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Structure of pipe wall turbulence in Newtonian and drag-reducing flow : a hologram-interferometric study Achia, B. Umesh 1975

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STRUCTURE OF PIPE WALL TURBULENCE IN NEWTONIAN AND DRAG-REDUCING FLOW:  A HOLOGRAM-  INTERFEROMETRIC STUDY by B. B.  T e c h . ,  M . A . S c ,  Indian  The  A THESIS THE  UMESH  ACHIA  I n s t i t u t e  U n i v e r s i t y  SUBMITTED  of  i n  Technology,  IN P A R T I A L  REQUIREMENTS DOCTOR  of  B r i t i s h  1968  C o l u m b i a ,  F U L F I L M E N T OF  FOR T H E DEGREE OF  OF P H I L O S O P H Y  the  Depa  rtment  of CHEMICAL  We  accept  requ i red  THE  t h i s  ENGINEERING  t h e s i s  as  conforming  to  standard  UNIVERSITY  OF B R I T I S H  February,  1975  1972  COLUMBIA  the  In  p r e s e n t i n g  requirements B r i t i s h f r e e l y that  f o r  a v a i l a b l e  p e r m i s s i o n  or  by  h i s  w r i t t e n  f o r  in  advanced  I  agree  f o r f o r  p a r t i a l degree  f i n a n c i a l  The  and  study.  I  granted  or  i n  g a i n  by It  w h o l e , s h a l l  or  not  f u r t h e r  t h i s  t h e s i s  the  Head  of  i s  understood  the be  my  copying  a l l o w e d  agree for Depart-  that of  t h i s  without  p e r m i s s i o n .  Department  of  U n i v e r s i t y  Vancouver  Date  make  of  B.  The  i t  r e f e r e n c e  be  the of  s h a l l  copying  of  U n i v e r s i t y  L i b r a r y  may  part  at  the  r e p r e s e n t a t i v e s .  i n  f u l f i l m e n t  that  e x t e n s i v e  purposes  p u b l i c a t i o n , t h e s i s  t h e s i s  an  C o l u m b i a ,  s c h o l a r l y ment  t h i s  8,  Chemi c a l  of  Engineering  B r i t i s h  Canada  Columbia  Umesh  Achia  my  ABSTRACT  The a d d i t i v e was 50  on  e f f e c t  the  Due  to  nique  in was  anomalous  was  f r i n g e  modulation  speed of  of  into  motion  the  f l o w ,  a  polymeric  t u r b u l e n c e  i n  The  s t u d i e d  system  2.63  of  f l o w s ,  observed in  and  cm  pipe  diameter  conventional  flow was  a  p i p e .  t u r b u l e n c e  n o n d i s t u r b i n g  o p t i c a l  a  generated r e g i o n  f r i n g e s  flow  at  the  spanwise  by  the  were  spanwise to  of  pipe  t e c h -  was  and  normal  s p a c i n g ,  i i  method  w a l l .  The  index  i n t e n s i t y  medium-  c o r r e l a t i o n s  p i c t u r e s .  to  the  ' b u r s t s '  Measurements  burst  enhancer  by  motion  and  r e a l - t i m e  measurements  d i r e c t i o n s  ' s t r e a k s ' f l o w .  h o l o g r a p h i c  temporal  from  for  i n t e r -  recorded  and  used  An  r e f r a c t i v e  obtained  i n v e s t i g a t e  streak  the  the  S p a t i a l  and  w a l l - l a y e r  by  a  was  measurements.  wall  f l u c t u a t i o n s flow  i n t e r f e r o m e t r y  t u r b u l e n c e  photography.  t u r b u l e n t  o r i g i n a t e  on  these  Both were  a  h o l o g r a p h i c  p a t t e r n  c o n c e n t r a t i o n  d u r i n g  i n  l o n g - c h a i n  developed.  superimposed  i n f u s e d  wall  behaviour  d r a g - r e d u c i n g  v i s u a l i z a t i o n  ference  of  e x p e r i m e n t a l l y .  