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An experimental study of flow about an airfoil with slotted flap and spoiler using Joukowsky profiles Allan, William D. E. 1988

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AN EXPERIMENTAL STUDY OF FLOW ABOUT AN AIRFOIL WITH SLOTTED FLAP AND SPOILER USING JOUKOWSKY PROFILES by William D.E. ALLAN B.Eng., Royal Military College, 1986  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineering  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April, 1988  ©William D.E. ALLAN, 1988  In presenting degree  this  at the  freely available copying  of  publication  or of  in  partial  University  of  British Columbia,  for reference  this  department  thesis  thesis by  this  his  for or  and study. scholarly her  Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  DE-6(3/81)  2i  AP£  of  the  I agree  requirements  for  may be  representatives.  It  is  fifi  advanced  that the Library shall make it  I further agree that permission  purposes  an  granted  by the  understood  for  extensive  head  that  thesis for financial gain shall not be allowed without  permission.  Date  fulfilment  of  my  copying  or  my written  ABSTRACT  An e x p e r i m e n t a l s t u d y has been c a r r i e d out on an a i r f o i l slotted  f l a p and s p o i l e r u s i n g Joukowsky p r o f i l e s .  t i o n s were measured as f u n c t i o n s angle,  The r e s u l t s  wind t u n n e l w a l l e f f e c t s but the d a t a base i s corrections.  The r e s u l t s  t h e o r e t i c a l model, yet  deflection  are uncorrected for  a v a i l a b l e t o c a r r y out  the  t o be worked o u t , which combines work p r e v i o u s l y P a r k i n s o n and Yeung.  flow about a two-element  The secondary a i r f o i l  flap  w i l l be used t o compare w i t h p r e d i c t i o n s o f a  done by W i l l i a m s , J a n d a l i , the p o t e n t i a l  Pressure d i s t r i b u -  of angle o f a t t a c k ,  s p o i l e r s i z e and i n c l i n a t i o n .  with  is  This theory w i l l  'near'-Joukowsky a i r f o i l  a simulated s l o t t e d  flap.  involve  system.  Various size  spoilers  are i n t r o d u c e d t o the system a t a r b i t r a r y a n g l e s of i n c l i n a t i o n u s i n g methods proposed by P a r k i n s o n and Yeung. The e x p e r i m e n t a l r e s u l t s interesting  effects  with slotted  flaps  are q u a l i t a t i v e l y r e a s o n a b l e  are o b s e r v e d .  The b e h a v i o u r o f s p o i l e r s ,  at v a r i o u s d e f l e c t i o n  angles,  a t t a c k which i s  flaps  alone p r o v i d e s the h i g h l i f t  beneficial  to a i r c r a f t taking o f f .  a r e proposed f o r f u r t h e r t e s t i n g  with t h i s  when used  corresponds w e l l  r e q u i r e m e n t s o f a i r c r a f t i n approach or l a n d i n g s i t u a t i o n s . the use o f s l o t t e d  and some  with  Similarly,  a t low a n g l e  of  Some recommendations  equipment.  TABLE OF CONTENTS Page  ABSTRACT  i i  LIST OF FIGURES  v  LIST OF SYMBOLS  vii  ACKNOWLEDGEMENT  viii  1.  INTRODUCTION  2.  THEORY 2.1 2.2 2.3 2.4 2.5  1  Two Circles in Uniform Flow Two Circles with Arbitrary Circulation Producing Two 'Near-Joukowsky' Airfoils The Introduction of a Normal Spoiler To Obtain Arbitrarily Inclined Spoilers  3.  APPARATUS  4.  EXPERIMENTATION 4.1 4.2 4.3  5.  16  The Process Uncertainties Wind Tunnel Wall Corrections  OBSERVATIONS  3 5 9 10 14  AND  22 25 26  RESULTS  5.1  General Configuration Phenomena  5.1.1 5.1.2 5.1.3 5.1.4 5.1.5 5.1.6 5.1.7  Trailing Edge of Main Joukowsky A i r f o i l Blockage Effects by Flap External A i r f o i l Flap Leading Edge Curvature Effects Coefficients of L i f t Versus Angle of Attack 'Single-Airfoil' Tendencies Trailing Edge Data Points Flap Upper Surface and Spoiler Back Pressure Correlation  5.2  Separation Effects  5.2.1 5.2.2 5.2.3 5.2.4 5.2.5 5.2.6  Unseparated Flow Separation on the Lower Flap Surface Separation on the Trailing Upper Flap Surface Pre-Spoiler Separation Bubble Separation on the Trailing Upper Wing Surface Leading Edge Separation Bubble - iii -  28 28 31 32 32 35 35 37 37 40 40 43 43  TABLE OF CONTENTS (Continued)  Page  5.3  Flap Effects  5.3.1  Flap Effects on Coefficient of L i f t  5.3.2  Flap Deflection Angle Comparison  5.A  Spoiler Effects  5.4.1 5.4.2 5.4.3 5.4.4 5.5  Curve F i t t i n g on Spoiler Back Pressure C o e f f i c i e n t s . . L i f t Coefficients with Spoilers Extended Spoiler Effects on Pressure D i s t r i b u t i o n Effects of Spoiler Size Effects of Spoiler Use with Slotted Flap  50 53 53 57  5.5.1 5.5.2  Effects of Flap Deflection Angle with 10% Spoiler . . . Flap Effects on L i f t Coefficient with Spoiler Extended Spoiler I n c l i n a t i o n Angle Effects with Flap Deflected Effects of Spoiler Size Changes with Flap Deflected..  57  5.5.3 5.5.4  '  46 46  63 63 67  6.  DISCUSSION AND CONCLUSIONS  70  7.  RECOMMENDATIONS  73  REFERENCES  76  APPENDIX A  - CALCULATIONS FOR FLAP CONSTRUCTION  77  APPENDIX B  - REYNOLDS NUMBER CALCULATIONS  81  APPENDIX C - COEFFICIENT OF LIFT CALCULATIONS  83  APPENDIX D - C vs o SLOPE CALCULATIONS  85  APPENDIX E  86  L  - THE JOUKOWSKY TRANSFORMATION  APPENDIX F - ERROR ESTIMATES  88  - iv -  LIST OF FIGURES Page 3.1(a)  Conventional Slotted Flap  17  (b) Two-Element Joukowsky A i r f o i l  17  3.2  Experimental Section  18  3.3  Experimental 'Optimum Gap and Overlap'  20  A.l  Data Acquisition Schematic  23  Pressure Distribution Plots 5.1  no spoiler  a=0°,  6=0°  29  5.2  no spoiler  a=A°,  6=0°  30  5.A  no spoiler  a=A°,  6=20°  3A  5.5  10% spoiler  a=0°,  6=0°  5.6  no spoiler  a=0°,  6=10°  38  5.7  no spoiler  a=2°,  6=-10°  39  5.8  no spoiler  a=-A°,  6=30°  Al  5.9  7% spoiler  o=6°,  6=10°  5.10  no spoiler  o=12°,  6=0°  AA  5.11  no spoiler  a=8°,  6=0°  A5  5.13  no spoiler  a=0°,  6=20°  A8  5.1A  no spoiler  o=A°,  varying 6  A9  5.15  7% spoiler  a=8°,  6=0°  £=90°  51  5.16  10% spoiler  a=8°,  6=0°  £=90°  52  5.18  no spoiler & 10% spoiler  a=A°,  6=20°  55  5.19  no spoiler & 10% spoiler  o=8°,  6=20°  56  5.20  7% & 10% spoiler  o=A°,  6=20°  58  5.21  7% i 10% spoiler  a=8°,  6=20°  59  5.22  10% spoiler  o=A°,  Varying 6  £=90°  60  5.23  10% spoiler  a=8°,  Varying 6  £=90°  62  5.25  10% spoiler  o=8°,  6=20°  varying £. 65  5.27  Varying spoiler size  a=A°,  6=20°  £=90° .... 68  - v-  £=90°  E=90°  36  A2  LIST OF FIGURES (Continued) Page  C  L  vs a P l o t s  573  ncTspoiler  6=0°  33  5.12  no s p o i l e r  varying 6  47  5.17  10%  spoiler  6=20°  54  5.24  10%  spoiler  Varying 6  £=90°  64  5.26  10%  spoiler  6=20°  varying I.  66  5.28  Varying  6=20°  £=90° . . . .  69  spoiler size  - vi  -  LIST OF SYMBOLS  a  radius of main circle used i n theory  b  radius of secondary circle used in theory  c  centre of secondary circle used in theory  C  chord ... sum of main a i r f o i l and flap chords  C  n  2-D coefficient of drag  Cj  chord of flap  C  2-D coefficient of l i f t  L  C£  corrected 2-D coefficient of l i f t  C  mc/4  coefficient of moment at the quarter-chord position  Cp  coefficient of pressure  C P C pav C  corrected coefficient of pressure average C p chord of wing  g  gravitational acceleration  h  manometer f l u i d height  H  span of aerofoil  Q  dynamic pressure  Re  Reynolds number  U  free stream velocity approaching a i r f o i l  V  free stream velocity i n wind tunnel  a  angle of attack or incidence  o  flap deflection angle, down i s positive  c  solid blockage factor in wall corrections = Ao  T  general circulation  r  specific circulation about main a i r f o i l  I*  specific circulation about flap a i r f o i l  A  a i r f o i l shape factor used in wall corrections  o 'a o "w o  density of air density of water  v  kinematic viscosity of air  w  £  a  r  6  TTV48  (C/H)  j  parameter from wall correction theory  spoiler inclination angle  - vii -  ACKNOWLEDGEMENT  T h i s r e s e a r c h work has been c o n f i n e d t o a v e r y s h o r t time span due to unforeseen  circumstances.  In view o f t h i s ,  support was thrown b e h i n d me by the s t a f f  enthusiastic  and f e l l o w  and r e l i a b l e  graduate  students  a t the U n i v e r s i t y o f B r i t i s h Columbia. Dave Camp from the M e c h a n i c a l E n g i n e e r i n g Workshops was for  a successful  responsible  model produced i n r e c o r d time d e s p i t e c o n c u r r e n t  design  modifications. Capt.  (RCAF R e t ' d )  G e r r y Desroches was i n v a l u a b l e i n d a t a  t i o n ; he d e d i c a t e d h i m s e l f ,  i n h i s time away from a j o b a t T r a n s p o r t  Canada, and through h i s own i n i t i a t i v e , The  enthusiasm o f t h e s t a f f  Department does not go w i t h o u t was as p o s i t i v e l y The  affected  Natural Science  to t h i s  deep a p p r e c i a t i o n .  by t h i s ,  The work environment  as i t was n e g a t i v e l y ,  by t i m e .  and E n g i n e e r i n g Research C o u n c i l o f Canada  f u n d i n g f o r me t o complete  and  1987.  I regret that  project.  i n the M e c h a n i c a l E n g i n e e r i n g  provided f u l l September  collec-  t h i s work between September  I s h a l l not be p r e s e n t  t o p r o v i d e my f e l l o w  1986  graduate  s t u d e n t s i n M e c h a n i c a l E n g i n e e r i n g the same i n f o r m a l and f r i e n d l y support which I r e c e i v e d from them. Most worthy note i s  I am i n t h e i r  extended  g u i d i n g hand i n t h i s endeavour.  debt.  t o D r . G . V . P a r k i n s o n , my a d v i s o r and H i s c o o l and unwavering s u p p o r t ,  in  f a c e o f a l l the e x t r a o r d i n a r y c i r c u m s t a n c e s by which t h i s t h e s i s was completed would have won him renown as a l e a d e r i n my more f a m i l i a r m i l i t a r y world.  I t has been a g r e a t p r i v i l e g e t o work w i t h h i m .  - viii  -  the  1  CHAPTER 1 INTRODUCTION  The aerodynamics of various wing sections and their control surfaces has played an important role i n the Mechanical Engineering Department at the University of British Columbia for some years now. Theoretical studies have been carried out on spoilers and various types of flaps.  Experimental work has always been necessary as well, to  verify the theories proposed.  