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Wall confinement effects for circular cylinders at low Reynolds numbers Mitry, Raafat Tawfic 1977

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WALL CONFINEMENT EFFECTS  FOR CIRCULAR  CYLINDERS  AT LOW REYNOLDS NUMBERS  by  RAAFAT TAWFIC MITRY B.Eng.Sc.  (Mechanical E n g i n e e r i n g ) , U n i v e r s i t y of A l e x a n d r i a , 1970  M.Eng.Sc. (Mechanical E n g i n e e r i n g ) , U n i v e r s i t y of A l e x a n d r i a , 1974  A THESIS SUBMITTED IN PARTIAL FULFILLMENT THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D  SCIENCE  in THE FACULTY OF GRADUATE  STUDIES  (Mechanical E n g i n e e r i n g Department)  We a c c e p t required  this  thesis  as c o n f o r m i n g  to the  standard  THE UNIVERSITY OF B R I T I S H COLUMBIA October, . Cc)  1977  Raafat T a w f i c M i t r y , 1977  OF  In p r e s e n t i n g t h i s requirements British freely  thesis  in partial fulfillment  f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f  Columbia, I agree t h a t the L i b r a r y available  that permission  f o r r e f e r e n c e and s t u d y . f o r extensive copying  s c h o l a r l y p u r p o s e s may be g r a n t e d  thesis written  s h a l l make i t I f u r t h e r agree  of this  thesis for  by t h e Head o f my  D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . publication,  of the  I t i s understood  i n part or i n whole, or the copying  for financial  of this  g a i n s h a l l n o t be a l l o w e d w i t h o u t  permission.  RAAFAT TAWFIC MITRY  Department o f M e c h a n i c a l E n g i n e e r i n g The 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 V a n c o u v e r , B.C. Canada V6T 1W5  that  my  ii  ABSTRACT  Formation,  development  and i n s t a b i l i t y  and a s s o c i a t e d  surface  experimentally  f o r a f a m i l y o f two d i m e n s i o n a l  cylinders  ratio  o f 2 - 50%.  and c o n s t r u c t i o n a l  solution briefly  tunnel  used  described  pressure  d i s t r i b u t i o n are  i n t h e R e y n o l d s number r a n g e  and t h e b l o c k a g e design  pressure  of Foppl  details  An a p p r o a c h t o t h e d a t a r e d u c t i o n , Reynolds  number,  is  pressure  coefficient,  on t e s t  facilities  Finally,  the t e s t  confinement  discussed  number on t h e s u r f a c e  pressure  confined  R  with the highest continues  a t low  t o be l e s s is  of the  dependent  explained.  as f u n c t i o n s  of  the  and R e y n o l d s number.  suggest that  to the range  models,  procedures.  so c r i t i c a l  gradients,  is  o f the  and t e s t  which promises  data are analyzed  The r e s u l t s  programme  and a new d e f i n i t i o n  and p r e s s u r e  condition  beginning,  by an e x p l a n a t i o n  instrumentation,  20,000  glycerol-water  i n the e x p e r i m e n t a l  followed  measuring  of a  investigated  circular  of 5 -  In t h e  vortices  n  influence  distribution is  < 1200.  blockage  t o show R e y n o l d s  ratio  of the  However, o f 50%, t h e  number dependency  Reynolds  primarily  f o r t h e model pressure f o r R^  ,  as  h i g h as  number i s  3000. to  increase  pressures. in  the  On t h e  blockage  profiles at  In g e n e r a l ,  the  other  ratio  become  lower  terms  end o f  Location  wall  the of  the  ratio  of  areas  particular, blockage studied  in  the of  the  number,  of  an  opposite. to  the  wake increase  The wall  pressure  confinement  number r a n g e u n d e r  study  using  and h i g h  speed  program.  layers  to  of  Reynolds  large  dye  retard,  the  tends  downstream  to  move  number, shift  as  likely  likely  ratio to  for  be  future to  effects  be  however,  in  the  25° for  investigation fruitful.  i n the  significant  in  near-wake.  501. suggests  study.  Photographs  is  evolution  i n the  promotes  which are  depth.  effect  blockage  shear  Reynolds the  still  test  the as  visualization  w h i c h c a n be as  aspect  are  the  Reynolds  an i n c r e a s e  point,  the  of well  sensitive  separating  The t h e s i s several  just  flow  Reynolds  confinement  separation blockage  the  influence  upstream with the  is  complements  that  of  hand,  in conjunction with  photography suggest  minimum as  extremely  An e x t e n s i v e injection  the  effect  In  presence  of  and s h o u l d  be  a  iv  TABLE OF CONTENTS Chapter 1.  INTRODUCTION  3.  4.  . . . .  . . . . .  1  1.1  P r e l i m i n a r y Remarks  1  1.2  D r a g R e d u c t i o n Due t o L o n g - C h a i n Polymers  2  1.3  Stationary Circular Cylinders: P r e s s u r e D i s t r i b u t i o n and Wake. . .  9  1.4  2.  Page  P u r p o s e and Scope o f t h e Investigation  12  DESIGN AND CALIBRATION OF THE LIQUID TUNNEL  15  2.1  Liquid  15  2.2  D e s i g n o f Honeycomb f o r T u r b u l e n c e Control  22  2.3  Calibration  27  Tunnel  of the L i q u i d  Tunnel  TEST PROCEDURES  38  3.1  Models  • • •  39  3.2  P r e s s u r e Measurements  43  3.3  Flow V i s u a l i z a t i o n  54  3.4  Critical  60  R e y n o l d s Number  RESULTS AND DISCUSSION 4.1  Choice of Reference V e l o c i t y Pressure  61 and - . .  62  V  Chapter  Page  4.2  Effect  4.3  Wall  4.4  Drag C o e f f i c i e n t  4.5  S t r o u h a l Number  4.6  Flow V i s u a l i z a t i o n Analysis . . .  4.7  of  Reynolds  Confinement  Number  .  .  .  .  .  Effects  79 89  .  .  .  .  .  .  .  .  .  .  91  and Near-Wake 94  C l o s i n g Comments  Ill  4.7.1  C o n c l u d i n g remarks  .  4.7.2  Recommendation study  future  for  .  .  .  .  REFERENCES APPENDIX I  69  Ill  113 117  - CONVENTIONAL PRESSURE COEFFICIENT C IN TERMS OF MEASURED P INFORMATION  126  vi  L I S T OF ILLUSTRATIONS Figure 1-1.  1-2.  1- 3.  Page A schematic diagram l i s t i n g hypotheses a t t e m p t i n g to e x p l a i n d r a g r e d u c t i o n due t o l o n g - c h a i n p o l y m e r s A summary o f l i t e r a t u r e i n d i c a t i n g the scope o f r e c e n t important c o n t r i b u t i o n s the f i e l d of flow p a s t a c i r c u l a r cylinder A schematic study  d i a g r a m showing •  the  2- 1.  A s c h e m a t i c d i a g r a m showing water s o l u t i o n tunnel  the  2-2.  Calibration plot  2-3.  A p h o t o g r a p h showing d e t a i l s o f the unit: A , a u t o t r a n s f o r m e r ; D, d r i v e P , p ump  for  the  plan  4  in 1  of 1  Venturi  4  glycerol-  meter••••  21  power motor; 23  2-4.  A p h o t o g r a p h o f the g l y c e r o l - w a t e r t u n n e l c a p a b l e o f g e n e r a t i n g R e y n o l d s number i n the range 1 - 1 8 , 0 0 0 : A, autotransformer; D, d r i v e m o t o r ; E , h e a t e x c h a n g e r ; F , f l o w d i s t r i b u t i n g vanes; H , p o r t h o l e s ; M, V e n t u r i meter; P , pump; S, s c r e e n s and h o n e y comb; T , t e s t - s e c t i o n ; V , v e n t 24  2-5.  A p h o t o g r a p h showing d e t a i l s o f the inlet: F , flow d i s t r i b u t i o n vanes; coarse screen; S £ , fine screen; H , honeycomb  tunnel S^, 28  2-6.  Arrangement f o r hot f i l m probe c a l i b r a t i o n : F , f e e d worm; P , p r o b e ; S, f l u m e ; V , s p e e d c o n t r o l gearbox 30  2-7.  C a l i b r a t i o n data TSI 12 39W  for  the  hot  f i l m probe ' 31  v i i  Figure •2-8.  2-9.  2- 10.  3- 1. 3-2. 3-3. 3-4. 3-5.  Page T y p i c a l p l o t s showing the e f f e c t o f s c r e e n s and honeycomb i n i m p r o v i n g v e l o c i t y p r o f i l e i n the t e s t - s e c t i o n  3  3  A comparison o f v e l o c i t y p r o f i l e s at t h r e e d i f f e r e n t s t a t i o n s i n t h e t e s t - s e c t i o n and f o r two v a l u e s o f mean f l o w v e l o c i t y . Note a l a r g e r e g i o n o f e s s e n t i a l l y u n i f o r m flow which i s d e s i r a b l e f o r the p l a n n e d t e s t programme . .  34  R e p r e s e n t a t i v e p l o t s showing v a r i a t i o n o f the t u r b u l e n c e i n t e n s i t y i n the t e s t section  36  T y p i c a l models t i o n study  41  used  i n the  flow  A p h o t o g r a p h showing t h e models surface pressure d i s t r i b u t i o n  visualizaused  in 44  A d i a g r a m showing c o n s t r u c t i o n a l d e t a i l s o f a t y p i c a l p r e s s u r e measurement model . .  45  A schematic diagram of pressure transducer  47  the  Barocel  A p r o c e d u r e f o r compensation of the e l e c t r o n i c d r i f t o f the p r e s s u r e m e a s u r i n g system  51  3-6.  A l i n e drawing o f the i n s t r u m e n t a t i o n s e t up u s e d d u r i n g s t a t i c p r e s s u r e measurements 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 . . . . 53  3-7.  Measurement o f mean f l o w r a t e u s i n g v e n turimeter: B, Barocel pressure transducer; D, d i g i t a l d . c . v o l t m e t e r ; E , h e a t exchanger; F , f i l t e r ; H , h e a t - s i n k ; P , power s u p p l y ; S, s i g n a l c o n d i t i o n e r ; V , V e n t u r i meter 55  3-8.  A p h o t o g r a p h showing probes  3-9.  A s k e t c h showing the equipment l a y o u t d u r i n g the flow v i s u a l i z a t i o n . . . . . . .  the  dye  injection  ^7 58  viii  Figure 4-1.  4-2.  '  -  .  Page  An i l l u s t r a t i o n showing p o s s i b l e e r r o r s i n t r o d u c e d by n o n - u n i f o r m i t y o f t h e velocity profile  66  R e p r e s e n t a t i v e p r e s s u r e p l o t s comparing p r e s e n t r e s u l t s w i t h t h o s e by Grove et a l . low R e y n o l d s number o f 175. Note a r e l a t i v e s e n s i t i v i t y o f t h e p r o p o s e d p r e s s u r e c o e f f i c i e n t to d i f f e r e n c e s i n test conditions 70 3  4  a  4-3.  '  t  a  A comparison of present r e s u l t s with by E l - S h e r b i n y a t a r e l a t i v e l y h i g h R e y n o l d s number o f 15 x 1 0  those 71  3  4-4.  S u r f a c e p r e s s u r e d i s t r i b u t i o n as a f f e c t e d by the R e y n o l d s number f o r a g i v e n b l o c k age r a t i o : a) S / C = b) S / C = 3 . 3 % ; c) S / C = 6.61 ; d) S / C = 1 2 . 5 % ; e) S / C = 25% ; f) S / C = 501 .  2% ;  4-5.  P r e s s u r e p l o t s as a f f e c t e d a g i v e n R e y n o l d s number: a) b) c) d) e)  4-6.  R == n R == n R == • n R == n R == n  by b l o c k a g e  73  at  3000; 1200; 400; 200; 30 ,  E f f e c t o f w a l l c o n f i n e m e n t on t h e minimum and b a s e p r e s s u r e s , 10 < R < 1 8 , 0 0 0 : n  a) b) 4-7.  minimum p r e s s u r e ; base p r e s s u r e  ......  V a r i a t i o n o f the p r e s s u r e drag c o e f f i c i e n t w i t h R e y n o l d s number and b l o c k a g e  87 88  90  ix  Figure  4-8.  4-9.  4-10.  4-11.  .  '  P  a  g  e  V a r i a t i o n o f t h e S t r o u h a l number w i t h b l o c k a g e a t the l o w e r end o f the R e y n o l d s number r a n g e (R < 1000)  93  A comparison o f measured S t r o u h a l w i t h t h o s e by o t h e r i n v e s t i g a t o r s  95  Onset of v o r t e x the b l o c k a g e  shedding  as  data . . . . . . . .  affected  by 96  A t y p i c a l p h o t o g r a p h showing f o r m a t i o n o f Foppl v o r t i c e s behind a two-dimensional c y l i n d e r ; R = 186, S / C = 50%  9  8  9  9  n  4-12.  A f l o w v i s u a l i z a t i o n s t u d y showing d e v e l o p m e n t and i n s t a b i l i t y o f v o r t e x w i t h R e y n o l d s number ( S / C = 15%): a) R = 4; b) R = 10; c) R = 17; n ' n ' n ' d) R = 21; e) R = 31; f) R =42; • n n n ' g) R = 56 ; h) R = 60 . n ' n A p h o t o g r a p h o f the c l a s s i c a l Karman v o r t e x s t r e e t ; R = 6 0 , S / C = 15% J  J  J  J  & J  4-13.  ring  J  J  103  n  4-14.  4-15.  4-16.  P o s i t i o n o f s e p a r a t i o n as a f f e c t e d by R e y n o l d s number .and w a l l c o n f i n e m e n t : a) f l o w v i s u a l i z a t i o n d a t a ; b) b a s e d on s u r f a c e p r e s s u r e p l o t s ( F i g u r e 4-4) E f f e c t o f b l o c k a g e on e v o l u t i o n o f wake a t a f i x e d R e y n o l d s number o f a) S / C = 25% ; b) S / C = 50% Photographs confinement vortices: a) R = 85, n  b) 4-17.  R^ = 150,  the 104 105  the 100: 107  emphasizing influence of w a l l on e v o l u t i o n o f the F o p p l S / C = 25%; S / C = 50%  Dependence o f v o r t e x number and b l o c k a g e  length  1  on t h e  0  8  Reynolds 110  X  L I S T OF TABLES  Table  3-1  Page P r e s s u r e models used i n the t e s t programme, c o r r e s p o n d i n g b l o c k a g e and a s s o c i a t e d R e y n o l d s number r a n g e a t t a i n e d t h r o u g h the v a r i a t i o n o f mean f r e e s t r e a m v e l o c i t y and c o n c e n t r a t i o n of the working f l u i d  4  2  xi  ACKNOWLEDGEMENT  I would l i k e my  gratitude  for  the  to  and s i n c e r e  enthusiastic  thesis.  this  thanks  guidance  programme and h e l p f u l the  take  o p p o r t u n i t y to to  P r o f e s s o r V . J . Modi  given  throughout  suggestions during  His help  express  the  and encouragement  have  the  research  preparation of been  invaluable. The gratefully greatly  cheerful  acknowledged.  accelerated Finally,  wife,  Ragaa,  difficult The  assistance  the  special  Their  Research Council  of  skillful  appreciation is  staff  is  assistance  was  Canada,  extended  and u n d e r s t a n d i n g  and t o my m o t h e r ,  investigation  the.technical  r e s e a r c h programme.  f o r her patience  times  of  Mary,  for her  s u p p o r t e d by t h e Grant No.  A-2181.  t o my during encouragement.  National  L I S T OF SYMBOLS  overheat tunnel total  ratio  cross-sectional drag  sectional  area  coefficient pressure  drag c o e f f i c i e n t ,  .  D /(l/2)pU D 2  p  skin  friction  coefficient  percentage concentration of s o l u t i o n by w e i g h t (P  0  - P )/(P r  0  -  glycerol-water  P ) r  conventional pressure (P " PJ/(l/2)pU  coefficient,  2  e  (P  e  r o  -  P )/(l/2)pU  2  r  mean f l u c t u a t i n g p r e s s u r e  coefficient  honeycomb c e l l - s i z e • cylinder sectional  diameter pressure  eccentricity vortex  of  shedding  drag  elliptic  cylinder  frequency  length parameter i n Roshko's d e f i n i t i o n ' u n i v e r s a l ' S t r o u h a l number honeycomb p r e s s u r e  drop  coefficient  of  xiii  I  length  L  m a c r o - l a y e r thickness i n polymer induced drag r e d u c t i o n h y p o t h e s i s .  L  length base  of  honeycomb  scale  of  turbulence  pressure  P  m  minimum p r e s s u r e  P  Q  stagnation  P  r  P  Q  P  ro  R , c  pressure,  pressure  s t a t i c p r e s s u r e at r e f e r e n c e p r e s e a t c a s e r = 50  at  6 = 0  tap,  in  s t a t i c p r e s s u r e on c y l i n d e r s u r f a c e from f r o n t s t a g n a t i o n p o i n t static R  Q  pressure  the  at  angle  9  of u n d i s t u r b e d stream  c o l d and o p e r a t i n g r e s i s t a n c e respectively  of  the  probe,  R^  R e y n o l d s number b a s e d on honeycomb  cell-size  R  g  R e y n o l d s number b a s e d on honeycomb  cell-length  R  n  R e y n o l d s number, U D / v  R ,  c r i t i c a l R e y n o l d s number c o r r e s p o n d i n g onset of v o r t e x shedding  S  diametral cross-sectional  S  R o s h k o ' s u n i v e r s a l S t r o u h a l number,  S  n  Strouhal  to  area fh/U  number, f D / U  •T  temperature of  u  rms v a l u e direction  solution  of v e l o c i t y  fluctuations  i n downstream  xiv  average v e l o c i t y i n t e s t - s e c t i o n based f l o w r a t e as g i v e n by o r i f i c e m e t e r characteristic Grove e t  velocity  on  as p r o p o s e d by  al.