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On the experimental investigation of vortex excited pressure fluctuations Heine, Walter 1964

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ON THE EXPERIMENTAL  INVESTIGATION  OF VORTBX EXCITED PRESSURE  FLUCTUATIONS  by  WALTER HEINE B.A.Sc, U n i v e r s i t y  of B r i t i s h Columbia, 1963  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n the Department of Mechanical  Engineering  We accept t h i s t h e s i s as conforming required  to the  standard  THE UNIVERSITY OF BRITISH COLUMBIA August, 1964  In presenting  t h i s thesis i n p a r t i a l f u l f i l m e n t of  the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study.  I further agree that permission  f o r extensive copying of t h i s thesis f o r scholarly purposes may granted by the Head of my Department or by h i s  be  representatives.  It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed v/ithout my written permission.  Department of Mechanical Engineering The University of B r i t i s h Columbia, Vancouver 8, Canada. D  a  t  e  Septpmher A,  1964  ABSTRACT C o n s t r u c t i o n and c a l i b r a t i o n of a p i e z o e l e c t r i o transducer of measuring a c o u s t i c l e v e l pressure  f l u c t u a t i o n s o c c u r r i n g on the surface  of a body due t o shed v o r t i c e s i s d e s c r i b e d . transducer pressure  as a wake survey  of s e v e r a l b l u f f and:.streamlined (1)  Fluctuating l i f t of the body  (2)  c a r r i e d out using two dimensional models bodies i n d i c a t e that  0  For square and r e c t a n g u l a r c y l i n d e r s ^ as w e l l as f o r the e l l i p t i c  pressure  0  of a t t a c k , the amplitude of f l u c t u a t i n g  i s minimum at the points where s t a t i c pressure  Fluctuating l i f t (e„g  is-maximums  c o e f f i c i e n t f o r the bodies with sharp l e a d i n g edge  square and r e c t a n g u l a r c y l i n d e r s ) i s considerably l a r g e r than  the corresponding elliptic  s t a t i c value, while f o r the c i r c u l a r c y l i n d e r , .  c y l i n d e r and the wing, the f l u c t u a t i n g c o e f f i c i e n t s were  found t o be smaller than t h e i r s t a t i c (4)  The f l u c t u a t i n g  c o e f f i c i e n t decreases with r e d u c t i o n i n b l u f f n e s s  c y l i n d e r a t large angles  (3)  The a p p l i c a t i o n of the  equipment i s a l s o explained.  and wake geometry study  capable  counterpart,,  The s e l f e x c i t e d motion of the. body, p a r t i c u l a r l y a b l u f f body, does not a f f e c t e i t h e r the frequency f l u c t u a t i n g pressure*  of shedding v o r t i c e s or the  f o r frequencies above vortex resonance.  ACKNOWLEDGEMENT  I would l i k e t o express my s i n c e r e thanks and a p p r e c i a t i o n to Dr„ V. J . Modi f o r the guidance and a s s i s t a n c e he has given me i n the p r e s e n t a t i o n of t h i s t h e s i s . Mr.  P. Hurren f o r h i s continued  work, e s p e c i a l l y  Thanks are a l s o due t o  a s s i s t a n c e i n the experimental  i n the design, and c o n s t r u c t i o n of the pressure  transducer*  Also, I would l i k e t o thank the Department of Mechanical Engineering  f o r the use of t h e i r f a c i l i t i e s , and the N a t i o n a l  Research C o u n c i l of Canada f o r f i n a n c i a l a s s i s t a n c e through grants  i n a i d of research.  given  TABLE OP CONTENTS Page I.  Introduction  1  II.  Statement  3  III.  Instrumentation C a l i b r a t i o n and Experimental Setup  of Problem  3.1.1  Wind Tunnel  3.1.2.  Calibration  3.2.  Models  3.3.  Model Mounting  3.4.  Pressure Transducer  4 4  of Betz Manometer  5  5  3.4.1. Calibration  System  8 16  of Pressure Transducer  3.5.  Wake Survey Equipment  3.6.  Bending and T o r s i o n a l  24 30  Displacement  Transducers  1  33  3 . 6 . 1 . C a l i b r a t i o n of Displacement Transducers  33  3.7.  Electromagnetic Darning  34  3.8.  Experimental Test Procedures  38  3.8.1.  S t a t i c and O s c i l l a t i n g Pressure Measurements  3 . 8 . 2 . Amplitude 3.8.3.  38  Measurements  Wake Measurements  3 . 8 . 4 . S t r o u h a l Numbers 3.8.5.  Static L i f t  Dynamic L i f t  40  41  C o e f f i c i e n t versus  Angle of Attack 3.8.6.  40  Coefficients  42  Page IV.  Experimental Results  46  4.1.1.  S t a t i o n a r y Square C y l i n d e r  46  4.1.2.  O s c i l l a t i n g Square C y l i n d e r  47  4.2.1.  S t a t i o n a r y Rectangular C y l i n d e r AR=2  60  4.2.2.  O s c i l l a t i n g Rectangular C y l i n d e r JBO  4.2.3.  2  74  S t a t i o n a r y Rectangular C y l i n d e r ARo  1/2  74  4.3.1.  Stationary C i r c u l a r Cylinder  79  4.3.2.  Oscillating Circular Cylinder  81  4.4.1.  Stationary E l l i p t i c  Cylinder  (a • 3 i n c h e s , e m 0 . 9 8 5 )  4.5.1.  S t a t i o n a r y and  V.  Discussion  of Results and  VI.  Bibliography  "'  Oscillating A i r f o i l  Concluding Remarks  89  100 103 107  LIST OP FIGURES  ^fiHEe  Pa$e.  1.  Aerodynamic  Outline of Wind Tunnel  2.  C a l i b r a t i o n Curve: Wind Tunnel  7  3.  Experimental Models  9  4.  L o c a t i o n of Pressure Taps on Models  10,  5.  D e t a i l s of Model Mounting System  12, 13  6..  C r o s s - s e c t i o n of A i r Bearings  15  7.  Pressure Transducer  18, 19, 20  8.  Effeot  9.  Pressure Transducer as Located i n  of Tube Length on Phase  A c o u s t i c a l l y Dead Chamber 10.  C a l i b r a t i o n Setup  11.  C a l i b r a t i o n Curve: V a r i a t i o n of Output w i t h Frequency  12.  (Pressure Transducer)  Wake Measurement Probe  14.  C a l i b r a t i o n Curve: L a t e r a l Displacement Transducer  28  29 32  35  C a l i b r a t i o n Curve: T o r s i o n a l Displacement Transducer  36  16.  C a l i b r a t i o n Curvet Electromagnetic Damper  37  17.  Equipment  39  18.  Numbering of Surfaces of Square and Rectangular  and Test S e c t i o n  Cylinders  11  23.  C a l i b r a t i o n Curve: V a r i a t i o n of Output  13.  ,  %2.  26,  w i t h Pressure (Pressure Transducer)  15.  6  43.  27  Figure  Page  19.  I n t e g r a t i o n about E l l i p t i c  20.  V a r i a t i o n of S t a t i c Pressure D i s t r i b u t i o n  Cylinder  44  with a: Square Cylinder 21.  V a r i a t i o n of S t a t i c L i f t at  22.  49, 50, 51  C o e f f i c i e n t with  Square C y l i n d e r  52  V a r i a t i o n of S t r o u h a l lumber with  Reynolds  :  Number f o r Square C y l i n d e r 23.  53  V a r i a t i o n of F l u c t u a t i n g Pressure D i s t r i b u t i o n with a: Square C y l i n d e r  24.  54, 55, 56  V a r i a t i o n of F l u c t u a t i n g L i f t C o e f f i c i e n t with ai Square Cylinder  25.  57  Pressure O s c i l l a t i o n s on the Surface of the Square C y l i n d e r  26,  Amplitude  58.  Modulations  of Pressure  Fluctuations  on the Surface of The Square C y l i n d e r 27.  Slowly Varying Amplitude Square C y l i n d e r  28.  and Frequency of  Motion  59  E f f e c t of Motion on Pressure F l u c t u a t i o n s on the Surface of Square C y l i n d e r  29.  59  V a r i a t i o n of S t a t i c Pressure D i s t r i b u t i o n w i t h 62, 63, 64, 65  a: Rectangular C y l i n d e r AR=2 30.  V a r i a t i o n of S t a t i c L i f t  C o e f f i c i e n t with a;  Rectangular C y l i n d e r £R=2 31.  59  V a r i a t i o n of Strouhal Number with Number; Rectangular  66. Reynold^;  C y l i n d e r AR=2  67  V a r i a t i o n of F l u c t u a t i n g Pressure D i s t r i b u t i o n w i t h a: Rectangular C y l i n d e r AR=2 V a r i a t i o n of L i f t C o e f f i c i e n t with a: Rectangular C y l i n d e r ARo2 Pressure O s c i l l a t i o n on the Surface of the Rectangular C y l i n d e r M =2 PressureTsyfluctuations as Recorded by Probe and Tap 17.3 Effect  1 of Rectangular C y l i n d e r ARB2, Probe inches Downstream of Model of Motion on Pressure F l u c t u a t i o n s on  the Surface of Rectangular C y l i n d e r AR=2 Pressure D i s t r i b u t i o n oyer Rectangular C y l i n d e r M «=l/2 V a r i a t i o n of S t r o u h a l Number w i t h  Reynolds^  Number: Rectangular C y l i n d e r AR=l/2 S t a t i c Pressure D i s t r i b u t i o n ; C i r c u l a r C y l i n d e r V a r i a t i o n of S t r o u h a l Number with Reynold&'s Number f o r C i r c u l a r C y l i n d e r F l u c t u a t i n g Pressure D i s t r i b u t i o n :  Circular  Cylinder C P  s i n & versus  f o r Circular Cylinder  fl  Pressure O s c i l l a t i o n s on the s u r f a c e of Circular Cylinder Amplitude Modulation of Pressure  Oscillation  on the surface of C i r c u l a r C y l i n d e r  Figure 45.  Page Variation of Phase on the Surface of Circular Cylinder  46.  Pressure Fluctuations as recorded by Probe 9.7 inches Downstream of Model  47.  88  Double Frequency Effect at the Center of Wake of Circular Cylinder  48.  87  88  Pressure Fluctuations on the Surface of Circular Cylinder as affected by i t s motion  49.  Variation of Static Pressure Distribution with o: E l l i p t i c Cylinder  50.  96, 97  Variation of Fluctuating L i f t Coefficient with a: E l l i p t i c Cylinder  54.  95  Variation of Fluctuating Pressure D i s t r i bution with as E l l i p t i c Cylinder  53.  94  Pressure Oscillations on the Surface of E l l i p t i c Cylinder  52.  91, 92, 93  Variation of Static L i f t Coefficient with a» E l l i p t i c Cylinder  51.  88  98  Variation of Strouhal Number with Reynoldss Number f o r E l l i p t i c Cylinder  99  55.  Self-Excited Motion of the A i r f o i l  101  56.  Lissajous Figure During Self. Excited Motion of the A i r f o i l  101  Figure  \ 57.a 57. b  Page  Tap 3 and L a t e r a l Displacement  of A i r f o i l  Tap 3 and T o r s i o n a l Displacement  of A i r f o i l  101 101  i  58.  O s c i l l a t i n g Pressure on the Surface of A i r f o i l Undergoing F l u t t e r  59.  