This particular study has concentrated on  the use of spoilers with slotted flaps. Spoilers are effective fences raised from the upper surface of the wing section.  They reduce circulation around the aerofoil which  contributes to a great reduction of l i f t and an augmentation of drag. One could see a use for these effects as air brakes or in the approach and landing of aircraft. As shown i n Fig. 3.1(a) they are of varying size and when closed, usually reach back to the trailing edge of the wing. They can be opened to any angle and are commonly used up to 60° deflection. Spoilers are frequently used i n conjunction with flaps of some type.  In this report, the effects of their use with slotted flaps i s  investigated.  Slotted flaps are individual a i r f o i l s which, when retrac-  ted, form to the trailing edge of the wing section i t s e l f , and when extended allow airflow between the new "trailing edge" of the wing and the leading edge of the flap (see Fig. 3.1(a)).  The flaps are used i n  the take-off and landing of aircraft. They effectively alter the camber of the a i r f o i l to create a higher l i f t wing. in measurably  higher drag as well.  This results, of course,  This plays an important role i n  2  reducing landing and take-off speeds.  This i s desirable for improved  safety and in reducing the runway length required to take off or land. As well, control i s retained, despite the increased ascent or descent angles of the aircraft. Both theoretical and experimental work has been completed on spoilers used alone, as well as i n conjunction with split flaps (refs. 6,16).  Studies have also been completed on simple and slotted flaps. To  further this work, the theory i s expected to be worked out for two-element aerofoils with spoilers.  This would make use of the Williams  methods (ref. 15) or producing an external a i r f o i l - f l a p , virtually a slotted flap behind a wing.  The work by Parkinson and Yeung (ref. 10) on  potential flow about spoilers w i l l be added to the aforementioned two-element systems to complete the theory.  Verification for this theory  w i l l be possible with the experiments conducted in this study, when the data are corrected for wind tunnel wall effects.  CHAPTER 2 THEORY  2.1  Two C i r c l e s i n Uniform Flow To o b t a i n c i r c l e s  i n uniform flow,  the Milne-Thomson t e c h n i q u e Ref.  8 i s used.  image d o u b l e t s  from  It effectively  uses  to place a c i r c l e of  r a d i u s b i n the v i c i n i t y o f a c i r c l e of  A c i r c l e of radius a i n  radius a.  u n i f o r m flow o f u n i t v e l o c i t y shown i n F i g . 2 . 1 ,  (2.1)  FAO  o  = Ce  is  plane £ .  i a  + f-  t  e^  Figure  2.1  a  To s i m p l y add a new c i r c l e o f r a d i u s b , t h e term (2.2)  is  added.  ,2 i a b e ... + C-c  (2.2)  T h i s term however a l t e r s shape o f the f i r s t c i r c l e o f a.  To m a i n t a i n i t s  the radius  o r i g i n a l shape a  c o u n t e r - b a l a n c i n g d o u b l e t must be p l a c e d i n s i d e the f i r s t is  circle.  This  the Milne-Thomson Technique from  Ref.  8  .2 (2.3)  b  2 C  2 -ia  a e  2 «-*->  Figure  2.3  The f i r s t  counter-balancing  d o u b l e t i s shown i n ( 3 ) . opposite  Note  its  s i g n t o (2) and i t has a 2  scaling factor b / c  2 .  S i n c e b<c i t s  v a l u e i s much l e s s t h a n 1. S i m i l a r l y , t h e d o u b l e t i n (2.1) alters  t h e shape o f t h e second  of radius b.  circle  A new image must be s e t  up a t C « c - — a c c o r d i n g t o t h e Milne-Thomson t e c h n i q u e ,  Figure  2.4  to regain  t h e second c i r c l e ' s o r i g i n a l shape, as shown i n F i g . 2 . 4 .  -ao (2.4)  «-<c  - f - »  f 2  ©  2  The new term (2.4) h a s , a / c  as t h e  b s c a l i n g f a c t o r , again l e s s than one. The s c a l i n g f a c t o r s a r e c o n v e r g i n g as is  expected,  not only  geometrically,  y  r  b u t i n magnitude as w e l l . As one p r o g r e s s e s  in this  manner, t h e image d o u b l e t s  diminish  i n s t r e n g t h and converge on p o i n t s  F i g u r e 2.5  V 2  5 inside the two circles near the outer bound. The next two terms are as follows:  (2.5)  ...+^ 2 c  ^ r2 - - a , b 2 (c - —)  2  2  (£  c  a  r  %  )  (c - b /c)  (shown i n Fig. 2.5)  vb a 2  (2.6)  2  1  / (c  a .2 --)  -ia e  • b  2  (t - (c -  r)) c -  (not shown to avoid clutter)  Each time the scaling factors are increasingly less than unity, promising convergence. The velocity field of this situation i s  dF  W (C) - ^  (2.7)  2.2  0  •  Two Circles with Arbitrary Circulation The Kutta condition entails a finite velocity or a stagnation point  at the trailing edges of a i r f o i l s .  To be i n keeping with reality one  avoids infinite velocity at the cusp of a Joukowsky trailing edge. To achieve this with the Joukowsky transformations, circulations must be introduced onto the two circles produced in part 1 of this theory section.  Once again an infinite convergent series i s encountered.  Two c i r c u l a t i o n s are r e q u i r e d f o r a two-element system.  T  Call  Joukowsky a i r f o i l c i r c u l a t i o n about  l  the main c i r c l e t h a t i s t h e main a i r f o i l .  t o be made i n t o  Let  be the  c i r c u l a t i o n about the s m a l l e r c i r c l e which w i l l become the f l a p . problem w i l l  be reduced t o  The two  complete i n f i n i t e convergent As b e f o r e ,  series.  the Milne-Thomson  C i r c l e Theorem from R e f . 8 i s  used,  Figure  2.6  but once a g a i n the r e s u l t i n g image c i r c u l a t i o n s must be accounted f o r . For s i m p l i c i t y , l e t is unity.  I = 2TT, SO I = 2n  ©  Now t o p l a c e c i r c u l a t i o n  about the l a r g e c i r c l e ;  (2.8)  FAO = iln(C) + iln(C-c)  - iln(C-(c - bVc)) . . .  where the l a s t  two terms  the image v o r t i c e s  represent  i n s i d e the s m a l l  c i r c l e caused by the presence o f v o r t e x a t the c e n t r e o f the circle,  shown i n F i g .  2.7.  large  the Figure  2.7  7  Once a g a i n an i n f i n i t e emerges,  series  w i t h terms 2 . 9 and 2 . 1 0  r e p r e s e n t i n g the f i r s t image p a i r i n s i d e the l a r g e c i r c l e , as i n F i g . 2.8  t  ©  2 (2.9)  . . . -iln(C -  (2.10)  . . . + iln(C -  f~)  2 8 2  c  The v e l o c i t y f i e l d  2  )  - b /c  Figure  is  2.8  dF. ( O (2.11)  Wjtf)  -  One must n o t e t h a t t h e s t r e n g t h does n o t d i m i n i s h i n t h i s series.  The o p p o s i t e p a i r s o f v o r t i c e s , however, do converge on t h e i r  complementary i n v e r s e p o i n t s .  The r e s u l t s  are n u l l vortex  which have c o n t r i b u t e d n o t h i n g t o t o t a l complex p o t e n t i a l . S i m i l a r l y f o r c i r c u l a t i o n about the s m a l l c i r c l e :  (2.12)  infinite  F (C) - ilnC + iln(C-c) a  -  - ilntt - aVc)  iln(C-(c - bVc))  + iln(C-(c c  + ...  2__)) a c  doublets  8  and s i m i l a r l y the v e l o c i t y f i e l d i s found by d e r i v a t i o n  dF, (2.13)  =  W,(C)  To combine the c i r c u l a t i o n s derived above with the c i r c l e s created i n part one of t h i s s e c t i o n , simple superposition i s required:  r (2.14)  W(r.)  = W (C)  r  + 2i i W  0  ( C )  +  2i * W  ( C )  The magnitudes of Tj and T are 3  determined, as s t a t e d above, from the Kutta c o n d i t i o n of f i n i t e v e l o c i t i e s at the t r a i l i n g edges of wing and f l a p s e c t i o n s , which correspond to zero v e l o c i t i e s at the respective  ©  p o i n t s i n the c i r c l e plane, Tj and T , as shown i n F i g . 2.9. 2  Boundary Conditions  r  1.  W(0  = 0 at Tj  2.  W(C)  = 0 at I ,  hv  (2.15)  With these boundary conditions i n (2.14), two unique equations for two unknowns T  l  and  T. 3  result  Figure 2.9  2.3  Producing Two 'Near-Joukowsky' Airfoils To obtain two Joukowsky a i r f o i l s from this existing state of two  circles with circulation in proximity, simply apply some translations, rotations, and the Joukowsky Transformation (Appendix E). The thickness and camber of the resulting a i r f o i l s i s dependent on the translations and rotations carried out. The gap between them is especially dependent on the circles' original distance apart (c-b)-a. To conserve the Kutta conditions, the axes about which  Figure 2.10  the Joukowsky Transformations are performed must pass through the stated points T  1  and T as 2  described above, and shown in Fig. 2.11. The Joukowsky Transformation is performed here to produce a Joukowsky main wing and a 'near circle'.  This slight alteration  in the shape of the smaller circle i s due to the small effects the Joukowsky Transformation does have at that relatively large distance from the origin.  New axes  Figure 2.11  are used to create the flap a i r f o i l at a different angle of incidence to the main a i r f o i l , as shown in Fig. 2.12. Now, the resulting two-element  J^"  Joukowsky a i r f o i l setup i s made up actually of two 'near Joukowsky' a i r f o i l s , as shown in Fig. 2.13.  The  Figure 2.12  main a i r f o i l i s not a true Joukowsky profile because i t has been slightly modified by the second use of the Joukowsky Transformation.  The flap's  shape i s slightly askew because i t originated from a 'near circle' not a perfect circle.  It would be a  perfect Joukowsky a i r f o i l had the f i r s t Joukowsky Transformation not  Figure 2.13  been carried out. To get the velocity field in this final configuration of two 'near Joukowsky' a i r f o i l s , one must simply manipulate the known flow field from (2.16),  (2.16)  2.4  v  *  ;  dz /dC 2  dZj/dZj • dZj/dz • dz dC  The Introduction of the Normal Spoiler To obtain a Joukowsky a i r f o i l with a normal spoiler, one must  simply apply the Joukowsky Transformation to a circle with a radial  fence.  Details for t h i s b r i e f  overview can be found i n Ref. 7. The Joukowsky Transformation i s of the form  (2.17)  Z = t + 1/t  The fence gets s l i g h t l y curved i n the transformation.  Figure  2.14  This i s not  undesirable because r e a l i s t i c a l l y , a spoiler retracts to form a section of the upper surface of the wing. This surface should be curved as well.  Points T and E i n F i g . 2.15  indicate the separation of flow. This i s i n keeping with a r e a l s i t u a t i o n when the working f l u i d ,  Figure 2.15  usually a i r , i s unable to achieve i n f i n i t e v e l o c i t y around the cusp of the t r a i l i n g edge and the spoiler.  