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Effects of porous tunnel walls on high lift airfoil testing Lim, A. K. 1970

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EFFECTS" OF POROUS TUNNEL WALLS ON HIGH LIFT AIRFOIL TESTING. by A 0 K0 Lim B 0 S c o , National Taiwan University 3 1967 A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of M0A0 S c o in the Department of Mechanical Engineering We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA February, 1970 In presenting this: thesis in partial fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t freely available for reference and study Q I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of ray Department or by hiff representatives^ It i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permissiono A 0 K0 Lim Department of Mechanical Engineering The University of British Columbia Vancouver 8 S B c Co i ABSTRACT When a model i s tested in a wind tunnel of either open or closed boundaries, the flow f i e l d around the model i s modified, so that the results of a wind tunnel test do not exactly correspond to f l i g h t results. In order to obtain reliable wind tunnel data, wall corrections must be known accurately or eliminated• One approach to the elimination of wall corrections i s the use of porous walls*, In this study, l i f t , drag and pitching moment about mid-chord were measured for two sets of two-dimensional Clark Y a i r f o i l s , one set having no flap,, the other set having a 30$ chord double slotted flap set at \5° * Each set consisted of four geometrically similar profiles with 9 inch, 1** inch, 19 inch and 2h inch chords e In order to simulate two-dimensional flow, a l l a i r f o i l s were mounted ver t i c a l l y in the wind tunnel test section spanning the 27. inch heighto The Reynolds number in a l l cases was maintained at 300,000o The a i r f o i l s were tested over a f u l l range of angle of attack i n the presence of different configurations of porous tunnel side wallso Longitudinally slotted side walls of open area ratios ranging from 5°5% to>2906$, transversely slotted side walls of open area ratios ranging from 9o3$ to 23*1$ and perforated side walls of open area ratios ranging from 1203% to lQ0h% were testedo Slot configurations were sought for which the C L versus 4§C data below ^i^^ was most nearly independent of model l i sizeo For t e s t i n g the a i r f o i l s with 3 ° % chord double s l o t t e d f l a p at ^ 5 ° 9 1 8 o % l o n g i t u d i n a l l y slotted side walls proved to be the best configuration while for t e s t i n g the basic a i r f o i l , llolfo l o n g i t u d i n a l l y slotted side walls proved the most satisfactory., The l i f t curve collapsed quite well at these two open areas f o r the two sets of a i r f o i l s , but the l i f t curve slope was about 15% lower than the expected value i n each case* This anomaly remains unresolved.. Although the open area r a t i o s found to be best i n the present tests are not necessarily optimum values f o r a l l tunnels, they should provide useful guidelines f o r future tests with porous wall configurations 0 i i i TABLE OF CONTENTS Page Io INTRODUCTION 1 I I . INSTRUMENTATION AND APPARATUS 5 2 d Wind Tunnel 5 202 Wind Tunnel Balance 6 2 0 3 Models 7 2oh Wall Configurations 10 2c5 Model Mounting System lh I I I . EXPERIMENTAL PROCEDURES 15 IV. EXPERIMENTAL RESULTS 18 V. DISCUSSION 28 5.1 Longitudinally Slotted Side Walls 28 a c L i f t C o e f f i c i e n t 28 bo Moment Coe f f i c i e n t At Quarter Chord 31 Co Drag C o e f f i c i e n t 32 5.2 Transversely Slotted Side Walls 33 a 0 L i f t C o e f f i c i e n t 33 bo Moment C o e f f i c i e n t At Quarter Chord 3k Co Drag Co e f f i c i e n t 3*+ 5*3 Perforated Side Walls 3*+ a a L i f t C o e f f i c i e n t 3k bo Moment C o e f f i c i e n t At Quarter Chord 35 Co Drag C o e f f i c i e n t 35 5»k Comparisons and General Comments 35 V I . CONCLUSIONS 39 BIBLIOGRAPHY kl APPENDICES k2& i v LIST OF TABLES Table Page l o T y p i c a l Longitudinal Slot Arrangements ^3 V LIST OF FIGURES Figure Page l o Wind tunnel outline ¥+ 20 Wind tunnel balance *+5 3o P r o f i l e of Clark Y a i r f o i l with double h6 s l o t t e d f l a p *+<> P r o f i l e of basic Clark Y a i r f o i l h-7 5o Test section side wall panel frame ^ 8 6 0 A t y p i c a l l o n g i t u d i n a l s l o t arrangement *+9 7o A t y p i c a l transverse s l o t arrangement *+9 ( foreground ) 8 0 A t y p i c a l perforated side wall 50 9o Mounting bracket 51 10o 2*+ inch model i n test section 52 11o Characteristics for 19 inch model tested 53 at two d i f f e r e n t Reynolds numbers» Wall configuration H 12c C h a r a c t e r i s t i c s f o r 19 inch model tested 5^  at two d i f f e r e n t Reynolds numbers0 Wall configuration A 13o Pressure d i s t r i b u t i o n s for Joukowsky 55 a i r f o i l , N R = 3 x 10? lh0 Uncorrected C L vs <@C for a i r f o i l with double 56 s l o t t e d f l a p 0 S o l i d walls l5o Uncorrected G M c / i f vs ®< f o r a i r f o i l with 57 double slotted f l a p . S o l i d walls v i Figure Page l 6 o Uncorrected C D vs ®€ for a i r f o i l with 5 8 double sl o t t e d flap*, S o l i d walls 17o Corrected C_ vs ©< for a i r f o i l 5 9 L with double slott e d f l a p 0 S o l i d walls 1 8 0 Corrected C^/i,. vs ©< for a i r f o i l with 60 double s l o t t e d f l a p e S o l i d walls 19o Uncorrected C^ vs &£ for basic a i r f o i l 0 6 1 S o l i d walls 20 o Uncorrected vs o< f o r basic a i r f o i l „ 62 So l i d walls 21o Uncorrected C D vs o< for basic a i r f o i l 0 6 3 Solid walls 22.0 Corrected C L vs ©< for basic a i r f o i l 0 (h Solid walls 2 3 o Corrected C^/^. vs f o r basic a i r f o i l 0 6 5 S o l i d walls 2ha Corrected C D vs &C f o r basic a i r f o i l 0 6 6 Solid walls 2 5 o C L vs o< f o r a i r f o i l with double slotted 6 7 f l a p 0 Wall configuration H, 1 1 0 1 # open area 2 6 0 C L vs ©< for a i r f o i l with double s l o t t e d 6 8 f l a p o Wall configuration G, 1 ^ 0 8 $ open area v i i F i g u r e Page 27o C L vs ©3 f o r a i r f o i l w i t h double s l o t t e d 69 f l a p 0 W a l l c o n f i g u r a t i o n X", l8Q5% open a r e a 280 C L vs o*> f o r a i r f o i l w i t h double s l o t t e d 70 fla p o W a l l c o n f i g u r a t i o n E, l805% open a r e a 29o C L vs o< f o r a i r f o i l w i t h double s l o t t e d 71 f l a p o Wall c o n f i g u r a t i o n D, 200k% open area 30o G L vs @* f o r a i r f o i l w i t h double s l o t t e d 72 f l a p 0 Wall c o n f i g u r a t i o n J , 2202% open a r e a 31o C L vs &< f o r a i r f o i l w ith double s l o t t e d 73 fl a p o Wall c o n f i g u r a t i o n B 5 25o9$ open area 32o C L vs f o r a i r f o i l w i t h double s l o t t e d 7k f l a p * Wall c o n f i g u r a t i o n A, 29o6% open area 33o VS « K f o r a i r f o i l w i t h double s l o t t e d 75 f l a p . Wall c o n f i g u r a t i o n H, 11 al% open area 3^ o C^/^. vs o< f o r a i r f o i l with double s l o t t e d 76 f l a p 0 W a l l c o n f i g u r a t i o n G, lkaQ% open a r e a 35o C M c / ^ vs o< f o r a i r f o i l w i t h double s l o t t e d 77 f l a p 0 ~ Wall c o n f i g u r a t i o n I , 18<>5$ open a r e a 360 C ^ / i ^ vs ®Z f o r a i r f o i l w i t h double s l o t t e d 78 f l a p o Wall c o n f i g u r a t i o n B s 25*9% open area 37o C ^ / ^ vs ©< f o r a i r f o i l with double s l o t t e d 79 f l a p 0 Wall c o n f i g u r a t i o n A, 2906$ open a r e a v i i i Figure Page 3 8 0 C D vs oi f o r a i r f o i l with double slot t e d 8 0 f l a p o Wall configuration H, 1101% open area 3 9o C D vs ok f o r a i r f o i l with double s l o t t e d 8 l f l a p o Wall configuration G, lh08fo open area ^ 0 o C D vs o( f o r a i r f o i l with double slotted 82 f l a p o Wall configuration I, l 8 < , 5 $ open area ^1 0 C D vs o< f o r a i r f o i l with double s l o t t e d 8 3 f l a p o Wall configuration B 5 25o9% open area *f2„ C D vs o< for a i r f o i l with double s l o t t e d 8*+ f l a p o Wall configuration A, 29 06% open area * f 3 o C L vs o< for basic a i r f o i l ? Wall con- 8 5 f i g u r a t i o n F, 5<>5% open area hh0 C L vs o< for basic a i r f o i l 0 Wall con- 8 6 f i g u r a t i o n H, 11<,1# open area ^ 5 o C L vs o< f o r basic airfoil» Wall con- 8 7 f i g u r a t i o n I, l8o5% open area h60 C L vs cA f o r basic a i r f o i l 0 Wall con- 8 8 f i g u r a t i o n E, 18<,5$ open area ^ 7 o C M c/i4. vs cK for basic a i r f o i l 0 Wall con- 8 9 f i g u r a t i o n F s 5 o 5 $ open area ^ 8 0 C^/^ vs « 5 < for basic a i r f o i l 0 Wall con- 9 0 f i g u r a t i o n H, 1101# open area h90 C^Q/I^ VS <S< for basic a i r f o i l 0 Wall con- 91 fi g u r a t i o n I, 18« 5 $ open area Ix Figure Page 50o C D VS O< f o r basic a i r f o i l o Wall con= 92 f i g u r a t i o n F, 5»5% open area 51o C D vs ©< fo r basic a i r f o i l o Wall con= 93 fi g u r a t i o n H, 1101% open area 52o C D vs cK f o r basic a i r f o i l o Wall con- 9h f i g u r a t i o n I, 1805$ open area 53o C L vs cK fo r a i r f o i l with double slotted 95 f l a p 0 Wall configuration T, 1805$ open area 9+o C L vs G< f o r a i r f o i l with double s l o t t e d 96 f l a p 0 Wall configuration TJ, 23al% open area 55o C M C / L + vs o< for a i r f o i l with double s l o t t e d 97 flapo Wall configuration T, l8 05$ open area 56o CMQ/\+ vs o< for a i r f o i l with double slotted 98 flapo Wall configuration U, 23d% open area 57o C D vs c* for a i r f o i l with double slotted 99 f l a p 0 Wall configuration T, 1805% open area 580 C D vs &< f o r a i r f o i l with double slotted 100 flapo Wall configuration U f l23 0l$ open area 59 o C L vs <?< for a i r f o i l with double slot t e d 101 f l a p 0 1^" holes perforated walls, 1203% open area 60 o C L vs &i for a i r f o i l with double slotted 102 flapo 1" holes perforated walls, lh05% open area gure Page 61 o C^/i^. vs &< for a i r f o i l with double slot t e d 103 f l a p 0 l i " holes perforated walls, 1203% open area 62o Cy[C/i+ vs «?< f o r a i r f o i l with double slotted ICh f l a p 0 1" holes perforated walls, \hQ5% open area 6 3o C D vs o< f o r a i r f o i l with double s l o t t e d 105 f l a p o l i " holes perforated walls, 1203% open area 0+o C D vs «s< f o r a i r f o i l with double s l o t t e d 106 f l a p 0 1" holes perforated walls, 1^0 5$ open area 65o dC L/dfi* vs C/H for a i r f o i l with double 10? slotte d f l a p o Longitudinally s l o t t e d side walls 660 dC L/d«< vs % open area f o r a i r f o i l with 108 double slotted f l a p c Longitudinally slo t t e d side walls 67o C L m a x vs % open area f o r a i r f o i l with 109 double slotted f l a p e Longitudinally slotted side walls 680 C M c / i , . vs % open area for a i r f o i l with 110 double s l o t t e d f l a p Q Longitudinally s l o t t e d side walls x i F i g u r e Page 69o S h i f t i n C L f o r a i r f o i l w i t h double s l o t t e d 111 f l a p due to l o n g i t u d i n a l s l o t s 70o d C ^ / d ^ vs C/H f o r b a s i c a i r f o i l o Longi= 112 t u d i n a l l y s l o t t e d s i d e w a l l s 71 o E f f e c t s o f l o n g i t u d i n a l s l o t s on C ^ / ^ and 113 cLraax f o r b a s i c a i r f o i l 72 o S h i f t i n C L f o r b a s i c a i r f o i l due to l o n g i t u d i n a l s l o t s 73o d C ^ / d ^ vs C/H f o r a i r f o i l with double 115 s l o t t e d f l a p 0 T r a n s v e r s e l y s l o t t e d s i d e w a l l s 7^ o d C L / d ^ vs % open area f o r a i r f o i l w i t h 116 double s l o t t e d f l a p Q T r a n s v e r s e l y s l o t t e d s i d e w a l l s 75o C L m a x vs % open area f o r a i r f o i l with 117 double s l o t t e d f l a p 0 T r a n s v e r s e l y s l o t t e d s i d e w a l l s 76o Cjjp/i,. vs % open area f o r a i r f o i l w i t h 118 double s l o t t e d f l a p e T r a n s v e r s e l y s l o t t e d s i d e w a l l s 77o S h i f t i n C L f o r a i r f o i l w i t h double s l o t t e d 119 f l a p due to t r a n s v e r s e s l o t s 780 dC^/deC vs C/H f o r a i r f o i l w i t h double 120 s l o t t e d f l a p o P e r f o r a t e d w a l l s x i i Figure Page 79o C L m a x vs C/H for a i r f o i l with double 121 slo t t e d f l a p 0 Perforated walls 80o C M c/^ vs % open area f o r a i r f o i l with 122 double slotted f l a p e Perforated walls x i i i ACKNOWLEDGEMENT The author wishes to express his gratitude and appreciation to Dr e Go V Q Parkinson for the invaluable advice and guidance throughout the research programme and during the preparation of the thesiso Thanks are also due to the Department of Mechanical Engineering for the use of th e i r f a c i l i t i e s , and to the s t a f f of the woodworking shop of the University of B r i t i s h Columbia fo r the construction of wind tunnel panels 0 F i n a n c i a l support was received from the Defence Research Board under grant 66=9513o 1 I o INTRODUCTION The wind tunnel, despite i t s l i m i t a t i o n s , remains as the single most useful t o o l i n the design of an aircraft» However, the r e s u l t s of a wind-tunnel t e s t do not exactly correspond to f l i g h t r e s u l t s a The lack of complete equivalence i s caused by a number of effects i n