Effect  102  of S t r e a m l i n i n g on  104 fl  ;  max  LIST OP SYMBOLS a  L a t e r a l spacing of v o r t i c e s  a  Semimajor a x i s of e l l i p s e  &  Aspect  b  Length of face of r e c t a n g u l a r c y l i n d e r p a r a l l e l t o flow  c  Characteristic  C  C o e f f i c i e n t per unit span  ds  Elementary  e  Eccentricity  h  Length of face of r e c t a n g u l a r c y l i n d e r perpendicular t o flow  h  L o n g i t u d i n a l spacing of v o r t i c e s  I  Current i n electromagnetic dampers  L'  L i f t per u n i t span  P  Pressure a t a point  ratio  chord  length of e l l i p t i c  cylinder  Vc He  —  r  Damping  Kt  ~  V  Free stream  x  Coordinate, a b s c i s s a  y a  Coordinate, ordinate Angle of a t t a c k  T  Angle between pressure and l i f t  *  Angular  V  Kinematic v i ^  (p u)  , Reynolds Number coefficient  , S t r o u h a l Number velocity  forelliptic  spacing of taps of c i r c u l a r  cylinder  cylinder  , •  Density Strouhal frequenoy,  i . e . , frequency  of shedding  vortices  Subscripts*  fl £  F l u c t u a t i n g measurement Lower surface  L  Pertaining to l i f t  max  Maximum value  P  P e r t a i n i n g to pressure  rms  Root mean square value  st  S t a t i c measurement  u  Upper surfaoe Value a t i n f i n i t y  I.  The bility  nature of the  INTRODUCTION  e x c i t a t i o n i n the  i s an important f a c t o r governing the  Hence p r e c i s e  determination of f l u c t u a t i n g  i s e s s e n t i a l i n the  The  situations  body or during part of the  gated to some extent by Duncan ( l ) , * Van Sttider  which forms one  (5) and  of the  (7).  others.  The  out  (lO) i n v e s t i g a t e d  Studies of the  de  involving  separation  characteristics  of the wake,  Karman i n h i s c l a s s i c a l ;  Roshko (9), while Chuan and ;  the vortex shedding as r e l a t e d  carried  out  cyl-  s i m i l a r flow measuring apparatus  to s e l f e x c i t e d  Magnus tor-  airfoil.  measurement of o s c i l l a t i n g pressure on a s t a t i o n a r y  c y l i n d e r was  (3),  Vooren (2), Mendelson  flow p a t t e r n i n the wake of b l u f f  by Cometta (8) and  s i o n a l o s c i l l a t i o n s of an The  involving  c y c l e ) have been i n v e s t i -  t h e o r e t i c a l l y by von  inders using hot wire anemometers and were c a r r i e d  problems  important parameters i n the a e r o e l a s t i c i n s t a b i l i t y  study, were i n v e s t i g a t e d papers ( 6 ) ,  pressure on e l a s t i c bodies  pressure c h a r a c t e r i s t i c s have r e c e i v e d  comparatively l i t t l e a t t e n t i o n .  (4),  response of a system.  l i t e r a t u r e r e v e a l s that  vortex-excited fluctuating  (over part of the  insta-  study of t h e i r i n s t a b i l i t y c h a r a c t e r i s t i c s . ,  A survey of e x i s t i n g  Slsto  study of a e r o e l a s t i c  by McGregor ( l l ) and  Prendergast  experimental arrangement r e q u i r e d e x t e r n a l r o t a t i o n obtain a complete d i s t r i b u t i o n of f l u c t u a t i n g  * Numbers i n brackets r e f e r to b i b l i o g r a p h y  of the  pressure.  circular  (12).  The  model to  2  A technique for  oscillating  and  later  used  for  the  this  the  of  was  their  the With  applied forced  a l l  body  and  the  was  and  however,  vibrations  of  (14).  its  transducer  Molyneux The  aerodynamic  solely  The m o d e l s  (13)  device  was  derivatives  integration  remained  interest.  type  d e v e l o p e d by  Ruddleston  pressure  of  gauge  over  for  were  the  by surface  airfoils  exposed  rather  than  oscillations  important  task  of  as  to  resulting  phenomenon.  this  characteristics  strain  determination  work,  main f i e l d  flutter  miniature  Molyneux and  oscillating Their  a  measurement  experimental  airfoil.  externally from  pressure  m o d i f i e d by  measurement of  involving  of  i n f o r m a t i o n an the  wake,  aeroelastic  oscillating  instability  of  pressure that  body  correlation  between  d i s t r i b u t i o n on remains.  a  3.  II.  STATEMENT OF THE PROBLEM  The measurement of unsteady aerodynamic pressure a survey  on a body and  of the a s s o c i a t e d wake and the a e r o e l a s t i c i n s t a b i l i t y of  the body forms the s u b j e c t of t h i s experimental i n v e s t i g a t i o n .  The  projeot may be c l a s s i f i e d i n t o four stages: (i)  Measurement of o s c i l l a t i n g pressure on b l u f f as w e l l as streamlined bodies, s t a t i o n a r y and v i b r a t i n g , when located i n steady  (ii)  flow.  Experimental  study  of wake t o a s s o c i a t e f l u c t u a t i n g  pressure  with the wake c o n f i g u r a t i o n , (iii)  Measurement of c r i t i c a l f l u t t e r speed f o r the b l u f f and aerodynamic bodies i n two degrees of freedom, plunging and t o r sion.  (iv)  C o r r e l a t i o n of information obtained i n ( i ) ,  ( i i ) , and ( i i i ) .  4. III.  INSTRUMENTATION, CALIBRATION AND  EXPERIMENTAL SETUP  The i n s t r u m e n t a t i o n used i n the experimental i n v e s t i g a t i o n corresponds as f o l l o w s to the f i r s t  three stages of the p r o j e c t mentioned  i n Chapter I I : (i)  a pressure measuring device, a transducer, and the  arrange-  ment f o r c a l i b r a t i n g i t (ii) (iii)  instrumentation f o r wake survey mounting of model i n the wind tunnel to provide freedom of motion i n plunging, and t o r s i o n , system f o r p r o v i d i n g des i r a b l e s t i f f n e s s and of  damping, arrangement f o r measurement  c r i t i c a l v e l o c i t y , frequency, and amplitude  elastic instability  during aero-  of the model*  Each of these systems i s described i n some d e t a i l below.  3.1.1  Wind  Tunnel  The wind tunnel used f o r the t e s t program was  of the  standard  low speed, low turbulence r e t u r n type with v e l o c i t y c o n t r o l over  the  range of 4 to 150 f e e t per second and a turbulence l e v e l of l e s s  than  0.5$  as i n d i c a t e d by sphere drag t e s t .  15 horsepower d i r e c t  The tunnel was  powered by a  current motor d r i v i n g a commercial a x i f l o w f a n  with a Ward-Leonard system of speed c o n t r o l .  The  tunnel v e l o c i t y i s  c a l i b r a t e d against the pressure d i f f e r e n t i a l across the c o n t r a c t i o n s e c t i o n of 7:1  ratio.  This pressure was  meter which can be read to 0.02  measured on a Betz micromano-  m i l l i m e t e r of water.  The t e s t s e c t i o n  5.  was  36 inches by 27 inches with corner f i l l e t s v a r y i n g from 6 inches  by 6 inches t o 4 3/4 inches by 4 3/4 inches t o compensate f o r boundary l a y e r growth. than 0.25$.  The s p a t i a l v a r i a t i o n of v e l o c i t y was found t o be less The aerodynamic o u t l i n e of the tunnel i s g i v e n i n Figure 1.  3 . 1 . 2 - C a l i b r a t i o n of Betz Manometer A standard p i t o t tube placed i n the t e s t s e c t i o n was used i n c o n j u n c t i o n with a Lambrecht Manometer to measure the dynamic pressure head.  The readings obtained from these measurements were then compared  with the readings of the pressure d i f f e r e n t i a l across the c o n t r a c t i o n s e c t i o n as measured by the Betz manometer.  The accuracy  meter was found t o be adequate f o r the purpose  of Betz mano-  (Figure 2 ) .  3.2 Models The models used were a l l of a l i g h t weight balsa c o n s t r u c t i o n . F i v e d i f f e r e n t models were made: (i) (ii) (iii) (iv)  a 2 i n c h sqare  cylinder  a 1 1/2 by 3 i n c h r e c t a n g u l a r c y l i n e r a 2 i n c h diameter an e l l i p t i c  circular  cylinder  c y l i n d e r with semimajor a x i s of 3 inches and  semiminor a x i s of 3/8 i n c h (v)  a 6 i n c h chord NACA 4412 a i r f o i l s e c t i o n wing  A l l models were constructed to span the e n t i r e wind tunnel t e s t thus s i m u l a t i n g two-dimensional  flow.  section  The models were made out of s o l i d  b a l s a with the exception of the wing which was made up of s t i f f e n i n g with s t r i n g e r s and covered with a 1/16 i n c h b a l s a sheet.  ribs  The models are  F i g u r e 1.  Aerodynamic  O u t l i n e of Wind T u n n e l  0  15 30 45 60 Wind Velocity, Pltot Tube, f p s .  Figure 2.  Calibration, Curve: Wind Tunnel  75  90  105  8.  shown i n Figure 3» A copper s t r i p 3/4  inch wide, was  the pressure taps i n the e l l i p t i c  placed at midspan to accommodate  c y l i n d e r and a i r f o i l .  c u l a r c y l i n d e r , a copper r i n g of 2 i n c h diameter and 3/4 was  For the  cir-  inch width  used, while the square and r e c t a n g u l a r c y l i n d e r s used 3/4  aluminum blocks f o r p o s i t i o n i n g the s t a t i c pressure h o l e s .  inch wide  Models  with the l o c a t i o n of the pressure taps are shown i n Figure 4. Each model was  supported by a l/2 inch diameter  shaft which  extended  beyond the tunnel w a l l s , the shaft i n turn being supported by a system of a i r bearings.  3.3  (Figure 5a).  Model Mounting System The mounting system e s s e n t i a l l y c o n s i s t e d of a channel  section,  a s t e e l frame supporting the a i r bearings at the top and bottom of of  the tunnel s e c t i o n which provided the plunging degree of freedom to  the model.  P o s i t i v e alignment  achieved by the use of 2 1/2  between upper and lower a i r bearings  by 2 1/2  was  i n c h angle i r o n s bolted at the  ends, while the s e v e r a l a d j u s t i n g b o l t s provided along the frame side helped i n v e r t i c a l p o s i t i o n i n g of the model. channels were machined  The  upper and  to provide accurate alignment  bearings supporting the l a t e r a l s h a f t s .  lower  between the a i r  The above arrangement  was  i d e n t i c a l to that used by Smith (15). For the study of f l u t t e r phenomena i t was the t o r s i o n a l degree of freedom. of  This was  e s s e n t i a l to incorporate  achieved by p r o v i d i n g a set  t o r s i o n a l a i r bearings which were s i m i l a r to the l a t e r a l a i r bearings  but on a smaller s c a l e .  