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By H a r r y H. Heyson and Kalman J. G r u n w a l d NASA Langley Research Center SUMMARY The wake skew angle used i n applying t h e theory of NASA TR R-124 t o data correction should be such t h a t the angular deflection of t h e wake v o r t i c i t y from the horizontal i s one-half t h a t calculated from momentum theory a t t h e l i f t i n g element. This usage i s i n contrast t o t h a t of t h e o r i g i n a l paper which used t h e angle of t h e mass flow. Because of large-scale r e c i r c u l a t i o n e f f e c t s , t h e r e i s a f i n i t e lower l i m i t t o t h e t e s t speed at which reliable and correctable data can be obtained i n closed wind tunnels. Although a zero-correction wind tunnel f o r V/STOL t e s t i n g has not yet been achieved, it can a l l e v i a t e i s shown t h a t t h e use of s u i t a b l y mixed wind-tunnel boundaries boundary e f f e c t s on V/STOL data.
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INTRODUCTION of f l i g h t give t h e aerodynamicist some of The very slow speed regimes
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h i s most d i f f i c u l t problems. The small perturbation assumptions inherent i n almost a l l configuration studies begin t o break down, and extreme i n t e r f e r - ences appear t o e x i s t between t h e various aerodynamic components of t h e air- c r a f t .
A s a r e s u l t , t h e wind tunnel is almost t h e only means of determining, even approximately, t h e performance and s t a b i l i t y of the e n t i r e a i r c r a f t .
Unfortunately, wind-tunnel r e s u l t s are not i d e n t i c a l t o t h e r e s u l t s obtained i n f l i g h t because of t h e wind-tunnel boundaries i n close proximity The purpose of t h e present paper is t o examine experimentally t o t h e model.
t h e adequacy of current theory i n predicting the e f f e c t of t h e wind-tunnel boundaries on t h e data from s p e c i f i c models. I n addition, some information i s presented on t h e degree of relief from corrections which can be obtained by appropriate s l o t t i n g and opening of t h e wind-tunnel w a l l s .
The present paper i s limited t o t h e effect of t h e wind-tunnel boundaries upon model data. I n p a r t i c u l a r , no attempt i s made t o evaluate t h e problems of scaling o r model d e t a i l i n g on t h e extrapolation of model d a t a t o f u l l - s c a l e Reynolds numbers.
SYMBOLS momentum area of l i f t i n g system
AM
cross-sectional area of wind-tunnel t e s t section AT semiwidth of wind-tunnel t e s t s e c t i o n l i f t c o e f f i c i e n t , L/qS T a i l normal force t a i l normal-force c o e f f i c i e n t , qs (Jet ~ S S f l O W ) ( V j ) j e t momentum c o e f f i c i e n t , q s difference between corrected and uncorrected values of CP mean aerodynamic chord semiheight of wind-tunnel t e s t s e c t i o n lift pitching moment, p o s i t i v e nose up dynamic pressure r o t o r radius wing area s t a t i c t h r u s t tunnel velocity j e t v e l o c i t y j e t v e l o c i t y i n s t a t i c t h r u s t mean o r momentum-theory value of longitudinal induced v e l o c i t y at model, p o s i t i v e rearward longitudinal interference v e l o c i t y due t o drag, p o s i t i v e rearward longitudinal interference v e l o c i t y due t o l i f t , p o s i t i v e rearward mean o r momentum-theory value of v e r t i c a l induced v e l o c i t y a t model, p o s i t i v e upward v e r t i c a l interference v e l o c i t y (general), p o s i t i v e upward v e r t i c a l interference v e l o c i t y due t o drag, p o s i t i v e upward v e r t i c a l interference v e l o c i t y due t o l i f t , positive upward distance rearward from center of l i f t angle of a t t a c k correction t o angle of a t t a c k resulting from presence of wind-tunnel boundaries r a t i o of wind-tunnel width t o wind-tunnel height, B/H jet-boundary correction f a c t o r , defined by equation h = 6 - S CL; A T a l s o , jet-boundary correction factor (general) correction f a c t o r f o r longitudinal interference due t o drag, defined by equation AUD = &,D AM - u, 4 2 correction f a c t o r f o r longitudinal interference due t o l i f t , defined
by equation AUL = 44 - wo
A T correction f a c t o r f o r v e r t i c a l interference due t o drag, defined by
9 4
equation
AWD = 6 , , ~ - ~0
AT
correction f a c t o r f o r v e r t i c a l interference due t o l i f t , defined by equation AWL = 6 w , ~ angle between v e r t i c a l and angle of wake at model
x + goo
e f f e c t i v e skew angle, RESULTS AND DISCUSSION Review of Theory
I The c l a s s i c a l corrections t o wind-tunnel data ( f o r example, ref. 1) are
applied according t o t h e equation C a = 6 - - L S (1) AT ~ Equation (1) appeared t o present considerable d i f f i c u l t y when VTOL models were first tested i n wind tunnels. The problem w a s t h a t , as t h e wind-tunnel v e l o c i t y w a s decreased at constant l i f t , t h e l i f t c o e f f i c i e n t increased without bound, and t h e correction angle approached i n f i n i t y . A s a point of f a c t , t h e problem w a s never r e a l l y q u i t e t h i s serious. Equation (1) w a s derived by obtaining t h e v e r t i c a l interference v e l o c i t y and then assuming t h a t t h e correction angle w a s s m a l l enough so t h a t t h e angle and i t s tangent were equal. Without t h i s f i n a l assumption, equation (1) would have been I n equation ( 2 ) , as t h e wind-tunnel speed approaches zero, t h e l i f t coef- f i c i e n t a t constant l i f t s t i l l approaches i n f i n i t y ; however, t h e correction angle only approaches goo. I n other words, i f t h e tunnel v e l o c i t y ( V ) i s zero, a closed wind tunnel s t i l l produces an upwash (Aw) i n t h e v i c i n i t y of a l i f t i n g Unfortunately, t h e assumption lying behind t h e calculation of t h e cor- model.
r e c t i o n f a c t o r 6, namely t h a t t h e wake passes d i r e c t l y downstream along t h e I wind-tunnel axis, i s severely violated at very low and zero wind-tunnel veloc- i t i e s . Thus, usable r e s u l t s cannot be anticipated from t h e application of e i t h e r equation (1) or ( 2 ) t o tests of VTOL models.