The r e s u l t i n g  infinite  negative pressure gradient induces the separation. One must work backwards from the c i r c l e with r a d i a l fence shown i n F i g . 2.14 to obtain the flow f i e l d for the a i r f o i l with normal s p o i l e r .  Figure 2.16  I f one t r a n s l a t e s  the c i r c l e  to  12  1 ©  be c o n c e n t r i c w i t h the o r i g i n and rotates i t  t o p l a c e the r a d i a l  a l o n g the h o r i z o n t a l a x i s ,  fence  Fig.  2.16,  a Joukowsky T r a n s f o r m a t i o n can reduce the shape t o a f l a t p l a t e ,  Fig.  2.17.  Figure  2.17  The v e r t i c a l a x i s however does not b i s e c t the  ©  plate.  By t r a n s l a t i n g the o r i g i n t o centre of the p l a t e , p e r f o r m i n g an i n v e r s e  F i g . 2.18,  the  and  TT  Joukowsky  Transformation, a c i r c l e with s e p a r a t i o n p o i n t s can be Another r o t a t i o n v i l l  created.  2.18  Figure  2.20  indicate  p a r a l l e l uniform flow with a t T and E ( F i g .  Figure  separation  2.20).  C i r c u l a t i o n remains unchanged b y any o f t h e s e t r a n s f o r m a t i o n s it  can be i n t r o d u c e d a t t h i s  so  point.  The wake s o u r c e model as p r o p o s e d by P a r k i n s o n and J a n d a l i , (Ref.  9)  can be u t i l i z e d t o  create  t h e s t a g n a t i o n p o i n t s a t T and E . They a r e c r i t i c a l p o i n t s and hence a n g l e s w i l l be doubled i n the Joukowsky T r a n s f o r m a t i o n .  This w i l l  produce the r e q u i r e d t a n g e n t i a l s e p a r a t i o n a t the s p o i l e r and trailing  edge.  13  The flow in Fig. 2.20 can be produced by placing two double sources of arbitrary strengths on the bound of the circle and corresponding image sinks at the centre.  The double sources are required because half  of the strength i s expended in the interior of the circle, hence having no effect on external flow.  (2.18) F(C) = V(C + 1/C) + — In (C - e l ) + — l 6  IT  ln (C - e" 2) i6  TT  ir  V 2 Q  /TT  2TT  Equation 2.18 describes the potential flow field for Fig. 2.20. The unknowns are  ,Q  b^, b^ and T.  2>  Four boundary conditions  are known using stagnation points and assumed constant back pressure. This assumption i s that separation occurs at an empirical back pressure coefficient, C p  b  . Using Bernoulli's equation the complex normal  velocity of separation can be determined: W(C)  =0  at T  W(C)  =0  at E  -ISMi  - V —  U  |W(z)I U  = Vl-C  at T P  b  P  b  at E  where U is the free stream velocity approaching the a i r f o i l . One more boundary condition i s required to solve for a l l five unknowns. This problem can be overcome by assuming a location for one of the sources as done by Jandali and Parkinson in Ref. 7.  Parkinson  and Yeung proposed a suitable f i f t h boundary condition in Ref. 10. w  r  =  v  ^  d  z  =  w(C)  dC = 0  Subscript  'w' i n d i c a t e s  wake.  T h i s i s based on the f a c t  i n the wake r e g i o n makes no c o n t r i b u t i o n t o the a i r f o i l which i s  o n l y dependent  trailing  edge.  This i s  into real circles  circulation,  can extend from the  13.  contemporary  T h i s p r o c e s s b a s i c a l l y reforms  'near*  Inclined  T  From a Joukowsky a i r f o i l w i t h an F i g . 2.21,  that i n c l i n a t i o n i s  where  l e s s than 90  d e g r e e s , one roust degenerate  the  airfoil  back t o a c i r c l e u s i n g an  inverse  Joukowsky t r a n s f o r m a t i o n .  Figure  2.21  Figure  2.22  The s p o i l e r w i l l t h e n become a n o n radial  fence,  Fig.  2.22.  By t r a n s l a t i n g t h i s  form one can  be i n a p o s i t i o n t o use the KarmanT r e f f t z mapping  (2.19)  circles  again.  To O b t a i n A r b i t r a r i l y Spoilers  inclined spoiler,  theoretical  done by the i n t r o d u c t i o n o f a method proposed by  Theodorsen i n R e f .  2.5  analysis  o f Joukowsky a i r f o i l s t o the a c t u a l shapes of  airfoils.  flow  on the flow upstream of the s p o i l e r t i p and the  I t must be noted t h a t t h i s shape  t h a t the  s = i R s i n I cot(w/2)  '0  4 This reduces Fig. 2.23 to a bounded flow with a semi-infinite plate parallel to the flow as shown i n Fig. 2.24.  (  y  Parkinson and Yeung  developed this method thoroughly i n Ref. 10.  Y  Figure 2.23  The inside of Fig. 2.24  maps to the outside of the circle.  0  4  Now a Schwarz-Christoffel Transformation w i l l map the inter-  E"  ior of Fig. 2.24 into the upper half complex plane.  The parameters i n  Equation 2.20 are shown i n Fig. 2.24.  (2.20)  u  = - | (2-n) + i h  Tl h i  (n-2)TT  2  "2"  - f [n l n (£ + 1) 2 n Figure 2.24 + (2-n) l n  2-n  - 1)]  ©  To complete the set of mappings a translation, a scaling, a bilinear transformation and a rotation w i l l map the upper half plane i n Fig. 2.25  ~7—7—7—7—r  y y  to the outside of a unit circle.  Figure 2.25  -?—/  J  S /  16 CHAPTER 3 APPARATUS  Slotted flaps, as shown in Fig. 3.1(a), normally are nested in the trailing edge of the main wing section.  This study's major approxima-  tion i s the use of a two-element a i r f o i l to simulate a slotted flap. Joukowsky a i r f o i l s are used for simpler mathematical modelling. Hence the experimental setup has a small Joukowsky a i r f o i l tucked in behind a larger Joukowsky wing section (Fig. 3.1(b)). Because pressure distribution data was the ultimate goal for experiments in this study, a maximum number of pressure taps was desirable.  This entailed the largest possible flap to be built, s t i l l  staying within the reasonable bounds set by flaps in use today. The largest realistic chord of a slotted flap i s 30% of the wing total chord.  It should be noted that the wing chord i s the sum of the  chords of the flap and the main a i r f o i l .  So i n a two-element wing  section, the sum of the chords of the large and small a i r f o i l s makes up the chord of the system. Since the existing Joukowsky wing section has a 12 inch chord, this would set the chord of the flap at 5.14 inches. As 30% of the f u l l chord, the value then of the wing chord i s 17.14 inches (see Fig. 3.2). By referring to data from the profiles of commonly used NACA wing sections, available in Ref. 1, i t was found that the maximum common, and realistic thickness of the section at the 70% chord position was 4.5%, although some wing sections had up to 5.4 thickness at the 70% chord point.  The 4.5% i s to say that a flap which makes up the last 30% of a  wing section has a thickness ratio of 15%.  So what was required  retracted  flap  Figure 3.1(a) Conventional Slotted Flap with Spoiler.  flap  retracted  Figure 3.1(b) Two-Element Joukowsky A i r f o i l .  18  12.08 in  5  0.7 C  Figure 3.2  Experimental Section.  y  in  0.3 C  19  for this study's flap construction was a Joukowsky wing section with a chord of 5.14 inches and a thickness ratio of 15%. Appendix A has a l l calculations used to determine the section required  as well as a profile sketch of the flap used in experimenta-  tion. Flap position in relation to the wing section was determined by referring to many NACA reports on experiments with slotted flaps and external a i r f o i l flaps. past experimentation. overlap".  Many different configurations have been used i n These were termed "best gap size" or "best  This "gap" referred to the space between the trailing edge of  the wing section and the leading edge of the flap section. The "overlap" was the amount by which the leading edge of the flap was positioned upstream, and below the trailing edge of the wing. Although many possibilities were identified, only one was r e a l i s t i c a l l y feasible with the thickness of the flap in this study. This configuration was found in Ref. 3. It called for an optimum gap of 2.0% C at 0° flap deflection, and 2.3% C at 30° flap deflection. Its w  w  best overlap was identified to be 1% C , where C i s the chord of the w  w  main a i r f o i l . This layout i s shown in Fig. 3.3. Graphical methods using a transparency of the proposed flap deflection and a layout of the trailing edge of the main Joukowsky a i r f o i l determined the pivot point for the flap that gave the desired overlap and the optimum gap points.  This also left the gap at not less  than 2.0% C at any flap deflection angle. w  This was also cited i n  reference 3 as best. The flap i t s e l f was constructed on the numerically controlled milling machine. The data points as shown in Appendix A were input to a  20  2.0% Cw gap  for  6=0  2.3% Cw gap f o r 6=30°  p i v o t _JY_  6=0  6=30° Figure  3.3  Experimental  Optimum Gap  and  Overlap.  21 built-in curve f i t t i n g routine.  The milling machine cut out two inch  thick aluminum profiles of the required section.  These were a l l stacked  to form the 27" chord for use in the wind tunnel. The centre section was drilled with nineteen pressure taps and the tubes were run out down the core of the flap span. Endplates were constructed to maintain experimental flap positions as well as to house the spoilers to be tested. Joukowsky wing section.  Spoilers existed for the  Given the new definition of wing chord however,  these took on new "sizes". What was originally a 10% spoiler for the wing section, became a 7% spoiler for this new two-element arrangement. A new spoiler was built 1.7 inches in width to serve as the 10% spoiler used in this study . The spoilers had variable deflection angle capability as well.  The 30°, 45°, 60° or 90° inclinations were set by  the endplate construction.  22 CHAPTER A EXPERIMENTATION  A.1  The Process The experiments i n t h i s study were a l l conducted i n the 27 inch  closed c i r c u i t wind tunnel i n the UBC Aerodynamics Laboratory. dynamic pressure chosen was A6.2 mm of water. Reynolds number of 7.0 x 10 inches.  The  This corresponded to a  based on the f u l l section chord of 17.IA  5  Calculations are found i n Appendix B.  tets varied from 75°F to as high as 9 0 ° F .  The temperature of the  This would s l i g h t l y a l t e r  the v i s c o s i t y used i n Reynolds calculations to the order of A%. study however, i s e s s e n t i a l l y Reynolds Number independent.  This  The only  separation incurred i n these tests i s behind the spoiler and t h i s independent of the nature of the boundary layer.  