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The measurement of vortex induced effects in flow past stationary and oscillating circular and D-section… Feng, C.C. 1968

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THE MEASUREMENT OF VORTEX INDUCED EFFECTS IN FLOW PAST STATIONARY AND OSCILLATING CIRCULAR AND D-SECTION CYLINDERS  by  C. C. Feng B. Sc., National Taiwan University, 1963  A Thesis Submitted i n P a r t i a l F u l f i l l m e n t of the Requirements f o r the Degree of M.A. Sc. i n the Department of Mechanical Engineering  We accept t h i s thesis as conforming t o the required s.tandard_  THE UNIVERSITY OF BRITISH COLUMBIA October 1968  In p r e s e n t i n g  this thesis  in p a r t i a l  fulfilment of  requirements f o r an advanced degree at the U n i v e r s i t y of Columbia,  I agree that  for reference extensive  and  t h e L i b r a r y s h a l l make i t f r e e l y  study.  I further agree that permission  British available for  c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may b e  g r a n t e d b y t h e H e a d o f my D e p a r t m e n t o r b y h i s  representatives.  It i s u n d e r s t o o d that c o p y i n g or p u b l i c a t i o n of t h i s t h e s i s financial  gain  shall  not  b e a l l o w e d w i t h o u t my w r i t t e n  D e p a r t m e n t o f Mechanical Engineering The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, C a n a d a Date  the  Columbia  Janaury 31, 1969  for  permission  i ABSTRACT Experiments were performed i n a wind tunnel on 3-inch diameter c i r c u l a r and D-section cylinders, shedding  A detailed investigation of the vortex  frequency, displacement amplitude, and the phase angle between  the fluctuating pressure and the displacement  signals of both c i r c u l a r  and D-section cylinders was made i n the "capture" region.  These pheno-  mena were investigated under various damping levels using magnetic dampers. Fluctuating  surface pressures on a c i r c u l a r cylinder were measured along  one h a l f of the circumference at 11 sections selected along the span.  The  r e s u l t i n g sectional fluctuating l i f t c o e f f i c i e n t s as well as the t o t a l l i f t c o e f f i c i e n t s were obtained by integration for several wind speeds for both stationary and o s c i l l a t i n g cylinders.  Interesting to note are the  vortex line i n c l i n a t i o n angles obtained from fluctuating surface pressure correlation.  Using linearized hot wire anemometers, spanwise wake v e l o c i t y  c o r r e l a t i o n functions were measured and c o r r e l a t i o n lengths computed.  ii TABLE OF CONTENTS Section  Page  1.  INTRODUCTION  1  2.  INSTRUMENTATION  3  2.1  Wind Tunnel  3  2.2  Models  3  2.3  Model Mounting System..  k  2.h  Wake Traversing Gear....  5  2.5  Displacement Transducer  6  2.6  Magnetic Damping......  6  2.7  Pressure Transducer  7  2.8  Correlator....*.;.....  • 2.9  3.  *  8  Hot Wire Anemometers and Linearizers  10  2.10  Band Pass F i l t e r s .  11  2.11  Other E l e c t r o n i c Instruments  12  EXPERIMENTAL PROCEDURES  13  3.1  Frequency, Amplitude, and Phase Measurements  13  3.1.1  Frequency Measurements  13  3.1.2  Phase Measurements.  13  3.1.3  Amplitude Measurements  1^  3.2  Spanvlse Fluctuating Surface Pressure Measurements  15  3.3  Spanwise Wake Velocity Correlation Measurements  15  iii Section  Page 3.h  k.  k.2  ^•3  k.h  l6 18  EXPERIMENTAL RESULTS... k.l  5-  Measurements of Non-Aero dynamic Viscous Damping  Frequency, Amplitude and Phase Measurements f o r a C i r c u l a r Cylinder  18  Frequency, Amplitude and Phase Measurement f o r a D-section Cylinder  19  Fluctuating Pressures on the Surface of a C i r c u l a r Cylinder  19  Spanvise Correlations f o r C i r c u l a r and D-section Cylinders Using Hot Wire Anemometers  21  DISCUSSION OF RESULTS  23  5.1  Frequency, Amplitude and Phase Measurements  23  5.2  Fluctuating Pressures on the Surface of a C i r c u l a r Cylinder  25  5.3  Spanvise Correlations f o r C i r c u l a r and D-section Cylinders Using Hot Wire Anemometers  6. ' SUMMARY OF RESULTS  ..  ..  .;.  A.  Tunnel Corrections to Wind Speed  B.  Correlator Phase Measurement  30 32  BIBLIOGRAPHY APPENDICES  ...28  3^ 3^+ 35  iv  LIST OF FIGURES Figure  Page  1.  Wind t u n n e l o u t l i n e  38  2.  Wind t u n n e l t e s t s e c t i o n w i t h model (downstream 39  direction)  kO  3.  Models  k.  Spanwise p r e s s u r e t a p p o s i t i o n s f o r t h e c i r c u l a r cylinder  kl  5•  Arrangement o f model mounting system  k2  6.  T r a v e r s i n g gear  43  7.  B l o c k diagram o f t h e c a l i b r a t i o n a p p a r a t u s .  kk  8.  C a l i b r a t i o n curves f o r B a r o c e l pressure transducer  45  9.  C a l i b r a t i o n curve f o r 55A01 DISA Anemometer w i t h o u t a linearizer C a l i b r a t i o n curve f o r 5 5 A 0 1 DISA Anemometer u s i n g linearizer  10.  11.  Instruments and wind t u n n e l t e s t s e c t i o n  12.  Phase a n g l e c a l i b r a t i o n s e t - u p  13.  B l o c k diagram o f t h e f l u c t u a t i n g p r e s s u r e  k-6 h-T 48 ..^9  measuring  set-up  50  Ik.  C o o r d i n a t e axes f o r wake probe p o s i t i o n s  51  15.  B l o c k diagram o f t h e spanwise measuring s e t - u p  52  16.  Phase s h i f t a n d d i s p l a c e m e n t phenomena f o r t h e  correlation function  c i r c u l a r c y l i n d e r a t v a r i o u s damping l e v e l s  53  V  Figure  Page  17(a)  S t a b i l i t y diagram f o r c i r c u l a r c y l i n d e r  17(b)  S t a b i l i t y diagram f o r D - s e c t i o n c y l i n d e r  18.  O s c i l l a t i o n phenomena f o r c i r c u l a r  19-  I , = 0 ma d O s c i l l a t i o n phenomena f o r c i r c u l a r T = 100 ma d  20.  21.  22.  23.  2k.  25.  26.  27.  28.  29.  30.  5k  cylinder,  55 cylinder,  56  O s c i l l a t i o n phenomena f o r c i r c u l a r T = 160 ma d  cylinder, •.  O s c i l l a t i o n phenomena f o r c i r c u l a r I , = 250 ma d  cylinder,  57  58  O s c i l l a t i o n phenomena f o r c i r c u l a r c y l i n d e r , I . = 3^0 ma d Oscilloscope traces of f l u c t u a t i n g surface pressure and d i s p l a c e m e n t s i g n a l s d u r i n g t h e a b r u p t changes Phase s h i f t and d i s p l a c e m e n t phenomena f o r t h e D - s e c t i o n c y l i n d e r a t v a r i o u s damping l e v e l s O s c i l l a t i o n phenomena f o r D - s e c t i o n I, = 0 ma d O s c i l l a t i o n phenomena f o r D - s e c t i o n r = 80 ma d  cylinder,  O s c i l l a t i o n phenomena f o r D - s e c t i o n I„ = ll<-5 ma d O s c i l l a t i o n phenomena f o r D - s e c t i o n I = 222 ma d  cylinder,  O s c i l l a t i o n phenomena f o r D - s e c t i o n I = k60 ma d  ..5^  59  60  6l  62 cylinder,  63  6)+ cylinder,  65 cylinder,  Beat phenomena f o r t h e o s c i l l a t i n g c i r c u l a r c y l i n d e r  66 .....67  vi Figure 31.  32.  33'  Page Cp d i s t r i b u t i o n on t h e s u r f a c e o f a circular cylinder, V = 11.8 f p s  c i r c u l a r cylinder,,' -V =.:13..2 f p s Cp'  Cp'  C_g  C£  kl.  k2.  k3.  V = 17-6 f p s . . .  71  C^  Cg  V = 13«6 fps..  72  V = 11.8  73  fps......  d i s t r i b u t i o n for' the s t a t i o n a r y c i r c u l a r V = 13-2. fps'.  Ik  d i s t r i b u t i o n f o r the o s c i l l a t i n g c i r c u l a r V = 11.3  75  fps  d i s t r i b u t i o n f o r the o s c i l l a t i n g c i r c u l a r  cylinder, kO.  70  d i s t r i b u t i o n f o r the s t a t i o n a r y c i r c u l a r  cylinder, 39.  V = 11.3' f p s  7  cylinder, 38.  V = 17-5  76  f p s  C£ d i s t r i b u t i o n f o r t h e o s c i l l a t i n g c i r c u l a r cylinder, V = 13-9 f p s •  ••  77  Spanwise phase s h i f t o f f l u c t u a t i n g on 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 ,  sectional l i f t V = 11.8 f p s  78  Spanwise phase s h i f t o f f l u c t u a t i n g on 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 ,  sectional l i f t V = 13.2 f p s  79  Spanwise phase s h i f t o f f l u c t u a t i n g s e c t i o n a l l i f t on an o s c i l l a t i n g c i r c u l a r c y l i n d e r , V = 11.3 f P  80  Spanwise phase s h i f t o f f l u c t u a t i n g s e c t i o n a l l i f t on an o s c i l l a t i n g c i r c u l a r c y l i n d e r , V = 17-5 f p s  81  s  kk.  69  Cp . d i s t r i b u t i o n on'- t h e s u r f a c e o f an o s c i l l a t i n g  cylinder, 37.  ..  d i s t r i b u t i o n on t h e s u r f a c e o f an o s c i l l a t i n g  circular cylinder, 36.  '  d i s t r i b u t i o n on "the s u r f a c e o f an o s c i l l a t i n g  circular cylinder, 35 •  68  .....  Cp' d i s t r i b u t i o n on-the s u r f a c e o f a s t a t i o n a r y  circular cylinder, 3^-.  stationary-  Vll  Figure  k-5 .  h6.  hf.  48.  h9.  50.  Page Span-wise phase s h i f t o f f l u c t u a t i n g s e c t i o n a l . l i f t an o s c i l l a t i n g c i r c u l a r c y l i n d e r , V = 13*9 f p s  on .....82  E f f e c t o f end c l e a r a n c e s on s p a n v i s e phase s h i f t o f fluctuating sectional l i f t . o n a stationary circular c y l i n d e r , V = 13.9 f p s . . . . . .  83  E f f e c t o f f l o o r and c e i l i n g s l o t s on s p a n v i s e phase s h i f t o f f l u c t u a t i n g s e c t i o n a l l i f t on 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 , V = 11.8 f p s  8h  Two-point f l u c t u a t i n g .-wake v e l o c i t y c o r r e l a t i o n s f o r an o s c i l l a t i n g ' c i r c u l a r c y l i n d e r '  85  Two-point f l u c t u a t i n g ' . w a k e v e l o c i t y c o r r e l a t i o n s f o r a s t a t i o n a r y and an o s c i l l a t i n g c i r c u l a r c y l i n d e r , V = 13.9 f p s . . . . . . . . . .  86  Two-point f l u c t u a t i n g ,vake..velocity c o r r e l a t i o n s , f o r a s t a t i o n a r y andian. o s c i l l a t i n g D - s e c t i o n c y l i n d e r , V = lk.1 f p s . . . . . . ' : . . .......  87  ;  V l l l  • LIST OF SYMBOLS o 4.n 4. 4. ' - n . ^ x • 4. Sectional.fluctuating-lxft coefficient,-  rms  of sectional l i f t f  , , '• ••< Total fluctuating l i f t m  • . , " rms coefficient,  a  • .v  • - ' •: , . F l u c t u a t i n g pressure t  Mean peak value;  of t o t a l •§- P  •••  v  V  P  h  lift  hi  p rms — —  coefficient,  - ^/^S ' (' ) 7  Spanwise s e p a r a t i o n o f t h e two probes I n s i d e diameter'of' t h e P o l y e t h y l e n e Dimensionless  tubing  spanwise. s e p a r a t i o n o f the'two p r o b e s ,  —  L a t e r a l aerodynamic f o r c e on t h e c y l i n d e r . Cylinder o s c i l l a t i n g Vortex shedding N a t u r a l frequency  frequency  frequency o f a n e l a s t i c system •  L a t e r a l dimension'of the c y l i n d e r s e c t i o n Damping c u r r e n t L e n g t h o f t h e • c y l i n d e r ; l e n g t h o f the- t u b i n g Mass o f o s c i l l a t i n g system; i n v e r s e o f t h e s l o p e o f t h e l i n e in Figure 9  D  „ n X e s s  .ss  ^  2m The N t h increment where t h e c o r r e l a t i o n f u n c t i o n reaches a l o c a l l y a l g e b r a i c maximum v a l u e , i m p l y i n g the. two s i g n a l s b e i n g i n phase w i t h d e l a y time o f N  Time d e l a y i n c o r r e l a t i o n  function.  