A more recent analysis made a t t h e Langley Research Center ( r e f s . 2 and 3 ) t r e a t s the case where t h e wake i s deflected s u b s t a n t i a l l y downward from t h e model. This theory obtains corrections i n t h e form of interference v e l o c i t i e s t h a t a r e functions of t h e wake skew angle. It w i l l be observed (See f i g . 1.)
t h a t , i n general, both horizontal and v e r t i c a l interference v e l o c i t i e s are obtained as a result of both lift and drag. I n a c t u a l l y applying corrections t o data, these interference v e l o c i t i e s a r e used t o obtain a new corrected angle of attack and a new e f f e c t i v e forward v e l o c i t y .
The correction f a c t o r s describing t h e interference v e l o c i t i e s have been
calculated and tabulated f o r a wide range of variables (refs. 4 t o 7). A sample
case f o r t h e center of l i f t i n a closed wind tunnel having a width-height r a t i o of 1.5 i s presented i n f i g u r e 2. The correction f a c t o r t h a t corresponds t o t h e c l a s s i c a l correction f a c t o r i s 6 w , ~ . A t X = 90°, it d i f f e r s f r o m t h e c l a s s i - c a l correction f a c t o r only by a f a c t o r of -4, which occurs s o l e l y because of t h e difference i n d e f i n i t i o n . Furthermore, at X = 900, a l l t h e other correc- t i o n factors are zero.
Thus, t h e c l a s s i c a l theory i s contained as a subcase of t h e newtheory. It will be observed, however, t h a t when t h e wake i s deflected substantially downward, t h e v e r t i c a l interference due t o l i f t increases sub- s t a n t i a l l y , and i n addition, a smaller upwash due t o drag i s encountered. Fur- thermore, both l i f t and drag contribute, i n general, t o a reduction i n effec- t i v e forward velocity.
Earlier Experimental Studies Over t h e past several years investigators at t h e Langley Research Center have conducted experimental studies of t h e adequacy of t h e new theory by t e s t i n g tilt-wing ( r e f . 8) and fan-in-fuselage ( r e f . 9) models i n d i f f e r e n t s i z e wind tunnels. Other investigators have t e s t e d rotors i n wind-tunnel i n s e r t s ( r e f . 10). The tunnels have ranged from about 15 t o over 1600 square f e e t i n area. In general, s u b s t a n t i a l l y improved agreement w a s obtained i n a l l cases, with a tendency toward overcorrection at the most severe l i f t c o e f f i c i e n t s .
A t t h i s point a fan-in-wing model was t e s t e d i n both a 7- by 10-foot wind tunnel and a 30- by 60-foot wind tunnel ( r e f . 11). This model w a s t h e first Once more t h e theory cor- model with a t a i l t o which t h i s theory was applied.
rected t h e model l i f t and drag reasonably well; however, t h e calculated cor- rection t o t h e pitching moment was approximately equal, but opposite i n sign, t o t h a t required t o bring t h e two sets of data i n t o agreement. Obviously, t h e r e w a s an unexplained f a c t o r i n t h e application of t h e corrections.
Location of t h e Wake Before proceeding f u r t h e r , it is well t o inquire i n t o t h e fundamental question of t h e a c t u a l location of the wake. Fortunately, some information on t h i s subject already e x i s t s . For example, figure 3 shows t h e measured v o r t i c - i t y d i s t r i b u t i o n i n t h e wake of a helicopter r o t o r (ref. 12). The wake of a r o t o r is usually represented f o r purposes of calculation as a s e r i e s of con- c e n t r i c vortex cylinders whose strength i s proportional t o t h e l o c a l disk-load d i s t r i b u t i o n . Thus it would be expected t h a t , i n t h e survey plane of figure 3 , t h e v o r t i c i t y would be found t o be concentrated within t h e i n t e r s e c t i o n of survey plane. (This i n t e r s e c t i o n i s shown by these vortex cylinders and the The f i g u r e shows t h a t t h e expected result i s t h e dashed e l l i p s e i n f i g . 3 . ) The dominant feature of t h e v o r t i c i t y d i s t r i b u t i o n i s t h e pres- not obtained.
ence of two large, and already w e l l rolled-up, v o r t i c e s behind t h e outermost portions of t h e r o t o r . It i s notable t h a t these v o r t i c e s are deflected down- ward only about one-half as far as indicated by momentum theory. This behavior i s i n contrast t o t h a t of t h e wake mass flow which behaves e s s e n t i a l l y as indi- cated by momentum theory.
Joppa (ref. l3), of t h e University of Washington, s t a r t i n g from t h e analy- sis of reference 14, has been able t o show t h e o r e t i c a l l y t h a t f o r low-aspect- r a t i o wings t h e r e s u l t is e s s e n t i a l l y i d e n t i c a l t o t h e previous observation.
That is, t h e f i n a l wake v o r t i c i t y i s deflected through approximately one-half of t h e angle calculated at the wing, r a t h e r than through twice t h e angle as predicted ( f o r t h e wake mass flow) by linearized theory.
Effective Wake Skew Angle The calculation of wind-tunnel boundary corrections may be accomplished by t h e use of s u i t a b l v arranged image systems around t h e real test. section. It w i l l be observed t h a t these image systems are comprised of t h e wake v o r t i c i t y r a t h e r than t h e wake mass flow. Furthermore, when t h e e f f e c t s of a l l t h e image wakes are added, it will be observed t h a t t h e calculated r e s u l t s a r e l a r g e l y produced by image wakes which are at a s u b s t a n t i a l distance from t h e model.