is  Similar tests  conducted at these endpoint temperatures did not show any perceptible variations i n coefficients  of pressure.  Most tests recorded tempera-  tures of 8 5 ° F . The pressure taps from the wing were plugged into a scanivalve. This instrument was set up i n series with an i d e n t i c a l scanivalve which linked i n the flap pressure taps.  A d i g i t a l readout provided voltage  measurements from a pressure transducer.  Figure A . l i l l u s t r a t e s  the  data a c q u i s i t i o n setup. Tufts were attached to the wing and flap 6 inches below the roof of the tunnel.  This i s out of the boundary layer along the top of the  tunnel and 7.5 inches from the pressure taps.  This distance should  ensure minimal interferences to the pressure data to be taken. r o l e of the tufts was flow v i s u a l i z a t i o n . was e a s i l y seen with them.  The  F u l l and p a r t i a l separation  They e f f e c t i v e l y  showed flow through the  gap and provided interesting insight into the interaction between the spoiler and the slotted f l a p .  23  Pressure Transducer  Signal and  Conditioner  Amplifier  D i g i t a l Voltmeter  Figure A.l  Data Acquisition Schematic.  24 The existing Joukowsky a i r f o i l with 12 inch chord had i t s mount at the quarter-chord position.  This allowed moment measurements to be  taken for normal testing with no flaps.  This was done with the help of  the six-degree-of-freedom balance on which the a i r f o i l was mounted.  Due  to the extended chord length of the wing arrangement and various interferences, this balance was of no use to these experiments beyond i t s ability to steadily support the setup.  The new 30% flap, fitted i n  behind the wing, placed the mount at about the 18% chord position: far upstream of any theoretical aerodynamic center. The new chord length introduced a need to advance the balance upstream so as to allow the pressure tubes from the flap to descend through the turntable hole i n the floor of the tunnel. Early i n the testing i t was observed that the added chord, as well as the higher l i f t abilities of the section at high flap deflections was sufficient to bend the whole setup as much as several inches at the top in the " l i f t " direction.  To rectify this, a pin was sunken through the  top of the wind tunnel to the upper pivot point of the system.  This  solved the lateral bending of the setup, but the torque created by the system continued to be a problem as w i l l be explained later in this section. It was deemed very important to have an estimate or close experimental approximation of the pressures at the trailing edges of the wing and the flap.  It was particularly important at the flap because i t s  thickness became too small for the trailing 1.5 inches of the flap to have pressure taps drilled.  For accurate plotting of the pressure data,  this trailing edge pressure reading was absolutely necessary.  To carry  out this task small pressure tubes were tightly taped to the trailing  edges o f the wing the  drilled  effects the  by  pressure the  tunnel  centre  constant.  To  pressure  flap. taps  tube.  According  two  and  As  T h e i r o p e n i n g s were about  f o r the wing well,  i t was  to avoid w a l l  to theory, monitor  and  i n c h below  to minimize  adverse  d e s i r a b l e t o have them c l o s e  to  effects.  the pressure  this,  flap  one  behind  when s p o i l e r s  t a p s were a t t a c h e d  i n the  a spoiler  were u s e d  separated  should  i n the  flow  be  experiments,  regions  behind  the  spoiler.  A. 2  Uncertainties Some e x p e r i m e n t a l  researchers in  this  i n comparing  work.  As  was  Appendix  the  The  This alone  A e r o d y n a m i c s Lab  extended chord high  effective  position, free  their F  theory  lists  mount  chord.  velocity  the  airfoil  setup  prone  to  and  degree  i n angle  +6  Since  the  f l a p was  t h e r e w e r e no flow.  T h e r e was  attack error.  and  degrees angle  concerns  was  secured about  This of  at  contained  existing  i t s quarter-chord  with  the  the  flap  balance  created an  l a r g e moments.  a t w h i c h t h e m o d e l was  attack  b e t w e e n -A  results  t h e mount a t a b o u t  t o t w i s t the model i n a streamwise  of  to aid further  added t o an  Unfortunately,  This placed  deflection.  and  f o r study  tended  flap  data  f l a p was  adequate  a t U.B.C.  l e a v i n g the  stream  f o r the  w o u l d be  to  mentioned  some q u a n t i t a t i v e e r r o r s .  p r e v i o u s l y mentioned, the  Joukowsky a i r f o i l . position.  u n c e r t a i n t i e s must be  observed torque  at high  t o be  was  not  as  moments  angles  high  very  percent  the  t e s t e d , these  direction  an  18  At  at  as  of  one  evident  attack.  t o the main a i r f o i l  i t s deflection  angle  by  being  solid  endplates  altered  by a i r  26 Pressure measurements were the main emphasis of experiments in this study.  The tiny pressure taps on the model were connected to the  scanivalves through small plastic tubes.  Although the area i s clean and  the air relatively dry, i t i s not out of the question that foreign objects may have entered the system. This could cause blockages of the tubes.  Total blockage i s easily detected.  more d i f f i c u l t to discover.  Partial blockage i s much  It may appear in a number of forms.  Perhaps the most common i s a sluggishness in voltage readout from port to port in the scanivalve.  The partial blockages would force the  researcher to allow more time for the readouts to settle.  So effect-  ively, the small tubes form dampers in the pressure data acquisition system.  4.3  Wind Tunnel Wall Corrections These data are not corrected for wall effects.  In Appendix C, the  trapezoidal method of determining experimental values for C^ i s shown. This method could be extended to determine C /4 for any given mc  configuration of flap, spoiler and wing.  As formula (4.1) shows, both »  t  C.and C ,, are needed to determine true C. and hence C_. L mcM L P  As shown in  Ref. 11  (4.1)  CJ = C. (1 - 2e - o) - f - (C. - 4 C L  where  L  ZTT  L  e = Ao; A = a i r f o i l shape factor; o =  To get  C  P  :  1  L  p  W .  3C ) r-^ m ., OCX c/4  TT*/A8  ( C / H )  J  ,  27  The agreed scope of this work did not allow for data reduction to be carried out towards the determination of corrected pressure distributions.  A l l the data have been collected and when the theory for these  experiments i s pursued, the corrected values C£ and Cp must be used to compare experiment with theoretical predictions.  28  CHAPTER 5 OBSERVATIONS AND RESULTS  5.1  G e n e r a l C o n f i g u r a t i o n Phenomena  5.1.1  T r a i l i n g Edge o f Main Joukowsky A i r f o i l The main Joukowsky a i r f o i l was b u i l t i n 1969 and used by J a n d a l i i n  h i s work on s p o i l e r s ,  R e f . 6.  I t was b u i l t o f mahogany by the  n i c i a n s i n t h e M e c h a n i c a l E n g i n e e r i n g Shops. have cusp t r a i l i n g e d g e s , i t difficulty.  S i n c e Joukowsky a i r f o i l s  i s p l a i n that t h i s presents  construction  To overcome t h i s p r o b l e m , the upper s u r f a c e o f t h e  i n t h e t r a i l i n g i n c h o f chord was r a i s e d .  This effectively  t h e t r a i l i n g edge f o r s t r e n g t h and s t i f f n e s s . a l t e r e d the c h a r a c t e r i s t i c s o f t h e a i r f o i l  line.  airfoil  thickened  Unfortunately, this  also  from what t h e o r y may p r e d i c t .  A l t h o u g h t h e d i s c r e p a n c i e s a r e s m a l l t h e y c a n be seen i n F i g . Note the  tech-  5.1.  'bump' a t about 65 p e r c e n t chord on t h e wing upper s u r f a c e  The e f f e c t s o f t h i s a r e n o t d e t r i m e n t a l t o t h e r e s u l t s  since  they  a r e s m a l l and l o c a l i z e d .  5.1.2  B l o c k a g e E f f e c t s by F l a p E x t e r n a l The t r e n d o f t h e c o e f f i c i e n t  t h e main f o i l nation point. ref.  6),  is  Aerofoil  o f p r e s s u r e a l o n g t h e lower s u r f a c e o f  t o r a p i d l y approach z e r o a f t e r b e i n g u n i t y a t the  T h e o r e t i c a l l y , and e a s i l y shown by experiment  i t does not r e a c h z e r o but r a t h e r approaches and  s l i g h t l y a g a i n as t h e t r a i l i n g edge o f t h e a i r f o i l Because  the f l a p a i r f o i l  i n t h i s study, i n F i g . 3.2  it  (Jandali,  increases  i s approached.  i s mounted b e h i n d and below t h e main a e r o f o i l  creates a blockage e f f e c t .  (pg. 1 8 ) .  stag-  The c o n f i g u r a t i o n i s  shown  One would expect a d e c e l e r a t i o n i n flow upstream  -5  •  WINGUPPER  O WINGLOWER  -4H  A FLAPUPPER_ O FLAPLOWER  -3  -2  CL  O  -H  0  20  40  r 60  T  80  PERCENT OF TOTAL CHORD FIGURE  5.1  PRESSURE  DISTRIBUTION:  oc=  0  NO SPOILER deg 6= 0  100  deg  -5-i  -4-  •  WINGUPPER  O  WINGLOWER  A FLAPUPPER O  FLAPLOWER  -3-  Q_ O  -1-  20  40  —r-  60  PERCENT OF TOTAL CHORD  FIGURE  5.2  P R E S S U R E DISTRIBUTION:  100  80  a  =  m  4  deg  S P 0 I L t R  <5= o deg  CO O  31  of the flap because of i t s thickness.  This would result in the increase  in Cp shown in Fig. 5.2. A great reduction in velocity contributes to the Cp increase to about 0.6 at the trailing edge lower surface of the main a i r f o i l .  Although the a i r f o i l s of the flap and wing are dissimilar  in cross-section as well as size, this dramatic increase in Cp is not observed on the flap.  Figure 5.2 shows the flap in an undeflected state.  This does not show this Cp increase well. When i t i s deflected 20° one can more easily see that no similar effects are experienced by the flap. Figure 5.13 on page 48 better indicates the almost imperceptible increase in Cp along the underside of the flap.  This supports the supposition  that the effects observed on the underside of the wing in Fig. 5.2 are caused by blockage by the leading edge of the flap.  5.1.3  Flap Leading Edge Curvature Effects As can be seen in Fig. 3.3 on page 20, the Joukowsky flap a i r f o i l  section i s relatively thick with a visible camber. The large curvature found on the leading edge, and particularly on the lower surface at the leading edge causes some effects worth noting.  When the flap i s in an  undeflected condition, a high negative Cp i s found in the area of concern.  