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Effects of Taper Ratio on Aircraft Wing Aerodynamic Parameters: A Comperative Study

Authors:
  • 21.49
  • University of Turkish Aeronautical Association
  • 1.57
  • Iskenderun Technical University

Abstract and Figures

Wing design is one of the most important tasks for a designer to overcome during an aircraft design process. Therefore, a designer need to optimize so many wing geometrical parameters with the aim of obtaining an efficient wing geometry complying with requirements of the design. Taper ratio is one of these parameters, which is the ratio of root and tip chord lengths of a wing. In this study, firstly, a high aspect ratio rectangular aircraft wing was numerically investigated in terms of some aerodynamic parameters including induced drag coefficient, Oswald efficiency factor and lift coefficient together with its span-wise distribution by means of XFLR5 computational fluid dynamics program. The assessment of mesh accuracy of the program was done at the beginning of the analyses. Later on, with the aim of observing the effects of taper ratio on aircraft wing aerodynamic parameters, the revised versions of the wing, which have the taper ratios from 0.2 to 1.2 (with the increment of 0.2) were analyzed. In conclusion, depending on the analyses results, the wings having different taper ratios were compared in terms of obtained aerodynamic parameters and span-wise lift distributions. Moreover, tip vortices of each wing, together with their sizes, were obtained and also compared.
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Conference Paper
8
1
0
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3rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
Çukurova University, Congress Center, October 24-26, 2018, Adana / TURKEY
Pages: 1-6, Paper ID:152
1. INTRODUCTION
An arcraft desgner has so many tasks to overcome durng
an arcraft desgn process. One of the most mportant tasks
s to desgn an ecent wng complyng wth the determned
requrements. s s generally possble wth optmzng so
many geometrcal and aerodynamc parameters of the wng
[1].
Geometrcally, arfol and planform geometres are the man
terms to defne a wng. An aerodynamcally ecent wng
can be desgned when the sutable arfol(s) and planform
geometry coupled. erefore, planform geometry s one of
the most mportant geometres durng an arcraft desgn
process. Taper rato s one of the parameters on planform
geometry whch means the rato of the root and tp chord
lengths of a wng. Hence, ts eects on wng’s aerodynamc
parameters are also mportant and should be taken nto con-
sderaton durng a wng desgn process [2] [3].
e eects of the taper rato on wng aerodynamc parame-
ters can be obtaned by means of numercal or expermental
analyses [4]. At the conceptual desgn phase of an arcraft,
t can be preferable to use computatonal ud dynamcs
programs rather than tme consumng expermental setups.
ere are so many programs to perform these analyses such
as Ansys Fluent, XFLR5 and Soldworks Flow Smulaton.
In the lterature, ncludng numercal analyses, there are so
many studes about nvestgatng the aerodynamc parame-
ters of arcraft wngs.
Della Veccha et al. [5] nvestgated eects of propellers on
wng aerodynamcs by means of a computatonal ud dy-
namcs program. e study ncludes eects of propellers
mounted at both tp and mddle of the wng. Frstly, mesh
accuracy of the program was done and t was shown that the
program results are n good agreement wth expermental
results. Later on, by means of usng the valdated method
on numercal analyses, they obtaned that the tp-mounted
propeller can decrease the nduced drag from up to 10% and
mddle-mounted propellers can ncrease the maxmum lft
coecent of the wng up to 30%. Bravo-Mosquera et al.
[6] presented conceptual desgn and prototype of an agr-
cultural arcraft. Followng the tradtonal desgn methods
appled, sx derent wnglet desgns, whch have derent
cant angles were analyzed by means of a computatonal ud
dynamcs program usng Reynolds–Averaged–Naver–Sto-
Eects of Taper Ratio on Aircraft Wing Aerodynamic Parameters:
A Comperative Study
İbrahim Halil Güzelbey1, Yüksel Eraslan2*, Mehmet Hanifi Doğru3
1Aircraft and Aerospace Engineering Department/Gaziantep University, Turkey; guzelbeyih@gantep.edu.tr
2Aircraft and Aerospace Engineering Department/Gaziantep University, Turkey; yeraslan@gantep.edu.tr
3Pilotage Department/Gaziantep University, Turkey; mhdogru@gantep.edu.tr
Abstract
Wing design is one of the most important tasks for a designer to overcome during an aircraft design process.
erefore, a designer need to optimize so many wing geometrical parameters with the aim of obtaining an
ecient wing geometry complying with requirements of the design. Taper ratio is one of these parameters,
which is the ratio of root and tip chord lengths of a wing. In this study, rstly, a high aspect ratio rectangular
aircraft wing was numerically investigated in terms of some aerodynamic parameters including induced drag
coecient, Oswald eciency factor and lift coecient together with its span-wise distribution by means of
XFLR5 computational uid dynamics program. e assessment of mesh accuracy of the program was done
at the beginning of the analyses. Later on, with the aim of observing the eects of taper ratio on aircraft wing
aerodynamic parameters, the revised versions of the wing, which have the taper ratios from 0.2 to 1.2 (with the
increment of 0.2) were analyzed. In conclusion, depending on the analyses results, the wings having dierent
taper ratios were compared in terms of obtained aerodynamic parameters and span-wise lift distributions.