*^  separation velocity S t r o u h a l number undisturbed free d.c. voltage anemometer  in.Roshko's universal  stream  output of  velocity constant  temperature  distance  from end o f honeycomb i n downstream d i r e c t i o n  vertical  co-ordinate,  angle  attack  of  origin  at  bottom of  test-section  angular l o c a t i o n of p r e s s u r e tap w i t h r e f e r e n c e to f r o n t s t a g n a t i o n p o i n t angular l o c a t i o n of s e p a r a t i n g shear l a y e r w i t h r e s p e c t to r e a r s t a g n a t i o n p o i n t thickness  of  differential  laminar sublayer pressure  across  Venturi  meter  e r r o r i n pressure at of v e l o c i t y p r o f i l e  9=0  e r r o r i n p r e s s u r e at of v e l o c i t y p r o f i l e  8=6  e r r o r i n p r e s s u r e at of v e l o c i t y p r o f i l e  0 due t o n o n u n i f o r m i t y  dynamic v i s c o s i t y  glycerol-water  of  due t o n o n u n i f o r m i t y  due t o n o n u n i f o r m i t y  solution  kinematic v i s c o s i t y y/p  of  glycerol-water  kinematic v i s c o s i t y  of  water  density  of  glycerol-water  solution  solution, ,  1.  1.1  Preliminary  Although  INTRODUCTION  Remarks  flow  study  for  years  there  are  several  past  a circular  resulting aspects  c y l i n d e r has  in a vast  body o f  associated with  been u n d e r  literature,  the  problem which  remain v i r t u a l l y u n e x p l o r e d  o r demand more a t t e n t i o n .  of  to  such  a s p e c t s was  associated with (i)  as the as  the d e s i g n platforms;  of  number f l o w s  as  s t r u c t u r a l members  problems encountered  for  biological  Even  i n the  free  flow, is  mechanical  absence of  has  of  several  pressure  facets  Reynolds  vortices  unrecorded,  remains of  the  complicating  blockage,  which are  d i s t r i b u t i o n on t h e  by t h e  systems.  factors  pulsatile  character  l o n g - c h a i n p o l y m e r s , e t c . , the  the  a study  any o t h e r  stream t u r b u l e n c e ,  presence  affected  fluid  challenging. surface  number i n the  above  mentioned  it  of  range  f o r m a t i o n and i n s t a b i l i t y although  in:  off-shore  (iii)  c o r r e l a t i o n with  in  through  the submarine d e t e c t i o n system u s i n g a c a b l e s u p p o r t e d h y d r o p h o n e e x p o s e d to an o c e a n current;  example, as  low R e y n o l d s  light  (ii)  the  it  brought  One  problem For  a cylinder S - 40  of  would be  problems.  of  the  and  its  Foppl  quite  useful  2  In t h e the  present  interest  case  mechanics  of  their  influence  on the  very  bluff  low R e y n o l d s  through a d e t a i l e d ponding  fundamental  for  comparison In t h i s  available  study  of  vividly  brings  knowledge. a p l a n of  to  to  it  for  i n the the  drag of  the  present  of  the  Long-Chain  Although  there  numerous  friction  drag r e d u c t i o n p r o p e r t y ,  common:  they  a basis polymers. and  described.  current  of  the This  literature This  available  is  information,  formulated.  Polymers  in a liquid  certain  different  are a l l long c h a i n  as  i n o u r search- f o r  thesis  presence  obtain  low R e y n o l d s ' n u m b e r s .  gaps  light  is  drag r e d u c t i o n  the  realized  corres-  long-chain  are b r i e f l y  a body submerged  70% i n the are  of  i n t r o d u c t i o n to  Drag R e d u c t i o n Due t o  much as  the  t a s k w o u l d be t o  the e f f e c t s o f  vorticity  quickly  polymers  of  the  of  absence  phenomenon  attention  Finally,  Friction  was  by  in p a r t i c u l a r ,  that  a c i r c u l a r c y l i n d e r at  study  it  on  literature  first  explain  by a s h o r t  past  and,  and d i s s i p a t i o n  However,  the  in evaluating  Chapter the  on f l o w  motivated  i n f o r m a t i o n which then would s e r v e  theories  followed  by as  in general  generation  O b v i o u s l y , the  the  1.2  bodies  numbers.  was  long c h a i n polymers  i n f o r m a t i o n even i n t h e  unavailable.  is  investigation  i n the e f f e c t s of  fluid  at  the  they  solutes all  polymers.  can  reduce  additives! with  have  one  the  skin  thing  in  3  The phenomenon was as  i n 1948  when he  polymer  solution  solvent  alone.  first  found the  r e p o r t e d by T o m s f r i c t i o n loss  t o be s u b s t a n t i a l l y Although this  is  less  1  as  early  in pipes  with  than that  r e f e r r e d to  as  with  the  'Toms Phenomenon'  2  actually  Mysels  napalm d u r i n g the  results  the  until  was  the  war  years  much  the  cation  of  the  the  (1945)  been  being  concept  discover  the  the  drag  is  further  accentuated  i)  w h i l e pumping  i n saving  the  researched  l a r g e l y due t o  reduced,  mechanism o f  it  b u t was u n a b l e  actively  fluid  marine p r o p u l s i v e e f f i c i e n c y .  that to  interest  to  to  publish  later.  The phenomenon has years,  first  there  drag  by t h e  no g e n e r a l  quantitative results widely d i f f e r ;  appli-  and i m p r o v i n g  A l t h o u g h everyone is  recent  potential  pumping power  reduction.  fact  the  in  agrees  agreement  The c o n f u s i o n  as is  that:  by d i f f e r e n t  investigators  3  ii)  even t h e same i n v e s t i g a t o r i s o f t e n u n a b l e t o r e p r o d u c e h i s d a t a as p o l y m e r p r o p e r t i e s change w i t h t i m e and s h e a r s t r e s s ^ ; 3 -  iii)  c o n v e n t i o n a l f l u i d dynamic i n s t r u m e n t s l i k e p i t o t t u b e , v e n t u r i m e t e r , hot f i l m p r o b e s , e t c . show anomalous b e h a v i o u r ~ 7 . D  Most the  investigators  two main h y p o t h e s e s ;  concepts described  as as  indicated follows:  e x p l a i n the each  phenomenon u s i n g  subclassified  in Figure  1-1.  into  Briefly  two  they  one  of  basic  c a n be  HYPOTHESES  EXPLAINING  DRAG  REDUCTION  /  TURBULENCE .SUPPRESSION HYPOTH ESES  SOLUTION H A S VISCOELASTIC PROPERTIES Figure  WALL LAYER MODIFICATION HYPOTHESES  MODIFICATION IN THE TURBULENCE STRUCTURE 1-1  WALL ABSORPTION REDUCTION OR IN THE WALL MOBILE LAYER GENERATED TURBULENCE  A schematic diagram l i s t i n g hypotheses a t t e m p t i n g to e x p l a i n d r a g r e d u c t i o n due to l o n g - c h a i n p o l y m e r s .  5  (a)  Turbulence Suppression  Hypotheses  (a-^)  S o l u t i o n has V i s c o e l a s t i c  tions  are v i s c o e l a s t i c  kinetic energy (a.2)  energy, of  and hence a b l e  normally lost  elongation  interact  with  the  characteristics.  dimensions  of  microscales.  solution.  In p r a c t i c e  of  the  Hence,  coiled  to  form  supermolecular  (b)  Wall  (b-j.) wall  Wall  are  (b2)  the  of  the  potential  Polymer  and m o d i f y to  be  the effective,  c o m p a r a b l e to K o l m o g o r o v  higher molecular  weight  these  in  dimensions  with  their  shear  stretching  neighbours  to  postulated.  Hypotheses  considered  to  Layer: be  making i t close  Characteristics  significantly smoother to  of  altered,  or t h r o u g h  the w a l l , r e s u l t i n g  the  by  orienin a  layer.  R e d u c t i o n i n the  appears  to  example  by G a d d  Polyuos"'"^  a part  this  hypothesis,  entwined  polymer molecules  mobile w a l l  eddies  a g g r e g a t e s has b e e n  absorbtion of molecules of  the  A b s o r b t i o n or M o b i l e  surface  tation  possess  solu-  deformations.  s h o u l d be  justify  Modification  as  Obviously for  even the  do n o t  molecules,  store  flow  turbulent  molecules  l o n g - c h a i n polymers  Polymer  Turbulence Structure:  turbulence  the  i n the  to  o r more g e n e r a l  M o d i f i c a t i o n i n the  molecules  Properties:  be t h e 8  (1974)  most  Wall  Generated Turbulence:  widely  (1971),  accepted.  Landahl  when t a k e n  9  (1972),  Several Hoyt  1 0  This  theory  reviews, (1972)  for  and  t o g e t h e r w o u l d c o v e r maj o r i t y  6  of  the  publications  results  i n the  can be b r i e f l y  field.  Some o f  summarized as  the  follows:  more  interesting  Walles  and  12 Spangter  (1967)  reducing  fluid  on d r a g core  wall so  into  the  (reduction)  region  effect  seem t o  of  until  the  suggest  wall  while  layer  injection  b u l k flow  has  (1970).  Later's  f r i c t i o n drag f o r pipes  conveying  a dilute  to  of  for  polymer  a given  an i m m e d i a t e  effect  the  same f l u i d little  It  was  experiments  of  solution  different of  fixed  R e y n o l d s number,  the p i p e diameter  exist.  a drag  relatively  comparing  value  of  of  consist  concentration.  there  is  there  must be  be  length is  laminar  enough  <5 <  depending  layer  6 still  (macro-layer)  exists  macro-layer thickness  predominate. that  the  damped by the e n t a n g l e d  sublayer  than the small  L of  g o v e r n e d by the  such t h a t But  if  6 >  the  long molecules.  L.  L then  If the  the  eddies  i n the  on t h e  concentrations  region of  the  L-6  polymer  assumed  eddying  or  a  smaller  number  stability  large will  This He  larger  sublayer  length  However,  Reynolds  R e y n o l d s number i s  L then  flow. i n which  w h i c h may be  ceases  some o t h e r  new l e n g t h  p a r a m e t e r must  He  a critical  below w h i c h d r a g r e d u c t i o n  concluded that  in  diameters  d r a g r e d u c t i o n phenomenon.  motion  the  o r no  parameter c o n t r o l l i n g the  a fixed  into  p o l y m e r has had enough t i m e t o d i f f u s e t o t h e 13 Kowalski (1968) a r r i v e d a t t h e same c o n c l u s i o n , 14  d i d Van D r i e s t  that  has  injection  the  region.  noticed  that  enough  be damped solutions.  is will such  7  A r u n a c h a l a m et the  drag reducing  used  a  arrive et  al.  also  showed a t h i c k e r w a l l than that  for  the  n o n d i s t u r b i n g photochromic  dye  trace  at  16 al.  (1972)  X J  the  solution  conclusion  (1972)  a change  using i n the  visually.  spectrum  On t h e  analysis  turbulent  solvent  for  alone.  technique  other  i n pipe  sublayer.  layer  to  hand, Fortuna  flow  More  They  observed  interesting  was  17 the  experiment  dye  i n the  the  turbulent  by L a t t o and E l R i e d y  boundary l a y e r  compared t o  diffusion  that  of  a consensus  region  of  of  the  mechanism  is  not  clear. of  the  of  and showed is  a  that  suppressed  can be c o n c l u d e d  d i l u t e d polymer  literature  i n polymer  of  extensive  information  on t h e  solutions on t h e  remain v i r t u a l l y u n e x p l o r e d ,  that  an e x i s t e n c e  drag r e d u c t i o n  submerged  metries  it  i n the  bodies the  plate  solution  opinion concerning  drag r e d u c t i o n  A review  polymer  discussion  However, still  of  a flat  who i n j e c t e d  water.  From the above is  over  (1976)  of  there  a major  solutions.  on a m o l e c u l a r  f l u i d dynamics suggests  subject,  that,  bluff  except  for  one  study  level  of in  body  a few  spite geo-  isolated  18 papers. of  Gadd  polymer  cylinder. an u n s t e a d y  (1966)  solutions  was  on v o r t e x  His r a t i o n a l e process,  model w o u l d a t t a i n  the  the  for time  first  shedding  the  study  dependent  to  the  effect  behind a c i r c u l a r was:  as  terms  particular significance  in  turbulence any  is  theoretical  in turbulent  drag  8  reduction.  He e x p e c t e d  drag  effectiveness  (in  terms  of  number by the  same amount,  reducing solutions  drag reduction) however,  his  to  of  equal  reduce  Strouhal  experiments  failed  3  to  support  the  this  frequency  c o n d i t i o n of decreased, of  the  conclusion.  of  vortex  the  shedding  solution  a reverse  (POLYOX). 19 al.  a freshly  with value  its  mixed  41. of  be a l w a y s  higher  formation of  than 41,  the  c o r r e l a t i o n with solutions  .unfortunate of  onset of  surface has  because  layer  course,  to  assess  it  w o u l d be n e c e s s a r y  the  of  wires,  of  suggests  have,  as  at  generation  of  the  lower  increases  Newtonian  of  that  with  in  of  drag  presence  a reference,  the  to  solution.  subject its  long-chain  all. and  the  the  and  character  phenomenon  influence  age  bodies  distribution  on t h e  Reynolds  is  but  the  aging  R e y n o l d s number  the  no a t t e n t i o n  some l i g h t  to  critical  thus  pressure  process  the  the  critical  shedding  exceeds  behind b l u f f  and hence on t h e  Of  frequency  study with the  found  the  corresponding experiments  received  the  on  the  polyethyleneoxide  irrespective  vortices  (1970)  observed with  of vortex  point,that  literature  v o r t i c i t y may throw  boundary  t r e n d was  Guar r e s i n . s h o w e d  The a c c u m u l a t e d  polymer  the  Unfortunately,  solutions  of  the  to  when f r e s h  concluded that  solution  degradation  of  be dependent  Through a l a t e r  (1976)  number c o r r e s p o n d i n g to in  to  polymer s o l u t i o n :  however,  Kalashnikow et  K a l a s h n i k o w and K u d i n  This  is  dissipation of  the  reduction. of  polymer  corresponding  9  information Newtonian seem,  a bluff  fluid,  such  Reynolds  for  mostly  fundamental  step  Newtonian  as  flow  particular  is  affected  However,  normally a  s u r p r i s i n g as  i n the  lower  v i r t u a l l y missing. to  Reynolds  number w i t h  Cylinders:  interest  i n the  may  the  Obviously  evolution  wake-body  it  end o f  understand  by t h e  on t h e  Circular  Historically,  solvent,  information  s h o u l d be  emphasis  Stationary and Wake  i n the  water.  number s p e c t r u m  t h e n , the f i r s t  1.3  body  of  the  a  interaction.  Pressure  flow  past  Distribution  a bluff  body  1  20 goes b a c k t o  the  fifteenth  sketched  a row o f  However,  it  that  phenomenon  the  the  was  pioneering  vortices  only  found  d i a m e t e r of the  in  the  field  tributions  wake later  of  Ever has  led  resulting  periodicity  . of  circular cylinder  since, to  a bluff  part  c o n t r i b u t i o n by S t r o u h a l  with  stream.  the  when L e o n a r d o da  some q u a n t i t a t i v e 21  number c o r r e l a t e s  fluid  i n the  towards  Strouhal the  century  theoretical  a continuous  in a vast  the  body. last  expression The  the  vortex  and p r a c t i c a l of  century through  well-known shedding  and v e l o c i t y  stream  body o f  of  Vinci  of  interest  important  literature.  the  This  conhas  been r e v i e w e d r a t h e r a d e q u a t e l y by s e v e r a l a u t h o r s i n c l u d i n g 22 23 20' 24 25 Rosenhead , Wille , Marris , Morkovin , Parkinson and Cermak  26  .  The c o l l e c t e d  literature  suggests that,  in  general,  10  nature wake  of  the  geometry  of  bluff  to  have  simple  body  the  configuration  boundary l a y e r  Reynolds  numbers.  summarizes the  carried have  more  present  butions,  This  thesis.  out h i s  for  cylinder  show q u e s t i o n a b l e  trends.  study  by Grove and h i s  it  l i m i t e d to  the  information  and i n i t i a t i o n are  several  cedure,  so  of  vortex  unresolved  < 175  are  of  the  hand,  appears  the  i n the  only  about  higher which relevant two  contriThorn  fortunate  surface  to  of  175  a  Reynolds  be more thus Foppl  to  His  although  formation of  shedding.  questions  blockage,  modern t i m e .  on t h e  other  its  fundamen-  noteworthy.  R e y n o l d s number o f  concerning  the  important  On t h e  the  area  v a r i a t i o n with the  associates  a single  i n the  and was n o t  distribution  and i t s  some o f  relatively  R  a l ? \  i n 1933  appears  Unfortunately,  from F i g u r e 1-2  range  instrumentation  pressure  to  contributions  In the  study  dynamically  distribution,  limited  apparent  experiments  the  fluid  separation.  by Thorn"^ and Grove et  dimensional  is  is  important  sophisticated  results  all  and t h e  type  are  i n the  and  p r o b a b l y because of  circular cylinder,  etc.  frequency  The c i r c u l a r c y l i n d e r  information concerning pressure geometry,  shedding  important parameters  most a t t e n t i o n ,  a stationary  n e a r wake  to  vortex  f l u i d mechanics.  symmetric  even w i t h  loading,  form t h r e e  received  distinctive  tal  surface  two number  the  careful, missing vortices  Furthermorethere the  low R e y n o l d s  data reduction  number s t u d i e s ,  proand  11  10  10  10  40 S/C  3  n  10  10  10  10  22  ., WAKE GEOMETRY  ROSENHEAD  4 1.7X10  2.IX 10  [1930]  27 F A G E & F A L K N E R [1931] 28  7X10'  2X10*  FLACHSBART 29  2.5X10  LI NKEet a l . 