the wind tunnel which are not present i n free air<> These e f f e c t s include static° pressure gradients:, Reynolds number e f f e c t s , mounting system tares and interference, s o l i d blockage, l i f t interference and wake blockageo Because of scale e f f e c t s i n low speed wind tunnel t e s t i n g , models are usually tested preferably at the highest Reynolds number possibleo Thus i t i s necessary to use models whose dimensions are as large as possible r e l a t i v e to the cross-sectional dimensions of the tunnel test s e c t i o n 0 The large size: of the model w i l l increase the magnitude of the tunnel wall i n t e r f e r e n c e 0 The r e s u l t s obtained i n the tunnel must therefore, be corrected accurately for the e f f e c t s of wall interference i f they are to be applied with confidence to the prediction of f r e e - f l i g h t c h a r a c t e r i s t i c s 0 The foundation of research on tunnel-wall interference i s a t tributed to Prandtl because his l i f t i n g l i n e theory led to many experimental investigations with the object of v e r i f y i n g the theoryo The method of analysis f o r closed and open tunnels was established by Prandtl, who developed the concept of t r a i l i n g v o r t i c e s 0 In 1933 G l a u e r t ^ ) had given a comprehensive account of the early developments i n 2 wall corrections^ In 19*+2 Goldstein^ 2) derived a theory for a two-dimensional cambered a i r f o i l of f i n i t e thickness which accounted f o r terms of order (C/H^o A l l e n and Vincenti (3) gave t h e o r e t i c a l wall corrections f o r a two-dimensional a i r f o i l of f i n i t e thickness and camber0 In t h e i r theory they took account of the wake effects and the compressibility of the f l u i d 0 In the past 50 years investigators have been active i n developing methods of correcting wind-tunnel data, and the use of such corrections generally leads to data very similar to that obtained i n free a i r 0 Most of the corrections have been based i m p l i c i t l y upon the concept of a l i g h t l y loaded model5 that i s , the force c o e f f i c i e n t s are assumed to be small and the model chord i s assumed smallo Thus perturbation v e l o c i t y i s small r e l a t i v e to the undisturbed stream v e l o c i t y 0 Two summaries of works about wall corrections, one by Rogers^) and the other by GarnerC5), give a l o t of references on wall corrections* The advent of the V/STOL a i r c r a f t has brought i n a d d i t i o n a l interference e f f e c t s a The large downwash f i e l d s of ST0L/VT0L l i f t systems d i s t o r t the main wind tunnel stream from Its uniform a x i a l course to a very great extent and cause very large wall corrections i n conventional wind tunnels, thus v i o l a t i n g the assumption of small force c o e f f i -cients o In the past decade researchers such as Heyson^°) have developed theories for VT0L/ST0L modelso However, the v a l i d i t y of these theories i s doubtful, because of the 3 assumptions on chord size and s t r a i g h t - l i n e wakes which do not exist i n p r a c t i c e Q Kirkpatrick^?) included wake curvature i n his analysis but he took too few images so h i s numerical r e s u l t s were i n e r r o r 0 As there are so many r e s t r i c t i o n s on the use of theory, there i s s t i l l a need for experimental data giving wall effects d i r e c t l y o Experimentally, there are two ways of eliminating wall effects? (1), t e s t i n g small models i n large test sections! (2), t e s t i n g i n a section with mixed s o l i d and open bound-aries which simulates a free a i r environment 0 The f i r s t method may lead to extremes, either t e s t i n g a very small model, with accompanying Reynolds number problems, or large and therefore expensive test f a c i l i t i e s o The second method i s based on a well known resu l t of c l a s s i c a l wall interference theory, that most important effects are t h e o r e t i c a l l y of opposite sign for closed and for open working sectionso In t e s t i n g a set of s i m i l a r a i r f o i l s of d i f f e r e n t chord i n the presence of s o l i d walls at the same Reynolds number, the bigger a i r f o i l w i l l give a higher l i f t c o e f f i c i e n t for the same angle of attack, while just the opposite occurs f o r an open boundary 0 In free a i r the values of l i f t c o e f f i -cient given by d i f f e r e n t sizes f o r the same angle of attack are the same0 The method became more popular a f t e r Theodorsen(8) proved that i t i s possible to eliminate wall e f f e c t s by testing models i n the presence of mixed boundarieso In North America, several groups of aerodynamicists have participated i n the use of mixed boundaries i n wind tunnel t e s t i n g , such as NASA, the Boeing Company and the Canadian National Aeronautical Establishment(NAE) 0 Th© Boeing Company has developed a test section geometry for a 20 8 ix 20 9 V/STOL wind tunnel„ The configuration has four equally spaced f u l l length 6" wide s l o t s along the f l o o r , c e i l i n g and walls with a d d i t i o n a l 1 foot gaps at top and bottom of each wall sectiono I n i t i a l r e s u l t s seemed to be unacceptable because of poor aerodynamic c h a r a c t e r i s t i c s and poor data r e p e a t a b i l i t y 0 At the N A E(9), they have tested a twin-prop t i l t wing a i r c r a f t i n the I5~ft diameter v e r t i c a l wind tunnel with various porous walls on the 7' x 7" test s e c t i o n 0 The results showed that wall porosity greater than 10% over the f u l l length gave the smallest induced e f f e c t s o The general objective of the present experimental work i s to determine wind tunnel wall corrections relevant to the high l i f t wings of ST0L/VT0L a i r c r a f t by t e s t i n g d i f f e r e n t sizes of the same high l i f t a i r f o i l system i n the low speed wind tunnel over the same range of conditions i n the presence of d i f f e r e n t porous wall configurations 0 The further objective i s to f i n d the most promising porous wall configu-rations to eliminate wall e f f e c t s o The phase of the general program described here deals with the testing of a i r f o i l s relevant to STOL, but not VTOL, a i r c r a f t 0 5 II INSTRUMENTATION AND APPARATUS 2«1 Wind Tunnel The main instrument used i n t h i s investigation was the departmental low speed, low turbulence, single-return wind tunnelo A simple sketch of the wind tunnel's aero-dynamic layout is. shown i n Figure lo The a i r stream i s created by a f i f t e e n horse-power d i r e c t current motor d r i v i n g a commercial a x i a l flow fan whose speed i s controlled by rheostats i n a form of Ward-Leonard system 0 The flow, smoothed by three screens i n s t a l l e d i n front of the s e t t l i n g chamber, enters the t e s t section through a 7s1 contraction cone which accelerates the flow and improves i t s uniformity 0 A r i n g of s t a t i c pressure holes i s located at the beginning and at the end of the^. contraction cone as marked S on Figure lo The four holes i n each ri n g are at the mid-points of the four wallso The pressure d i f f e r e n t i a l across the contraction section of 7;1 area r a t i o i s measured on a Betz Micromanometer which can give the dynamic pressure head to 0o02 millimeter of water 0 The a i r speed i n the test section i s given d i r e c t l y from the Bet2 reading which takes care of a l l the effects except s o l i d wall c o n s t r a i n t 0 The v e l o c i t y i n the test section can be varied between h feet per second and 150 feet per second with a turbulence l e v e l of less than 0ol%o The test section i s 10*+ inches long and has a rectangular cross section 36 inches wide and 27 inches higho The cross-section i s modified by the i n s t a l l a t i o n of four *+5 degree corner fillets» 6 The si z e of the f i l l e t s decreases from 6 inches at the up-stream end to h075 inches at the downstream end of the test section to compensate for the growth of the boundary l a y e r along the wind tunnel walls<, At the end of the test section i s a breather to ensure that the test section pressure i s atmospherico 2o2 Wind Tunnel Balance L i f t , drag and pitching moment measurements fo r the a i r f o i l s were taken on a six component Aerolab Pyramidal S t r a i n Gauge Balance SystemCFigure 2)„ The balance system i s designed to support a model i n a wind tunnel, adjust i t s angle of attack over a + 30 degree range, adjust i t s angle of yaw over a 360 degree range and separate and measure the six force and moment components which determine the resultant force exerted by the a i r stream on the model 0 The angular, positions of the model i n yaw and p i t c h are indicated on Veeder Root counters to the nearest tenth of a degreeo The components are separated mechanically and measured through i n d i v i d u a l s t r a i n gauge load c e l l s 0 Readout i s accomplished through a Leeds & Northrup Amplifier which has coarse and vernier zero adjustments for each componento Component ranges are =50 to +100 lbs i n l i f t , 0 to +75 lbs i n drag, ; =50 to +50 lbs i n side force, =150 to +150 inch=lbs i n yawing moment, =250 to +250 inch=lbs i n pitching and r o l l i n g momento The ' l i v e 0 turntable on which the model i s mounted i s carried by a central spider supported on four diagonal st r u t s o A l l forces and moments are measured with respect 7 to the balance center which i s on the t e s t section center l i n e * The load c e l l s are equipped with s t r a i n gauge bridges composed of four active 1 2 0 ohm gauges 0 The bridges are energized by 6 v o l t d i r e c t current supplied by s t a b i l i z e d power supplies i n the Aerolab balance and control boxes« Power and si g n a l connections are made through six i n d i v i d u a l cables with five-pronged plugs to each load c e l l o The balance and control units not only energize the bridges but also provide means for balancing them Q The units are calibr a t e d to give outputs i n lbs or inch-lbs d i r e c t l y 0 As the balance i s designed f o r testing models mounted ho r i z o n t a l l y , whilst i n the present investigation models were mounted v e r t i c a l l y and spanned the short dimension of the test section, the l i f t force, pitching moment and angle of attack of the models were measured as side force, yawing moment and angle of yaw respectively on the balanceo The dummy turntable i n the test section f l o o r , consisting of two semi-circular plates with a T slo t through which model mountings pass, was attached to the test section f l o o r by three clamps<, F i l l e r blocks were used to cover the gap between the dummy turntable and the modelo 2o3 Models This investigation involved l i f t , drag, and pi t c h i n g moment measurement on four similar double slotted f l a p Clark Y a i r f o i l s and four similar basic Clark Y a i r f o i l s within the same range of Reynolds Number and other conditionso 8 The p r o f i l e , which had been tested by NACA a number o f years ago, was selected because of i t s r e l a t i v e s i m p l i c i t y of shape including a f l a t lower surface and a maximum thickness of lh% chord at 2,0% chord point and i t s s a t i s f a c t o r y aerodynamic c h a r a c t e r i s t i c s i n the Reynolds Number range of the tests® These two sets of a i r f o i l s were of the same four chord s i z e s , 9 i n O J I 1* In», 1 9 in«, 2k i n c and uniform spans of 2 6 7 / 8 incheso (a) Clark Y A i r f o i l With Double Slotted Flap The modified Clark Y a i r f o i l has a fixed rear s l o t and s l o t t e d t r a i l i n g edge f l a p c The a i r f o i l configuration was one tested by Fred E 0 Weick and Joseph A G Shortal i n an NACA v e r t i c a l wind tunnel at Langley F i e l d , V i r g i n i a i n 1 9 3 2 ^ 1 0 ^ o The 1 0 inch chord model was tested i n a 5-foot open j e t at a Reynolds Number of 6 0 9 , 0 0 0 based on the chorda The present a i r f o i l s were designed by two senior students Jo Hodson and A Q Ryneveld i n 1 9 6 7 ° The models were made of laminated mahogany by the woodworking shop of the Univer-s i t y of B r i t i s h Columbia 0 The whole a i r f o i l , c o n sisting of the main a i r f o i l , f l a p and middle piece between the s l o t s , was b u i l t i n three equal spanwise sections connected together by an aluminum spar 31 5/8 Inches long and of cross section 3 inches by O o 7 5 incheso The spar with center-line at 26<,7% chord, served as a mounting support f o r the a i r f o i l o Four 1/8 inch thick aluminum plate r i b s with the same p r o f i l e as the 9 a i r f o i l , except f o r the rear portion modified f o r f l a p d e f l e c t i o n settings, were located one on each end and the other two between the spanwise sections, to give additional supports The p r o f i l e of the modified a i r f o i l with the f l a p deflected at h5 degrees i s shown i n Figure 3 , including the l i p which dir e c t s the flow through the s l o t smoothly over the f l a p 0 Different f l a p deflections need d i f f e r e n t sizes of l i p 0 To increase the strength and r i g i d i t y of the model, and