Thus, the f a r portions o f t h e wake have a proportionately l a r g e r e f f e c t on t h e model (insofar as w a l l interference is concerned) than does t h e s m a l l portion of t h e wake immediately near the model. Therefore, it i s proposed t h a t a skew angle yielding just one-half t h e downward angular displacement of momentum theory (such as r e f . 13) be used i n applying t h e corrections of reference 2 t o wind-tunnel data. I n terms of skew angle, t h e e f f e c t i v e skew angle Xeff i s It i s recognized t h a t equation ( 3 ) cannot be correct i n hovering or at extremely low forward speeds. This i s evident since i n t r u e hovering t h e skew angle, whether based on wake v o r t i c i t y o r on w a k e mass flow, i s indeed Oo and not 4 5 O as would be indicated by equation (3). O n t h e other hand, t h e r e a r e limitations on t h e minimum speed at which t e s t s can be made i n a meaningful fashion i n wind tunnels, and it i s believed t h a t these l i m i t a t i o n s w i l l gen- e r a l l y be encountered before t h e f a i l u r e of equation (3). I n any event, it appears t h a t t h e e f f e c t i v e skew angle i s a superior approximation t o t h e a c t u a l wake over t h e bulk of reasonable t e s t conditions.
Jet-Flap Model Recently, data have been obtained f o r a j e t - f l a p model ( f i g . 4) i n t h e Langley 300-MPH 7- by 10-foot tunnel as w e l l as i n a small wind tunnel 2.70 f e e t high and 1.88 f e e t wide. (These wind tunnels a r e designated 7' x 10' and 2.70' x 1.88' herein.) The model was equipped with a s e n s i t i v e t a i l balance, which measured t a i l normal force, and a l s o w a s equipped with t h e usual s t i n g balance, which w a s arranged so as t o measure only t h e forces on t h e wing.
Roughness s t r i p s were applied t o both t h e wing and t h e t a i l surfaces t o minimize Reynolds number e f f e c t s .
A sample of the data obtained with t h i s model i s shown i n f i g u r e 5 . Cor- ~ rections have been applied t o t h e data from both wind tunnels. (The corrections t o t h e 7 ' x 10' wind-tunnel data a r e very s m a l l , on t h e order of s e v e r a l t e n t h s of a degree; consequently, t h e uncorrected data are not shown.) The corrections used are those of reference 2 with finite-span e f f e c t s ( f o r uniform loading) on both wing and t a i l accounted f o r by t h e superposition methods outlined i n t h a t paper. Inclusion of t h e finite-span e f f e c t s s u b s t a n t i a l l y improves t h e cor- relation. The small differences i n C p r e s u l t i n g from t h e horizontal i n t e r - ference v e l o c i t i e s have been removed from t h e lift data ( f i g . 5 ( e . ) ) by finding dCL/dC,, from closely spaced t e s t runs i n t h e 7 ' x 10' wind tunnel and then sub- t r a c t i n g an amount equal t o (dCL/dCp)&!p from t h e lift coefficient,. I n t h e t a i l normal force, case of t h e t h e behavior of dCN,t/dCp w a s very e r r a t i c with respect t o both Cp and a; consequently, no s i m i l a r correction has been applied t o the tail-normal-force data. (See f i g . 5(b).) The a c t u a l changes i n as a r e s u l t of t h e h o r i z o n t a l interference were small f o r t h i s model.
C , I n addition, no correction has been made t o t h e data t o account f o r the e f f e c t i v e aerodynamic warpage of t h e model as a r e s u l t of t h e nonuniformity of t h e wall-induced interference over t h e model. I n p a r t i c u l a r , t h e t a i l location i s aerodynamically equivalent t o a t a i l location t h a t i s s l i g h t l y d i f f e r e n t Also neglected i s from t h e a c t u a l geometric location on t h e physical model.
t h e v e r t i c a l motion of t h e t a i l i n t h e wind tunnel as t h e model angle of a t t a c k i s changed by pivoting about the quarter-chord.
Despite t h e unaccounted-for f e a t u r e s mentioned, it is evident t h a t t h e application of corrections according t o reference 2 has g r e a t l y improved t h e c o r r e l a t i o n between the data from t h e two wind tunnels. This t r e n d i s p a r t i c - C , = 1.5. I n t h e u l a r l y evident i n t h e s t a l l angle of a t t a c k of the wing at corrected data, t h e s t a l l angle i s reproduced f a i t h f u l l y i n both wind tunnels, d e s p i t e t h e f a c t t h a t t h e wall-induced interference i s about 10 percent g r e a t e r at t h e wing t i p s than it is at t h e center of t h e model. The improved agreement i s equally obvious i n t h e f i d e l i t y with which the angle f o r r e v e r s a l of t a i l normal force i s reproduced i n t h e corrected data at Cp = 5.0.
The t r e n d of g r e a t l y improved agreement i s evident throughout t h e study Data f o r except f o r t h e highest momentum c o e f f i c i e n t a t which t e s t s were made.
t h i s case ( C , = 10) a r e shown i n f i g u r e 6. The corrected l i f t c o e f f i c i e n t s obtained i n t h e two wind tunnels a r e i n reasonable agreement up t o an angle of a t t a c k of about loo, after which t h e two s e t s of data diverge. Since t h e t a i l normal-force data have s u b s t a n t i a l s c a t t e r and the corrections a r e large, these data a r e a l s o i n reasonable agreement up t o an angle of a t t a c k of approximately
loo, after which these two s e t s of data a l s o diverge. The physical reason f o r
t h i s divergence is discussed i n a subsequent section of t h i s paper.
