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Conference Paper

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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 arcraft desgner has so many tasks to overcome durng

an arcraft desgn process. One of the most mportant tasks

s to desgn an ecent wng complyng wth the determned

requrements. s s generally possble wth optmzng so

many geometrcal and aerodynamc parameters of the wng

[1].

Geometrcally, arfol and planform geometres are the man

terms to defne a wng. An aerodynamcally ecent wng

can be desgned when the sutable arfol(s) and planform

geometry coupled. erefore, planform geometry s one of

the most mportant geometres durng an arcraft desgn

process. Taper rato s one of the parameters on planform

geometry whch means the rato of the root and tp chord

lengths of a wng. Hence, ts eects on wng’s aerodynamc

parameters are also mportant and should be taken nto con-

sderaton durng a wng desgn process [2] [3].

e eects of the taper rato on wng aerodynamc parame-

ters can be obtaned by means of numercal or expermental

analyses [4]. At the conceptual desgn phase of an arcraft,

t can be preferable to use computatonal ud dynamcs

programs rather than tme consumng expermental setups.

ere are so many programs to perform these analyses such

as Ansys Fluent, XFLR5 and Soldworks Flow Smulaton.

In the lterature, ncludng numercal analyses, there are so

many studes about nvestgatng the aerodynamc parame-

ters of arcraft wngs.

Della Veccha et al. [5] nvestgated eects of propellers on

wng aerodynamcs by means of a computatonal ud dy-

namcs program. e study ncludes eects of propellers

mounted at both tp and mddle of the wng. Frstly, mesh

accuracy of the program was done and t was shown that the

program results are n good agreement wth expermental

results. Later on, by means of usng the valdated method

on numercal analyses, they obtaned that the tp-mounted

propeller can decrease the nduced drag from up to 10% and

mddle-mounted propellers can ncrease the maxmum lft

coecent of the wng up to 30%. Bravo-Mosquera et al.

[6] presented conceptual desgn and prototype of an agr-

cultural arcraft. Followng the tradtonal desgn methods

appled, sx derent wnglet desgns, whch have derent

cant angles were analyzed by means of a computatonal ud

dynamcs program usng Reynolds–Averaged–Naver–Sto-

Eects 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

ecient 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

coecient, Oswald eciency factor and lift coecient 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 eects 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 dierent

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 coecient.

*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

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

kes (RANS) equatons. e am of the analyses was deter-

mnng the wnglet desgn provdng the best aerodynamc

characterstcs. Later on, these analyses were expanded to

complete arcraft and obtaned lft, drag and ptchng mo-

ment coecents were nvestgated together wth wngtp

vortex structures. At the end of the study, they obtaned that

mult wnglet devces were contrbutng on mprovng per-

formance of the arcraft, provdng control on the sprayed

product, reducng the nduced drag and bendng moment

of the wng. Qn et al. [7] performed computatonal ud

dynamcs analyses usng Reynolds-averaged Naver–Stokes

(RANS) equatons on a baselne blended wng body conf-

guraton wth the am of obtanng the eects of span-wse

lft dstrbuton. After the grd senstvty study on total drag,

they obtaned the man factor decreasng the aerodynamc

performance of the baselne body s wng loadng together

wth shock wave. ey revsed the body to three models

havng derent span-wse lft dstrbutons and nvestga-

ted the change n aerodynamc performances. Lee et al. [8]

nvestgated the eect of wnglet dhedral on a tapered and

swept wng at a low Reynolds number. Expermental analy-

ses of the wnglets havng derent dhedral angles were

performed at a wnd tunnel n McGll Unversty at 35 m/s

freestream velocty. Accordng to results of the analyses, t

was obtaned that the nduced-drag of a wng always reduces

wth the use of a wnglet and the wnglet, whch have nega-

tve dhedral, decreases lft-nduced drag more than postve

dhedral. Moreover, t was revealed that, the nner regon

of the tp vortex behavors s smlar for the wng wth or

wthout wnglets.