R e a l - t i m e flow  d r a g - r e d u c i n g  p o l y a c r y l a m i d e - w a t e r the  probes  a  s t r u c t u r e  i n v e s t i g a t e d wppm  of  frequency  of and  wall that gross s u b l a y e r  period the  were  obtained  appeared  shear  d r a g - r e d u c i n g  p h y s i c a l l y  comparison  was  made  v e l o c i t y .  i n c r e a s e d  spanwise  streak  the  rate  of  computed  using  equal  in  both  equal  wall  l a y e r  d i f f e r e n t  from  at  equal  both  the  i m p r e s s i o n s  of  wall  during  same  i n c r e a s e d  drag  Newtonian  of  r e d u c t i o n  flows  rate  that  or  the  and  equal  wall  non-dimensional  a l s o  d r a s t i c a l l y  i n t e r v a l  water  when  d r a g - r e d u c i n g  between  K i m - K l i n e - R e y n o l d s , and  flows  flows  b u r s t s ,  was  when  reduc-  almost  compared  of  streak  a  longer  shear.  l i f e t i m e  showed  Newtonian  the  non-dimensional the  value  than  by  a  that  of  sublayer  f a c t o r  streak  c o r r e s p o n d i n g  wall  drag-  d r a g - r e d u c i n g  the  to  the  l i f e t i m e  The  using  almost  spacing  wall  shear  v a l u e .  polymeric  r e s u l t s  s o l u t i o n  s o l v e n t ,  reduced  v i s c o s i t y  have  over  r a t i o  These  Newtonian  of  time  a u t o c o r r e l a t i o n s  the  the  water  flow  p h y s i c a l  measurements  water  to  the  s o l u t i o n  shear.  to  equal  AP30  showed  The  d r a g - r e d u c i n g  sublayer  and  v i s u a l  T h e . a d d i t i v e  model  reducing  period  the  b u r s t i n g .  c o n c e n t r a t i o n  at  e i t h e r  s p a c i n g .  D i r e c t  the  to  Separan  Measurements  a d d i t i v e  at  a d d i t i o n  flow. The  ed  in  of  flow  r e s u l t i n g  f r i c t i o n a l the  suggest  d i l u t e  d r a g .  as  a  s t a b i l i z e d  compared  in  l e s s e r  The  polymer  r o l e  to  wall  that  of  t u r b u l e n c e of  s o l u t i o n  l a y e r  in  the p r o d u c t i o n  e l o n g a t i o n a l i s  d i s c u s s e d  as  a  p o s s i b l e  mechanism  phenomena.  to  e x p l a i n  the  v i s u a l i z e d  and  measured  TABLE OF CONTENTS  Page  ABSTRACT  i i  LIST  OF  TABLES  .  x i  LIST  OF  FIGURES.  xi i i  ACKNOWLEDGEMENTS  x v i i  Chapter 1  DRAG  REDUCTION  WITH  POLYMERIC  ADDITIVES  1  1 .1  Preambl e  1  1.2  H i s t o r i c a l  2  1.3  C h a r a c t e r i s t i c s of  1.4  Features  1.5  Gross  1.4.2  Mean  1.4.3  T u r b u l e n c e  Nature  Reducers  Drag-Reducing  1.4.1  The a  of  Drag  of  3  Flow  7  Flow  7  V e l o c i t y  P r o f i l e  9  Measurements  Turbulence  13  Near  Boundary  14  T . 5 . 1 W a l F T u r b u l e n e e ^ 1.5.2  i nNNewtoni  an  Flow  14  Turbulence Flow  i n  Drag-Reducing 2  v  0  Chapter  Page 1.6  Mechanisms Drag  1.7 2  and  Models  Reduction  24  1.6.1  M o l e c u l a r  1.6.2  Macromolecule-Eddy  1.6.3  Continuum  C l o s i n g  E f f e c t s  ,  WALL  26 I n t e r a c t i o n s  .  .  27  Approaches.  29  Remarks  35  HOLOGRAM-INTERFEROMETRIC THE  f o r  INVESTIGATION  REGION  OF  . •  2.1  Flow  V i s u a l i z a t i o n  2.2  P r i n c i p l e  2 . 