Effect of F i n i t e Span A s previously mentioned, inclusion of finite-span e f f e c t s s u b s t a n t i a l l y improves t h e agreement between t h e two wind tunnels. I n t h e 7' X 10' wind tunnel, of course, t h e 1-foot-span model i s a reasonably good representation of a vanishingly s m a l l model i n comparison t o the 10-foot width of t h e tunnel. On t h e o t h e r hand, t h e 1-foot-span model i n the 1.88-foot width of t h e small wind tunnel cannot be considered vanishingly small under any circumstances. It was f o r t h i s reason t h a t finite-span e f f e c t s were included. The importance of including t h e s e e f f e c t s can be seen by comparing f i g u r e s 7 and 8 with f i g u r e s 5 and 6. The d a t a of f i g u r e s 7 and 8 were corrected by using t h e correction fac- t o r s f o r a zero-span model. It i s evident from t h i s comparison t h a t it i s nec- essary t o include finite-span e f f e c t s i f complete correction of data is desired.
J e t Thrust It will be observed t h a t (depending on t h e value of Cp) from 4c! t o ever TO percent of t h e l i f t of t h e j e t - f l a p model is due t o t h e d i r e c t t.hrust of t h e compressible j e t a t the t r a i l i n g edge of t h e wing.
- A l l t h e j e t t h r u s t w a s
included i n t h e l i f t c o e f f i c i e n t when correcting the data. The close correla- t i o n between t h e two s e t s of data after correction indicates t h a t , as assumed 2 and 3 , t h e exact nature of t h e l i f t i n g system i s inconsequential, i n references whether it be propeller, r o t o r , wing, fan, o r j e t . The only feature of t h e configuration t h a t i s s i g n i f i c a n t i s the d i s t r i b u t i o n of l i f t and drag within t h e wind. tunnel.
The foregoing comments a r e reinforced by t h e information presented i n paper no. 13 by Richard J. Margason. I n t h a t paper it i s shown t h a t even t h e compressible j e t rapidly rolls up i n t o a subsonic wake of a d i r e c t , c i r c u l a r , vortex p a i r when operated i n t r a n s i t i o n . Thus, t h e application of corrections t o such j e t s should require l i t t l e o r no change i n procedure.
Fan-In-Wing Model Pitching-moment data from a fan-in-wing model have been mentioned previously i n t h i s paper. The model i s shown i n f i g u r e 9. The pitching-moment data from both the 7 ' x 10' and 30' x 60' wind tunnels a r e shown i n figure 10 as it w a s o r i g i n a l l y presented i n reference 11. The curve labeled "7' x lo', corrected" w a s obtained by applying the corrections of reference 2 i n accordance with X
r a t h e r than Gff. It w i l l be observed t h a t t h e correction displaces t h e
pitching-moment data i n a d i r e c t i o n opposite t o t h a t required i n order t o cor- r e l a t e the data from the two wind tunnels.
The same data corrected according t o reference 2, but with t h e use of t h e effective skew angle, are shown i n f i g u r e 11. The corrections as applied i n t h i s case are extremely crude. It i s assumed t h a t the model i s vanishingly s m a l l . Obviously, t h e 64.5-inch-span model i s not s m a l l i n t h e 7' x 10' wind tunnel. Examination o f t h e r e s u l t s of reference 2 indicates t h a t t h i s assump- i n t h e present case overestimates t h e required correction. The e f f e c t of t i o n the f l o w d i s t o r t i o n over t h e r e a r portion of t h e fuselage (which has substan- t i a l area and moment compared with t h e r e l a t i v e l y s m a l l t a i l plane) has a l s o been neglected. This assumption would r e s u l t i n a smaller correction. I n t h e absence o f measurements of t h e load d i s t r i b u t i o n between t h e fans and t h e wing, it has been assumed t h a t t h e load i s c a r r i e d e n t i r e l y upon the fans. I n prac- t i c e , of course, t h e wing does carry s u b s t a n t i a l l i f t , and two wakes, at d i f - ferent skew angles, e x i s t i n t h e wind tunnel. If t h e l i f t d i s t r i b u t i o n between the t w o l i f t i n g systems was accounted f o r , t h e upwash at t h e t a i l would be reduced. I n addition, t h e v e r t i c a l displacement of t h e t a i l from t h e wing plane, as well as t h e l a r g e motion of t h e t a i l within t h e wind tunnel as a r e s u l t Of changes i n angle of a t t a c k , has been neglected. Furthermore, no cam- b e r e f f e c t s on t h e wing and no pitching-moment changes due t o induced flow gra- dient on t h e fans were considered.
I n addition t o t h e foregoing assumptions, a l l t h e data shown herein f o r t h i s model were obtained a t speeds far below an apparently l i m i t i n g lower speed f o r VTOL t e s t s i n closed wind tunnels. This l i m i t will be discussed i n a sub- sequent section of t h i s paper.
As a r e s u l t of t h e f a c t o r s mentioned previously, t h e close c o r r e l a t i o n of t h e corrected pitching moments i s fortuitous. Actually, unpublished t a i l - o f f x 10' and 30' x 60' wind tunnels i n d i c a t e t h a t t h e e f f e c t d a t a from both t h e 7' of t h e walls on t h e pitching moment due t o the t a i l i s q u i t e s m a l l . Examination of t h e c i r c u l a t o r y flow discussed i n a subsequent section i n d i c a t e s t h a t t h e r e s u l t of such flow should l a r g e l y counteract t h e wall-induced upwash at t h e t a i l i n t h i s p a r t i c u l a r test. O n t h e other hand, f i g u r e 1 1 does indicate, at l e a s t , t h a t t h e correction i s not i n t h e wrong d i r e c t i o n as it appeared t o be when calculated with t h e use of X instead of &ff (as i n f i g . 10).