The t o r s i o n a l a i r bearings were designed to  be mounted i n the upper and  lower l a t e r a l support s h a f t s (Figure  5b).  Figure  3.  Experimental Models. 1. E l l i p t i c S e c t i o n Wing 4. C i r c u l a r C y l i n d e r  Cylinder 2. Square C y l i n d e r 5. R e c t a n g u l a r C y l i n d e r Mm  3. NACA 1/2,2  4412  15  >  16  1  1  2  1  (-  V  14  IS  13-h  6  2 in. x 2 in.  12 11  ••  y—A—i—h 10 9  8  6  7  (a) Square C y l i n d e r -*j a k i n  16 - -  15  14  r 13  12  11  10  (b) Rectangular C y l i n d e r  (c) C i r c u l a r  Cylinder  9  Figure 4.,  (d) E l l i p t i c  Cylinder  (e) NACA 4412  Airfoil  L o c a t i o n of Pressure Taps on Models  Figure 5a.  1. L a t e r a l Displacement Transducer 2. L a t e r a l S t i f f n e s s Spring 3. L a t e r a l A i r Bearing 4. L a t e r a l Support Shaft 5. L a t e r a l Damper 6. T o r s i o n a l A i r Bearing 7. Model Shaft  13  Figure 5b.  1. L a t e r a l A i r Bearing 2, L a t e r a l S t i f f n e s s Spring 3. L a t e r a l Support Shaft 4. Model Shaft 5. T o r s i o n a l A i r Bearing 6. T o r s i o n a l Displacement Transducer 7. T o r s i o n a l S t i f f n e s s Spring  Figure 5» D e t a i l s of Model Mounting System  14.  The a i r bearing c a r r i e s a load on a shaft passing through i n a s i m i l a r manner to an o i l j o u r n a l bearing. an o r i f i c e  (Figure 6) at a pressure P . o  along the s i d e s of the shaft and value P^.  Due  the bearing  A i r i s supplied  through  to viscous f o r c e s a c t i n g  b e a r i n g walls the pressure drops to some  A p p l i c a t i o n of a load causes the s h a f t to p o s i t i o n i t s e l f  c e n t r i c a l l y with respect to the bearing. and bearing:now becomesiless  The d i s t a n c e between s h a f t  on the side opposite to the load.  r e d u c t i o n i n distance' between s h a f t and  1  the bearing thus decreasing the flow out of the bearing.  creased and s i n c e P o  decreased,  The  j o u r n a l o n the side opposite  to the load i n c r e a s e s the viscous f o r c e s on the a i r flowing  volumetric flow i s now  ec-  the pressure drop  i s constant P., must i n c r e a s e . 1  through  Since the  (P  - P^) i s de-  The  opposite  occurs on the load side where the distance i n c r e a s e s .  effect  y y  A pressure  d i f f e r e n t i a l i s t h e r e f o r e set up which supports the load.  A quanti-  t a t i v e a n a l y s i s of a i r bearings i s given by Laub (16). A i r f o r the bearings was compressor, pumping i n t o a 250  s u p p l i e d by an Ingersoll-Rand 2-stage cubic foot storage tank.  A i r was  carried  from the tank by a f l e x i b l e hose to a t h r o t t l i n g valve which d i s t r i b u t e d a i r at 60 pounds per square  inch to a l l a i r bearings from the main supply  at 118 pounds per square i n c h . L a t e r a l s t i f f n e s s was  s u p p l i e d by springs attached between the  mounting frame and the t o r s i o n a l a i r bearing. c a n t i l e v e r springs were used.  This was  For t o r s i o n a l s t i f f n e s s ,  done by t a k i n g a s t r i p of b e r y l l i u m -  copper and a t t a c h i n g i t at one end to the t o r s i o n a l fair bearing serving as the r o o t and at the other end i n such a way  as to r e s t r a i n  torsional  \ V  Y/////////A  V///////2  Model Support Shaft  77mY7777777, r 7 Orifice  Figure 6 ,  CrosB-section  s  of A i r Bearing  16.  motion.  The d e t a i l s of the two mode s t i f f n e s s e s are shown i n Figure  5.  3.4 Pressure  Transducer  The main problem encountered  i n the i n v e s t i g a t i o n was the design  and c a l i b r a t i o n of a dynamic pressure transducer s u i t a b l e f o r the measurement of f l u c t u a t i n g pressure on the surface of the models, which may be s t a t i o n a r y or o s c i l l a t i n g and may be l o c a t e d i n unseparated  or separated  A c o u s t i c l e v e l pressure v a r i a t i o n s i n the frequency range of 2  flow.  to 200 c y c l e s per second made most of the commercially ducers u n s u i t a b l e f o r the purpose.  available trans-  The i d e a l transducer would be one  with high s e n s i t i v i t y , l i n e a r response, and n e u t r a l t o v a r i a t i o n s i n atmospheric  conditions.  With t h i s i d e a l i n mind a v a r i e t y  of t r a n s -  ducers i n v o l v i n g the p r i n c i p l e of s t r a i n gage, capacity change, r e s i s t a n c e change and p i e z o e l e c t r i c i t y were designed. The r e s i s t o r and c a p a c i t o r type transducers f a i l e d to provide enough s e n s i t i v i t y f o r the s i z e of the transducer intended.  A s t r a i n gage type  of transducer designed a c c o r d i n g to the arrangement suggested by Perry (l6) was found t o be q u i t e s e n s i t i v e t o s t a t i c pressures but r e l a t i v e l y i n s e n s i t i v e to pressure f l u c t u a t i o n s conducted  The t e s t s  with a diapnragm of 2 inches diameter and 0 . 0 0 2 i n c h thickness  r e v e a l e d . r a t h e r extreme s e n s i t i v i t y imperfections i n the diaphragm. reduced  of a c o u s t i c l e v e l .  of the transducer output to the minor  Increase i n diaphragm thickness only  the s e n s i t i v i t y without improving  It i s b e l i e v e d that with a r e l a t i v e l y transducer suggested  the s i t u a t i o n  substantially.  s t i f f diaphragm the s t r a i n gage  by Perry may be used f o r measurement of s t a t i c or  17.*  large amplitude  dynamic pressure but f u r t h e r i n v e s t i g a t i o n i s necessary  to make i t s u i t a b l e f o r minute pressure Transducers  fluctuations.  using Rochelle s a l t , quartz, and  ceramic  piezoelectric  c r y s t a l s i n the form of a phonograph c a r t r i d g e as used i n the  arrange-  ment shown i n Figure 7 were found to be h i g h l y s e n s i t i v e and  capable  of measuring intended low l e v e l pressure changes on a body.  The  tivity  of the device to s t a t i c pressure d i d not present any  the i n t e n t i o n was pressure.  problem as  to measure f l u c t u a t i n g pressure rather- than  static  C r y s t a l s of Rochelle s a l t and quartz were discarded i n  preference to the ceramic changes.  insensi-  type because of t h e i r s e n s i t i v i t y to temperature  Thus the p i e z o e l e c t r i c transducer using a ceramic  crystal  i  met  the necessary  requirements  adequately  pressure measurement throughout  and hence was  used f o r the  the experiment.  In a p i e z o e l e c t r i c device i t can be shown that the voltage i s d i r e c t l y p r o p o r t i o n a l to the f o r c e a p p l i e d across one dimensions of the c r y s t a l istics  (17).  This phenomenon i s due  of the c r y s t a l s t r u c t u r e and advantage was  to provide a l i n e a r pressure The  of the s e n s i t i v e to the character-  taken of t h i s property  transducer.  o s c i l l a t i n g pressures at the surface of the body were sensed  pressure taps and transmitted by polyethylene tubing to the I t was  important  tubing of d i f f e r e n t diameter ence of s e n s i t i v i t y  and  of the  Experiments c a r r i e d out with  lengths revealed considerable depend-  on the diameter  of the  tube.  very f i n e tubing (0.010 inches diameter) response  by  transducer.  to determine the e f f e c t of length and diameter  tubing on s e n s i t i v i t y and phase l a g .  With  output  of the  18.  Figure 7a. Sohematic  Figure 7b.  Exploded View  Figure  7ff. A s s e m b l y  (V)  o I  Figure  7.  Pressure  Transducer  21. transducer was almost n e g l i g i b l e while with a large diameter tubing ( l / 8 i n c h i n s i d e diameter) the transducer turbulent.  response was observed to be  The tube s i z e of 0.07 i n c h i n s i d e diameter showed no l o s s  i n the s e n s i t i v i t y and hence was used i n the experiment.  To study  the e f f e c t of length of the tubing on phase s h i f t , the f l u c t u a t i n g pressure at a point on a model was transmitted to two i d e n t i c a l pressure  transducers,  one located w i t h i n the model and the other  l o c a t e d at the end of 30 inches  of 0.07 inch diameter tube.  measureable phase l a g was observed i n the frequency 10 cycles per second t o 70 c y c l e s per second made i t p o s s i b l e t o locate the pressure  range of  (Figure 8 ) .  transducers  No  This  outside the  tunnel thus e l i m i n a t i n g i n e r t i a e f f e c t s which would be present if  the transducer were located i n s i d e the model. To e s t a b l i s h the technique  of c o n s t r u c t i o n g i v i n g transducers  of i d e n t i c a l performance three u n i t s were constructed and c a l i brated although  only one of them was used.  made to connect the pressure by a l l o w i n g the pressure  The arrangement was  taps s e p a r a t e l y .  This was accomplished  tubes t o hang f r e e l y from the bottom of  the model and t o be i n d i v i d u a l l y connected t o an a c o u s t i c a l l y dead chamber designed  t o eliminate the i n t e r f e r e n c e from e x t e r n a l noise.  The a c o u s t i c a l l y dead chamber was construoted plywood l i n e d with 1 i n c h t h i c k foam rubber.  from 3/4 i n c h  The chamber was then  placed on a 1 i n c h foam rubber pad t o e l i m i n a t e mechanical v i b r a t i o n s transmitted through the f l o o r . transducer  The a c o u s t i c a l l y dead chamber with  i n place i s shown i n Figure 9.  22.  Figure 8.  E f f e c t o f Tube L e n g t h 67 c y c l e s per second  on  Phase,  24.  3.4.1  C a l i b r a t i o n of Pressure  Transducer  C a l i b r a t i o n of the pressure transducer was d i f f e r e n t ways.  c a r r i e d out i n two  In the f i r s t arrangement the c a l i b r a t i o n was  using a f l u c t u a t i n g pressure source c o n s i s t i n g of a f i x e d with a r e c i p r o c a t i n g p i s t o n .  