Time i n seconds C y l i n d e r Reynolds number,  —  v Hot w i r e probe c o l d 'resistance Probe o p e r a t i n g r e s i s t a n c e C o e f f i c i e n t o f v i s c o u s damping f h v S t r o u h a l number, v Dimensionless v i n d v e l o c i t y ,  V  CD h n  Wind v e l o c i t y B r i d g e d.c. v o l t a g e . ,  .  B r i d g e v o l t a g e a t zero v i n d  speed  Stream wise ;';eoordiriate • T r a n s v e r s e c o o r d i n a t e o r displacement Spanwise c o o r d i n a t e Dimensionless  t r a n s v e r s e displacement,  ^  D i m e n s i o n l e s s t r a n s v e r s e , amplitude, — . .'•-'.;.-'•. • n ,'. Spanwise d i m e n s i o n l e s s d i s t a n c e from t h e mid-span,  Dimensionless  damping c o e f f i c i e n t ,  2  ^  m co n  Tap p o s i t i o n angle w i t h r e s p e c t t o t h e up-stream d i r e c t i o n The a n g l e between t h e v o r t e x l i n e and the model Phase a n g l e by which c y l i n d e r l i f t  leads  z - axis  displacements;  phase s h i f t angle w i t h r e s p e c t t o No. 9 t a p s i g n a l s Normalized  c o r r e l a t i o n f u n c t i o n , d e f i n e d i n Appendix B.  Circular  frequency o f t r a n s v e r s e  Natural c i r c u l a r  oscillation  frequency,2 u f  C r o s s - c o r r e l a t i o n f u n c t i o n , d e f i n e d i n Appendix B A u t o - c o r r e l a t i o n f u n c t i o n , d e f i n e d i n Appendix B Correlation length, defined i n text  xi  ACKNOWLELXJEMEKT The author wishes to express h i s sincere appreciation f o r the guidance and encouragement given by Dr. G. V. Parkinson during his supervision of t h i s i n v e s t i g a t i o n . Sincere appreciation i s also expressed to Mr. J . E. S l a t e r , a fellow graduate student, f o r h i s h e l p f u l advice i n many areas. Thanks are also due to the Department of Mechanical Engineering f o r use of the f a c i l i t i e s and to technicians of the Department f o r t h e i r valuable advice and assistance. F i n a n c i a l support was received from the National Research Council of Canada, Grant A586.  I.  IMTEODUCTIOW  I t i s w e l l known t h a t b l u f f c y l i n d e r s , when e l a s t i c a l l y mounted, e x h i b i t v a r i o u s forms o f o s c i l l a t i o n . oscillation.  One  important  form i s the v o r t e x - e x c i t e d  T h i s o s c i l l a t i o n o c c u r s when the v o r t e x s h e d d i n g f r e q u e n c y  proaches a n a t u r a l frequency  o f the e l a s t i c system.  i s t i c o f t h e f l o w f i e l d causes a f l u c t u a t i n g p r e s s u r e  The  ap  periodic character  d i s t r i b u t i o n on the  c y l i n d e r s u r f a c e and t h e r e s u l t i n g p e r i o d i c f o r c e s e x c i t e c y l i n d e r o s c i l l a t i o n s o v e r a d i s c r e t e range o f w i n d speeds. der a m p l i t u d e  T y p i c a l l y , a graph o f c y l i n -  v e r s u s w i n d speed has a f o r m not u n l i k e t h a t o f a f o r c e d v i -  b r a t i o n w i t h damping, w h i l e a g r a p h o f v o r t e x f r e q u e n c y p o r t r a y s a 'capture' or  ' l o c k i n g - i n ' phenomenon.  v e r s u s w i n d speed  Vortex-excited o s c i l l a -  t i o n s a r e o f c o n s i d e r a b l e e n g i n e e r i n g s i g n i f i c a n c e s i n c e t h e y can  affect  systems s u c h as t r a n s m i s s i o n l i n e s , smoke s t a c k s , submarine p e r i s c o p e s ,  and  launch v e h i c l e s . Numerous i n v e s t i g a t i o n s o f t h i s and o t h e r a s s o c i a t e d phenomena have been r e p o r t e d .  Most o f t h e i n v e s t i g a t i o n s r e l a t e t o t h e 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 , such as K e e f e ' s ^ " ^  (2)  d i r e c t measurement o f f l u c t u a t i n g f o r c e s  (3.4)  and McGregor's^ ' and G e r r a r d ' s ' w  i n v e s t i g a t i o n s on f l u c t u a t i n g  p r e s s u r e s and the s t r u c t u r e o f the wake.  surface  For o s c i l l a t i n g c y l i n d e r s , very  few d i r e c t measurements o f c y l i n d e r s u r f a c e l o a d i n g and c o r r e l a t i o n o f wake  (5) v e l o c i t i e s have been r e p o r t e d .  B i s h o p and Hassan  d e s c r i b e d the measure-  ment o f f l u c t u a t i n g l i f t and drag on a m e c h a n i c a l l y o s c i l l a t i n g  circular  c y l i n d e r i n a water c h a n n e l .  Heine  f c\p r e s e n t e d  measurements o f f l u c t u a -  t i n g s u r f a c e p r e s s u r e on a c i r c u l a r c y l i n d e r i n f r e e o s c i l l a t i o n i n a wind  (7) tunnel.  Den H a r t o g \  on i t s v o r t e x wake.  d e s c r i b e d the e f f e c t o f the c y l i n d e r ' s Recently.Ferguson  oscillations  i n v e s t i g a t e d wake and s u r f a c e  e f f e c t s on a c i r c u l a r c y l i n d e r i n v o r t e x - e x c i t e d o s c i l l a t i o n s and Koop-  ( 9 10) mamr  '  r e p o r t e d some r e s u l t s on t h e v o r t e x wakes o f b o t h m e c h a n i c a l l y  and w i n d - e x c i t e d v i b r a t i n g  cylinders..  However, t h e r e i s s t i l l a l a c k o f i n f o r m a t i o n on some o f t h e c h a r a c teristic  features of vortex-excited o s c i l l a t i o n s  observed  on c i r c u l a r and D - s e c t i o n c y l i n d e r s , i n c l u d i n g d e t a i l e d measure-  ments o f f r e q u e n c i e s , displacement  i n t h e c a p t u r e r e g i o n , as  a m p l i t u d e s , phase s h i f t o f t h e e x c i t i n g  f o r c e w i t h r e s p e c t t o t h e d i s p l a c e m e n t , and spanwise c o r r e l a t i o n o f wake v e l o c i t i e s and f l u c t u a t i n g s u r f a c e p r e s s u r e s on o s c i l l a t i n g  cylinders.  These a r e t h e t o p i c s i n v e s t i g a t e d b y t h e a u t h o r as p a r t o f a c o n t i n u i n g programi.-: i n t h i s l a b o r a t o r y t o s t u d y t h e a e r o e l a s t i c b l u f f bodies.  i n s t a b i l i t y of  3  II. 2.1  INSTRUMENTATION  Wind Tunnel The wind tunnel used i s a low speed, low turbulence, r e t u r n type.  The a i r  speed can be v a r i e d through the range 4 f t / s e c t o 1 5 0 f t / s e c w i t h a turbulence l e v e l l e s s than 0 . 1 $ .  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 r  of 7 : 1 r a t i o can be measured on a Betz micromanometer which gives a reading t o 0 . 0 2 m i l l i m e t e r of water.  The t e s t s e c t i o n v e l o c i t y i s c a l i b r a t e d against the  above pressure d i f f e r e n t i a l .  The rectangular c r o s s - s e c t i o n , 3 6 i n . x 2 7 i n . ,  i s provided w i t h 4 5 ° corner f i l l e t s which vary from 6 i n . x 6 i n . t o 4 . 7 5 i n . x 4 . 7 5 i n . t o compensate f o r the boundary l a y e r growth.  The s p a t i a l v a r i a t i o n of  mean v e l o c i t y i n the t e s t s e c t i o n i s l e s s than  The t u n n e l i s powered by  0.25$.  a 1 5 horsepower d i r e c t current motor d r i v i n g a commercial a x i f l o w fan w i t h a Ward-Leonard system of speed c o n t r o l .  Figure 1 shows the o u t l i n e of the tunnel  and Figure 2 shows a model mounted i n the wind tunnel during t e s t . 2.2  Models Three models were used, two 3 - i n c h diameter c i r c u l a r c y l i n d e r s and one 3-  i n c h D-section c y l i n d e r (Figure 3 ) « They are a l l 2 7 inches long. tubing of  0.066  inch i n s i d e diameter and  0.095  Polyethylene  inch outside diameter was used •  t o convey the f l u c t u a t i n g pressure from the surface taps.  0.022  inch w a l l  thickness aluminum tube and c l e a r p l a s t i c provided the body of the models. Pressure t a p holes i n the model surface were  0.025  inch i n diameter.  For measurements of frequency, amplitude, and phase, the c i r c u l a r c y l i n d e r (8) and D-section c y l i n d e r both designed and used by Ferguson  were used.  F o r spanwise f l u c t u a t i n g s u r f a c e p r e s s u r e measurements, a n o t h e r c i r c u l a r c y l i n d e r was made.  3-inch  P l a s t i c end f i t t i n g s w h i c h a l l o w e d t h e model t o  he r o t a t e d about i t s own a x i s , y e t r e m a i n a t t a c h e d t o the a i r b e a r i n g s h a f t b r a c k e t s , were s e c u r e d by an epoxy a d h e s i v e t o t h e aluminum t u b e . c y l i n d e r a x i s IT p r e s s u r e taps-were e q u a l l y spaced h a l f a c y l i n d e r a p a r t w i t h the n i n t h t a p l o c a t e d a t midspan.  The  t h e i r a n g u l a r d e f i n i t i o n a r e shown i n F i g u r e  h.  Due  Along  diameter  d i s t r i b u t i o n of taps  t o the advantages o f the symmetry o f the s e c t i o n and the  s u r f a c e , was adhesive  A p l a s t i c b l o c k , ' w h i c h was  and  rotatabil-  i t y o f the model on t h e mounting system, t h e number o f p r e s s u r e t a p s was t o a minimum.  the  kept  r a d i u s e d t o f i t the model i n s i d e  d r i l l e d t o e f f e c t 90° bends i n the p r e s s u r e t u b i n g .  An epoxy  s e r v e d t o bond t h e p l a s t i c b l o c k t o the p o l y e t h y l e n e t u b i n g and t o  t h e aluminum tube w i t h the b l o c k h o l e s a l i g n e d w i t h the 0 . 0 2 5 - i n c h t a p s i n t h e aluminum s k i n . 2.3  Model Mounting. System The a i r b e a r i n g s y s t e m d e s i g n e d -  by S m i t h ^ V was u s e d f o r the  experiment.  The models were c o n s t r a i n e d t o o n l y the l a t e r a l p l u n g i n g degree o f freedom w i t h a minimum o f damping f r o m the mounting system.  A d j u s t m e n t s were p r o v i d e d t o  ensure the p a r a l l e l i s m o f the two s e t s o f b e a r i n g s and the p e r p e n d i c u l a r i t y t o the t u n n e l f l o o r o f the b e a r i n g p l a n e .  S l o t s i n t h e t o p and bottom p a n e l s of  t h e t e s t s e c t i o n a l l o w e d the model t o be a t t a c h e d t o the a i r b e a r i n g s h a f t s . To p r o v i d e the e l a s t i c system f o r t h e models d e s i g n e d by F e r g u s o n  (8)  were u s e d .  four h e l i c a l tension springs  They were a t t a c h e d t o the s h a f t b r a c k e t s  5  and t o t h e a i r h e a r i n g frame.  A s t r e a m l i n e d aluminum b a r was u s e d t o determine  t h e damping due t o t h e s p r i n g - b e a r i n g system. A i r s u p p l y f o r t h e b e a r i n g s was produced b y a n I n g e r s o i l - R a n d  2-stage-com-  p r e s s o r , model 1 1 3A x 7 x 8 VHB-2, v i a a 2 5 0 c u b i c f o o t s t o r a g e t a n k . A i r pressure  o f 6 0 pounds p e r square i n c h was u s e d f o r t h e a i r b e a r i n g system from  the main s u p p l y a t a maximum o f 1 1 8 pounds p e r square i n c h . A d i a g r a m m a t i c arrangement o f t h e model, b e a r i n g s , s h a f t s and s p r i n g s i s shown i n F i g u r e 5• 2.h  Wake T r a v e r s i n g Gear To e n a b l e two h o t w i r e probes t o be p o s i t i o n e d w i t h c o n t r o l o f movement i n (8)  a l a t e r a l , v e r t i c a l , and l o n g i t u d i n a l s e n s e , t h e e x i s t i n g t r a v e r s i n g gear was m o d i f i e d so t h a t a sequence o f d e s i r e d spanwise s e p a r a t i o n s o f t h e two probes c o u l d be made.  