Moreover, tip vortices of each wing, together with their sizes, were obtained and also compared.
Keywords: Aircraft wing design, taper ratio, lift distribution, induced drag coecient.
*Corresponding authour
Email: yeraslan@gantep.edu.tr
23rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY, http://www.imsec.info
Eects of Taper Ratio on Aircraft Wing Aerodynamic Parameters: A Comperative Study
kes (RANS) equatons. e am of the analyses was deter-
mnng the wnglet desgn provdng the best aerodynamc
characterstcs. Later on, these analyses were expanded to
complete arcraft and obtaned lft, drag and ptchng mo-
ment coecents were nvestgated together wth wngtp
vortex structures. At the end of the study, they obtaned that
mult wnglet devces were contrbutng on mprovng per-
formance of the arcraft, provdng control on the sprayed
product, reducng the nduced drag and bendng moment
of the wng. Qn et al. [7] performed computatonal ud
dynamcs analyses usng Reynolds-averaged Naver–Stokes
(RANS) equatons on a baselne blended wng body conf-
guraton wth the am of obtanng the eects of span-wse
lft dstrbuton. After the grd senstvty study on total drag,
they obtaned the man factor decreasng the aerodynamc
performance of the baselne body s wng loadng together
wth shock wave. ey revsed the body to three models
havng derent span-wse lft dstrbutons and nvestga-
ted the change n aerodynamc performances. Lee et al. [8]
nvestgated the eect of wnglet dhedral on a tapered and
swept wng at a low Reynolds number. Expermental analy-
ses of the wnglets havng derent dhedral angles were
performed at a wnd tunnel n McGll Unversty at 35 m/s
freestream velocty. Accordng to results of the analyses, t
was obtaned that the nduced-drag of a wng always reduces
wth the use of a wnglet and the wnglet, whch have nega-
tve dhedral, decreases lft-nduced drag more than postve
dhedral. Moreover, t was revealed that, the nner regon
of the tp vortex behavors s smlar for the wng wth or
wthout wnglets.
In ths study, frstly, a hgh aspect rato rectangular arcraft
wng was numercally nvestgated n terms of some ae-
rodynamc parameters ncludng nduced drag coecent,
Oswald ecency factor, and lft coecent together wth
span-wse lft dstrbuton by means of XFLR5 computato-
nal ud dynamcs program. e assessment of mesh accu-
racy of the program was done at the begnnng of the analy-
ses. Later on, wth the am of observng the eects of taper
rato on arcraft wng aerodynamc parameters, the revsed
versons of the wng, whch have the taper ratos from 0.2
to 1.2 (wth the ncrement of 0.2) were analyzed. In conc-
luson, dependng on the analyses results, the wngs havng
derent taper ratos were compared n terms of obtaned
aerodynamc parameters and span-wse lft dstrbutons.
Moreover, tp vortces of each wng, together wth ther s-
zes, were obtaned and also compared.
2. MATERIAL AND METHOD
2.1 Planform Geometry and Aerodynamic Parameters of
an Aircraft Wing
Planform geometry is the top-view shape of a wing and ef-
fective on wing aerodynamic performance [9] [10]. ere-
fore, the geometrical parameters of a wing planform geom-
etry are also important for a wing design. Changing these
geometrical parameters properly with respect to their ef-
fects on the wing aerodynamic parameters can provide an
improved aerodynamic performance to wing. Taper ratio
(λ), as a part of the wing planform geometry, is one of these
important parameters to take into consideration during an
aircraft wing design process. It is the ratio as stated in Equa-
tion (1), which is the ratio of the root (cr) and tip () chord
lengths as shown in Figure 1.
t
r
c
c
λ
=
(1)
Figure 1: Aircraft wing root and tip chords
e main aerodynamic parameters of an aircraft wing are
drag (CD), lift (CL) and pitching moment (CM) coecients.
e other aerodynamic performance parameters can be de-
rived from these parameters, such as glide ratio, which is the
ratio between lift coecient and drag coecients. Lift, drag
and pitching moment coecients can be calculated using
the Equations (2) - (3) - (4). In these equations, A is the re-
lated area (m2), V is the freestream velocity (m/s), is the lift
force (N), is the drag force (N) and M is the moment (Nm).