the spar size to support the model, p r o f i l e coordinates obtained from R i e g e l s ^ 1 1 ^ for the Clark Y a i r f o i l of 1107% thickness were modified proportionally to a maximum t h i c k -ness of lh%0 The double slotted f l a p a i r f o i l has a 30$ chord f l a p and the front and rear s l o t s varied i n s i z e from 5*2-5% to 2<>3$ chord from lower to upper surface and were located at h-5% and 62 0 5% chord r e s p e c t i v e l y 0 The f l a p was supported on a simple pinned hinge and the settings were held by a screw at both ends 0 The angle of flap d e f l e c t i o n could be set at 0 , 1 5 , 3 0 , h5 and 60 degrees„ The a i r f o i l has a leading edge, radius of 20l6% chord 0 (b) Basic A i r f o i l This set of a i r f o i l s was designed by junior student Me Lundberg i n 1 9 6 9 , and made by the woodworking shop from laminated mahogany0 The dimensions of these a i r f o i l s are the same as f o r the others without the s l o t s and f l a p 0 The structure i s very simple, the a i r f o i l i s made i n a whole 10 piece with two 1/8 inch aluminum end r i b s which have the same p r o f i l e as the a i r f o i l o The aluminum spar 31 e75 inches long and of cross section 3 inches by 0o75 inches i s located at mid-chordo Figure k shows the p r o f i l e of the a i r f o i l o 20h Wall Configurations-Two pairs of one-inch thick wooden rectangular wind tunnel side-wall panel frames (Figure 5) were made for the purpose of this investigation»> One p a i r of the frames had bolts b u i l t i n along both of the short sides and spaced appropriately i n the 15 inch useable space so that d i f f e r e n t combinations of l o n g i t u d i n a l slots could be arrangedo The other p a i r had bolts b u i l t i n a l l around the frame and spaced evenly so that l o n g i t u -dinal and transverse s l o t s and perforated walls could be arrangedo The porosity of a wall i s defined as the r a t i o of the t o t a l open area to the area of s o l i d wall which i s 27 inches by 96 incheso (a) Longitudinally Slotted Side Walls Combinations of l o n g i t u d i n a l l y slotted side walls were arranged from wood s t r i p s of 1 inch square section and 96 inch length, and other wood s t r i p s of rectangular cross section 1 inch by 105 inches and 96 inch lengtho Both ends of each s t r i p had metal f i t t i n g s so that i t could be attached to and removed from the frame without any d i f f i c u l t y o The s t r i p s a f t e r attachment to the frame were reinforced by a 3-inch wide v e r t i c a l metal plate located a f t of the mid-span 11 of the frame, so that the plate would not a f f e c t the flow over the model while holding the 9 6 inch long s t r i p s straight and i n desirable configurationo Several d i f f e r e n t l o n g i t u d i n a l configurations were tested, and a t y p i c a l arrangement of the sl o t s i s shown i n Figure 60 With the presence of the corner f i l l e t s , the possible space for arranging wall s l o t s i s 15 inches i n height and 96 inches i n length*. Some of the l o n g i t u d i n a l l y slotted side v a i l configurations are presented i n Table 1, A number was assigned to each bolt which i s at the mid-point of a one inch space numbered from the top (Figure 5 ) T h e s e configurations are combinations of 1 inch l o n g i t u d i n a l s t r i p s and gaps. In arranging a l l the porous wall configurations great care was taken i n an attempt to maintain symmetry with respect to the horizontal center l i n e of the t e s t sec-t i o n and otherwise to approach two-dimensional conditions*, Longitudinal s l o t configurations not described i n Table 1 are as follows,, Configuration C i s arranged by using seven pieces of l i inch l o n g i t u d i n a l s t r i p spaced evenly among the f i f t e e n bolts provided on the panel frames, leaving top and bottom f inch gaps and six intermediate i inch gaps 9 Configuration D i s arranged by s t a r t i n g with a 1 inch gap and a 1 inch l o n g i t u d i n a l s t r i p followed by a.| inch gap, then followed by f i v e l i inch l o n g i t u d i n a l s t r i p s with 12 four % inch gaps spaced evenly i n between, and f i n i s h i n g with the same arrangement as at the beginning i n reverse to give symmetry0 Configuration E i s arranged by using two 5 inch l o n g i -tudinal 1 inch thick boards with three 1 2/3 inch gaps 0 Configuration F i s arranged by the combination of 1 and 1-g- inch l o n g i t u d i n a l s t r i p s to give two s o l i d pieces cl-inches wide, with three inch gaps 0 (b) Transversely Slotted Side Walls In arranging transversely s l o t t e d side walls, two d i f f e r -ent sizes of 1 inch thick board were used, one h inches by 15 inches, the other 2 inches by 15 incheso Both ends of each piece have metal f i t t i n g s for attachment to the panel frameo Several d i f f e r e n t configurations of transversely slotted side walls were arranged from these M- and 2 inch blockso A t y p i c a l configuration i s shown i n Figure 7o Configuration 0 i s started with s o l i d walls for the f i r s t 2 feet downstream from the beginning of the test section,, Beyond t h i s point the configuration i s arranged a l t e r n a t e l y with 2 inch gaps and k inch s o l i d pieces, and terminated at the eighth gap with the r e s t of the t e s t section s o l i d 0 Configuration P consisted of twelve 2 inch gaps, eleven h inch s o l i d pieces, and 2 1/3 feet of the rear t e s t section s o l i d o Configuration R started with h inch gaps and h inch s o l i d pieces a l t e r n a t e l y from a point 2 feet downstream 13 o f the s t a r t o f the t e s t s e c t i o n , and the l a s t s e c t i o n o f 2 1/3 f e e t was s o l i d o C o n f i g u r a t i o n S i s almost the same as c o n f i g u r a t i o n R except t h a t a l t e r n a t e gaps and s o l i d p i e c e s covered the f i n a l 2 1/3 f o o t s e c t i o n C o n f i g u r a t i o n T i s arranged a l t e r n a t e l y with 2 i n c h gaps and h- i n c h s o l i d p i e c e s f o r the whole t e s t s e c t i o n 0 C o n f i g u r a t i o n U i s arranged with 2 i n c h gaps and *f i n c h s o l i d p i e c e s a l t e r n a t e l y up to a p o i n t 60 i n c h e s downstream and the r e s t i s arranged w i t h h i n c h gaps and h i n c h s o l i d p i e c e s a l t e r n a t e l y * . C o n f i g u r a t i o n Q i s a combination o f 2 i n c h gaps and 2 i n c h s o l i d p i e c e s a l t e r n a t e l y from a p o i n t 8 i n c h e s down-stream o f the s t a r t o f the t e s t s e c t i o n 0 (c.) P e r f o r a t e d Walls With the help o f the p r e l i m i n a r y t e s t i n g on l o n g i t u -d i n a l l y s l o t t e d s i d e w a l l s , the p e r f o r a t e d w a l l s were made with p o r o s i t y w i t h i n the most promising r a n g e 0 Two s e t s o f p e r f o r a t e d w a l l s were made, each w a l l c o n s i s t i n g o f ten i n d i v i d u a l p i e c e s a The s i z e o f the p i e c e s f o r one s e t i s 15 by 7i i n c h e s and 1 i n c h t h i c k with f o r t y - e i g h t 1 i n c h holes spaced u n i f o r m l y 0 The h o l e s i z e was modified to 1 1/8 i n c h l a t e r to o b t a i n h i g h e r p o r o s i t y o The s i z e o f the p i e c e s f o r the o t h e r set i s 15 by 8 inches and 1 i n c h t h i c k w i t h eighteen l i i n c h h o l e s spaced u n i f o r m l y o A t y p i c a l p e r f o r a t e d w a l l i s shown i n F i g u r e 80 The l i i n c h holes were l a t e r modified to i f inches 0 A l l four combinations of perforated walls were started from the beginning of the test section with the f i n a l portion downstream s o l i d 0 2o5 Model Mounting System The model was mounted v e r t i c a l l y i n the wind tunnel on the balance ' l i v e ' turntable with center at a point 3 feet from the small end of the contraction cone 0 The mount-ing support was provided by the model spar which has four 3/8 inch holes f o r the bolts: to tighten the model to the bracket which was designed to hold the model f i r m l y 0 The bracket was fastened by six a l i e n screws to i t s base<> The base with s l o t s was fastened by four screws to the " l i v e 8 balance turntable 0 It could be moved along the channel cut i n the turntable surface to a l i g n the model with the center l i n e of the wind tunnel test s e c t i o n 0 For the purpose of mounting the model at d i f f e r e n t chord points, three p a i r s of supporting brackets were made, each having appropriate v e r t i c a l s l o t t e d holes so that the height of the model could be adjustedo One pair of these brackets was for 26<>7% chord mounting, the other two pairs were for 50% chord mountingo Figure 9 shows the bracket and the model on the balance* 15 III EXPERIMENTAL PROCEDURES In order to simulate two-dimensional flow, a l l the models tested were mounted v e r t i c a l l y on the wind tunnel balance so that they spanned the 27 inch height of the t e s t section, except f o r small clearances at the c e i l i n g and f l o o r (Figure 10) 0 The wind tunnel balance was set up according to the instructions to avoid any damage or unnecessary s t r a i n on the d e l i c a t e linkages <. When se t t i n g up the model, the b a l -ance was clamped to avoid damage, and i t was undamped when taking measurements of l i f t , drag, and pitching momento A dummy turntable with three clamps to hold i t on to the wind tunnel test section f l o o r was used to permit model ro t a t i o n about a v e r t i c a l a x i s , and the open s l o t s i n i t for passing the supporting bracket were f i l l e d with spacers; as close as possible to the model to prevent flow through the f l o o r over the model 0 Any serious flow leakage might have affected the flow f i e l d around the model, that i s the re s u l t s taken might have had ad d i t i o n a l e r r o r s 0 Masking tape was used to hold the spacerso Before operating the wind tunnel the model was turned through the test range of angle of attack to check that there was no touching between model and c e i l i n g , f l o o ^ and the dummy turntableo A l l the models tested were mounted at the i r 50$ chord points which were located on the center l i n e of the wind tunnel„ The pit c h axis coincided with the v e r t i c a l l i n e 1 6 passing through the balance center Q However, a small error i n t h i s l o c a t i o n would not have affected the pitching moment appreciably because of the comparatively large chord sizes» Because of power l i m i t a t i o n , the Reynolds Number tested i n t h i s Investigation was approximately 300,000o Though i t i s quite low i t i s above the minimum Reynolds Number as recommended by Pope^ 2),, As far as scale effect i s concerned the results obtained at t h i s Reynolds Number are: comparable to the r e s u l t s obtained for a f u l l scale model which was tested at quite high Reynolds Number,, The cables which are the si g n a l and power connections between the load c e l l s and amplifier were connected to the appropriate load cellso The control unit was turned on f o r at least f i v e minutes or more to allow for the complete system to warm up c After the warm up period, a l l the com-ponents were adjusted to zero with the wind off„ The zeroing was accomplished by rotating the balance knob either clock-wise or anticlockwise u n t i l the Indicator on the unit read zero, waiting f o r a while to check for d r i f t i n g , and zeroing again u n t i l i t was stable,. Force and moment measurements were taken by r o t a t i n g the control unit selector switches to the appropriate range so that accurate readings could be obtainedo The wind tunnel speed, determined d i r e c t l y from the Betz Micromanometer was controlled by rheostats of the Ward-Leonard system,,. 17 P r i o r to taking any measurements zeroing of the Betz Micromanometer with the wind o f f i s necessary 0 Using the yaw mechanism of the balance, the angle of attack of the model could be varied by increments of ± one°tenth of a degree 0 The angle of attack of the model was read d i r e c t l y from the Veeder Root counter 0 For a l l double slotted f l a p air=> f o i l s angle of attack started from < = l 8 ° , a few degrees below zero l i f t angle, and increased by increments of one degree to a few degrees beyond the s t a l l i n g angle 0 A control plot of l i f t versus angle of attack was madeQ Within the region where abrupt changes were expected to occur i n the force measurement, the angle of attack of the model was increased i n in t e r v a l s of 0 o 5 degree D The wind tunnel was shut o f f aft e r every six readings were taken to check the zero of the control unit and Betz Micromanometer0 It was found that the zero errors f o r l i f t , drag and moment were negligible*, A f t e r reaching the s t a l l the angle of attack was decreased i n the same way as before*. It was found that reattachment of the flow was at a few degrees lower angle of attack than the s t a l l i n g angle 0 18 IV EXPERIMENTAL RESULTS The test Reynolds number was 3°0s.