Two probe mounting b r a c k e t s were c a r r i e d b y f o l l o w e r  n u t s on t h e v e r t i c a l \ i n c h - 2 0 NC end screws w h i c h were s e p a r a t e l y e n c l o s e d i n t h e i r r e s p e c t i v e g u i d e t u b e s . e a c h s o l d e r e d s o l i d l y i n p a r a l l e l w i t h t h e model a x i s on t h e l a t e r a l l e a d screw f o l l o w e r p i e c e .  The l a t e r a l l e a d screw w i t h  5/8 i n c h 1 0 acme double t h r e a d spanned t h e t e s t s e c t i o n .  The e n t i r e assembly  was mounted on a h o r i z o n t a l r i g i d frame w h i c h w i t h i t s grooved wheels c o u l d be p o s i t i o n e d l o n g i t u d i n a l l y a l o n g t h e r a i l s on t h e e x t e r i o r o f t h e t u n n e l s i d e panels.  Hand wheels and f l e x i b l e s h a f t s e n a b l e d t h e v e r t i c a l l e a d screws t o  rotate.  E a c h probe was e l e c t r i c a l l y i n s u l a t e d from t h e e n t i r e t r a v e r s i n g gear  a s s e m b l y so t h a t s e p a r a t e probe c i r c u i t s were  maintained.  The t r a n s v e r s e d e v i a t i o n i n p o s i t i o n i n g t h e probe was c a l i b r a t e d t o be  6  0.177 inch or about 5'9$ of cylinder diameter.  Since the probes were always  positioned at the flat portion of the probe signal amplitude vs. transverse lateral distance (section 3»3)> this deviation gave negligible probe signal error. 2.5  Figure 6 shows the modified"traversing gear.  Displacement Transducer A signal corresponding to model amplitude was obtained from an a i r core  transformer designed by S m i t h - T h e coaxial cylindrical construction a l lowed the a i r bearing shaft to be inserted between the primary and secondary windings, thus varying the magnetic coupling. A 10 kc frequency signal of k rms volts supplied by a Hewlett-Packard 200 CD oscillator was modulated by the shaft oscillations and this signal was in turn rectified to give the resulting displacement signal which was  displayed either on a storage oscillo-  scope, or fed into a Honeywell Visicorder to record time-amplitude traces, or fed into the correlator to give the phase value between fluctuating surface pressure and cylinder displacement.  The displacement transducer was mounted  on the top channel of the a i r bearing mounting system as shown in Figure 5. For calibration of the transducer a wooden scale was mounted close to the shaft under the floor of the tunnel, and a calibration was performed during each series of tests. 2.6  Magnetic Damping In addition to the inherent damping of the springs and a i r bearing sys-  tem, magnetic damping was produced by means of electromagnetic eddy-current dampers designed by S m i t l / ^ . 11  The a i r bearing shafts passed through the mag-  7  netic f i e l d created by the damper and eddy currents induced in the shafts dissipated energy from the oscillating system. An appreciable amount of undesirable residual magnetism built up on the damper was removed periodically by switching the damper coils over to a variable a.c. source.  The a.c. voltage is raised to give a greater magnetic  f i e l d than that produced by the d.c. source, this effectively erasing the residual magnetism. Positions of the dampers are shown in Figure 52.7  Pressure  Transducer  A Barocel Modular Pressure Transducing System developed by Datametrics Inc. of Waltham, Massachusetts was used for measuring surface fluctuating pressures.  The Barocel is a high precision, stable capacltive voltage divid-  er, the variable element of which is a thin prestressed stainless steel diaphragm. Positioned between fixed capacitor plates, the diaphragm deflects proportionally to the magnitude of the applied pressure.  An a.c. carrier volt-  age at 10 kc is applied to. the stationary capacitor plates. The diaphragm attains a voltage level determined by i t s relative position between the fixed capacitor plates. With the Barocel appropriately arranged in a bridge circuit, the output voltage is determined by the ratio of capacitance of the diaphragm to each of the stationary electrodes. The carrier voltage is thereby amplitude modulated in accordance with the input pressure. Since the frequency range required for this investigation also f e l l in the  (12)  range between 5 and 35 cps used by Wiland  v  , the basic calibration system he  8 d e v i s e d was  used.  No resonance c o n d i t i o n e x i s t e d between t h e t r a n s d u c e r w i t h  t u b e and p r e s s u r e t a p on one was  s i d e and t h e volume where t h e c a l i b r a t i o n s i g n a l  g e n e r a t e d on the o t h e r s i d e .  The  b l o c k diagram of t h e c a l i b r a t i o n a p p a r a -  t u s i s shown i n F i g u r e 7, and t h e c a l i b r a t i o n curve t o g e t h e r w i t h W i l a n d ' s i s shown i n F i g u r e 8.  The  s m a l l d i f f e r e n c e i s due  t o s l i g h t l y larger tube i n s i d e  diameter i n the present c a l i b r a t i o n . 2.8  Correlator A c o r r e l a t i o n f u n c t i o n computer, Model 1 0 0 ,  Research Corporation,  was  acquired  produced by P r i n c e t o n  d u r i n g the i n v e s t i g a t i o n and was  measure c o r r e l a t i o n f u n c t i o n s and phase a n g l e s ( s e c t i o n s 3.2  and  Applied  used to  3'3)«  The  s i g n a l c o r r e l a t o r i s d e s i g n e d - t o compute the c r o s s - c o r r e l a t i o n f u n c t i o n , R  ( r ) , o f two l,d  e l e c t r i c a l signals defined  p  by  T R  J T )  1,2  V  =  '  l  l  m  T-+  oo  -  f  T  J  f , Ct)  r  o  f (t-T)  dt  0  2>  1  '  and the a u t o - c o r r e l a t i o n f u n c t i o n , R.. - (T), o f two  i d e n t i c a l signals defined  by.  1,1  R  1  1.1  M  T  =m  T-* 3  J  I  1  00  WT J\  f  N  1  l (  t  dt  f 1( t " 0  )  n  U t i l i z i n g b o t h a n a l o g and d i g i t a l t e c h n i q u e s , t h e s e i n s t r u m e n t s o p e r a t e as h y b r i d computers t o s o l v e e i t h e r of the two  i n t e g r a l s f o r one  t a l l y i n c r e a s i n g v a l u e s of the time delay,  AT •  The  r e l a t i o n f u n c t i o n computed i s c l o s e l y r e p r e s e n t e d t-t' R  i  X,d  pC*)  =  RC  b  t J-oo  \  e RC  " n " t h p o i n t on the  by.  -  M*') 1  d  hundred incremen-  EpC*'-two  it  cor-  9 where "RC" i s t h e t i m e c o n s t a n t time coordinate  of the averaging  o f t h e computed p o i n t , a n d  computation, o r by d e f i n i t i o n ,  circuit,  "nAx"  defines the  t ' represents the past h i s t o r y of  t '> t .  Computation a t each p o i n t i n v o l v e s t h r e e b a s i c o p e r a t i o n s : i n p u t wave f o r m a n d d e l a y i n g t h e samples, m u l t i p l y i n g t h e d e l a y e d  sampling the samples b y  e i t h e r t h e o r i g i n a l i n p u t wave f o r m ( a u t o - c o r r e l a t i o n ) o r b y a second wave f o r m ( c r o s s - c o r r e l a t i o n ) , and averaging The  t h e l a g g e d p r o d u c t s i n an RC i n t e g r a t o r .  r a t e o f time s h i f t i n g determines the incremental value o f time delay,  AT ,  and t h u s s e t s t h e t i m e base a g a i n s t w h i c h each p o i n t o f t h e c o r r e l a t i o n f u n c t i o n i s computed.  M u l t i p l i c a t i o n - o f t h e two i n p u t s i g n a l s i s p e r f o r m e d a u t o -  m a t i c a l l y a t each p o i n t . time constant  I n t e r n a l RC networks p e r f o r m t h e i n t e g r a t i o n w i t h a  o f kO seconds i n t h i s c o r r e l a t o r . F i v e t i m e s t h i s c o n s t a n t , o r  200 s e c o n d s , i s r e q u i r e d f o r t h e f u n c t i o n t o grow t o w i t h i n one p e r c e n t f i n a l value.  Because a l l t h e m a t h e m a t i c a l o p e r a t i o n s  each p o i n t a r e performed simultaneously  of i t s  involved i n evaluating  i n r e a l t i m e , t h e l e n g t h o f time r e -  q u i r e d t o compute t h e complete f u n c t i o n depends o n l y on t h i s a v e r a g i n g  time  constant. As i t i s computed, t h e c o r r e l a t i o n f u n c t i o n i s s t o r e d i n t h e 100 c h a n n e l a n a l o g memory.  V e r s a t i l e r e a d o u t c i r c u i t r y a l l o w s t h e f u n c t i o n t o be d i s p l a y e d  on an o s c i l l o s c o p e as i t i s b e i n g computed, and t o be n o n - d e s t r u c t i v e l y  read  out e i t h e r a f t e r o r d u r i n g c o m p u t a t i o n . As w i t h any computer, t h e computed f u n c t i o n i s o n l y a good o f an i d e a l r e s u l t .  approximation  C o n f o r m i t y o f t h e computed and t h e i d e a l f u n c t i o n i s ex-  10  c e l l e n t f o r Model 1 0 0 .  I t s d i f f e r e n c e t y p i c a l l y does n o t exceed one p e r c e n t  at any p o i n t . According t o standard p r a c t i c e , the normalized c r o s s - c o r r e l a t i o n function, ot^r^i)  , i s d e f i n e d a n d computed a s f o l l o w s : R a  l 2  (  T  )  =  1  2  ( T )  • R ^ O )  R (0) 2  To measure t h e phase a n g l e "between two p e r i o d i c s i g n a l s , t h e f o l l o w i n g f o r m u l a was d e v e l o p e d  i n Appendix A:  <t> = 3.6 N  2.9  T  Hot W i r e Anemometers a n d L j n e a r i z e r s Two h o t - w i r e s were u s e d .  was  f v  E a c h was made o f p l a t i n u m - p l a t e d t u n g s t e n a n d  o f 0 . 0 0 5 mm. d i a m e t e r and a p p r o x i m a t e l y 1 . 2 mm. l o n g .  temperature  Two DISA c o n s t a n t  anemometers s u p p l i e d t h e b a s i c c i r c u i t s f o r t h e t r a n s d u c e r s .  The  p r i n c i p l e o f measurement i s b a s e d on t h e c o n v e c t i v e heat l o s s i n a n e l e c t r i c a l l y heated w i r e ( o r f i l m ) by the f l o w o f f l u i d surrounding the w i r e .  Fun-  d a m e n t a l l y , what i s measured i s t h e amount o f power r e q u i r e d t o keep t h e temperature constant. put v o l t a g e  E  The r e l a t i o n between f l o w v e l o c i t y  a n d anemometer o u t -  c a n be r e p r e s e n t e d b y 2  E where  V  n = A + BV  A , B , and n  ,,,  (1)  a r e c o n s t a n t s whose v a l u e s depend on t h e probe con-  n e c t e d t o t h e anemometer. The o u t p u t v o l t a g e o f a c o n s t a n t temperature  anemometer i s t h u s a non-  11 l i n e a r f u n c t i o n o f the f l o w v e l o c i t y  V  under measurement.  This n o n l i n e a r i t y  i s u n d e s i r a b l e i n c o r r e l a t i o n f u n c t i o n measurement.' T h e r e f o r e two DISA Type 55D10, were a c q u i r e d and u s e d t o e l i m i n a t e d i s t o r t i o n .  linearizers, The  linear-  i z e r i s an e l e c t r o n i c a n a l o g computer whose b a s i c t r a n s f e r f u n c t i o n a t  constant  s e t t i n g s o f t h e o p e r a t i n g c o n t r o l s can be w r i t t e n a s :  E  out where  2  ,2 . = K (E.  - E.  in  .m )  (2)  mo  ^ '  i s t h e output v o l t a g e a t z e r o f l o w v e l o c i t y and i s a c o n -  s t a n t , as i s  K .  