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Unsteady aerodynamics of stationary elliptic cylinders in subcritical flow Wiland, Erling 1968

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UNSTEADY AERODYNAMICS OF STATIONARY ELLIPTIC CYLINDERS IN SUBCRITICALFLOW (  by E. WILAND B.Sc. (Hons.), The University of Strathclyde, 1965  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.A.Sc. in the Department of Mechanical Engineering  We accept this thesis as conforming to requi red standard  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1968  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t freely available for reference and study.  I further agree that permission for extensive copying  of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives.  It is understood.that  copying or publication of this thesis for financial gain shall not be allowed without my written permission.  E. Wiland  Department of Mechanical Engineering The University of B r i t i s h Columbia Vancouver 8, B.C.  i  ABSTRACT  The aerodynamics of a set of two-dimensional e l l i p t i c cylinders with e c c e n t r i c i t y of 0 . 8 and 0.6 i s studied experimentally during the organised wake c o n d i t i o n .  The dynamic c a l i b r a t i o n of the transducer  used f o r measurement of f l u c t u a t i n g pressures i s described in d e t a i l . The data on Strouhal number, unsteady pressures and wake geometry are presented as a function of angle of attack during s t a t i c condition of the models.  The e f f e c t of Reynolds number on the f l u c t u a t i n g pressure  is also examined.  The results i n d i c a t e dependence of the unsteady  forces on Reynolds number at zero angle of attack.  Basing the  Strouhal number on projected width appears to reduce i t s dependence on the angle of attack of the models.  The existence of a large phase  angle between the f l u c t u a t i n g pressures i s of i n t e r e s t .  The wake  geometry study indicates a gradual reduction in the r a t i o o f t h e :  l a t e r a l to the l o n g i t u d i n a l spacing with increase in angle of attack.  n  TABLE OF CONTENTS  Section  Page  1  Introduction  2  Purpose and Scope of the Investigation  3  Models and Supporting S y s t e m . . . .  4  Instrumentation and C a l i b r a t i o n  5  Test Procedures  6  Test Results and Discussion  7  Concluding Remarks  Bibliography Appendix I Appendix II  ..........  ........ .•  ••••  1  ....  5  ..........  6 12  ......  32 38 .  .-.....  62 65 68 70  iii  LIST OF TABLES  *  Table  Page  1  Model data  ..........  6  2  Effect of phase shift on fluctuating l i f t coefficient...  54  3  Spacing of vortices in-fully developed wake, Nr = 70,000  58  /  iv  LIST OF FIGURES  Figure  Page,  1  Constructional d e t a i l s of models  -..  2  Numbering of pressure taps  3  Wind tunnel o u t l i n e  4  Wind tunnel test section with model  5  Schematic of Barocel pressure transducer  6  Block diagram of pressure generator and set-up f o r  9 ....  comparison of dynamical r e s p o n s e . . . . 7  10 11 • 13  ..  • 15  Response of c a l i b r a t i o n system to d i f f e r e n t input wave forms  8  8  ••  .' • • 18  Pressure attenuation as a function of tube length and frequency (tube diameter = 0.066 i n . ) . . . . . - . .  9  19  C a l i b r a t i o n plots f o r Barocel pressure t r a n s d u c e r . . . . . . . . . 20  10  Block diagram of the c a l i b r a t i o n apparatus  11  C a l i b r a t i o n apparatus  12  C a l i b r a t i o n plots f o r Barocel pressure transducer with  ...  damping b o t t l e 13  ......  22  ..  23  ..•  24  Comparison between c a l i b r a t i o n curves f o r Barocel pressure transducer with and without damping b o t t l e  ..  14  Geometry of the d i s c probe  15  Typical f l u c t u a t i n g pressure s i g n a l s  16  R-C damping c i r c u i t  17  Block diagram of the f l u c t u a t i n g pressure measuring set-up  ...  ..-  ......  25 27  ...  28 ........  •  31  33  V  Figure  Page  18  Block diagram of the phase measuring system  34  19  Instrumentation set-up during a t y p i c a l t e s t run  35  20  Traversing gear with probe during wake measurements  37  21  V a r i a t i o n of Strouhal frequency with Reynolds number-  39  22  V a r i a t i o n of Strouhal number with angle of attack  40  23  Variation of f l u c t u a t i n g pressure c o e f f i c i e n t with Reynolds number, e = 0 . 6 . .  24  •  Variation of f l u c t u a t i n g pressure c o e f f i c i e n t with Reynolds number, e = 0 . 8  25  42  ................  43  D i s t r i b u t i o n of mean and f l u c t u a t i n g pressure c o e f f i c i e n t s , a = 0  26  D i s t r i b u t i o n of mean and f l u c t u a t i n g pressure c o e f f i c i e n t s , a = 30°  27  45  ..................................  D i s t r i b u t i o n of mean and f l u c t u a t i n g pressure c o e f f i c i e n t s , a = 60°  28  •..  47  D i s t r i b u t i o n of mean and f l u c t u a t i n g pressure c o e f f i c i e n t s , a = 90°  29  D i s t r i b u t i o n of mean and  ......  •..  ...  51  Amplitude modulation of the pressure s i g n a l s on the surface of the model, e = 0.6 . . . .  32  • • • • 52  Amplitude modulation of the pressure signals on the surface of the model, e = 0 . 8 - . . . . . . . . .  33  49  V a r i a t i o n of l i f t and maximum f l u c t u a t i n g pressure c o e f f i c i e n t s with angle of a t t a c k . . . . . . . . . . . . . . . . .  31  48  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 surface of a c i r c u l a r c y l i n d e r (e = 0) 30  46  ....  53  Phase s h i f t between pressure signals on the surface of the model, e = 0 . 6 , a = .0,-90°  • • •• -.-  55  vi  Figure 34  Page Phase s h i f t between pressure s i g n a l s on the surface of the model, e = 0 . 8 , a = 0 , 90° and Nr = 67,000.  35  ....  Representative results of wake m e a s u r e m e n t s . . . . . . .  56 59  (a) Typical wake traverse (b) Typical amplitude decay in wake 36  V a r i a t i o n of drag and moment c o e f f i c i e n t s with angle of a t t a c k . . . . . . . . . .  61  ACKNOWLEDGEMENT  The author wishes to express his appreciation f o r the helpful supervision and advice by Dr. V . J . Modi. Thanks are also due to the Department of Mechanical Engineering f o r use of t h e i r 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 assistance. F i n a n c i a l support was received from the National Research Council of Canada, Grant A-2181.  LIST OF SYMBOLS  Drag c o e f f i c i e n t ,  % 3 1/2 V* 2 ac  P r e s  u r e  d r a  P  Lift coefficient,  — l/2pV? 2 ac L  l  f  t  Fluctuating l i f t c o e f f i c i e n t (average amplitude)  Moment c o e f f i c i e n t , — 1/2 V? 4 a c o m e n t  2  P  P-P Pressure c o e f f i c i e n t , —  V2pV? P'  Fluctuating pressure c o e f f i c i e n t ,  —51/2PV!  Longitudinal spacing between vortices  Reynolds numbers  Strouhal number,  V 2a  y—  or  —  Percentage circumference, measured clockwise from tap 0 Free stream v e l o c i t y Lateral spacing between vortices Semi major axis of model Semi mi nor axis of model Length of model  Eccentri ci t y ,  Frequency of vortex formation, Strouhal frequency  Projected height of model,  2 / a  sin  a+b  cos  Distance downstream from centre of model Mean pressure Fluctuating pressure (average amplitude) about mean Free stream s t a t i c pressure Transverse distance from centre of model Angle of attack A i r density A i r kinematic v i s c o s i t y  a  1. INTRODUCTION  It i s well known that under certain conditions e l a s t i c a l l y mounted b l u f f bodies, when exposed to a f l u i d stream, may e x h i b i t self-induced o s c i l l a t i o n s .  