3.5  175 C  p  , S/C  5 10  5 2.1X10  |c ,c p  THOM  40  [1933] 31  F  4  10  G I E DT  GEOMETRY  WAKE  GEOMETRY 40  IC  ROSHKO 175 5X10 C  P' F' D' S C  C  9  1.2X10"  10 c  p  . c  , S/C 2.2X10  0-23  2.6  1-2.  A summary o f l i t e r a t u r e i n d i c a t i n g the scope of r e c e n t important contributions i n the f i e l d of flow p a s t a c i r c u l a r cylinder.  [1953] 33  6X 10  Figure  [1951] 32  2X10'  0-1  [1932]  30  ( 1.1 - 7.6 % )  WAKE  [1932]  4X10  5  5X10  5  TANEDA  [1955] 34 G R O V E e t a l . [1963] 35 ACHE NBACH [1968] 36 E L - S H E R B I N Y [1972] 37 F A R E L L et a l . [ 1 9 7 6 ] 38 F A R E L L e t a l . [1977] 39 H U N E R e t a l . [1977]  12  the  definition  of undisturbed free  and p r e s s u r e  employed by  1.4  and Scope  Purpose  The p r o j e c t aims for  at  the  Investigation  two main o b j e c t i v e s .  i n the  low R e y n o l d s number r a n g e .  and e f f o r t  the  of  were expended construction,  tunnel  particularly  suitable  Considerable  i n f i n a l i z i n g the modifications,  it  design,  and c a l i b r a t i o n  tunnel. stage  confinement  instability  of  Ka'rman v o r t e x  vortices  Finally, technique  the  on the  Primarily  surface  of  the  flow  the  test  investigators trends.  character  elongation  resulting the  pressure  i n the  attention  of  and  focussed the  around 5-20,000  and  2-501. visualization  results. are  still  using  the  and movie  included for  and s h o u l d p r o v e u s e f u l studies  dye  injection  photography  When a v a i l a b l e , r e s u l t s c o m p a r i s o n and to  The i n f o r m a t i o n o b t a i n e d  more c o m p l i c a t e d  is  of  classical  d i s t r i b u t i o n of  R e y n o l d s number r a n g e  ratio  an i n v e s t i g a t i o n  formation,  Foppl v o r t i c e s  in conjunction with  complements  establish  concerned with  street..  i n the  blockage  is  effects  the  on c o r r e l a t i n g  other  a liquid  Firstly,  studies  wall  for  of  of  The n e x t  in  them.  design  supervision  the  velocity  the  time  of  has  stream  with  as  is  a basis  long-chain  by help  fundamental of  comparison  polymers,  13  pulsatile briefly  flow,  etc.  summarizes  mentioned  the  plan of  earlier. study.  Figure  1-3  W A L L  C O N F I N E M E N T  F O R L O W  Design of Test  C I R C U L A R R E Y N O L D S  Design  a n d Calibration Facilities  * Glycerol-water  C Y L I N D E R S N U M B E R S  Reynolds  Number  (calibration)  * Pressure  Effect  Blockage  1  Distribution  Strouhal  drag  *  * Approximate of  location  separation  Critical number vortex  N u m b e r Reynolds  o f onset of shedding  Flow  Visualization  * Formation,  A schematic of  study.  d i a g r a m showing  the  plan  evolution  and i n s t a b i l i t y o f Eoppl  shear  1-3.  Effect I  vortices  * Location  Figure  P r o g r a m m e  I  anemometer  Pressure  Test  solution  Venturimeter  * Hot-film  A T  o f Models  tunnel *  E F F E C T S  of  layer  * Approximate of  separating  evaluation  the Strouhal  number  15  2.  As tion  DESIGN  p o i n t e d out b e f o r e  and c a l i b r a t i o n o f  formed one This  of  chapter  aspects  of  involved  the  the  is,  therefore,  features. geometry tion  of  at  tunnel  of  the  combs  to  level  are d i s c u s s e d .  restrict  uniform  Liquid  to  One salient and  by a d e s c r i p -  control  systems.  of  the  stream t u r b u l e n c e  to  a  the  honey-  permissible  calibration plots to  the  are regions  .  Tunnel  for  the  t u n n e l were  low R e y n o l d s number s t u d i e s  necessary  followed  details  important  selection  Finally,  flow.  more i m p o r t a n t  specifications  are e x p l a i n e d  free  project.  t o more  w h i c h p r o v i d e some, a p p r e c i a t i o n as  Specifications the  design  tunnel  entirety.  attention  procedure for  the  the  though  in their  confine  the  construc-  and c o n s t r u c t i o n a l  power d r i v e and t e m p e r a t u r e  details  2 .1  be c o v e r e d  of  solution  of  and h e n c e ,  beginning,  Next,  presented  objectives  numerous  f o r c e d to  the  the  a glycerol-water  i n t r o d u c i n g some o f  cannot  In t h e of  supervision  programme. The d e s i g n  are often  relevant,  design,  principal  aims  and  of  AND CALIBRATION OF THE LIQUID TUNNEL  have  planned.  a f a c i l i t y w i t h the  largely  dictated  For t h i s  following  it  by  was  characteristics:  16  (i)  The t u n n e l s h o u l d be c a p a b l e o f p r o d u c i n g a maximum v e l o c i t y o f a r o u n d 30 cm/s l e a d i n g t o R e y n o l d s numbers i n t h e r a n g e 1 - 2 0 , 0 0 0 b a s e d on t h e c y l i n d e r d i a m e t e r .  (ii)  The t u n n e l t e s t - s e c t i o n s h o u l d be l a r g e enough t o p e r m i t wake and b l o c k a g e . s t u d i e s .  (iii)  The t e s t - s e c t i o n w a l l s s h o u l d be f l a t to allow' flow v i s u a l i z a t i o n o p t i c a l methods.  (iv)  The v e l o c i t y p r o f i l e s h o u l d be s u f f i c i e n t l y f l a t to permit uniform flow s t u d i e s . The t u r b u l e n t i n t e n s i t y s h o u l d be l e s s t h a n 2%.  (v)  The t e s t - s e c t i o n s h o u l d be p r o v i d e d w i t h a s i m p l e model s u p p o r t s y s t e m . When mounted i n t h e t e s t - s e c t i o n , a model s h o u l d be readily accessible.  (vi)  T h e r e s h o u l d be a p r o v i s i o n f o r i n t r o d u c i n g p r e s s u r e , v e l o c i t y and o t h e r m e a s u r i n g instrumentation.  B a s e d on t h e s e water  solution  desired  range  diameter 2-1).  as of  The c h o i c e a degree as  Primarily  Reynolds  velocity  i n the  of  flexibility,  tunnel  designed  produce  to  test-section  of  working to  a  characteristics  of  the  of  the  consisting  a pump and a d r i v e  but  the  three  r e t u r n system; motor.  the  on c y l i n d e r  only  consists  fluid  glycerol-  based  concentration  by the  tunnel with  number,  test-section; of  was  of  governed the  criteria a liquid  a working f l u i d  and a v e r a g e  provided extent,  sufficiently through  (Figure fluid  certain power  subassemblies: and t h e  power  unit. the  unit  vent  Figure  2-1.  A s c h e m a t i c d i a g r a m showing water s o l u t i o n t u n n e l .  the  glycerol-  18  The t e s t - s e c t i o n 2.1  m (6.9  enough (24  to  in.  ft.)  is  long,  1.9  produce the  x 6 in.).  built  inside  Both the  thermally s t a b l e  glass  flow v i s u a l i z a t i o n . each w i t h to  a collar  prevent  front  30 cm a p a r t , a model at  This  permits  as  carry  screens the  at  tunnel.  In a l l  duct  and c o n t r o l  at  fluid  14 and 18,  attainment followed located  test-section  and honeycombs  diverging  size  the  inlet  3.8  7.5  to  intensity  facilitate  stations, in  and low  distributing the  supporting  delay  vanes,  cm  to  the separation  screens  helped  (0.32  turbulence  entrance  of  mesh-  towards  distribution.  This  was  cell-size)  f i n e r mesh  screen.  g o v e r n e d by t h e  al?^'^  The  maximum p e r -  i n accordance with  p r o c e d u r e p r o p o s e d by Lumley et  cm d i a . ) ,  test-section.  Two b r a s s  (<2%)  are  and an O - r i n g  three  effectively  honeycomb were  missible . turbulence  ports  incorporated in  cm downstream from t h e the  (2.5  cm a p a r t ,  cm  homogeneous  three  i n t r o d u c e d at  of uniform v e l o c i t y  of  flat,  profile  flow  distribution.  located  rear walls  to  i n the  9 v a n e s were  the  61 cm x 15.2  flexibility  by a 15 cm l o n g honeycomb  dimensions  design  were  of  cm x 61 cm)  p r o v i s i o n of  locations  walls  and wide  a model s u p p o r t  To promote u n i f o r m v e l o c i t y intensity  (88  a reasonable  different  thick,  and t h e  optically  panels  serving  in.)  cross-section  They a l s o  leakage.  four p l e x i g l a s  cm ( 3 / 4  provided with recess-mounted and  of  Like  the screens,  19  honeycomb a l s o profile  tends  through flow  not p a r t i c u l a r l y were  resistance,  efficient.  top  face  of  the  smaller portholes, drilled  i n j e c t i o n system  the  outlet,  providing  section for  carried  a 10.2  a vent  used the  (8.9  to as  over p r e s s u r i z a t i o n of  heat  as  the  end o f  comprising of m x 10.2  cm PVC p l a s t i c  exchanger.  to  pipe  With the  cm p l u g s ,  a heat cm,in  were  test-section. film  61 cm x 15.2  that  at  end o f  the the  cm  for  fluid air  working f l u i d an e f f e c t i v e  inlet) test-section  accommodate route  At  through a  bubbles.  during  check  plexiglas is  the  exchanger  converging  return  section  and a V e n t u r i  meter.  c o n j u n c t i o n w i t h a 1.4 m  formed an a n n u l a r s i n g l e coolant  probes,  test-section.  the  power d r i v e s y s t e m  A copper p i p e , 1 . 6 x 17.8  the  located  several  PVC d u c t  f o r the  against  essentially  of  Exit  t u n n e l and s e r v e d  L o c a t e d between  portholes  the  p r o v i d e an e s c a p e an i n l e t  is  conducting tubings.  cm d i a . )  of  and t h e  of  (same as  filling  section  1.6  cm d i a .  w i t h vanes  velocity  process  i n i n t r o d u c i n g hot  smooth t r a n s i t i o n .  e x p a n s i o n as w e l l also  top w a l l  and p r e s s u r e  to  the  In a d d i t i o n ,  rectangular section  changes  converging  was  tunnel.  the  honeycomb and models  large  which c o u l d take  dye  gradually  Screens,  proved u s e f u l  the  however,  t h r o u g h two  and t a p p e d i n t h e  These openings  It  promote u n i f o r m i t y o f  readily accessible  on t h e  also  to  pass  s u p p l i e d by a w a t e r  main,  20  it  was  fluid  possible  to  maintain temperature  within ±0.1°C.  radiator  PVC elbows  free  contraction  connections.  ratio  of  4:1  the working  and s e c t i o n s  hose p r o v i d e d r e l a t i v e l y  vibration  of  easy  of  a n t i c o r r o s i o n and  The b r a s s V e n t u r i  was  designed  the  meter  a c c o r d i n g to  with a  the  ASME  42 specifications inlet.  ances  associated  sump i n t o flow  rate.  pressure Barocel  44 5 kg  was u s e d The  for  assembly  the  (1000  power u n i t 3V/6,  in section  the  its  at  lb.) was the  the  l/s  d r i v e n by a t h r e e  setting  state  t h e pump  and  constant  condition,  meter  as  In g e n e r a l ,  valve  settings  of  (160  controlled  time with  three  horsepower  9.4  and t h e i r (Figure  m head,  variable  to  the the  readings  a c e n t r i f u g a l pump: gpm),  the taken  g i v e n by  c a l i b r a t i o n chart  test  head  and a f t e r  recorded together  Venturi  consists  9.6  meter  A gate v a l v e  valve  steady  of  Venturi  from a l a r g e  transducer.  each  make  c a l i b r a t e d , under s i m u l a t e d  i n p r e p a r i n g the  mount model  change  known v o l u m e .  drop a c r o s s  taken  to  etc.  For a given  pressure  as  t h e pump  t o u p s t r e a m and downstream d i s t u r b -  by pumping w a t e r  a tank of  74 cm u p s t r e a m o f  selected  elbows,  final  had a t t a i n e d  collect  is  the  so  p l u m b i n g were  conditions,  It  form o f  pump s u c t i o n ,  Before  were  insensitive  i n the  inlet,  flow  located  The l o c a t i o n was  performance  the  and was  speed  mean 2-2). Para-  1750 rpm. d.c.  motor.  R x l O  -5  n  U,cm/s  VP,  Figure  2-2.  Calibration  plot  for  P  the V e n t u r i  s i  meter.  22  The pump i m p e l l e r and h o u s i n g a r e against three  possible  phase  grid,  autotransformer further  corrosion. the  It  the  the  d.c.  o u t p u t was  power s y s t e m  tunnel  fluid.  lOu  filter  i n a bypass  the  of  to  entire  T h i s was  e n e r g i z e d by a  is  required.  shown i n F i g u r e  c i r c u i t across  Figure  No A 2-3.  contamination of  a c h i e v e d by i n c o r p o r a t i n g a  volume a t  operation.  guard  b e i n g a d j u s t e d t h r o u g h an  was' i m p o r t a n t t o m i n i m i z e d i r t  filters  brass  The motor i s  voltage  the  hours  cast  and r e c t i f i e d by s e l e n i u m d i o d e s .  smoothing o f  photograph of  of  least 2-4  the  once  pump.  in  shows t h e  The  system  twenty-four entire  tunnel  assembly.  2.2  D e s i g n o f Honeycomb f o r T u r b u l e n c e C o n t r o l  Although screens wind t u n n e l s  to  reduce  improving m i x i n g , they factory  for  screens,  the  withstand  i n water  tunnels.  d i a m e t e r d i c t a t e d by i n e r t i a of water,  R e y n o l d s number r a n g e where v o r t e x  and hence On t h e  have n o t p r o v e d p a r t i c u l a r l y  with t h e i r wire to  are  susceptible  other hand,  length-to-diameter  in  t u r b u l e n c e and make f l o w u n i f o r m  reducing turbulence  requirements in  have been u s e d r a t h e r r o u t i n e l y  to  honeycombs  resonance  satisFurthermore,  strength  normally operate  shedding  occurs  and a s s o c i a t e d  i n which the  by  cells  have  r a t i o have been u s e d s u c c e s s f u l l y  failure^ a to  large  Figure  2-3.  A p h o t o g r a p h showing d e t a i l s o f the unit: A , a u t o t r a n s f o r m e r ; D, d r i v e P , pump.  power motor  Figure  2-4.  A p h o t o g r a p h o f the g l y c e r o l - w a t e r t u n n e l c a p a b l e o f g e n e r a t i n g R e y n o l d s number i n the range 1-18,000: A , a u t o t r a n s f o r m e r ; B , d r i v e motor; E , heat exchanger; F , flow d i s t r i b u t i n g v a n e s ; H , p o r t h o l e s ; M , v e n t u r i m e t e r ; P , pump; S, s c r e e n s and h o n e y comb; T , t e s t - s e c t i o n ; V , v e n t . t o  25  reduce are  turbulence  to  particularly effective  honeycombs  tend  to  As m e n t i o n e d 18  an a c c e p t a b l e  (mesh s i z e  turbulence.  earlier,  two' b r a s s  and 0.09  cm a p a r t were u s e d  to  The honeycomb  size  cell  to  the  procedure  involves  the-knowledge length  scale  Of c o u r s e ,  of  the  must  be  be  101  of  turbulence  the  actual  were  of  design  level,  14 and  located  maximum f o r  operation  as  flow .uniform.  The  velocity  input  the  (i.e.  3.8  which r e q u i r e  mean f l o w  honeycomb  while  selected  charts  and  information.  turbulence  with  the  length  tunnel  it  was  nated with p l a s t i c . s u c h honeycombs and 1 5 . 2 5  t u r b u l e n c e measurements  and h o n e y c o m b ) w h i c h showed  intensity  consideration  size  use  when t h e  The p r e d o m i n a n t height  no.  p r o p o s e d by L u m l e y ^ ' ^ .  turbulence  end t h e  screens  about  uniform  screens,  length  screens  honeycomb)  identified.  To t h i s  to  the  flow  i n r e n d e r i n g the  and i t s  permissible  during  (without  assist  theory  Thus  cm, r e s p e c t i v e l y ) ,  i n a b s e n c e of t h e  intensity also  i n making t h e  reduce  0.18  according  level.  mean f l o w  s c a l e was  velocity  estimated  were the  intensity  was at  undertaken  15  cm/s.  61 cm,  the  test-section.  The maximum p e r m i s s i b l e  was  2%.  l i m i t e d to  decided  to  use  B a s e d on t h e  are manufactured, cm l e n g t h  was  From c o r r o s i o n  a p a p e r honeycomb  standard sizes the  one w i t h  tentatively  i n which  0.32  selected  impreg-  cm c e l l  for  use.  26  However, the  it  was n e c e s s a r y  desired In t h e  4  check  its  performance  against  specification. present  case  i and R,. = 4 . 76 x 1 0  10 ,  to  2  cl  £ / d = 48,  L / £ = 4,  R  = 2.28  x  where:  L = length  scale;  I = length d = cell  of  the  honeycomb;  diameter;  R ^ , R ^ = R e y n o l d s numbers b a s e d on c e l l d i a m e t e r and l e n g t h , respectively. With these  data,  coefficient factor to  of  the  However, incoming  the  present  450  based  model  the  turbulence while the  the  and t h e  bulence  Thus  flow,  In g e n e r a l , cells  friction  =0.09.  