The pressure coefficient on the lower side i s even more  negative than that of the upper surface.  Pehaps the restriction caused  by the small gap above the flap also contributes to these effects. The cause of the high negative pressure coefficients around the lower surface leading edge i s the increased airflow velocity in that region. This i s only found in the undeflected flap configuration however, no matter what the angle of attack i s .  As Fig. 5.6 on page 38 shows, at a  32 ten-degree deflection, the effects of the curvature have already been overcome and lower flap surface Cp's are once again higher than those of the upper flap surface.  Figure 5.14 on page 49 also shows the absence of  these effects at flap deflections of 20 and 40 degrees.  5.1.4  Coefficients of L i f t Versus Angle of Attack The C^ vs a curves for the experiments i n this research complied  very well with what theory might predict.  Fig. 5.3 shows that the curve  i s v i r t u a l l y linear with a dC /da of about 0.1. L  these calculations.  See Appendix D for  According to Houghton and Carruthers, Ref. 5, the  theoretical value i s 2n/rad which corresponds with 0.1097 per degree. Also i n Fig. 5.3 one must note the small upward deflection of the curve towards the lower end of the o scale.  This could be caused by the  beginnings of negative s t a l l at these low angles of attack.  5.1.5  "Single-Airfoil" Tendencies This two-element Joukowsky a i r f o i l system appears to take on single-  a i r f o i l tendencies.  As Fig. 5.4 shows, the pressure distribution on the  upper surface of the main a i r f o i l ceases to descend as theory predicts i t should, were i t a single a i r f o i l .  Instead i t turns upwards as the  flap i s approached. This i s a form of upstream negative pressure recovery.  "Upstream" i s , of course, with reference to the flap.  5.4 there i s a 20 degree deflection of the flap.  In Fig.  This results i n a high  negative pressure coefficient at the leading edge of the flap.  The  trailing edge of the wing, because of i t s close proximity to the flap, tends to this high negative pressure coefficient.  A more obvious  comparison of this effect i s shown on Fig. 5.14, page 49.  At a higher  3n  -5 •  W1NGUPPER  O WINGLOWER A  [LAPUPPER  O  FLAPLOWER  C L  o  -H  H 0P  •o  0  O' •©••••O  20  O  ©  o  40  60  80  PERCENT OF TOTAL CHORD  FIGURE  5.4  P R E S S U R E DISTRIBUTION:  a=  4  100  NO SPOILER deg 6= 20 deg  35 flap deflection than Fig. 5.4 shows, this negative increase in Cp i s very dramatic.  The upper surface of the f u l l wing section appears to  effectively "ignore" the gap.  5.1.6  ;  Trailing Edge Data Points In the 'Experimentation' section of this report, i t was mentioned  that external pressure tap lines were secured to the trailing edges of the wing and flap a i r f o i l s .  The data recovered from these positions  leave the analyst with doubts as to their accuracy.  Figure 5.4 shows a  point for the trailing edge of the wing i n good comparison with those ' positions slightly upstream on the upper surface. According to theory, a stagnation point exists on the trailing edge of an a i r f o i l i n airflow. This is in keeping with the Kutta condition. This i s not achieved experimentally for the wing i n Fig. 5.4 but usually trailing edge data may be expected to represent more of a balance between upper and lower surface pressure data.  The trailing edge of the flap i n Fig. 5.4,  however, has a Cp of about zero.  This appears to complement the more  exact data upstream of this point. One might suspect that the pressure tap in the f i r s t case was more sensitive to the upper surface flow than the lower.  This i s easily possible as the taps are held in position  along the knife-edged trailing edge, by tape.  Slight shifts to the upper  or lower surfaces of the wing are not unlikely.  5.1.7  Flap Upper Surface and Spoiler Back Pressure Correlation Figure 5.5 shows an interesting effect along the top surface of the  flap.  The almost constant Cp along this surface corresponds very  closely to the back pressure measured behind the 10% normal spoiler.  -5  -4  •  WINGUPPER  O  WINGLOWER  A  FLAPUPPER_  O  FLAPLOWER  -3H  CL O  -2 -H  1 0 0  PERCENT OF TOTAL CHORD  FIGURE  5.5  PRESSURE DISTRIBUTION:  Z°\ %™ ' z  7  90 de 0 de  37 This happened despite the unstalled condition of the flap.  Light flow  separation was noted in the last 1.5 inches of the upper surface of the flap.  Once again this supports the hypothesis presented in section  5.1.5  that the two-element wing expresses characteristics of a simple one element a i r f o i l .  Were a spoiler used on a simple a i r f o i l , flow would  remain separated through to the trailing edge on the upper surface.  The  empirical constant back pressure assumption used in Ref. 7, holds validity because of this.  This remarkable effect is consistent  throughout tests in this work where spoilers were used, irrespective of flap deflection, and despite an unstalled flap condition.  5.2 5.2.1  Separation Effects Unseparated Flow In the experiments carried out in this report, very few were  entirely free of separation effects, however light.  Fig. 5.6 is one that  does show a configuration where separation is absent.  Succeeding  sections and figures w i l l briefly describe some of the experiments where separation was noticeable.  The tufts described in Section 3 were the  means by which the separation and i t s degree were visually noted. It i s also important to note that the tufts did not indicate any three-dimensional  5.2.2  effects in any of the tests in this study.  Separation on the Lower Flap Surface Attention is drawn, when studying Fig. 5.7, to the unusual Cp  distribution around the slotted flap.  The high negative Cp on the lower  flap surface hsa been discussed in section 5.1.3  but the example used in  that discussion was far from as adverse as this case. negatively or upwardly deflected.  The flap was  This i s not a practical configuration  -5-i  -4  A  •  WINGUPPER  O  WINGLOWER  A  FLAPUPPER_  O  FLAPLOWER  -3  -2H Q_ O  60  PERCENT  FIGURE  OF TOTAL  5.6 P R E S S U R E D I S T R I B U T I O N :  100  80  CHORD a  _  0  ex— v  "°  S P 0 , L  a e g  /  R in  o=  ,  10  deg  00  -5  n  -4.H  •  WINGUPPER  O  WINGLOWER  A FLAPUPPER_ O FLAPLOWER  -3  A  -2  CL  O  -1  0  20  40  I  60  80  PERCENT OP TOTAL CHORD FIGURE  5.7  P R E S S U R E DISTRIBUTION:  A  =  2  100  NO  SPOILER  deg  6=  -10deg  40 i n r e a l i t y , but for study purposes proved i n t e r e s t i n g .  The underside of  that high camber flap a e r o f o i l was experiencing separation but was not completely s t a l l e d .  The tufts were pulled away from the surface but  were not drawn anywhere but downstream.  In s t a l l e d conditions, they  would have been usteadily f l u t t e r i n g upstream.  5.2.3  Separation on T r a i l i n g Upper Flap Surface In the configuration corresponding to F i g . 5.8, moderate  separation i n the rear several inches of the flap surface was observed. The high flap deflection of 30 degrees i n concert with a negative angle of attack of the wing are responsible for t h i s .  The gap before the flap  i s i n the shadow of the negative angle of attack on the wing.  Less  airflow can make i t s way through to the upper flap surface to help with boundary layer control and delay separation.  The upper flap airflow i s  more affected by the free stream and deflects from the surface that effectively  at a 25° angle of attack.  is  In this study, i t was shown that  the flap can remain unstalled at 40 degree deflections up to 8 degrees angle of attack when spoilers are extended.  This form of separation was  less l i k e l y at p o s i t i v e angles of attack even without spoilers due to the greater exposure of the gap to airflow.  5.2.4  Pre-Spoiler Separation Bubble Yeung i n his t h e s i s , Ref. 16, cites some of Jandali's unpublished  work on a separation bubble upwind of a s p o i l e r .  This can be easily  explained because the flow w i l l undoubtedly be slowed down by the v i r t u a l fence erected i n i t s path.  The slowing of the f l u i d results i n  increased C , followed by l o c a l boundary-layer separation and a p  -5  •4H  •  WINGUPPER  O  WINGLOWER  A  FLAPUPPER •m a— mm mm • • • • • • • • • • • • i s  O  FLAPLOWER  -3J  Q_ CJ  o FIGURE  20  40  60  80  PERCENT OF TOTAL CHORD  5.8  P R E S S U R E DISTRIBUTION:  cx=  100  NO SPOILER — 4 deg 6= 30 deg  •  WINGUPPER  O  WINGLOWER  A  FLAPUPPER  O  FLAPLOWER  •A  .© •o-  •©•  "T 20  •  , 40  ,  - r - — 60  7  ,  PERCENT OF TOTAL C H O R D  5.9  PRESSURE DISTRIBUTION:  , 80  ,  H°Y%  , 100  7 %  e g  ^  ? ° 0  de  43 constant-pressure bubble.  This phenomenon i s observed on F i g . 5.9.  7% spoiler exists i n t h i s test and, as one can see, surface pressure coefficients  A  the wing upper  a c t u a l l y swing to the p o s i t i v e sense  upwind of the spoiler despite a 6 degree angle of attack.  Although the  tufts did not show t h i s e f f e c t , had smoke or some other means of flow v i s u a l i z a t i o n been t r i e d as Jandali d i d , i t would have shown t h i s bubble.  5.2.5  Separation on the T r a i l i n g Upper Wing Surface Although the curves drawn for the upper wing on F i g . 5.10 do not"  show i r r e g u l a r i t y , flow v i s u a l i z a t i o n detected l i g h t separation on the rear upper surface of the wing.  This can e a s i l y be explained by the  high angle of attack of the system.  A highly adverse pressure gradient  set up i n the upper surface of t h i s wing w i l l seek boundary layer separation.  The highly exposed gap between wing and flap at t h i s  elevated  angle of attack unquestionably serves as boundary layer c o n t r o l , delaying the s t a l l i n g of t h i s wing and undeflected flap arrangement.  5.2.6  Leading Edge Separation Bubble In many of the experiments at high angles of attack, regardless of  s p o i l e r existence, a constant r i p p l e i n pressure d i s t r i b u t i o n was experienced on the upper surface of the wing within the f i r s t 5% t o t a l chord.  This i s probably caused by a small separation bubble incurred at  such a high angle of attack.  Reattachment i s very quick.  shows t h i s r i p p l e very c l e a r l y .  