The v i b r a t i o n of smoke s t a c k s , transmission  l i n e s , periscopes, a i r c r a f t wings, bridges, launch v e h i c l e s , e t c . , has been of i n t e r e s t to engineers.  The v i b r a t i o n of a structure  is  undesirable f o r many reasons, one of which is the danger of i t s collapse due to fatigue of the m a t e r i a l .  In general, the nature of the f o r c i n g  f u n c t i o n , wake geometry, and Strouhal number form three important parameters in an a e r o e l a s t i c i n s t a b i l i t y study.  The determination of  the corresponding information f o r a set of s t a t i o n a r y e l l i p t i c cylinders 4  in the Reynolds number range of 3 x 10  5  - 10  forms the subject of t h i s  presentation. In general, the e l a s t i c a l l y supported b l u f f bodies e x h i b i t two d i s t i n c t forms of aerodynamically induced v i b r a t i o n transverse to the flow d i r e c t i o n .  The f i r s t type, commonly known as vortex resonance,'  refers to the condition where the p e r i o d i c i t y of the organized vortex shedding coincides with the natural frequency of the system.  The  second form of o s c i l l a t i o n arises due to negative slope in the t r a n s verse, force versus angle of attack diagram.  This causes the body to  be unstable under transverse disturbances r e s u l t i n g in o s c i l l a t i o n that grows in amplitude u n t i l the energy extracted from the f l u i d stream balances that d i s s i p a t e d through various forms of damping. Strouhal'' was the f i r s t to correlate the p e r i o d i c vortex shedding with the diameter of a c i r c u l a r c y l i n d e r and f l u i d  velocity.  2  This was followed by the c l a s s i c a l study of wake geometry and s t a b i l i t y 2 by Von Karman .  Ever s i n c e , academic and p r a c t i c a l i n t e r e s t in the  vortex shedding phenomenon has resulted i n many t h e o r e t i c a l and experimental i n v e s t i g a t i o n s , e . g . , by Roshko, Kovasnay, T r i t t o n ,  3  B i r k h o f f , Humphreys, Schaeffer, E s k i n a z i , and others. Marris has presented an e x c e l l e n t review of t h i s l i t e r a t u r e . More r e c e n t l y , Grove 4 5 et al as w e l l as Bishop and Hassan measured f l u c t u a t i n g forces 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 over a range of Reynolds number.  The  corrresponding preliminary results f o r square and rectangular cylinders were presented by Modi and Heine**. In contrast to t h i s , the unsteady pressure variations and wake structure associated with the o s c i l l a t i n g two dimensional b l u f f cylinders have hardly been i n v e s t i g a t e d .  The study of Bishop and  Hassan^ showed that the vortex frequency, over,a range of c i r c u l a r o  c y l i n d e r frequencies, i s c o n t r o l l e d ; while Ferguson and Parkinson measured f l u c t u a t i n g pressure and wake pattern related to the c y l i n d e r executing vortex induced o s c i l l a t i o n s . A study of the r e l a t e d but somewhat modified problem i n v o l v i n g c a l c u l a t i o n of the boundary layer and i t s separation over an i n f i n i t e , g yawed c y l i n d e r was c a r r i e d out by Chiu number using a flume.  who also measured i t s Strouhal  It was suggested that the vortex shedding of  a yawed c y l i n d e r depends only on the cross component of the l o c a l v e l o c i t y . Among the numerous papers w r i t t e n on the aspects of f l u i d mechanics and dynamics of b l u f f bodies, only a few are concerned with the actual measurements of unsteady pressures.  McGregor"^ and G e r r a r d ^  measured f l u c t u a t i n g forces on a c i r c u l a r c y l i n d e r using a condenser  3 microphone system b u i l t into the model.  The pressure d i s t r i b u t i o n was 12  obtained by turning the c y l i n d e r .  Pendergast  obtained spanwise  pressure c o r r e l a t i o n r e s u l t s , f o r a s t a t i o n a r y c y l i n d e r , using a 13 modified form of McGregor's apparatus.  Keefe  c a r r i e d out f l u c t u a -  t i n g force measurements with the help of a c a r e f u l l y designed s t r a i n 14 gauge transducer which also acted as a test model.  Molyneux  has  also described a low frequency strain-gauge type transducer mounted i n s i d e the model to measure pressures on o s c i l l a t i n g wings. H e i n e ^ and Ferguson^ designed pressure transducers, using a p i e z o l e c t r i c c r y s t a l and l i g h t s e n s i t i v e resistances  respectively,  which were located e x t e r n a l l y and connected to the pressure taps on the model by a series of polyethylene tubings. several undesirable f e a t u r e s .  The devices e x h i b i t e d  The former has a marginal s e n s i t i v i t y  while the l a t t e r , though s e n s i t i v e , was s u b s t a n t i a l l y affected by the ambient temperature and humidity. The a v a i l a b l e information concerning b l u f f body i n t e r a c t i o n with the separated flow of s t a b l e vortex s t r e e t type i s not l i m i t e d to the cylinders of c i r c u l a r c r o s s - s e c t i o n .  Investigations with square,  rectangular, t r i a n g u l a r and hexagonal c y l i n d e r s , s t r u c t u r a l H and angle s e c t i o n s , as well as several i r r e g u l a r geometries are reported.  But  i t must be emphasized that the bulk of the l i t e r a t u r e i s indeed devoted to the c i r c u l a r geometry.  This point i s well emphasized by the fact  that the previous work on e l l i p t i c a l cylinders seems to be l i m i t e d 15 to rather preliminary unsteady pressure measurements by Heine the Strouhal number study by Schramm^.  and  4  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 bodies has been under i n v e s t i g a t i o n in t h i s department since 1958.  The review of the progress  18 19 made has been reported in two survey papers  '  .  The i n v e s t i g a t i o n  described here forms the part of t h i s continuing programme and intends to study, experimentally, the e f f e c t of e c c e n t r i c i t y of the c y l i n d r i c a l b l u f f body on the fundamental parameters l i s t e d before.  5  2. PURPOSE AND SCOPE OF THE INVESTIGATION  As pointed out before, considerable information about the vortex e x c i t e d motion of a c i r c u l a r c y l i n d e r i s reported in l i t e r a t u r e . The long range aim of t h i s project i s to obtain corresponding i n f o r mation f o r two dimensional c y l i n d e r s , of intermediate c r o s s - s e c t i o n s , obtained by s y s t e m a t i c a l l y varying the e c c e n t r i c i t y from zero  (circular  cylinder) to i n f i n i t y ( f l a t p l a t e ) . In general the accuracy of the measured data depends on the c a p a b i l i t y of the instrumentation and the accuracy of i t s c a l i b r a t i o n . This being the case, the project studies i n d e t a i l the dynamic c a l i b r a t i o n of a transducer used to measure the magnitude, phase r e l a t i o n , and frequency of the acoustic l e v e l pressure v a r i a t i o n s . The main aim of the project i s to study the aerodynamics of two dimensional, e l l i p t i c c y l i n d r i c a l models, of e c c e n t r i c i t i e s 0.6 and 0 . 8 , under the condition conducive to vortex e x c i t e d o s c i l l a t i o n s . The thesis presents experimental results on: (i)  the v a r i a t i o n of Strouhal number with Reynolds number;  (ii)  the mean and f l u c t u a t i n g s t a t i c pressure d i s t r i b u t i o n ;  (iii)  wake geometry  as a function of angle of attack during s t a t i c condition of the model. 