reduce  Lumley's design  gave  level  from  10% t o  turbulence  honeycomb c r e a t e s  wake e m a n a t i n g  on c e l l  the  from t h e  flow  diameter),  may be n e g l e c t e d , is  i n the its  i.e.  entirely  its  due t o  2  2  =  x/d  expected  0.9%. level  of  the  own t u r b u l e n c e . flow w i t h i n  individual cells  is  turbulence t h e wake  cell.  the In .  laminar (R  c o n t r i b u t i o n to  the  , 41 by ,  u /U  reduction  s e l e c t e d honeycomb c a n be  r e d u c i n g the  as  pressure  (K) = 7 and t u r b u l e n c e  c o n t r i b u t i o n comes from t h e  case,  location  charts  the  energy  and c a n be  n  =  turat  the  given  27  Here x c o r r e s p o n d s of  the  to  turbulence  However,  it  condition  Figure  2-5  shows d e t a i l s  intensity.  i n the  of  to  the  of v e l o c i t y  of  the  at  intensity hot-film  o f utmost  different  7.9P-). the  flow  distribution.  the  worse  lower.  of  vanes,  the  tunnel.  profiles  and t u r b u l e n c e  following  section.  Tunnel  various  rates  the  above p r e d i c t i o n by  i m p o r t a n c e were  d i s t r i b u t i o n at  uniformity of  stations  and t h e  T h i s was  the  i n the  associated  achieved through  test-  turbulence the  anemometry.A Thermo-Systems h e m i s p h e r i c a l probe  (model TSI 1239W) the  Liquid  the  1.81.  t o be  design  the  Calibration  items  i.e.  of  distributing  i n the  d e s c r i b e d i n the  velocity  design,  flow  confirm  measurement  0.9%,  end  the  has been c o n s i d e r e d , h e n c e  is  section  in  that  as  gives  test-section  This  The  at  the  honeycomb u s e d  was n e c e s s a r y  a systematic  the  at  This  intensity  t u r b u l e n c e c a n be e x p e c t e d  and  It  intensity  downstream from t h e  cell-size.  turbulence  (maximum v e l o c i t y )  tunnel  screens  the  must be n o t e d  actual  2.3  distance  honeycomb and d i s  honeycomb g e n e r a t e d total  the  overheat However,  w i t h the  r a t i o of the  c a l i b r a t i o n of  cold resistance  1.0972  (i.e.,  of  7.20,  tunnel.  used  operating resistance  p r o b e must be c a l i b r a t e d f i r s t the  was  For t h i s  it  to  use  of it  was mounted on  29  the in  tool  holder  a slotted  multispeed the  of  a lathe  flume  gear  employing the  box a l l o w e d  tow v e l o c i t i e s .  a depth of worked  at  least  the of  satisfactorily  affected  towing the  time  flume  could not ment  ten  is  the  m),  the  countered on t h e of  surface  a i r bubbles  promotes life.  its  and d u s t  changes p r o b e ' s sensitivity  corrosion'of  of  gear  a "wetting  a property of  the  to  arrangement cm/s  substan-  higher  velocities  limited  signal  length  from the  The t e s t  probe  arrange-  calibration plot  the  the  is  formation of  contamination.  accuracy  air  The  cold resistance  probe c o a t i n g  bubbles  thus  Furthermore,  thus  eliminated  tension  en-  presence  reducing  its  through  the  (Kodak P h o t o - F l o 200)  surface  was  two p r o b l e m s  and c a l i b r a t i o n .  agent"  probe  a positional  to mention  essentially  reducing  profile,  with  measurements:  The p r o b l e m was  addition  while  w o u l d be u s e f u l  d u r i n g the  probe  affecting  has  It  the  condition.  fluid  a r o u n d 16  vibrations  output  velocity  s u p p o r t e d by a t r a v e r s i n g ± 0 . 1 cm.  of  The  of  2-7.  For c h a r t i n g of  of  the  state  i n F i g u r e 2-6  in Figure  diameter.  due t o  The  i n the  F u r t h e r m o r e , at  short,  that  reach a steady  its  speeds  determination  immersed  by s p u r i o u s  so  mechanism.  a velocity  signal.  became  (1.52  shown  presented  caused  controlled  satisfactory  times  up t o  at  feed  The p r o b e was  beyond w h i c h n o i s e tially  and towed  of  the  it  which solvent.  31  300  • /  /  /  •  250  V  2  .volt  2  200  Probe:TSI /•  /  A  /  A  R  c  -  7-2  n  R  0  = 7 - 9  A  a  =  1-097  T  -  2 0  v  50  ,1/2 U Figure  2-7.  C a l i b r a t i o n data TSI 12 39W. '  for  the  d  • 1/2  , (cm/s) hot  1 2 3 9  film  probe  W  °C  32  Contamination deposits nation  of  posed  the  to  p r o b e by d u s t  a serious  surface  Furthermore, filtered.  the  of  In s p i t e  c l e a n the  of  comb i n r e n d e r i n g t h e a typical station  and w i t h t h e are  these p r e c a u t i o n s  the  velocity  is  essentially  to  profile  zero  rise  was  f o u n d t o be  at  in velocity,  is  stations  2-9  and f o r  and 12  observed  it  was  top  Thus t h e  two v a l u e s  i n the  in position.  Note, t h e  t u n n e l has  suitable  without The  results  improvement velocity  the  test-  increase,  of  the  the  diagram.  at  finally  Even  during  mean  adequate planned  three  tests.  different  mean f l o w v e l o c i t y ,  U =  approximately e s t a b l i s h  the  plots  an  f o r the  profiles  used d u r i n g  previous  out  and b o t t o m w a l l s .  These v a l u e s  character of  measurements  carried  to  honey-  maximum d e v i a t i o n f r o m t h e  shows v e l o c i t y  cm/s.  necessary  alcohol.  velocity  a tendency  continuously  and t h e  c e n t r a l 30 cm o f  contami-  shielded.  was  Rather spectacular  is  the the  8%.  range o f v e l o c i t i e s Essential  kept  screens  apparent.  of uniform v e l o c i t y  Figure  7 cm/s  2-8.  uniform over  the  region  devices  beyond w h i c h t h e r e  diminishing  the  (x = 90 cm) were  straightening  in  of  flow u n i f o r m ,  compared i n F i g u r e  section  always  circulating fluid  effectiveness  other  To m i n i m i z e d i r t  l i q u i d was  the  and  probe p e r i o d i c a l l y u s i n g methyl  To a s s e s s  at  challenge.  the  a part of  particles  pressure  remains the There  measurements. same as  continues  that  t o be a  the  Y,  c m  33  + 30  • •  • •  • • •  • •  •  o  • without s t ra igh ten ing devi • with straightening device  • •  H  •  - 15 H  • • •  •  •  -30  •  -I  10  Figure  2-8.  20  T y p i c a l p l o t s showing t h e e f f e c t o f s c r e e n s and honeycomb i n i m p r o v i n g v e l o c i t y p r o f i l e i n the t e s t - s e c t i o n .  U , c m / s  34  Y,  c m  x =•3 0 «  9 0  •  1 3 0  •B4  U =7 c m / s  '"•11.9  •  5 gure  2-9.  cm/s  "4*  1 0  A c o m p a r i s o n ' o f v e l o c i t y p r o f i l e s at three d i f f e r e n t s t a t i o n s i n the t e s t - s e c t i o n and two v a l u e s of- mean flow v e l o c i t y . Note a l a r g e r e g i o n of e s s e n t i a l l y u n i f o r m flow w h i c h i s d e s i r a b l e f o r the p l a n n e d t e s t programme'.  U , c m / s for  35  large  region  tunnel  ( ± 1 5 cm)  centerline  uniform. a large  change  at  vanes  tend to  'they  where t h e v e l o c i t y  the  i n the  are not  the  test-section.  distribute  the  flow  of  their  entirely  evenly  effective, at  Although  the  test  programme d i d n o t  mechanics  of b l u f f  apprecitation  as  the  the  by a f a c t o r  of  Although over  the  guide  testapparently  non-  entrance. aim at  turbulence effects  bodies,  to  to  p r o b a b l y due t o  flow  the  essentially  c a r e f u l l y arranged s e t t i n g ,  the  study of  is  the  p r o b a b l y due  area,  of  systematic  is  to  because  uniformity  cross-sectional  entrance  around  profile  The n o n u n i f o r m i t y b e y o n d t h i s  11.5;,  section  symmetrically located  it  was  average  on t h e  desirable  level  of  a  to  fluid  have  turbulence  some in  the  40 test - sect i o n . the  average  however,  turbulence  this  intensity stations pendent  B a s e d on t h e  has  across  to the  and f l o w of  the  however,  as  w i t h the  flow  Figure 12  t h e o r y p r o p o s e d by Lumley  level  was  expected  be v e r i f i e d . tunnel  rates  location  (over  can be e x p e c t e d ,  it  short  1.8%,  different  span o f  turbulence  ,  turbulence  t o be e s s e n t i a l l y  the the  at  '  be a r o u n d  Measurement o f  test-section  showed  to  41  40  level  indecm},  increased  rate.  2-10(a)  was  about  cm/s.  the  m i d d l e - h a l f of  shows t h e  c a s e when t h e  The t u r b u l e n c e the  test-section  level  is  mean f l o w around  and g e n e r a l l y  velocity  1% i n less  than  36  Y,cm  ( b )  (a)  •(c)  3 0 -  o o U = "11 • 9  ox  cm/s  n  n  = 9 0c m  U - 7 cm/s X ;  > U= 7 cm/s  9 0 c m  > x -13 0  c m  15 -  o  0-1  o  •  0  >  •  a  -15o o o o - 3 0 -  I  0  2  i  4  2  0  u/u Figure  2-10.  4  0  i  i  2  4  A  R e p r e s e n t a t i v e p l o t s showing v a r i a t i o n o f the t u r b u l e n c e i n t e n s i t y i n t h e test-section,  37  21 e x c e p t  for  flow  o r a change  in station  of  plot  remains  i n the  value  rate  character for  the  the  a reduction W i t h the  lower  design  quarter.  of  the  the  design  test  selection  instrumentation for  flow  chapter.  models,  attention  These  was  are  of  same  except  intensity.  focussed  a dye  satison  the  measuring  injection  described  the  the  the ,tunnel  of pressure  and c o n s t r u c t i o n  visualization.  the  turbulence  and c a l i b r a t i o n o f  accomplished  in  (Figure 2-10b,c),  essentially  factorily of  With a decrease  i n the  system following  3.  Before their  the  it  present  equipped f l u i d  hence needs no e l a b o r a t i o n .  reference  to  a specific  account  on  more s i g n i f i c a n t  to  the  completely.  study  The  a higher working  fluid  (glycerol-water  of  quite  difficult.  specific  considerations  However, that  employed a r e  o r d e r , mainly because  that it  hand,  design,  involved  often is,  too  with numerous  therefore,  instrumentation  implementation often  ities  trivial  are  the  the  l a b o r a t o r y and  other  The a t t e n t i o n of  describe  a standard equip-  features  equipment  aspects  procedures  their  programme.  and  focussed relevant  i n hand.  test  known b u t  results  In g e n e r a l ,  mechanics  On t h e  and o p e r a t i o n a l  to  test  procedures.  employed c o n s t i t u t e s  i n any w e l l  constructional  the  w o u l d be a p p r o p r i a t e t o b r i e f l y  important test  instrumentation ment  PROCEDURES  p r o c e e d i n g to  discussion  some o f  TEST  experiments  of  the  the  factors  is  on p r a c t i c a l  experimental seemingly,  them a s e c o n d o f most  apparently simple  the  measurements  involved are,  a common e x p e r i e n c e of  the  of  Often p e c u l i a r -  make c e r t a i n  one w o u l d seldom g i v e  resolution  character of  solution).  involved in executing  well  attains complexity  T h r o u g h o u t , t h e emphasis  At times  is  conceptually  look.  experimenters  problems  occasionally  so  39  takes  days,  true  i n the  if  n o t weeks o r m o n t h s .  c a s e where  liquid  The g l y c e r o l - w a t e r fundamental  facility  is  the  the  earlier,  c h a p t e r models  are  In t h i s  the  highly  in  the  measurement  Finally,  details  proved extremely as  3.1  to  the  This  sensitive  of  of  is  used  the  test  by a  pressure  its  described programme  discussion  t r a n s d u c i n g system  surface  a  programme and  i n the  followed  pressure  the  used  distribution.  flow v i s u a l i z a t i o n p r o c e d u r e , which  useful  character of  test  fluid.  representing  h o t - f i l m anemometry was  introduced f i r s t .  of  tunnel  entire  c a l i b r a t i o n using  is p a r t i c u l a r l y  the working  solution  for  This  in obtaining physical the  flow,  are  appreciation  presented.  Models  Two s e t s  of  surface  pressure  ization  study,  models  circular  cylindrical  measurements  were u s e d  and t h e  i n the  test  located  of  the  pressure  mechanism f o r  changing r e l a t i v e  tap w i t h r e s p e c t  draining  of  models.  Flow v i s u a l i z a t i o n models  tunnel  to  fluid  the  free  during  for  because  conducting l i n e  pressure  the  other  one  for  flow  programme.  were r e l a t i v e l y more e l a b o r a t e  presence  models,  visual-  The p r e s s u r e  of  and t h e  the externally  orientation  stream.  the  of  the  This  required  changing of  the  pressure  were s i m p l e r  (no  pressure  40  tap,  models  this  time  rigidly  can be  The ends were  position  (Figure  against  0 . 5 - 3 0 cm and 15.2  be  adequate was  so  2-50%, the  for  0.2%.  the  chosen  test  as  and t h e  to  concentration  central ning  tap,  inside  externally  the  steel  ing  line  110  cm l e n g t h )  cylinder  in  or p l e x i g l a s  the  of  to  c a r e f u l l y chosen the  7-20,000  located  (1.7  the the  time  from  through  A  3-1).  0-rings static  on  the tube,  pressure pressure  - 5 mm i n s i d e  resulting  quite  (Table  a polyethylene  of  found  diameter  sleeves with  was  Size  was  ratio variation  of  model, which conveyed transducer.  from  Deviation  working f l u i d .  mm i n d i a m e t e r ,  that  of  the working f l u i d  the  two-  considered  The r a n g e  blockage  and c o n n e c t e d  so  tubes.  using micrometer,  programme.  cover  seven  c a r e f u l l y machined  The a c c u r a c y was  leakage  located  was  were  c o n t r o l of  0.5  station  tunnel.  ranging i n diameter  s u p p o r t e d by t w o - e n d  guard against  pressure  a family of  R e y n o l d s number r a n g e  A model was to  i.e.,  emptying the  w a l l h e l d the  geometry,checked  than  messy o p e r a t i o n ,  black rubber pads,  models,  cm l o n g ,  from s t a i n l e s s  less  the  measurements,  cylindrical  from c i r c u l a r  soft  avoided  3-1).  For p r e s s u r e dimensional,  and hence  introduced without  provided with  w h i c h when p r e s s e d  to  in position)  c o n s u m i n g and n e c e s s a r i l y  t h e s e models  either  fixed  to  runan  conduct-  diameter,  constant  has  a  Figure  3-1.  T y p i c a l models used i n the  flow v i s u a l i z a t i o n  study.  Table  NO.  3-1  S/C %  P r e s s u r e models u s e d i n t h e t e s t programme, c o r r e s p o n d i n g b l o c k a g e and a s s o c i a t e d R e y n o l d s number r a n g e a t t a i n e d t h r o u g h t h e v a r i a t i o n o f mean f r e e s t r e a m v e l o c i t y and c o n c e n t r a t i o n o f t h e w o r k i n g f l u i d \  C  ,  °"o  . D ,cm  0 (v/v = 1) w  41 (v/v = 4) w  1  0.8  0.5  200  - 600  2  2  1.2  600  - 1500  150  3  3.3  2  1200  - 3000  300 -  600  4  6.6  5  3000  - 7300  800 -  2500  5  12. 5  7.6  4500  - 11000  3000  6  25  15  9000  - 15000  7  50  30  12000  - 30000  7 5 - 200 .  - 400  66 (v/v = 15) w  30 - 60  40  - 150  60 - 300  76 (v/v = 40) w  7 - 13  16 - 30  30  - 50  150  - 750  - 11000  250  - 1100  120  -  2000  - 6000  450  - 2200  200  - 500  3000  -  300  - 3000  150  -  8000  75 -  200  250  300  43  reasonable in  small  value.  increments  distribution the  set  while  over  F i g u r e 3-3  rotation  of  the  cylinder  through 1 8 0 ° provided d e s i r e d  the  of p r e s s u r e  typical  3.2  A systematic  cylinder  models  presents  surface.  used  i n the  pressure  F i g u r e 3-2 test  constructional  shows  programme  details  of  a  model.  Pressure  Measurements  The mean p r e s s u r e  component  being  extremely  small  2 (of  the  order of  instrumentation using  the  developed The t y p e  0.7 for  N/m ) its  demanded a h i g h l y  measurement.  " B a r o c e l Modular Pressure by D a t a m e t r i c s  Inc.  This  was  is  accomplished  T r a n s d u c i n g System"  of Watertown,  550-5 B a r o c e l s e n s o r  sensitive  designed  Massachusetts.  to  operate  with 2  fluids  over  the  pressure  range  The U n i t  is  divider,  the  stressed  steel  plates.  