In ths study, frstly, a hgh aspect rato rectangular arcraft

wng was numercally nvestgated n terms of some ae-

rodynamc parameters ncludng nduced drag coecent,

Oswald ecency factor, and lft coecent together wth

span-wse lft dstrbuton by means of XFLR5 computato-

nal ud dynamcs program. e assessment of mesh accu-

racy of the program was done at the begnnng of the analy-

ses. Later on, wth the am of observng the eects of taper

rato on arcraft wng aerodynamc parameters, the revsed

versons of the wng, whch have the taper ratos from 0.2

to 1.2 (wth the ncrement of 0.2) were analyzed. In conc-

luson, dependng on the analyses results, the wngs havng

derent taper ratos were compared n terms of obtaned

aerodynamc parameters and span-wse lft dstrbutons.

Moreover, tp vortces of each wng, together wth ther s-

zes, were obtaned 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) coecients.

e other aerodynamic performance parameters can be de-

rived from these parameters, such as glide ratio, which is the

ratio between lift coecient and drag coecients. Lift, drag

and pitching moment coecients 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 coecient is divided into two com-

ponents named as zero-lift drag coecient (CDo) and in-

duced drag coecient (CDi) as shown in Equation (4). In the

Equation (5), AR is the wing aspect ratio and e is the Oswald

eciency factor.

oi

DD D

CC C=+

(4)

2

i

L

D

C

C

AR e

π

=

**

(5)

Oswald eciency 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 eciency factor of 1 and generally this is the

maximum value of this parameter. ere is another single

parameter, which can represents wing eciency 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 coecient.

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3rd International Mediterranean Science and Engineering Congress (IMSEC 2018)

October 24-26, 2018, Adana / TURKEY, http://www.imsec.info

.

1

1

e

δ

=

+

(6)

2.2 Numerical Analyses

e main objective of this study is to investigate the eects

of taper ratio on aerodynamic parameters of a wing design.

In order to examine the eects, 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

Numercal analyses of the sx derent wng models were

performed by XFLR5 program, whch uses Vortex Lattce

Method [13]. On the purpose of obtanng accurate results,

before the analyses, the mesh accuracy of the program was

done on the rectangular model for both drag and lft coe-

cents and results were shown n Fgure 3. Accordng to the

results, all of the models were prepared to have number of

mesh elements hgher than 20000 to have accurate results

ndependent from mesh. e mesh grd of the rectangular

model s shown n Fgure 4. e geometrcal dmensons of

the models, whch were desgned to have sucent number

of mesh elements, were gven 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 numercal analyses performed on XFLR5

program at 106 Reynolds number n terms of the span-wse

local lft coecents of the models were gven n Fgure 5.

e model 1 (λ=0.2) and model 2 (λ=0.4) have ther hghest

lft coecents near the tp secton of the wng. From model

3 (λ=0.62) to model 6 (λ=1.2), t was clearly seen that the

maxmum lft coecent regon has moved near the mddle

and root secton of the wngs.

Figure 5: Local lift coeicient distributions of the models along their half

spans

Span-wse lft dstrbutons of each model were gven toget-

her wth ther ellptcal lft dstrbutons n Fgure 6. When

the lft dstrbutons of the models were compared wth the-

r ellptcal dstrbutons, near the root secton of the wng,

the lft dstrbuton of the model 3 (λ=0.62) was found to be

most smlar. Moreover, at the regon from the mddle to tp

secton of the wng, model 2 (λ=0.4) was found to have most

smlar lft dstrbuton.

43rd International Mediterranean Science and Engineering Congress (IMSEC 2018)

October 24-26, 2018, Adana / TURKEY, http://www.imsec.info

Eects 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

Fgure 7 and Fgure 8 presents the numercal analyss re-

sults of the models n terms of the Oswald ecency factor

and nduced drag parameter. As seen n the fgures, at -6

degree angle of attack, Oswald ecency factors of models

were n order smlar to ther taper ratos. Between the angle

of attacks -4 to 6 degrees, model 2 (λ=0.4) has the hghest

and the model 6 (λ=1.2) has the smallest Oswald ecency

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 ecency factors hgher than 0.9; model 5 (e=0.884)

and model 6 (e=0.851) has ths values between 0.8 and 0.9.