4  5  In most cases the Reynolds number range is confined to 3 x 10 - 10 . Since the influence of the wind tunnel walls on the measured parameters i s not w e l l e s t a b l i s h e d , the results presented are uncorrected f o r that e f f e c t  (Appendix  I).  6  3. MODELS AND SUPPORTING SYSTEM  Two e l l i p t i c c y l i n d r i c a l models, 27 inches l o n g , were designed to span the wind-tunnel c r o s s - s e c t i o n thus approximating the twodimensional flow c o n d i t i o n .  The constructional d e t a i l s are shown in  Figure 1 and the physical parameters are l i s t e d below:  Model  e  a/b  Wei ght, Lb.  Materi al  t  1  0. 6  2.5/2  2  0.8  2.5/1.5  Aluminum Plexiglass  Table 1.  Number of Bulkheads  Skin Thi ckness, In. .  4.20  7  0.02  1.45 -  7  0.02  Model data  The models were so constructed that they can be mounted on the wind tunnel balance or brackets attached to the t u n n e l , or may be supported by the e x i s t i n g a i r bearing system f o r measurements under vibrating condition.  At the central bulkhead of each model there are  32 pressure taps (d = 0.025 i n . ) equally spaced around the circumference (Figure 2 ) .  Two taps were provided i n the spanwise d i r e c t i o n , at a  distance of 4.5 i n . and 9 i n . from the m i d - s e c t i o n , in the plane of the minor a x i s .  The pressure taps are connected to p l a s t i c tubes of  inside diameter 0.066 i n . which are brought out from one end of the c y l i n d e r (Figure 1).  In case of the p l e x i g l a s s model i t was thought  a d v i s a b l e , due to the t h i n s k i n , to ascertain the r i g i d i t y of the  7  panel.  A simple t e s t of d e f l e c t i o n and natural frequency showed the  panels to be of adequate s t i f f n e s s with a maximum d e f l e c t i o n of less than 0.0004 i n . and natural frequency of 180 cps during operating conditions. The models were tested i n a low speed, low turbulence, return type wind tunnel where the a i r speed can be varied from 4 - 150 ft/sec with a turbulence level less than 0.1%. The pressure d i f f e r e n t i a l across the contraction section of 7:1 r a t i o can be measured on a Betz micromanometer with an accuracy of 0.2 mm of water.  The t e s t  section v e l o c i t y is 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 , 36 i n . x 27 i n . , i s provided with 45° corner f i l l e t s which vary from 6 i n . x 6 i n . to 4.75 i n . x 4.75 i n . to compensate p a r t l y f o r the boundary layer 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 in the t e s t section is less than 0.25%. The tunnel i s powered by a 15 horsepower d i r e c t current motor d r i v i n g a commercial axiflow fan with a Ward-Leonard system of speed c o n t r o l . An outline of the tunnel i s shown in Figure 3. mounted in the wind tunnel during t e s t .  Figure 4 shows a model  gure 1 .  Constructional  d e t a i l s of models  Figure 2.  Numbering of pressure taps  i—Turning vanes  5350  Figure 3.  Wind tunnel outline  12  4. INSTRUMENTATION AND CALIBRATION  4.1  Pressure Transducer Recently a new pressure transducer, c a l l e d Barocel Modular  Pressure Transducing System, has appeared on the market.  An extensive  experimentation with the unit showed i t to be quite s u i t a b l e f o r the intended measurements.  Consequently, two pressure transducers together  with the necessary power and signal conditioner units were acquired. Developed by Datametrics Inc. of Waltham, Massachusetts, the Barocel i s a high p r e c i s i o n , stable capacitive voltage d i v i d e r , the variable element of which i s a thin prestressed s t a i n l e s s s t e e l diaphragm (Figure 5 ) .  Positioned between f i x e d capacitor p l a t e s , the  diaphragm deflects proportional to the magnitude of the applied pressure. An a . c . c a r r i e r voltage at 10 Kc. i s applied to the stationary capacitor plates.  The diaphragm attains a voltage l e v e l determined by i t s  t i v e p o s i t i o n between the f i x e d capacitor p l a t e s .  rela-  With the Barocel  appropriately arranged in a bridge c i r c u i t , the output voltage i s determined by the r a t i o of capacitance of the diaphragm to each of the stationary electrodes.  The c a r r i e r voltage i s thereby amplitude  modulated in accordance with the input pressure. The units have 8 ranges.  0-10 mm of mercury on the least  s e n s i t i v e , and 0-0.001 mm of mercury on the most s e n s i t i v e range. Further data given by the manufacturer are: Output:  0-5 volts d.c f u l l scale  Linearity:  _ 0.1% in ranges used  Accuracy of S t a t i c C a l i b r a t i o n : _ 0.5% of f u l l scale +  13  Figure 5. Schematic, of Barocel pressure transducer  14  Transient response: T y p i c a l l y less than 2 milliseconds to step input f o r l i n e pressure of 750 mm of mercury Stability:  (a) - 0.1% f o r t 15° ambient pressure change (b) t 0.01% f o r t 10 volts l i n e voltage change For (a) and (b) constant, t 0.01% day to day  The Barocel i s accurately c a l i b r a t e d f o r s t a t i c pressures.  For  the f l u c t u a t i n g pressure s i g n a l s transmitted through r e l a t i v e l y long tubes considerable attenuation i s to be expected.  The attenuation of  the signal w i l l depend on such variables as tube l e n g t h , tube diameter, number and s i z e of c o n s t r i c t i o n s (pressure t a p s ) , frequency and shape of the pressure s i g n a l and, in a d d i t i o n , the basic frequency response of the Barocel i t s e l f . The inconsistencies in the r e s u l t s , obtained with the c a l i b r a t i o n methods previously developed in the department, were a t t r i b u t e d to a resonance condition w i t h i n the system and/or e r r o r in the theor e t i c a l p r e d i c t i o n of pressure. It was therefore r e a l i z e d that a system had to be developed where no resonance condition would e x i s t between the transducer with tube and pressure tap on one side and the volume where the c a l i b r a t i o n s i g n a l was generated on the other s i d e . This condition was obtained with s u f f i c i e n t accuracy by using as a pressure source a 5 gallon drum with a thin latex diaphragm on one end.  The pressure signal was generated by a b a f f l e plate actuating  the diaphragm.  The b a f f l e plate was driven by a v i b r a t i o n generator  which in turn received i t s impulse from a function generator as shown in Figure 6.  The natural frequency of the drum with diaphragm, b a f f l e  15  Amplifier  Function generator i  Barocel wtMumnnnunnihiiinnnnininninni  Diaphragm Baffle  Sound level meter yf-n.  5 gallon drum Vibrator  'h))l))))))))))))))))))})i))))hiiiiiiiiiiiiiiii7TTTm,  Barocel  Signal conditioner  o  o  iA/WWV JWAAAA  Power supply Oscilloscope Figure 6.  Block diagram of pressure generator and set-up f o r comparison of dynamical response  16 and v i b r a t i o n generator was found to be 60 cps.  However, t h i s does  not l i m i t the use of the apparatus to lower frequencies provided the natural frequency of the transducer used to measure the source pressure i s s u f f i c i e n t l y high.  To measure the source pressure a  sound l e v e l meter could be used but these meters have a decibel s c a l e , and an accuracy of - 1 db i s equivalent to about 25% v a r i a t i o n in the absolute pressure.  A l s o , most sound level meters have a poor,frequency  response below 20 cps. This led to an i n v e s t i g a t i o n of the open port frequency response of the Barocels with a view to use one of them f o r measuring the c a l i bration pressure at, the source. The natural frequency of the Barocel diaphragm i t s e l f i s given by the manufacturer to be 2500 cps or higher* ,response i s s p e c i f i e d to be less than 2 ms.  