction strength Q, are kept as
the control variables while the suction slot location
5, the trailingedge stagnation point location A, the
camber control parameter a: and the thickness con
trol parameter It are ﬁxed a design variables. The
location of the stagnation point downstream of the
suctionslot, i.e. 6, is determined numerically for the
speciﬁed value of the suction strength Q. and the de
sign variables such that either (A21r) < 6 < 5 if the
suction slot is on the upper surface, i.e. 0 < [3 < 7,
or B < 6 < A if the suction slot is on the lower
surface, i.e. 7 < 3 < 21. Figure 4 shows the results from a typical analy
sis run, which, illustrates the effects of varying the
amount of suction Q, (Fig. 4(a)) and the angle of
attack a (Fig. 4(b)) on the velocity distribution and
the aerodynamic characteristics of the Joukowski
airfoil. The values of the design variables in the
example presented in Fig. 4 are; B = 100.5 deg,
A = 355 deg, ac = 140 deg, w = 5 deg, R = 1.1207
and (o = 0.152. Interpretation of Results The results indicate that the magnitude of velocity
becomes inﬁnite at the suctionslot which is then
immediately followed by a stagnation point. If the
effects of true suction are accounted for, then ideally
one should expect such a behaviour.20 The airfoil in
Fig. 3(a) has a C; that varies from 1.209 to 1.322 and (8) {IE Fig. 4 Velocity distribution over a Joukowski
airfoil: (a) with and without suction at a = 5
deg (b) with a constant suction of strength
Q, = —0.1 at different angles of attack. a C; that varies from 0.000 to 0.148 as the amount
of suction Q, is increased (more negative) from 0.0
to 0.3 at a constant angle of attack a = 5 deg. The
airfoil in Fig. 3(b) has a C; that varies from 0.644
to 2.420 and a constant C; of 0.049 as the angle of
attack is increased from 0 to 15 deg with the same
amount of suction Q, = —0.1. The explanation for this high value of the drag co
efﬁcient is as follows. If the forces of the airfoil are
being measured on a balance, the measured drag co—
efﬁcient will include an amount —2Q,/c due to the
removal of air; this quantity should therefore be sub tracted to give the drag due to the wake alone.20 For
this, it is assumed that the ﬂuid removed by suction
is discharged so that its static pressure and velocity
are identical to the pressure and velocity at inﬁn
ity or, in other words, there is no loss of momentum
within the suction system. Thus, the suction system
contributes zero drag and the wake drag is the to
tal drag which ha to be overcome by the propulsive
system. In reality, the efﬁciency of the suction sys
tem will dictate the actual contribution of the drag
due to suction to the total drag. As evident from these example, a signiﬁcant
amount of prwsure recovery can be achieved by em
ploying suction in the vicinity of the trailing edge.
This fact alone is useful in many of the applications
related to the advancedconcept wings. For exam
ple, suction could be employed over very thick wings
to prevent separation of the boundarylayer, which
would otherwise result in a huge drag penalty. As
another example, thin airfoils could be made to op
erate at very high angles of attack without ﬂow sep
station. To explore these interesting ideas, a method16
for the multipoint inverse design of airfoils with
slotsuction was formulated and successfully applied
in the design of airfoil with slotsuction. A brief
overview of the method is given in the next section
along with design of slotsuction airfoils for various applications. A GENERALIZED METHOD FOR
SLOTSUCTION AIRFOIL DESIGN Overview ofthe method The generalized multipoint inverse design
method“ls for slotsuction airfoils is based on the the
ory ﬁrst published by Epplerlma and later reﬁned
by several others but primarily draws on the work
of Selig and Maughmer”. The method is based on
conformal mapping. Multipoint design is achieved
by dividing the airfoil into a number of segments
and then specifying the desired velocity along with
the desired angle of attack, the location of suction
slot, and the munt of suction for each segment.