°00 based on the undeflected chord of the a i r f o i l o It was owing to power l i m i t a t i o n that tests were at such a low Reynolds numberc To reach t h i s Reynolds number, the 9 inch a i r f o i l had to be tested at a f a i r l y high wind speed, 6 3 0 8 feet per second 0 Wind speeds higher than t h i s were t r i e d , but at higher angles of attack such speeds could not be reached, and the tunnel was vibrating at an audible frequency c The double s l o t t e d f l a p Clark Y a i r f o i l with the flap set at h$° was tested with l o n g i t u d i n a l l y slotted, trans-versely slotted and perforated side wallso Eleven d i f f e r e n t arrangements of l o n g i t u d i n a l s l o t s with open area r a t i o s ranging from 1101% to 29 0 6$, seven d i f f e r e n t arrangements of transverse s l o t s with open area r a t i o s ranging from 9»3$ to 23ol% and four d i f f e r e n t arrangements of perforated walls with open area r a t i o s ranging from 12o3% to l80hfo were testedo The basic Clark Y a i r f o i l was tested with four d i f f e r e n t arrangements of longitudinal s l o t s with open area ratios; ranging from 5o5% to l8<,5$° As experimental re s u l t s obtained under free a i r condi° tions (free from wall effects) are unavailable, the present r e s u l t s can only be compared with a set of data obtained for the double s l o t t e d f l a p Clark Y a i r f o i l tested previously with s o l i d side walls at a Reynolds number of 3^1,000 i n 19 the same wind tunnel, and also with those data corrected by applying modified standard wall corrections» It had been shown previously that the data i s Reynolds number independent over the f u l l range of angle of attack with Reynolds number ranging from 3*+l,000 to 576 ,000 i n the presence of s o l i d w a l l s 0 Figures 1 1 and 12 show that with the presence of slotted walls the data i s also Reynolds number independent*, The r e s u l t s were obtained for the 19 inch double s l o t t e d flap a i r f o i l tested with two d i f f e r e n t longitudinal s l o t arrangements and at two d i f f e r e n t Reynolds numberso Interaction between the wing and c e i l i n g boundary layers, and wing and f l o o r boundary layers of the tunnel test section does not appear to cause s i g n i f i c a n t spanwise e f f e c t s , as seen i n Figure 13*> This figure shows the r e s u l t s obtained for a 12 inch chord Joukowsky a i r f o i l with twenty-four pressure taps around the upper surface and thirteen pressure taps around the lower surface at the mid-span sectiono The model was mounted on the wind tunnel balance with the best l o n g i t u d i n a l l y slotted side walls ( l 8 e 5 $ , configuration I) and tested at a Reynolds number of 3 0 0 , 0 0 0 o The pressure d i s t r i b u t i o n s over the mid-span were taken for 0 ° , h° and 8° angle of attack, and the l i f t for each angle of attack was obtained by using a planimetero These values were com-pared with the r e s u l t s for the corresponding angle of attack obtained from wind tunnel balance measurement at the same Reynolds numberQ The comparison shows that there i s very 2 0 l i t t l e d i f f e r e n c e , s u g g e s t i n g t h a t the above i n t e r a c t i o n s can be neglectedo For the double s l o t t e d f l a p a i r f o i l a simple f l o w v i s u a l i z a t i o n u s i n g wool t u f t s taped on the a i r f o i l s u r f a c e was done 0 The spanwise t u f t s e c t i o n s spaced 3 inches a p a r t had t u f t s l o c a t e d a t 159 30, *f5, 60 and 75 per cent c h o r d 0 No wing t i p s e p a r a t i o n o c c u r r e d a t angles o f a t t a c k o f 10° o r l e s s , but a d i s t i n c t wing t i p s e p a r a t i o n beyond 15° angle o f a t t a c k was observed and s e p a r a t i o n over the f l a p c o u l d be seen Q Below and a t =13° angle o f a t t a c k f l o w s e p a r a t i o n was observed over the lox^rer s u r f a c e , and fl o w was f u l l y r e a t t a c h e d a t =11° angle o f at t a c k o P o s i t i o n o f mounting had l i t t l e e f f e c t , as r e s u l t s o b t a i n e d p r e v i o u s l y by t e s t i n g the f o u r a i r f o i l s mounted a t 26o7% and 50% chord p o i n t had l i t t l e e f f e c t on l i f t and drag c o e f f i c i e n t and moment c o e f f i c i e n t a t q u a r t e r chordo The r e s u l t s a re presented i n the form o f l i f t c o e f f i c i e n t C L, drag c o e f f i c i e n t C D and moment c o e f f i c i e n t about q u a r t e r chord CMC/L,. versus a n g l e o f a t t a c k oC i n degrees f o r the f o u r d i f f e r e n t chord-width ratios„ L i f t c o e f f i c i e n t and drag c o e f f i c i e n t a r e obt a i n e d by d i v i d i n g l i f t and drag by the product o f dynamic pressure and a i r f o i l p l a n a r a r e a c Moment c o e f f i c i e n t a t q u a r t e r chord i s obtained by t r a n s -forming the measured p i t c h i n g moment c o e f f i c i e n t about mid-chord which i s o b t a i n e d by d i v i d i n g the p i t c h i n g moment by the product o f dynamic press u r e , a i r f o i l p l a n a r a r e a and a i r f o i l chordo As the measurements were taken on the 2 1 wind t u n n e l balance system t h e r e f o r e C^, C D and C ^ / ^ a r e values averaged over the e n t i r e span o f the modelo F i g u r e s lk9 15 and 16 showing u n c o r r e c t e d C L , c M C / V A X I^ L C D versus a n g l e o f a t t a c k f o r the double s l o t t e d f l a p a i r f o i l w i t h s o l i d w a l l s a t a Reynolds number o f 3 ^ 1 , 0 0 0 were measured by Mo H i l l , J 0 Hodson and A c Ryneveld i n the departmental wind t u n n e l ^ B ) . F i g u r e s 17 and 18 show C L and C^c/lx v e r s u s ©4 f o r the double s l o t t e d f l a p a i r f o i l c o r r e c t e d f o r w a l l e f f e c t s by a p p l y i n g standard w a l l c o r r e c t i o n s modified e m p i r i c a l l y by R. H i r s c h f i e l d ( l l f ) (Appendix B ) . F i g u r e Ik shows the great change i n with chord-width r a t i o ( C / H ) 0 The C L m a x i n c r e a s e d from 2,k7 to 3«3 f o r the 9 i n c h and 2k i n c h a i r f o i l s r e s p e c t i v e l y 0 The mean l i f t curve s l o p e over the u n s t a l l e d range i n c r e a s e d from 0 .078 per degree f o r the 9 i n c h a i r f o i l to 0 . 0 9 7 f o r the 2k i n c h a i r f o i l o The aero-dynamic center l a y between 23$ and 2k% o f chord f o r a l l s i z e s and C ^ c A i n c r e a s e d n e g a t i v e l y from - 0 . 3 f o r the 9 i n c h a i r f o i l to - 0 , ^ f o r the three l a r g e r a i r f o i l s . F o r the 2k i n c h a i r f o i l C M c / i f l a y between v a l u e s f o r the lk and 19 i n c h a i r f o i l s , p o s s i b l y because o f i n a c c u r a c i e s i n the i p r o f i l e s . There was no dominant e f f e c t o f model s i z e on the drag c o e f f i c i e n t f o r lower angles o f a t t a c k , but values were spread out a t h i g h e r angles o f a t t a c k approaching the s t a l l o f the a i r f o i l . The C D m i n i s between 0Blk and 0 . 1 6 a t oC - - 1 3 ° f o r a l l s i z e s . The zer o l i f t a ngle o f a t t a c k 22 i s at oC = =15° and negative s t a l l i s at about -13°. The p o s i t i v e s t a l l i n g angle i s around 17° for the three larger a i r f o i l s and s l i g h t l y lower for the 9 inch a i r f o i l . This i s probably due to the roughness over the leading edge. As shown roughness over the leading edge w i l l make the a i r f o i l s t a l l e a r l i e r than i t otherwise would. S t a l l i n g C h a r a c t e r i s t i c s of a i r f o i l s are controlled by the behaviour of the boundary la y e r over the surface of the a i r f o i l . The nose radius i s important as larger nose r a d i i generally produce a more gentle adverse pressure gradient* At the s t a l l , the l i f t dropped abruptly. This i s due to the f a i l u r e of the separated boundary layer at the leading edge to re-attach on the a i r f o i l surface. The s t a l l i n g curve shape would be rounded i f separation occurred f i r s t at the t r a i l i n g edge and moved forward slowly. For r e l a t i v e l y t h i n a i r f o i l s the s t a l l i s usually quite s h a r p ^ c O . A f t e r the modified wall corrections were applied, the l i f t curves collapsed quite n i c e l y . The average l i f t curve slope taken over the range -5°iS ®£ £ +5° "was between 0.070 and 0.072 f o r a l l four sizes of a i r f o i l . cLmax i s i n t n e region of 2.25 and 2Q3 f o r a l l s i z e s . CMCA ^ o r ^ e ^ i n c n a i r f o i l i s -0.25 and f o r the rest ranges from -0.275 to -0.315 at «*< = 0°. 1 The data f o r the basic a i r f o i l s i n the presence of s o l i d walls were measured by M. Lundberg and the data were reduced by applying standard wall corrections^ 1?) (Appendix A). Figures 19, 20 and 21 show C L, C M C / L F and C D versus angle of attack © < for a l l four sizeso The changes i n aerodynamic c h a r a c t e r i s t i c s with chord s i z e are not as great as for the double s l o t t e d fl a p a i r f o i l , since the wake of the double slotted f l a p a i r f o i l was deflected more from the free stream d i r e c t i o n G The l i f t curve i s almost l i n e a r below the s t a l l i n g r e g i o n 0 This i s because the basic a i r f o i l has a simple profile,, The average l i f t curve slope i s 0o105 for the two smaller a i r f o i l s and 0 o l l and 0o119 for the 19 and 2h inch a i r f o i l s r e s p e c t i v e l y 0 The s t a l l i n g region i s rounded, thus i n d i c a t -ing that the flow separated from the leading edge and r e -attached to the surface again c F u l l separation from the leading edge occurred at a few degrees beyond the s t a l l , . Zero l i f t angle of attack was between °6° and -6o5°° The pitching moment data showed considerable scatter, but cy[c/)+ became more negative with increasing a i r f o i l s i z e 0 cj)m±n for the three larger a i r f o i l s i s about 0o02 and 0o017 for the 9 inch a i r f o i l , a l l at = «V> 0 Figures 22, 23 and 2h show the corrected data f o r the basic a i r f o i l o The l i f t c o e f f i c i e n t s are seen to be over-corrected since the bigger a i r f o i l s gave lower l i f t c o e f f i -cients, reversing the trend of the uncorrected data 0 The standard corrections for the drag c o e f f i c i e n t were small and did not collapse the measured data Q Figures 25 to 32 i n c l u s i v e show C L versus ©C for the double s l o t t e d f l a p a i r f o i l tested i n the presence of d i f f e r e n t arrangements of l o n g i t u d i n a l l y s l o t t e d side walls 2h presented i n order of increasing open area. The figures show a progressive change i n l i f t c o e f f i c i e n t as the open area increased* The negative s t a l l i n g angle and zero l i f t angle of attack remained constant. The p o s i t i v e s t a l l i n g angle increased with the open area. The data were over-correct ed( based on the trend of C L vs and dd L/d®< which w i l l be discussed l a t e r ) f o r open area of 26% and greater and undercorrected for open area of 15% and lower. The l i f t f o r the 9 inch a i r f o i l does not change below = 8 ° for open area between 1 6 . 6 7 $ to 2 9 « 6 $ . Figures 33 to 37 i n c l u s i v e show C ^ c A versus ©( . The value became l e s s negative as open area increased. For open areas of 2 2 . 2 $ and higher the gap between the value for the 9 inch a i r f o i l and the others be-came closer but not well organized. For 1 8 . 5 $ the curves for the three larger a i r f o i l s collapsed but the 9 inch a i r -f O i l gave lower C ^ / ^ for a l l angles of attack. Open area rat i o s lower than 1805% gave sim i l a r curves. CMCA f o r i the 9 inch a i r f o i l i s about - 0 . 