Figure 5.10  Figure 5.11 i s a similar flap deflec-  t i o n with no spoiler and s l i g h t l y reduced angle of attack. case, the r i p p l e i s absent yet the coefficient  In this  of l i f t i s only about .2  0  20  —r40  -r— 60  i  80  PERCENT OF TOTAL CHORD  FIGURE  5.10 P R E S S U R E DISTRIBUTION:  a=  12  NO SPOILER deg 6= 0  100  deg  ~ r —  0  FIGURE  22 00  40  ~1~ 60  4S  80  PERCENT OF TOTAL CHORD  5.11 PRESSURE DISTRIBUTION:  cx=  100  NO SPOILER  8  deg  (5=  0  deg  Cn  46 lower.  (This corresponds to a dC /da of about 0.05:half the theoretical  value).  At a = 12° as in Fig. 5.10, C  5.11,  = 1.25.  L  = 1.47; at o = 8 ° as in Fig.  Examination of the two figures shows that the flap  pressure distributions are almost identical for the two cases.  5.3 5.3.1  Flap Effects Flap Effects on Coefficient of L i f t As Fig. 5.12 shows, the effects of flap deflection are substantial  on the l i f t i n g capabilities of a wing section. a curves are unaltered as would be expected.  The slopes of the C^ vs The various configurations  stalled at lower angles of attack as flap deflection angle was increased.  The important zero l i f t angle found near -5° angle of attack  with no flap, was pushed substantially further negatively with the addition of a flap deflection. effects of the flap.  Fig. 5.13 shows the great l i f t i n g  It i s used as a high l i f t device and the reasons  are evident when the flap pressure distribution i s seen in Fig. 5.13. Another phenomenon observed on Fig. 5.12 i s the greater effect on l i f t found between 6 = 0 ° and 6 = 20°, than exists between fi = 20° and 6 = 40°.  5.3.2  This w i l l be noted again in the following section.  Flap Deflection Angle Comparison The pressure distributions in Fig. 5.14 give good perspective on the  effects of flap deflection angle.  Note the great effects on flap pres-  sure distribution between 6=0° and 6=20°, and again, but to a lesser degree, between 6=20° and 5=40°.  The main a i r f o i l l i f t increases measurably.  In  the 6=20° and 6=40° conditions, separation was experienced on the last two inches of the upper flap surface.  No separation was incurred in the  -5-i  -4  •  WINGUPPER  O  WINGLOWER  A  FLAPUPPER  O  FLAPLOWER  -3  CL  O  0  • i  •G-  o "  H  0  —r— 20  — r -  40  60  80  PERCENT OF TOTAL C H O R D  FIGURE  5.13 P R E S S U R E DISTRIBUTION:  a  =  100  NO SPOILER 0  deg  6= 20  deg  00  0  20  40  60  PERCENT OF TOTAL CHORD  FIGURE  5.14 P R E S S U R E DISTRIBUTION: NO SPOILER AND CONSTANT a , VARYING S  80  a=  100  4  deg  VO  50 6 = 0 ° case.  The greatest changes once again appear between 6 = 0 ° and  6 = 20° as was noted in section 5.3.1 and on Fig. 5.12. It is" also interesting to note the pressure trend of the trailing edge of the main a i r f o i l as the flap i s approached.  As was noted in Section 5.1.5, a  single-airfoil behaviour becomes apparent. trailing edge measurement inaccuracy.  This could also be due to  Since the gap i s only 0.28 inches  at i t s widest point, and the pressure tap i s almost a third of that, the data point at the trailing edge of the wing could be greatly affected by the leading edge of the flap.  5.A  Spoiler Effects  5.4.1  Curve Fitting on Spoiler Back Pressure Coefficients As the data points symbolized i n Fig. 5.15 show, spoiler back  pressure was measured to be constant.  The curve drawn, however, does not  indicate such a condition. This i s due to the spline curve f i t t i n g routine used i n plotting these graphs.  Some variation i n spoiler back  pressure measurement was observed when using the 10% spoiler i n testing. This i s easily seen by the symbols on Fig. 5.16 using upper surface data.  When the 10% spoiler was fitted to the end plates, i t was not as  snug to the main a i r f o i l as the 7% spoiler was.  One will notice four  spoiler back pressure data points, excluding the trailing edge point. The forward two of these points were taps 23 and 24 on the main a i r f o i l . The rearward two points were pressure taps taped to the back of the spoiler as explained in section 3.1.  The airflow seeping under the  spoiler over pressure taps 23 and 24 on the wing can account for their consistency in being more negative pressure coefficients than the more reliable data obtained on the spoilers' downstream surfaces.  -5-1  •  WINGUPPER  O  WINGLOWER  A  ELAPUPPER am mm mm mm mm mm mm •  O  •  FLAPLOWER  -3H  QL A'^-A A,  20  40  60  80  100  PERCENT OF TOTAL C H O R D  FIGURE  5.15 P R E S S U R E DISTRIBUTION:  ll a \ on  £  7 g  %  9 0 de 0 de  •5-n  -4  •  WINGUPPER  O  WINGLOWER  A  FLAPUPPER  O  FLAPLOWER  -3H  -2H  a  C L  0  —r— 20  40  60  80  100  PERCENT OF TOTAL C H O R D  FIGURE  5.16 P R E S S U R E DISTRIBUTION:  i^Vg  055  90 0  deg deg  53 5.4.2  L i f t Coefficients vith Spoilers Extended As would be expected, the zero l i f t angles calculated for wing  configurations with spoilers are higher than those without spoilers. Fig. 5.17  shows this angle to be about -3 degrees.  Fig. 5.12  on page 47  showed a value of -5° for a similar configuration without spoiler.  To  be noted as well, the theoretical dC /da value is obtained L experimentally once again: 0.1 even with spoiler extended.  5.4.3  Spoiler Effects on Pressure Distribution Figure 5.18  shows the monumental reduction in l i f t i n g capability of  the main wing section with the extension of a spoiler. spoiler i s 1.88.  C^ for no  When a 7% spoiler i s extended, i t i s reduced to  0.82.  This control surface's usefulness for the approach and landing of an aircraft i s understood when one sees the effects of such a small spoiler in a typical flying configuration  of angle of attack and flap  deflection. Figure 5.19 attack.  shows the effects of a spoiler at a higher angle of  An interesting point to note i s the small change in flap  pressure distribution despite the addition of a spoiler.  The pressure  distribution about the wing was collapsed with the intrusion of a spoiler, yet the flap i s not as significantly affected. main reason for this effect.  The slot is the  The influx of air from the lower surface  serves as boundary layer control as well as maintaining flap effectiveness regardless of what is happening upstream on the upper wing surface. Were the trailing edge points of the flap more certain, one might be able to see them better correspond as well.  -1 10  FIGURE  -8  -4  5.17 C v s L  -2  0  2  a  a  CONSTANT SPOILER AND  6  4  8 SPOILER:  10%  10  12  £=  90  deg  6=  20  deg  SPOILER •  NO-SPOILER  O  10%&90deg  CL  O  m  ^  I  i  r  _  •  FIGURE 5.18 PRESSURE DISTRIBUTION: CONSTANT  Ln  PERCENT OF TOTAL CHORD  «= 4  a A N D <5, VARYING S P O I L E R  d e g  6=  20  deg  -5  SPOILER  i_  |  0  .  ,  1  20  •  FIGURE  1  .  40  1  1  60  1  80  '  1  100  PERCENT OF TOTAL CHORD  5.19 P R E S S U R E DISTRIBUTION:  a= 8 deg  CONSTANT a A N D (5, VARYING SPOILER  6= 20 deg  5 7  A note on the plotting of these curves, only every fourth data point was drawn on the curves to promote clarity.  5.4.A  Effects of Spoiler Size Although some change in pressure distribution and hence l i f t i n g  capability was observed between 7 % and 1 0 % spoilers, i t was nowhere near as evident as the change between no spoiler and a 7 % spoiler. not surprising.  As Fig.  This i s  5 . 2 0 shows, the flap pressure distribution i s  virtually unchanged with the 3 % spoiler increase.  The wing however,  experiences a more substantial reduction i n l i f t .  The  spoiler i n this configuration spoiler i s 0 . 5 6 .  is 0 . 8 2 .  for the 7 %  The same quantity for a 1 0 %  Most of the l i f t lost i s a result of the spoiler size  increase effect on the main wing's l i f t i n g capabilities. Another plot i s presented i n Figure 5 . 2 1 which compares spoiler size effects at a higher angle of attack.  Once again the same results  are obtained and l i f t i s lost from the main a i r f o i l whereas the flap remains unchanged.  5.5 5.5.1  Effects of Spoiler Use with Slotted Flap Effects of Flap Deflection Angle With 1 0 % Spoiler Figure 5 . 2 2 shows some interesting effects of increased flap  deflection when a spoiler i s extended.  Of worthy note i s the increase  in spoiler back pressure corresponding to increased flap angle. As Section 5 . 1 . 7  describes, this i s reflected i n the flap upper surface  pressure coefficients as well.  When the spoiler i s extended with no  flap, one can see that the positive pressure coefficient distribution shown i n Fig. 5 . 2 on page 3 0 with no spoiler, i s collapsed in Fig. 5 . 2 2 ,  -5  SPOILER  -4H  •  7%&90deg  O  10%&90deg  -3  -2 C L  O  0  20  40  ,  FIGURE  60  80  100  PERCENT OF TOTAL CHORD  5 . 2 0 P R E S S U R E DISTRIBUTION:  a= 4 deg  C O N S T A N T a A N D (5, VARYING S P O I L E R  6=  20  deg  Cn Oo  - 5 i  •  FIGURE  PERCENT OF TOTAL CHORD  5.21 P R E S S U R E DISTRIBUTION: CONSTANT  a=  a A N D 6, VARYING S P O I L E R  -5  -4H  •  0_  0  20  A  40  -3H  QL O  -2H A  0  20  40  ..  FIGURE  60  80  100  PERCENT OF TOTAL CHORD  5.22 P R E S S U R E DISTRIBUTION: CONSTANT SPOILER AND a, VARYING  S P 0 I L E R :  6  ON  o 1 0 %  a=  *=  4  9 0  deg  d e  9  61  to the point of producing a negative l i f t coefficient:  C = -0.025. L  Although t h i s recovers to a positive value with increased flap deflection,  i t is most c e r t a i n l y the result of l i f t created almost  e n t i r e l y by the f l a p . Fig.5.23 shows some interesting effects upstream of the s p o i l e r . As mentioned in Section 5 . 2 . 4 ,  the r e c i r c u l a t i o n zone upstream  of the spoiler has a detrimental effect on the main wing l i f t capabilities.  The reduced negative pressure coefficients  observed  between the 30 and 60 percent chord positions are due to t h i s zone of reduced v e l o c i t y .  Obvious dips are experienced by a l l three curves at  the point immediately upstream of the s p o i l e r .  Port 22 on the main  a i r f o i l i s very close to the base of the 10% spoiler and hence v e l o c i t y i s close to zero.  The poor curve f i t t i n g immediately behind the spoiler  i s explained i n Section 5.4.3. The tests described i n F i g . 5.23 are very illuminating when considering the effects of s p o i l e r on flap performance. i s d r a s t i c a l l y reduced on the main a i r f o i l , attack  Where the  lift  even at high angles of  the flap s t i l l produces high l i f t and i s maintained free of  s t a l l effects.  In f a c t , the spoiler extension actually allowed  increased angle of attack without s t a l l i n g the f l a p . and 40 degrees flap d e f l e c t i o n , angle of attack.  