The p i s t o n was  attempted  cylinder  d r i v e n through  an  e c c e n t r i c whose speed arid e c c e n t r i c i t y could be v a r i e d so as to provide pressure f l u c t u a t i o n s of v a r i e d amplitude Two  and  frequency.  pressure taps were taken from the top dead centre of the c y l i n d e r  w i t h one  connected  sure transducer.  to a sound l e v e l meter and the other to the presThe arrangement was  found to have some inherent  limitations. (i)  The apparatus;iwas  r a t h e r crude and would r e q u i r e consider-  able improvement before i t could be used f o r r e f i n e d calibration. (ii)  Mechanical nature of the device introduced considerable noise thus d i s t o r t i n g the  (iii)  signal,  With the a v a i l a b l e d r i v i n g u n i t i t was  not p o s s i b l e to  a t t a i n frequencies beyond 30 c y c l e s per second, i t was  while  necessary to obtain a c a l i b r a t i o n curve up to  cycles per  100  second.  Although the magnitudes of the pressures obtained from the o s c i l l a t i n g pressure source were found  mechanical  to be i n a c c u r a t e as icompared  to that p r e d i c t e d by the theory or measured by the Sound Level Meter, i t was  observed  that the output  of the c r y s t a l transducer was  i n the frequency range of 0 t o 25 c y c l e s per second.  linear  This i n f o r m a t i o n  25.  proved  t o be h e l p f u l i n l a t e r  calibration.  The second arrangement made use of a U n i v e r s i t y ID-60 horn d r i v e r i n conjunction with a General Radio 1551 sound l e v e l meter as shown i n Figure 10.  The horn d r i v e r produced the o s c i l l a t i n g  pressure i n s i d e the c a l i b r a t i o n box, constructed of mild s t e e l , which was sensed  by the microphone of the sound l e v e l meter and by  the c r y s t a l transducer. was  The frequency  c o n t r o l l e d by a Hewlett  - Packard  of pressure  oscillations  202 A low frequency  generator  and a m p l i f i e d by a Bogen 60 watt A m p l i f i e r . The  c a l i b r a t i o n s were conducted  l e v e l a t v a r y i n g frequency.  by h o l d i n g a constant  pressure  This was made p o s s i b l e by keeping  the Db sound l e v e l , as detected by the sound l e v e l mater, at a constant value and v a r y i n g the frequency  of the generator.  From  the data obtained curves r e p r e s e n t i n g v a r i a t i o n of output with frequency were p l o t t e d as shown i n Figure 11. i t was s t r a i g h t forward and voltage output was  From these  plots  to obtain the r e l a t i o n between pressure  of the transducer f o r a given frequency.  It  p o s s i b l e t o r e l a t e the Db readings of the sound l e v e l meter to  pressures i n pounds per square  i n c h by the f a c t that the Dbs are  defined as a f u n c t i o n of pressure r a t i o s with a reference pressure of 0.0002 microbars. were found Due  The p l o t s of pressure versus voltage  to be l i n e a r  output  (Figure 12").  t o the l i m i t a t i o n s imposed by the a m p l i f i e r and horn  d r i v e r the minimum frequency  obtainable was 15 cycles per second.  It thus remained t o c a l i b r a t e the transducer i n the low range of 0 t o 15 c y c l e s per second.  This was achieved by e x t r a p o l a t i o n  ro  -J o  Figure 10b.  Assembly  1, Bogen A m p l i f i e r 2. Sound Level Meter Box 5. A c o u s t i c a l l y Dead Chamber Figure 10,  C a l i b r a t i o n Setup  3. Horn D r i v e r  4. C a l i b r a t i o n  28.  320  280  Frequency, cps  Figure 11.  C a l i b r a t i o n Curves V a r i a t i o n of Output with Frequency  Figure 12.  C a l i b r a t i o n Curve: V a r i a t i o n of Output with Pressure  30.  based  on the f a c t that the v a r i a t i o n of voltage output with f r e -  quency was  found t o be l i n e a r i n the range of i n t e r e s t i n both of  the c a l i b r a t i o n The  procedures.  c a l i b r a t i o n was  checked  by comparing the pressure  a t i o n s on the surface of a s t a t i o n a r y c i r c u l a r c y l i n d e r by the pressure transducer with those The  fluctu-  registered  obtained by McGregor ( l l ) .  comparison between the two sets of r e s u l t s i s presented i n  F i g u r e 41.  3.5  Wake Survey  Equipment  P r e l i m i n a r y surveys of the wake behind a c i r c u l a r  cylinder,  c a r r i e d out with hot wire anemometer equipment, gave the impression that i t would be r a t h e r d i f f i c u l t vortices.  to l o c a t e , p r e c i s e l y , the shed  The fundamental s i g n a l was  the random background noise which was the a v a i l a b l e equipment. noise was was  An attempt  completely difficult  camouflaged by to suppress  with  to eliminate the background  made with the use of an i n t e g r a t i o n o s c i l l o s c o p e , but i t  found that the random voltages superimposed on the fundamental  s i g n a l t r i g g e r e d the sweep at d i f f e r e n t points i n the fundamental cycle each time so no build-up occurred.  Thus the i n t e g r a t i o n  o s c i l l o s c o p e could not properly detect the fundamental s i g n a l . The Karman vortex s t r e e t causes v e l o c i t y f l u c t u a t i o n s and accompanying these are pressure f l u c t u a t i o n s . was  As the transducer  designed to measure f l u c t u a t i n g pressure,- a p o s s i b i l i t y  t h a t i t might serve as a wake survey  instrument.  existed  3 1 .  A simple experiment  showed t h a t a pressure transducer placed  i n a s t a t i o n a r y body located i n the a i r s t r e a m would sense  the  frequency  surprising  of the v o r t i c e s shed from r that  body..- I t was  to note that the output from the c r y s t a l transducer gave a more c l e a r l y defined i n d i c a t i o n of the fundamental shedding than the output from the hot wire anemometer. quency was  that of the shed v o r t i c e s was  of the S t r o u h a l number as determined  frequency  Proof that the  obtained by  fre-  comparison  from the frequency  recorded  by the transducer to the S t r o u h a l numbers over a given range of Reynolds number f o r a c i r c u l a r c y l i n d e r as given by Fung (18). Thus the pressure transducer designed to measure the a c o u s t i c l e v e l pressure v a r i a t i o n s can be used shedding v o r t i c e s behind t e s t  to determine  the frequency  of the  bodies.  Further experimentation revealed that a pressure tap placed at the t i p of a slender probe when used i n c o n j u n c t i o n with the pressure transducer could be used e f f e c t i v e l y as a wake survey vice  (Figure 13).  A 36 i n c h length of tubing was  de-  used to transmit  the pressure f l u c t u a t i o n s at the probe t i p to the transducer. Using the probe and the transducer i n t h i s manner gave by movement of the probe i n the wake an i n d i c a t i o n of the vortex l o c a t i o n s . output s i g n a l from the pressure transducer with wake was  The  the probe i n the  much c l e a r e r than the corresponding s i g n a l from hot wire  anemometer equipment.  Experimentation with the probe i n the wake  of a c i r c u l a r c y l i n d e r y i e l d e d a value of 0.29  f o r the r a t i o of  l a t e r a l to l o n g i t u d i n a l spacing between the adjacent v o r t i c e s  which  i s ; l i t t l e higher than the t h e o r e t i c a l l y ; r e s t a b l i s h e d value of 0.281.  32  Figure  13.  Wake S u r v e y  Probe  33.  3.6  Bending and T o r s i o n a l Displacement  Transducers  The l a t e r a l displacement transducer was type developed by Smith  (l5).  an i n d u c t i v e  coil  Two" c o i l s were used, one as the  primary and the other as the secondary.  They were c o n c e n t r i c a l l y  mounted so as to provide an annular r e g i o n through which the l a t e r a l s h a f t could pass.  A s i g n a l of 20,000 c y c l e s per second  was f e d i n t o the primary c o i l which was  sensed by the  secondary  c o i l through inductance.  The amplitude of the s i g n a l .received  by the secondary  dependent on the number of primary  c o i l was  turns cut o f f by the l a t e r a l s h a f t , i . e . on the plunging d i s p l a c e ment of the model. The output from the secondary lated signal.  By f i l t e r i n g  c o i l was  an amplitude modu-  the c a r r i e r frequency; i . e . the 20,000  cps s i g n a l fed to the primary, an exact time-history of the l a t e r a l displacement was  obtained.  The t o r s i o n a l displacement was in  one of the t o r s i o n a l c a n t i l e v e r springs used to provide  t o r s i o n a l s t i f f n e s s to the model. at  measured by sensing s t r a i n  The s t r a i n gages were mounted  the root of the- c a n t i l e v e r s p r i n g and the s i g n a l was fed  through an E l l i s Bam-1  s t r a i n gage bridge a m p l i f i e r .  Both  l a t e r a l and t o r s i o n a l displacement outputs were fed i n t o a Tektronix 502A o s c i l l o s c o p e .  3.6.1  C a l i b r a t i o n of Displacement  Transducers  The l a t e r a l displacement transducer was  c a l i b r a t e d by  34.  d i s p l a c i n g the aluminum l a t e r a l support s h a f t i n the annular r e g i o n of the transducer i n equal increments output.  and noting the  This c a l i b r a t i o n showed the l a t e r a l transducer to  be l i n e a r w i t h i n 1% (figure 14). The t o r s i o n a l displacement  transducer was  calibrated  by d i s p l a c i n g the end of the c a n t i l e v e r s p r i n g i n equal increments  and noting the output.  The t o l e r a n c e s of l i n e a r i t y  were found t o be comparable to those of the l a t e r a l transducer  (Figure  3.7 Electromagnetic  displacement  15).  Damping  The damping, i n a d d i t i o n to inherent damping withinthe system, was introduced by means of electromagnetic eddy current dampers. The dampers created a magnetic f i e l d c a r r y i n g the model was exposed.  