3 for a l l d i f f e r e n t open areas at <s< = 0 ° . Cjjc/if for each of the four a i r f o i l s was nearly constant below the s t a l l and increased negatively a f t e r the s t a l l . Figures 38 to h2 i n c l u s i v e show C D versus 1 • o4 o There was not any appreciable change i n C D f o r a l l open area r a t i o s below = V , and the data spread out most beyond this angle of attack f o r llal% and 1^ .8$ open areas. The curves f o r the three l a r g e r a i r f o i l s became closer for l8<>5% open area and tended to collapse and gave 25 s l i g h t l y lower value as the open area increasedo The 9 inch a i r f o i l gave lower drag c o e f f i c i e n t s than the others for a l l open area ra t i o s o Figures **3 to *f6 i n c l u s i v e show versus f o r the basic a i r f o i l tested with four d i f f e r e n t l o n g i t u d i n a l l y s l o t t e d side w a l l s 0 The data were overcorrected for the two 1805% open area r a t i o s , although the curves f o r the three la r g e r a i r f o i l s almost collapsed into one l i n e even beyond the s t a l l o For l l o l $ open area a l l the curves collapsed to the s t a l l i n g region and spread out beyond that© The curves collapsed below = 6° f o r 5»5% open area,/ The zero l i f t angle remained the same f o r a l l a i r f o i l s , between =6° and ~6o5°° The s t a l l i n g angle for a given a i r -f o i l remained the same f o r a l l open area ra t i o s except the 5o5%° Figures h-7 to ^-9 i n c l u s i v e show C ^ c A v e r s u s 0 The data collapsed well below oC - 6° f o r the two higher open area ratios and not so well f o r the two lower open area ratioso A l l points spread out i n the neighbourhood of the s t a l l o Figures 50 to 52 show C D versus oC o A l l points f e l l mostly into one curve f o r t h e two 1805% open area r a t i o s below oC = 6° and spread out beyond t h a t o For the other two lower open r a t i o s the curves did not collapse as w e l l o However, the minimum drag c o e f f i c i e n t was about 0o02 f o r a l l r a t i o s at at - -=h°0 Figures 53 and 5^  show versus oC f o r sl o t t e d f l a p a i r f o i l s tested with transversely s l o t t e d side w a l l s 0 As the 26 r e s u l t s do not show a d i s t i n c t and consistent trend of progressive change with the open area only two sets of re-suits are presentedo The zero l i f t angle of attack as well as the negative s t a l l does not change with the open area r a t i o s and i s at =15° and =13° respectively*. Figures 55 and 56 show C^cA versus ©C 0 The values given seemed to be smaller than the s o l i d wall data*, Configurations R and S, not shown, gave inconsistent values*. Data obtained from a l l configurations except R and S show a consistent trend of change with open area ratio*> CMc/lf f o r t n e 9 inch a i r f o i l i s about the same as given by a l l configurations but R and S D Figures 57 and 58 show C D versus *> Trans-versely slotted side walls did not give a very good drag c o e f f i c i e n t as values were spread out*. Figures 59 and 60 show C L versus o£ for two d i f f e r e n t perforated side walls*. The data were undercorrected*. Figures 61 and 62 show c-^ c/^ versus oC *> The r e s u l t s for the three larger a i r f o i l s seemed to collapse whilst those of the 9 inch a i r f o i l were 0„05 lower*. Figures 63 and (h show C D versus QC ° Data for two d i f f e r e n t walls were very s i m i l a r and not well collapsed*> The average l i f t curve slopes for the a i r f o i l s i n the presence of l o n g i t u d i n a l l y s l o t t e d side walls taken over the most l i n e a r part of the l i f t c o e f f i c i e n t curves were plotted against chord-width r a t i o and percentage of open 27 a r e a r e s p e c t i v e l y and a r e shown i n F i g u r e s 65 and 660 F o r c o m p a r i s o n , v a l u e s f o r s o l i d w a l l s , b o t h u n c o r r e c t e d and c o r r e c t e d a r e a l s o p l o t t e d o The f i g u r e s show t h e e f f e c t o f l o n g i t u d i n a l s l o t s on a v e r a g e l i f t c u r v e s l o p e w i t h i n t h e r a n g e - 5 ° < C X < +5°o c j j m x f o r a l l f ° ' u r s i z e s seemed t o a p p r o a c h t h e same v a l u e as t h e open a r e a r a t i o i n c r e a s e d as shown i n F i g u r e 67o F i g u r e 68 shows t h e e f f e c t o f l o n g i -t u d i n a l s l o t s on C ^ / ^ a t oC = 0 ° o As c a n be seen from t h e f i g u r e o n l y s l i g h t changes i n C ^ c A o c c u r f o r t h e 9 i n c h a i r f o i l f o r a l l open a r e a r a t i o s 0 The s h i f t i n l i f t c u r v e s due t o l o n g i t u d i n a l s l o t s i s shown i n F i g u r e 69 f o r t h r e e d i f f e r e n t a n g l e s o f attack*. E f f e c t o f l o n g i t u d i n a l s l o t s on a v e r a g e l i f t c u r v e s l o p e f o r t h e b a s i c a i r f o i l i s shown i n F i g u r e 70o E f f e c t s on Cj^/i^ and C L r a a x a r e shown i n F i g u r e 7 1 and s h i f t o f l i f t c o e f f i c i e n t i s shown i n F i g u r e 72o The e f f e c t s o f t r a n s v e r s e s l o t s on a v e r a g e l i f t c u r v e s l o p e , C L m a x , c M c A a n d s n i f - f c ^ l i f t c o e f f i c i e n t a r e shown i n F i g u r e s 73 t o 77o F i g u r e s 78 t o 80 show t h e e f f e c t o f p e r f o r a t e d w a l l s on a v e r a g e l i f t c u r v e s l o p e , C L m a x and Cjf lcA 0 28 V DISCUSSION 5d Longitudinally Slotted Side Walls (a) L i f t C o e f f i c i e n t For the double slotted f l a p a i r f o i l s , the results show a progressive change as the open area i s varied from 2 9 0 6 $ to llol% except that for the 9 inch a i r f o i l the l i f t c o e f f i -cient does not change below the s t a l l with open areas of 16067% and higher, as can be seen from the summary plots for s h i f t and average l i f t curve slope (Figures 69 and 6 6 ) 0 As shown i n Figure 6 6 , the bigger a i r f o i l s gave higher dC^/dee for open areas smaller than l8o5% except l6c67%o This might be because the distance between the adjacent slots i s too small for 1 6 C 6 7 $ (Configuration C ) c When the open area i s greater than 1 8 0 5 $ , dC^/do^ tends to the values obtained f o r open j e t s c In open j e t testing bigger a i r f o i l s give lower dC^/do^ 0 The zero l i f t angle of attack of a l l four sizes remained the same at c?£- = =15° for a l l open area r a t i o s tested, although there was consider-able change i n the l i f t coefficient<, This indicated that the s l o t s only changed the strength of c i r c u l a t i o n but not the e f f e c t i v e camber of the a i r f o i l 0 That i s , the induced v e l o c i t y normal to the tunnel axis i s constant along the axis, so that the s l o t s have not induced an extra streamline curvature which would increase the e f f e c t i v e a i r f o i l camber0 The maximum l i f t c o e f f i c i e n t of a l l four sizes approaches the same value as open area i s increased and s t a l l occurs 2 9 a t h i g h e r angles o f attacko In the neighbourhood o f the s t a l l , the c h a r a c t e r i s t i c s a r e mainly dependent on the boundary l a y e r behaviour. V i s c o u s e f f e c t s can not be neg-l e c t e d and p o t e n t i a l flow t h e o r y i s , u n a b l e to p r e d i c t the c h a r a c t e r i s t i c s near the s t a l l o As many workers^-^) have shown, f o r two-dimensional t e s t i n g , the e f f e c t o f i n t e r a c t i o n o f the boundary l a y e r a t c e i l i n g and f l o o r w i t h the a i r f o i l i s s m a l l a t low a n g l e s o f a t t a c k o As can be seen from the u n c o r r e c t e d C L curves o b t a i n e d f o r the double s l o t t e d f l a p a i r f o i l , dCL/d$C f o r the b i g g e s t a i r f o i l i s about 17% h i g h e r than t h a t o f the s m a l l e s t a i r f o i l , and the d i f f e r e n c e became g r e a t e r as the angle o f a t t a c k i s i n c r e a s e d . T h i s i n d i c a t e d t h a t w a l l c o r r e c t i o n s a r e l a r g e r a t h i g h angle o f a t t a c k o The d e s i r e d e f f e c t o f s l o t s i s to a l t e r the s t r e a m l i n e s In such a way t h a t the w a l l e f f e c t s do not e x i s t and as a r e s u l t a l l o w the f l o w to separate a t a h i g h e r angle w h i l e g i v i n g a lower value o f l i f t c o e f f i c i e n t • The n e g a t i v e s t a l l o f a l l f o u r a i r f o i l s i s a t about @& - -13°0 T h i s i s because the s e p a r a t i o n from the l e a d i n g edge over the lower s u r f a c e i s n e a r l y a p o i n t s e p a r a t i o n r a t h e r than a l a m i n a r boundary s e p a r a t i o n . The l i f t c o e f f i c i e n t does not v a r y l i n e a r l y w i t h angle o f a t t a c k and there i s an abrupt change i n shape a t the n e g a t i v e s t a l l . These a r e a t t r i b u t e d t o the complicated p r o f i l e o f the h i g h l i f t a i r f o i l o The r e g i o n between - 5°^^t £ +5° i s q u i t e l i n e a r and the l i f t •i 30 curve slope i s taken over t h i s region. The 2h inch a i r f o i l gives a lower value of f o r angles of attack below h° over the whole range of open area r a t i o s o The cause of t h i s consistent lower value i s not known0 Results obtained f o r the 9 inch a i r f o i l with the 2906% open area are not very smooth. This might be due to the d i f f i c u l t y i n set t i n g the wind speed steady because of the large quantity of a i r passing through the s l o t s , with a corresponding f l u c t u a t i n g energy l o s s 0 For 11*1% and lh08% open areas the results (Figures 25 and 26 ) agreed quite well up to 0 ^ = 6 ° , and spread out beyond t h i s ®C . Of a l l open areas, lQo5% gives the best agreement for a l l four a i r f o i l s . The r e s u l t s obtained show that with open area V+98% and below the wall i effects can not be eliminated and with 2 0 . 3 8 $ or higher the data were over-corrected. For the basic a i r f o i l , because of i t s simple p r o f i l e , the l i f t c o e f f i c i e n t i s l i n e a r and rounded at the s t a l l o The trends of over-correction and under-correction can be observed c l e a r l y for the various open areas. L i f t c o e f f i c i e n t (Figures *+3 to h-6) and average l i f t curve slope (Figure 70) increased accordingly as the open area decreased. For 5<>5% the data collapsed quite well below &i = 6° and below ,p(, = 1 2 ° for 1 1 . 1 $ , which i s regarded as the best configura-t i o n f or t h i s set of a i r f o i l s . The data were over-corrected 1 with 18 .5^9 which was the best configuration for the double slotted f l a p a i r f o i l . Though the two sets of a i r f o i l s have i 1 . 31 the same chord°width r a t i o , the open areas required are different*. This suggests that wall corrections not only depend on the chord s i z e of the a i r f o i l but also depend on the degree of the flow d e f l e c t i o n from the free stream direction*. The zero l i f t angle of attack remained the same as that tested with s o l i d walls, thus the s l o t s only affected the strength of the c i r c u l a t i o n but not the a i r f o i l camber*. The p o s i t i v e s t a l l angle for a given a i r f o i l becomes higher and C^m^ becomes lower as open area i s increased from 0% to 1 8 0 5$° The reasons are given i n the previous paragraph*, (b) Moment C o e f f i c i e n t At Quarter Chord c M c A f o r d o - u ^ l e s l o t t e d f l a p a i r f o i l i s not constant fo r a l l angles of attack as predicted by t h i n a i r f o i l theory*. The theory shows that C^cA ^ s o n l v a function of camber and i s independent of ° The aerodynamic center for the double slotted f l a p a i r f o i l i s between Z$% and 2h% chord instead of at 2% chordo C^/^ f o r the 9 inch a i r f o i l at oC - o° i s about °0o3 f o r almost a l l open area ratios*> The 9 inch a i r f o i l always gave a lower C^/^ than the others*. The cause of t h i s consistent lower value might be inaccuracy i n camber i n the a f t section of the profile*> As indicated by the theory of t h i n wing sections, increasing the amount of camber causes a nearly uniform negative increase of the c M c A ° C M c A i s S^t® s e n s i t i v e to the camber of the air«= f o i l at the t r a i l i n g edge Q Reflexing the camber at the 32 t r a i l i n g edg© would give a lower negative value of C^/^. Thus i t might be that the pin was not set properly, and as a r e s u l t gave a faul t y f l a p deflection„ Tested with the two 1 8 0 5 $ longitudinal arrangements, Cftc/i). f o r the basic a i r f o i l collapsed below oC - 8 ° and spread out beyond t h i s point. For the 1 1 . 1 $ arrangement c M c A o n l y collapsed below oC = 2 ° and does not show any sign of collapsing for 5o5%° Thus i n order to eliminate wall effects: on C^y^, higher open area percentage than fo r l i f t c o e f f i c i e n t i s required 0 The data show a clear trend to smaller values as the open area i s increased 0 (c) Drag C o e f f i c i e n t The drag correction i s very s l i g h t f o r angles of attack below 8 degreeso The values are s l i g h t l y higher for the l l o l $ and 1 ^ 0 8 $ than f o r the rest of the open areas c The drag increased gradually with angle of attack and increased abruptly at the s t a l l 0 For open areas of 1 8 . 