A l s o , the t r a n s i e n t The Helmholtz resonator  frequency of the cavity and the connection on one side of the diaphragm was c a l c u l a t e d to be 290 cps.  The experimental value obtained by  actuating one side of the Barocel with a horn d r i v e r was found to be around 210 cps.  Both these values are of the order of magnitude  suggested by the t r a n s i e n t response given above.  It was e s t a b l i s h e d ,  through preliminary experiments j that the required frequency range would be from 5 to 35 cps.  Considering the lower value of 210 cps  f o r the natural frequency, and a d r i v i n g frequency of 40 cps, one would get an output w i t h i n - 4% of the input i f a l i n e a r system with damping c o e f f i c i e n t somewhere between zero and c r i t i c a l 1s assumed. This j u s t i f i e s the use of the s t a t i c a l l y c a l i b r a t e d Barocel f o r measuring the pressure Inside the drum.  Figure 6 i l l u s t r a t e s the  17  set-up of the pressure generator during the i n i t i a l evaluation of the Barocel response.  It was found that f o r s i n u s o i d a l inputs the signals  from the Barocel and the function generator could be superimposed on the o s c i l l o s c o p e .  Even in the extreme cases of square and t r i a n g u l a r  wave inputs the response of the c a l i b r a t i o n system was quite good as i n d i c a t e d i n Figure 7.  The results of the i n i t i a l c a l i b r a t i o n with  i  varying tube length and frequency are shown in Figure 8.  The approxi-  mate exponential decay of output amplitude with tube length i s as 20 expected  .  The appearance of "bumps" at shorter tube lengths, most  i  pronounced at 15 cps, cannot be a t t r i b u t e d to a resonance condition between the drum and the Barocels.  The same phenomena w i l l occur under  actual measuring condition in the wind t u n n e l , and i t may be considered as a p e c u l i a r i t y of t h i s combination of tube, pressure tap and t r a n s ducer. 1  Since noticeable attenuation occurred due to the presence of a  c o n s t r i c t i o n in the tube a l l c a l i b r a t i o n s were performed with a pressure tap in the c i r c u i t .  The c a l i b r a t i o n plots f o r a Barocel  when connected to a pressure tap through a tube of given length and diameter are shown in Figure 9.  This also demonstrates the l i n e a r i t y  of the system. For work i n the wind tunnel i t was found impossible to use atmospheric pressure as reference.  This i s because the difference  between the s t a t i c pressure at the tap and the atmospheric pressure was found to be so large as to throw the Barocel off scale at s e n s i t i v e settings.  Moreover, surges in the base pressure affected the pressure  f i e l d around the model and gave r i s e to the same e f f e c t .  Hence, the  Willi  • •j i  ••••111 (b)  Figure 7.  Response of c a l i b r a t i o n system to d i f f e r e n t input wave forms (1 cps, 0.0016 p s i ) . (a) Triangular wave input (b) Square wave input  19  1.2  Figure 8.  Pressure attenuation as a function of tube length and.frequency (tube diameter = 0,066 1n.)  0  500  1000 Input, mV  1500  Ffgsarae -SL- Eallfiforatiioni plots for Barocel pressuire transducer  2000  21 f i n a l c a l i b r a t i o n set-up incorporated a damping volume between the pressure ports of the B a r o c e l , thus using the s t a t i c pressure of the tap in question as reference.  A block diagram and a photograph of the  c a l i b r a t i o n set-up are shown in Figure 10 and 11 r e s p e c t i v e l y .  The  e f f e c t of amplitude and frequency on output, with the damping b o t t l e in the c i r c u i t , i s shown in Figure 12,.  For convenience the c a l i b r a t i o n  curves in Figures 9 and 12 are p l o t t e d in Figure 13 as a r a t i o of output to input.  It can be noticed that above 15 cps there i s no attenua-  t i o n due to the damping b o t t l e .  The s p e c i f i c tube length and diameter  were chosen f o r p r a c t i c a l reasons.  Sinusoidal signals were used  throughout the c a l i b r a t i o n .  4.2 Manometer An i n c l i n e d Lambrecht manometer with ethyl alcohol was used to measure s t a t i c pressure on the surface of the model.  The manometer  can be read with an accuracy of l/10th of a m i l l i m e t e r .  It was found  necessary to reduce the f l u c t u a t i o n s of the l i q u i d column caused by the pressure surges previously mentioned.  The c o n s t r i c t i o n s in the  tubing formed by four hypodermic needles (#19) in series gave adequate damping.  4.3 Wake Probe The wake survey was c a r r i e d out using a disc probe constructed by Ferguson  16  21 and described in d e t a i l by Bryer et al .  As pointed  out by these i n v e s t i g a t o r s , the probe i s r e l a t i v e l y i n s e n s i t i v e to  22  Function generator  Amplifier  Barocel  Vibration generator  Polyethylene tube 1=5',  dj = 0-066'  R.M.S. Voltmeter  Oscilloscope Figure.10.  Block diagram of the c a l i b r a t i o n apparatus  23  Figure 11.  Calibration apparatus  1000  > E 3  o. O  500  500  1000  1500  2000  Input, mV f i g u r e 12.  C a l i b r a t i o n plots f o r Barocel pressure transducer with damping b o t t l e  ro  Figure 13.  Comparison between c a l i b r a t i o n curves f o r Barocel pressure transducer with and without damping b o t t l e  26  p i t c h (- 4°) and yaw (- 20°).  The main dimensions of the probe are  given in Figure 14.  4.4 Band Pass F i l t e r There are several sources of disturbances, e . g . fan d r i v e , . o t h e r laboratory equipment, surges in the t u n n e l , e t c . , which superpose undesirable pressure v a r i a t i o n s on that created by the shedding v o r t i c e s . In general, the i n t e n s i t y of the ' n o i s e ' may be considered constant.  On  the other hand the pressure f l u c t u a t i o n s due to shedding vortices depend on location of the tap and a t t i t u d e of the model.  This being  the case there were s i t u a t i o n s where the noise had a tendency to overshadow the vortex-generated pressure v a r i a t i o n s .  It was, there-  f o r e , necessary to introduce a band pass f i l t e r in the pressure measuring system to eliminate the undesirable n o i s e .  The t y p i c a l  pressure traces of f i l t e r e d and u n f i l t e r e d s i g n a l s are compared in Figure 15.  At a = 0 , where the signals are weak in r e l a t i o n to n o i s e ,  the necessity of using a f i l t e r i s obvious.  At a = 90°, where the  signals are more powerful, the noise level becomes r e l a t i v e l y n i f i c a n t and the f i l t e r i s no longer e s s e n t i a l .  insig-  It was also observed  that the pressure signal from the separated flow region was s l i g h t l y more<irregular than that from the laminar f i e l d .  This may be due to  higher turbulence l e v e l in the wake. During measurements the f i l t e r was c a l i b r a t e d f o r every change a f f e c t i n g the vortex shedding frequency.  Operating the f i l t e r at  mid-band frequency and with the high and low c u t - o f f settings separated by a f a c t o r of 1.5 gave an attenuation between 0 . 8 and 0 . 9 .  This was  27  Figure 14.  Geometry of .the disc probe  e = 0.6  e = 0.8 (b)  Figure 15.  Typical f l u c t u a t i n g pressure traces (not to the same scale) (a) a = 0 ,  (b) a = 90°  Upper trace represents f i l t e r e d s i g n a l  29  found by feeding a sinusoidal signal from the function generator to the rms voltmeter and measuring the difference in output with and without the f i l t e r .  4.5 R.M.S. Voltmeter Due to considerable, seemingly random, amplitude modulations of the f l u c t u a t i n g pressure i t was necessary to present the results as time-average values.  