to which the aluminum s h a f t  Eddy currents induced i n the  shaft d i s s i p a t e d energy from the o s c i l l a t i n g The damping was found  system.  to be almost v i s c o u s .  For higher  currents the damping was s t i l l as c l o s e to viscous as i t was for  lower  currents.  Damping l e v e l s were c o n t r o l l e d by the amount  of D. C. current passing through b r a t i o n curve i s shown i n Figure  the electromagnet. 16.  The  cali-  37.  0.Q3Q  0.025  0.020  0.015  0.010  0.005  0  0.10  0.20  0.30  0.40  0.50  I, amps  Figure 16.  C a l i b r a t i o n Curve: Electromagnetic Damper  38. 3.8 Experimental Test  Procedures  3.8.1 S t a t i c and O s c i l l a t i n g Pressure Measurements Measurements of s t a t i c and o s c i l l a t i n g Pressures were made s e p a r a t e l y f o r each i n d i v i d u a l pressure tap. from the taps were connected  individually f i r s t  The tubings  t o a Lambrecht  manometer f o r s t a t i c pressure measurements and second to the pressure transducer f o r o s c i l l a t i n g pressure measurements. The transducer output was f e d d i r e c t l y t o the Tektronix 502A o s c i l l o s c o p e .  The g r i d i n s c r i b e d onthe o s c i l l o s c o p e screen  made i t p o s s i b l e t o read with the accuracy f u l l scale.  of l e s s than 1%  A l l readings of pressure f l u c t u a t i o n s were made  peak t o peak and i n the ease of amplitude maximum amplitude  modulated s i g n a l s the  only was recorded and taken to be the maximum  pressure f l u c t u a t i o n at that p o i n t .  The readings from the os-  c i l l o s c o p e were recorded i n m i l l i v o l t s and conversion to pounds per square i n c h was made using the c a l i b r a t i o n curves. frequency  The  of pressure o s c i l l a t i o n s was noted during each t e s t  as output of the pressure transducer was a f u n c t i o n of frequency. The experimental t e s t setup i s shown i n Figure 17. Pressure measurements were made with a l l the models i n i t i a l l y stationary.  The square, r e c t a n g u l a r , e l l i p t i c a l  c y l i n d e r s and  wing were t e s t e d at v a r i o u s angles of a t t a c k and the v a r i a t i o n of  s t a t i c and f l u c t u a t i n g pressure d i s t r i b u t i o n was noted.  These measurements with s t a t i o n a r y models were c a r r i e d out as s e v e r a l values of Reynolds  number.  Figure  17*  Equipment and  Test  Section  40.  Once the models were t e s t e d when s t a t i o n a r y , a i r was supplied to the bearings, and tunnel speed was v a r i e d u n t i l the model executed  s e l f excited o s c i l l a t i o n s .  the o s c i l l a t i n g The  The e f f e c t  pressure d i s t r i b u t i o n  of motion on  was noted.  o s c i l l a t i n g pressures as w e l l as the model  oscillations  were recorded p h o t o g r a p h i c a l l y .  3.8.2 Amplitude Measurements The i n d i v i d u a l model was made f r e e to o s c i l l a t e  by supply-  ing a i r t o the l a t e r a l and t o r s i o n a l a i r bearings which permitted two degrees of freedom. of o s c i l l a t i o n s  Once the body was i n motion, the nature  was. observed  on the o s c i l l o s c o p e .  Since the  o s c i l l o s c o p e was of the dual beam type i t was p o s s i b l e to d i s p l a y and photograph the two degrees of freedom of motion simultaneously. It was a l s o p o s s i b l e t o observe displacements  the e f f e c t  of t o r s i o n a l and l a t e r a l  on the o s c i l l a t i n g pressure d i s t r i b u t i o n  by t h e  dual beam f e a t u r e .  3.8.3 Wake Measurements The  probe connected  t o the pressure transducer was placed  i n the wake of each body and s l i g h t l y t o one,side. fluctuations  The pressure  produced by the wake were displayed on the screen  of the o s c i l l o s c o p e along w i t h tiujse produced a t a point on the surface of the model.  The probe, l o c a t e d on the same side of  the model as the point, was then moved from the v i c i n i t y of the body down stream u n t i l the two s i g n a l s were i n phase.  41.  The  procedure was repeated  with the probe ongthe opposite s i d e .  Twice the d i f f e r e n c e between the two readings gave the vortex spacing i n the flow d i r e c t i o n .  I t was found that t h i s measure-  ment could be made with a f a i r degree of accuracy.  For example,  F i g u r e 3 5 shows two such t r a c e s i n phase, the upper trace being the pressure and  o s c i l l a t i o n s at the surface of the body  (tap l )  the lower t r a c e the o s c i l l a t i o n s at the probe t i p . The  probe was moved across the wake of the models t o obtain  the spacing i n the d i r e c t i o n perpendicular to the airstream. The  measurements were made by noting the distance between the  maximum f l u c t u a t i o n s t o e i t h e r side of the wake. ment could be made but not with the accuracy  This measure-  of the l o n g i t u d i n a l  d i s t a n c e since the maximum f l u c t u a t i o n s appeared over a subs t a n t i a l distance r a t h e r than a t t a i n i n g a w e l l defined peak.  3.8.4  S t r o u h a l Numbers Comparison of the frequency (  of the pressure  o s c i l l a t i o n s of  the c i r c u l a r c y l i n d e r with published data on Strouhal showed the two frequencies to be i d e n t i c a l . by the pressure  transducer  The trace  sensing the o s c i l l a t i n g  at the surface of the model d i s p l a y e d the frequency  frequencies obtained  pressures of vortex shed-  ding i n a more defined manner than was obtainable with hot wire anemometer equipment.  A l l Strouhal frequency  f o r e made from the f l u c t u a t i n g pressure model.  measurements were there-  trace at the surface of the  42.  Strouhal frequencies were recorded a t various Reynolds numbers for  the c i r c u l a r , square, r e c t a n g u l a r and e l l i p t i c  angles  of attack  angles  of attaok in the case of the e l l i p t i c  c y l i n d e r a t high  (no pressure f l u c t u a t i o n s were observed at low  3.8.5 S t a t i c L i f t  cylinder).  C o e f f i c i e n t Versus Angle of Attack  C i r c u l a r C y l i n d e r and MACA 4412 S e c t i o n Wing  Pressure  distributions  and s t a t i c l i f t  c o e f f i c i e n t s on the  c i r c u l a r c y l i n d e r and NACA 4412 a i r f o i l are w e l l e s t a b l i s h e d and i t was not necessary  to measure them during t h i s experiment.  Square and/ Rectangular Static l i f t g r a t i o n of the The  lift  Cylinders  c o e f f i c i e n t s were  pressure  for a  determined  d i s t r i b u t i o n s about the model.  square  or r e c t a n g u l a r c y l i n d e r can be obtained  from the r e l a t i o n ^  L'=[ Defining l i f t  by g r a p h i c a l i n t e -  ^  (^--?,)dS,  coefficient  Cos*  +${%-Vj  cL$^ sJ^oi  as:  c' •= (where c i s the length of a face on the square c y l i n d e r and the length of -the"longest face on the r e c t a n g u l a r  cylindejO  gives:  43.  i.e.  |  (  Here the s u b s c r i p t s 1, 2, 3, and 4 denote the value of the parameter at the faces as shown i n Figure  18.  " t  Figure  18  here  a - angle  Elliptic The following  of attack.  Cylinder lift  f o r the e l l i p t i c  relation: /  c y l i n d e r can be obtained from the  44.  t  f  CO  S©<  g i v i n g the l i f t  c o e f f i c i e n t per u n i t span as:  C=( f c a - T Q  __ er>^- no)!  *L/S\  i.e.  ,C0So<  The s u b s c r i p t s respectively  I and u denote the lower and upper surfaces  of the e l l i p t i c  3.8.6 F l u c t u a t i n g  Lift  c y l i n d e r as shown i n Figure 19.  Coefficients  From phase d i f f e r e n c e  measurements around a model under t e s t  i t was observed that: (a)  a l l pressure f l u c t u a t i o n s occurring  on the same  surface,  45.  j i.e.  the lower or the upper Burfaoe, were.in phase  with one (b)  another  pressure f l u c t u a t i o n s on the upper surface were  180°  out of phase with those on the lower s u r f a c e . The: to  C t i , : g r a p h i c a l i n t e g r a t i o n was  performed  i n a manner s i m i l a r  the one presented before with the exception that here the os-  d i l a t i n g pressure d i s t r i b u t i o n was  i n t e g r a t e d over the top and  bottom surfaces s e p a r a t e l y and the two r e s u l t s were added to get the t o t a l f l u c t u a t i n g l i f t All  coefficient.  measurements of o s c i l l a t i n g pressures and l i f t  e f f i c i e n t s as presented here are peak t o peak.  Thus«...  , " fluctuating l i f t  per u n i t span  co-  46.  IV.  EXPERIMENTAL  RESULTS  4.1.1 S t a t i o n a r y Square C y l i n d e r The The of  square  pressure  c y l i n d e r was p r o v i d e d w i t h s i x t e e n p r e s s u r e  distribution,  a t t a c k , and v a r i a t i o n  variation  of l i f t  in  figures  constant  (l5")>  appeared by  of 0.12.  number  other  are presented t o be  At h i g h e r Reynolds  The v a l u e  i s slightly  lower  value  than that  obtained  (20X. fluctuating  pressure  of a t t a c k range  c o n s t a n t a t 41,000. The  results  angle  were c o n s i d e r a b l y s c a t t e r e d y e t t h e a v e r a g e  t o be t h e same.  the a n g l e held  o b t a i n e d by  The S t r o u h a l number was f o u n d  a t the approximate value  Brooks The  ( 2 0 ) . The r e c o r d e d  20, 21 and 22,  number t h e r e s u l t s  with  o f S t r o u h a l number w i t h R e y n o l d s  showed v e r y good agreement w i t h t h e r e s u l t s investigators  coefficient  taps.  plot  of C' f l  d i s t r i b u t i o n d a t a were r e c o r d e d f o r  of 0° - 17° 30' w i t h R e y n o l d s The r e s u l t s  versus angle  are presented  of a t t a c k  number  i n F i g u r e 23.  ( F i g u r e 24) shows t h e  L  maximum v a l u e value  of 1.4 a t 1 4 ° .  fluctuating the  t o be 2.4 a t an a n g l e  static  lift lift  I t i s of i n t e r e s t  coefficient coefficient  t r a c e s a t taps  angle  t o note  t h a t t h e minimum  occurs a t the angle  of a t t a c k f o r w h i c h  i s maximum.  