5 $ and higher the drag c o e f f i c i e n t collapsed quite well but i t spread out for lower open area r a t i o s . Drag c o e f f i c i e n t for the 9 inch a i r f o i l i s lower than that for the three larger a i r f o i l s beyond &L = 0°o With the presence of the s o l i d walls, the streamlines around the model can not expand f r e e l y as they would i n free a i r but are squeezed together. As the e f f e c t i v e cross-sectional area i s decreased, the v e l o c i t y around the model i s higher than the undisturbed stream v e l o c i t y i n order 33 to s a t i s f y the c o n t i n u i t y e q u a t i o n 0 From B e r n o u l l i ' s e q u a t i o n , as the v e l o c i t y i s i n c r e a s e d , the s t a t i c p r e s s u r e i s decreased o In the wake r e g i o n v e l o c i t y i s low Q In o r d e r to s a t i s f y the c o n t i n u i t y equation the v e l o c i t y o u t s i d e the wake w i l l t h e r e -f o r e be h i g h e r than the und i s t u r b e d stream v e l o c i t y 0 Thus pre s s u r e i s lower than the upstream v a l u e , and a s o r t o f s u c t i o n f o r c e a c t s on the model, i n c r e a s i n g the d r a g o The drag data f o r the b a s i c a i r f o i l do not show a good t r e n d o f c o l l a p s i n g and spread out f o r angles o f a t t a c k h i g h e r than ^f 0 f o r a l l open a r e a s 0 F o r 18<>5$ the drag co-e f f i c i e n t c o l l a p s e d below &C= h°„ The drag f o r the b a s i c a i r f o i l i s v e r y s m a l l and the a c c u r a c y o f measurement i s a c c o r d i n g l y reducedo 5o2 T r a n s v e r s e l y S l o t t e d Side Walls (a) L i f t C o e f f i c i e n t The data do not show a c l e a r t rend o f d e c r e a s i n g w i t h the i n c r e a s i n g o f open a r e a 0 C o n f i g u r a t i o n s P, T and U which have open areas o f 1 0 $ , 1 8 0 5 $ and 23<>2$ r e s p e c t i v e l y g ive the same s o r t o f c u r v e 0 C o n f i g u r a t i o n s 0 and S having open areas o f 9<>3$ and 2 0 o 8 $ a l s o g i v e the same s o r t o f curveo Though c o n f i g u r a t i o n s P and R have the same 10$ open a r e a , c o n f i g u r a t i o n R gives a h i g h e r value o f C^o The poor shape o f the curve obtained f o r c o n f i g u r a t i o n s R and S was due t o the i n d i v i d u a l openings being too wide, h i n c h e s , so t h a t the s t r e a m l i n e s were o v e r - d i s t o r t e d 0 The arrangement of t r a n s v e r s e l y s l o t t e d s i d e w a l l s permits the d e f l e c t e d 3h flow leaving the t r a i l i n g edge of the a i r f o i l to go through a s l o t or to s t r i k e on a s o l i d piece. Transversely s l o t t e d side walls are not suitable for t e s t i n g models associated with highly deflected flows, but could be appropriate for te s t i n g simple a i r f o i l s associated with s l i g h t l y deflected flowso The i n d i v i d u a l gaps for the slotted wall should not be too large, perhaps 2 inches or l e s s . (b) Moment C o e f f i c i e n t At Quarter Chord There i s no consistent change of data for d i f f e r e n t open area r a t i o s . The values are lower than for s o l i d walls, but the var i a t i o n i s l e s s smooth. This i s further evidence that transversely s l o t t e d side walls are not very e f f e c t i v e for t e s t i n g h i g h - l i f t a i r f o i l s . (c) Drag Co e f f i c i e n t Configurations T and U give the same (lower) drag data and configurations 0, P, R and S give the same (higher) drag data. The former values are the same as those f o r so l i d walls except at a few points. The l a t t e r configurations give higher drag between =8° < &C < +8° f o r the two larger a i r f o i l s . The discrepancy may be due to the over-corrected flow. 5°3 Perforated Side Walls (a) L i f t C o e f f i c i e n t The data do decrease with the increase of open area, but the curves are not very smooth. This i s due to the complicated flow through the holes. Since the data were under-corrected at these two open areas, so two other higher 35 open areas were t e s t e d s The r e s u l t s were not very encouraging a f t e r t e s t i n g the 9 i n c h and 2h i n c h airfoils„ (b) Moment C o e f f i c i e n t A t Quarter Chord Both c o n f i g u r a t i o n s g i v e about the same c u r v e 0 The v a l u e f o r the 9 i n c h a i r f o i l i s the same as t h a t o f s o l i d w a l l s d a t a Q The data f o r the t h r e e l a r g e r a i r f o i l s c o l l a p s e d w e l l but were as h i g h as those o f s o l i d w a l l d a t a D P e r f o r a t e d w a l l s do not c o r r e c t the data but b r i n g the d a t a c l o s e r together,, (c) Drag C o e f f i c i e n t Data f o r both open areas g i v e the same drag c o e f f i c i e n t and w i t h i n the r e g i o n =8° S oC < +8° g i v e h i g h e r drag co-e f f i c i e n t s than the s o l i d w a l l s do c 5o*+ Comparisons And General Comments The l i f t c o e f f i c i e n t s o f the double s l o t t e d f l a p a i r -f o i l o b t a i n e d from t h i s experiment f o r 1 8 „ 5 $ open a r e a c o l l a p s e d b e t t e r than the c o r r e c t e d l i f t c o e f f i c i e n t f o r oC >6° and below the s t a l l r e g i o n 0 F o r oC < 6° the c o r r e c t e d l i f t c o e f f i c i e n t c o l l a p s e d b e t t e r than the p r e s e n t data because the 2h i n c h a i r f o i l gave lower l i f t c o e f f i c i e n t s f o r oC l l f ° 0 At the s t a l l the c o r r e c t e d data c o l l a p s e d n i c e l y w h i l s t the present data spread out and gave a h i g h e r CLmax° T n e r e was n 0 change i n zero l i f t a ngle o f a t t a c k and n e g a t i v e s t a l l f o r both c o r r e c t e d and present d a t a 5 but the present data gave s l i g h t l y h igher a n g l e of p o s i t i v e stallo P o s s i b l y with the s o l i d w a l l s the e f f e c t s of the 36 i n t e r a c t i o n of c e i l i n g and f l o o r boundary layers with the a i r f o i l s are more serious at higher oC , thus causing the flow to separate e a r l i e r . C^ at oC - o from the present work i s about 16$ lower than the corrected value for a l l a i r f o i l s o Average l i f t curve slope taken over the range -5° - °^ - *5° i s 0.065 per degree for the present r e s u l t s and the corrected value i s 0o073 per degree*. The d i s c r e -pancy was f i r s t suspected to be the i n t e r a c t i o n of the c e i l i n g and f l o o r boundary layers with the a i r f o i l but l a t e r t h i s effect was found to be n e g l i g i b l e at low angles of attack and appreciable only at high angles of attack*, With the 2\ inch chord Clark Y a i r f o i l with double slotted f l a p mounted on the balance at zero angle of attack i n the presence of the 18.5$ s l o t t e d walls, a p i t o t - s t a t i c tube mounted about 6 inches from the nozzle was used to make a v e l o c i t y traverse vertically*, The readings were quite constant which suggested that the flow i s nearly two-dimensional 0 The v e l o c i t y across the tunnel was measured using the same device 0 The results showed a 5$ lower value than that of the Betz Micromanometer reading, whereas when the same traverse was made with the 2h inch a i r f o i l i n the presence of s o l i d walls, the results showed that the average value was the same as the Betz*, Thus the discrepancy might be p a r t l y due to t h i s lower dynamic pressure. The stream was affected by the models about three-quarter chords upstream from the leading edge*, .37 For the 1805% l o n g i t u d i n a l l y s l o t t e d side walls, con-sidered to be the best configuration, C^/^. i s about -0.285 for the 9 inch a i r f o i l and f o r the other three larger a i r f o i l s whose CMe/lf. collapsed quite w e l l , i s about -00 3*+ at oi - 0° a The corrected C ^ ^ spread out, the C^/^ f o r ih and 2h inch a i r f o i l s l y i n g between those of 9 Inch and 19 Inch, and ranging from -0.25 to -00315 at ^ = 0° o No corrected drag c o e f f i c i e n t f o r double s l o t t e d f l a p a i r f o i l was a v a i l a b l e . For the basic a i r f o i l the data collapsed quite well for the 11.1$ l o n g i t u d i n a l l y slotted side walls* The average l i f t curve slope (Figure 70) for a l l four sizes i s nearly the same at about 0.0825 per degree e For a p a r t i c u l a r wall configuration the r e s u l t s are regarded as overcorrected i f a : bigger a i r f o i l gives a lower dC^/d Q& value than that of a smaller a i r f o i l 0 When the converse applies, the results are considered to be undercorrected. The l i f t c o e f f i c i e n t s measured with s o l i d walls and adjusted using standard wall corrections do not collapse as well as the experimental r e s u l t s and are overcorreeted. More s p e c i f i c a l l y the average l i f t curve slope f o r the 9 and Ik inch a i r f o i l s i s 0 o l per degree while the 19 and 2*+ inch a i r f o i l s give values of 0.095 and 0.09 per degree res p e c t i v e l y . The value of dCj/dQL found by R i e g e l s ^ 1 1 ) was 0.096 for a lk% thick Clark Y a i r f o i l tested at a j 38 Reynolds number of 7 , 9 7 0 , 0 0 0 and the zero l i f t angle of attack was - 6 . 2 ° . The zero l i f t angle obtained from present results was between - 6 ° and - 6 . 5 ° « Although there i s a discrepancy i n average l i f t curve slope, a l l of the basic a i r f o i l s gave the same zero l i f t angle of attack*, The l i f t curve slope f o r a f l a t plate i s 0 .1096 per degree as pre-dieted by t h i n a i r f o i l theory* In tx-jo-cl imens i o n a l i n v i s c i d flow the value i s increased as the thickness i s increased, but the value i s s i g n i f i c a n t l y decreased by viscous e f f e c t s . The established value f o r the present basic a i r f o i l i s about Ooi at th i s low Reynolds number range, a value f o r the double slotted f l a p a i r f o i l i s not available« The l i f t curve slope obtained f o r the basic a i r f o i l using porous side walls was lower than the established value and for the a i r f o i l s with double slotted f l a p was lower than the value obtained by applying modified standard wall c o r r e c t i o n s ( l l f ) • The d i s c r e -pancy i s suspected to be the defect i n dynamic pressure as mentioned previously. The present C M c /Aj. for a l l sizes i s -0-.086 at d ~ 0 ° obtained from t e s t i n g with 11.1$ l o n g i t u -d i n a l l y s l o t t e d side walls. It seemed that 18<,5$ l o n g i t u d i n a l l y slotted side walls give better r e s u l t s f o r CMC/1+ , -0.082 for a l l sizes at C< = 0 ° . (The value given by Riegels i s -0.08.) The corrected i s -0.08 for the 9 inch a i r f o i l and increased negatively to - 0 . 0 8 7 5 for the three larger a i r f o i l s . For drag c o e f f i c i e n t the corrected data collapsed better than the data obtained from testing with the 1101% 38a l o n g i t u d i n a l l y slotted side w a l l s 0 CDmin i s °°02 f o r t n e 9 inch a i r f o i l and increased to OoC^ fo r the other s i z e s 0 The corrected drag c o e f f i c i e n t i s 0o017 fo r the 9 inch a i r -f o i l and i s 0o019 for the three bigger sizeso For both corrected and experimental drag c o e f f i c i e n t the C^min i s at = -h°0 39 VI CONCLUSIONS Based on the experimental r e s u l t s the following conclusions can be drawn: (1) Longitudinally slotted side walls proved to be the most promising arrangement f o r eliminating wall effects i n the present approximately two-dimensional wind tunnel t e s t s . (2) Longitudinally slotted side walls having an open area r a t i o of 18.5$ were the best for t e s t i n g a double slotted f l a p Clark Y a i r f o i l with the f l a p deflected at *f5°. (3) For t e s t i n g the basic Clark Y a i r f o i l , which developed lower l i f t , 11.1$ l o n g i t u d i n a l l y slotted side walls provided Ci, data most nearly independent of model s i z e . (.h) Though the r e s u l t s obtained f o r the two sets of a i r f o i l s were collapsed for d i f f e r e n t open areas, the values of dC L/d oC were lower than expected. For the basic a i r f o i l , the average l i f t curve slopes were about 15$ loxrer than the established values? the double slotted f l a p a i r f o i l s had values of d'CL/d OC which were also about 15$ lower, although the correct value i n t h i s case i s more uncertain. This discrepancy has not been completely resolved. (5) The measured values of zero l i f t angle of attack did not depend on open area r a t i o or s l o t configuration. (6) There was only a s l i g h t e f f e c t on drag c o e f f i c i e n t of changes i n wall s l o t configuration. i ho ( 7 ) To eliminate wall effects on C^/^ f o r the Clark Y a i r f o i l s 9 higher open area r a t i o s were required than to eliminate effects on l i f t c o e f f i c i e n t o (8) The flow was s t i l l quite uniform and apparently two-dimensional over the tested Reynolds number range with s l o t s or holes i n the side w a l l s . (9) The i n t e r a c t i o n of c e i l i n g and f l o o r boundary layers with the a i r f o i l s i s small at low angles of attack and appreciable i n the neighbourhood of the s t a l l . Thus span-, wise e f f e c t s are n e g l i g i b l e at low angles of attack. (10) Although the open area r a t i o s found to be best i n the present tests are not nec e s s a r i l y optimum values for a l l tunnels, they should provide useful guidelines f o r future tests with porous wall configurations. i BIBLIOGRAPHY hi l o Glauert, H 0 2 e Goldstein, S» 3o A l l e n , Ho J o Vincenti, W. Go h0 Rogers, E c W. E. 5* Garner, H G C. 6. Heyson, H. H. 1 7o Kirkpatrick, D c L e I o 8 0 Theodorsen, To 9 » South, P 0 10. Weick, F o E e Shortal, J Q A 0 -11o Riegels, F o We "Wind Tunnel Interference on Wings, Bodies and Airscrews", B r i t i s h ARC R & M 1 5 6 6 , 1 9 3 3 o "Two-Dimensional Wind-Tunnel Interference", B r i t i s h R & M 1 9 0 2 , 1 9 ^ 2 0 "Wall Interference i n a Two-Dimensional Flow Wind-Tunnel with Consideration of the Ef f e c t of Compressibility", NACA Report 7 8 2 , 19T"4"O "A Background to the Problems of Wind-Tunnel Interference", AGARD Report 2 9 2 , 1 9 5 9 o "Subsonic Wind Tunnel Wall Corrections", AGARDograph 1 0 9 , October, 1 9 6 6 o -"Linearized Theory of Wind-Tunnel Jet-Boundary Corrections and Ground E f f e c t for VTOL . - S T 0 L A i r c r a f t " , NASA TR R - 1 2 l f , 1 9 6 1 . "Wind-Tunnel Corrections for V/STOL Model Testing", M.A.Sc. Thesis, University of V i r g i n i a , August, 1 9 6 2 o "The Theory of Wind-Tunnel Wall