lift interference

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Aerodynamic Interference Correction MethodsCase: Subsonic Closed Wind Tunnels.

Surjatin Wiriadidjaja1,a, Mohd Rafie A. S.2,b, F. I. Romli3,c and O. K. Ariff ,d

1,2,3,

!e"artment of Aero#"ace $n%ineerin%, &ni'er#iti (utra Mala)#ia,3** &(M Serdan%, Mala)#ia

a#urjatin+en%.u".edu.m), b#harine+en%.u".edu.m), cfiromli+en%.u"m.edu.m),doariff+en%.u"m.edu.m)

Keywords- aerod)namic#, ind tunnel, all interference, #ub#onic

Abstract. The approach to problems of wall interference in wind tunnel testing is generally based

on the so-called classical method, which covers the wall interference experienced by a simple small

model or the neo-classical method that contains some improvements as such that it can be applied to

larger models. Both methods are analytical techniques offering solutions of the subsonic potentialequation of the wall interference flow field. Since an accurate description of wind tunnel test data is

only possible if the wall interference phenomena are fully understood, uncounted subsequent efforts

have been spent by many researchers to improve the limitation of the classical methods by applying

new techniques and advanced methods. However, the problem of wall interference has remained a

lasting concern to aerodynamicists and it continues to be a field of active research until the present.

The main obective of this paper is to present an improved classical method of the wall interference

assessment in rectangular subsonic wind tunnel with solid-walls.

Introduction

The wind tunnel test is supposed to relate the condition during measurement to the situation in an

unbounded flow, which means that the flow about a model in a wind tunnel should be in agreement

with that in free flight. !t is recogni"ed, however, that those two flows are different. !n a free flight,

the flow about the model must satisfy the condition that it is undisturbed at infinity. #eanwhile, in a

wind tunnel, certain other conditions must be satisfied at the tunnel boundaries. This phenomenon

modifies the free stream flow at the model location and thus the model characteristics.

The foundation of research on wind tunnel wall interference is attributed to $randtl because his

basic principles of the lifting-line theory are essential to understand the simplest calculation of wall

interference on finite wings. %urthermore, the classical approach based on $randtl regards the model

as a lifting line when the problem of wall interference reduces to a solution of the two-dimensional

&aplace equation in the transverse plane containing the model. The solution may be obtained by the

method of images in which the wall interference flow field is that due to the doubly infinite array ofmirror images of the model reflected by the tunnel walls.

Theories of lift and bloc'age interferences are now highly developed for steady subsonic flows

without separation. !mprovements to the classical approach have been developed, however, mainly

in more elaborate methods for model representation and upwash interpretation. These methods are

ta'en together under the collective term, neo-classical approach. This approach provides a more

accurate correction and applicable to larger models with wings spanning nearly 70% of the tunnel

width, and equipped with engine simulation and positioned in various attitudes relative to the tunnel

centre. %urthermore, the allowance for compressibility increases the applicability of the methods to

a wider range of subsonic #ach numbers. #any references on this subect can be found in ())*.

This paper is intended to present some useful information about the bac'ground and origin of the

wall correction formulae that were derived on the basis of the neo-classical approach. +n examplecase study is given to demonstrate the application of the wall correction formulae in a rectangular

subsonic wind tunnel with solid-walls.

Applied Mechanics and Materials Vol. 225 (2012) pp 60-66 Online available since 2012/Nov/29 at www.scientific.net © (2012) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/AMM.225.60

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 113.210.12.208, Universiti Putra Malaysia, Serdang, Malaysia-19/09/13,17:29:32)

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Background

ssentially, solid walls surrounding the finite tunnel flow will affect the flow field at the model

position. This is because the normal outward displacement of the streamlines is prevented and the

airspeed in the neighbourhood of the model and its wa'e is consequently increased. !n addition, the

up-flow, which neutrali"es the down-flow at the walls, is introduced at the model position. The first

phenomenon is 'nown as bloc'age effect while the second one is regarded as the lift interference.

The total bloc'age effect, , is a sum of corresponding velocity increments due to solid bloc'age,

s that is associated with the model volume and wa'e bloc'age, w that is associated with the model

wa'e. nli'e the solid-bloc'age velocity increment which is approximately symmetrical over the

model, the wa'e-bloc'age velocity increment is gradually increasing over the model length. This

condition causes a longitudinal buoyancy effect that imposes a drag correction to the model, ∆C D1.