P h o t o g r a p h s showing p r e s s u r e c y l i n d e r a t zero  o f a t t a c k o f 6° and minimum  oscillations  about  the square .  o f a t t a c k a r e g i v e n i n F i g u r e 25.  13 and 14 a r e p u r p o s e l y  reproduced  s e n s i t i v i t y " (XlO, X 2 t h e n o r m a l s e n s i t i v i t y  with  The  higher  respectively).  The  47.  pressure f l u c t u a t i o n s are n e a r l y s i n u s o i d a l except at the r e a r of the c y l i n d e r .  At tap 4 a high frequency s i g n a l seems to be  super-,  imposed on the fundamental s i g n a l while tap 5 shows marked i n f l u e n c e of the second harmonic. d i s p l a y e d the amplitude  Decreasing the sweep time modulation  of the pressure  of the o s c i l l o s c o p e oscillations  (Figure 26). The phase study of the o s c i l l a t i n g pressure showed that a l l pressure f l u c t u a t i o n s on the same side of the model were i n phase while those on the opposite side were 180°  out of phase thus  indicating  that the breaking of a vortex from one side of the model i n s t a n t aneously affects- the pressure d i s t r i b u t i o n " on that s i d e . The wake geometry was  a l s o i n v e s t i g a t e d , making use of the  designed pressure transducer i n the manner explained e a r l i e r ( s e c t i o n 3.8.3). 12.13  The  l o n g i t u d i n a l spacing (h) was  inches while the l a t e r a l spacing  (a) was  5.75  found  to be  inches thus  g i v i n g an a/h r a t i o of 0.474.  4.1.2  O s c i l l a t i n g Square C y l i n d e r The wind v e l o c i t y was  self excited o s c i l l a t i o n s .  now  i n c r e a s e d u n t i l the model e x h i b i t e d  The v a r i a t i o n i n amplitude  with v e l o c i t y l e a d i n g to two stable l i m i t Smith (l5)  was  observed.  c y c l e s as reported by  Figure 27 shows plunging  oscillations  of the model at a wind v e l o c i t y of 60 f e e t per second cycle).  of o s c i l l a t i o n  (larger  limit  48.  The the  comparison of pressure f l u c t u a t i o n s at a l l taps with  square c y l i n d e r s t a t i o n a r y  they were i d e n t i c a l .  or o s c i l l a t i n g revealed  The r e p r e s e n t a t i v e  that  photographs comparing the  pressure f l u c t u a t i o n s at tap 15 with model s t a t i o n a r y and o s c i l l a t i n g are shown i n Figure  26 and Figure  28.  Figure 20  (cont'd). V a r i a t i o n of S t a t i c Pressure D i s t r i b u t i o n with as Square  Cylinder  52  v i.o  0  4  8  12 o,  Figure  21  Variation  16  18  20  deg.  of S t a t i c L i f t C o e f f i c i e n t with as Square C y l i n d e r  o  o  O  o  O  Ov  o  I o  o o  0  Oo  t  "-  •  1.5x10  F i g u r e 22.  2.0  2.5  3.0  4.0  5.0  6.0  7.0  8.0  He  V a r i a t i o n of Strouhal Number with Reynold^: Number f o r Square C y l i n d e r  9.0  10'  54.  Figure  23  (cont'd). V a r i a t i o n of F l u c t u a t i n g Pressure D i s t r i b u t i o n with a : Square C y l i n d e r  Figure  23  (cont'd). V a r i a t i o n of F l u c t u a t i n g Pressure D i s t r i b u t i o n with o: Square C y l i n d e r  Figure 24.  V a r i a t i o n of F l u c t u a t i n g L i f t C o e f f i c i e n t with Square C y l i n d e r  Figure 25.  Pressure O s c i l l a t i o n s  on the Surface of Square C y l i n d e r  59  Figure 26. Amplitude Modulations of Pressure F l u c t u a t i o n s on the Surface of Square Cylinder, Tap 15 ( S t a t i o n a r y )  Figure 27. Slowly Varying Amplitude and Frequency of Square C y l i n d e r Motion  Figure 28. E f f e c t of Motion on Pressure F l u c t u a t i o n s on the Surface of Square C y l i n d e r , Tap 15  60. 4.2.1  S t a t i o n a r y Rectangular C y l i n d e r , J&»2 , A r e c t a n g u l a r c y l i n d e r with AR=2 was t e s t e d f o r s t a t i c and  f l u c t u a t i n g pressure d i s t r i b u t i o n under s t a t i o n a r y as w e l l as dynamic c o n d i t i o n s .  The surface of the c y l i n d e r was provided with  s i x t e e n pressure taps eaoh connected for  to the Lambrecht manometer  s t a t i c pressure measurements and t o the designed  transducer f o r f l u c t u a t i n g pressure measurement.  pressure  The s t a t i c  pressure d i s t r i b u t i o n over a range of angle of a t t a c k i s presented i n F i g u r e 29 while Figure 30 shows v a r i a t i o n of l i f t c o e f f i c i e n t with angle of attaok. the maximum l i f t  I t may be pointed out that  c o e f f i c i e n t of 0.B3 at 10.5° i e lower than that  obtained f o r the square  cylinder.  The measurements c a r r i e d out t o study v a r i a t i o n of S t r o u h a l number with Reynolds number showed i t t o remain constant at the value of 0.081 as i n d i o a t e d i n Figure 31.  There was l e s s  s c a t t e r of data f o r t h i s case as compared t o the square  cylinder.  The f l u c t u a t i n g pressure measurements a t 0° and 3.5° angle of  attaok were nearly i d e n t i c a l on e i t h e r side of the c e n t e r l i n e  of  the body as i n the case of the square  of  a t t a c k of 14° the surfaoe f a c i n g the upstream; i . e . taps 9  cylinder.  At an angle  and 14 showed signs of turbulence probably due t o reattachment Of the flow while the opposite face r e g i s t e r e d sudden r i s e i n f l u c t u a t i n g pressure c o e f f i c i e n t s  (taps 4 and 5). F l u c t u a t i n g  pressure c o e f f i c i e n t s on the surfaoe of the rectangular c y l i n d e r at  s e v e r a l angles of a t t a c k are shown i n Figure 32 while  the p l o t of f l u c t u a t i n g l i f t  c o e f f i c i e n t per u n i t span against  61  angle  of attack i s presented Photographic  i n Figure 33.  r e p r e s e n t a t i o n of the pressure  oscillations  at v a r i o u s points on the surface of the r e c t a n g u l a r c y l i n d e r are shown i n Figure 34. zero angle  The photographs are f o r the model a t  of attack with the o s c i l l o s c o p e attenuator main-  t a i n e d a t the same s e n s i t i v i t y . f l u c t u a t i n g pressure  Amplitude modulation of the  i n the Reynolds number range of 55,000  to 70,000 i s worth p o i n t i n g out since the modulations d i d not appear anywhere except i n t h i s range. f o r t h i s can be g i v e n here. gated  further.  No d e f i n i t e  explanation  The phenomenon should be i n v e s t i -  Note a l s o the expected double frequency  effect  at the rear of the c y l i n d e r as shown by the photograph f o r tap 7. The  study  of phase r e l a t i o n between the o s c i l l a t i n g  sures about the r e c t a n g u l a r c y l i n d e r showed the taps and  pres-  1 to 7  16 t o be i n phase while taps 8 t o 15 t o be 180° out of phase  with respect t o tap 1. The wake study revealed the l o n g i t u d i n a l and l a t e r a l spacing between the consecutive v o r t i c e s t o be 17.3 and 5.5 inches thus g i v i n g a/h=0.318. pressure  Figure 35 shows the f l u c t u a t i n g  traces produced by the probe located 17.3 inches  the model and that e x i s t i n g at tap 1. apparently  i n phase.  The two s i g n a l s are  behind  62.  Figure 29.  V a r i a t i o n of S t a t i c Pressure D i s t r i b u t i o n with a: Rectangular C y l i n d e r »2  M  Figure 29 (cont'd). V a r i a t i o n of S t a t i c fraesur© D i s t r i b u t i o n with «« C y l i n d e r Mm2  Rectangular  64o  65.  Figure 29 (cont'd). V a r i a t i o n of S t a t i c Pressure D i s t r i b u t i o n with O J Rectangular C y l i n d e r AR»2  Figure 30.  V a r i a t i o n of S t a t i c L i f t C o e f f i c i e n t with o: Rectangular C y l i n d e r JR »2  0.17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09  o  o  0.09  o  o  ° ©  O"  <  0.07 0.06 0.05 0.04 0.03  1.5x10  2.0  2.5  3.0  4.0  5.0  Re  Figure 31.  V a r i a t i o n of Strouhal Number with ReynoldSs Number f o r Rectangular C y l i n d e r ffi»2  Figure 32# Va?latien of fluctuating freseufe Distribution With tt: Rectangular Cylinder & «g  Figure  32  (cont'd). V a r i a t i o n of F l u c t u a t i n g Pressure D i s t r i b u t i o n with at Rectangular C y l i n d e r JR»2  f i g u r e 32 (cont'd). Variation of Fluctuating Pressure D i s t r i b u t i o n with o: Rectangular Cylinder 43 -2  Figure  33.  V a r i a t i o n of F l u c t u a t i n g L i f t C o e f f i c i e n t with a: Rectangular C y l i n d e r £Rn2  73  F i g u r e 35. P r e s s u r e F l u c t u a t i o n s a s R e c o r d e d by P r o b e a n d Tap 1, R e c t a n g u l a r i, C y l i n d e r SL w2 P r o b e 17.3 i n c h e s downstream of t h e M o d e l t  a. No M o t i o n , Sweep Time 50wvSh/cin. b. M o t i o n , Sweep TimeolOOmSVcm F i g u r e 36. E f f e c t of M o t i o n on P r e s s u r e F l u c t u a t i o n s on t h e S u r f a c e o f R e c t a n g u l a r C y l i n d e r £R «2  74. 4.2.2 O s c i l l a t i n g Rectangular C y l i n d e r .  2  Next the wind speed was g r a d u a l l y i n c r e a s e d u n t i l the model e x h i b i t e d s e l f e x c i t e d o s c i l l a t i o n s .  The o s c i l l a t i n g  pressure at a l l taps on the surface of the model was found to be i d e n t i c a l t o the corresponding pressure under s t a t i o n a r y conditions.  This i s shown f o r a r e p r e s e n t a t i v e pressure tap  i n Figure 3 6 .  4.2.3 S t a t i o n a r y Rectangular Cylinder., AR= l/2 As a matter of c u r i o s i t y the previous model; i . e . r e c tangular c y l i n d e r with /SR = 2, was r o t a t e d through a r e c t a n g u l a r c y l i n d e r with Mm l / 2 .  90° t o give  The model i n t h i s  p o s i t i o n represented a body with g r e a t e r b l u f f n e s s thus g i v i n g large drag p a r t i c u l a r l y at higher angle of a t t a c k and speed. The i n s u f f i c i e n t  s t i f f n e s s of the model caused i t t o d e f l e c t  under the i n f l u e n c e of drag hence the t e s t s were l i m i t e d to zero angle of a t t a c k . The  s t a t i c and f l u c t u a t i n g pressure d i s t r i b u t i o n s f o r t h i s  case are presented i n Figure 3 7 .  