Interference", NACA Report if 1 0 , 1 9 3 1 o "Research on Reduction of Wall Eff e c t s i n Low Speed Wind Tunnels", NRC Report no. DME/NAE 1 9 6 8 ( 1 ) o " The E f f e c t of Multi p l e Fixed Slots and a Trailing-Edge Flap on the L i f t and Drag of a Clark Y A i r f o i l " , NACA Report ^27 , 1 9 3 2 . " A i r f o i l Sections" translated by D o G o Randall, London, Butterworths, 1 9 6 l o h2 1 2 0 Pope, Ao-13o Parkinson, Go V 0 Ih-o Parkinson, Go V c l 5 o L o f t i n 2 L 0 K 0 B u r s h a l l , W0 J o I 6 0 Abbott, I o Ho Doenhoff, A 0 E 0 V c 1 7 o Pope, A o Harper, J o J< l 8 o Mendelsohn, Ro A Q Polhamus, J o F o "Wind-Tunnel Testing™, New York, Wiley, 195*+o "Steady and Non-Steady Flow About Wings At High Incidence", DRB Grant 9551=139 Annual Report, October, 1967o "Steady and Non-Steady Flow About Wings At High Incidence", DRB Grant 9551=139 Annual Report, October, 19680 "The E f f e c t s of Variations In Reynolds Number Between 3o0 x 10° and 25 x 10° Upon the Aerodynamic Characte r i s t i c s of a Number of NACA 6-Series A i r f o i l Sections", NACA Report 96^, 19^8» "Theory of Wing Sections", New York, Dover, 1959° "Low Speed Wind Tunnel Testing", Chapter 6, New York, John Wiley and Sons Inc Q, 1966o "Effects of the Tunnel-Wall Boundary Layer on Test Results of a Wing Protruding from a Tunnel Wall", NACA 12¥f, A p r i l , 19^70 h2eL APPENDIX A STANDARD TWO-DIMENSIONAL WALL CORRECTIONS The tunnel wall corrections f o r an a i r f o i l of f i n i t e thickness and camber i n a two-dimensional flow wind tunnel, where the a i r f o i l chord i s located near the tunnel centre-l i n e , can be calculated by considered the s o l i d blockage, wake blockage and streamline curvature e f f e c t s separately© (a) S o l i d Side Walls S o l i d Blockages The base p r o f i l e i s represented by source-sink d i s t r i -bution along the chord, and the s o l i d boundaries can be represented by an i n f i n i t e series of images above and below the base p r o f i l e * Induced v e l o c i t y at the base p r o f i l e due to the images i s calculated«- The s o l i d blockage correction factor i s defined as the r a t i o of the v e l o c i t y increment to free stream v e l o c i t y . This effect i s a function of model thickness, thickness d i s t r i b u t i o n , and model s i z e , and i s independent of the camber. Wake Blockage: The wake i s simulated by a source at the t r a i l i n g edge and a sink f a r downstream to preserve continuity. The boundaries are represented by an i n f i n i t e s e r i e s of images. The strength of the source i s calculated from the drag. The induced a x i a l v e l o c i t y due to the image sink i s calculated, and a correction factor s i m i l a r to that for s o l i d blockage i s defined. ""-.-.Jr.--' S t r e a m l i n e C u r v a t u r e ( C a m b e r e f f e c t ) : The camber i s r e p r e s e n t e d by a d i s t r i b u t i o n o f v o r t i c e s a l o n g t h e camber l i n e e F o r t h e s a k e o f ease i n c a l c u l a t i o n t h e v o r t i c e s may be d i s t r i b u t e d a l o n g t h e c h o r d l i n e r a t h e r t h a n a l o n g t h e camber l i n e and t h e i n d u c e d v e l -o c i t y a t a n y c h o r d w i s e s t a t i o n on t h e camber l i n e may be t a k e n as e q u a l t o t h e i n d u c e d v e l o c i t y -on t h e c h o r d l i n e a t t h e same s t a t i o n * . The images n e c e s s a r y t o p r e s e r v e t h e t u n n e l -walls as s t r e a m l i n e s a r e r e f l e c t e d a c r o s s t h e b o u n d a r i e s w i t h o p p o s i t e s i g n s so as t o meet t h e r e q u i r e -ment o f no n o r m a l f l o w a c r o s s t h e b o u n d a r i e s <> The i n d u c e d v e l o c i t y i s summed up and i n d u c e d a n g l e o f a t t a c k i s o b t a i n e d , w h i c h a r i s e s from t h e c o n s t r a i n t imposed by t h e t u n n e l walls*. ! The r e s u l t s o f t h e t w o - d i m e n s i o n a l s o l i d w a l l c o r r e c -t i p n s a r e g i v e n below*. F o r d e t a i l d e r i v a t i o n see r e f e r e n c e 3<, The d a t a w i t h t h e p r i m e a r e u n c o r r e c t e d data*. v = v-1- ( i + 6 ) , q = q 1 (1 + 2 £ ) ., R = R' (1 + 6) o< + ?7,«3.<r* (c« + he* „ ) k2c C L = C £ ( l - f T - 2 6 ) C M c A = C M c A C 1 - 26) + c d s S 4 < i - 3 e s b - 2 € w b ) where V = V e l o c i t y q = dynamic p r e s s u r e R = Reynolds number C*~ X2 ( C / H ) 2 a f a c t o r dependent upon s i z e o f a i r f o i l r e l a t i v e to t u n n e l £ = € s b + £ w t ) c o r r e c t i o n f a c t o r ^ s b =A^~ a f a c t o r due t o s o l i d blockage ^wb ~ % (C/H) a f a c t o r due to wake blockage A = 5C f I / t 1 " C p ] [ 1 + (2Z)54a factor depending upon shape o f base p r o f i l e Cp base p r o f i l e (no camber) p r e s s u r e d i s t r i b u t i o n x, y the base p r o f i l e c o o r d i n a t e s (b) Open Side Walls In the case o f the f r e e two-dimensional j e t , the c o r r e c -t i o n s f o r blockage and wake a r e n e g l e c t e d , and the vortex images a r e r e f l e c t e d across f r e e boundaries w i t h l i k e s i g n so as to meet the requirement o f a continuous p r e s s u r e g r a d i e n t a c r o s s the boundaries» An a d d i t i o n a l f a c t o r i s r e q u i r e d to account f o r the downward d e f l e c t i o n o f the a i r s t r e a m . h2d The f i n a l r e s u l t s are as follows i = 0< - 57«3 [i(C/H) C L + fc (C/H) 2 C L| C L = CI CMeA = C 8 M c A "f§ ( C / H ) 2 C L C d = Cj - i (C/H) C 2 A l l the notations are the same as f o r the s o l i d wall correctionso !+2e APPENDIX B HIRSCHFIELD'S MODIFIED STANDARD WALL CORRECTIONS These c o r r e c t i o n s were c a l c u l a t e d "by m u l t i p l y i n g t h e s t a n d a r d s o l i d wall c o r r e c t i o n f a c t o r s by a c o n s t a n t t o o b t a i n t h e b e s t c o l l a p s e o f t h e C T d a t a f o r a l l s i z e s o f N o t a t i o n s are t h e same as i n Ap p e n d i x A, The value o f A, f i n a l l y selected was 0o6, and was determined from t e s t s on t h e double s l o t t e d f l a p a i r f o i l s d e s c r i b e d i n s e c t i o n 2*3 o f t h e p r e s e n t r e p o r t 0 the s i m i l a r a i r f o i l s Thus: o< ~ ai p e r c e n t a g e o p e n a r e a n-i 14-8 18.5 18-5 22-2 22-2 25.9 29.6 "*"^^£on f i g u r a t i o n p o s i t i o n ^" " - " - ^^^ H G 1 K J L B A 1 G S G G G G S G 2 S S , S S ;S S G S 3 S G s S S S S G 4 S G s G G S G S 5 S S G S S G S G 6 S S S S S G G S 7 S S S S G S S G 8 G S G G S S G S 9 S S S S G S S G 1 0 S S S S S G G S 11 S s G S S G S G-1 2 S G S G G S G S 1 3 S G S S S S S G 1 4 S S S S S S G S 1 5 G S G G G G S G G = GAP S = SOLID Table l e Typical Longitudinal Slot Arrangements Figure 1. Wind tunnel outline h5 F i g . 2. Wind tunnel balance F i g o 3o P r o f i l e of Clark Y a i r f o i l with: double slotted f l a p -r CN for l ong i tud ina l a r r a n g e m e n t f o r t ransversa l a n d p e r f o r a t e d a r r a n g e m e n t F I g o 5o Test section side wall panel frame F i g * 7. A t y p i c a l t r a n s v e r s e s l o t arrangement ( foreground ) F i g . 8 . A t y p i c a l perforated side wall F i g , 9# Mounting bracket F i g , 1 0 . 2h inch model i n t e s t section i j r 2 8 -1.4 N T ~ i — 1 r i — 1 — i — T ? R o 3 5 8 , 5 9 0 EI 3 1 3 . 0 0 0 Me/4 56 3-2 2 - 8 2 - 4 2 0 1-6 1-2 8 Oh C H o U D . 2 5 0 A • 3 8 9 • • 5 2 8 V • 6 6 7 N R = 3 4 1 , 0 0 0 v v c P v v • v o • S • A o a o ° • A O Q O a o A O a ; " o B A ° o o 9 • A • A O o A o • A o H O O ' • J L J I I L i i t II - 1 6 - 1 2 - 8 - 4 0 4 8 12 16 2 0 2 4 F i g o l*fo Uncorrected Cj, vs c< f o r a i r f o i l w ith double s l o t t e d f l a p o S o l i d w a l l s H o 0-250 A 0.389 • 0.528 v 0-667 • V V A • E O • v A • X • A O • V A O • V A • V A • V A • • • • o o X o F i g o 15< Uncorrected CM slotted f l a p o i ..- 0 . 4 8 vs c< for a i r f o i l >olid walls 1.2 with double o 0-250 A 0-389 • 0-528 O 6 s 8 § 8 § • D A _ • g ° £ O §SSSS§ooo° o • • V • V A o o o A O O =16 =12 0 J_L F i g o 16 0 Uncorrected CD vs c< f o r a i r f o i l w i t h double s l o t t e d f l a p o S o l i d w a l l s F i g o . 17o- C o r r e c t e d C L vs c< f o r a i r f o i l w i t h double s l o t t e d f l a p o S o l i d w a l l s • V o A • • j _ L -12 • A 5 • • A A 0 • • V V V • o O 0 0 0 O o o o V o 0 Q V o V O s o 0 .250 A 0 .389 • 0 .528 g 6 • o V O A v O v J L _ i oC 12 1 F i g o l 8 0 Corrected CMC/I+ V S C< for a i r f o i l with double slotted f l a p o Solid walls 2 0 -j 3 1 1 1 1 f~ V V v _ D D • ° • ° a • • o 0-250 v • A 0-389 V • A • 0 528 A A v D o o o v 0-667 A O 2 V © 0 O °5 o A 9 fi AO D A ° o v A O • A V O A • o V V A D o V A D O © v • A o v o • © I j 1 i I I I I I I I I I I I L -12 -8 -4 0 4 oC° 8 12 16 2 0 Figo 19o Uncorrected C L vs o< f o r basic a i r f o i l o S o l i d v a i l s 62 0 .04 .06 .08 • 10 • 12 o 0-250 A 0°389 • Q«528 v 0-667 o - i o o ° o o o o o © ° o o A A A A A — J A • • El • • -I • O A A A • B * A < § > | @ 13 G g A A D G v v W v V V V v V V V V • • V v V V J _ J I L oC F i g o 20o. Uncorrected 0^/1+ vs ©< for basic a i r f o i l o Solid walls .20r I 4 .1 2 • 1 0 -.08 06 • 02 0 o A • V 0 - 2 5 0 0 . 3 8 9 0 - 5 2 8 0 -66 7 • A O 63 1 r — f V -1 V A • V o o • V • • v • A O o V • A o • A 0 O A O O A A O A O O O _ J J _ J L 12 16 F i g o 21o Uncorrected C D vs <X f o r basic a i r f o i l „ Solid walls oh Figo- 22o C o r r e c t e d C L vs ©< f o r b a s i c a i r f o i l 0 S o l i d w a l l s 65 ~~|—r c H © 0.250 A 0.389 • 0-528 v 0.' r V V O 0 O 9 O °B • c7c | V ° A °cP • A 9 V r— A A i i A ^ V A Q A V • A A • V O © A • • O v 0 1 _ 1 2 -8 -4 0 4 oC 8 12 16 g o 2 3 o Corrected C M C A v s f o r basic airfoil„ Solid walls 66 c © 0-' A 0-389 0 0-5 2 8 • • • A • V - A O v a V • o o B V A V o © A -o © o ° • V A V • V A o V U A O • A ^ ° o o o "8 "4 0 4 0C0 8 12' 16 0. 2h. C o r r e c t e d C D v s c* f o r b a s i c a i r f o i l o S o l i d w a l l s - i « r-n * i r—. ' ' 1 ' 1 1 1 ' r o 0 - 2 5 0 A 0 . 3 8 9 v v 1=1 • 0 - 5 2 8 g * V n O) v 0 - 6 6 7 v ^ v 6 O • A e v • 8 • © V V 1-2^ n 8 V • • •8h e V V V 0 • =E • ' ' i » i i i I i i t i i i i i - 1 6 - 1 2 - 8 - 4 0 4 ^ 8 . 12 F i g 0 . 25o vs o< f o r a i r f o i l w i t h double s l o t t e d f l a p e Wall 1 c o n f i g u r a t i o n H, 11„1$ open a r e a 3.0i 2-8 2-4 2.0 1.6 1-2 •8 i r 1 r o A • V C H 0 - 2 5 0 0 - 3 8 9 0 -528 0 . 6 6 7 o v v 8 v v 8 v © V V V V • i r s A V V • •• V • • • AA v ^ A A V A O • • A A 0 - . 4 1 6 v l i l t - 1 6 - 1 2 F i g . J L - 8 - 4 0 i i » i i i » i 8 12 16 26 0 Ci vs G& f o r a i r f o i l w i t h double s l o t t e d f l a p e Wall c o n f i g u r a t i o n G ? lh0&% open area J L 20 24 2 - 4 2 -0 1.6 1-2 . 8 . 4 0 - - 4 o A • V A o • c H 0 - 2 5 0 0 - 3 8 9 0 - 5 2 8 0 - 6 6 7 T 1 r j 1 j 1 1 r l 1 1 r v v 2 • N s 5 A A V O O • v A O V n v A O • — V A O V • 23 s 9 f A A 6 6 A 9 D A • A O v • A O ° V O D V 6 • 6 D v v v • v - 1 6 -12 - 8 S A - 4 0 oC 8 1 2 16 F i g o 27* C L vs <X for a i r f o i l with double s l o t t e d flap, Wall configuration I , 18 071 open area o A o H A A 2 0 2 4 $ 2-8i 2.4 2 - 0 1-6 8 i r o A • V C H 0 - 2 5 0 0 - 3 89 0 - 5 28 0 - 6 6 7 A Q A i V O V A 9 1 I I I A o a V A s e • 6 V V v v ° 8 V V n • • • A AAA 8 ooo A o • 4\-0 - . 4 1 ! A o A • 8 J L I I I i - 1 6 - 1 2 - 8 - 4 0 4 oC 8 12 1 6 F i g o 28o C L V S f o r a i r f o i l w i t h double s l o t t e d f l a p Q Wall c o n f i g u r a t i o n E, 18Q5$ open area 2 0 24 c H o 0 - 2 5 0 A 0 . 3 8 9 n 0 - 5 2 8 v 0 - 6 6 7 T  V 6 • v 6 v e • ° • V V V A § V 6 • 8 D V v v 8 . A A A A A A A " vOOoSoooo O 9 o 9 o D D O A A A • OO vv • A a A Q V V V 9 V 8 v V - 1 2 - 8 - 4 0 4 o 8 12 16 2 0 2 4 F i g o 2 9o C L vs ©< f o r a i r f o i l w ith double s l o t t e d f l a p Q Wall c o n f i g u r a t i o n D, 20oh% open area 2 . 8 i 1 . 2 •4 0 T i 1 « 1 1 1 1 1 1——i j 1 1 j — — i r C i r H V V 2 . 4 h v DA O 0 . 2 5 0 n 0 I @ A 0 - 3 8 9 A O g • 2 - 0 H • 0 . 5 2 8 J O D ^ A D $ d R 9 v 0.667 6 6 o H v v ' I ^ ® • © • v V @ • •8h ^ & ° v V v • V -.41 = - 1 6 - 1 2 - 8 -4 0 4 o C ° 8 1 2 1 6 2 0 2 4 F i g o 3"0o C E V S f o r a i r f o i l with double s l o t t e d f l a p 0 Wall c o n f i g u r a t i o n J , 22Q2% open area G H O 0-250 A 0-389 • 0.528 v 0-667 2 o 9 o O A • v v v v o ^ O A g 6 D ^ v v o 8 o A • • • V V V V 8 • v 6 m -12 -8 ^4 ' 0 4 8 ' f2 ' 1*6 F i g o 31o C L VS §C for a i r f o i l with double slotted flap* Wall configuration B, 25o9$ open area 2-4 2 0 1-6 c L 1-21 o A D V 0 - 2 5 0 0 - 3 8 9 0 - 5 2 8 0 - 6 6 7 ° 2 O A O A D o 2 2 ^ o ° ° A D o A n o A • v V o A V o A 8 A ^ 1^ ^ I SI 0 O A 8 A ftv^ • - 8 4 0 V • S O — 4 t - 1 6 - 1 2 - 8 - 4 0 ©C 4 8 1 2 1 6 F i g o 3 2 o C L vs @< for a i r f o i l with double slotted flap, Wall configuration A, 2906% open area 2 0 2 4 © A m v H 0 . 2 5 0 0 - 3 8 9 0 . 