Under certain conditions several minutes of  averaging was required to get reproducible r e s u l t s .  This led to the  necessity of using a true rms voltmeter converting the f l u c t u a t i n g pressure s i g n a l to an equivalent d . c . s i g n a l .  An external r-c damping  c i r c u i t was used to reduce the variations caused by the amplitude modulations.  The f i n a l steady d . c . level was then measured on the  vafcuum tube voltmeter.  Because of the extremely high input resistance  of the l a t t e r no measurable voltage drop occurred over the damping r e s i s t o r s (Figure 16).  4.6 E l e c t r o n i c  Instruments  Following i s the l i s t of the e l e c t r o n i c apparatus used in the experimental work: Filters:  Krohn-Hite, band pass variable models 330B & 330A.  filter,  Voltmeters:  Hewlett Packard, HP-3400A true rms voltmeter, and HP-412 vacuum tube voltmeter.  Function Generator:  Hewlett Packard, low frequency generator, model 202A.  function  30  Vibration Generator:  Goodmans, type V47.  Oscil1oscope:  T e c t r o n i x , type 564, dual trace storage oscil1oscope.  Chart Recorder:  Honeywell, 906c v i s i c o r d e r .  Low frequency amplif i e r with power supplies: R-C damping c i r c u i t :  B u i l t in the department  22  .  B u i l t in the department (Figure 16).  31  HP-3400A R.M.S. Voltmeter Output resistance 1 KO O 0  HP-412A V.T. Voltmeter Input resistanc 200 M O O O  *-A/WW  Figure 16,  R-C damping c i r c u i t  32  5. TEST PROCEDURES  5.1 Fluctuating Pressure Measurements  ;  The diagrammatic lay-out of the apparatus used f o r f l u c t u a t i n g pressure measurements i s given in Figure 17.  During measurements the  r - c damping c i r c u i t was set to give minimum v a r i a t i o n of the voltmeter reading.  The f l u c t u a t i n g pressure signal was also displayed on the  o s c i l l o s c o p e to determine the maximum amplitude and Strouhal  frequency.  5.2 Phase Measurements The phase between the f l u c t u a t i n g pressures at d i f f e r e n t taps was obtained by feeding the s i g n a l s to the V i s i c o r d e r and measuring the average phase s h i f t over 10-cycles..  The e f f e c t of any phase s h i f t  i n the instrumentation was n u l l i f i e d by. measuring a l l phase s h i f t s from a permanent reference tap at 90° to the wind d i r e c t i o n .  The data  showed considerable s c a t t e r which increased with the distance from the reference tap.  Figure 18 shows, s c h e m a t i c a l l y , the arrangement  of the instrumentation f o r phase measurements.  The set-up during a  t y p i c a l t e s t run i s shown in Figure 19.  5.3 Mean S t a t i c Pressure D i s t r i b u t i o n Mean pressure on the model was measured using a Lambrecht manometer.  One leg of the manometer was "connected to a t o t a l head  tube 1n the s e t t l i n g chamber and the other to the pressure tap on the model.  33 \  Power supply Damping bottle  Voltmeter  R - C damping circuit  R. M. S. voltmeter Oscilloscope  Figure 17.  Block diagram of the f l u c t u a t i n g pressure measuring set-up  34  Barocel  Barocel Damping bottle  Signal conditioner  E7  Signal conditioner  Power supply  Filter  Figure 18.  Visicorder  Filter  Block diagram of the phase measuring system  Figure 19.  Instrumentation set-up during a t y p i c a l t e s t run  w  36  5.4 Wake Measurements The determination of wake geometry was accomplished using the method described by H e i n e ^ and Ferguson^.  The transverse distance  between the vortex centrelines was measured by the wake probe connected to the pressure transducer i n a manner s i m i l a r to that shown in Figure 17. A photograph of the wake probe and the pressure transducers connected to the damping bottles i s given in Figure 20.  Moving the probe across  the wake and p l o t t i n g the rms value of the s i g n a l gave two peaks at the vortex c e n t r e l i n e s .  The distance-between these peaks represents  the l a t e r a l spacing between the vortex core l i n e s at that s t a t i o n . The longitudinal spacing between the consecutive vortices was obtained by using a pressure tap as reference and moving the probe downstream on the same side of the model u n t i l the signals were 180° out of phase. From t h i s p o s i t i o n the probe was moved further downstream so that the the s i g n a l s were in phase.  The process was repeated u n t i l l i m i t e d by  the t r a v e l of the t r a v e r s i n g gear.  Twice the distance between two  successive measurements gave the desired l o n g i t u d i n a l spacing between the v o r t i c e s .  The instrument arrangement was s i m i l a r to the one used  f o r phase measurements (Figure 18), except that the signals were d i s played on the o s c i l l o s c o p e .  Figure 20.  Traversing gear with probe during wake measurements  38  6. TEST RESULTS AND DISCUSSION  6.1 Strouhal Number The Strouhal frequency was measured in the Reynolds number 4 range of 2 x 10  5 - 10  f o r three d i f f e r e n t angles of a t t a c k , and i t  was observed to be l i n e a r with increasing wind speed as shown i n Figure 21.  The e f f e c t of angle.of attack on the Strouhal number was  also obtained in the same Reynolds number range.  These variations  based on the minor axis as well as the projected height are shown in Figure 22. The Strouhal number based on projected height (h) showed comparatively less dependence on the angle of attack (a) in the Reynolds number range i n v e s t i g a t e d .  An observation concerning the Strouhal  number v a r i a t i o n at low angles of attack i s pertinent here.  For the  t h i c k e r e l l i p s e a slow r i s e in the projected height with a small drop in shedding frequency leads to an almost uniform Strouhal number in this range.  On the other hand, f o r the thinner e l l i p s e the very sharp drop  in shedding frequency o f f r s e t s the r e l a t i v e l y greater  rise  height thus leading to a decrease in Strouhal number. 17  The s i m i l a r  tendency was also observed by Schramm  in projected  who c a r r i e d out Strouhal  number measurements f o r the e l l i p s e s of four d i f f e r e n t e c c e n t r i c i t i e s (e = 0.662, 0.866, 0.969, 0.998).  In a l l cases except one the measure-  ments were limted to 0 - 45°, range due t o , as reported by him, "lack of stable vortex s t r e e t " .  This i s in contrast to the strong and well  defined f l u c t u a t i n g s i g n a l s observed in the t e s t results presented here.  40  0-22  0  Naurs l l .  30  oc°  60  Variation.-©f Stf§uhaT number with -angle ©f.attaek  90  41  Schramm does not give any d e t a i l s of the wind tunnel t e s t section geometry and the measuring equipment,used. A modulation of the vortex shedding frequency .was present at a l l times.  It amounted to as much as - 5%, and may be r e l a t e d , to some  e x t e n t , to the amplitude modulation., The frequency:modulation was too small to a f f e c t the f i l t e r c a l i b r a t i o n .  6.2 Fluctuating Pressure D i s t r i b u t i o n For both e l l i p s e s , the e f f e c t of varying the Reynolds number in the range 3 x 10 t o . 1 0 4  5  was investigated f o r a = 0 , 30°, 60°, 90°.  The f l u c t u a t i n g pressure measurements were taken at four t a p s , two in the laminar and other two in the separated flow regions. results are p l o t t e d i n Figures 23, 24.  The  These curves represent the  percentage v a r i a t i o n about the mean of the pressure c o e f f i c i e n t at each of the ports in question. No s i g n i f i c a n t Reynolds number e f f e c t was noticed except f o r the abrupt increase in the f l u c t u a t i n g pressure c o e f f i c i e n t at zero angle of attack and low wind speed.  