The l a r g e f l u c t u a t i o n s i n  pressure on the top, bottom and r e a r faoe w i t h r e l a t i v e l y small values on the upstream face are worth p o i n t i n g out. the comparatively large value of C'  T  Note a l s o  a 4 . 8 with reference to the  f l ' = £.4 with reference to the broad L  narrow s i d e , and C L  side.  fl  The v a r i a t i o n of S t r o u h a l number with Reynolds number i s shown i n Figure 38.  The r e s u l t s are q u i t e s c a t t e r e d p r i m a r i l y  due t o the f a c t that the o s c i l l a t i n g pressure f l u c t u a t i o n s  were g e n e r a l l y unorganized showing a large amplitude modulation  effect.  76.  Figure 37a.  S t a t i c Pressure D i s t r i b u t i o n Over Rectangular C y l i n d e r iR «el/2  77.  O O  c  o o  o  o o  o  O  -  0,03  l,5x!0  4  2 .0  2 .5  3 .0  4 .0  5.<  5.0  7.0  8.0  9.0  Re  F i g u r e 38,  V a r i a t i o n of S t r o u h a l Number with Reynolds;) Number f o r Rectangular C y l i n d e r AR« 1/2  1  79  4.3*1  Stationary C i r c u l a r Cylinder The s t a t i c pressure d i s t r i b u t i o n around a c i r c u l a r  c y l i n d e r i s w e l l known yet f o r completeness i t s measurement was  c a r r i e d out at three d i f f e r e n t values of Reynolds number  (Figure 39). The measurement of Strouhal number as a f u n c t i o n of Reynolds number gave r e s u l t s which were s c a t t e r e d around the curve obtained by ReIf and Simmons ( 2 l ) , and as shown i n Figure 40. The measurement of f l u c t u a t i n g pressure around a s t a t i o n a r y c i r c u l a r o y l i n d e r was  distribution  c a r r i e d out by  McGregor ( l l ) making use of a microphone as mentioned His r e s u l t s served as a guide i n checking the accuracy  of the designed transducer.  earlier.  calibration  The dynamic pressure  d i s t r i b u t i o n shown i n Figure 41 agreed q u i t e w e l l with that obtained by McGregor. was  The v a r i a t i o n of C . p  Q  with  » 0.60  c o e f f i c i e n t per u n i t span  was  which i s comparable to that obtained by McGregor  - 0.58, Re*53,000). fl The pressure f l u c t u a t i o n s on the surface of the c y l i n d e r are shown p h o t o g r a p h i c a l l y i n F i g u r e 43. harmonic e f f e c t appears 7.  Q  p l o t t e d (Figure  The r e s u l t a n t f l u c t u a t i n g l i f t C  s]n  The amplitude  circular  The  second  to be q u i t e prominent at pressure tap  modulation  of the pressure o s c i l l a t i o n s  found to be more random than that f o r the square  was  c y l i n d e r as  80.  shown i n Figure The. survey  44. of phase between the o s c i l l a t i n g pressures r e -  v e a l e d taps 2 to 7 to be i n phase and out of phase. oscillations  taps 8 to 12 to  be  Figure 45a portrays the s i g n a l s of the on one side of the c y l i n d e r to be  180°  pressure  i n phase and  F i g u r e 45b show 180° phase s h i f t f o r the pressure s i g n a l s o r i g i n a t i n g from the opposite s i d e . The e f f e c t i v e n e s s of the pressure transducer as a wake survey instrument  was  s u b s t a n t i a t e d by a p p l y i n g i t to the  of wake geometry behind the c i r c u l a r the r e s u l t s with t h e o r e t i c a l l y  c y l i n d e r and  comparing  e s t a b l i s h e d values.  The wake  survey probe operating i n conjunction with the pressure gave l o n g i t u d i n a l spacing of 9.7 of 2.8  inches and  This i s s l i g h t l y higher than the  c a l l y e s t a b l i s h e d value of 0.281.  pressure tap 4.  model with those  The two responses  the  theoreti-  Figure 46 compares the pres-  sure f l u c t u a t i o n s sensed by the probe l o c a t e d 9.7 stream from the center of the  transducer  l a t e r a l spacing  inches between the adjacent v o r t i c e s , thus g i v i n g  r a t i o a/h m 0.29.  study  inches down-  ocourring at  are apparently i n phase.  The dominance of the second harmonic f l u c t u a t i o n s along the c e n t e r l i n e of the wake i s shown i n Figure 47 where the upper and  lower t r a c e s represent the output from tap 4 and the probe  l o c a t e d i n the center of the  wake  respectively.  81.  4.3.2  Oscillating Circular  Cylinder  The c r i t i c a l wind speed causing s e l f excited of the c i r c u l a r c y l i n d e r  was  oscillations  observed to be 26 feet  per second,,  Obviously t h i s was not the vort@x e x c i t e d o s c i l l a t i o n should occur at the wind v e l o c i t y  of 4.9 f e e t  The o s c i l l a t i o n s t h e r e f o r e were a t t r i b u t e d i n model c o n s t r u c t i o n - o r end  effects.  which  per second.  t o imperfections  0.2J  0. ®  Experimental  Results  R e i f and Simmons (21)  0.2  o  0.1  0 o  o  O  0.]  o  o  o  0.17  10  -xrr  1.5  2.0  2.5  3.0  4.0  5.0  6.0  Re  Figure 40.  V a r i a t i o n of Strouhal Number with Reynoldss Number! C i r c u l a r C y l i n d e r  7.0  8.0  Figure 41.  Fluctuating  Pressure D i s t r i b u t i o n :  Circular  Cylinder  Figure 42.  C  s i n •& P  fl  versus $ f o r C i r c u l a r  Cylinder  Figure  43.  Pressure  Oscillations  on t h e  Surface  of C i r c u l a r  Cylinder  87.  Figure 4 4 . Amplitude Modulations of Pressure O s c i l l a t i o n s over C i r c u l a r Cylinder  a. Same Side. Taps 2 and 6 b. Opposite Side, Taps 4 and 10 Figure 45. V a r i a t i o n of Phase on the Surface of the C i r c u l a r C y l i n d e r  88.  Figure 46. Pressure F l u c t u a t i o n s as Recorded by Probe and Tap 4, C i r c u l a r C y l i n d e r , Probe 9.7 inches Downstream of the Model  I  Figure 47. Double Frequency E f f e c t at the Center of Wake of C i r c u l a r Cylinder  H i  a. No Motion Figure 48.  b. Motion  Pressure F l u c t u a t i o n s on the Surface of C i r c u l a r as A f f e c t e d by i t s Motion  Cylinder  89.  4.4.1 S t a t i o n a r y E l l i p t i c  C y l i n d e r (~a=3  S t a t i c pressure measurements elliptic  inches . e=0.985)  on the surface of the  c y l i n d e r were c a r r i e d out over a wide range of angle  of attack as shown i n Figure 49. as f u n c t i o n of a i s presented  The s t a t i c l i f t  coefficient  i n Figure 50.  The pressure f l u c t u a t i o n s were not observed u n t i l an angle  of attack of 9.5°.  From t h i s point oh to the angle  of attack of 28.5° the pressure were not w e l l d e f i n e d .  f l u c t u a t i o n s though present  But beyond 28.5° the pressure v a r i a t i o n s  were observed to be quite r e g u l a r .  Photographs of the pressure  o s c i l l a t i o n on the surface of the e l l i p t i c i n Figure 51. pressure  Figure 52 shows the v a r i a t i o n i n f l u c t u a t i n g  coefficient  s e v e r a l values  of a.  f u n c t i o n of angle The study  c y l i n d e r are given  on the surface of the c y l i n d e r f o r Fluctuating l i f t  c o e f f i c i e n t as a  of attack i s presented  i n F i g u r e 53.  of phase d i f f e r e n c e between f l u c t u a t i n g  pres-  sures at d i f f e r e n t p o s i t i o n s on the s u r f a c e . o f the e l l i p t i c c y l i n d e r at angles  of a t t a c k of 28°, 38° and 48° showed  taps 1 t o 5 i n phase, tap 6 out of phase by 90° and taps 7 t o 12 out of phase by 180° a l l with respect to tap 11 At an angle pressure to  of a t t a c k of 57° the phases of the  o s c i l l a t i o n s with respect to tap 1 were found  be as f o l l o w s :  taps 1 to 5 i n phase, tap 6 lagging  by 45°, tap 8 lagging by 135°, tap 9 t o 12 lagging by 180°.  At pressure  tap 7 phase d i f f e r e n c e f l u c t u a t e d  randomly between 0° and 180°.  90.  The measurement of v a r i a t i o n i n Strouhal number with Reynolds number at d i f f e r e n t angles  of attack gave readings  which were quite s c a t t e r e d as shown i n Figure 54. The  study  of the nature  of the wake revealed the l o n g i -  t u d i n a l d i s t a n c e between the v o r t i c e s of 17.6 inches and the l a t e r a l spacing of 4.5 i n c h e s . only a t an angle The  study  This t e s t was conducted  of attack of 30°.  of s t a t i c pressure  d i s t r i b u t i o n showed the  presence of large t w i s t i n g moment f o r angles than zero. divergence  of attack  other  This l e d the e l l i p t i c c y l i n d e r t o e x h i b i t pure under the c o n d i t i o n of s t i f f n e s s and damping present  i n the system.  This made measurement of f l u c t u a t i n g  under dynamic c o n d i t i o n s of the model impossible.  pressure  Figure 49.  V a r i a t i o n of S t a t i o Pressure D i s t r i b u t i o n with a: E l l i p t i c C y l i n d e r  Figure 49 (cont'd). V a r i a t i o n of S t a t i c Pressure D i s t r i b u t i o n with a: E l l i p t i c C y l i n d e r  Figure 49 (cont'd). V a r i a t i o n of S t a t i c Pressure D i s t r i b u t i o n with as E l l i p t i c C y l i n d e r  94.  Figure 50.  V a r i a t i o n of S t a t i c L i f t C o e f f i c i e n t with a t E l l i p t i c Cylinder  Figure 52.  V a r i a t i o n * o f F l u c t u a t i n g Pressure D i s t r i b u t i o n with a: E l l i p t i o C y l i n d e r  Figure  52 (cont'd). V a r i a t i o n of F l u c t u a t i n g Pressure D i s t r i b u t i o n with a: E l l i p t i c Cylinder  Figure 53.  V a r i a t i o n of F l u c t u a t i n g L i f t with o: E l l i p t i c C y l i n d e r  Coefficient  >—  •  /  O ?  -  o  o°<> °  D n  1  u  o  c  . 28*5° O  ^  ?  10  Figure 54.  1.5  •• 38°  o C  <  n  ° • f <*>  c  • o 'y  c DO c  o= 57°  2.0  n  o  OCs  .am 4 7 . 5  •  71 n  <3 v < 0  v  u.  o  3.0  4.0  5.0 6.0 7.0 He  9.0  1.5  2.0  V a r i a t i o n of Strouhal Number with Reynolds,,- Number : E l l i p t i c C y l i n d e r  3.0  100.  4.5.1  S t a t i o n a r y and The  Oscillating  Airfoil  a i r f o i l s e c t i o n used being standard  not necessary  to measure s t a t i c pressure  its  When t e s t e d from 0° to 35° angle  surface.  