The d i a p h r a g m d e f l e c t s  magnitude pressure system,  of  a high p r e c i s i o n ,  of  variable  the  unit  filled  with  sensor  uses h i g h l y bellows,  degassed  a thin  pre-  p r o p o r t i o n a l l y to To i s o l a t e  kN/m ) .  voltage  between f i x e d  the  capacitor the external  diaphragm-capacitance  sensitive isolator  silicone  (68.98  capacitive  of which i s  applied pressure.  medium from the the  stable  diaphragm p o s i t i o n e d  volume between t h e is  element  0 - 10 p s i a  metallic  bellows.  The  and s e n s o r d i a p h r a g m  o i l which serves  both  as  3-2.  A photograph showing  the  models  used  i n surface  pressure d i s t r i b u t i o n .  To pressure transducer  End sleeve  End sleeve  Figure  3-3.  A d i a g r a m showing c o n s t r u c t i o n a l d e t a i l s a t y p i c a l p r e s s u r e measurement m o d e l .  of  46  pressure  transmitting  pressure  signal  m i t t e d by the deflects  the  the  An a . c .  plates.  of  the  the  input  a dielectric.  produce  carrier  the  plates,  is  which i n  at  on t h e  of  the  therefore  The u n i t  turn  10 Hz i s  and a b r i d g e  each  trans-  r e q u i r e d change  dependent  voltage  A  medium i s  oil  voltage  diaphragm to  pressure.  liquid  silicone  voltage  The c a r r i e r  to  the  capacitor  an o u t p u t  capacitance  to  and as  external  diaphragm to  stationary  determines  ing  from t h e  bellows  capacitance. to  fluid  in  applied circuit  ratio  of  the  stationary  modulated  sensitivity  accord-  is  10 ^  2 psi  (0.07  isolated was  N/m )  p r o v i d e d the  from e x t e r n a l  imperative  to  pockets  from t h e  Barocel  is  Figure  3-4  sources  ensure pressure  accurately presents  pressure of  all  for  calibrated for  a schematic  is  fully  v i b r a t i o n and n o i s e .  removal of ducting  sensor  traces  of  air  statisfactory steady  diagram of  It  operation.  pressures. the  pressure  transducer. It  was  temperature was  achieved  large  important to excursions  minimize  on t h e  by m o u n t i n g t h e  the  effect  Barocel's  temperature  v i r t u a l l y eliminated  transients.  ambient  performance.  t r a n s d u c e r on a h e a t  aluminum b l o c k w i t h w o r k i n g f l u i d  The a r r a n g e m e n t  of  the  sink,  circulating influence  This a  inside. of .  47  Power input  Stationary Diaphragm c a p c i t o r plates  Figure  3-4.  A schematic transducer.  diagram of  the  Barocel.pressure  48  After fluid, its  a model was  center  Next,  the  and was set  a complete  pressure  from t h e  b a l a n c e d to  the  pump o p e r a t i n g  at  i n the  d e s i r e d R e y n o l d s number and t h e  meridional  cross-section  A point size  of  the  systematic time  to  large  pressure  tubings  by s e v e r a l  constant  theoretical  mic r e s p o n s e  volume  of  of  fluid  the  unit  fluid  signals,  was  to  give  h e l d at  of  a  a  constant vertical  the  the  4  an  transducer's  of  suggested  cavity,  on t h e  constant  the  dyna-  would  diameter  fluid,  character  mean p r e s s u r e  with  excessively  studies  time  A  associated  tubes  as  i n c l u d i n g the  viscosity  and  showed t h e  and e x p e r i m e n t a l  F o r the  size  Of c o u r s e ,  lines ^  etc.  air  condition.  speed  mm-to have  min.).  tubings,  i n c l u d i n g the  pressure  no-flow  different  depend on -a number o f p a r a m e t e r s and l e n g t h  removal of  must be e m p h a s i z e d h e r e .  t h a n 1.6  (>20  fluid  d i s t r i b u t i o n around the  state pressure  less  test  measured.  study w i t h tubes of  diameter  time  was  with  honeycomb.  c o n c e r n i n g an a p p r o p r i a t e c h o i c e  reach steady  internal  after sensing  test  the  transducer v i a a  a preselected  mean p r e s s u r e  the  f i l l e d w i t h the  The p r e s s u r e output  from  section  end o f  and M y l a r t u b i n g s  line.  the  test  a Barocel pressure  r e a d zero  temperature,  a i r bubbles  i n the  d u c t i n g was  to  of polyethylene  With the  positioned  90 cm downstream o f  connected  pockets  removal of  inline of  measurements  49  under c o n s i d e r a t i o n ,  it  1.7.-5 mm d i a . r e s u l t i n g  was  convenient  i n the  time  to use  constant  fluid  of  lines  of  around 3  minutes. To i n s u r e  a c c u r a c y as w e l l  measured d a t a ,  it  was  o f utmost  compensate  for  any d r i f t  associated  electronic  of  as  repeatability  of  the  i m p o r t a n c e t o m i n i m i z e and  the  pressure  circuitry.  t r a n s d u c e r and  Minute  character of  the  -4 pressure long all  time the  periods at  times  well  time  This  is  (10  involved  psi)  of  24-48 h o u r s  as  large  as  Chart showed  50% o f  pattern.  three  c o r r e s p o n d i n g to  w i t h the  steady  recordings them t o  the  in d e t a i l  time  of  c y l i n d e r at  point  pressure  at  a reference  point.  pressure  source  given  location  the  present  the  t u n n e l was  i n the  case p r e s s u r e used  to  'a'  a liquid tunnel at  serve  the  but  over  of  no  procedure  equal of  drift  significant,  signal,  at  this  intervals  the  system.  below.  the  (e.g.  of  constant  L e t t h e o b j e c t i v e be t o measure pressure P - P , where P r e p r e s e n t s a r a face  s t a t e made  compensation  measurements the  relatively  be q u i t e  actual  The d r i f t  successive  explained  together  i n r e a c h i n g the  more n e c e s s a r y .  defined  involved of  signals  a differential p r e s s u r e on t h e  and P^. c o r r e s p o n d s  In g e n e r a l , column)  can serve a point this  or p r e s s u r e this  on t h e  end.  a known  surto  external at  purpose.  a ,In  bottom w a l l  Let the  the  of  arbitrary  zero  drift  Figure drift AP  a  3-5. of  = P  a  AP„ a  the  electronic  s y s t e m be  The d i a g r a m a l s o  the  pressure wall  of  differential  - P at  w  a suitable  i n the  present  shows t h e  pressures  and AP = P r r  - P . w  location,  case.  as  Thus,  A-P and A P ^ , where a  taken  to  represents 1  be  desired  - AP.. . r Now,  (AP )  r 1 J  a  + 6  + (AP ) „ . ^ r 3  1  + 6  P  tunnel  - P  cl  T*  + 6  +•  2  (AP^. +. 6 J + (AP  2  2 = AP  Hence,  on t h e  f r o m F i g u r e 3-5 :  AP  ^  in  corresponding  Here P w  the  indicated  r  + 6  1  6  +  6  )  51  <*fV^^— (Ap ), r  < r'3 Ap  (^Pr^-  r"  "  I  h 3  Drift  \1 Vb< I! '  !I  | —  *j  j  T  T  1  Ti  Figure  3-5.  T  2  3  1  T  4  ? "  i |  T  5  A procedure f o r compensation o f the e l e c t r o n i c d r i f t o f t h e p r e s s u r e measuring system.  05  52  Assuming linearly ments  that  during  (AP ) r 1  the  the  zero  setting  i n t e r v a l marked by t h e  (AP ) „ r 2  v  electronic  drifts  pressure  measure  then  S  2  " «3  i.e. , (AP ) a  (AP ) ^  2  + (AP ) I_i.=  Thus d e t e r m i n a t i o n o f involved that  the  measurement  order.  within  - P  a  differential  (AP )  ,  (AP )  The p r o c e d u r e gave d a t a t h a t  an a c c u r a c y o f  differential cylinder  of  the  P  pressure  ±2%.  Note,  the  P^ - P^, a t  would f o l l o w  the  u  b  - P =• ( A P , ) , r b '4  and (AP )  r  5  in  can be r e p r o d u c e d  evaluation  same p r o c e d u r e .  -  (3.1)  pressure  some d i f f e r e n t  (AP ) P  .  r  of  the  location  Thus  + (AP ) ^—i •  4 6 47 Modi  et  al.  '  compensation  have u s e d in their  and s p h e r i c a l m o d e l s . layout  during  the  s i m i l a r procedure  s t u d i e s w i t h an a o r t i c Figure  static  3-6  pressure  shows  for  drift  heart  valve  instrumentation  measurments.  on the  53  ss/sssj?sssssssssss/ssssssssss\  r  air supply tof lush liquid in line  fo fo fo fo fo: manifold reference \ pressure Jj Barocel  signal conditioner d.c. d i g i t a l voltmeter  osci Hoscope  u- v. recorder  filter  1i  Figure  3-6.  A l i n e drawing o f the i n s t r u m e n t a t i o n s e t - u p u s e d d u r i n g s t a t i c p r e s s u r e measurements 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 .  54  The mean f l o w  rate  constant  d u r i n g the  achieved  by a c o n t i n u o u s  output  as  the  due t o  changes  exchanger  the  field  under  confined  was  Venturi  pressure  voltage.  meter  transducer  i n t h e pump  Temperature of  (±0.1°C)  using  Figure  the  3-7  mean f l o w measurement  appreciate  associated  system.  that  of  the  upstream of cochineal pure  test  the  food  colour.  flow  was  of  the  injecting  (0.38  constructed.  the  same  of  the  employed was  produce as  - 1.0  a  that of  concentration  an of  10 cm  imitation the  dye  of  the  test  fluid.  syringe  stainless  A  needles  on a s t r e a m l i n e d  O c c a s i o n a l l y a long  and  glycerol-water  s e v e n #23  cm a p a r t  undertaken.  approximately  A p p r o p r i a t e volumes  same d e n s i t y  0.5  of  injected  probe,consisting  mm) p l a c e d  character  v i s u a l i z a t i o n was  The dye  g l y c e r i n were m i x e d t o  solution  physical  solution  fluid  model.  the  w i t h c i r c u l a r c y l i n d r i c a l models  condition,  The dyed g l y c e r o l - w a t e r  was  This  any f l u c t u a t i o n s line  maintained  Flow V i s u a l i z a t i o n  fluid  dye  the  system d e s c r i b e d b e f o r e .  To b e t t e r  as  for  held constant  shows a p h o t o g r a p h o f  3.3.  measurements.  differential  i n the  was  t u n n e l was  monitoring of  and c o r r e c t i n g  working f l u i d  heat  pressure  i n d i c a t e d by t h e  (Barocel) speed  t h r o u g h the  steel  support,  Measurement o f mean f l o w r a t e u s i n g v e n t u r i m e t e r : B, Barocel pressure D, d i g i t a l d . c . v o l t m e t e r ; E, h e a t e x c h a n g e r ; F , f i l t e r ; H , h e a t - s i n k ; s u p p l y ; S, s i g n a l c o n d i t i o n e r ; V , v e n t u r i m e t e r .  transducer; P , power  56  tubing the It  tip,  was  The. r a t e  needle valves. i.e.,  suspended  Figure  to  right  angle  3-8).  provide  f r o m the  diagram of  to  the  was  adequate  sufficient  ceiling  injecting  connect  injection  To e n s u r e  syringe. dye  "Intramedic"  were u s e d of  in  needles  controlled  head,  complete  in  tubings  the  flow  4 m above  near  through  the the  set-up  with each  supply  bottle  injection  is  shown  level.  in  3-9. After  assembly,  ascertaining  flow  16 mm movie blockage.  patterns  cameras,  as  It  over  evolution  affected  successful  a range was  and o n s e t  by t h e s e  system used  as  photographing process.  intensity  photo  illuminated eliminate masking  the  hot  the  floods  test  it  the  section  the  using  of  focussed  entire  still  and  on c a p t u r i n g  instability  of  the  Foppl  parameters. point  out  here  played a c r i t i c a l  A combination of  through the light  of  R e y n o l d s number and  (maximum 500 w a t t s ,  subject  spots,  of  primarily  w o u l d be a p p r o p r i a t e t o  lighting  operation  were p h o t o g r a p h e d ,  The a t t e n t i o n  formation,  vortices  the  (Figure  a manifold.  A schematic  of  region  diameter)  needle,  at  in conjunction with a c l i n i c a l  mm i n s i d e  brass  the  30 cm l o n g ) , b e n t  be p a r t i c u l a r l y u s e f u l  near-wake  (0.6  was  used  proved to  the  to  ( 3 mm d i a . ,  tunnel  beam was  wall with  the  type  role  three  3400°K)  in  variable back-  g l a s s window.  evenly  diffused  a t r a c i n g paper.  A  To by set  Cn  camera  Figure  3-9.  A s k e t c h showing the equipment l a y o u t d u r i n g the f l o w v i s u a l i z a t i o n .  59  of  trial  setting high  runs helped and e x p o s u r e  speed  (movie),  During  fluid was  the  that  (==265&) ,  no c l e a r  in  to  a rather  serious  involved  in replenishing  necessary  to  find  in  the  fluid.  the  an a g e n t  oxidizing  w h i c h has  all  the  a g e n t was  sufficient  keep  the  amount o f the  the  agents  of  of  to  or  test  of  the  presented and  cost  the  it  sodium  has  been  patient  reported  hypochlorite 300  cc  neutralize  the  dye.  dye r e m o v i n g  of  testing  Only  fluid  was  dye  properties  constant,  g l y c e r i n was p e r i o d i c a l l y added t h u s  diluting effect  point  circulating  amount o f  led'to  cc)  Clearly,  physical  attributes.  the  the  effort  its  test  (200  This  time,  was  the  dye  no s u c h a g e n t  to" c o m p l e t e l y  concentration  of  material  alter  desirable  of  it  would n e u t r a l i z e  A considerable  w i t h numerous  volume  working f l u i d .  that  tunnel  81A) .  study,  taken.  (Kodak  or EF-7242  working f l u i d  Unfortunately,  literature.  filter  amount  c o u l d be  s y s t e m and w h i c h does n o t test  small  aperture  f i l m used  (still)  large  p r o b l e m i n terms  w i t h o u t a t t a c k i n g the  the  the  the  photographs  of  visualization  of  pollute  type  ASA 125,  of  spite  appropriate  EHB-135  3200°K,  course  the  f o r the  a relatively  sufficient  that  time  Ektachrome type  tungsten,  discovered  a r r i v e at  agent.  of  the To  sufficient  offsetting  60  3.4  Critical  R e y n o l d s Number  The f l o w determination by t h e  visualization of  the  blockage.  models  critical  R e y n o l d s number as  studies,  to  onset  of  vortices.  The wake b u b b l e b e g i n s  results  Karman v o r t e x  the  i n the  of  instability to  and w i t h  R e y n o l d s number beyond t h e  critical  of v o r t i c e s  leading  of  the  critical  accomplished  strong  clear  gradually of was  turbulence  suitably  the  using  film  noise.  diameters  a hot  the  was  the  organized  The o n s e t  film of  the  probe.  pump rpm.  response  as  to  to probe yield  flow  was  Evolution  injection  and  displayed  on  i n s t a b i l i t y was  i n d i c a t e d by a s t r o n g  film  the  a  anemometer  filter  downstream  t r a c e d t h r o u g h dye  hot  film  The h o t  The R e y n o l d s number o f  by i n c r e a s i n g  Fbppl v o r t i c e s  correlated with  hot  a few  signals.  an o s c i l l o s c o p e .  the  generated  located  increased  s h a r p and was  to  R e y n o l d s number f o r  system i n c o n j u n c t i o n w i t h a h i g h frequency  was  Foppl  street.  c y l i n d e r was  eliminate  the  oscillate  i n shedding  Determination given  affected  low R e y n o l d s number  refers  value  for  In the  'critical'  any i n c r e a s e  were a l s o u s e d  sinusoidal  reasonably signal  from  4.  With  RESULTS AND DISCUSSION  some a p p r e c i a t i o n  instrumentation  used  adopted,  ready to  their  we a r e  has  is  rather  been t o  relevance definite results  to  the  only  tests.  so  c r i t i c a l at  is  followed  Next,  integrated  drag data  studied  wall  are  assist  of  the  immediate  establishing i n which  the  chronological  an a p p r o a c h t o is  principle  w h i c h have  sequence  number,  data  guiding  in  and  data  reduction,  discussed.  surface  order  This  pressure  dis-  functions  of  Reynolds  number and  the  attention  is  focussed  on t h e  flow  and 16 mm movie literature  with,  results  as  and the  confinement.  using  the  results  the  problem,  experimental  a l s o denotes the  by p r e s e n t a t i o n  blockage.  of  the  procedures  test  however,  those  low R e y n o l d s  results  the  i n hand and h e l p  To b e g i n  tribution  by the  into  In g e n e r a l ,  are p r e s e n t e d  the  look  The amount  study  trends.  experimental  extensive,  include  of  and t o  and the  interpretation.  obtained  of background to  S t r o u h a l number as  Finally,near-wake  visualization  photography. i n c l u d e d where  i n emphasizing  pressure affected  structure  in conjunction  with  Available results  from  appropriate the  influence  for of  is still  comparison blockage.  62  4.1  Choice of  Before of  the  test  questions  Reference  V e l o c i t y and P r e s s u r e  proceeding with presentation  and  results,  several  one must  address  which are p a r t i c u l a r l y  R e y n o l d s number f l o w  studies.  