The cause of t h i s phenomenon i s  not quite c l e a r , but i t should be emphasized that i t i s not associated with any noticeable change i n base pressure.  T h i s , together, with  the Reynolds number at which the behaviour occurred, makes i t u n l i k e l y to be due to e i t h e r proximity to the c r i t i c a l Reynolds number or any other change i n character of the s e p a r a t i o n . , However, i t should also be mentioned that f l u c t u a t i n g signals in this region are very.weak and d i s t o r t e d by noise.  42  Figure 23,  VariaticW of f l u c t u a t i n g pressure c o e f f i c i e n t with Reynolds number, e = 0o6  43  2  4  6  8  Nr Figure 24.  V a r i a t i o n of f l u c t u a t i n g pressure c o e f f i c i e n t .with Reynolds number, e = 0.8  10x10  In general, the best signals were obtained at a wind speed around 28 ft/sec ( N r ^ 68,000).  It was, t h e r e f o r e , decided to carry  out f l u c t u a t i n g pressure measurements at t h i s wind speedc The unsteady pressures on the surface of the two e l l i p t i c models were recorded f o r a = 0 , 30°, 60°, 90°,  These results are p l o t t e d in  Figures 25-28 together with the mean pressure d i s t r i b u t i o n .  For  comparison the corresponding data f o r a c i r c u l a r c y l i n d e r are presented in Figure 29. Based on these results the f o l l o w i n g remarks can be made: (i)  There are two points where the f l u c t u a t i n g pressure tends to vanish.  They occupy positions which are approximately 180°  from the stagnation p o i n t s .  One would expect this due to  c a n c e l l a t i o n of pressures which are 180° out of phase.  As  shown i n the figures t h i s e f f e c t i s less complete at the rear of the c y l i n d e r , probably due to i r r e g u l a r i t i e s in the wake. (ii)  The f l u c t u a t i n g pressure increases as the mean  pressure  decreases and, in g e n e r a l , the v a r i a t i o n s can be represented by curves following a s i m i l a r trend. (iii)  The mean pressure increases negatively with angle of attack. The same i s true f o r the unsteady pressure* mean  But, while the  pressure c o e f f i c i e n t approximately doubles in the range  a = 0 - 90° the corresponding increase in f l u c t u a t i n g pressure c o e f f i c i e n t i s as high as 10 to 20 times. (iv)  As expected, at zero angle of a t t a c k , the f l u c t u a t i n g pressure c o e f f i c i e n t f o r the slender e l l i p s e is considerably less than that f o r the t h i c k e r e l l i p s e , but at 90° they are p r a c t i c a l l y equal.  0  s  25  2  4  6  8  50  10  12  14  16  75  18  20  22  24  Tap number Figure 27.  D i s t r i b u t i o n of mean and f l u c t u a t i n g pressure c o e f f i c i e n t s , a = 60°  100  26  28  30  0  49  Figure 29.  D i s t r i b u t i o n of mean and 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, surface of a c i r c u l a r c y l i n d e r , (e = 0)  50 V a r i a t i o n of the maximum f l u c t u a t i n g pressure c o e f f i c i e n t with angle of attack i s shown in Figure 30. To i l l u s t r a t e the amount of amplitude modulation present in the f l u c t u a t i n g pressure s i g n a l s , the r a t i o between the maximum and the average amplitude has been p l o t t e d i n Figures 31 and 32.  The maximum  amplitude used i s a representative value observed during a two minute period. The results showed considerable s c a t t e r , but the increase in maximum/average r a t i o towards the rear "stagnation point" was quite distinct.  There was also a trend towards a reduction of the r a t i o i n .  the laminar flow region.  As stated by several i n v e s t i g a t o r s  1 0 , 1 1  »^,1  the amplitude modulations were found to be in phase around the models.  6.3 Phase S h i f t Gerrard  11  was probably the f i r s t one to measure phase r e l a t i o n  between the f l u c t u a t i n g pressure s i g n a l s on a c i r c u l a r c y l i n d e r .  He  used two b u i l t - i n pressure transducers which could be rotated i n d i v i d u a l l y and concluded that the pressures were e s s e n t i a l l y in phase over one side of the model and 180°.,out of phasewith that on the other s i d e . Any deviation from t h i s was a t t r i b u t e d to the spanwise separation between the pressure taps. The present experiments confirmed the 180° phase difference between pressures on two sides of the model.  But contrary to Gerrard's  observation i t i n d i c a t e d s u b s t a n t i a l phase s h i f t between the signals from the neighbouring pressure taps.  The phase measurement .was c a r r i e d  out on both e l l i p t i c models at a = 0 , 90°, and the results are p l o t t e d  51  Figure 30% Va'fialion oT l i f t and rfiaxjRIUm- fiU§|U&tjfifj. pressure coefficients With angle of attack 1  52  S 50  25  75 i  'Pff  ' & r- — w  w  —  W  •  J  w  w  v  / IV  •  .,„  0°  a =  •  i>  •  »  • 4 " • *  •. •  ^ 2 x o  |  •  • -  100  30  o 4 E  •  • > 9  • • • a  )  «  A ./  60°  =  /  \ 1  0  K  • m • *  4  8  a —  4»  12  i  • • •  " • • —•  16  Tap position Figure 31  \  90 •  I  20  •  24  Amplitude modulation of the pressure signals on the surface of the model, e = 0.6  28  /  53  Figure 32.  Amplitude modulation of the pressure signals on the surface of the model, e = 0.8  54  in Figures 33, 34. It is apparent that for the models at a = 0 the signals from upstream and downstream pressure taps are lagging and leading respectively with respect to the reference located at the 90° position (tap 16 or 3 2 ) .  On the other hand at a = 90° a l l signals lag the reference  (tap 8 or 2 4 ) .  The phase difference between two pressure signals was  found to be as large as 60°.  6.4 Fluctuating L i f t The fluctuating l i f t coefficients for both ellipses at  a.='0,  30°, 60°, and 90° were calculated from the pressure data given e a r l i e r . The results are plotted in Figure 30. fluctuating l i f t coefficient  (1.0)  f i  =  For either e l l i p s e the maximum 0  >  6  ,  (0.72)  e  0.8)  was found  at 90° while the minimum value occurred at a = 0. The fluctuating l i f t coefficient for a circular cylinder as obtained by McGregor* was 0  0.6.  It may be pointed out that the maximum and minimum values given above were obtained without taking phase s h i f t into account. With phase angle .between the pressure signals the corresponding values are modified as shown in Table 2.  e  a,  Deg.  V  a phase  % change in C-,  0.6  0 90  0.156 1.007 .  0.152 1.001  2.5 0.5  0.8  0 90  0.064 0.719;  0.060 0.710  6.0 1.0  Table 2.  Effect of phase s h i f t on fluctuating l i f t coefficient  55  S  50  25/75 I  i  10 -8  o  c  -5-10 D  a-20  A"' J  i  a c  4  •  k  V  •  L  i  •  • N r = 33,0CK) - A Nr = 67,0C • Nr = 100,000  -30  ^-^-Vq>  1 u  •  0  2/30  4/28  6/26 8/24 10/22 12/20 14/18 Tap position (a)  16  S  0/50  75  25 c)  •  20 O)  10  «T  0  a> -o  A  a  ] i  n  (\  iL 3  rT ^  1  ^—  i - VCD  ^—  1  •  4  ik.  A^V^L  •  s-io  o f  *—J  • N r = 33,000 - A Nr - 67,000 -30 • N r = 100,000  -20  24  i  26/22  i  28/20  1  30/18 0/16 2/l4 Tap position  4/12  6/10  (b)  Figure 33. Phase s h i f t between pressure s i g n a l s  on the surface ef the model,. e = O.i, a = 0, I 0 §  a  M J  a  8  56  S  75 40  25  0/50  1  1  1  0  30 *  voo  20  \  •  10 0 - 10  •  • Top surface  -20  A Bottom surface  i >  24  26/22  Figure 34.  28/20  30/18  0/]6 2/14 Tap position (b)  < >  4/12  Phase s h i f t between pressure signals on the surface of the model, e = 0.8, a = 0 , 90° and Nr = 67,000  6/10  8  57  For f l u c t u a t i n g drag and moment c o e f f i c i e n t s the influence of phase angle.may be greater, but no attempt has been made to evaluate these parameters since they are more s e n s i t i v e to errors i n pressure and phase measurements, which occur near the stagnation p o i n t s .  