5 2 8 0 - 6 6 7 ED • • • A D • V V V A V V V o o o o o o o • Q • • V A • 0 v O v O v J v E § ° o o © © o " V v1 v v v _ f I A V A B v v 1 v A A O Q © o © ® 13 I $ A © © Q v  I © 0 - 1 6 - 1 2 - 8 -4 0 8 1 12 1 6 F i g o 33o Cuc/^ V S for a i r f o i l with double slotted f l a p c Wall configuration H, 11 01$ open area 2 0 0 • V O o 0 O 15 V E3 v B V A A A V A O O O O o © O o o o o 0 8 12 1 6 2 0 F i g o 3ho C^cA v s ®£ f o r a i r f o i l with double slotted flap< Wall configuration G, lk08% open area j 2 4 •^ 0 ON c H 0-250 0-389 0-528 0-667 © o A A A „ | a a o A A • * V v v | 9 * A o o o A © © © © 0 g A $ A A A A A A A ° D I S I 9 » 1 I • © © © ® © © © © © © © V © -1 2 -8 -4 0 8 12 F i g o 35» c M c A v s ^ f o r a i r f o i l with double s l o t t e d flap, Wall configuration I, l8<,5$ open area I m a A V V O O £ a • A A a B 8 v v v o „ 0 o o o E A V D v O o o © ® o o o o A • Q V v © Q E I A Q A O 0 m o 9 I - 1 6 - 1 2 - 8 -4 0 4 oC 8 1 2 16 Figo 3 6 o CKc/^ vs f o r a i r f o i l with double s l o t t e d flap, Wall configuration B ? 25o9$ open area 2 0 4 - C , Mc/4 • 3 © —! C H 0 - 2 5 0 0 - 3 8 9 0 - 5 2 8 0 - 6 6 7 A A A V Q • O v v v o o © 3 v V V A • © 13 V o o V1 A V O 8 5 A V © A H © © V O • V D V A V © • 5 0 g O v • OO © © AA AA v v v $ v g V JL J_ - 1 6 1 - 1 2 1 4 8 12 1 16 Figo 37o C M c > ^ . vs f o r a i r f o i l w i t h double s l o t t e d f l a p , Wall c o n f i g u r a t i o n A, 290.6% open area 2 0 c H o 0 . 2 5 0 • 0 . 3 8 9 A 0 . 5 2 8 O 0 - 6 6 7 a a i e o a 6 8 Q 8 o o • o o o • o 6 O o D O o A • O o A • oo o A • o <0 A • o o o D o A - 1 2 - 8 - 4 0 8 1 2 16 2 0 Figo 380 C D vs ©C for a i r f o i l with double slotted f l a p D Wall configuration H, 11 01$ open area 24 c H o 0 . 2 5 0 o 0 - 3 8 9 A 0 - 5 2 8 O 0 - 6 6 7 - 1 2 - 8 - 4 0 4 ^ 8 12 16 F i g o 59° C D vs for a i r f o i l with double s l o t t e d f l a p 0 Wall configuration G s lh0o\% open area 0 - 2 5 0 0 - 3 8 9 0 - 5 2 8 0 - 6 6 7 E A O • V V V A .8 o o o o =12 - 8 ' = 4 0 4 @<0 8 1 2 1 6 F i g o ^ 0 o C D V S f o r a i r f o i l with'double s l o t t e d f l a p o Wall c o n f i g u r a t i o n I , l 8 E 5 $ open a r e a 2 0 1 . 2 1 - 0 • A c H 0 . 2 5 0 0 - 3 8 9 0 . 5 2 8 0 - 6 6 7 6 • o o . 8 'D •6 o & o o o e 0 o § § o o o * o i3 - 1 2 8 - 4 0 8 12 16 Fig» hle V S ©4 for a i r f o i l with double s l o t t e d flap. Wall configuration B, 25o9% open area 2 0 2 4 H o 0 - 2 5 0 • 0 . 5 8 9 A 0 . 5 2 8 O 0 - 6 6 7 - 6 •4 & $ [^ <& B$ • V O O <§> • o o o o o 6 o 0« 1 1 1 - 1 6 - 1 2 - 8 -4 1 0 4 8 12 16 Figo h2o C D vs f o r a i r f o i l with double s l o t t e d f l a p Q Wall configuration A, 2906% open area 1-2 0 I t c H o 0 - 2 5 0 A 0 - 3 8 9 • 0 - 5 2 8 v 0 - 6 6 7 f - 1 ' V 1 -• V t 3 \ V 7 i O • [ i A V ] a • V 7 -1 ( © 3 ) i A > o 0 q ( A , ) o * A A -- -- I -I » a 1 i - 1 • - 8 - 4 0 4 8 ® 1 2 1 6 2 0 2 4 2 8 ^ OC Figo h3o C L vs $C f o r basic a i r f o i l o Wall configuration P, 5o5% open area 2 0 1-6 1-2 'I •8 -j — — j — — r — — i 1 c H o 0 -2 5 0 A 0 - 3 8 9 • 0 - 5 2 8 v 0 - 6 6 7 k  » i 1— y 1 --' V V V --I ! 3 0 ' j o o o c ] u -} u u • r -< a > -1 B i « - i n n -0 - - 4 1 - 8 -i 0 8 oC 12 1 6 2 0 2 4 2 8 F i g o hh0 C L vs f o r b a s i c a i r f o i l o Wall c o n f i g u r a t i o n H , 11„1$ open area 1 2 . 4 «— -C H o 0 - 2 5 0 A 0 - 3 8 9 ° 0 - 5 2 8 v 0 6 6 7 • 1 1 — r — 1 ll i --- o o 1 > 9 o c i . A B 9 * ) O ° r ! S v v A I A A 1 1 D H -< o i o S A > V n • c t o < A • >-- -i 1 i i « ' • ! i ! i ! I I » » j I I I i I  I Jl I I - 8 - 4 0 4 , o 8 12 16 2 0 2 4 Figo- h5<> C L vs f o r b a s i c a i r f o i l o Wall c o n f i g u r a t i o n I , 18<,5$ open area •4 0 f . . c . H © 0-250 A 0-389 a 0-528 v 0-667 i i 1 " K i "—*= • -• 0 E i © « ! I a 1 1 © © © r I V ID in 0 c A A ^ V V -c o ^ A \ v - ° \ A 5 - s 0 : 1 ' a s i « 1 • I -8 -4 0 4 8 12 16 20 24 Figo * f 6 o C L vs ©€ f o r b a s i c a i r f o i l o Wall c o n f i g u r a t i o n E , 1 8 0 5 # open a r e a Figo. h?o C M c / 1 + ys a< f o r basic a i r f o i l o Wall configuration F, 5 o 5 % open area 9 0 3> O O 00 K » 0 CO CN « 0 CN co in o CD CD CD CD © <J E !> i — ^ — i — 1 — r > © > ES3 © t> H < © >• <1© > O <3 © O • < O ' > • © X © £0 CSO > E 3 lis] 0 CN O CN CN I o •H (0 £j P bO •H o o H rH crj 0 H •H O « H f « •H as o •H to a) . a U cd o CD X CD W ft > o O O rH 6 00 6 bO •H CN O CN ^ CN o 0-250 0 389 0-528 0-667 V V V 8 s ® • A o © © © A © V V © a A ^OA d 1 A l l • © A ^9o C M c /^. vs@C f o r b a s i c a i r f o i l o Wall c o n f i g u r a t i o n I , 1&O5% open area • 3 2 C. 1 6 •08 r 0 s © © 0 - 2 5 0 A 0 - 3 8 9 a 0 - 5 2 8 v 0 -i t t ? i F i g o 5o0 C D vs A © m 1 i v A V B A © A 5 1 13 A m B © 4 0 4 ^ 8 1 2 1 6 2 0 2 4 f o r basic a i r f o i l 0 Wall configuration.P, 5.5% open area ro .48 . 4 0 C • 3 2 D . 2 4 » 0 8 A 0-3 8 9 • 0 - 5 2 8 v 0-6 6 7 1—r V 8 O V v B o o o V • v • D A A O A O o 6 • A O o • A O A O o 1 2 2 0 2^ Fig 0, 510. % vs for &asie a i r f o i l o Wall configuration I l d f e open area . 4 0 • 32 C D • 24 ,0! C' H o 0 . 2 5 0 A 0-389 • 0-528 v 0-667 0 o V • • D 0 6 V 0 a A o • A o 6 6 o § o i i oC 12 16 20 24 F i g 0 , 520 Cj) vs ©C f o r basic a i r f o i l o Wall configuration I 5 1805% open area o A • V c H 0-250 0.389 0. 528 0-667 9 A O E3 A A S V • A ,oooo ES 9 A ^ £3 O O Q O D 9 A A @ 9 • 9 9 1 16 C L vs ©C f o r a i r f o i l w ith double s l o t t e d f l a p , Wall c o n f i g u r a t i o n T , 1 8 0 % open a r e a 3-2 2.8 2.4 2-0 1-6| 1-2 •8 .4 0 -.2 i — 8 — r c H O 0.250 A 0-389 • 0.528 v 0-667 A 6 9 v U o A 1 -16 -12 El S V 0 V v w H H A v A g o o V • A O o o S • A ^ v. Jfr w • H • • o o 4 c*L° 8 12 16 20 F i g o 5^o C L vs ©€ for a i r f o i l w i t h double s l o t t e d f l a p Q Wall configuration U , 23 Olfo open area ON 24 H .250 . 3 8 9 528 6 6 7 V A v A. y o ° ° o o o o o X v o o o o o V g 1 a A t A ° ° o OOO 0 ° F i g o 55o C^cA vs © t for a i r f o i l with double slotted f lap c Wall configuration T, 18.5$ open area H •250 • 389 •528 •667 A A O O O A A A B O O ° o v O • ° o o o o v AA • • W v CD 6 o F i g o 56o C ^ / ^ vs ©C f o r a i r f o i l w i t h double s l o t t e d f l a p 0 Wall c o n f i g u r a t i o n U , 2301% open area 2 C H © 0 . 2 5 0 A 0 - 3 8 9 s 0 - 5 2 8 v 0 - 6 6 7 A v a • v I— ^ e S V A V • A ®EB A I J I D O A 8 0 6 o & A A © O A O O © o o V f EJ A V • A v g A O 2 A o © o V A © A -I - 1 6 12 - 8 - 4 0 4 8 12 1 6 2 0 2 4 F i g o - 57° C D vs f o r a i r f o i l with double slotted f l a p Wall configuration T, 18«,5# opert area I J i I c H ~~ © 0 . 2 5 0 A 0 . 3 8 9 L • 0 . 5 2 8 • 0 . 6 6 7 A 1 1 I r — | — 1 — I— !—!— 1— I — > — 1 — r J . L A - - n 8 fi I 1 © e ° m v V ® © A A © 7 a © V A f ® - 1 6 - 1 2 - 8 - 4 0 4 8 12 16 2 0 2 4 oC F i g . 58., C D vs ©C for a i r f o i l with double slotted f l a p . Wall configuration U 9 23.1$ open area c H O 0-250 A 0-38 9 • 0.528 v 0-6 6 7 o o 5 A V 8 V • A A v o D A A A o oo OO O • P 6 A • 6 5 B v S v o o o A A A o oo o o 1 1 -12 - 8 -4 0 4 oC° 8 ]2 1~6 F i g o 59° CL vs oC f o r a i r f o i l with double s l o t t e d f l a p , l i " holes perforated walls, 12,3% open area 2 8 2 4 2 0 1 -2 0 C H o 0 - 2 5 0 g A 0 3 8 9 H g A A • 0 . 5 2 8 J v o o o° v 0 - 6 6 7 g o • V o A 2 V O A V V O A • „ ° o 1 ^ A A • A • ° C L • § U • • A @ • 8 l — * § A 8 O A - J — 8—1 — i — 1—i—1 — i — I — i 1 i i i l ' i I - 1 6 - 1 2 = 8 = 4 0 4 8 12 16 F i g o 6offl C L vs ©C f o r a i r f o i l w i t h double s l o t t e d f l a p . 1" h o l e s p e r f o r a t e d w a l l s , lh05% open a r e a 0.250 0 -389 0.528 0 6 6 7 A 9 o o V V o o n o o 6 o o o o o o 0 o V 8 X • o o o 12 F i g o , 6 l o C M c / l f , v s © 4 for a i r f o i l with double slot t e d l i " holes perforated walls, 12*3$ open area .250 .389 °528 A A • A V v v o o A 9 o o o o o o o o o o o o o A a • n M X A „ v ° o . o o oo°°oo 0 F i g o 6 2 o C M c / l f vs ©C for airfoil w i t h double slotted flap, 1 " holes perforated walls, lka5% open area 1 . 2 f 1 . 0 •8 C H • 0 - 2 5 0 A 0 - 3 8 9 a 0 - 5 2 8 v 0 - 6 6 7 A A A @ D A « m ® g I 8 si; © o o v I S g s „ „ V 0 1 A A 0 S O 0 A © O O ° ° V 2 V I © o © © 0 l L - 1 6 1 2 - 8 - 4 0 4 ,o 8 12 16 2 0 F i g o 63o- C D vs f o r a i r f o i l with double s l o t t e d flap, l i - " holes perforated walls, 12e3$ open area 2 4 H O 0 c H o 0 . 2 5 0 A 0 . 3 8 9 o 0 . 5 2 8 v 0 . 6 6 7 S Q u 6 - 1 6 - 1 2 s - 8 s # ° o o 2 9 o 0 A o v • o o o o V a V A V a V • A D A o A O o O o V • o o © -•SHI v -v a • E A A A A O o • 4 y o 8 oC 12 16 2 0 F i g o 6 V o . C D vs ©C f o r a i r f o i l - with double slott e d flap, 1" holes perforated walls, lha5% open area 2 4 H O ON 1 Oi 107 0 9 0 8 _ 0 7 d Q 6U, . 0 5 .04 h . 0 3 .02 .01 d C L -r± f o r - 5 < c * < 5 dot O A © V o % o p e n a r e a 2 9 . 6 2 5 - 9 1 6 - 7 2 0 - 4 1 8 - 5 1 4 - 8 1 1-1 18 -5 2 2.2 0 • c o n f i g u r a t i o n A B C D E G H I J O v O 1 o i _ J FIg 8 65. dC L/d©4 vs C/H f o r a i r f o i l with double s l o t t e d f l a p e Longitudinally slotted side walls .1 O r — i r • 0 9 •08 <P corrected • 0 7 dc* 06 05 0 4 0 3 02 •01 © • V A O dC. j - t for -5 <c* 15 c o - 2 5 0 A . 3 8 9 • - 5 2 8 v -667 • A O o 2 0 percentage open area O A 3 0 F i g , 6 6 0 dCi/d@£ vs % open area f o r a i r f o i l with double slotted f l a p . Longitudinally slotted side walls 109 T r 1 -l 1 i r c o r r e c t e d O • v • 2 5 0 • 3 8 9 • 5 2 8 • 6 6 7 V • • A O V V • • A A « O H A o v m v 8 o 0 30 10 20 percentage o p e n a r e a 67• GLmax v s ^ o p e n a r e a f o r a i r f o i l M h d 0 U D l e slotted flap, Longitudinally slotted side walls • 5 A 1(1— • o o B v 0 6 V S v cor rec ted 2 o A • V c H 0-250 0-389 0-528 0-667 1 _ L 10 2 0 3 0 percentage open area F i g o 68o C M C / L. vs % open area for a i r f o i l with double slot t e d flap< l o n g i t u d i n a l l y slotted side walls M H O corrected r X = 5 v v v v o A • o A oC=-5 • V 10 2 0 p e r c e n t a g e of open a r e a A 0 - 3 8 9 • 0 - 5 2 8 • 0 - 6 6 7 1 0 2 0 3 p e r c e n t a g e of o p e n a r e a . 69 * S h i f t i n C L for a i r f o i l with double slotted f l a p due to l o n g i t u d i n a l s l o t s doc • 01 0 • 11 — .10 — o o .09 — m a 08 — <m o 07 — °l 06 — lo o p e n a r e a c o n f i g u r a t i o n ® 0 — a 5 5 F 05 <$> 11.1 H - O 1 8 5 E .04 • 1 8 - 5 | O c o r r e c t e d 03 d C L for -5 < 5 d a : 02 2 3 C H o • • o Q F i g . 70o dCi/d©C vs C/H f o r b a s i c a i r f o i l o L o n g i t u d i n a l l y s l o t t e d s i d e w a l l s 113 l-2i -c 8 Mc/4 4 h S o cor rec ted 2 - 4 2-Oj 1 - 6 ( max 1-2 •8 f 0 0 J I I L J L • O O G H O 0 - 2 5 0 A 0 - 3 8 9 • 0 - 5 2 8 v 0 - 6 6 7 j L J i i L o cor rec ted J= i • > 10 2 0 percentage of open area J L 3 0 F i g . 71. Effects of lon g i t u d i n a l s l o t s on C^/^ and C L m a x for basic a i r f o i l 1-6 1-. 8 •8 c • 4 0 c H O 0 . 2 5 0 A 0 - 3 8 9 • 0 -5 2 8 v ° ' 6 6 7 corrected o =5 > - 5 o J L I I I ! ! _ ! ! ! * l l • • v J i i 0 1 0 2 0 3 0 peccentage of open a r e a F i g o 72o S h i f t i n C L for basic a i r f o i l due to lon g i t u d i n a l s l o t s 115 10 . 0 9 0 8 . 0 7 dcL doc •06 . 0 5 • 0 4 •03 • 0 2 • 01 r o © E3 o O V • A o © © o % o p e n a r e a 0 c o nf i g u r a t i o n 9 - 2 6 1 0 . 0 1 0 . 0 2 0 . 8 1 8 - 5 2 3 1 c o r r e c t e d O , P R S T U ^ L L f o r - 5 < oC < 5 dot J i L c H @ • 9 J • 7 F i g o 73o dCL/d©C vs C/H f o r a i r f o i l w ith double s l o t t e d f l a p 0 T r a n s v e r s e l y s l o t t e d s i d e w a l l s 116 l r i p — ¥ c H O 0-250 A 0.389 • 0-528 v 0-667 dC L v f o r -5 < oc < 5 dc< c o r r e c t e d ! o v. v # o © Q v 0 10 2 0 30 percentage of open a r e a F i g . 7*+« dCx/d®£ vs % open area for a i r f o i l with double slott e d f l a p 0 Transversely slotted side walls 117 "i 1 r 1 1 1 r 3 - 6 r — 3.2>P-2-8 0) 2-4 "Lmax 2-0 1-6 1*2 • 8 k -0 • A ) O c H O 0 - 2 5 0 A 0 - 3 8 9 • 0 - 5 2 8 v 0 - 6 6 7 J L • A O V J I L • A corrected 1 0 10 2 0 3 0 p e r c e n t a g e of open a r e a F i g o 75° cLmax v s ^ open a r e a f o r a i r f o i l w i t h double s l o t t e d f l a p 0 T r a n s v e r s e l y s l o t t e d s i d e w a l l s 1 oo c H O 0 - 2 5 0 A 0 - 3 8 9 • 0 - 5 2 8 v 0 - 6 6 7 I I o o o 1 correc • 3 0 1 0 2 0 percentage of open a r e a F i g o 76 0 vs % open area f o r a i r f o i l with double slotted f l a p o Transversely s l o t t e d side walls 119 2 - 2 C H O 0 - 2 5 0 A 0 - 3 8 9 • 0 - 5 2 8 • 0 - 6 6 7 OO • o corrected 1 - 8 1-4 fc o v m tl 6 1-0 J L J I I L 1.4| C H O 0 - 2 5 0 A 0 - 3 8 9 • 0 - 5 2 8 • 0 - 6 6 7 O 9 J L corrected S § j c < r O J I 1 1 I ' I I I I L 1 0 2 0 • percentage of open area F i g . 7 7 . S h i f t i n C L for a i r f o i l with double plotted f l a p due to transverse slots 3 0 .1 0 • 0 9 • 0 8 0 6 doc •051 . 0 4 0 2 0 1 O a A 7 ° P e n con f igura t ion a r e a O 1 2 - 2 7 1 5 holes A 1 4 - 5 0 l " holes 3 " • 1 6 - 7 0 1 ^ holes 0 3 | _ v 1 8 - 4 0 1 1" holes d C , — for - 5 <oc <5 C H O 0 7 h v • n — • L—' 1 — ! — 1 — i I i L 0 .1 - 2 - 3 - 4 . 5 J F i g * 7 8 e dC L/d©C V S C/H for a i r f o i l with double slott e d f l a p . Perforated walls 121 3.6 3 . 2 2.8 2 . 4 'Lmax 2.0 1.6 1.2 .8 . 4 T r 1 -T - T 1 I I i r .1 o A • O ° P e n con f igura t ion a r e a 1 2 - 2 7 1 4 - 5 0 1 6 - 7 0 1 8 - 4 0 I \ holes l " holes l 4 holes l I holes o J L O A i i I L .2 . 3 •, . 4 C H . 5 i i I I .6 . 7 F l g 7 g 8 c vs C/H for a i r f o i l with double slotted flap'. B ° ' Lmax Perforated walls H O 0-250 A 0.389 • 0.528 v 0-667 v v o o o -I 1 I 1 L I I i J_ 10 20 30 '.• 40 percentage of open area F i g . 80o Cj^/^ vs % open area for a i r f o i l double slotted f l a p e Perforated walls 

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