P u t t i n g t h e anemometer o u t p u t v o l t a g e 1  in  zer input voltage  Thus, f o r '  E. . E  2 E. mo  E  as b e i n g e q u a l t o t h e  , we have., on s u b s t i t u t i n g ( l ) and 2 'm . = K (A ,* BV '- E. )  (2),  11  = A  and  p r o p o r t i o n a l t o the v e l o c i t y  m =— V •  1 n  the l i n e a r i z e r output v o l t a g e w i l l  :  The  be  F i g u r e 9 shows t h e c a l i b r a t i o n curve w i t h -  out u s i n g a l i n e a r i z e r and" F i g u r e 10,'.shows c a l i b r a t i o n c u r v e s u s i n g zers.  lineari-  lineari-  d i f f e r e n t slopes" Of t h e two c u r v e s i n F i g u r e 10 a r i s e from d i f f e r e n t  s e t t i n g s of gain adjustment. B o t h t h e anemometers and t h e l i n e a r i z e r s show n e g l i g i b l e phase s h i f t f o r f r e q u e n c i e s below 300 2.10  kc.  Band P a s s F i l t e r s To e l i m i n a t e the random wake t u r b u l e n c e and p e r m i t c o n c e n t r a t i o n on the  d i s c r e t e v o r t e x shedding  phenomena as f a r as p o s s i b l e , a band pass f i l t e r ,  K r o h n - H i t e , Model 330B, i n the pressure measuring D u r i n g measurements t h e f i l t e r was t i n g t h e v o r t e x s h e d d i n g frequency.-  system was i n t r o d u c e d .  c a l i b r a t e d f o r e v e r y change a f f e c -  The f i l t e r was  f r e q u e n c y and t h e a t t e n u a t i o n f a c t o r was  o p e r a t e d a t mid-band  formed, by f e e d i n g a  sinusoidal  s i g n a l f r o m a f u n c t i o n , g e n e r a t o r t o t h e o s c i l l o s c o p e and m e a s u r i n g t h e  dif-  f e r e n c e i n o u t p u t w i t h and w i t h o u t , t h e f i l t e r . 2.11  Other E l e c t r o n i c  Instruments  F o l l o w i n g i s a l i s t of other e l e c t r o n i c apparatus used i n the e x p e r i m e n t a l work: Voltmeters:  H e w l e t t P a c k a r d , HP^3^00A t r u e rms v o l t m e t e r , and HP-412 vacuum tube v o l t m e t e r .  Function Generators:  H e w l e t t P a c k a r d , low f r e q u e n c y f u n c t i o n g e n e r a t o r , M o d e l 212A, and H e a t h k i t a u d i o g e n e r a t o r , Model I G - 7 2 .  V i b r a t i o n Generator:  Goodmans, Type V  T e k t r o n i x , Type 5 6 4 ,  Oscilloscopes: Chart Recorder: Low  47.  dual trace storage o s c i l l o s c o p e .  H o n e y w e l l , 906 C v i s i c o r d e r  f r e q u e n c y a m p l i f i e r w i t h power s u p p l i e s :  B u i l t i n t h e Department (12)  RC Damping C i r c u i t : V a r i a b l e Transformer: F i l t e r e d D.C  B u i l t i n t h e Departments \ Ohmite, C a t . No. VT8-F.  Power S u p p l y :  E l e c t r o , Model D - 6 1 2 T  Most e l e c t r o n i c i n s t r u m e n t s t o g e t h e r w i t h a s i d e v i e w o f t h e t u n n e l t e s t s e c t i o n a r e shown i n F i g u r e 1 1 .  13 III. 3.1  EXPERIMENTAL PROCEDURES  F r e q u e n c y , A m p l i t u d e and Phase Measurements F o r each o f t h e f o l l o w i n g e x p e r i m e n t s , t h e non-aerodynamic  l e v e l was s e t f o r t h e o s c i l l a t i n g small steps.  damping  system and t h e w i n d speed i n c r e a s e d i n  A t each w i n d speed t h e d e s i r e d measurement was made.  W i t h the  c y l i n d e r s t i l l o s c i l l a t i n g , t h e w i n d speed was i n c r e a s e d by the n e x t s t e p , and t h e p r o c e s s was r e p e a t e d .  I t was c o n t i n u e d t o t h e h i g h e s t w i n d speed  and t h e n r e p e a t e d f o r d e c r e a s i n g w i n d speeds w i t h t h e w i n d speed b e i n g s e t w h i l e t h e c y l i n d e r was s t i l l 3.1.1  decrement  oscillating.  F r e q u e n c y Measurements  Vortex shedding f l u c t u a t i n g pressure s i g n a l s or v e l o c i t y s i g n a l s or c y l i n d e r d i s p l a c e m e n t s i g n a l s were d i s p l a y e d on a s t o r a g e s c o p e . The  vortex  s h e d d i n g f r e q u e n c y was measured f r o m t h e p r e s s u r e s i g n a l f r o m a s u r f a c e t a p at the t r a n s v e r s e diameter f o r the c i r c u l a r e s t t h e edge f o r t h e D - s e c t i o n c y l i n d e r .  c y l i n d e r , and from the t a p n e a r -  The t i m e base o f t h e s t o r a g e s c o p e  was c a l i b r a t e d a g a i n s t a Type l8k Time-mark g e n e r a t o r ( T e k t r o n i x I n c . ) .  The  e r r o r i n v o l v e d was c a l c u l a t e d t o be l e s s t h a n 2$. 3.1.2  phase Measurements  The phase between two p e r i o d i c s i g n a l s was o b t a i n e d e a r l y i n the program by f e e d i n g them t o t h e V i s i c o r d e r and m e a s u r i n g t h e average phase s h i f t over 15  c y c l e s , and l a t e r i n t h e program by f e e d i n g them t o t h e c o r r e l a t o r and c a l -  c u l a t i n g the phase v a l u e ( s e c t i o n 2.8) e q u i v a l e n t l y over 1800  cycles.  w h i c h was a v e r a g e d o v e r 200 seconds o r  F o r spanwise phase measurements t h e e f f e c t o f  Ik  any phase s h i f t i n t h e i n s t r u m e n t a t i o n was n u l l i f i e d by measuring a l l phase  (8) s h i f t s f r o m a permanent r e f e r e n c e d i s c probe c o n s t r u c t e d by Ferguson mounted b e h i n d one s i d e o f t h e model a t t h e midspan.  and  F o r measurement o f the  phase between t h e s u r f a c e f l u c t u a t i n g p r e s s u r e s i g n a l from a t a p a t the midspan and a t 90° v a l u e was  and t h e n e g a t i v e c y l i n d e r d i s p l a c e m e n t , a c o r r e c t i v e phase  i n t r o d u c e d i n t h e r e s u l t b y measuring t h e phase between t h e model  s u r f a c e t a p and t h e output o f t h e f i l t e r . a p p a r a t u s r e f e r r e d t o i n s e c t i o n 2.7  To a c h i e v e t h i s , t h e c a l i b r a t i o n  was u s e d b y f e e d i n g a s i n u s o i d a l s i g n a l  o f t h e same v o r t e x s h e d d i n g f r e q u e n c y i n t o t h e system and t h e n t a k i n g t h e r e a d i n g from e i t h e r a V i s i c o r d e r o r a c o r r e l a t o r . b r a t i o n set-up.  F i g u r e 12  shows t h e  cali-  the s c h e m a t i c diagram o f w h i c h i s t h e same as F i g u r e 10  ex-  c e p t a V i s i c o r d e r o r t h e c o r r e l a t o r was u s e d t o measure t h e phase a n g l e between t h e two o u t p u t s i g n a l s . As can.be s e e n , t h e phase r e s u l t from t h e c o r r e l a t o r i s much more r e p r e s e n t a t i v e o f t h e t i m e average v a l u e t h a n t h a t f r o m the V i s i c o r d e r . When t h e c a p t u r e r e g i o n was r e a c h e d , a phase a n g l e s u r e and t h e d i s p l a c e m e n t s i g n a l s c o u l d be measured.  <t> between the p r e s -  T h i s phase a n g l e  <t>  was t h e a n g l e by w h i c h t h e s u c t i o n a t t h e t a p mentioned above l e a d s t h e d i s placement  i n the d i r e c t i o n of t h a t t a p .  ( T h i s i s t h e same as t h e phase a n g l e :  by which the t r a n s v e r s e e x c i t i n g f o r c e leads the displacement.) 3.I.3  D i s p l a c e m e n t A m p l i t u d e Measurements  T h e s i g n a l was s,  d i s p l a y e d on a s t o r a g e s c o p e and d u r i n g each s e r i e s o f  t e s t s , a c a l i b r a t i o n was made.  F o r t h e minimum damping l e v e l o n l y f o r each  15  c y l i n d e r , t h e measurement was made a g a i n o v e r t h e complete w i n d speed range w i t h t h e c y l i n d e r s t a r t i n g f r o m r e s t a t each w i n d speed. For  i n v e s t i g a t i n g t h e s t a b i l i t y o f t h e o s c i l l a t i n g systems a t v a r i o u s  damping l e v e l s , t h e non-aerodynamic  damping was s e t a t v a r i o u s l e v e l s up t o  the maximum a v a i l a b l e b y t h e magnetic dampers, and t h e range o f w i n d speeds over which each c y l i n d e r o s c i l l a t e d w i t h Y  max  3-2  Y > .01 was d e t e r m i n e d , a s was  i n t h e range. Spanwise F l u c t u a t i n g S u r f a c e P r e s s u r e Measurements F i g u r e 13 shows t h e s c h e m a t i c arrangement o f t h e i n s t r u m e n t a t i o n f o r span-  w i s e f l u c t u a t i n g s u r f a c e p r e s s u r e measurements. the  F o r each angular p o s i t i o n o f  s u r f a c e t a p s , measurements were t a k e n s u c c e s s i v e l y .  Then a n o t h e r t a p a n -  g u l a r p o s i t i o n was assumed b y r o t a t i n g t h e c y l i n d e r 15° and a n o t h e r s e r i e s o f measurements a l o n g t h e span was t a k e n . g u l a r t a p p o s i t i o n s were assumed.  Due t o symmetry, o n l y h a l f o f t h e a n -  F o r each r e a d i n g t h e a v e r a g i n g t i m e was 200  seconds o r more. 3.3  Spanwise Wake V e l o c i t y C o r r e l a t i o n Measurements F o r e a c h w i n d v e l o c i t y and a t a f i x e d spanwise p o s i t i o n , t r a v e r s i n g t h e  hot w i r e probe f r o m t h e c e n t e r a c r o s s t h e wake a n d p l o t t i n g t h e rms v a l u e o f the  s i g n a l gave a peak a t t h e v o r t e x c e n t e r l i n e .  t i o n due t o t r a n s v e r s e movement ( s e c t i o n 2.k)  To reduce t h e r e a d i n g d e v i a -  o f t h e probe a t v a r i o u s spanwise  p o s i t i o n s i t was d e s i r a b l e t o p u t t h e probe near a f l a t t e r peak.  This p o s i t i o n  was f o u n d f o r each w i n d speed b y m e a s u r i n g t h e rms v a l u e o f t h e f l u c t u a t i n g v e l o c i t y s i g n a l a m p l i t u d e a c r o s s t h e wake and a t s e v e r a l downstream p o s i t i o n s  16  and p i c k i n g out the d e s i r a b l e one. t i o n a r e shown i n F i g u r e  The  Ik.  F i g u r e 1 5 shows the schematic  s e t - u p o f the i n s t r u m e n t a t i o n f o r spanwise  wake v e l o c i t y c o r r e l a t i o n measurements. shedding  f r e q u e n c y was  c o o r d i n a t e axes f o r wake probes p o s i -  S i n c e o n l y the fundamental v o r t e x  o f i n t e r e s t , two band pass f i l t e r s were i n t r o d u c e d i n  t h e c i r c u i t t o s c r e e n t h e u n d e s i r a b l e n o i s e and t h u s g i v e a c l e a r e r s i g n a l . T h i s , however, a l s o i n t r o d u c e d phase s h i f t s due t o t h e f i l t e r s .  Time d e l a y i n  t h e c o r r e l a t o r c o u l d have been u s e d w i t h some time s a v i n g f o r each s e r i e s o f t e s t s by measuring t h e phase o f the system i n terms o f -the amount o f d e l a y time t o a c h i e v e no phase s h i f t c o n d i t i o n when two probes a r e v e r y c l o s e l y p l a c e d , and t h e n t a k i n g the r e a d i n g o f the c o r r e l a t o r output c o r r e s p o n d i n g t h e same amount o f d e l a y time d u r i n g the measurement.  to  However due t o t e c h n i -  cal  d i f f i c u l t y i n p l a c i n g two probes v e r y c l o s e l y , the f o l l o w i n g a l t e r n a t i v e  was  used.  