6.5 Spanwise Effects. The v a l i d i t y of assuming two dimensional flow in the present 1o case may be questionable  .  Measurements at two spanwise taps (4.5 i n . '  and 9 i n . from center s e c t i o n , taps 33 and 34) i n d i c a t e d s u b s t a n t i a l phase d i f f e r e n c e .  Occasionally the phase s h i f t between the signals  was observed to remain steady f o r a short p e r i o d , but e s s e n t i a l l y varied randomly.  it  T h i s , in p a r t , may be a t t r i b u t e d to end conditions.  It was not p r a c t i c a l with a v a i l a b l e instrumentation to measure, q u a n t i t a t i v e l y , the time dependent phase s h i f t .  However, the presence  of spanwise phase difference may not necessarily influence the f l u c t u a t i n g l i f t too much.  The c a l c u l a t i o n s showed a maximum drop of 10%  in f l u c t u a t i n g l i f t f o r a,phase s h i f t up to 50° at a = Oj or up to 30°.at a = 90°.  This holds f o r both e l l i p s e s .  Measurements showed the amplitude modulation to be e s s e n t i a l l y i n . phase. 6.6 Wake Geometry Typical average amplitude s i g n a l s across the wake are given in Figure 35a.  It was found that a f t e r a downstream distance of  nearly three major axes the spacings between the vortices approximately constant.  remained  The wake signals at a = 0 became too weak  58  to be recorded at 20-30 i n . downstream.  On the other hand more power-  f u l signals at higher angles of attack could be observed down to 45 i n . which was the l i m i t f o r the measuring r i g .  For a = 30° and 60° the  wake was s l i g h t l y unsymmetrical, the vortex from the rearmost separat i o n point being the stronger.  Typical decay of pressure amplitude  with downstream distance i s given i n Figure 35b.  Average values f o r  the spacing between vortices are given in Table 3.  e = 0.6 a  L,  In.  W, In.  e = 0.8 W/L  L,  In.  W, In.  e = 0* W/L  W/L 0.32  0  16.00  5.0  0.31  10.00  4.3  0.42  30  19.25  5.2  0.27  16.50  5.1  0.31  60  21.75  5.7  0.26  20.75  5.7  0.28  90  22.75  5.8  0.26  22.25  5.9  0.26  *Ref erence 16 Table 3.  Spacing of vortices in f u l l y developed wake, Nr = 70,000 ;  No q u a n t i t a t i v e pressure measurements were made in the wake as the probe was.not c a l i b r a t e d , but the maximum pressure s i g n a l s immediately behind the model were estimated to be around 5 times higher than that on the model s u r f a c e . Within the Range of the . 4 5. Reynolds number i n v e s t i g a t e d (3 x 10 < N < 10 ), no s i g n i f i c a n t change in wake geometry occurred.  60  6.7 S t a t i c L i f t , Drag and Moment The stationary values of l i f t , drag and moment were c a l c u l a t e d from the s t a t i c pressure results given e a r l i e r (Figures 25-28).  The  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 angle of attack i s given i n Figure 30.  The drag and moment . c o e f f i c i e n t s are p l o t t e d in Figure 36.  The measured results are uncorrected for wall e f f e c t s and therefore are somewhat higher than the values corresponding to the unconfined stream. Approximate corrections to the drag c o e f f i c i e n t s may be obtained 23 from the expressions given by Whitbread both e l l i p s e s a t a = 90°. e = 0.8.  .  It amounts to 12% f o r  At a = 0 i t i s 10% f o r e = 0.6 and 8% f o r  As suggested by Whitbread the same corrections may be applied  to the l i f t and moment c o e f f i c i e n t s  (Appendix  I).  61  Figure 36.  Variation of drag and moment c o e f f i c i e n t s with angle of attack  7. CONCLUDING REMARKS  Based on the experimental results the f o l l o w i n g general remarks can be made concerning unsteady aerodynamics of the e l l i p t cylinders t e s t e d : (i)  The Strouhal frequency, which shows s l i g h t modulation,  !  increases l i n e a r l y with wind speed.  The v a r i a t i o n of  '  Strouhal number with angle of attack i s considerably less when based on projected height.  (ii)  The f l u c t u a t i n g pressure c o e f f i c i e n t s tend to increase with angle o f . a t t a c k .  In the range a = 0 - 90°, C-,  increased from 0.1 to 0.8 f o r e = 0.6 and from 0 . 0 4 to 0.8 f o r e = 0 . 8 .  m a X  Marked dependency on the Reynolds  number appears to be l i m i t e d to zero angle of attack condition.  The pressure signals are always amplitude  modulated and the extent of modulation, as expressed by :  i s of the order 2 - 4.  p' (iii)  Pressure signals on the surface of the models have considerable phase d i f f e r e n c e s .  At times t h i s can be as high as  60°. (iv)  S i m i l a r to the f l u c t u a t i n g pressure c o e f f i c i e n t s , the  lift  c o e f f i c i e n t s are affec t ed by the a t t i t u d e of the models. The maximum l i f t c o e f f i c i e n t s (based on the major axis) were found to be.1,0 and 0.7 f o r e = 0.6 and 0.8 r e s p e c t i v e l y .  The phase s h i f t has only small e f f e c t on these values. (v)  The q u a n t i t a t i v e observations indicate the unsteady flow condition to be f a r from two dimensional. observation in (iv)  Based on the  the spanwise v a r i a t i o n s in phase between  the pressure s i g n a l s i s not l i k e l y to a f f e c t the f l u c t u a t i n g l i f t substantially. (vi)  The r a t i o of the transverse to the l o n g i t u d i n a l spacing decreases with increasing angle of attack.  This was  observed to be true f o r both e l l i p s e s but the reduction was more pronounced f o r the thinner e l l i p s e . (vii)  For a = 0 the separation points f o r the boundary layer as i n d i c a t e d by the s t a t i c pressure d i s t r i b u t i o n occurs at approximately the same angular p o s i t i o n ( « f o r both e l l i p s e s . *  75° - 80°)  This appears reasonable compared to  the experimentally measured value of  82° f o r a c i r c u l a r  cylinder.  It may be pointed out that the v a r i a t i o n of separation points with e c c e n t r i c i t y , and angle of a t t a c k , does not seem to be reported i n literature.  * Appendix  II  A few suggestions concerning the future studies may be appropriate here:  (i)  For b e t t e r appreciation o f t h e t r a n s i t i o n a l e f f e c t s from :  c i r c u l a r c y l i n d e r to f l a t p l a t e , f u r t h e r i n v e s t i g a t i o n s of cylinders with d i f f e r e n t e c c e n t r i c i t y should be under^ taken. (ii)  The present technique f o r phase measurements involves considerable e f f o r t s to get meaningful r e s u l t s .  Some  d i r e c t method of obtaining the time average of the phase s h i f t is certainly desirable. (iii)  The Reynolds number e f f e c t s at zero angle of attack should be studied in d e t a i l .  (iv)  A study of the three-dimensional nature of the flow should be of i n t e r e s t .  A refined phase measuring device might  prove useful i n such a study. (y)  The experimental measurements of separation points on cylinders of d i f f e r e n t e c c e n t r i c i t y and i t s c o r r e l a t i o n with theory should prove to be a valuable study.  (vi)  Of course, the study of aerodynamics and dynamics of the models during s e l f - e x c i t e d motion would be the l o g i c a l extension of t h i s work.  65  BIBLIOGRAPHY  1.  S t r o u h a l , V , , "fiber eine Besondere Art der Tonerregung," Wied. Ann. Physik u. Chem,, Neue Folge, V o l . .V, 1878, pp. 216-2FT  2.  Karman, T h . , Von, " F l u s s i g k e i t u. Luftwiderstand," Phys. Z . , V o l . 13, 1911, p.49.  3.  