With no spoiler  f u l l s t a l l i n g occurred after 4 degrees  The curve shown on F i g . 5.23 i s the same flap  d e f l e c t i o n , with spoiler this time but at 8 degrees angle of attack. F u l l s t a l l i n g occurred beyond that point.  This effect i s due to the  spoilers r e s t r i c t i n g flow over the top surface of the wing (reducing c i r c u l a t i o n ) , hence reducing the s t i l l adverse pressure gradient, and delaying separation u n t i l a  greater angle of attack i s reached.  g_ , 0  '  1  20  1  1 40  1  1 60 "  1  1 80  '  I  100  PERCENT OF TOTAL CHORD  FIGURE  5 . 2 3 P R E S S U R E DISTRIBUTION: CONSTANT SPOILER AND c c , VARYING  S P 0 , L E R :  6  1 0 % a  9 0 =  8  d e g  d e g  63 5.5.2  Flap Effects on L i f t Coefficient vith Spoiler Extended As one might expect, the l i f t v i l l s t i l l increase vith flap deflec-  tion.  The magnitude, hovever, i s substantially lover than vith no  spoiler extension. Fig. 5.12 on page 47 shovs phenomenal vertical translation of C^ vs a curves vith no spoiler extension, as flap deflection angle i s increased. This trend i s also seen on Fig. 5.24 but by no means to the same extent. Once again more change occurs in the 20° increase from 6 = 0 ° than in the same increase from 6 = 20°. Another interesting note concerns the zero l i f t angles of the three curves on Fig. 5.24.  When the spoiler i s extended vithout flap  extension, the zero l i f t angle i s actually positive at about 4°. This reduces to -3° and -6.5° vith 20° and 40° flap deflections respectively. This i s especially useful i n landing aircraft.  A positive l i f t at  negative angle of attack allovs steeper glide angle and slover approach speed because drag varies vith l i f t . One further point obvious on Fig. 5.24 i s the consistency i n dC^/da around 0.1 as predicted by theory and seen before in this vork.  5.5.3  Spoiler Inclination Angle Effects vith Flap Deflected Once again the slotted flap immunity to spoiler deflection i s  observed in Fig. 5.25.  The l i f t curves of the main ving at 8° angle of  attack are substantially collapsed.  It i s easily seen again that the  effects of a control surface are more substantial vhen i t i s i n i t i a l l y deployed.  Here a greater l i f t reduction happens betveen £ • 30° and  I = 60° than betveen £ = 60° and £ = 90°. This latter point i s more readily seen in the C Fig. 5.26.  L  vs a curves on  Very l i t t l e happens betveen £ = 60° and £ = 90°.  In  3-i  2H  Cf  c5 •  0_  O  20  A  40  1-  .A .A" .O  ,A' A  FIGURE  5.24 C v s L  a  10% SPOILER AND VARYING  a  6  -5-1  CL O  100  ..  FIGURE  P E R C E N T O F TOTAL C H O R D  5 . 2 5 P R E S S U R E DISTRIBUTION: CONSTANT  C D n i l  r  D  a = 8 d°e g SP  a A N D 6 A N D SPOILER SIZE, VARYING  L  f  i n q r  ER:  T°  20 deg  Ol  ON  FIGURE 5.26 C v s L  CONSTANT  a 6 WITH 10% SPOILER, VARYING £  20  deg  67 fact their zero l i f t angle only varies by about half a degree. More substantial effects are noted between I = 30° and I = 60° with" a 3.5° decrease in zero l i f t angle. Again one can see that the slope of the curves in Fig. 5.26 i s constant at about 0.1 per degree. The pre-spoiler dip mentioned in Section 5.5.1  i s again evident on  the curves in Fig. 5.25.  5.5.A  Effects of Spoiler Size Changes with Flap Deflection Figure 5.27 shows some further evidence of slotted flap immunity to  spoiler l i f t reduction. Virtually no change i s noted in pressure distribution around the flap. 5.4.3  This i s further explained i n Sections  and 5.5.1. The boundary layer control from the gap creates  reattachment of the flow at the flap after i t was separated at the spoiler t i p and the trailing edge of the wing. The phenomenon of i n i t i a l control surface effectiveness i s once again noted as l i t t l e change occcurs between 7% and 10% spoilers. Substantial circulation reduction by the 7% spoiler on the undisturbed configuration i s apparent as the pressure distribution collapses, apparent on Figure 5.27. This point i s reiterated with more evidence presented on the C^ vs a curves of Fig. 5.28.  Once again the curve slopes are unchanged from  previous observation, and the major l i f t reduction occurs i n i t i a l l y : between no spoiler, and a 7% spoiler.  SPOILER • NONE  Q. O  -H  FIGURE  PERCENT OF TOTAL CHORD 5.27 P R E S S U R E DISTRIBUTION: ^ CONSTANT a AND c5 AND ^.VARYING SPOILER SIZE E  R  d  e  g  100  90 20  deg deg  oo  SPOILER • O  NONE 7%  FIGURE 5.28 C vs a L  CONSTANT 5 AND £ , VARYING SPOILER SIZE  70 CHAPTER DISCUSSION AND  6  CONCLUSIONS  Encouraging results were obtained from pressure measurement experiments on a Joukowsky a i r f o i l with Joukowsky slotted flap and spoiler.  The results are qualitative only and are not to be compared  quantitatively with theory until wind tunnel wall correction factors are applied.  A l l data are presented or available in a data bank to complete  the required corrections. The experimental setup was effectively a two-element Joukowsky a i r f o i l arrangement with variable secondary a i r f o i l deflection. secondary a i r f o i l was modelling a slotted flap.  The  Several spoilers of  varying size and inclination were used in the testing. Theory, f i r s t proposed by Williams (Ref. 15) for the production of a two-element Joukowsky aerofoil was combined with the work by Parkinson and Jandali (ref. 7), on separated flow and Parkinson and Yeung, on potential flow about a i r f o i l s with spoilers (ref. 10).  The end product  of this theory was a system incorporating two 'near-Joukowsky' airfoils with a spoiler, of arbitrary inclination.  Despite the resulting 'near-  Joukowsky' a i r f o i l s , the assumption was made that they were not too different from true Joukowsky airfoils and experimental results would coincide within error margins.  In his paper, Halsey, Ref. 4, shows that  the variations on shapes situated away from the origin, under conformal transformations, are small, and can be reduced further by repeated mappings. The use of the Theodorsen method explained in ref. 13 can extend this work to the use of slotted flaps and spoilers on real a i r f o i l s .  71  The Joukowsky a i r f o i l s are used in this analysis for two reasons. First, an existing Joukowsky model could be put to use and more importantly, much simpler theory would be required to compare with the experiments in this report. As one studies the overview of theory provided in Section 2 , one can acquire an idea of the complexity of the theory already required to combine the three works cited earlier in this section.  Once the comparisons are made however, Theodorsen mappings  w i l l make this work more applicable to real a i r f o i l control system design. Of great encouragement in this report  are the qualitative results  obtained for the behaviour of slotted flaps and spoilers.  The effects  they had on l i f t coefficients are complementary to these control surface used in real situations.  The high l i f t characteristics of slotted flaps  without spoilers demonstrate their effectiveness on takeoff. The a b i l i t y of the flap to remain unstalled despite large deflection supported the role of slotted flaps over normal or split flaps i n aircraft today.  Higher l i f t at lower angles of attack w i l l also allow  aircraft to take off at lower velocities, reducing runway requirement and hence increasing the effective range of uses of an aircraft. When used in concert with spoilers, the balance of great l i f t reduction and retained control, i.e. unseparated flow over the model, shed light on the configuration's role in approach, air-braking, and landing of aircraft.  The much-reduced zero l i f t angles of attack would  allow steep, controlled approach paths.  As well, high l i f t normally  signifies high drag; so slower approaches and landings are possible. These effects were a l l noted experimentally, and, considering the safety  72 which accompanies steep glide paths and slow approach velocity, the roles of spoilers and slotted flaps are supported. Interesting phenomena were noted on the i n i t i a l uses of flaps and spoilers.  The effects of these controls were more evident when they  were f i r s t introduced into the flow.  For example i t was observed, at  various points i n this research, that slotted flaps made a more significant difference between 0° and 20° deflection than they did after 20°, to AO deflection.  Similarly, the effect of increasing spoiler  0  inclination beyond 60° was not remarkable. This supports the requirement of aircraft for maximum effectiveness of controls with minimum added linkage and hence minimum contribution to overall weight of the aircraft. There i s l i t t l e need to extend flaps beyond AO and no need to incline spoilers beyond 60°. 0  The added  deflection makes l i t t l e or no difference to flight characteristics. This latter point also i s important i n the future theoretical study of this configuration.  Since the theory to produce inclined spoilers  involves many complex mappings, then perhaps approximations can be made from the less complicated theory to produce normal spoilers. Finally, the research found i n this report i s useful in providing a better idea to aerodynamicists, of the effects of control surfaces. Spoilers and slotted flaps are not new to the real flying world. Analytical theory can do nothing but improve their effectiveness further understanding.  through  This experimental work brings real a i r f o i l  design and modification closer to the arcane world of conformal mapping and theoretical a i r f o i l s .  73 CHAPTER 7 RECOMMENDATIONS  This work has shed light on some promising future developments for aerodynamics at the University of British Columbia.  Some work related  to this research is required and some equipment modifications are recommended. It is understood that the time constraints on this thesis leave much to be done to complete the study of the flow about a Joukowsky a i r f o i l with slotted flap and spoiler. It is imperative that wind tunnel correction factors be applied to the data bank created i n this experimental study. As well, the theories proposed i n Section 2 must be concluded to determine velocity potentials for the two-element Joukowsky a i r f o i l on which the experiments were carried out.  