The change i n t h e correction by changing t o t h e e f f e c t i v e skew angle may be explained by examination of figure 12. This f i g u r e shows t h e v a r i a t i o n of (which i n t h i s case i s t h e most s i g n i f i c a n t correction f a c t o r ) along t h e Z i W , ~ longitudinal axis of t h e model. Note t h a t i n correcting pitching moments t h e t a i l t o coincide problem i s generally one of correcting t h e contribution of t h e with t h e t a i l moment t h a t would be obtained at t h e conditions t o which the l i f t i n g system has already been corrected. Thus, it is t h e r e l a t i v e difference between, r a t h e r than t h e absolute values o f , t h e correction at t h e center of l i f t and t h e t a i l which is of i n t e r e s t . A t X = O o , which approximates t h e o r i g i n a l skew angles f o r t h e fan-in-wing model, it w i l l be seen t h a t there i s a lesser upwash at t h e t a i l than at t h e wing. Thus t h e t a i l i s working with less l i f t i n t h e wind tunnel than i f it were at t h e same condition as t h e wing.
To correct f o r t h i s s i t u a t i o n , an appropriate amount of l i f t must be added t o i n f i g u r e 10. O n t h e other hand, t h e t a i l t o make t h e moment more negative as f o r X = 45O, which approximates t h e effective skew angle f o r t h i s case, t h e l i f t . Conse- tunnel produces more upwash at t h e t a i l than a t t h e center of quently, correction makes t h e moment more positive ( f i g . 11).
T i l t -Wing Model The earlier studies of w a l l e f f e c t s on t h e tilt-wing model (ref. 8) indi- cated t h a t t h e wind-tunnel interferences calculated i n reference 2 overcor- rected t h e d a t a i n extreme conditions. The use of the e f f e c t i v e skew angle would have reduced t h e corrections somewhat f o r t h e tilt-wing model, too, and would have l e d t o improved correlation.
Comparison With Flight I n view of s c a l e e f f e c t s and differences i n model d e t a i l i n g and t h e d i f - f e r i n g accuracies and types of corrections required, comparison between f l i g h t tests and wind-tunnel tests can be a p a r t i c u l a r l y d i f f i c u l t task. This com- parison is unusually d i f f i c u l t when t h e comparison i s attempted i n order t o evaluate only one of t h e many e f f e c t s t h a t are being considered.
Paper no. 5 by Kenneth W. Goodson, f o r example, showed t h a t a 0.09-scale model suffered from l a r g e Reynolds number e f f e c t s ( f i g . 6 of paper no. 5 ) , but t h a t a 0.60-scale model d i d y i e l d reasonable results i n predicting t h e m a x i m u m rate of descent f o r a four-propeller tilt-wing configuration. A s noted i n paper no. 5 , t h e d a t a f o r t h e 0.60-scale model were corrected f o r wall e f f e c t s . The corrections iised t h e e f f e c t i v e skew angle m d considered t h e effect of f i n i t e span. The correction, resulted i n a change of flight-path angle of sev- as obtained i n t h i s manner, e r a l degrees and s u b s t a n t i a l l y improved t h e c o r r e l a t i o n between r e s u l t s from t h e large model and f l i g h t data.
L i m i t on Testing i n Closed Wind Tunnels Rae, of t h e University of Washington, by t e s t i n g r o t o r s i n i n s e r t s i n t h e UWAL 8- by 12-foot wind tunne1,l has shown t h a t t h e wake, upon meeting t h e f l o o r behind the model, spreads l a t e r a l l y on t h e f l o o r , i s turned upward by t h e sidewalls, and produces a flow p a t t e r n i n t h e wind tunnel as indicated on t h e Normally, t h i s disturbance i s too far behind t h e left-hand side of f i g u r e 13.
model t o produce any discernible e f f e c t on t h e data. However, i f t h e wake i s deflected downward sharply enough, t h e r e c i r c u l a t i o n p a t t e r n envelops t h e model I n t h e present case, t h e point of diver- and the data a r e severely affected.
gence occurs at an e f f e c t i v e skew angle of 65O and produces a t h e o r e t i c a l intersection of wake and f l o o r about 2- spans behind t h e point of o r i g i n of t h e w a k e . This point agrees quite closely with t h e value obtained by Rae.
The close correlation between such widely divergent models ( r o t o r and j e t 7 = 0.7) i n d i c a t e s two f l a p ) and wind-tunnel configurations (7 = 1.5 and i s a f i n i t e lower l i m i t t o t h e test speed at which r e l i - things.
F i r s t , t h e r e able and correctable data can be obtained i n a closed wind t - D e l ; and, sec- ond, t h i s l i m i t i s not seriously a f f e c t e d by model configuration but is l a r g e l y determined only by the s i z e of t h e v e r t i c a l - l i f t elements of t h e model. This limiting e f f e c t i s s t i l l r e l a t i v e l y unexplored. It may be t h a t c e r t a i n wind- tunnel configurations w i l l be affected d i f f e r e n t l y from others. It f u r t h e r i f the model configuration were extremely long, o r i f t h e seems possible t h a t l i f t i n g elements were disposed over a large longitudinal distance, t h e l i m i t i n g speed could be adversely affected. S u b s t a n t i a l a d d i t i o n a l experimental work w i l l be required i n order t o define these (and similar) e f f e c t s .
Actually, t h e onset of t h i s l i m i t i n g lower speed follows a r u l e r a t h e r s i m i l a r t o t h a t presented i n paper no. 25 by Thomas R. Turner, i n which it i s noted t h a t a moving b e l t i s required i n order t o simulate ground e f f e c t when t h e combination of l i f t c o e f f i c i e n t and height above t h e ground produces an intersection of e f f e c t i v e wake and f l o o r which i s l e s s than 2L spans behind t h e model.
Thus, t h e boundary l a y e r on t h e w a l l s i s probably a major causative fac- t o r i n producing these r e c i r c u l a t i o n e f f e c t s . The study of a number of boundary- layer control features is indicated i n t h e hope t h a t s i g n i f i c a n t gains could be obtained.
A s stated previously, t h e study of l i m i t i n g forward speeds f o r VTOL tests i n wind tunnels i s s t i l l i n an e a r l y stage and, consequently, l a r g e uncertain- t i e s are present. I n view of t h i s uncertainty, a value of 3 spans i s suggested ~ 'Rae, W i l l i a m H., Jr.: An Experimental Investigation of t h e M a x i m u m Size Rotor That Can be Tested i n a Rectangular Wind Tunnel.