The up-flow velocity due to the lift interference requires corrections to the angle of attac', ∆α

that is applied at the three-quarter-chord line and drag, ∆C D2 that is determined at the one-quarter-

chord line. #oreover, the up-flow varies along the model length. This streamline curvature, which

is interpreted as an induced camber, results in a corresponding change in the wing moment, ∆C M1.

%urthermore, the up-flow at the tail can be corrected in terms of the stabili"er setting, (∆αt – ∆α) thatis associated with an additional correction to the pitching moment, ∆C M2 and a correction to the lift

coefficient, ∆C L.

Lift Interference

!n a closed tunnel with solid walls, the model experiences an upwash that will consequently

increase its lift. The usual treatment is to compare free and constraint conditions on the basis of

equal lift. The important corrections to the incidence and the drag coefficient of the model have

been derived as in q. ), where C is the tunnel cross-sectional area, S is the wing area, and δ is the

interference parameter that is determined by the shape of the tunnel, the si"e of the model, the type

of lift distribution, and whether the model is located in the centreline of the tunnel (*.

∆ = , and ∆ =

. /)0

!t has been proven that the wall constraint imposes only little distortions on lift distribution of an

elliptic wing. sing this 'nowledge, the interference experienced by any wing in any type of tunnel

can be sufficiently and accurately estimated based on the assumption of a wing of finite span with

elliptic distribution of lift or, in a more simple approximation, a small wing with the total lift

concentrated at its midpoint (*.

Small Models (Classical Theory). The boundary-induced upwash angle might be calculated by

assuming that the pair of trailing vortices will oin to form a doublet of strength µ = 2sГ . The total

upwash angle at the wing center is given in q. , where and ! are, respectively, the width and theheight of the tunnel, m and n are extending for all positive and negative integers except "ero.

=

∑ ∑ −1 !"!""

"" . /0

The interference parameter, defined as = #$%&

'() , can be reduced to1

= ∑ ∑ − !

"!"""" . /20

valuation of the double summation leads to the interference-upwash parameter for the quarter-chord point1

* = !+ !

∑ -./0 "2

342 . /30

Applied Mechanics and Materials Vol. 225 61



The tail part at a distance #t behind the wing experiences a different interference compared to

that by the wing. The tail setting will be measured effectively smaller in the tunnel than in free

flight such that it requires correction as outlined by q. 4, where $=(1-M 2 )12 is the allowance for

compressibility and δ1 is the streamline-curvature factor connected with the local derivative of the

upwash at the wing (2*.

∆5 = 6789:! . /40

Large Models. #odern wind tunnel models have to be large and thus the small wing assumption

can no longer be applied. 5ith the assumption that the slope of the circular-arc airfoil at its three-

quarter chord point is close to its theoretical angle of "ero lift, the interference correction to

incidence can be applied at the three-quarter chord point and this is approximated by q. 6, where ;< is the aerodynamic mean chord (2*.

∆ = * > <:! 2?

. /60

Since the lift is centered at about the quarter-chord line, the drag will also be corrected at thequarter-chord line according to q. 7.

∆ =

. /70

The correction to the angle of incidence is chosen such that no correction to lift will be needed.

However, an additional pitching moment correction arises and calculated by means of q. 8, where

&' is the aspect ratio of the wing and 0* is its mid-chord sweepbac'.

∆2 = > @892A:! B> <

> @? 1 CD EF GHI9*JK L − > <

> @?M

NNO . /80

The value NNO may be determined during the test-run using q. :, or calculated with q. );,

provided there is no separation (4,6*.

NNO = ,,P9

OOP9 . /:0

NNO = Q

2"R 2"SQT D U:"5VWXJY. /);0

The interference parameters δ0 and δ1, depend on the model representation including the choice

of a vortex model. !t will be also influenced by the aspect ratio, sweepbac' and yaw of the wing.%or general purposes /for not too small aspect ratios and not too large sweep angles0, a swept

lifting-line model with a symmetrical /elliptic0 loading can be ta'en to be adequate. Similar to the

small-model assumption, the interference factor is given in q. )), where wi is the interference

upwash velocity at the wing.

* = !