This will be no mean feat when  one considers the multitude of spoiler and slotted flap combinations obtainable and used today i n real flight situations. Perhaps some testing i n the 'smart' wind tunnel at UBC would provide some insight towards the magnitude of and accuracy of wind tunnel corrections to be applied. It was discovered that the scanivalves used i n the testing are prone to blockage and require more frequent maintenance attention. Small leaks are common to such a complex apparatus and can be a severe impediment to an experiment.  It i s recommended that the instruments be  compared to manometer readings before major testing situations. A computerized data acquisition system for the existing scanivalve arrangement would save enormous amounts of time and contribute greatly  74 to the accuracy and r e l i a b i l i t y of the researcher's work. The monotony and slow process of manual data recording on the existing scanivalve equipment leaves a margin of error because of the human l i a b i l i t i e s of fatigue and impatience. Some recommendations to further the accuracy and expand the capability of existing equipment are proposed as follows. To accurately measure the cusp trailing  edge pressures on existing Joukowsky a i r f o i l s ,  perhaps a small groove can be cut down the metal surface of the section containing pressure taps.  This could be sealed from the surface yet  open at the delicate trailing  edge. The groove could be accessed from  the inside of the section, just as a l l the other taps are.  The cover  must be thin and must not pose alterations to the cross-section of the airfoil. Problems were also encountered with twisting of the a i r f o i l due to the moments caused by the 43% increase in effective chord of the section: the flap addition. Further studies on this setup should include a means of securing the a i r f o i l s from such torque.  A mounting  device which places the mount at a new effective quarter-chord position is proposed to reduce the magnitude of the moments on the base. The time constraints on this project insisted on a quick production of a 27-inch-span, 5.14-inch-chord shape requirements.  Joukowsky a i r f o i l meeting designated  This was done in aluminum on the numerically  controlled milling machine. The exactness and quality of the result was a testament to the capabilities of i t s production methods.  It i s  recommended that, i f costs allow, this method be used to produce more test models i n the future. The durability and toughness of aluminum are  75  great improvements and the cusp requirement of a Joukowsky trailing edge has been f u l f i l l e d . Perhaps an area of further study could be to delve into the use of slats at the leading edge of a wing section. A less common control surface than flaps, the slat is also used in high l i f t low speed situations like take-off and landing of aircraft.  The small a i r f o i l  extension of the leading edge helps in boundary layer control, and basically i s the slotted flap's leading edge counterpart. Control surface theory for a i r f o i l s i s far behind the requirements of today's complex aircraft industry.  Further work in this area would  prove fascinating and would be of great economic and engineering importance to contemporary flight advances.  76 REFERENCES  1.  Abbott, I.H. and von Doenhoff, A.E. Dover, 19A9.  "Theory of Wing Sections".  2.  Brown, G.P. "Steady and Nonsteady Potential Flow Methods", Ph.D. Thesis, University of British Columbia, 1971.  3.  Foster, D.N., Irwin, H.P.A.H., Williams, B.R. "The Two Dimensional Flow Around A Slotted Flap", RAE Reports and Memoranda No. 3681, September 1970.  4.  Halsey, N.D. "Potential Flow Analysis of Multielement Airfoils Using Con formal Mapping", AIAA Journal, Vol. 17, pp. 1281-8, December 1979.  5.  Houghton, E.L. and Carruthers, N.B. "Aerodynamics for Engineering Students", 3rd ed., London, 1982.  6.  Jandali, T. "A Potential Flow Theory for A i r f o i l Spoilers", Ph.D. Thesis, University of British Columbia, 1970.  7.  Jandali, T. and Parkinson, G.V. "A Potential Flow Theory for A i r f o i l Spoilers", CASI Transactions, Vol. 3, No. 1, March 1970.  8.  Milne-Thomson, L.M. "Theoretical Hydrodynamics", Macmillan &. Co., Ltd., 1955.  9.  Parkinson, G.V. and Jandali, T. "A Wake Source Model for Bluff Body Potential Flow", JFM, Vol. AO, No. 3, pp. 577-59A, Feb. 1970.  10.  Parkinson, G.V. and Yeung, W.W. "A Wake Source Model for A i r f o i l s with Separated Flow", JFM, Vol. 179, pp. Al-57, May 1986.  11.  Pope, A. and Harper, J.J. "Low-Speed Wind Tunnel Testing", John Wiley and Sons, 1966.  12.  Shames, I.H. Mechanics of Fluids, 2nd ed., McGraw-Hill Inc., New York, 1982.  13.  Theodorsen, T. "Theory of Wing Sections of Arbitrary Shape", NACA Rep. No. A l l , 1931.  IA.  Watt, G.D. "Multi-Element Thin A i r f o i l Theory", Ph.D. Thesis, University of British Columbia, 198A.  15.  Williams, B.R. "An Exact Test Case for the Plane Potential Flow About Two Adjacent Lifting Aerofoils", RAE Technical Report 71197, September 1971.  16.  Yeung, W.W. "A Mathematical Model for Airfoils with Spoilers or Split Flaps", M.A.Sc. Thesis, University of British Columbia, 1985.  77 APPENDIX A CALCULATIONS FOR JOUKOWSKY FLAP CONSTRUCTION  As Appendix E w i l l elaborate, the following geometric configuration i s the starting point to create a Joukowsky a i r f o i l .  Fig.  A-1.  When the Joukowsky Transformation i s applied an a i r f o i l  results:  Fig. A-2  The t/c r a t i o and camber of the resulting a i r f o i l are dependent on the values of p and e as defined i n F i g . A-1. The requirements of the flap to be b u i l t , as described i n Section 3 of t h i s report, include a t / c  78 r a t i o of 0.15,  a chord o f 5.14  i n c h e s and a r e a s o n a b l e camber was  r e q u i r e d t o be i n keeping w i t h r e a l i s t i c s l o t t e d  flaps.  G r a p h i c a l means were used t o combine these requirements t o o b t a i n the a i r f o i l  shown i n F i g . A - 3 .  calculated a i r f o i l  The C a r t e s i a n c o o r d i n a t e s o f  the  were s i m p l y s c a l e d t o the p r o p e r chord l e n g t h .  V a l u e s o f p and e a r e g i v e n below t o c r e a t e the s e t l i s t e d i n Table A . l .  p = 0.2343 e = 1 3 0 ° = 2.269 r a d i a n s  of  coordinates  TABLE  A-1  COORDINATES FOR A JOUKOWSKY SLOTTED 5.087392  0.237742  5.063474  0.246118  5.034182  0.256559  4.999739  0.269019  4.960370  0.283432  4.758093  0.358719  4.494440  0.456257  4.182193  0.566638  3.832910  0.679930  3.457114  0.786745  3.064577  0.878932  2.664547  0.949957  2.265892  0.995101  1.877157  0.011519  1.506531  0.998225  1.161777  0.956005  0.850131  0.887294  0.578185  0.796008  0.351796  0.687344  0.176002  0.567541  0.054989  0.443602  -0.00791  0.322974  -0.01017  0.213175  0.049991  0.121358  0.173749  0.053793  0.361692  0.015266  0.613808  0.008373  0.929239  0.032764  1.305677  0.084444  1.738295  0.155357  2.218204  0.233657  2.730750  0.305112  3.254400  0.355917  3.761330  0.376513  4.220495  0.365094  4.602802  0.328954  4.886739  0.282556  4.940532  0.271376  4.987562  0.260896  5.027609  0.251363  •5.060695  0.243003  5.125012  0.225052  FLAP  80  Figure A-3  Flap Joukowsky Section.  81  APPENDIX  B  REYNOLDS NUMBER CALCULATIONS  The experiments were carried out at a Reynolds Number of 700,000. The results however are theoretically independent of Reynolds number at this order. Knowns:  so  g  = 32.2 f t / s  p  = .002378 slug/ft  fl  2  p  •= 1.936 slug/ft  C w  = 12 i n  C  = 5.14 i n  f  C  3  3  = C + C, - 17.14 i n w I -i,  air temperature of 80°F gives v * 1.8 x 10  Re  =  VC/v  vRe/C 1.8xl0~*»7xl0  5  17.14  in • ^2  = 89 ft/s  f  t  /  i  n  2  f t / s : Ref. 12.  82 To determine the corresponding manometer height:  =  h  1 2a  „  p  V  =  u  2  p  f  g h  - I ^ y i 2 P g f  1 2  X  .002378 89 1.936 32.2 X  ft x 12 in/ft  h = 1.817 i n x 25.4 mm/in  h •= 46.2 mm  83 APPENDIX C LIFT COEFFICIENT CALCULATIONS  A trapezoidal scheme was used to calculate coefficients of l i f t for both the main a i r f o i l and the flap.  Fig. C-l.  Any Ax increments used must be corrected for a and/or 6 depending whether i t is found on the wing or the flap. Since i t was contributed to by positive Cp regions on the lower surfaces and negative C  p  regions on the upper surfaces, the quantities  were added or subtracted as applicable.  84  C  tav>i  1  L "  iC  * Ax. * cos a -  lower wing surface  +  2  ( C  pav i * }  I  (C  p a v  ) . * Ax. * cos o  upper wing surface  *  c o s  ^  ) "  a + 6  lower flap surface  *  ^vavh  * Ax. * cos(a+6)  upper flap surface  When spoilers were used the following adjustment to x increments were made  x  l  x  s jk x  A  Ax. « x -x. 1 s 1  rather than x.-x. j i  Ax.. = \ ~  rather than a^-x^  x s  85  APPENDIX D C vs a CALCULATIONS L  This approximation of a C^ vs a curve w i l l demonstrate the dC^/da calculation.  a)  Determine a when C^ = +1.  b)  Determine zero l i f t angle, i.e. a when C^ = 0.  c)  Determine resulting Aa, i.e. (a)-(b).  Calculate dC /da = 1/Aa L  here  dC /da =0.1 L  86  APPENDIX E THE JOUKOWSKY TRANSFORMATION  The Joukowsky Transformation i s I = z + l/z The results of such a transformation on several figures are shown  Fig. E - l . A unit circle i s flattened to a flat plate.  Fig. E-2. A larger circle becomes an ellipse.  Fig. E-3. A vertically translated circle becomes a circular arc airfoil.  87  Fig. E-4.  A horizontally translated circle becomes a symmetrical airfoil.  1  Fig. E-5.  0  ©  A horizontally and vertically translated circle becomes a cambered Joukowsky a i r f o i l .  This last transformation i s the focus of this paper's attention. The degree to which the a i r f o i l i s cambered depends on the magnitude of e.  The thickness of the resulting a i r f o i l i s dependent on the value of  p.  Note that the trailing edges of any Joukowsky a i r f o i l , Figs. E-3,  E-A, and E-5, are cusped.  88 APPENDIX F ERROR ESTIMATES  Quantity Flow Temperature  T  Kinematic Viscosity Reynolds Number  % Error  Error  -  + 10°F  Affects Reynolds Number  ± 3x10*  4.0  Affects Flow Pattern Affects Dynamic Pressure  6  ftVs  Flow Velocity  V  ± 3 ft/s  3.4  Dynamic Pressure  Q  ± 0.6 psf  6.7  Manometer Height  h  + 1 mm  2.0  ± .03 V  1.8  Voltmeter Readout  Affects kinematic viscosity  2.8  ± 5x10" Re  Remarks  

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