significant  Clearly,  immersed i n an unbounded u n i f o r m ambiguity  concerning reference  and p r e s s u r e : of  the  It  is  stream f a r  number f l o w  the  velocity  however,  the  pressure vary  significantly  along the  section,  i n absence  the  growth a l o n g the  walls.  compromise  is  Acrivos directly ence  et  model a b s e n t  al?^'^ the  at  and t h e the  velocity.  this  reference  choice  of  the  model l o c a t i o n ,  affected  velocity  axis  velocity of  the  of  the  boundary l a y e r  model and  of  associated  O b v i o u s l y some these of  parameters. the  t h e i r model as  centerline  pressure  the  the  with  the  as  pump,  pressure  is  the  the  blockage  be  acceleration  reference  refer-  velocity,  p r e s s u r e may p r o v e t o due t o  and  test .  F o r models w i t h a s m a l l  but w i t h a l a r g e r b l o c k a g e , at  of  same s e t t i n g  characteristic  no  and p r e s s u r e  fluid  s u g g e s t e d use  centerline  pressure but  have  is  F o r low R e y n o l d s  problem.  indicated in selection  below  static  the  of  low  a model  model due t o  Presence  wake w o u l d o n l y a c c e n t u a t e  with  or c h a r a c t e r i s t i c  constant  of  fundamental  i n the  stream there  away from t h e m o d e l .  in a tunnel,  even  to  analysis  adequate  of  the  flow  indeed  and becomes a f u n c t i o n o f w a l l c o n f i n e m e n t  (besides  63  other  parameters).  reference optimism  pressure implicit  upstream adverse the  model  in  gaps a t  to  take  without kept  it  the  the  as  this  velocity  profile  the  Usefulness  that  pump speed  of  used the  and t h e  total  velocity  considered  portion  of  the  to  account  for  depend upon the  in  In  tunnel,  general,  by  mesh s i z e , Hence,  p r o p o s e d by Grove et  used,  tunnel  a charac-  affected  resistance.  blockage, the  a l , can  reference. take  uniform  f a r u p s t r a m and use i t , - a s  However,  boundary l a y e r  (but  position.  questions.  circuit  velocity.  tunnel  the  as  screen's  profile  of  would  in a given  growth,  c  the  investigators.  substantially  U  o t  changes  velocity  several  of  in  the  section  P  location  condition  for  of  desired P ^ .  of  compromise would be t o  velocity  a characteristic  to  a suitable  Another p o s s i b l e  the  model  of  acceleration  model  centerline  boundary l a y e r  of  at  the  of  by p r e s e n c e  choice  by d i f f e r e n t  are  effects  giving  the  choice  a degree  i n the  account  a l s o poses  the  created  thus  operating  cannot  has  influence  used w i t h  profiles  characteristic h a r d l y be  the  from s e c t i o n  velocity  location,  gradient  pressure  with  still  differently,  assumes t h a t  improvement  and between t u n n e l s  velocity  It  cancels  model)  However,  the  it.  model l o c a t i o n  same as  teristic  it  s u g g e s t e d above  pressure  exactly the  as in  One p o s s i b l e be  To p u t  effects model  the  distance  would,  and i t s  in  involved  general,  location.  64  A rather significant data  is  using  to  ensure  different  With t h i s  based has  test  methods  velocity,  on t h e  several  average  mean f l o w  Obviously, the  the  average  not  o n l y does  type  of  section  tunnel, but  and b l o c k a g e . R , reference Furthermore, only  profile due t o  velocity  This  test-section  adopted.  This approach  eliminates  this  of  most  of  the  to  earlier,  model  would  o f model  location,  u s e d and s i z e  b e i n g more p r e c i s e l y quite  and hence  the  of  the  gradient  defined.  simple  and it  involves  must  f o r changes  in  be velocity  r e s u l t i n g pressure  effects  model. that the  elusive  task  of  test  d u p l i c a t i o n of  However,  correct  leave Thus,  would f a c i l i t a t e  is  (but  unchanged.  problems of p r e s s u r e  does n o t  the  model)  question  instrumentation.  b r i n g s us  As d i s c u s s e d  the  measurement  with distance location  i n the  test-section  straighteners  The c h o i c e  emphasized t h a t  It  the  a compromise c h a r a c -  as w i t h t h e  overcomes  conventional  presenting  investigators,  c o n d u c t e d w i t h and w i t h o u t  i n the  flow  its  above  ( U ) , was  eliminate  also  in  to permit comparison.  velocity  rate  setting  velocity it  i n mind  above.  tests  same m e t e r  keep  c a r e f u l consideration of  advantages.  problems mentioned  at  facilities,  discussed  obvious  to  r e p e a t a b i l i t y by o t h e r  i n mind and a f t e r  alternative teristic  its  point  selecting  P^ a d v o c a t e d by A c r i v o s  et  P , 48 al.  65  has  little  presented ability  by t h e  for  model.  tap  on the  quite  at  compensate  data,  attractive.  the for  of  large  of  the  use  the  model as  present  of  repeat-  of pressure  it  at  a  reference  cannot  effects  model),  blockage  of view  the  blockage  i n an a v e r a g e  Thus one way t o  the  Although this  due t o  surface it  of  From t h e p o i n t  surface  local variations  to p o i n t  i n view  and c o m p a r i s o n o f  specified appears  meaning here  account  (from p o i n t  could  effectively  fashion.  pressure  data  in  coefficient  2 form w o u l d be ponds the  to  the  as  C  p  = (P  pressure  at  c y l i n d e r and U as  - P ) / ( p U /2)  Q  a specified  calculated  (average  flow  rate/test-section  However,  this  definition  is  because  the  One way t o pressure Let velocity  tap  and t h e  reference  v i r t u a l l y eliminate  velocity  location)  errors profile  ing pressure  as  at  coefficient  between t h a t  due  P^, e as  at  nation point with respect  flow  Q  a tap the  at  P  ratio  Q  (at  particularly by t h i s  and  at  the  in question reference  rate  errors,  profile  (Figure  of  of  cm).  is  change. to  express  4-1).  to n o n - u n i f o r m i t y o f  a  to  to  shortcoming  e x p l a i n e d below  in pressure be  this  surface  61 cm x 15  susceptible  the  corres-  r  average  denominator remains u n a f f e c t e d  coefficient  pressures,  from t h e  still  P  t a p on t h e  area of  i n t r o d u c e d by n o n - u n i f o r m i t y o f a pressure  where  r  P^.  the Express-  differential and t h e  pressure,  staggives  66  Figure  4-1.  An i l l u s t r a t i o n s h o w i n g p o s s i b l e e r r o r s i n t r o d u c e d by n o n - u n i f o r m i t y o f t h e velocity profile  c  CP  =  e  + e )  -  9  (P  r  +  S  ) 5  where P , Q  velocity  P ^ , pprofile.  P. 0  correspond  to  pressures with  uniform  Thus  - P r  j  1  1  +  (e  0  " e )/(P - r  0  P ) r  Note  that  On t h e large  e  -  Q  other  likely  compared t o  the  to  be v e r y  represent  respective  small.  relatively '  error  dif-  Therefore,  =  9r  likely  are  N  quantities  e  -  hand, P - P and P . - P ' 8 r O r  ferentials.  are  and  £ - £ 19 _x_ P - P O r  a  n  d  ,  e  N  to  be v a n i s h i n g l y  F ^0  =  0r  P  small.  - £ ^r - P O r  N  Consequently,  the  term  1 + £ 1 + £  9r  and  proposed d e f i n i t i o n adequate  uniformity  of  reach ± P^.  was zero  the  inthis  is  the  velocity  0  r  i n the  general  pressure for  coefficient  errors  test  taken to  the promises  to  i n t r o d u c e d by n o n -  be a t  6 = 50°.  d a t a w h i c h showed  v i c i n i t y of location  arbitrary.  the  sensitive,  profile.  in general,  entirely  c h a p t e r use  being  l o c a t i o n was  p r o m p t e d by the  Of c o u r s e ,  pressure  of  compensation  The r e f e r e n c e choice  r  Or  B o t h n u m e r a t o r and d e n o m i n a t o r  provide  _o  definition  C^ t o  8 = 50°, i.e., of  the  The p r e s s u r e of pressure  The  P^QO  reference data  presented  coefficient  as  68  P  C  It  is  easy to  P  P  recognize  the  x i m a t i o n to  (1/2)pU^.  account  the  for  velocity has  velocity  profile  on a v e r a g e to  assist  tigators 1  this other  term PQ - P^QO  flow  pressure  and p o s s i b l e  errors  drifts  drift  velocity  was  of  as  to  As shown  P  the  pressure  sensing  i n Chapter  R e y n o l d s number diameter),  it  3). (based  promises inves-  facilities.  information.  C  the  measure-  s i m i l a r d a t a by o t h e r  test  may a r i s e  for  in pressure the  the  coefficient  discussed  and s p h e r e  different  coefficient as  to  i r r e g u l a r i t y of  any p r o b l e m .  information  likely  effects,  new d e f i n i t i o n may c a u s e published  an a p p r o -  blockage  in comparison with using  as  compensate  i n c o n j u n c t i o n w i t h the  A question  present  50°  tends to  electrical  Furthermore,  P  it  c a u s e d by e l e c t r i c a l (the  -  50°  i n summary, t h i s  advantages:  gradient,  system  P  H o w e v e r , now we a r e  Thus,  pressure  ments  0  -  e r r o r s itttroduced'by n o n - u n i f o r m i t y of  profile.  several  0  the  possible  difficulty  i n comparing t e s t  data with  Fortunately, this  does  i n Appendix I ,  can be w r i t t e n  not  conventional  i n terms  of  measured '  with  an e r r o r  gated  of  <3% i n t h e  R e y n o l d s number r a n g e  investi-  here. It  is  of  interest  to  r e d u c t i o n p r o c e d u r e was  point  first  out  here  that  similar  e m p l o y e d by Modi  data  and  46 Aminzadeh where  . in t h e i r  the  studies with  R e y n o l d s number r a n g e  aortic  of  heart  interest  was  valves 100-1200.  49 More r e c e n t l y , substantiated  extensive  tests  relative  coefficient  profile,  R e y n o l d s number and  set  Effect  of  Figure  4-2  of  number f o r information pressure of  a given  surface  it  the  proposed  geometry,  velocity  blockage.  presented  pressure  discussed  the  as  i n the  using  definition  magnified  summarize  cylinders  blockage  coefficient  conventional  trends,  t h r o u g h 4-4  circular  is  test-section  of  have  R e y n o l d s Number  d a t a on t h e  dimensional  s p h e r e s by A k u t s u  insensitivity  pressure  4.2  to  with  the  a rather  d i s t r i b u t i o n for  affected range  by the  2-50%.  (CT) showed of  two  Reynolds The  new d e f i n i t i o n  before.'  influence  comprehensive  of  the  A l t h o u g h the  use  essentially  the  same  R e y n o l d s number and  70  1.0  0.8  -1-5  * R  0.6  \  1  C. 0.4  L05  0.2  0  0  34 G R O V E etal  A  -1.0\  n -175  •  12.5%  PRESENT  U -0.5  c  S/C 10 %  p ,Grove etal  •  •  0-2 U - 1 0 A  - 04 L-1-5  -0.6 0  30  .6 0  120  90  150  180  e Figure  4.2.  R e p r e s e n t a t i v e p r e s s u r e p l o t s comparing present r e s u l t s w i t h t h o s e by Grove e t a l . a t a low R e y n o l d s number o f 175. Note a r e l a t i v e i n s e n s i t i v i t y o f t h e p r o p o s e d p r e s s u r e c o e f f i c i e n t to d i f f e r e n c e s i n t e s t c o n d i t i o n s .  71  1.0  .1-0  A  0.8 >0.5 \f  • 0.6  36 - H EL-SHERBINY 15x10 3 PRESENT 15x10 3  -0 C  P  0.4  -0-5  0.2  L -10 Cp , El-Sherbiny  0  _1.5  A  --2.0  0-2  *  A •  AV  0.4 0  30  90  60  120  150  9 Figure  4-3.  A c o m p a r i s o n o f p r e s e n t r e s u l t s w i t h t h o s e by E l - S h e r b i n y a t a r e l a t i v e l y h i g h R e y n o l d s number o f 15 x 10^.  ,72  wall to  confinement  the  same  models. sets  conclusion  Note  of  the  results  investigations At number the  the is  (Figures  quite  blockage  during his  well  conducted  outset  R^ o f up t o  ratios  of  the  minimum as of  the  approximate by t h e wake)  beginning tend to  At the  same  to note in his the  is  here  of the  the  study with  effect  and even except  point  a circular  R e y n o l d s number r a n g e  of  the  it  of  is  higher  an i n c r e a s e  in  in  Furthermore,  together  with  (as  the  indicated  region of  the  upstream. (Figures  around R 36  here  for  separation point  ratios  Sherbiny  Reynolds  a corresponding increase  uniform pressure  to  of  r e g i o n downstream  maintained., however,  extended that  the  to  facilities.  wake p r e s s u r e s .  a little  blockage  trend is  dependency  of  shift  higher  to  spherical  correspond  In g e n e r a l ,  minimum p r e s s u r e  location  the  a r o u n d 1200,  R e y n o l d s number l e a d s  location  to  came  different  test  the  ( F i g u r e 4-4)  the  as  correlates  that  25% and 501.  well  studies with  in different  confined  point  Akutsu  although they  one can say  essentially  to  and 4 - 3 ) .  new d e f i n i t i o n  zero p r e s s u r e  limited  4-2  also  4-4 e, f) the  observed  c y l i n d e r of 5 x 10  R e y n o l d s number  = 3000.  n  4  essentially  It the  35.5  - 12 x 10  is same  of  interest  trend  % blockage 4  .  '  in  73  1-0 0.8  S / C =2% [D 1.2cm] =  R  n=  0.6 0.4  18 • 34 o 160 A 400 A 720 • 1200 * 1560 o  0.2 C.  0  A  Km*-  - 0.2  •  •  A  •  O  A  o A  \ A  0-4  A  A  a \ \  ^ ° o o o  J3'  o a-  50  -0-6  Dennis and Chang  0.8 -1.0 0  30  60  90  120  0° Figure  4-4  S u r f a c e p r e s s u r e d i s t r i b u t i o n as a f f e c t e d number f o r a g i v e n b l o c k a g e ratio: a) S / C = 21.  150 by the  180 Reynolds  74  1.0 S/C 3.3'%CD= 2 cm] =  30 55 . 300 • 12 00 • 3000 <  R =  0.8  n  0.6 0.4 T  0.2 c  p  0  -0.2 - 0-4 - 0-6  D  n  D  •  -08 -1.0  0  30  60  90  o  120  150  0 Figure  4-4  S u r f a c e p r e s s u r e d i s t r i b u t i o n as a f f e c t e d number f o r a g i v e n b l o c k a g e ratio: b)  S/C =3.3%.  by t h e  Reynolds  75  to S/C= 6.6%  60 80 130 600 120 0 3000 6000  R: n  0-8  CD = 4cm]  0-6  0-4  D  O A •  <  c 0-2 0 e  l  2  «1  -0-2  A  O  A  8  •0-4  A  f  A  A  O •  a o  A D  O  A  O A A O ° o o ^ oo •  • • D  • •a  -0-6 -0-8  i  < •  0  30  60  90  120  150  0 Figure  4-4.  S u r f a c e p r e s s u r e d i s t r i b u t i o n as a f f e c t e d number f o r a g i v e n b l o c k a g e ratio: c)  S/C  = 6 . 6 % .  by t h e  Reynolds  76  10 S/C =12.5 % [ • =7.6 cm] 110 • n= o 230 o 120 0 3000 61 50 11000  0-8  R  0-6 0-4 0- 2  c  p  a  0 u  -0-2  ®•  . J o o  n  °  o  o  o  o  o a  D  OoO°  -0-4 •  •  •  •  •  - 0-6 -0-8 -1.0  30  60  90  120  150  1  8 0  0 Figure  4-4  S u r f a c e p r e s s u r e d i s t r i b u t i o n as a f f e c t e d number f o r a g i v e n b l o c k a g e ratio: d)  S / C = 12.5%.  by the  Reynolds  77  1-0  S/C= 25 % [ D=15 cm J R  0-8  = 190 360 800 120 0 2000 3000 5000  0  0-6 0.4 C  p  V  o  o  0.2  0 O  -0-2  8~o<> o  o V  0  V  -0-6  o  v  -0-4  o  O  4*  •  6  o  v  D  •  -0-8  O  30  60  a n  90  1 20  1 50  e Figure  4-4  S u r f a c e p r e s s u r e d i s t r i b u t i o n as a f f e c t e d number f o r a g i v e n b l o c k a g e ratio: e)  S / C = 25%.  by t h e  Reynolds  78  1.0 S/Cz50 % CD= 30 cm]  0-8  R= R  0.6  350 730 1200 240 0 3000 18000  0-4  V  o  o  0-2 C  0  P  0.2 - 0,4 A  A  - 0-6 •  T  0-8  - 1.0  0  30  60  90  120  150  180  6° Figure  4-4  S u r f a c e p r e s s u r e d i s t r i b u t i o n as a f f e c t e d number f o r a g i v e n b l o c k a g e ratio: f)  S / C = 50%.  by the  Reynolds  79  It  must be e m p h a s i z e d  of pressure cylinder  not  been  i n absence  range  of  the  His  access  the  experiments,  fluid for  to  pressure  differential system  out w i t h  trends  other hand, r e s u l t s  indeed  reliable, 145.  than  constant and a r e  however,  they fail  pressure  of  Foppl  leading  shedding.  Recently,  difference  scheme  results  tend to  (Figure  4-4a).  4.3  Wall  for  4-5  of  the  are to  have attempts  And t h a t  of  required, with too w i t h  His results  considered  and h i s  l i m i t e d to  throw any l i g h t  have  equations  show  are  a single  instability  the  misleading.  associates  d i s t r i b u t i o n and to  a working  a manometer  and C h a n g ^  solution  as  3-174,  Reynolds  on c o r r e -  evolution and  vortex  developed of motion.  c o n f i r m t h e i r p r e d i c t i o n up t o  Confinement  Figure  Dennis  the  instrumentation.  