2
05.
L
L
AV
C
F
**
=
(2)
2
05.
D
D
AV
C
F
**
=
(3)
2
05.
M
M
AV
C
F
**
=
(4)
On the other hand, drag coecient is divided into two com-
ponents named as zero-lift drag coecient (CDo) and in-
duced drag coecient (CDi) as shown in Equation (4). In the
Equation (5), AR is the wing aspect ratio and e is the Oswald
eciency factor.
oi
DD D
CC C=+
(4)
2
i
L
D
C
C
AR e
π
=
**
(5)
Oswald eciency factor (e) is the value, which gives an idea
about the similarity of a wing’s span-wise lift distribution to
the elliptical lift distribution. e elliptical lift distribution
has Oswald eciency factor of 1 and generally this is the
maximum value of this parameter. ere is another single
parameter, which can represents wing eciency in terms
of induced drag, named as induced drag parameter (δ) and
can be calculated from Equation (6) [11]. is parameter
depends on only planform geometry and independent from
angle of attack and lift coecient.
3
3rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY, http://www.imsec.info
.
1
e
δ
=
(6)
2.2 Numerical Analyses
e main objective of this study is to investigate the eects
of taper ratio on aerodynamic parameters of a wing design.
In order to examine the eects, rstly, a high aspect ratio
rectangular wing was modelled with a typical sailplane air-
foil named as Wortmann FX 61-184 as a baseline model
[12]. Later on, for the comparison, the baseline model’s ta-
per ratio was revised to 0.2, 0.4, 0.62, 0.8 and 1.2 by changing
tip and root chord lengths while keeping wing area, aspect
ratio and mean geometric chord (M.A.C.) values constant,
as shown in Figure 2.
Figure 2: Planform geometries of revised wing models
Numercal analyses of the sx derent wng models were
performed by XFLR5 program, whch uses Vortex Lattce
Method [13]. On the purpose of obtanng accurate results,
before the analyses, the mesh accuracy of the program was
done on the rectangular model for both drag and lft coe-
cents and results were shown n Fgure 3. Accordng to the
results, all of the models were prepared to have number of
mesh elements hgher than 20000 to have accurate results
ndependent from mesh. e mesh grd of the rectangular
model s shown n Fgure 4. e geometrcal dmensons of
the models, whch were desgned to have sucent number
of mesh elements, were gven n Table 1.
Figure 3: Baseline rectangular model mesh accuracy results
Figure 4: Mesh grid of the rectangular model with 20000 mesh elements
Table 1 Geometrical dimensions of the models
Model Root Chord
(m)
Tip Chord
(m)
M.A.C.
(m)
Wing Area
(m2)
Aspect
Ratio
Tap er
Ratio
1 0.078 0.016
0.047 0.037 16.6
0.2
2 0.067 0.027 0.4
3 0.058 0.036 0.62
4 0.052 0.042 0.8
5 0.047 0.047 1
6 0.043 0.051 1.2
Lastly, the models revised from the baseline rectangular
wing model were numerically analyzed at 106 Reynolds
Number. As all the models have high aspect ratios, which is
common on sailplane wing designs, the airspeed was used as
33.5m/s as a typical sailplane cruise speed [14] [15]. As the
stall condition angle of attack or higher values are not scope
of this study, angle of attack range was used as changing be-
tween -6 to 6 degrees [1] [16].
3. RESULTS AND DISCUSSION
e results of numercal analyses performed on XFLR5
program at 106 Reynolds number n terms of the span-wse
local lft coecents of the models were gven n Fgure 5.
e model 1 (λ=0.2) and model 2 (λ=0.4) have ther hghest
lft coecents near the tp secton of the wng. From model
3 (λ=0.62) to model 6 (λ=1.2), t was clearly seen that the
maxmum lft coecent regon has moved near the mddle
and root secton of the wngs.
Figure 5: Local lift coeicient distributions of the models along their half
spans
Span-wse lft dstrbutons of each model were gven toget-
her wth ther ellptcal lft dstrbutons n Fgure 6. When
the lft dstrbutons of the models were compared wth the-
r ellptcal dstrbutons, near the root secton of the wng,
the lft dstrbuton of the model 3 (λ=0.62) was found to be
most smlar. Moreover, at the regon from the mddle to tp
secton of the wng, model 2 (λ=0.4) was found to have most
smlar lft dstrbuton.
43rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY, http://www.imsec.info
Eects of Taper Ratio on Aircraft Wing Aerodynamic Parameters: A Comperative Study
(a)
(b)
(c)
(d)
e)
(f)
Figure 6: Span-wise lift distributions with elliptical lift distributions of
the models; a) model 1, b) model 2, c) model 3, d) model 4, e) model 5, f)
model 6
Fgure 7 and Fgure 8 presents the numercal analyss re-
sults of the models n terms of the Oswald ecency factor
and nduced drag parameter. As seen n the fgures, at -6
degree angle of attack, Oswald ecency factors of models
were n order smlar to ther taper ratos. Between the angle
of attacks -4 to 6 degrees, model 2 (λ=0.4) has the hghest
and the model 6 (λ=1.2) has the smallest Oswald ecency
factors. At zero angle of attack, model 1 (e=0.954), model
2 (e=0.977), model 3 (e=0.955) and model 4 (e=0.921) has
Oswald ecency factors hgher than 0.9; model 5 (e=0.884)
and model 6 (e=0.851) has ths values between 0.8 and 0.9.
As expected, nvestgaton of nduced drag parameter of
each model also shows that, model 1 (λ=0.2) and model 3
=0.62) has the same values (δ=0.05). Moreover, they have
very smlar Oswald ecency factor changes at -6 to 6 deg-
rees angles of attacks.
Figure 7: Induced drag parameters (δ) versus taper ratios of the models
5
3rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY, http://www.imsec.info
.
Figure 8: Oswald eiciency factors of the models versus angle of attack
from -6 to 6 degrees
In Fgure 9, the numercal results for nduced drag coe-
cents changng wth taper ratos of the models were gven.
As expected, the change of nduced drag coecent valu-
es are n good agreement wth the values of nduced drag
parameter. Model 2 (λ=0.4) has the mnmum (=0.00543)
and model 6 (λ=1.2) has the maxmum value (=0.005886)
of nduced drag coecent. Model 1, 3, 4 and 5 has nduced
drag values of 0.005449, 0.005488, 0.005622 and 0.005806,
respectvely.
Fgure 10 shows the streamlnes of each model at zero angle
of attack at the same dstance from the leadng edges of the
wngs. As seen, the mnmum sze of the wng tp vortces
has seen at model 1 (λ=0.2). e maxmum sze has seen
on model 6 (λ=1.2). erefore, the szes of wng tp vortces
were found to be ncreased wth the decrease n taper rato.
Figure 9: Induced drag coeicients versus taper ratios of the models
e change n total drag coecent wth angle of attack was
gven n Fgure 11. It s seen from the fgure that, model 1
=0.2), has lower drag coecents than other models at
angle of attacks lower than 2 degree. On the contrary, t has
hgher values than other models at angle of attacks hgher
than 2 degree. Models 2, 3, 4, 5 and 6 was found to have s-
mlar changes between angle of attacks of -6 and 6. At zero
angle of attack, models 5 and 6 has approxmately same drag
coecent values of 0.550. Models 1, 2, 3 and 4 has drag co-
ecent values of 0.0521, 0.0528, 0.0538 and 0.0546, respe-
ctvely.
Figure 10: Front-view of streamlines and wing tip vortices of the models
Figure 11: Drag coeicients of models versus angle of attack from -6 to 6
degrees
4. CONCLUSION
In ths study, wth the am of nvestgatng eects of taper ra-
to on arcraft wng aerodynamc parameters, the hgh aspe-
ct rato wngs havng derent taper ratos were numercally
analyzed. For the comparson of ther aerodynamc parame-
ters, a rectangular wng model was revsed to fve derent
models, whch have derent taper ratos, but have same
wng area, aspect rato and mean aerodynamc chord. Nu-
mercal analyses of the models were performed on XFLR5
program whch uses Vortex Lattce Method. After the as-
sessment of mesh accuracy of the program was done, all
the models havng taper ratos from 0.2 to 1.2 (wth the nc-
rement of 0.2) were analyzed n terms of nduced drag co-
ecent, Oswald ecency factor, and lft coecent toget-
her wth span-wse lft dstrbuton. Accordng to numercal
analyss results, t was obtaned that, there s an optmum
taper rato value for a wng, whch have mnmum nduced
drag coecent and maxmum Oswald ecency factor va-
lues. On the other hand, decreasng taper rato so much was
found to have the possblty of causng wng-tp stall due
to hgher local lft coecents at the tp regon of the wng.
In addton, t was found that, sze of wng-tp vortces were
ncreased wth the ncrease n taper rato.
63rd International Mediterranean Science and Engineering Congress (IMSEC 2018)
October 24-26, 2018, Adana / TURKEY, http://www.imsec.info
Eects of Taper Ratio on Aircraft Wing Aerodynamic Parameters: A Comperative Study
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