Z . /))0

%or rectangular tunnels, by treating a complete 2-< motion, upwash field wi(#+,+) can be

calculated completely to get the streamline-curvature parameter1

2 = :! NZ D ?NS6 !D U . /)0

62 AEROTECH IV



%or most purposes, it is sufficient to consider wi

as a linear fuction of #, as represented in q. 6. But

for large model, this may lead to overestimated

upwash at the tail. !nstead of q. 4, the actual local

value of

[\ at the tail should be used to calculate

∆5. The interference parameter δ1 can be obtainedin terms of δ1=δ0, which is 'nown from the small

model approximation as shown in %ig. ) (2*.

q. 6 and q. 7 can now be expressed as q. )2

and )3, where the subscript ] denotes that the

interference parameter (δ0 ) . is calculated as an

elliptically weighted mean value over the span. This

parameter depends also on the ratio of wing span to

tunnel width, / = 2s as well as on ! of the

tunnel. The analysis of /δ0 ) . , based on Sander and

$ounder, resulted in a useful graph in %ig. (2*.

∆ = *^ 1 > <:!

898X?

/)20

∆ = *^

. /)30

!t is common to treat wing, body and tail

separately and to ignore the body lift. By considering

q. )2 as a correction to the incidence of the whole

model, additional correction to the incidence of the

tail can be derived by q. )4, where δt depends on wi

at three-quarter chord line of the tail plane.

∆5 = 5^ . /)40

q. )4 is a function of the tail plane location. This

correction is related to the additional lift produced by

the tail plane, which is included into the correction of

C L through q. )6 and q. )7, whereN7NO7 _

2

Q7Q7" ;`a9*JK. +ccordingly, the additional pitching

moment correction is captured by q. )8.

∆5 = >5 − > N7NO7 . /)60

∆ = −>5 − > 7 b7 b

N7NO7 . /)70

∆ = >5 − > 67> <

7 b7 b

N7NO7 . /)80

Blockage ffect

The bloc'age effects act on the longitudinal flow component only. !n a closed tunnel, this will

increase the tunnel flow velocity. #oreover, solid and wa'e bloc'age effects are assumed to bemutually independent, yielding1

= c Z = d . /):0




Solid Blockage. The solid bloc'age factor depends on model and tunnel dimensions, which can be

prepared before test and calculated as soon as the #ach number is 'nown. The following formula in

q. ; includes fuselage and engine simulator, where = lt is the body fineness ratio with the

subscripts and . denote, respectively, fuselage and engine. ef is the tunnel shape parameter,

whose value may be approximated, e.g. according to Thompson in q. ) (2, pp. :7*.

cg = ef 2?h D ijkl

:m 1 nJo :pl?, and c^ = ef 2

?h D ijkq:m 1 nJo :

pq?. /;0

ef = JCr ! !

?. /)0

Treating the wing as identical to a body of revolution,

the related solid bloc'age factor can be calculated

according to q. , where tc is the ratio of wing

thic'ness to chord and is the tunnel shape parameter

that can be obtained from %ig. 2.

c = e 2?h D ijks

:m 1 1JL 5>?. /0

!f n engine simulators are used, the above relations

yield1

c = cg I c^ cZ. /20

Since w can only be determined if the measured lift-

and drag-coefficients are 'nown, s has a practical use to

obtain a temporary dynamic pressure according to1

t*3 = t"u1 L − v"cw. /30

such that the temporary C L4 5 and C D4 5 can be reduced to q. 4, where 41 and 42 are the

relevant measured balance forces and, S is the wing area.

33 = x2 St*3 &Uy , and 33 = x St*3 &Uy . /40

!ake Blockage. !t is important to indicate, prior to or during a test-run, two regions in the alpha

polar, where one expects, respectively, an attached flow and a separated flow.

The wa'e within the region of attached flow is represented by an equivalent source at model position and a sin' at a far distance downstream, yielding q. 6 where +? is the wing aspect ratio

and S is the wing or reference area.

33 = + z33 − s33

QT{. /60

The correction formulae that is appropriate to the separated flow condition is derived through a

method that relies on experimental evidence (2*. !t is given by q. 7, where C D is the total

measured drag, C DM is the minimum or viscous drag and C Di is the induced drag approximated by

the q. 8.

= − | − \. /70

\ = s} QT . /80

64 AEROTECH IV



The C DS value may be interpreted as the difference between the measured total drag and the

theoretical C L-C D curve as extrapolated from the measured wing properties prior to stall. +t least,

seven data points from the attached flow condition are needed to fit an extrapolation curve.