one h o u r !  generally  between s u r f a c e vortices  in  for  or water  1 mm!  of  lation the  oil  by Grove  Hence t h e y  circular  < 20,000)  except  reading of  less  On the  number o f  (R  R e y n o l d s number r a n g e  column o f  a  U n f o r t u n a t e l y , Thorn d i d n o t  3 4  measurements,  of  measurements  effects)  modern s o p h i s t i c a t e d  h a v i n g a time  questionable  blockage  literature,  al.  carried  and i n t h e  of  surface  R e y n o l d s number  r e c o r d e d i n the  by Thom*^ and Grove et have  such d e t a i l e d  d i s t r i b u t i o n on.the  (even  indicated  that  a  finite Present  R^ = 100  Effects  summarizes  results  on the  influence  of  blockage  80  for  circular cylinders  be  recognized  that  in  any l i q u i d  tunnel  F o r the  present  respectively. by the load  at  the  a given  are  However, of  imposed on t h e  l i m i t e d by d e s i g n t h e y were 0.5  the  the  drive  useful  pressure  a given blockage,  possible  cover  the  desired  -  3000).  presented  This  here.  established. the  wall  reduce point  point  4.6)  only  over  the  of  it  trends it at  are  is  confirmed this As c a n be  although  visualization  study  always  i n the  reasonably that,  results  well as  before,  of  the  are  zero  tendency  to  The minimum p r e s s u r e with of it  an i n c r e a s e the  is  in  the  separation  not  described  always later  quite (section  trend.  expected  from the  previous  blockage  effects  remain e s s e n t i a l l y  However,  what  more s i g n i f i c a n t  is  gaps  a definite  rearward s h i f t  blockage  was n o t  downstream  S i m i l a r downstream movement  A flow  high  R e y n o l d s number  minimum and b a s e p r e s s u r e s .  discerned,  and a d d i t i o n a l  apparent  a given  has  restricted  R e y n o l d s number  unavoidable  region  The b l o c k a g e  can a l s o be  distinct.  the  effects  shows a d i s t i n c t  blockage.  to  From F i g u r e 4-5  point.  the  led  However,  confinement  significant pressure  has  range  speeds  cm/s,  further  s y s t e m d u r i n g the  for  (10  is  and 15  transducer  Hence  must  considerations.  cm/s  range  condition. to  It  minimum and maximum a t t a i n a b l e  facility,  sensitivity  R e y n o l d s number.  the is  discussion,  same f o r  R  an i n c r e a s i n g  n  the  > 3000. dependence  81  1.0 =3000  R n S/C %  .0,8  3.3  .  6.6 o  12.5  0-6  04  A  25  •  50  .  0.2 C 0 •o • o• • A  •o •  o o• • o • o a  0.2  D  •  2  2  A  •  •  aa a  .0.4  -0-6  -0-8  - 1-0  Figure  0 4-5.  30  60  Pressure plots number:  90 0°  120  as a f f e c t e d by b l o c k a g e a) R = 3000. . n  150 at  a given  180 Reynolds  82  1-0  R  z1200  p  S/C % ,  0.8  •  3.3 6.6  o  12.5  0-6  25 50  0-4  c 0.2 0 •  rt • O •V •O '* A * ° •  v  *  V  .0-2  <5 •  o • o •o • A  •  V  V  -0-4  •  a  .0-6  •  •  0-8 -1.0  0  30  60  90  120  150  180  9°  Figure  4-5.  Pressure plots number: b) R  as a f f e c t e d = 1200.  by b l o c k a g e  at  a given  Reynolds  83  to R = 400  0.8  S/cL  2  .  3.3 o  0-6 C. 'P 0-4  12.5  -  25  D  50  T  0-2  0 • 9  0-2  - 0-4  o  • o • o • o • o • o •  o  • • • •  0-6  P •  0.8  1-0  0  30  60  90  120  150  180  0° Figure  4-5.  Pressure plots number:  as. a f f e c t e d by b l o c k a g e c) R = 400. n J  at  a given  Reynolds  84  i-o R .-200 n  •  0-8  S/C;  T  2 12.5 25  0-6  °/o  T  °/o  a  I. •  0-4  0-2 C 0  •  •  r a  - 0-2  r  •  D  •  •  • •  T  n •  • •  •  •  -0-4  0.6  0.8  1-0  • -  0  30  60  90  o  12 0  150  180  6 Figure  4-5.  Pressure plots number:  as a f f e c t e d by b l o c k a g e d) R = 200. n  at  a given  Reynold*  85  1.0,  0.8  R  n=30  S/C = 2 0.6  /  Q  3-3  °/  0  r  0.4 C 0.2  0  - 0.2 T  -0.4  -0.6  T  • •  T  T  •  -0.8  -1-0 0  30  60  90  120  150  180  e Figure  4-5.  Pressure number  plots  as a f f e c t e d by b l o c k a g e e) R = 30 n J  at  a given  Reynolds  86  of  the  surface  The p o i n t  is  substantial change  well  modification  at  in this  lower  Reynolds numbers.  4-5e,  w h i c h shows a  pressure  t h a n 1.5%.  d i s t r i b u t i o n for  In g e n e r a l ,  of  the  R e y n o l d s number have  be u n r e l i a b l e b e c a u s e  of  the  drastic  other  are  Figure  4-5  Figure the  average  In g e n e r a l ,  In t h e s e  represent  4-6  rise  tions  of  ditions  with  is  to  effects  presented  information.  minimum p r e s s u r e  and  somewhat  b o t h t h e minimum  R e y n o l d s number  = 3000.  For a given  reduce  of  ratio,  the  r a t h e r s t e e p under the  25%and 50%.  blockage  is  the  blockage  around R  cases  results  On  w i t h R e y n o l d s number and b l o c k a g e .  increase  uniform values  b u t becomes  circumstances,  a constant  i n b o t h the  involved  on b l o c k a g e  an i m p o r t a n t p i e c e  base p r e s s u r e  and b a s e p r e s s u r e s nearly  predictions  shows v a r i a t i o n o f  for  assumptions  tended  schemes o f n u m e r i c a l i n t e g r a t i o n ^ .  hand, t h e o r e t i c a l  indeed none.  a  analytical  range  _the  of  i n the  by l e s s  and breakdown i n t h e  in  on b l o c k a g e  e m p h a s i z e d by F i g u r e  i n blockage  approaches to  pressure  Note,  g r a d u a l at higher  lower  rate  of  blockage  confinement  condi-  R e y n o l d s number, t h e  these parameters,  rather dramatically.  the  attaining  effect  under c e r t a i n  Interestingly,  ~ Cp  1  conS  n  o  t  m  49 independent  of blockage,  with spheres, Numerical  but  results  Unfortunately, o n l y up t o  R  n  is  as  strongly  by D e n n i s  their = 100  o b s e r v e d by A k u t s u  finite and t h a t  dependent  on i t  in his (not  shown).  and Chang*^ compare r a t h e r difference too  procedure is  i n absence  of  studies  well.  valid  blockage.  S/C %  c.  *  ml  o  * a * •  0  2 3-3 6-6 12.5 25 50 o  0.2  A •  o A  D  0-4  0-6  0.8  10'  10 Figure  4-6  E f f e c t o f w a l l confinement a) minimum p r e s s u r e .  10  v  on t h e minimum and base p r e s s u r e s ' , .  10 10 < R < 18,000 n  R  n  CO  c P  b  I r  0  S/C7 • . 92 o 3-3 A 6-6 • 125 • 25 • 50  0  _Dennisand C h a n g O  5 0  A  A  D  A A  A  A  •  0-2 A  •  0-4  0-6  0-8 10  Figure  4-6.  10  2  io  3  E f f e c t o f w a l l . c o n f i n e m e n t on t h e minimum and base b) base p r e s s u r e .  io  4  R  p r e s s u r e s , ' 10 <. R < 18 , 0 0 0 : n '  n  89  4.4  Drag  Coefficient  Pressure h a v i n g been pressure  d i s t r i b u t i o n on t h e  established,  integrated  on b l o c k a g e . friction ment o f range  the  value  This,  of  course,  contribution.  On the  6 x 10  number r a n g e  of  are  other  confined  generally  pressure  R  n  = 1000  R  n  = 3000 at  drag  -  profiles  to  effect  of  marily  because  velocity.  do n o t = 1000  of  Note,  coefficient  the  the  drag  direct  for  is the  over  the  the  the  increase  blockage  can i n c r e a s e  be  primarily  it.  Since  beyond  values  and  pressure  to  remain  of  the  anticipated,  drag i n the  ratio  and  the  expected  critical  As can be  increase  local  before,  ratios  condition), is  Reynolds  minimum p r e s s u r e  lower blockage  beyond these  to  low  to  substantially  confinement  measure-  study.  coefficient of  skin  h i g h R e y n o l d s number  present  change  (Figure 4-7).  blockage  for  As p o i n t e d out  for a given blockage  constant  R e y n o l d s number  the  obtain  dependence  d i s t r i b u t i o n downstream o f  higher  coefficient  essentially  drag  (R  the  account h a n d , the  to  and l o c a t i o n  pressure  3000  its  to  considered u n r e l i a b l e ,  relevant  g o v e r n e d by m a g n i t u d e  the  s t e p was  - 300 by Thom^"*".  are not  and the  logical  cannot  One w o u l d e x p e c t p r e s s u r e  point  a cylinder  5 x 10^ by A c h e n b a c h * ^ and the  10  Thorn's r e s u l t s Achenbach's  -  4  of  d r a g and ass,ess  of  skin f r i c t i o n is  of  next  surface  coefficient free  range  by as much as  the  of  125%.  pri-  stream 50%,  the  Numerical  cD,  S/C% . 2-3.3 12.5 Present A25 50 54 Rosenhead 50 Dennis and Ghang  •  A  I  I  I  I  I  I  I  10  I  I  10'  Figure  4-7.  Variation  of  the  10  pressure  drag  coefficient  with  v  R  Reynolds  10  n  number and  blockage.  91  results  by D e n n i s  ably with  the  experimental by  and C h a n g  ,  measured d a t a . results  by R e l f  for  < 100,  The s o l i d 52  line  and P r a n d t l  compare  favor-  corresponds 53 al. as  et  to  quoted  Rosenhead^ . 4  4.5  S t r o u h a l Number  The  factors  frequency  governing  for b l u f f  the  bodies  length  parameters  to  direct  r e l a t i o n with  have  this  is  stream) forms  the  which w i t h  the  it  Reynolds J  define  does n o t  have  incident  i n the  tends  to  fact  of  yet  a model  S .  4  for  depend on the  understood.  ( n o r m a l to  and v o r t e x of  a given  < R < R . n .n,cr  a more g e n e r a l  shedding  frequency.  Importance  n  be u n i f o r m i n t h e  number, 1 0 '  clearly  shedding  velocity  that,  f o r m a t i o n and  been p r o p o s e d w h i c h a r e  the  height  S t r o u h a l number,  number l i e s body,  projected  vortex  are not  Several  to  J U  form o f  body shape  the  r  range  have  of  a  of  the  been  S t r o u h a l number  or i t s  free  Strouhal  orientation  Attempts '  the  One o f  frequency  the  subcritical  thought  made'  that  orientation.  The  55 most w e l l tance  known i s  between the  parallel,  h,  that  separated  and t h e  characteristic  due  to  shear  separation  parameters  to  Roshko -  layers  velocity  give  where after  the  normal  they  u" a r e u s e d s  dis-  become as  92  *  fh U  =  b  s  The of  'universal' 0.181  plates. layers  for  vortex  In t h i s with  0.98)  S at  the  it  to  the  with  4-8.  Figure  of  normal  value  between the  flat  shear  associated  at  to mention here  cylinders  the  and a n g l e  ellipses  (e  of =  attack 0.92,  between s e p a r a t i o n  S t r o u h a l number  (based  on t h e  R e y n o l d s number and b l u f f n e s s  with  the  around R  t h o s e by Roshko  over a  c o r r e l a t i o n improved sub-  distance  In g e n e r a l ,  (for  c o n d u c t e d by Modi  correlating results  slender  experi-  points  length.  the  the  a uniform value  58  pertinent  However,  the  number i n c r e a s e s  El-Sherbiny  is  effort  characteristic  in  distance  important parameters  poorly for  a < 50°.  with  the  the  9 0 ° wedges and n o r m a l  cylinder eccentricity  fair  diameter)  the  elliptic  Their  Variation  with  of  a f a m i l y of  stantially as  one  context  range,of  showed  that  f o u n d t o have  shedding.  and D i k s h i t " ^ . wide  cylinders,  suggests  represents  w i t h the  ments  S t r o u h a l number was  circular  This  '  32  ,  for  is  a given blockage,  R e y n o l d s number t e n d i n g n  = 1000.  Relf  negligible  Comparing these  and Simmons blockage)  57  cylinder presented  the to  approach results  , and Modi  i n the  Strouhal  and  ' R e y n o l d s number  4 range  of  40  < R^ < 10  value  represents  a peak  suggests followed  that  this  apparently  by a drop i n the  constant  Strouhal  S/C %  0-4  A  5  •  1 5  •  25  0-3  'n 0-2  •  A  A A*  0-1 A  0  J  L  •  I  J  20  Figure  4-8.  I  L».  J-  I  100  V a r i a t i o n of number range  the (R  S t r o u h a l number w i t h b l o c k a g e < 1000).  I  R  at  the  1000  n  lower  end o f  the  Reynolds  94  number f o r  10  < R '5 1 0  J  As a n t i c i p a t e d , hal  number  velocity. apparent the  F o r the for R  trend is  vortex  rate  increase  i n the is  information  effect the  blockage  > 2000.  at  of  4-9).  of blockage  local  increase  ratios  of  i m p o r t a n t to on t h e  4-10  corresponding function  4.6  to  of wall  vortex to  was  trend  is  R e y n o l d s number,  the  delay  i n the  Thus,  at  emphasize  subject  is of  here  that  due t o Modi 4 10  - 1.2  shows v a r i a t i o n o f the  i n i t i a t i o n of  confinement. initiates  R  for  = 300  onset  lower  of  Reynolds w i t h an  only other  and S h e r b i n y 5  x 10  for  the  .  Their  comparison  58  relevant  in  results in  the  the the  Note, at  R  R e y n o l d s number vortex  shedding  i n absence = 41.  blockage  of  However,  ratio  of  as  a  blockage it  is  501!  Flow V i s u a l i z a t i o n and Near-Wake A n a l y s i s  To p r o v i d e b e t t e r of  this  of v o r t i c i t y diminishes  shedding n  the  a p p r e c i a t i o n as w e l l  c e r t a i n b e h a v i o u r e x h i b i t e d by t h e  decided  to  Strou  freestream  4 - 9.  Figure  delayed  i n the  the  lower  show s i m i l a r t r e n d and a r e p r e s e n t e d  the  increase  blockage.  R e y n o l d s number range  Figure  to  at  higher blockage.  generation  is  considered,  However,  r e v e r s e d because  numbers,  the  n  shedding  It  the  . because of  (Figure  H  undertake  an e x t e n s i v e  flow  as  substantiation  measured d a t a , visualization  it  0.4 'n S/C°A "  5  )  • 15 / Present • 25  0.3  Roshko  35.5 %  32  ..---26.5 ?  Q  14.8 % S/C = 4-5 \  0.2 59 Nishioka and Sato  Modi and £ El-Sherbiny  8  0.1 10 Figure  4-9  10  R  10"  A c o m p a r i s o n o f measured S t r o u h a l d a t a w i t h  t h o s e by o t h e r  n  investigators  10  V  to  on  300 n R n  .cr.  Flow visualization Hot film probe measurements 200-  100 -  0  10 Figure  4-10.  20  Onset o f v o r t e x  30 shedding  as  affected  40 by the  blockage  50  S/C % <o ON  97  programme.A s e t were u s e d  of  i n the  cylinders  ranging i n diameter  glycerol-water  solution  by w e i g h t .  The main o b j e c t i v e  was  to  development  and i n s t a b i l i t y  the  Foppl  associated  influence  on the  a l s o hoped t h a t  this  location  separation  use  of  dye  proved It  of  to  injection be q u i t e  showed  fashion  the  procedure,  effective  presented at  systematic  Only  of  the  a few  symmetric followed  by t u r b u l e n t  The e x i s t e n c e  in  of  shedding  For to  turbulence  the the  R^ -  is  first  2),  a closed  the  formation of streamlines  region  s t r e a m emerges  from the  spectacular  to  a long distance  is  such  as  to  Numerous of  the  Reynolds  and  are p r e s e n t e d  essentially  b e h i n d the  of  the  formation,  in Figure vortex free  4-12(f).  (corresponding vortices,  surface  and form  cylinder. A  cylinder.  for  o f macro-  or Foppl  closed  4-12.  system  through  a c r i t i c a l value  b e h i n d the  number.  instability  stable  from t h e  earlier,  photographs  illustrating  asymmetry  separate  vertex  The  in a rather  a s t a b l e bubble  immediately  concerning  movement.  i n F i g u r e 4-12(a)  R e y n o l d s number above  was  objectives.  an a x i s y m m e t r i c ,  shown  It  these  low R e y n o l d s number i n a s t r e a m , scopic  data.  the  achieving  increments  of  and  in detail  vortices  onset  formation,  explained  typical pictures  elongation,  the  vortices  and i t s  i n F i g u r e 4-11.  were t a k e n  observe  cm  concentration  some i n d i c a t i o n  position  the  761  measured p r e s s u r e  would p r o v i d e  formation of  as  of  of  from 1-10  single  region  The s i z e  m a i n t a i n an e q u i l i b r i u m between the  of  extending the  rate  at  bubble  98  99  Figure  4-12  A flow v i s u a l i z a t i o n s t u d y showing development and i n s t a b i l i t y o f v o r t e x r i n g w i t h R e y n o l d s number ( S / C = 15%): (a) R = 4; (b) R = 10; (c) R = 17; (d) R = 21 n  n  n  n  100  Figure  4-12  (cent.)  A flow  development  m \ ( ) f  R n  showing  and i n s t a b i l i t y o f v o r t e x  ?J = 42;  R e y n  v i s u a l i z a t i o n study  d s  n  u  (g)  m  b  R  e  r  R  =  ( 5  S / C  6;  ring  = 15%): (e) R (h) R ^ ' = 6 0  = 31N  101  which v o r t i c i t y  is  stream.  