The two f i l t e r s were a d j u s t e d f o r each v o r t e x shedding  frequency  so  t h a t e a c h gave the same phase s h i f t . B e f o r e e v e r y s e r i e s o f measurements, hot w i r e r e s i s t a n c e was  measured  w i t h i t s o p e r a t i n g r e s i s t a n c e s e t , the b r i d g e c i r c u i t o f the anemometer  was  b a l a n c e d and the l i n e a r i z e r t e m p e r a t u r e compensation and z e r o adjustment made. F o r each probe p o s i t i o n two a u t o - c o r r e l a t i o n s and one q r o s s - c o r r e l a t i o n were measured. nal 3.h  S i n c e o n l y the n o r m a l i z e d c o r r e l a t i o n f u n c t i o n was  of i n t e r e s t ,  a m p l i t u d e a t t e n u a t i o n s i n the two measuring systems were not  sig-  balanced.  Measurements o f Mon-Aerodynamic V i s c o u s Damping The non-aerodynamic damping was  s e t a t v a r i o u s l e v e l s up t o the maximum  IT a v a i l a b l e b y t h e m a g n e t i c dampers.  These l e v e l s c o r r e s p o n d e d r e s p e c t i v e l y  t o t h o s e f o r e v e r y s e r i e s o f f r e q u e n c y , a m p l i t u d e and phase measurements. F o r e a c h damping l e v e l t h e model was p u l l e d t o one s i d e and t h e n T h i s was done w i t h w i n d o f f . decay.  released.  A V i s i c o r d e r was u s e d t o r e c o r d t h e a m p l i t u d e  To determine t h e e f f e c t o f t h e s t i l l - a i r aerodynamic damping o f t h e  model, a s t r e a m l i n e d  aluminum b a r o f t h e same w e i g h t as t h e model was u s e d  i n s t e a d and t h e same p r o c e d u r e s were  applied.  IV. . EXPERIMEEEAL RESULTS k.l  F r e q u e n c y , A m p l i t u d e and Phase Measurements f o r a C i r c u l a r C y l i n d e r A t o t a l o f f i v e damping l e v e l s w e r e . s e t f o r measuring f r e q u e n c y ,  and phase s h i f t .  These f i v e ; l e v e l s c o r r e s p o n d  l 6 0 , 250 and 3^0 ma.  amplitude  t o damping c u r r e n t s o f 0, 100,  F i g u r e l 6 shows a summary o f t h e c h a r a c t e r i s t i c s o f v o r -  t e x - e x c i t e d o s c i l l a t i o n phenomena.  They a l l d i s p l a y t h e c a p t u r e , over a d i s -  c r e t e range o f w i n d speed, o f t h e v o r t e x f r e q u e n c y b y t h e c y l i n d e r f r e q u e n c y , w h i c h remains n e a r l y c o n s t a n t and c l o s e t o t h e n a t u r a l f r e q u e n c y system.  The phase a n g l e  ;  <t>  increases w i t h t h e wind v e l o c i t y during  A t a w i n d speed b e y o n d . t h a t c o r r e s p o n d i n g t e x frequency  of the e l a s t i c capture.  t o t h e maximum d i s p l a c e m e n t ,  the vor-  r e v e r t s a b r u p t l y t o i t s v a l u e f o r t h e s t a t i o n a r y c y l i n d e r a t the  end o f t h e c a p t u r e range.. F i g u r e 17(a) shows t h e e f f e c t o f damping on v o r t e x - e x c i t e d o s c i l l a t i o n ""  ""  phenomena i n t h e f o r m o f t h e s t a b i l i t y d i a g r a m i n t r o d u c e d by S c r u t o n f i g u r e shows t h e u p p e r a^^&vef -botpdaries :  Y  against  2TT  max  2rfU  and  •''••"•„. •• . .  19, 20, 21 and 22 show t h e d e t a i l s o f t h e above phenomena a t  each damping l e v e l . , I n t h e s e f i g u r e s against  plotted with  . The  . n  F i g u r e s 18,  Y = 0.01  (Ik)  Y , f / f , f / f v n c n  U . A reference l i n e corresponding  and  <t> a r e p l o t t e d '  t o t h e known S t r o u h a l number f o r  t h e s t a t i o n a r y c y l i n d e r i s i n c l u d e d on each f i g u r e .  (S = O.198  f o r the c i r k  c u l a r c y l i n d e r i n t h e range o f Reynolds, number under c o n s i d e r a t i o n , from 10  t o 5(io)\)  19 The b e h a v i o r o f f l u c t u a t i n g s u r f a c e p r e s s u r e and t h e c y l i n d e r t i o n d u r i n g t h e a b r u p t decrease o f  Y  from  Y^^.  i s interesting.  2 3 ( a ) , ( b ) and ( c ) show s u c c e s s i v e l y t h e phenomena..  oscillaFigures  I t i s seen t h a t a 5  p e r c e n t w i n d speed i n c r e a s e r e s u l t s i n 80 p e r c e n t f l u c t u a t i n g s u r f a c e p r e s sure decrease and 60 p e r c e n t d i s p l a c e m e n t d e c r e a s e .  F i g u r e 23(d), on t h e  o t h e r hand, shows t h e phenomena when w i n d speed i s d e c r e a s e d u n t i l t h e Y  abrupt increase of  takes place.  I t i s seen t h a t a 3-6 p e r c e n t w i n d  speed decrease b r i n g s 60 p e r c e n t f l u c t u a t i n g s u r f a c e p r e s s u r e i n c r e a s e but o n l y 11 k.2  percent displacement i n c r e a s e .  F r e q u e n c y , A m p l i t u d e and Phase Measurement f o r a D - s e c t i o n C y l i n d e r S i m i l a r t o t h e c i r c u l a r c y l i n d e r measurements as above, a t o t a l o f f i v e  damping l e v e l s were s e t w h i c h c o r r e s p o n d t o damping c u r r e n t s o f 0, 222,  and k6o ma.  F i g u r e 2k shows a s i m i l a r summary o f the  80,  1^5,  characteristics  o f v o r t e x - e x c i t e d o s c i l l a t i o n phenomena. F i g u r e 17(b)  shows t h e phenomena i n terms o f t h e s t a b i l i t y  Comparing w i t h F i g u r e 17(a)  diagram.  i t i s seen t h a t D - s e c t i o n c y l i n d e r o s c i l l a t i o n s  a r e much h a r d e r t o s u p p r e s s by i n c r e a s e d damping t h a n t h o s e o f t h e c i r c u l a r cylinder. F i g u r e s 25,  26,  27,  28 and 29 show  t h e d e t a i l s o f the phenomena a t  v a r i o u s damping l e v e l s mentioned b e f o r e . 4.3  F l u c t u a t i n g P r e s s u r e s on t h e S u r f a c e o f a C i r c u l a r C y l i n d e r F o r b o t h a s t a t i o n a r y and a v o r t e x - e x c i t e d o s c i l l a t i n g c i r c u l a r c y l i n d e r ,  20  t h e f l u c t u a t i n g s u r f a c e p r e s s u r e s a t each s e c t i o n e x p e r i e n c e d a m p l i t u d e modul a t i o n w h i c h was t h e fundamental i n d e r and l 8 0 °  i n phase a r o u n d t h e c y l i n d e r .  These f l u c t u a t i n g p r e s s u r e s a t  f r e q u e n c y were a p p r o x i m a t e l y i n phase over one s i d e o f t h e out ,of phase w i t h t h e o p p o s i t e  cyl-  side.  For a s t a t i o n a r y c y l i n d e r , the f l u c t u a t i n g pressure s i g n a l experienced a random a m p l i t u d e m o d u l a t i o n . tude m o d u l a t i o n was  F o r an o s c i l l a t i n g c i r c u l a r c y l i n d e r , an a m p l i -  e x p e r i e n c e d by t h e c y l i n d e r a t w i n d speeds i n i t i a t i n g  cyl-  i n d e r o s c i l l a t i o n . The m o d u l a t i o n showed a b e a t phenomenon. I t s f r e q u e n c y roughly the d i f f e r e n c e  between t h e f l u c t u a t i n g p r e s s u r e f r e q u e n c y and t h e  inder o s c i l l a t i o n frequency. Figure 30' 'capture  1  Representative oscilloscope  was cyl-  t r a c e s a r e shown i n  T h i s a m p l i t u d e m o d u l a t i o n d i s a p p e a r e d a t h i g h e r w i n d speeds i n the range.  S i m i l a r phenomena were a l s o o b s e r v e d by Ferguson  for a  (15)  vortex-excited  c y l i n d e r and b y Toebes  f o r a mechanically vibrating  cylin-  der. F i g u r e s 31 t o 35 i n c l u s i v e show t h e f l u c t u a t i n g p r e s s u r e c o e f f i c i e n t d i s t r i b u t i o n a r o u n d one h a l f o f t h e c y l i n d e r c i r c u m f e r e n c e a t v a r i o u s s u c c e s s i v e sections  along the c y l i n d e r .  Fluctuating  pressure c o e f f i c i e n t  as t h e r a t i o o f f l u c t u a t i n g p r e s s u r e r o o t mean square a m p l i t u d e , dynamic p r e s s u r e ,  \ pv  o f t h e f r e e stream.  The v a l u e o f  a l s o o f rms v a l u e i n a l l the subsequent f i g u r e s u n l e s s o t h e r w i s e  C '  i s defined  P ' , t o the i s therefore indicated.  C ' d i s t r i b u t i o n c o r r e s p o n d i n g t o the w i n d v e l o c i t y p r o d u c i n g n e a r l y  the  maximum model d i s p l a c e m e n t and t h a t c o r r e s p o n d i n g t o the same w i n d v e l o c i t y b u t w i t h t h e model h e l d s t a t i o n a r y a r e shown r e s p e c t i v e l y  i n F i g u r e s 35 and  32.  21 F i g u r e s 33  34  and  show the  responding r e s p e c t i v e l y and  -C ' d i s t r i b u t i o n of an o s c i l l a t i n g c y l i n d e r  t o the. w i n d v e l o c i t y i n i t i a t i n g c y l i n d e r o s c i l l a t i o n  a w i n d v e l o c i t y somewhere a f t e r i the  distribution for.a stationary W i t h the  the  V = 11.8  ures 4l,  h2,  9 = 90°,  UU and  the  37,  38,  be  c e n t r a l t a p and  t h a t from one The  39 and  40.  center tap ( l l o . 9  the phase s h i f t between the  f i v e c a s e s mentioned i n the above. U3,  fluctuating  f i v e cases i n the p r e v i o u s p a r a g r a p h ,  l i n e o f spanwise t a p s f i x e d a t  t a k e n as t h e r e f e r e n c e and  s u r e d f o r the  31.  s u b s e q u e n t l y , the t o t a l l i f t c o e f f i c i e n t may  F o r each o f the  p r e s s u r e s i g n a l from the  C '  f p s i s shown i n F i g u r e  l i f t c o e f f i c i e n t d i s t r i b u t i o n i s shown i n F i g u r e s 36,  t a p ) was  Another  f l u c t u a t i n g p r e s s u r e s a r o u n d each s e c t i o n known, the  numerically.  W i t h the  and  resonant wind v e l o c i t y .  cylinder at  s e c t i o n a l l i f t c o e f f i c i e n t and integrated  cor-  o f the  fluctuating  o t h e r s was  r e s u l t s are  mea-  shown i n F i g -  P o i n t s w i t h d i f f e r e n t symbols on F i g u r e s U l ,  45.  UU were o b t a i n e d on a d i f f e r e n t day  t o show the r e p e a t a b i l i t y of the  43 ex-  periment . As a p r e l i m i n a r y a p p r o a c h t o u n d e r s t a n d i n g the causes of the phase s h i f t , the  gap  t u n n e l f l o o r was  v a r i e d and  shown i n F i g u r e U6. were a l s o a l t e r e d and U.U  between the model end  The the  Spanwise C o r r e l a t i o n s W i r e Anemometers  and  e i t h e r the t u n n e l c e i l i n g or  the phase s h i f t measurements t a k e n .  s i z e s o f the result,  spanwise  The  s l o t s i n the t u n n e l c e i l i n g and  i s shown i n F i g u r e  f o r C i r c u l a r and  result  is  floor  U7.  D-section Cylinders Using  Hot  For an o s c i l l a t i n g c i r c u l a r c y l i n d e r , t h r e e w i n d speeds were s e l e c t e d  for  22 spanwise c o r r e l a t i o n f u n c t i o n measurements:  the wind speed i n i t i a t i n g  oscil-  l a t i o n , a wind speed near the resonant wind s p e e d , and a wind speed somewhat beyond the r e s o n a n t wind s p e e d .  F o r the 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 , the  speed p r o d u c i n g n e a r l y imximum model displacement was s e l e c t e d . are  wind  The r e s u l t s  shown i n F i g u r e s 48 and 49F o r the D - s e c t i o n c y l i n d e r , the spanwise c o r r e l a t i o n f u n c t i o n was measured  a t o n l y one wind s p e e d , f o r b o t h the s t a t i o n a r y and o s c i l l a t i n g c y l i n d e r , p r o d u c e d n e a r l y maximum displacement f o r the o s c i l l a t i n g model. are shown i n F i g u r e  50.  which  The r e s u l t s '-  23 V. 5.1  DISCUSSION OF RESULTS  F r e q u e n c y , A m p l i t u d e and Phase Measurements As shown i n ' F i g u r e s 16 and 2k, i r r e s p e c t i v e o f t h e damping l e v e l s f o r the  o s c i l l a t i n g c i r c u l a r c y l i n d e r , t h e v a r i a t i o n o f t h e phase a n g l e , i s n e a r l y t h e same, i n c r e a s i n g g r a d u a l l y from around 100°  after  Y  v a r i a t i o n of  max 0  i s reached.  <t> w i t h  0° and jumping t o around  This a l s o a p p l i e s t o the D-section c y l i n d e r , the '  b e i n g f r o m around 1 5 ° t o 30°without any jump except f o r t h e  l o w e s t damping l e v e l f o r w h i c h t h e r e does e x i s t an a b r u p t i n c r e a s e o f Y  U  <t>  '•  near  max The  ' c a p t u r e ' o r ' l o c k i n g - i n ' r e g i o n , over w h i c h t h e v o r t e x shedding f r e -  quency remains t h e same a s t h e c y l i n d e r o s c i l l a t i o n f r e q u e n c y , and become s m a l l e r as t h e damping l e v e l i s i n c r e a s e d f o r b o t h c y l i n d e r s .  Y  both However,  f o r t h e c i r c u l a r c y l i n d e r , b o t h t h e c e n t e r o f t h e c a p t u r e r e g i o n and t h e l o c a t i o n of  Y  occur a t lower  U  v a l u e s a s t h e damping c u r r e n t i s i n c r e a s e d ;  max on t h e o t h e r hand, f o r t h e D - s e c t i o n c y l i n d e r , t h e y - b o t h o c c u r a t h i g h e r  U  v a l u e s a s t h e damping is- s t e p p e d up. . For the c i r c u l a r c y l i n d e r , the  Y  vs. U  c u r v e s seem t o share t h e same  r i s i n g s i d e and t h e n s e p a r a t e l y and s u c c e s s i v e l y t a k e t h e r e s p e c t i v e  Y  msix v a l u e s and t u r n t o t h e d e s c e n d i n g s i d e w i t h a p p r o x i m a t e l y t h e same s l o p e s . F o r t h e D - s e c t i o n c y l i n d e r , on t h e o t h e r hand, same d e s c e n d i n g  Y  vs. U  c u r v e s seem t o share the  side.  For the c i r c u l a r c y l i n d e r amplitude v a r i a t i o n w i t h  U  a t low damping  2k l e v e l s ( F i g u r e s 18 and 19) a c l o c k w i s e o s c i l l a t i o n h y s t e r e s i s l o o p r e s u l t s ; t h a t i s , w i t h t h e c y l i n d e r s t i l l o s c i l l a t i n g , as t h e w i n d speed i s i n c r e a s e d beyond t h a t f o r Y , max r e s t a t t h a t w i n d speed. ues o f  Y  Y  drops s u d d e n l y t o t h e v a l u e t h a t was r e a c h e d  I f t h e w i n d speed i s t h e n d e c r e a s e d , t h e ' r e s t '  a r e o b t a i n e d as i n d i c a t e d b y t h e arrows i n t h e f i g u r e s .  from  val-  The phase  a n g l e v a r i a t i o n a t t h e s e low damping l e v e l s a l s o d i s p l a y s s i m i l a r h y s t e r e s i s loop, but counter-clockwise.  There i s no h y s t e r e s i s l o o p f o r e i t h e r  d a t a f o r t h e h i g h e r damping l e v e l s ( F i g u r e s 20, 21 and 22).  <t> o r  Y  For the D-section  c y l i n d e r on t h e o t h e r hand, t h e c l o c k w i s e o s c i l l a t i o n h y s t e r e s i s l o o p e x i s t s a t a l l t h e f i v e damping l e v e l s .  E x c e p t f o r t h e l o w e s t damping l e v e l ,  <t> was  n o t measured w i t h d e c r e a s i n g w i n d speed. The r e l a t i v e p o s i t i o n o f t h e c a p t u r e range i s w o r t h y o f comparison. the c i r c u l a r c y l i n d e r capture f i r s t occurs as c l o s e l y approaches  f  f  f o r the stationary cylinder  i r r e s p e c t i v e o f t h e damping l e v e l s , and  Y  c  f  occurs max  i n t h e middle o f t h e c a p t u r e r a n g e , when  For  F o r t h e D - s e c t i o n , however, c a p t u r e  occurs  i s o n l y from J&fo a t t h e l o w e s t damping l e v e l t o 91$ a t t h e h i g h e s t  damping l e v e l o f  f  , and c  Y  o c c u r s a t t h e end o f t h e range. max  A l t h o u g h b o t h models have t h e same mass, w i t h t h e maximum magnetic damping (3^0 ma.) t h e c i r c u l a r c y l i n d e r g i v e s a maximum d i m e n s i o n l e s s a m p l i t u d e o f o n l y 0.087; w h i l e t h e D - s e c t i o n c y l i n d e r , w i t h k60 ma. damping c u r r e n t , g i v e s maximum d i m e n s i o n l e s s a m p l i t u d e o f 0.311.  I t i s seen t h a t t h e D - s e c t i o n c y l i n d e r  o s c i l l a t i o n i s much h a r d e r t o s u p p r e s s , r e i n f o r c i n g t h e c o n c l u s i o n by P a r k i n son^"*"^ t h a t t h e f i x e d f l o w s e p a r a t i o n l i n e s a t t h e edges o f t h e f l a t f a c e o f  25 t h e D - s e c t i o n c y l i n d e r make g r e a t e r e f f e c t i v e s t r e n g t h o f t h e wake v o r t i c e s . This i s f u r t h e r strengthened by the r e s u l t s i n S e c t i o n 4.4. 5.2  F l u c t u a t i n g P r e s s u r e s on.the S u r f a c e o f a C i r c u l a r C y l i n d e r In g e n e r a l ,  center section. Spanwise,  C  JO  d i s t r i b u t i o n s are f a i r l y symmetrical w i t h respect t o the  The u n s y m m e t r i c a l shape o f F i g u r e 37 i s n o t e x p l a i n e d . C ' d i s t r i b u t i o n s a r e f a i r l y d i s p e r s e d , and t h e y p r e s e n t t h e  same g e n e r a l d i s t r i b u t i o n p a t t e r n a n d range o f v a r i a t i o n . o s c i l l a t i o n a m p l i t u d e ( F i g u r e 35) t h e maximum  However, a t l a r g e  C ' jumps t o more t h a n t h r e e  t i m e s t h e v a l u e f o r v e r y low a m p l i t u d e o r f o r t h e s t a t i o n a r y c y l i n d e r c a s e , and t h e range o f s p r e a d i n g a l o n g t h e span i s a l s o g r e a t l y a m p l i f i e d . The a m p l i t u d e m o d u l a t i o n o f t h e s u r f a c e p r e s s u r e s f o r b o t h a s t a t i o n a r y and an o s c i l l a t i n g c y l i n d e r and t h e beat phenomena have been observed i n an  (8) e a r l i e r ' i n v e s t i g a t i o n by Ferguson  .  I n h i s experiment on t h e w i n d - i n d u c e d  (9) v i b r a t i o n s o f c i r c u l a r c y l i n d e r , Koopmamr  also noticed short bursts of p e r i -  o d i c m o t i o n o f t h e c y l i n d e r i n t h e p l a n e normal t o t h e d i r e c t i o n o f t h e w i n d a t a w i n d speed i n i t i a t i n g a repeated e f f o r t of  f  the o s c i l l a t i o n . t o c a t c h up w i t h  The beat phenomena c a n be r e g a r d e d as f ^ . When a t a g r e a t e r w i n d  i t does s u c c e e d i n t h e e f f o r t , , t h e beat phenomena d i s a p p e a r .  speed  The g o v e r n i n g  mechanism p r o b a b l y i n v o l v e s t h e a l i g n m e n t o f v o r t e x - l i n e s o r t h e spanwise  cor-  r e l a t i o n s i n c e , as n o t e d b e f o r e , a t l a r g e c i r c u l a r c y l i n d e r o s c i l l a t i o n a m p l i tude, the vortex l i n e s are a l i g n e d p a r a l l e l t o the c y l i n d e r instead of i n c l i n e d w i t h i t as when t h e c y l i n d e r i s s t a t i o n a r y o r o s c i l l a t i n g a t v e r y low a m p l i t u d e ( F i g u r e s 4 l , 43, 44 and 45).  •  26  From the phase a n g l e d i s t r i b u t i o n a l o n g the c i r c u l a r c y l i n d e r span, the i n c l i n a t i o n w i t h r e s p e c t t o the t h e model may presentation  c y l i n d e r a x i s of the f i r s t v o r t e x  be c a l c u l a t e d s i n c e are s i m i l a r .  line  i n t h i s case a t i m e h i s t o r y and 4l,  As shown i n F i g u r e s  42,  k-3, 44  leaving  spatial  and 45,  re-  the  av-  erage i n c l i n a t i o n f o r the s t a t i o n a r y c y l i n d e r and the o s c i l l a t i n g c y l i n d e r w i t h v e r y low d i s p l a c e m e n t a m p l i t u d e i s f r o m 7° p r o x i m a t e l y 17°  and  25°  t o 9° •  T h i s i s compared w i t h  ap-  r e s p e c t i v e l y f o r the f o r c e d and w i n d - i n d u c e d v i b r a t i o n s  o f c i r c u l a r c y l i n d e r s a t low R e y n o l d s numbers i n the i n v e s t i g a t i o n s by Koopmann^' ^.  On t h e o t h e r hand, G e r r a r d ^ ^ r e p o r t e d  1 0  l i n e s a l m o s t s t r a i g h t and p a r a l l e l t o the  the presence o f  vortex  s t a t i o n a r y c y l i n d e r measured t h r e e  4 d i a m e t e r s down s t r e a m o f the c y l i n d e r a x i s a t the v o r t e x  l i n e appear t o t i l t backwards and  + 15° .• A t  Re  = 85  he r e p o r t e d the  ent  but  showed t h a t  f o r w a r d s between the l i m i t s  i n c l i n a t i o n t o be 14°  ameters down s t r e a m o f the c y l i n d e r a x i s . f i r s t vortex  = 2 x 10  Re  However, the  of  measured a t 17.2  i n c l i n a t i o n of  the  l i n e l e a v i n g the model, as r e p r e s e n t e d by the r e s u l t of the l e s s t h a n 14°  i n v e s t i g a t i o n , i s e x p e c t e d t o be c o n s i d e r a b l y  t o be n e a r e r t o the p r e s e n t r e s u l t . i n g smoke v i s u a l i z a t i o n l i n e n e a r e s t t o the  technique, at  As  and  di-  pres-  + 15°  and  shown i n Koopmann's^' '^ photograph u s 1  Re  = 200  :  the i n c l i n a t i o n o f t h e  c y l i n d e r i s a p p r o x i m a t e l y 17-5°  w h i l e about IT  down s t r e a m o f the c y l i n d e r a x i s the i n c l i n a t i o n i n c r e a s e s  vortex  diameters  to 65 . 0  A t l a r g e o s c i l l a t i n g a m p l i t u d e , however, the average i n c l i n a t i o n i s n e a r (3)  ly  0°  as shown i n F i g u r e  45.  S i m i l a r r e s u l t s were r e p o r t e d by G e r r a r d  (9)  Koopmann  .  I t i s i n t e r e s t i n g t o note t h a t l a r g e o s c i l l a t i o n caused the  and  27 alignment  o f v o r t e x l i n e s p a r a l l e l t o t h e c y l i n d e r a x i s and t h u s enhanced  d i m e n s i o n a l i t y o f t h e e a r l y wake f l o w . as r e p o r t e d by Toebes  (15)  and Koopmann  two-  This i s also true f o r forced v i b r a t i o n  (10)  I n t h e above d i s c u s s i o n t h e p e c u l i a r end p o r t i o n s o f t h e v o r t e x l i n e s were not c o n s i d e r e d .  C o n s i d e r i n g t h i s p a r t i c u l a r model, i t i s not s u r p r i s i n g t h a t  low a s p e c t r a t i o e f f e c t s were p r e s e n t a t the ends. k-3 and kk  k2,  As shown i n F i g u r e s hi,  t h e d a t a p o i n t s n e a r b o t h ends i m p l i e d c u r v e d v o r t e x l i n e s .  Figure  U6 shows t h e e f f e c t o f t h e gaps between model ends and t u n n e l c e i l i n g and  floor  on t h e phase a n g l e change.- I t i s seen t h a t t h e b l o c k i n g o f end gap causes the phase a n g l e o f t h e c o r r e s p o n d i n g I n F i g u r e kj  end p o r t i o n o f t h e v o r t e x l i n e t o d e l a y .  i t seems t h a t a moderate change i n s l o t s i z e does not show  a d i s t i n c t i v e i n f l u e n c e on t h e phase a n g l e .  I n g e n e r a l , however, presence o f  t u n n e l - s l o t s , s i z e o f end gaps, and the t u n n e l w a l l boundary l a y e r r e t a r d e d f l o w p l a y r o l e s i n s h a p i n g t h e end p o r t i o n s o f t h e v o r t e x l i n e s f o r the  oscil-  l a t i n g c y l i n d e r i n t h i s experiment. A t e a c h s e c t i o n o f t h e o s c i l l a t i n g c i r c u l a r c y l i n d e r , a phase s h i f t  be-  tween t h e s i g n a l s from t h e n e i g h b o r i n g p r e s s u r e t a p s on t h e same s i d e e x i s t e d . The maximum phase s h i f t w i t h r e s p e c t t o t h e s i g n a l s f r o m the t a p a t 90°  a t each  s e c t i o n i s l a r g e r a t t h e s e c t i o n s near t h e ends w i t h t h e average b e i n g approxi m a t e l y 4-5° .  