G r a n t NO. IX-ARO(D)-31-124-&81 (U.S. Anqy R e s . Office, Durham, N . C . ) , Jan. 5, 1966.
as an adequately accurate number t o use i n deciding t h e speed above which f u l l confidence i n t h e d a t a is j u s t i f i e d . I n considering t h e span of t h e model, it should be adequate t o consider only t h e span of t h e v e r t i c a l - l i f t elements of t h e configuration.
It might be noted t h a t t h e r e could be two ways of locating t h i s l i m i t . I n t h e present paper, t h e wake v o r t i c i t y i s assumed t o be responsible f o r t h e c i r - culatory flow around t h e wind-tunnel w a l l s . An a l t e r n a t i v e viewpoint i s t h a t t h e c i r c u l a t o r y flow i s a r e s u l t merely of the w a k e mass flow dividing at t h e tunnel f l o o r . If so, t h e proper skew angle t o use f o r t h e l i m i t would be t h e o r i g i n a l o r momentum-value skew angle, and t h e corresponding l i m i t would be an i n t e r s e c t i o n of wake and f l o o r j u s t 1 1 spans behind t h e model. A t t h e present time, i n s u f f i c i e n t experimental evidence e x i s t s and therefore a choice between t h e two concepts i s d i f f i c u l t .
Size of Models The real l i m i t a t i o n on t h e ailowable size of a model is not r e a l l y t h e w i l l be engendered by t e s t i n g a given absolute s i z e of t h e correction which s i z e model i n a given wind tunnel.
Instead, t h e l i m i t a t i o n s on model s i z e a r e defined l a r g e l y by t h e v a r i a t i o n of t h e wall-induced interference over t h e extent of t h e model. As pointed out previously, t h i s v a r i a t i o n can be con- sidered i n terms of e f f e c t i v e aerodynamic d i s t o r t i o n (such as t w i s t and camber) of t h e model. "he maximum s i z e model t h a t can be used, therefore, i s deter- mined by t h e extent t o which t h e e f f e c t of such d i s t o r t i o n s can be determined.
For simple i s o l a t e d wings, as well as f o r isolated r o t o r s and propellers, such e f f e c t s can be determined with reasonable accuracy, and r e l a t i v e l y l a r g e models may be accepted. For more exotic means of producing l i f t , as well as f o r many i n t e r a c t i n g combinations of simple elements, t h e prediction of t h e e f f e c t of these interference d i s t o r t i o n s is doubtful a t best. I n such cases, it may be necessary t o l i m i t t h e s i z e of VTOL models t o one-quarter t o one-third of t h e wind-tunnel width i f accurate, r e l i a b l e r e s u l t s a r e desired.
On t h e other hand, scale e f f e c t s and the physical s i z e l i m i t a t i o n s i n pro- viding s m a l l powered models may override considerations of w a l l e f f e c t s . Thus t h e eventual s i z i n g of a p a r t i c u l a r model w i l l be t h e result of many engineering compromises and t h e o v e r a l l accuracy of predication of f u l l - s c a l e f l i g h t char- a c t e r i s t i c s w i l l be determined by t h e Segree t o which such compromises are optimized.
Application t o Langley Data The close c o r r e l a t i o n of data from d i f f e r e n t wind tunnels, both i n t h i s paper and i n references 8 t o lO,-as a result of applying t h e corrections of reference 2 i s q u i t e encouraging. A s a result, t h e decision has been made t o incorporate these corrections i n t o a l l new VTOL data from t h e Langley 300-MPH 7- by 10-foot tunnel at t h e earliest possible date.
Wind-Tunnel Configurations f o r Small Wall Effects A s indicated i n t h e foregoing sections of t h i s paper, w a l l e f f e c t s can be large and troublesome i n a closed wind tunnel; however, a large degree of r e l i e f can be obtained by t h e use of wind tunnels with mixed boundaries. A n example, suggested by Ray H. Wright of t h e Langley Research Center, i s shown i n figure 14. In t h i s example, t h e wind tunnel i s 1.5 t i m e s as deep as it i s w i d e , has an T e n lower boundary, a closed upper boundary, and s l o t t e d sidewalls.
The c l a s s i c a l correction f a c t o r (eq. (1)) f o r a vanishingly small model i n
t h i s wind tunnel has been calculated and i s a l s o presented i n f i g u r e 14 as a
function of t h e percentage of t h e sidewalls t h a t is opened by t h e s l o t s . The correction f a c t o r is observed t o f a l l very rapidly f o r very s m a l l s l o t openings.
The curve then becomes less s e n s i t i v e t o s l o t opening, and t h e correction fac- t o r becomes zero with a 5-percent s l o t opening.
This calculation was made f o r a wake which passes d i r e c t l y rearward with- out deflection. I n order t o determine t h e e f f e c t o f deflecting t h e wake, t h e small (2.70' x 1.88') wind tunnel w a s b u i l t . Extensive t e s t s have been con- ducted on t h e j e t - f l a p model previously described. A sample of t h e r e s u l t s i s A t a momentum c o e f f i c i e n t of 3.0, t h e w a l l e f f e c t s on t h e shown i n f i g u r e 15.
model l i f t are e s s e n t i a l l y negligible ( f i g . l3(a)). However, w a l l e f f e c t s at t h e t a i l a r e not zero ( f i g . l ? ( b ) ) . Despite t h e l a r g e s c a t t e r , t h e r e seems t o be some, but c e r t a i n l y not t o t a l , r e l i e f from w a l l e f f e c t s a t t h e t a i l .
A t t h e highest momentum c o e f f i c i e n t (Cp = 10.0), t h e boundary e f f e c t s on t h e tail a r e far more severe ( f i g . 16). Figure 16 shows t h a t t h e wind tunnel with mixed boundaries leads t o measurements l e s s accurate than eTren those f r o m t h e small closed wind tunnel. This e f f e c t i s believed t o be due t o t h e gross disruption of t h e tunnel flow r e s u l t i n g from t h e l a r g e s p i l l a g e of air from the lower open boundary of t h e tunnel.