M a r r i s , A.W., "A Review on Vortex S t r e e t s , P e r i o d i c Wakes, and Induced Vibration Phenomena;" J : Basic Engng., V o l . , 8 6 , 1964, •pp. 185-196.  4.  Grove; A . S . , S h a i r , F . H . , Petersen, .E.E-. and A c r i v o s , A . , "An Experimental Investigation o f : t h e Steady Separated Flow Past 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 . 19, part 1, 1964, pp. 60-80.  5.  Bishop, R.E.D. and Hassan, A . Y . , "The L i f t and Drag Forces on a C i r c u l a r Cylinder 1n a Flowing F l u i d , " Proc. Roy. S o c . , Series A, V o l . 277, 1964, pp. 32-50.  6.  Modi, V . J . and Heine, W., "On the Pressure Fluctuations and Wake Geometry Associated with Several B l u f f Bodies," Proc. 15th Japan Nat. Cong. Appl. Mech., Japan Soc. Mech. Engrs. 1965, pp. 7-18.  7.  Bishop, R.E.D. and Hassan, A . Y . , "The L i f t and Drag Forces on a C i r c u l a r Cylinder O s c i l l a t i n g 1n a Flowing F l u i d , " Proc. Roy. S o c , Series A, V o l . 277, 1964, pp, 51-75.  8.  Ferguson, N. and Parkinson, G.V.» "Surface and Wake Flow Phenomena of the Vortex-Excited O s c i l l a t i o n of a C i r c u l a r Cylinder,'" ASME Vibration Conference, Paper 6 7 - V 1 b r . - 3 l , 1967.  9.  Ch1u W.S.,."The Boundary Layer Formation and Vortex Shedding on Yawed'Cylinders," Washington State U n i v e r s i t y . College of Engng,. B u l l e t i n 299, 1966, B  10. McGregor^ D.M. "An Experimental Investigation of the O s c i l l a t i n g Pressures on a . C i r c u l a r Cylinder 1n a F l u i d Stream," University of Toronto, I n s t i t u t e of Aerophyslcs, Tech. Note 14, 1957. (  11. Gerrard, J . H . . , "An Experimental Investigation o f . t h e O s c i l l a t i n g Pressures on a C i r c u l a r Cylinder Shedding Turbulent V o r t i c e s , " Journal of F l u i d Mechanics, V o l . 11; 1961, pp. 244-256. 12. Prendergast, V . , "Measurement of two-Point Correlations of the Surface Pressure on a C i r c u l a r C y l i n d e r , " University of Toronto, I n s t i t u t e of Aerophysics, Tech. Note 23, 1958.  66  13. Keefe, R.T., "An Investigation of the Fluctuating Forces Acting on a Stationary C i r c u l a r Cylinder in a Subsonic Stream, and of the Associated Sound F i e l d , " University of Toronto, I n s t i t u t e of Aerophysics, Report 76, 1 9 F T 14. Molineux, 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 Report. 35, 1956. 15. Heine, W., "On the Experimental Investigation of Vortex Excited Pressure F l u c t u a t i o n s , " U n i v e r s i t y of B r i t i s h Columbia, M.A.Sc. T h e s i s , 1964. 16. Ferguson, N . , "The Measurement of Wake and Surface Effects i n the S u b c r i t i c a l Flow Past a C i r c u l a r Cylinder at Rest and in Vortex Excited •Oscillations,'" University of B r i t i s h Columbia, M.A.Sc. T h e s i s , 1965. 17. Schramm, W. , Wirbelfrequenzmessungen an umstromten B a u t e i l e n , " I f L - M i t t . , V o l . 5 , 1966, pp. 308-318. ;  18. Parkinson, G.V., " A e r o e l a s t i c Galloping in.One Degree of Freedom," Proc. F i r s t Int. Conf. on Wind Effects on Bldgs. and S t r u c t s . , N P L . London, V o l . I I , 1965, pp. 581-609. t  19. Parkinson, G.V. and Modi, V . J . , "Recent Research on Wind Effects on B l u f f Two-Dimensional Bodies," Int. Research Seminar: Wind Effects on Bldgs. and S t r u c t s . , NRC, Ottawa, 1967. 20. Morse, P . M . , "Vibration and Sound," McGraw-Hill, New York, 1948, pp. 233-265. 21. Bryer, D.W., Walshe, D.E. and Garner, H.C., "Pressure Probes Selected f o r Three-Dimensional.Flow Measurement," Aeronautical Research C o u n c i l , R. and M. No. 3037, 1958. 22. Cheng, S . , "An Experimental Investigation of the Autorotation of a F l a t P l a t e , " University of B r i t i s h Columbia, M.A.Sc. Thesis, 1966. 23. Whitbread, R . E . , "Model Simulation of Wind Effects on S t r u c t u r e s , " Proc. F i r s t Int. Conf. on Wind Effects on Bldgs. and S t r u c t s . ,  N P l , London, V o l . 2 , 1965, p7 581-610. P  24. Pankhurst, R.C. and Holder,' D.W;, "Wind-Tunnel Pitman & Sons L t d . , London, 1952, chapter 8.  Technique,"  25. M a s k e l l , E . C . , '!A Theory of the Blockage Effects on B l u f f Bodies and S t a l l e d Wings in a Closed Wind Tunnel," RAE_ Report No. Aero 2685, Nov. 1963.  67  26. S c h l i c h t i n q , H . , "Boundary - Layer Theory," McGraw-Hill, New York, 1968, pp. 2 1 , 202-206, 475. 27. Meksyn, D., "New Methods in Laminar Boundary - Layer Theory," Pergamon Press, London, 1961, chapter 11. 28. G o r t l e r , H., "A New Series for the Calculation of Steady Laminar Boundary Layer Flows," Journal of Mathematics and Mechanics, V o l . 6 , No. 1, 1957, pp. 1-66.  APPENDIX I  REMARKS CONCERNING WIND TUNNEL WALL CORRECTIONS  • There i s considerable information a v a i l a b l e f o r p r e d i c t i o n of equivalent free f l i g h t results from wind tunnel measurements as f a r as steady flow i s concerned..  Unfortunately, the same cannot  be s a i d f o r unsteady flow around a body. 24  As i n d i c a t e d by Pankhurst and Holder  the interference from  wind, tunnel walls during steady flow conditions may be subdivided into: (i)  S o l i d blockage  (ii)  Wake blockage  (iii)  L i f t effect  (iv)  Interference due to s t a t i c pressure gradient  (v)  Wall boundary-layer interference on model spanning a closed tunnel  For an e l l i p s e at a = 0° and 90° ( i i i ) would not e x i s t . (iv)  and (v)  V  where  gives a correction to wind speed as f o l l o w s :  + n cd  corr. K  =  constant  x  =  shape f a c t o r  n  =  wake blockage f a c t o r  W4. =  tunnel width  h w  Neglecting  69  This expression gives a correction s i m i l a r to the one obtained using 23 Whitbread's  equation, which i s a p a r t i c u l a r form of a more general  expression given by Maskell  25  .  For f l u c t u a t i n g pressures apparently no corrections are a v a i l a b l e , probably because the s i t u a t i o n i s considerably more complex. In addition to blockage i n f l u e n c i n g both f l u c t u a t i n g pressure and vortex frequency, i t i s l i k e l y that the boundaries w i l l impose a v e l o c i t y f i e l d due to the wake, v o r t i c e s .  Moreover, the periodic,  nature.of the flow'may lead to an expression f o r wall correction which i s also p e r i o d i c a l .  APPENDIX  II  LOCATION OF SEPARATION POINTS ON ELLIPTIC CYLINDERS  The a v a i l a b l e information on the laminar boundary  layer  separation on b l u f f bodies i s somewhat scarce and u n r e l i a b l e . The bulk of the information i s obtained a n a l y t i c a l l y using boundary layer separation c r i t e r i a with external flow d i s t r i b u t i o n assumed p o t e n t i a l . This information i s summarised in the f o l l o w i n g chart. The positions of minimum pressure as given by the present set of experiments are also included.  X  Laminar separation as calculated by Schlichting and 111 r i c h Laminar separation as measured by.Schubauer and calculated by.Meksyn ' Laminar separation as calculated by Polhausen 2 6  A  2  •  26  B  Laminar separation as calculated by Gortler' 2i ® , Minimum pressure as measured by Flachsbart O Minimum pressure as given by present measurements  1  2  4  Dependence of points of separation and minimum pressure on bluffness, a = 0; x = distance along circumference, V = semi circumference.  6  8  Ah! v o i l a quatre-vingts  volumes de recueils  d'une academie des sciences! s ' e c r i a Martin, peut q u ' i l y a i t l a du bon. - - II y en a u r a i t ,  II  se dit  Pococurante, s i un seul des auteurs de ces fatras avait invente seulement T a r t de f a i r e des epingles; mais i l n'y a , dans tous ces l i v r e s , que de vains systemes, et pas une seule chose u t i l e . VOLTAIRE  

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