Like in any inverse design method, speciﬁcation of
velocity is not completely arbitrary and is subject to
three integral constraints and several conditions that
must be satisﬁed in order for the multipoint inverse
design problem to be well posed. Additional restric
tions result if the airfoil is to have a speciﬁed pitching
moment, thickness ratio, or other constraints. The
resulting system of equations is then solved partly as
a linear system and partly through multidimensional
Newton iteration. In the next section, the generalized multipoint in
verse design method16 for slotsuction airfoils is ap
plied to obtain airfoil sections that were designed us
ing Glauert’s approach and are being used in aircraft
sizing studies of some of the advanced concept air
crafts. Apart from its multipoint design capability,"3
the new method is not only able to relate pressure
recovery to the amount of suction but also is capable
of predicting the component of the drag coefﬁcient
due to suction alone. 0n the basis of which, the
power requirements for the suction system could be
determined. Application A class of suction airfoils was designed by
Glauertla based on the idea suggested by
Dr. A. A. Grifﬁth that an airfoil could be de
signed with a favourable pressure gradient every
where along the chord except at one location where
there would be a discontinuity and a sharp pressure
rise. If suction was applied just ahead of the loca~
tion of discontinuity, potential ﬂow would exist and
ﬂow would not separate. By applying this method,
Glauert designed the GLAS lIV series of suction
airfoils. GLAS stands for Grifﬁth Laminar Airfoil
(with) Suction. As mentioned earlier, Glauert’s design method for
the design of slotsuction airfoils does not take into
account the effects of true suction at the slot loca
tion. Figure 4 clearly indicates that for slot suc
tion on an airfoil, a stagnation point must exist
on the airfoil surface just downstream of the slot.
Glauert’s airfoils do not exhibit this characteristic
feature. Moreover, there is no speciﬁed parameter
related to the amount of suction. Instead, the veloc
ity d'ntributions of Glauerttype airfoils, Fig. 5(a),
show a step drop in the velocity at the location of
the slot. It was shown in Ref. 16 that this type of velocity
distribution can be obtained by making the pressure
recovery inﬁnitely steep at the slot location. Math
ematically, a logarithmic spiral is used to represent
this discontinuity. To achieve this physically, the
suction slot must be included in the treatment of
the discontinuity. In Fig. 5(b), a Glauerttype air
foil was designed with suction at the slotlocation.
As evident from Fig. 5(b), the ﬂow experiences a fa—
vorable pressure gradient which is seen as a rise in
the velocity, as the ﬂow enters or leaves the slot. A
stagnation point also exists downstream of the slot location.
Figure 6’“ shows a comparison between the theo
retical and experimental velocity distributions over a GLAS II airfoil. The ﬁgure highlights the essen (a) 2.4
2.0 1.0 0.0 0.4 0.2 0.0 0.2 0.4 0.0 0.0 1.0 (b) 2.4 1.0
V 1 .2
0.0
0.4 0.0
43.2 0.0 0.2 0.‘ 0.0 0.0 1 .0 ale C} Fig. 5 Velocity distribution over a Glauert
type airfoil (a) without suction at a = 15.3 deg
(b) with a suction of strength Q, = 0.00001
at a = 15.5 deg. tial difference in the behaviour of the ﬂow in the
vicinity of the suction—slot between the theoretical
model, that uses a step discontinuity at the slot lo
cation, and experiment. A comparison between the
experiment, Fig. 6, and the theoretical velocity dis
tribution, Fig. 5(b), obtained from the new method
indicates that the presence of a sink at the slot lo
cation represents a good model for the ﬂow in the
vicinity of the suction slot. Thus, slotsuction airfoils
could be designed using the new method, in a man
ner similar to Glauert’s approach, for applications
where a favorable pressure gradient over the whole Fig. 6 Chordwise distributions of velocity'“‘1
on a 30 per cent thick Grifﬁth airfoil. Fig. 7 Velocity distribution over the slot
suction airfoil at a = 5 dog and a suction
strength of Q, = —0.02. airfoil chord is essential. Examples of such appli
cations include thick airfoils for allwing spanloader
conﬁgurations, maximum and highlift airfoils.
Examples of thick ailfoils for all wing spanloaders
are shown in Figs, 1 and 2. The multipoint inverse
design method for slotsuction airfoil was used to
design a slotsuction airfoil, shown in Fig. 7, which is
similar to the 18% transouic Grifﬁth airfoil in Fig. 2.
The location of the suction slot was ﬁxed at 87%
chord for the design. The velocity distribution along
with the airfoil geometry are shown in Fig 7 at a =
5 deg and suction strength Q, = —0.02. At these (a) 10.2 0.0 0.2 0.4 as as 1.0 (b) Fig. 8 Velocity distribution over the airfoil at
a = 12 deg (a) for different values of suction
strength (b) for different values of net pres
sure recovery. conditions, the airfoil lift and drag coeﬂicients are
0.675 and 0.0116, respectively, based on the inviscid
results since transonic ﬂow is beyond the scope of
th'm paper. Slotsuction could also be employed over the
trailingedge ﬂaps to obtain highlift. Since the ve
locity over the upper surface of a deﬂected trailing
edge ﬂap, shown in Fig. 2, reaches a maximum near
the hinge a...
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