As expected, nvestgaton of nduced drag parameter of

each model also shows that, model 1 (λ=0.2) and model 3

(λ=0.62) has the same values (δ=0.05). Moreover, they have

very smlar Oswald ecency factor changes at -6 to 6 deg-

rees angles of attacks.

Figure 7: Induced drag parameters (δ) versus taper ratios of the models

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3rd International Mediterranean Science and Engineering Congress (IMSEC 2018)

October 24-26, 2018, Adana / TURKEY, http://www.imsec.info

.

Figure 8: Oswald eiciency factors of the models versus angle of attack

from -6 to 6 degrees

In Fgure 9, the numercal results for nduced drag coe-

cents changng wth taper ratos of the models were gven.

As expected, the change of nduced drag coecent valu-

es are n good agreement wth the values of nduced drag

parameter. Model 2 (λ=0.4) has the mnmum (=0.00543)

and model 6 (λ=1.2) has the maxmum value (=0.005886)

of nduced drag coecent. Model 1, 3, 4 and 5 has nduced

drag values of 0.005449, 0.005488, 0.005622 and 0.005806,

respectvely.

Fgure 10 shows the streamlnes of each model at zero angle

of attack at the same dstance from the leadng edges of the

wngs. As seen, the mnmum sze of the wng tp vortces

has seen at model 1 (λ=0.2). e maxmum sze has seen

on model 6 (λ=1.2). erefore, the szes of wng tp vortces

were found to be ncreased wth the decrease n taper rato.

Figure 9: Induced drag coeicients versus taper ratios of the models

e change n total drag coecent wth angle of attack was

gven n Fgure 11. It s seen from the fgure that, model 1

(λ=0.2), has lower drag coecents than other models at

angle of attacks lower than 2 degree. On the contrary, t has

hgher values than other models at angle of attacks hgher

than 2 degree. Models 2, 3, 4, 5 and 6 was found to have s-

mlar changes between angle of attacks of -6 and 6. At zero

angle of attack, models 5 and 6 has approxmately same drag

coecent values of 0.550. Models 1, 2, 3 and 4 has drag co-

ecent values of 0.0521, 0.0528, 0.0538 and 0.0546, respe-

ctvely.

Figure 10: Front-view of streamlines and wing tip vortices of the models

Figure 11: Drag coeicients of models versus angle of attack from -6 to 6

degrees

4. CONCLUSION

In ths study, wth the am of nvestgatng eects of taper ra-

to on arcraft wng aerodynamc parameters, the hgh aspe-

ct rato wngs havng derent taper ratos were numercally

analyzed. For the comparson of ther aerodynamc parame-

ters, a rectangular wng model was revsed to fve derent

models, whch have derent taper ratos, but have same

wng area, aspect rato and mean aerodynamc chord. Nu-

mercal analyses of the models were performed on XFLR5

program whch uses Vortex Lattce Method. After the as-

sessment of mesh accuracy of the program was done, all

the models havng taper ratos from 0.2 to 1.2 (wth the nc-

rement of 0.2) were analyzed n terms of nduced drag co-

ecent, Oswald ecency factor, and lft coecent toget-

her wth span-wse lft dstrbuton. Accordng to numercal

analyss results, t was obtaned that, there s an optmum

taper rato value for a wng, whch have mnmum nduced

drag coecent and maxmum Oswald ecency factor va-

lues. On the other hand, decreasng taper rato so much was

found to have the possblty of causng wng-tp stall due

to hgher local lft coecents at the tp regon of the wng.

In addton, t was found that, sze of wng-tp vortces were

ncreased wth the ncrease n taper rato.

63rd International Mediterranean Science and Engineering Congress (IMSEC 2018)

October 24-26, 2018, Adana / TURKEY, http://www.imsec.info

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

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