The  d a t a i s not i n c l u d e d .  S i m i l a r phase s h i f t s were a l s o r e -  (12) p o r t e d by W i l a n d  on h i s e l l i p t i c c y l i n d e r s .  As a r e s u l t o f measuring s u r f a c e f l u c t u a t i n g p r e s s u r e a l o n g and a r o u n d the circular cylinder,  C , , = 0.1+13 L(mpv)  and  0.kk5  at  V = 11.9  fps  and 13.2  fps  28 4 respectively cylinder. 0.42  = 1.8  (Re  x 10  4 and  Without considering  at  Re  = 1.5  x 10  4  2 x 10  respectively)  spanwise e f f e c t Ferguson .  w h i l e McGregor  (2)' v  found  f o r the found  C , = 0.58 L( mpv) N  stationary C , = L(mpv) N  at  Re  =  4 5 x 10  .  I t i s a p p a r e n t f r o m the p r e s e n t i n v e s t i g a t i o n t h a t the g i v e , a lower value of o v e r a l l  spanwise e f f e c t s  C  because o f the drop i n s e c t i o n a l C near L £ b o t h ends as shown i n F i g u r e s 36 t o 40. At l a r g e o s c i l l a t i n g amplitude, C , . = 1 . 9 1 a t V = 13'9 fps. ComL(, mpv; p a r i s o n w i t h the s t a t i o n a r y v a l u e o f C , v = 0.44-5 a t V = 13-2 fps indiL( mpv) c a t e s a h i g h degree o f spanwise c o r r e l a t i o n , as f u r t h e r v e r i f i e d by the  subse-  quent c o r r e l a t i o n measurements. 5-3  Spanwise C o r r e l a t i o n s W i r e Anemometers Due  t o the  f o r C i r c u l a r and D - s e c t i o n C y l i n d e r s  l i m i t e d a s p e c t r a t i o , end  Using  Hot  gaps, presence o f t u n n e l s l o t s  and  the boundary l a y e r r e t a r d e d f l o w , the c o r r e l a t i o n c u r v e s o b t a i n e d do not  ap-  p r o a c h z e r o as t h e imum a v a i l a b l e . ations  due  s e p a r a t i o n between the two  S i n c e the  hot w i r e s i n c r e a s e s t o the max-  c o r r e l a t i o n f u n c t i o n must go t o z e r o a t l a r g e  t o the random n a t u r e o f the two  s i g n a l s , the  been e x t e n d e d u n t i l t h e y meet the h o r i z o n t a l a x i s .  separ-  c o r r e l a t i o n c u r v e s have  They were extended by  ne-  g l e c t i n g the d a t a p o i n t s n e a r the model ends s i n c e t h o s e d a t a p o i n t s were under p r o b a b l e e f f e c t s o f end The  c l e a r a n c e and w a l l boundary l a y e r .  c o r r e l a t i o n l e n g t h i s d e f i n e d as the e q u i v a l e n t l e n g t h over w h i c h v e l -  ocity fluctuations  i n the wake may  be  d e s c r i b e d as p e r f e c t l y c o r r e l a t e d .  The  29  correlation ation  l e n g t h i s then o b t a i n e d by i n t e g r a t i n g the area under the c o r r e l -  curve. I t i s seen t h a t  lation  f o r both c i r c u l a r and D - s e c t i o n c y l i n d e r s , the  l e n g t h s f o r the o s c i l l a t i n g models a t resonant wind speeds  h i g h e r than those a t o t h e r wind speeds For  s t a t i o n a r y models, A  the c i r c u l a r c y l i n d e r  A  corre-  are much  or those f o r s t a t i o n a r y models.  = 5.85h f o r the D - s e c t i o n c y l i n d e r w h i l e f o r  = 4.56h o n l y .  For the c i r c u l a r c y l i n d e r  the v a l u e  i s comparable i n magnitude to those o b t a i n e d by o t h e r i n v e s t i g a t o r s . Measurements o f two-point c o r r e l a t i o n by P r e n d e r g a s t a n d  el Baroudi^^  resulted  (19") in a  A o f about 3.5h Interesting  and  those by V i c k e r y  are the h i g h v a l u e s o f A  a t t h e i r r e s o n a n t wind speeds.  ,  5.6h.  f o r both c y l i n d e r s  For. the c i r c u l a r c y l i n d e r  oscillating  this result i s i n  c l o s e agreement w i t h the r e s u l t from the 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 calculations discussed previously.  30 VI.  SUMMARY OF. RESULTS  Based on t h e e x p e r i m e n t a l r e s u l t s t h e f o l l o w i n g may he c o n c l u d e d : (1)  There a r e l a r g e r o s c i l l a t i n g a m p l i t u d e s and much l a r g e r wake v e l o c i t y  c o r r e l a t i o n l e n g t h s f o r a D - s e c t i o n c y l i n d e r o s c i l l a t i n g a t near maximum amp l i t u d e than f o r a c i r c u l a r c y l i n d e r . (2)  F o r "both c i r c u l a r a n d D - s e c t i o n o s c i l l a t i n g c y l i n d e r s , t h e v a r i a t i o n o f  t h e phase a n g l e  <t> w i t h  U  i s n e a r l y t h e same i r r e s p e c t i v e o f t h e magnetic  damping l e v e l s . (3)  I r r e s p e c t i v e o f t h e damping l e v e l s . , f o r t h e c i r c u l a r c y l i n d e r " c a p t u r e "  f i r s t occurs as Y  max  f  f o r t h e s t a t i o n a r y c y l i n d e r c l o s e l y approaches  o c c u r s i n t h e m i d d l e o f t h e c a p t u r e range.  however, " c a p t u r e " o c c u r s when  f v  f ^ , and  For the D-section c y l i n d e r ,  i s o n l y f r o m 78$ t o 91$ o f  f  and  Y  c  max  o c c u r s a t t h e end o f t h e range. (4)  The amount o f t h e gap between t h e model end and t h e t u n n e l c e i l i n g o r  f l o o r d e f i n i t e l y a f f e c t s t h e r e l a t i v e p o s i t i o n s o f t h e end p o r t i o n s  of the  vortex l i n e s . (5)  A t each s e c t i o n o f t h e o s c i l l a t i n g c i r c u l a r c y l i n d e r , a phase s h i f t be-  tween t h e s i g n a l s from t h e n e i g h b o r i n g p r e s s u r e t a p s on t h e same s i d e e x i s t s . (6)  Wake v e l o c i t y c o r r e l a t i o n l e n g t h i s h i g h e r f o r a D - s e c t i o n c y l i n d e r  for a circular cylinder.  than  Also, f o r a given c y l i n d e r , the c o r r e l a t i o n length  i s h i g h e r f o r l a r g e a m p l i t u d e o s c i l l a t i o n s t h a n f o r low a m p l i t u d e o s c i l l a t i o n s o r when t h e c y l i n d e r i s s t a t i o n a r y . (7)  I n g e n e r a l t h e v o r t e x wake i s h i g h l y t h r e e - d i m e n s i o n a l b o t h f o r t h e s t a -  31 t i o n a r y and the o s c i l l a t i n g c i r c u l a r c y l i n d e r .  I f the e f f e c t s due t o boundary  l a y e r f l o w a t t u n n e l w a l l s and the s l o t s i n the t u n n e l c e i l i n g and f l o o r  are  n e g l e c t e d , the v o r t e x l i n e s a r e n e a r l y s t r a i g h t but i n c l i n e d a t about 7° t o w i t h r e s p e c t t o the c y l i n d e r a x i s f o r b o t h the s t a t i o n a r y c i r c u l a r and the o s c i l l a t i n g c i r c u l a r c y l i n d e r w i t h low a m p l i t u d e .  cylinder  F o r the o s c i l l a t i n g  c i r c u l a r c y l i n d e r w i t h n e a r l y the maximum o s c i l l a t i n g a m p l i t u d e , the l i n e s form i n n e a r l y s t r a i g h t l i n e s p a r a l l e l t o the  9°  cylinder.  vortex  32 • BIBLIOGRAPHY 1.  K e e f e , R. T.  "An I n v e s t i g a t i o n o f t h e F l u c t u a t i n g F o r c e s A c t i n g on 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 i n a S u b s o n i c Stream and o f t h e A s s o c i a t e d Sound F i e l d " , U.T.I.A. R e p o r t 76, September 1961.  2.  McGregor, D. M.  "An E x p e r i m e n t a l I n v e s t i g a t i o n o f t h e O s c i l l a t i n g P r e s s u r e s 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"., I n s t i t u t e of Aerophysics, U n i v e r s i t y of Toronto, U.T.I.A. T e c h n i c a l Note No. 14, June 1957-  3.  Gerrard,  J . H.  "The T h r e e - d i m e n s i o n a l S t r u c t u r e o f t h e Wake o f a C i r c u l a r C y l i n d e r " , J . F l u i d Mech., V o l . 25, 1966,  pp. 4.  Gerrard,  J . H.  143-164.  "An E x p e r i m e n t a l I n v e s t i g a t i o n o f t h e O s c i l l a t i n g L i f t and Drag o f a C i r c u l a r C y l i n d e r Shedding T u r b u l e n t V o r t i c e s " , J.F.M., V o l . 11, 1 9 6 l , pp.  244-256. 5.  B i s h o p , R. E. Hassan, A. T.  "The L i f t and Drag F o r c e s on an O s c i l l a t i n g C y l i n d e r " , Proceedings of the Royal S o c i e t y of London, S e r i e s A, V o l . 277, 1964, pp. 51-75-  6.  H e i n e , W.  "On t h e E x p e r i m e n t a l I n v e s t i g a t i o n o f V o r t e x E x c i t e d P r e s s u r e F l u c t u a t i o n s " , M.A. S c . T h e s i s , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1964.  7«  Den H a r t o g , J . P.  "Recent T e c h n i c a l M a n i f e s t a t i o n s o f Von Kantian's V o r t e x Wake", P r o c e e d i n g s o f t h e N a t i o n a l Academy o f S c i e n c e s o f USA, V o l . 40, No. 3, 1954.  8.  F e r g u s o n , K.  "The Measurement o f Wake and S u r f a c e E f f e c t s i n the S u b c r i t i c a l F l o w P a s t a C i r c u l a r C y l i n d e r at R e s t and i n V o r t e x - E x c i t e d O s c i l l a t i o n " , M.A. Sc. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia , September ;  1965. 9-  Koopmahn, G. H.  "On t h e Wind-Induced V i b r a t i o n s o f C i r c u l a r C y l i n d e r s " , M.A. S c . T h e s i s , C a t h o l i c U n i v e r s i t y , March 1967.  10.  Koopmann, G. H.  "The V o r t e x Wakes o f V i b r a t i n g C y l i n d e r s at Low R e y n o l d s Numbers", J . F l u i d Mech., V o l . 28, 1967,  pp. 501-512.  33  Smith,  J.D.  "An E x p e r i m e n t a l Study o f the A e r o e l a s t i c I n s t a b i l i t y o f R e c t a n g u l a r C y l i n d e r s " , M.A. Sc. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, August 1962.  Wiland, E.  "Unsteady Aerodynamics o f 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 s i n S u b c r i t i c a l Flow", M.A. Sc. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, A p r i l 1968.  Cheng, S.  "An E x p e r i m e n t a l I n v e s t i g a t i o n o f the A u t o r o t a t i o n o f a F l a t P l a t e " , M.A. Sc. T h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, 1966.  Scruton,  C.  "On the Wind-Excited O s c i l l a t i o n s o f Stacks, Towers and Masts", P r o c . I n t . Conf. on Wind E f f e c t s on B u i l d i n g s and S t r u c t u r e s , N. P. L., London, 1965. H.  Toebes, G.  " F l u i d e l a s t i c F e a t u r e s o f Flow Around C y l i n d e r s " , Proc. I n t . Res. Sem. Wind E f f e c t s on B u i l d i n g s and S t r u c t u r e s , v o l . 2 , Ottawa, September, 1967.  Parkinson, G.V. Ferguson, N. Feng, C.C.  "Mechanisms o f V o r t e x - E x c i t e d O s c i l l a t i o n o f B l u f f C y l i n d e r s " , Proc. Symp. Wind E f f e c t s on B u i l d i n g s and S t r u c t u r e s , v o l . 2 , Loughborough, April,1968.  Prendergast,  V.  "Measurements o f Two-Point C o r r e l a t i o n s o f the Surface P r e s s u r e on a C i r c u l a r C y l i n d e r " , U.T.I. Tech. Note 23, J u l y 1958.  el  M.Y.  "Measurement o f Two-Point C o r r e l a t i o n s of V e l o c i t y Near a C i r c u l a r C y l i n d e r Shedding a Karman V o r t e x S t r e e t " , U.T.I.A. Tech. Note 31, January 1960.  Baroudi,  Vickery,  B.J.  Pankhurst, R.C. Holder, D.W.  " F l u c t u a t i n g L i f t and Drag on a Long C y l i n d e r o f Square C r o s s - S e c t i o n i n a Smooth and i n a T u r b u l e n t Stream", NPL Aero Rep. No. 1146, A p r i l 1965. "Wind Tunnel Technique", Pitman,  1948.  