= E* E2 E. /:0

The remaining parameters can then be obtained, i.e. the effective aspect ratio1 &' = (6&2 )-1, theminimum lift coefficient1 C LM = - &1 (2&2 ), the minimum drag coefficient1 C DM = &0 – C LM

2 (6 &'),

and the bloc'age factor1 = 28 – 0098 &'. %inally, the wa'e bloc'age factor can be found1

Z3 = ~•}

+ € 33 − | − zs33 }

QT {‚ƒ. /2;0

<epending on flow conditions, the total bloc'age factor is one of the relations1

= c Z3 , or = c Z„„ . /2)0

Buoyancy. $resuming a linear pressure gradient along the length of t he model, the analysis

resulted in a correction of the drag coefficient within the region of the attached flow /q. 20 and

within the region of the separated flow /q. 220, where M 0 + C: D4 and C: L4 are, respectively, the

reduced #ach number, drag and lift coefficients on the basis of the corrected ;0.

∆2 = −c1 nJov* 3 − 3 sQT ?. /20

∆2 = −c1 nJov* …3 − Ss3 }UQT †. /220

"ff#Center Model $osition. !f the model is offset from the center line by a distance of /!2-<),

where d is the model height from the floor, a small increase in the solid bloc'age factor will appear1

i = JLC ‡Lˆ $D 1‰ Š ;`a‹G. /230

Such that the bloc'age factor from q. 2) yields1

c , Z3 , i or c , Z„„ , i. /240

%&erimental 'erification

+ small, simple and unpowered aircraft modelhas been investigated in a small wind tunnel, the

so-called #odel Tunnel, #T ;.8x;.6m, and in a

relatively large wind tunnel, the so-called &owSpeed 5ind Tunnel, &ST 2x.4m. Both wind

tunnels were two of the various research facilities

at @ational +erospace &aboratory, @etherlands.

The cross-sectional impression of the model and

the two wind tunnels are illustrated in %ig. 3. The

model seems large in the small wind tunnel but

very small in the large wind tunnel (7*.

The tests were conducted at constant 'e = 0 #109 >-1 and Ma = 018. +n internal balance was

used to measure the aerodynamic forces. The moment reference point and the balance center were

located at the wing mid-chord point. The experiment produced three sets of data consisting of the




uncorrected data obtained from tests in the small

tunnel, the inte?e?ence ?ee data from tests in the

large tunnel and the final corrected data. They are

presented in graphs C L – α+ C L – C D, and C L – C M in

%ig. 4, %ig. 6, and %ig. 7, respectively. These figures

show clearly that the correction procedure applied tothe uncorrected data resulted in a new data that is in

good agreement with the interference free data.

Acknoledgement

This research wor' has been financially supported

by niversiti $utra #alaysia through the ?esearch

niversity Arant Scheme ;4-;3-))-)4)6?.

eferences

()* T. Theodorsen, The Theory of 5ind-Tunnel 5all

!nterference, @+C+ ?eport 3); /):2)0.

(* H. Alauert, !nterference on 5ings, Bodies and

+irscrews, +?C ? D # )466 /):220.

(2* H.C. Aarner, et.al., Subsonic 5ind Tunnel 5all

Corrections, +A+?<ograph );: /):660.

(3* E.B. Barlow, 5.H. ?ae, Er. and +. $ope, &ow-

Speed 5ind Tunnel Testing, E. 5illey D Sons, !nc.,

@ew For', ):83.

(4* <. c'ert, Correction %ormulae for Gn-line

$rocessing of #easurements, <@5 /):840.

(6* ?.+. #aarsingh, Summary of @eo-Classical

Tunnel 5all Correction, @&? /):860.

(7* S. 5iriadidaa, @eo-classical 5all Correction

#ethod, B$$T @&? /):870.

(8* #. #o'ry, #. halid and F. #ebar'i, The +rt

and Science of 5ind Tunnel 5all !nterference1 @ew

Challenges, nd Congress of !nternational Councilof the +eronautical Sciences /!C+S0, Harrogate,

/;;;0.

(:* B. ?asuo, Gn Status of 5ind Tunnel 5all

Correction, !C+S, Hamburg, Aermany /;;60.

();* @. lbrich, 5ind Tunnel 5all !nterference

Corrections, Eacobs Tech. !nc., S+ /;;:0.

())* +erodynamic of 5ind Tunnel Circuits and their Components, +dvisory Aroup for +erospace

?esearch and <evelopment /+A+?<0, %rance /)::70.

66 AEROTECH IV



AEROTECH IV

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Aerodynamic Interference Correction Methods Case: Subsonic Closed Wind Tunnels

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