As the  Reynolds  vortices  become e l o n g a t e d  this  the  plots  the  front  separation presented  wall in  confinement  the  ble  flow  separation point.  points  also  was  (Figure  itself  see  of  a small  enlarges  maintain  upstream movement  s u g g e s t e d by t h e  pressure  (depending  Figure 4-10), the  i n the  and a r e s u l t a n t  beginning  gressively  asymmetry  to  move  main  Foppl  This forward  number between 42-300 condition,  the  direction points  the  4-4).  c i r c u l a t o r y motion w i t h i n  a corresponding  the  i n the  into  increased,  stagnation  earlier  For Reynolds  and d i s s i p a t e d  number i s  e q u i l i b r i u m , and the  towards of  generated  from t h e  sheet  produces  the  i n the  centerline.  i n F i g u r e 4-12 (g)  accentuating  the  asymmetry  c i r c u l a t o r y motion  shift  vortex  vortex  an  on  asymmetry  as  Note  which in  bub-  pro-  Figure  4-12(h). The  state  by f u r t h e r vorticity fluid rate  of  increase is  but  from the  remain p r a c t i c a l l y  at which  it  is  bubble  transferred vortex  b u i l d - u p and r e l e a s e , escapes  to  sheet.  cycle.  into  but  vortices  Basically,  i n the  at  the  which  the  portion of  the  unstable  process  the  the  increased  creates  end o f  T h i s i n t u r n causes  disturbed  main body o f  constant, the  is  The r a t e  the  b u t no s i z e a b l e  t h r o u g h an o p e n i n g  d u r i n g the  number.  sheet  to  the  s t e a d y wake  Reynolds  appears  of  sheet  i n the  diffused  condition within one  unsymmetrical  is  the  vortex  oscillation  102  of  the  4-12  a s y m m e t r i c a l wake  g , h)  .  about  the  When t h e v o r t e x  axis  of  symmetry  strength  of  the  a critical  value,  a sudden m o t i o n o f  turbs  sheet,  which i n turn  the  vorticity  and a c o n s e q u e n t  original  position  release,  the  and s h a p e .  is  the  In t h e  cycle  for  i n the  i n which the  strength  is  the  main body o f sheet  is  greatest  the  carried  stream i n t e r a c t s wake p a t t e r n , (Figure  The s e c t i o n s are  fluid.  with  The v o r t e x the  familiarly  known as  layer.  of  results In t h e  as as  To t h i s  end,  and the  flow  the  vortex the the  discharged into to  the  form a r e g u l a r  Karman v o r t e x  street  visualization results  p h o t o g r a p h s were  the  the  the  4-14(a). are  of  s e p a r a t i o n p o i n t moves  separating  as  a func-  The c o r r e s p o n d i n g shown i n F i g u r e  R e y n o l d s number ( R two s e t s  pro-  analyzed  separation position plotted  g i v e n by p r e s s u r e p l o t s  common r a n g e o f  that  the  shown i n F i g u r e  c o r r e l a t i o n between Note  axis  a p o r t i o n of  information concerning l o c a t i o n of  systematically tion  flow  4-13).  useful  shear  liquid  the  the  becomes  discharged into  element  dispersed  As m e n t i o n e d b e f o r e , vide  alternately  of  With each e j e c t i o n ,  away.  its  boundary l a y e r  within  sheet.  of  o f b u i l d - u p and  sides  vortex  dis-  release  the bubble to  c o n c e n t r a t e d on d i a m e t r i c a l l y o p p o s i t e the  reaches  vortices  responsible of  v o r t i c i t y generated  bubble  Foppl  return  (Figures  n  results  -  4-14(b).  10 •-. 260) , is  rather  f o r w a r d by about  the  good. 10° for  the  100  u  Figure  4-14.  P o s i t i o n o f s e p a r a t i o n as a f f e c t e d a) flow v i s u a l i z a t i o n d a t a . •  200 by the  Reynolds  number and w a l l  300 confinement:  !  150  o »o  • •  T  o  •  •  o  S/C  100  6.6% . 12.5 % 25 % 50 % o 2%  -  50 10  Figure  10'  4-14.  Position  •u ^ 1  ^„J  o£ separation  1Cf  as  affected  1 _ J. _  by t h e /" ^  R  1CT  n  R e y n o l d s number and w a l l  confinement  106  the  blockage  range the  of  9-28,  range  R  available Here  the  results tions also  ratio  = 30  n  line  sheet. move  by  as  much as  must be point  unstable  Typical offering 4-16.  2 5 ° over  the  blockage  that  the  the  governing  scheme. of  the  confinement  range  downstream,  of  Considering this scatter  figure  separating  separation  ratio  equa-  The  2-50%.  determination of  process,  photographs  blockage  of blockage  ( F i g u r e 4-15  of  i n the  100  is  t h e wake a s s o c i a t e d are presented  on e v o l u t i o n  It  separation  and  the  experimen-  of  25%,  a)  , however,  in  the  wake b e h i n d a c y l i n d e r o f  and  is  stable  this  at  of  the  b)  point.  .  4-15  in Figure  a  and fixed  4-15.  t h e wake has  just  same R e y n o l d s n u m b e r , is  still  Photographs  Note,  cylinders  t h e wake a t  50% b l o c k a g e  ( F i g u r e 4-15  f u r t h e r emphasize  of  instability  with  in Figure  v i v i d l y depicted  set  4-16  the  included.  represents  of wall  layer  visual  approximate.  also  surprisingly small.  a lower blockage  quite  effect  shear  R e y n o l d s number o f At  are  on p o s i t i o n  the  45° o v e r  For comparison,  and C h a n g ^  the  different  Effect  Dennis  of  best,  is  b ).  a finite-difference  In g e n e r a l ,  character, of  results  R e y n o l d s number  investigators  of blockage  location  at  small  ( F i g u r e 4-14  by o t h e r  emphasized  is,  the  numerical i n t e g r a t i o n .of  shows e f f e c t  to  over  a t t r i b u t e d to  the  is  tal  - 6000  of motion using  vortex  5%  and can move u p s t r e a m by as much as  results  of  of  the  developing in  Figure  wake b u b b l e  108  (b)  Figure  R  n  = 150 , S/C= 50%  4-16  Photographs confinement  emphasizing i n f l u e n c e of w a l l on e v o l u t i o n o f t h e F o p p l v o r t i c e s :  (a)  R  n  = 85,  (b)  R  n  = 150,  S / C = 25%; S / C = 50%  109  associated stable other is  even hand,  the  Foppl  25%.  Figure  4-17  the  50% b l o c k a g e  a R e y n o l d s number as  of  Foppl of  at  c y l i n d e r of  h i g h as  v o r t i c e s have e v o l v e d  approaching i n s t a b i l i t y  blockage  of  w i t h the  attempts  at  to  R  n  = 85 f o r  assess,  the  flow  by u s i n g  as  length  a measure  of  smaller  150.  on the  the  f u r t h e r and wake the  c y l i n d e r with  effect  development  cavity  for comparison.  and  On t h e  quantitatively,  R e y n o l d s number and b l o c k a g e vortices  is  i n the  of  the  direction  Experimental  results  33 by T a n e d a Chang^,  and n u m e r i c a l v a l u e s i n absence  expected,  the  cavity  However,  wall  growth.  Note,  present  results  as  Dennis  in  1956  known,  there  is  Dennis the  considerable  is  likely  of  to  Navier-Stokes authors  instability  diminish with  out  data of are  equations  as  themselves,  an i n c r e a s e  his  technique  give  and has  As  R e y n o l d s number.  Taneda  condensed  and C h a n g ' s r e s u l t s  susceptible to  the  and  its  rate  d i s c r e p a n c y between 33  coated with  by t h e  length  with  included.  d r a s t i c a l l y diminishes  As p o i n t e d out to  also  increases  in experimental  procedure  of  are  Taneda c a r r i e d  cylinders  excellence  accuracy.  o b t a i n e d by D e n n i s  f o r S / C = 5% and t h o s e  and C h a n g * ^ .  the  analysis  length  confinement  towing  Taneda's  of blockage,  as  the  well  experiments milk. is  Although  quite  well  limited  through numerical mentioned the  earlier.  procedure  occasionally i n the  as  of  shown  is vortex  R e y n o l d s number!  33 Taneda 50 Dennis&Chang  o T  •  s/c 5 15 25 50  %  » R 100 Figure  4-17  Dependence  of vortex  200 length  on the  R e y n o l d s number and b l o c k a g e  n  300  4.7  C l o s i n g Comments  Before some o f  on p o s s i b l e  l i k e l y to  4.7.1  it  w o u l d be. a p p r o p r i a t e t o  t h e more s i g n i f i c a n t  thoughts are  closing  avenues  results  and e x p r e s s  review a  few  f o r f u t u r e e x p l o r a t i o n which  be p r o f i t a b l e .  C o n c l u d i n g remarks  Important results  conclusions  may be s u m m a r i z e d as  (i)  The use  (based  on t h e mean f l o w  together  of  b a s e d on t h e follows:  average v e l o c i t y rate)  as  i n the  test-section  a reference  w i t h the p r e s s u r e c o e f f i c i e n t  velocity  defined  as  Pn - P J 1  =  C  experimental  P  p r o m i s e s t o p r o m o t e r e p e a t a b i l i t y and c o m p a r i s o n o f by o t h e r used. of  the  investigators This  approach tends to  velocity  measurements measuring  regardless  o f the  compensate  p r o f i l e and p o s s i b l e  for  facilities irregularity  errors in pressure  c a u s e d by e l e c t r i c a l d r i f t  system.  test  data  of  the  pressure  112  (ii)  For pressure  the  effect  the  r e g i o n downstream o f  it  is  of  d i s t r i b u t i o n on t h e  R e y n o l d s number i s  l i m i t e d to  R  R e y n o l d s number i s wake p r e s s u r e s . pressure  (iii) is  tend to  become at  affected  sensitive  the  end o f  there  is  a definite  in  the  (iv)  shows a d i s t i n c t  confined  to  and even  here  of  of  surface  the  the  t h e minimum  little  to  as  upstream.  of  a cylinder  Pressure  the  wall  confinement  R e y n o l d s number r a n g e .  tendency  to  reduce  the  The minimum p r e s s u r e  rearward s h i f t  w i t h an  increase  blockage.  Drag c o e f f i c i e n t  distribution at  a cylinder,  effect  blockage.  extremely lower  the  of  minimum as w e l l  shift  by t h e  minimum and b a s e p r e s s u r e s . point  the  d i s t r i b u t i o n on t h e  substantially  In g e n e r a l ,  In g e n e r a l ,  increase  and s e p a r a t i o n  particularly  point  Furthermore, locations  Pressure  profiles  to  essentially  zero p r e s s u r e  < 3000.  n  surface  data agrees r a t h e r w e l l w i t h the  small blockage,  reliability  o b t a i n e d by i n t e g r a t i n g  of  the  drag  the  local rise  the  by o t h e r  investigators  i n the  increases free  with blockage  stream  results,  substantiating  measuring i n s t r u m e n t a t i o n .  coefficient  pressure  velocity.  In  general,  because  of  113  (v) as  Flow v i s u a l i z a t i o n p r o v i d e d b e t t e r to  the  physical  formation, It  elongation  showed  the  an i n c r e a s e  (iv)  in  reference  o b t a i n e d here  long c h a i n polymer  shear  Recommendation f o r  vortices.  out  effects  before,  at  beginning.  as  a  useful  In t h e  on t h e  surface  present  the to  present the  efforts  physics  of  at wall  low R e y n o l d s numbers r e p r e s e n t  only  T h e r e a r e numerous  avenues  along  in future.  recommended f o r  Some  future  below:  set  pressure  flows;  the  summarized  (i)  in:  study  r e s e a r c h programme may p r o g r e s s  are  with  solutions.  future  more i m p o r t a n t a s p e c t s ,  studies,  Foppl  t o move downstream  and p u l s a t i l e  some a p p r e c i a t i o n as  confinement  the  the  of  i n comparing c o r r e s p o n d i n g data o b t a i n e d  (b)  which the  of  i n terms  should serve  turbulent,  a modest  flow  blockage.  As p o i n t e d  of  location  (a)  obtaining  the  and i n s t a b i l i t y  separation  Results  4.7.2  character of  appreciation  of  experiments,  blockage  d i s t r i b u t i o n c o u l d not  be  effects studied  114  over  the  entire  range  Limiting  factors  sitivity  of  surface so  the  [0(10  measurement  pressure  with  repeatability.  blockage) picture  at  at  of  interest  of  the  n  in a l l  it  presented degree of  Therefore,  is  found to  suggested that  lower Reynolds numbers(and  confinement  effects.  The be  a c c u r a c y and  This  pressure,  higher  s h o u l d be u n d e r t a k e n t o p r o v i d e a  of w a l l  sen-  a problem of  an a c c e p t a b l e it  cases.  instrumentation.  R e y n o l d s numberswas  that  the  d r i v e s y s t e m and  measuring  lower  ^)psi]  measumrenents  R  were power  pressure  small  of  comprehensive can be  accomplished  using:  (a)  more s e n s i t i v e (e.g.,  (b)  Digiquartz pressure  a m o d i f i e d d r i v e and t h e that  higher  solution  (ii)  No e f f o r t  distribution, wake.  has  shear  even i n a b s e n c e o f number r e m a i n s  concentration  c a n be  blockage,  unrecorded.  in evaluating  transducers);  pump s y s t e m of  so  glycerol-water  evaluate  character  stress  transducer  handled.  been made t o  turbulence  In f a c t  important  and s t a b l e p r e s s u r e  on the  pressure  and s h e a r surface  i n t h i s range  stress of  of  the  a cylinder,  of Reynolds  The , i n f o r m a t i o n i s  performance  in  quite  long-chain  polymers.  115  (iii)  A direct  desirable other the  presents  is  for  purpose  measurement hand,  of  this  the  skin f r i c t i o n  challenging the  total  problems.  d r a g as  is  simple.  drag balance  be  and a s y s t e m a t i c  programme o f  total  With the  pressure  should y i e l d rather u s e f u l  of  designed drag  drag data  in  i n f o r m a t i o n on near  the  lower  end  R e y n o l d s number r a n g e .  Tests  turbulence universal  s h o u l d be c a r r i e d o u t w i t h c y l i n d r i c a l models conditions  and p r e s s u r e  of v e l o c i t y gradient  to  profile, firmly  blockage,  establish  character  of  the  pressure  distribution  proposed d e f i n i t i o n  of  the  pressure  coefficient.  Blockage  circular  corrections  cylinder,  flat  should provide useful  (vi)  On t h e  a sensitive  initiated.  under d i v e r s e  (v)  though  a function  relatively  f r i c t i o n v a r i a t i o n with blockage  the  (iv)  of  of  number and b l o c k a g e  suggested that  the  skin  several  h a n d , measurement  Reynolds  It  measurement  plate,  bluff  bodies  sphere,  etc.  such  as  i n shear  flow  information.  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C~ p  of pressure pressure  relative coefficient,  coefficient  2 =  (Pg - P^) ( 1 / 2 ) p U ^  pressure  data  The  measured  x component  stagnation  1  TT-  ~  —  3x  3u , dx 3x  -r—  +  3x  front  u  2 CO  2  =  using  - — p  •  differential  the experiment. equation  y = 0 c a n be w r i t t e n  o f the sphere  u J —CO  from  during  ,  "TT—  p  Integrating upstream  3P  —  readily  o f Navier-Stokes  streamline  3u U  quite  3 u  V  as  , 3 u, [ T + o] .2 2 3x 3y2  r  along the  stagnation  2  point  to,minus  infinity  yields,  ' -co  . — dx + v 3x  J-co  [ n . 2  a  x  +  —sH 2 3y  J  J  dx ,  127  2 9 u [—j  u  +  +  V  r  +  2 9 u, —2"^  .  3x*  0  +  1/2 P u;  rd  +  where  6  is  vanishes' in  the  U  L—o  3x'  the  f i r s t  ,  +  1/2  u"  3 U, — t - J  dx  of  >  U  ,  n  dy  thickness.  usual  boundary  The  the  second  outer  layer  flow  Since  °o  =  constant  at  1  and  =  0  3u  -  ^  x  1/2 u f  R  is  3  the  x  x = 6 y = 0  Reynolds  integral while  approximation  3 u 3y  1/2 P  a  -6 3x  3v 3y  0  is  ,3  2 >  introduced.  A  U  i r r o t a t i o n a l i t y of  integral  3u 3x  where  3  ,  •3y  2  be  r  boundary-layer  because  3 u 3x* can  3y  00  1  ,  =  1  +  i  +  number.  128  Here  the  numerical  outer  flow  et  to  8.  be  of  A follows directly  from  the  solution.  Using Grove  value  the  a l .  3  potential have  4  flow  analysis,  Hon  shown,  independently,  _  8  1 3 1 1 1 1  the  a  s  well  value  as  of A  Thus,  P  - P  0  1/2  °°  p U  ,  .  .  _[_ -\- — -J- • • • •  — 2  R  i.e., P  -  P  50°  =  (  P  0- 50^ P  ~  • • " ) l / 2 PU  +  2  Now  p  p  e-  < «,- 5tf> p  e  p  »  _ ~  2" 1/2  Recognizing tribution reduces  p  Vt  that  of  r  p  =  p  e  { ( p  a Reynolds  8/R term  is  o- 5o p  "5 0° '<d 2 ~ p u: 1/2  1/2  for  e-  less  r  o )  5(f 2 p  ( 1 +  „  ±  6 -  P  ~  V2 p l£  ( =  P  3%,  8- 5(^-< 0- 5^ P  1/2  P  p  uj  +  j  )  1  /  2  p  U  c»  ±  R  as  l o w as  the  above  to  P  l ---*  ui  number  than  -  P  +  x  300  con-  expression  }  >  

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