34 APPENDIX  A  TUNNEL CORRECTIONS TO WIND SPEED 20.  Wind speeds were c o r r e c t e d a c c o r d i n g t o R e f e r e n c e  I n t h e absence o f  b e t t e r d a t a , c o r r e c t i o n s t o w i n d speed f o r t h e o s c i l l a t i n g c y l i n d e r were t h e same f o r t h e s t a t i o n a r y c y l i n d e r . Solid  Blockage:  1 + CX, (|)  V = V  uncorr.  where  C = 0.822 X = 1.0  for a closed tunnel (model shape f a c t o r )  h = model w i d t h H = tunnel width Wake B l o c k a g e :  i  V = V  uncorr.  where  C  d  +  0.25 ( ) c 5  d  = Measured d r a g c o e f f i c i e n t (assumed  1.25)  Therefore  V =V  3 j 1 + 0.82 ( ^ )  uncorr. L  + 0.25 (1.25)  3°  = 1.032  3 3°  V  uncorr.  35 B  APPENDIX  CORRELATOR PHASE MEASUREMENT The s i g n a l s f r o m e i t h e r t h e B a r o c e l p r e s s u r e t r a n s d u c e r o r t h e h o t w i r e anemometer d u r i n g t h e e x p e r i m e n t s have a s t r o n g fundamental f r e q u e n c y b u t a r e random i n a m p l i t u d e .  F o r a n a l y t i c a l p u r p o s e s , t h e mean a m p l i t u d e w i l l r e p l a c e  t h e random one. The c r o s s - c o r r e l a t i o n f u n c t i o n ,  R  ( T ) , o f two v a r i a b l e s i s d e f i n e d b y  (1)  T , i s independent o f  where t h e time d e l a y , If  f^(t)  fg(t)  and  a r e i d e n t i c a l s i g n a l s , we o b t a i n t h e a u t o - c o r r e l a -  t i o n f u n c t i o n o f one v a r i a b l e ,  **-]_-]_( ) T  T R-MC-O  =  11  ^  t .  ['  £  T-*°° T  J  0  f ( t ) f . ( t - ) at n  1  1  T  (2)  S i n c e , f o r t h e purpose o f t h i s i n v e s t i g a t i o n , o n l y t h e fundamental  signal  f r e q u e n c y i s o f i n t e r e s t a n d s i n c e t h e mean a m p l i t u d e s r e p l a c e t h e random ones, we assume A  f  where  2  =  A  2  (3)  s i n ait  n  S  ±  n  ^  +  * "  < x i N A T  )  OD = fundamental a n g u l a r f r e q u e n c y = mean s i g n a l a m p l i t u d e s  * = phase a n g l e between t h e two s i g n a l s N = t h e N t h increment where t h e . t o p p o i n t o f : t h e c o s i n e f u n c t i o n i s reached  •  A T  I5o  =  T  = t h e amount o f phase a n g l e d e l a y e d by t h e c o r r e l a t o r .  OSNAT  As a r e s u l t o f t h e a p p r o x i m a t e d p e r i o d i c i t y , ( l ) and . l /  (2)  become  T  -T-i./ /2  1  x  T  R ( T )  = ±-  U  where  2  V  2  J  f (-t) f ( t - ) d t x  1  (6)  T  - i s t h e p e r i o d o f t h e f u n c t i o n i n seconds,.and 2TT  T  =  — ^  1  D e f i n e t h e n o r m a l i z e d c r o s s - c o r r e l a t i o n f u n c t i o n as R 1  a  i2  (  r  =  )  2  ( T )  V^io)  R (o) 2  W i t h t h e h e l p o f (3) and ( 4 ) , t h e n T  1 R  ii  ( 0 )  =  T" J 1  Similarly, A  2  = T  r  l / '2 f  -T "72 1 ;  l / r 12 ? T  2  i  ( t ) dt  1 =  T~  1  J  A  i  s i n  " l/ /2 T  i  A  2 dt  = T  2  i  37  i rV R  1  ( T )  2  =  J  —  A  and  A  Q;  1  2  (T)  I  2  S  I  °^  N  S  I  N  (  A  I  F  C  +  *  -  CJCMAT)  dt  l 2 A  = co's(0 =- O—I N—A T—)  Without delaying time,  A  cos(<t> - aiNAx)  (7)  T,  a ( 0 ) = cos 0 , l 2  showing t h e c o r r e l a t i o n i s t h e g r e a t e s t i f 0 = 0 . On t h e o t h e r hand, b y u s i n g t h e d e l a y i n g mechanism i n t h e c o r r e l a t o r t h e Nth i n c r e m e n t , where t h e t o p p o i n t o f t h e c o s i n e f u n c t i o n i s r e a c h e d , may he counted.  The phase a n g l e between t h e two s i g n a l s i s , a c c o r d i n g t o  0  =  OJNAT  T  But  since  CD = 2TT f v a n d A T = z~z^r  0 = 3-6  NT  fv  ,  (7)  Figure 1.  Wind tunnel outline  F i g u r e 2.  Wind t u n n e l t e s t s e c t i o n w i t h model (downstream d i r e c t i o n )  CO  Figure 3>  Models  Tap  No.  -12.0 -10.5 -9-0 -7-5 -6.0 -4.5 -3-0 -1-5 0.0 +1.5 +3.0  1 2 3 4 5 6 7 8 9 10 11 12 13 i4 15 16 17  Figure  z(lnch)  +6.0 +7-5 +9.0 +10.5 +12.0  4.  z/h  -4.0 -3-5 -3-0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 +0.5 +1.0 +1.5 +2.0 +2.5 +3-0 +3-5 +4.0  Spanwise p r e s s u r e t a p p o s i t i o n s f o r the c i r c u l a r  cylinder  k2  F i g u r e 5»  Arrangement o f model mounting system  hh  Barocel  Vibration generator  Polyethylene tube Jt=5', di = 0.066'  R.M.S. Voltmeter  Oscilloscope Figure  7.  Block diagram of the c a l i b r a t i o n apparatus  F i g u r e 8.  C a l i b r a t i o n curves f o r B a r o c e l pressure  transducer 4=-  o  Flow velocity, Figure 9 .  m/sec  C a l i b r a t i o n curve f o r 55AQLDISA Anemometers w i t h o u t a l i n e a r i z e r  -p-  12 —©— —-A----  10  Upper probe, R at 77 °F I 3.56 ohm, R ."6.4C1 ohm Lowei' probe, R at 80°F I 153 ohm, R I6.33i ohm 0  0  co  o co  8  O) 03  •<—  o > 6  >  o  TJ CD  O)  m 4  Eo I 5.4 volts m I 2.03  St*  0  10  20 Wind speed, fps  30  40  F i g u r e 1 0 . C a l i b r a t i o n c u r v e s f o r 5 5 A 0 1 DISA Anemometers u s i n g  51D linearizers 4=-  F i g u r e 11.  I n s t r u m e n t s and w i n d t u n n e l t e s t  section CO  50  Cylinder top view  RMS voltmeta  l - C damping circuit  F i g u r e 13.  Oscilloscope  B l o c k diagram o f t h e f l u c t u a t i n g p r e s s u r e measuring s e t - u p  F i g u r e Ik.  C o o r d i n a t e axes f o r wake probe p o s i t i o n s  Model  Hot wire probes  Linearizer  DISA anemometer  Krohn-Hite filter  F i g u r e 15.  DISA anemometer  Linearizer  Krohn-Hite filter  B l o c k diagram o f t h e spanwise c o r r e l a t i o n measuring s e t - u p  function  F i g u r e 16.  Phase s h i f t and d i s p l a c e m e n t phenomena f o r t h e c i r c u l a r c y l i n d e a t v a r i o u s damping l e v e l s  8  .8  "1 i  u-*0-  o  u Ymax  \ %  \  27TU  \o  \ \ \ \ \ • \ \ \  rmax '£  \ \  *  Figure 17(a).  .2  'r^  S t a b i l i t y diagram f o r the c i r c u l a r  cylinder  8  u—D-  o  U  Ymax  8  27TU  rmax  27rfi/n F i g u r e 17(b).  10  S t a b i l i t y diagram f o r D - s e c t i o n c y l i n d e r  F i g u r e 19•  O s c i l l a t i o n phenomena f o r c i r c u l a r c y l i n d e r ,  I , = 100  ma  F i g u r e 21.  O s c i l l a t i o n phenomena f o r c i r c u l a r w i t h a damping c u r r e n t o f 250 ma.  cylinder  Fig. 22 O s c i l l a t i o n Phenomena for Circular Cylinder,  1^ = 3^0  ma.  6o  firwmm  f .11  Lij  ••  m  (a)  V  = 14.4 fps  (b)  • • • • • 1  D u r i n g t h e change  E i i i i i i i i i • i  (c)  V -  15-2  (&)  fps  T r a n s i t i o n from to  V = 13-9 i\P V =  13.4  9  90°  Top t r a c e , p r e s s u r e s i g n a l from No. 9 t a p a t Bottom t r a c e , Time base, 2  F i g u r e 23.  Oscilloscope  aisplacement sec/div.  traces  of f l u c t u a t i n g surface  aisplacement s i g n a l s a u r i n g  p r e s s u r e and  the abrupt changes.  6  fps  F i g u r e 2k.  Phase s h i f t and d i s p l a c e m e n t phenomena f o r t h e D - s e c t i o n c y l i n d e r a t V a r i o u s damping l e v e l s  F i g . 25  O s c i l l a t i o n Phenomena f o r D - s e c t i o n C y l i n d e r ,  I, = 0  ma  Figure  26.  O s c i l l a t i o n phenomena f o r D - s e c t i o n c y l i n d e r ,  I  = 80 ma  F i g u r e 2J.  O s c i l l a t i o n phenomena f o r D - s e c t i o n  cylinder,  I  = 1^5  ma  65  F i g u r e 28.  O s c i l l a t i o n phenomena f o r D - s e c t i o n c y l i n d e r ,  I  = 222  ma  66  ill.  nun JftdL i  IliilHIil I n II  PH  V = 1 1 . 3 fps  Top t r a c e , s u r f a c e p r e s s u r e a t  f = 9 . 0 4 cps c  Bottom t r a c e , d i s p l a c e m e n t  f = 8 . 7 3 cps  Time b a s e , 1 s e c / d i v .  F i g u r e 3 0 . Beat phenomena  0 =9 0 °  Legend  Tap  No.  •  1  to  3  cr a.  5  X  o 0  7  .#9^  9  to  11  £>  13  Q  15  O  17  V  4X  I  CD  J-*l  X  •  CD  ft * cr to  o  D  g  to  D  o Re :  30 F i g u r e 31.  60"  18100  ir-  120  c' d i s t r i b u t i o n on t h e s u r f a c e o f a s t a t i o n a r y c i r c u l a r  150 cylinder,  V = 11.8  180 fps  Legend  o p D  cr  a, x t» P Q  cr o  Tap  No. 1 2 3 5 7  cr  9  Q  4a-  11 13  cr o  15 16 17  x>  o.  O,  x b p  ca i  a _CE_  P  T o  ti cr  D  §  cr  P  Re : 19600  30  Figure 32.  60  er 90  120"  C ' d i s t r i b u t i o n on t h e s u r f a c e o f 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 ,  V = 13«2  fps  Legend  •8-  Tap No. 1 2  • p  t)  3 5 7  d  a  X  9  D CX  11 13 15  o  16 17  P  cr  b x  I  X  I  f cr  P  X  a  -X .  ar ti  P-  B Q  t»  .P  tl  a  o  O  I  4-  a  o •  ft ft  Re I 17000  9 0«r  30  F i g u r e 33.  C ' distribution  60  0°  90  120  on the s u r f a c e o f an o s c i l l a t i n g c i r c u l a r c y l i n d e r ,  V = 11.3 f p s  0.3  Legend o  p  tl cr a X  0.2  o c Q cr o  Tap No. l 2 3 5 7 9  +*9  11 13 15  3-*1  16 17  F i g u r e 3^.  .C ' d i s t r i b u t i o n on the s u r f a c e o f an o s c i l l a t i n g c i r c u l a r c y l i n d e r ,  V = 17.6  fps  F i g u r e 35.  c'  d i s t r i b u t i o n on t h e s u r f a c e o f an o s c i l l a t i n g c i r c u l a r c y l i n d e r ,  V = 13-6  fps  78  79  Figure  k2.  Spanwise phase s h i f t o f f l u c t u a t i n g s e c t i o n a l l i f t on 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 , V = 13.2 f p s  80  F i g u r e 43.  Spanwise phase s h i f t o f f l u c t u a t i n g s e c t i o n a l on an o s c i l l a t i n g c i r c u l a r c y l i n d e r , V =; 11.3  lift ip s  81  F i g u r e kk.  Spanwise phase s h i f t o f f l u c t u a t i n g s e c t i o n a l l i f t on an o s c i l l a t i n g c i r c u l a r c y l i n d e r , V = 17•5 f p s  82  Figure  k-5.  Spanwise phase s h i f t o f f l u c t u a t i n g s e c t i o n a l l i f t on an o s c i l l a t i n g c i r c u l a r c y l i n d e r , V = 1 3 • 9 f p s  Figure k6.  E f f e c t o f end c l e a r a n c e s on spanwise phase s h i f t o f f l u c t u a t i n g s e c t i o n a l l i f t on a s t a t i o n a r y c i r c u l a r cylinder, V = 13•9 f p s  84  A  *• I  6-  17900 -6  <  O  O•  i  r  BO—A—o  B—U  >  O  A-  A  o  Same s l o t s s i z e s as "before  •  S l o t s l e n g t h e n e d and widened  A  S l o t s l e n g t h e n e d and widened T r a v e r s i n g gear moved downstream  o—o  -40  -A  Figure  &  20  -20  kf.  •  D  40  60  80  100  E f f e c t o f f l o o r and c e i l i n g s l o t s on spanwise  phase shift  of f l u c t u a t i n g s e c t i o n a l l i f t  circular  cylinder,  V = 11.8 f p s  on a s t a t i o n a r y  V : 11.3 fps, Y = 0.025, V : 17.0 fps. Y = 0.270,  k  Z 5.6  i  1  Re : 16900 Re Z 26200  I  —,  X:4.22h  (  ^^^^  u -—  *  :  :  •  r  A  1  D  1  '  o "  1  '>  1  I D diameters  Figure 48.  Two-point fluctuating wake velocity correlations for an o s c i l l a t i n g circular cylinder  8  F i g u r e 49.  Two-point f l u c t u a t i n g wake v e l o c i t y c o r r e l a t i o n s f o r a s t a t i o n a r y and an o s c i l l a t i n g c i r c u l a r  cylinder,  V=13-9fps  - e — Oscillating, — Stationary  Y : 0.58, Re 121200  D diameters  F i g u r e 50.  Two-point f l u c t u a t i n g wake v e l o c i t y c o r r e l a t i o n s f o r a s t a t i o n a r y and an o s c i l l a t i n g c y l i n d e r , V = lk.1 f p s  D-section  oo -3  

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