Despite t h e f a c t t h a t a zero-correction wind tunnel f o r VTOL t e s t i n g has not been achieved as yet, t h e results obtained t o date a r e s u f f i c i e n t l y encour- aging so t h a t work on s e v e r a l s l o t t e d wind tunnels i s continuing. This work i s being expanded t o include several other low-correction wind tunnels such as t h e closed-on-bottom-only configurations.
CONCLUSIONS T h i s study of t h e application of jet-boundary corrections t o VTOL wind- tunnel data indicates t h e following conclusions : 1. The skew angle used i n applying t h e corrections of NASA TR R-124 t o VTOL data should be such that t h e angular deflection of t h e wake v o r t i c i t y from t h e horizontal is e s s e n t i a l l y one-half of t h e wake deflection obtained from momentum theory at t h e l i f t i n g element.
2. When t h e e f f e c t i v e skew angle is used, t h e corrections of NASA TR R-124 provide g r e a t l y lmproved agreement between t h e data obtained i n d i f - f e r e n t wind tunnels, not only f o r l i f t , but also f o r pitching moment and t a i l normal force.
3 . For accurate corrections, it i s necessary t o include t h e e f f e c t s of at l e a s t when the model span i s on t h e order of one-half f i n i t e model span, t h e wind-tunnel width.
4. There appears t o be a lower l i m i t t o the test speed at which r e l i a b l e and correctable r e s u l t s can be obtained from closed wind tunnels. I n view of present u n c e r t a i n t i e s , it i s suggested t h a t t h i s l i m i t be taken a s an i n t e r - section of e f f e c t i v e wake and f l o o r t h a t is three times t h e span of t h e v e r t i c a l - l i f t system behind t h e wake origin.
5 . Considerable a l l e v i a t i o n of boundary e f f e c t s may be obtained by t h e use of wind tunnels employing mixed boundaries.
REFEmCES 1. Theodorsen, Theodore: The Theory of Wind-Tunnel Wall Interference. NACA Rept. 410, 1931.
2. Heyson, Harry H.: Linearized Theory of Wind-Tunnel Jet-Boundary Correc- tions and Ground Effect f o r VTOL-STOL Aircraft. NASA TR R-124, 1962.
3. Heyson, Harry H.: Wind-Tunnel Wall Interference and Ground Effect f o r
VTOL-STOL A i r c r a f t . J. Am. Helicopter SOC., vol. 6, no. 1, Jan. 1961,
PP* 1-9-
4. Heyson, Harry H.: Tables of Interference Factors f o r Use i n Wind-Tunnel
and Ground-Effect Calculations f o r VTOL-STOL A i r c r a f t . P a r t I - Wind
Tunnels Having Width-Height Ratio of 2.0.
NASA TN D-933, 1962.
5 . Heyson, Harry H.: Tables of Interference Factors f o r U s e i n Wind-Tunnel
and Ground-Effect Calculations f o r VTOL-STOL A i r c r a f t . Part I1 - Wind
Tunnels Having Width-Height Ratio of 1.5.
NASA TN D-934, 1962.
6. Heyson, Harry H.: Tables o f Interference Factors f o r Use i n Wind-Tunnel
and Ground-Effect Calculations f o r VTOL-SML A i r c r a f t . Part I11 - Wind
Tunnels Having Width-Height Ratio of 1.0. NASA TN D-935, 1962.
7. Heyson, Harry H.: Tables of Interference Factors f o r Use i n Wind-Tunnel
and Ground-Effect Calculations f o r VTOL-STOL A i r c r a f t . Part IV - Wind
Tunnels Having Width-Height Ratio of 0.5.
N A S A TN 0-936,1962.
8. Grunwald, K a h n J.: Experimental Study of Wind-Tunnel Wall E f f e c t s and Wall Corrections f o r a General-Research V/STOL Tilt-Wing Model With Flap.
N A S A TN D-2887, 1965.
9. Davenport, Edwin E.; and Kuhn, Richard E.: Wind-Tunnel-Wall E f f e c t s and Scale Effects on a VTOL Configuration With A Fan Mounted i n t h e Fuselage.
N A S A TN D-2560, 1965.
10. Lee, J e r r y Louis: An Experimental Investigation of t h e U s e of T e s t Section I n s e r t s as a Device To Verify Theoretical Wall Corrections f o r a L i f t i n g Rotor Centered i n a Closed Rectangular T e s t Section. M. S. Thesis, Univ.
of Washington, Aug. 20, 1964.
11. Staff of Powered-Lift Aerodynamics Section, NASA Langley Res. Center: Wall Effects and Scale Effects i n V/STOL Model Testing.
AulA Aerodynamic Testing Conf., Mar. 1964, pp. 8-16.
12. Heyson, Harry H.; and Katzoff, S.: Induced Velocities Near a L i f t i n g Rotor
With Nonuniform Disk Loading. NACA Rept. 1319, 1957. (Supersedes NACA
T N 3690 by Heyson and Katzoff and TN 3691 by Heyson.)
Theoretical Investigation of Wind Tunnel 13. Joppa, R. G.: Experimental and Pertinent to V/STOL Vehicles Testing.
Geometry, Emphasizing Factors Progr. Rept. No. 2 (NASA Grant NGR-48-002-010), Univ. of Washington, Jan. 15, 1966.
14. Cone, Clarence D., Jr. : A Theoretical Investigation of Vortex-Sheet Defor- NASA mation Behind a Highly Loaded Wing and Its Effect on L i f t .
m D-657, 1961.
Nomographic Solution of t h e Momentum Equation f o r VML- 15. Heyson, Harry H.: (See a l s o 'T-STOL Momentum Equa- STOL A i r c r a f t . NASA TN D-814, 1961.
t i o n , " Space/Aeron., vol. 38, no. 2, July 1962, pp. B-18 - B-20.)