i t d i d not show existence critical  of any The  d i s t r i b u t i o n around  The  of a t t a c k  of any f l u c t u a t i n g pressure.  f l u t t e r speed of the a i r f o i l was  per second.  i t was  WAEA 4412,  small value  The  found to be 32 f e e t  of v e l o c i t y was  due  e x t e r n a l damping except that provided  s t i f f n e s s of the system i n plunging and  to absence  by the a i r b e a r i n g s . torsion is indicated  by i t s n a t u r a l frequencies i n those degrees of freedom which were 5.3  and  5.6  cycles per second r e s p e c t i v e l y .  shows the time record of plunging and  The  Under t h i s  degrees of  oscillating  c o n d i t i o n the a i r f o i l d i d e x h i b i t f l u c t u a t i n g pressure  at and  surface.  Figure 57 shows the o s c i l l a t i n g  a r e p r e s e n t a t i v e point  V  plunging  Figure 58 surveys  l a t i n g pressure at the surface of the model.  on  pressure  (tap 3) together with the  t o r s i o n a l motion of the model.  of  Lissajous f i g u r e  r e p r e s e n t i n g the phase d i f f e r e n c e between the two  its  55  t o r s i o n a l displacement  the model during a e r o e l a s t i c o s c i l l a t i o n s .  freedom i s shown i n Figure 56.  Figure  the  oscil-  101,  SMSHSSBS  II  iivitftfjiviivi i'iv*!iiirj,ir*v 'miiWmvaiM'A  p ijii ij M  Figure 55. S e l f Excited Motion of the A i r f o i l  Figure 56. L i s s a j o u s Figure During S e l f E x c i t e d Motion of the A i r f o i l  iiwjiwiiBi uteri*,  ftafehifcii! I Figure 57a.  Lateral Figure 57.  ESRI Figure 57b.  Torsion  Pressure f l u c t u a t i o n s a t tap 3 with L a t e r a l and T o r s i o n a l Displacement of the A i r f o i l  Figure 58.  O s c i l l a t i n g Pressures on the Surface of A i r f o i l Undergoin F l u t t e r  103.  V.  It  DISCUSSION OF RESULTS AND  was  interesting  efficient body.  t o observe the o s c i l l a t i n g  decrease with  fluctuating parallel  i t s broad  lift  a square  of a t t a c k  of 4.6  As the body  c y l i n d e r the l i f t  showed  s i z e was  coefficient  the o s c i l l a t i n g  f u r t h e r d e c r e a s e t o 1,2  parallel only  M =2  t o the f l o w w h i l e  0.60.  cylinder  Further  schematically note  t h a t C'  if For  circular  streamlining 59.  showed  of a t t a c k .  o f t h e body i s  I t i s a l s o of i n t e r e s t  f o r the r e c t a n g u l a r c y l i n d e r s  fl  square and r e c t a n g u l a r  perpendicular  lift  t h e p o i n t s where  to the  flow.  c y l i n d e r s as w e l l as f o r the  c y l i n d e r at large angles  of f l u c t u a t i n g at  with  i t i s r e f e r r e d t o the f a c e  elliptic  c y l i n d e r i t was  c y l i n d e r and t h e n i n t o a i r f o i l  i s constant L  rectangular  r e f e r r e d t o the face  for circular  fl shown i n F i g u r e  2,4.  coefficient  f l u c t u a t i o n a t a l l at zero angle  T h i s r e d u c t i o n i n C'  to  dropped t o  into a  lift  reduced  s t r e a m l i n i n g of t h e body f r o m  into elliptic  no p r e s s u r e  the r e c t a n g u l a r  r e f e r r e d t o the face  W i t h f u r t h e r s t r e a m l i n i n g of t h e body cylinder with  co-  s i d e u p s t r e a m (AR=l/2) had a  coefficient  t o the f l o w .  lift  r e d u c t i o n i n t h e b l u f f n e s s of t h e  F o r example a t z e r o a n g l e  c y l i n d e r with  to  CONCLUDING REMARKS  of a t t a c k  coefficient  was  static  coefficient  lift  the magnitude  o b s e r v e d t o be minimum was  maximum.  104.  (c)  O  O referred^ to  b  •  O  h  r e f e r r e d to  For bodies with sharp l e a d i n g edge p r o v i d i n g w e l l defined separation e.g. the r e c t a n g u l a r c y l i n d e r s , pressure and l i f t  fluctuating  c o e f f i c i e n t s were observed  t o be considerably  l a r g e r than the corresponding s t a t i c values, while f o r the circular cylinder, e l l i p t i c  c y l i n d e r and a i r f o i l the  fluc-  t u a t i n g c o e f f i c i e n t s were found to be smaller than t h e i r s t a t i c counterpart. (d)  Due  to the model and model mounting system design, vortex  e x c i t e d o s c i l l a t i o n s of the bodies were not p o s s i b l e . unbalancing f o r c e s produced  Other  the s e l f - e x c i t e d motions which,  p a r t i c u l a r l y f o r a b l u f f body, does not seem to a f f e c t e i t h e r the frequency tuating pressure.  of the shedding v o r t i c e s or the f l u c -  105 Probably the most s i g n i f i c a n t outcome of the p r o j e c t  was  the development of a transducer capable of measuring  acoustic  l e v e l pressure f l u c t u a t i o n s over a wide range The  of frequency.  c a p a b i l i t y of the device to serve as a wake survey  instrument f u r t h e r enhances i t s u s e f u l n e s s .  106,  . 1,  RECOMMENDATION FOR FUTURE INVESTIGATION  Although the pressure transducer was found t o be quite adequate . f o r the present set of experiments,  f u r t h e r refinement i n i t s  c o n s t r u c t i o n and c a l i b r a t i o n would make i t a more u s e f u l u n i t * 2,  Usefulness of the transducer as a wake survey u n i t was described before.  For p r e c i s e measurement of wake geometry, a mechanical  device capable of p r o v i d i n g motion to the probe, i n threedimension i s necessary, 3,  Measurement of f l u c t u a t i n g pressure and wake geometry should be undertaken  f o r a r e c t a n g u l a r c y l i n d e r of AR» 1/2 over a range of  angles of a t t a c k f o r completeness of i n v e s t i g a t i o n , 4,  Dynamic r e s u l t s were not obtained i n the case of e l l i p t i c as i t e x h i b i t e d pure divergence.  Use of higher s t i f f n e s s and/or  damping should c o r r e c t t h i s tendency oscillating 5o  cylinder  and provide self»excited  motion of the body,  In the i n v e s t i g a t i o n presented here, the wake measurements were c a r r i e d out f o r s t a t i o n a r y c o n d i t i o n of the model.  Corresponding  measurements during dynamic c o n d i t i o n of the model should a l s o be undertaken, 6,  Study of pressure f l u c t u a t i o n s and wake during vortex excited motion of the body should be of i n t e r e s t ,  7,  S i m i l a r study of I - s e c t i o n , T - s e o t i o n , channel and angle s e c t i o n , dumbbell shaped body, e t c , should prove  8,  useful,  Study of f l u c t u a t i n g pressure, wake geometry and a e r o e l a s t i c instability  of a body when l o c a t e d i n the wake generated by  another body should be of importance  i n VTOL design.  107BIBLIOGRAPHY 1,  Duncan, W J., E l l i s , D L., Smyth, E , " F i r s t Report on the General I n v e s t i g a t i o n of T a i l B u f f e t i n g , " Br, ARC R&M 1457, 1933.  2,  Van de Vooren, A I , and Bugh, H , "Spontaneous O s c i l l a t i o n s of an A e r o f o i l due t o I n s t a b i l i t y of Laminar Boundary Layer," N a t l , Luchvaartlab, Amsterdam, Repto F96, 1951.  3,  Mendelson, A,, "Aerodynamic H y s t e r e s i s as Factor i n C r i t i c a l F l u t t e r Speed of Compressor Blades a t S t a l l i n g C o n d i t i o n s , " J . Aeronaut, S c i , , 1949.  4,  S i s t o , F , " S t a l l F l u t t e r i n Cascades," J . Aeronaut. S c i , 1953.  5,  Studer, H.L,, "Experimental Study of Wing F l u t t e r , " T r a n s l a t i o n ARC 2777, 1946.  6«  Karman, Th. v o n , " F l u s s i g k e i t s u. Luftwiderstand," Physik Z„ 13, 1911.  7..  Karman, Th. von., " F l u s s i g k e i t s u. Luftwiderstand," Nachr, Ges, Wiss., Gottingen, 547, 1913.  8.  Cometta, Co, "An I n v e s t i g a t i o n of the Unsteady Flow Pattern i n the Wake of C y l i n d e r s and Spheres Using a Hot Wire Probe," Tech. Rept, WT-21, Brown Univ., 1957.  9.  Roshko, A,, "On the Development S t r e e t s , " NACA TN 2913, 1953.  0  a  0  0  0  0  0  0  Brit,  0  of Turbulent Wakes from Vortex  10.  Chuan, R.L., and Magnus, R,"J,y "Study of Vortex Shedding as Related to S e l f - E x c i t e d T o r s i o n a l O s c i l l a t i o n s of an A e r o f o i l , " NACA TN 2429, 1951.  11.  McGregor, D.M., "An Experimental I n v e s t i g a t i o n of the O s c i l l a t i n g Pressures on a C i r c u l a r C y l i n d e r i n a F l u i d Stream," UTIA TN 14, 1957.  12.  Prendergast, V , "Measurement of Two-Point C o r r e l a t i o n s of the Surface Pressure on a C i r c u l a r C y l i n d e r , " UTIA TN 23, 1958,  13.  Molyneux, W.G., "Measurement of the Aerodynamic Forces on O s c i l l a t i n g A i r f o i l s , " AGARD Rept, 35, 1956.  14.  Molyneux, W.G,, and Ruddleston, F., "A Technique f o r the Measurement of Pressure D i s t r i b u t i o n on O s c i l l a t i n g A e r o f o i l s , w i t h Results f o r a Rectangular Wing of Aspect Ratio 3.3," Br, ARC TR 18,018, 1956,  0  /OS,  15o  Smith, J.D., "An Experimental Study of the A e r o e l a s t i c I n s t a b i l i t y of Rectangular Cylinders," M,A.Sc. T h e s i s , Univ. B r i t . C o l . , 1 9 6 2 ,  16.  Laub, J.H,, " E x t e r n a l l y Pressurized Journal Gas Bearings," Presented at the ASIE/ASME L u b r i c a t i o n Conference, Boston, Preprint 6 0 1 0 - 1 5 , I960,  17.  Perry, C , C , L i s s n e r , H,R,, "A S t r a i n Gage Primer," McGraw-Hill Book Co., Inc., New York, 1 9 6 2 »  18.  Heuter, T,F,, "Sonics,"  John Wiley & Sons Inc., New  York,  1955.  19.  Fung, Y.C., "The Theory Inc., New York, 1 9 5 5 .  20.  Brooks, N.P.H., "Experimental I n v e s t i g a t i o n of the A e r o e l a s t i c I n s t a b i l i t y of B l u f f Two-Dimensional C y l i n d e r s , " M,A,Se. T h e s i s , Univ. of B r i t . C o l , , I 9 6 0 ,  21.  R e l f , E,P,, Simmons, L.R,G, "The Frequency of Eddies Generated by the Motion of Circular' C y l i n d e r s through a F l u i d , " Br. ARC, R&M 9 1 7 , 1 9 2 4 ,  of A e r o e l a s t i c i t y , " John Wiley & Sons,  9  

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