Figure 1.- Notation and positive direction of interference velocities and skew angle used i n correction theory of NASA TR R-124.
s 1 I I 0 30 60 90 WAKE SKEW ANGLE, X , DEG = 1.5.
Figure 2.- Typical behavior of correction factors as a function of wake skew angle. Closed tunnel: E 1 . 2 . 8 .4 0 .4 . e 1 . 2 l - LATERAL DISTANCE, RADII Figure 3.- Vor .ticity distribution measured at x = 0.07R = 750.
behind the t r a i l i n g edge of a l i f t i n g rotor. x
4 3" I-
Figure 4.- Jet-flap model.
I2r I O - Cp.5.0 '%IO' WIND TUNNEL 0 - CL 6 - 4- Cp'1.5
2t
s: - 1 ; -5 A ; Ib I& i o 25 3 ' 0
a , DEG (a) Lift coefficient CL.
-.05 CN.+ I 7'x IO' WIND TUNNEL o\.
I I I I -.I5 -15 -10 -5 0 5 IO 1 5 20 25 a, DEG (b) Tail-normal-force coefficient CN,t. C , , = 5.0; tail incidence, 21.60.
Figure 5 . - Comparative data for jet-flap model tested in two different closed w i n d tunnels. Solid symbols denote values corrected bY u s i n g Xeff; correction factors include effect of f i n i t e span of both wing and tail.
181- I r2.70'x1.88' WIND TUNNEL
I O L I
s: - 1 ; -4 b 5 Ib 1 ; 2'0 25 3b
a , DEG (a) Lift coefficient CL, 7'x IO' W I N D 0 .
-.05 1 TUNNEL
0 .
I
0 .
(b) Tail-normal-force coefficient CN,t. Tail incidence, 29O.
Figure 6.- Comparative data f o r jet-flap model at C , = 10.0 tested in two different closed w i n d tunnels. Solid symbols denote values corrected by u s i n g Xeff; correction factors include effect of f i n i t e span of both w i n g a n d tail.
l 2 r
.... CP= 5.0
IO' WIND TUNNEL CL CP= 1.5 -15 -10 - 5 0 5 IO 1 5 20 25 a , DEG (a) Lift coefficient CL.
@@ 2.70'x1.88' p m o @ 7 ' , . .
- . I O WIND TUNNEL
c N ' + I
O 1
7'XIO' WIND TUNNEL I I I I I I I (b) Tail-normal-force coefficient cN,t. C , , = 5.0: tail incidence, 21.6O.
Figure 7.- Comparative data for the jet-flap model tested in two different closed w i n d tunnels. Solid symbols denote values corrected by u s i n g Xeff; correction factors for a zero-span model.
1 r2.70'x1.88' WIND TUNNEL
IO L
I
-15 -10 -5 0 5 IO 1 5 20 25 30 a , DEG (a) Lift coefficient CL.
.lor
I r2.70'x 1.88' WIND TUNNEL
71x10' WIND TUNNEL
I
I I I (b) Tail-normal-force coefficient CN,t. Tail incidence, 290.
Figure 8 . - Comparative data for t h e jet-flap model at C , , = 10.0 in two different closed w i n d tunnels. Solid symbols denote values corrected by u s i n g Xeff; correction factors for a zero-span model.
Figure 9.- Sketch of fan-in-wing model.
3 0 A v 0 - 7'XlO: U N C O R R E C T E D MY
=&z
7 ' x IO', C O R R E C T E D
- . I I
<
I I I I I - I _ _ I 1
-. 2 -10 - 5 0 5 1 0 1 5 20 25 a , D E G Figure 10.- Comparison of pitching-moment data obtained in two w i n d t u n n e l s w i t h f a n - i n - w i n g model. Corrections have been applied by using method of N A S A TR R-124 w i t h the original skew angle. -!- = 0.48; exit-louver angle, Oo.
"1,s 30x60' FREE AIR MY - T,E - -I
-.21 I I I I I I I
IO 1 5 20 25 -10 - 5 0 5 a, DEG Figure 1.- Comparison of pitching-moment data obtained in two w i n d tunnels with f a n - i n - w i n g model. Corrections have been applied by using method of NASA TR R-124 with effective skew angle. -!!- = 0.48; exit-louver angle, 00.
V j s
x = 0"
sw, L
, " x = 45"
'< ' / 4 /
Figure 12.- Variation of vertical interference due to l i f t (&,$ along the longitudinal axis of fan-in-wing model.
43 1 Figure 13.- Sketch of flow behind model in a closed w i n d tunnel, a n d l i m i t found in tests of jet-flap model.
I "0 2 4 6 8 SLOTTED WALL OPEN1 N G , '10 Figure 14.- Calculated classical correction factors for a w i n d t u n n e l w i t h mixed boundaries. Model i s assumed to be vanishingly small.
43 2
7-- - L7'x10' WIND TUNNEL
CL -15 -10 - 5 0 5 IO 1 5 20 a, DEG (a) Lift coefficient CL.
I 7'XIO' WIND T U N N E L 7 CN, + -.05
-.IO1 I I 1 I I I J
-15 -10 -5 0 5 IO 1 5 20 a , DEG (b) Tail-normal-force coefficient CN,t.
Figure 15.- Comparison of data obtained in three wind t u n n e l s for jet-flap model a t C , , = 3.0.
WIND TUNNEL r2.70' X I . 88' SLOTTED I , nu- v 0 1
I n v g -
Tq Y 7 ' X l O ' CLOSED
'N, t
I
B
- .05/
t I 2.70'~ 1.88' CLOSED
' g
-.IO d
-15 -10 -5 0 5 IO 1 5 20 a, DEG Figure 16.- Comparative data on tail-normal-force coefficient f o r jet-flap model a t C , , = 10.0 in three different w i n d tunnels.
43 4 .