3  H o l o g r a p h i c  2.4  The  2.5  H o l o g r a p h i c  2.6  Flow  of  Hologram  and  i t s  37 Requirements.  .  37  Holography Study  of  and  i t s  39  the  Wall  .  .  .  40  P r o p e r t i e s  I n t e r f e r o m e t r y  V i s u a l i z a t i o n  Region  with  4  .  47  H o l o g r a p h i c  I n t e r f e r o m e t r y 2.7  3  A p p l i c a t i o n  47  of  Moire  2.7.1  I n f i n i t e  2.7.2  F i n i t e  EXPERIMENTAL The  Blowdown  3.2  The  h o l o g r a p h i c  Flow  .  .  .  .  .  4  AND  Pipe  50  PROCEDURE  Flow  Flow  Apparatus  .  .  .  .  .  52  .  52  V i s u a l i z a t i o n 55 55  Laser V i s u a l i z a t i o n  S e c t i o n  D e t a i l s 3.3  The  8  50  F r i n g e s  3.1  3 . 2 . 2  T e c h n i q u e s .  F r i n g e s  APPARATUS  Apparatus 3.2.1 The  4  60  H o l o g r a p h i c  I n t e r f e r o m e t e r  Design.  .  .  63  3.3.1  The  Amplitude  D i v i s i o n  H.I  63  3 . 3 . 2  The  Wavefront  D i v i s i o n  H.I  65  vi  Chapter  Page  3.4  Test  L i q u i d s  3.5  Experimental  Laser  3 . 5 . 2  Test S e c t i o n P r e p a r a t i o n  Beam  S o l u t i o n 70  Runs.  QUANTITIES Flow  AND  4.2  I n t e r p r e t a t i o n  4 . 3  Method  4.4  W a l l - l a y e r  of  DATA  .  .  .  .  71  ANALYSIS  76  Measurements of  Fringe  the  76  Fringe  F i e l d .  .  .  .  79  Readout  Turbulence  Streak  83  Parameters  Spacing  S p a t i a l 4 . 4 . 2  71  V i s u a l i z a t i o n  Gross  X  84  from  C o r r e l a t i o n  Streak L i f e t i m e A u t o c o r r e l a t i o n  T  $  84 from 86  4 . 4 . 3  T u r b u l e n t  I n t e n s i t y  88  4 . 4 . 4  The  Rate  89  4 . 4 . 5  Time  Burst  I n t e r v a l  Bursts EXPERIMENTAL A  and  69  Flow  4.1  5.1  Alignment  and  4.4.1  5  68  Hologram Recording P r o c e s s i n g  3 . 5 . 4 MEASURED  Procedure  3.5.1  3 . 5 . 3  4  67  Note  RESULTS on  T  AND  F between  90  B  DISCUSSION  91  P r e s e n t a t i o n  5.1.1  Gross  Flow  5.1.2  P r e l i m i n a r y  vi i  91  Measurements Dye  I n f u s i o n  92 Tests  .  96  Chapter  Page  5.2  Hologram 5.2.1  Experiments  98  O p t i c a l Density Hologram  5 . 2 . 2  Moire  Fringe  5 . 2 . 3  The  5 . 2 . 4  E f f e c t  of  Fringe  P a t t e r n  5 . 2 . 5  Fringe  v s .  5 . 2 . 6  Double-Exposure  of  the 98  P a t t e r n  Speckle  Formation  .  E f f e c t  103  V i b r a t i o n  on  the 104  Dye  V i s u a l i z a t i o n  .  .  5.4  V i s u a l Observations Measurements i n the 5.3.1  The  Streaky  5 . 3 . 2  The  Nature  Measurements  of  5.4.1  Burst  5 . 4 . 2  Streak  5 . 4 . 3  Comparison  5 . 4 . 4  An  Summary During  6  Drag  Flow  Frequency  118  P e r i o d .  and  Period  .  L i f e t i m e of  and f o r  T  .  .  125  During 138 Changes  Reduction  5 . 5 . 2  Burst  S t r u c t u r e .  RELATED  EVIDENCE  vi i i  125  Increased  S t a b i l i t y  S t r u c t u r e  MECHANISM.  .  130  g  Reduction  Flow  .  128  Streaky  OF  108  B u r s t i n g  5.5.1  DISCUSSIONS REDUCTION  of  107  S t r u c t u r e  Explanation  Drag;5  S t r u c t u r e Layer  Sublayer  Sublayer  5.5  106  and Wall  of  105  Flow  Interferograms 5.3  101  141  S t r u c t u r e  141 142  AND  A  DRAG 144  Chapter  Page  6.1  Related  Evidence  on  Streaks  and  Bursts  144  . 6 . 1 . 1  Streak  6.1.2 6.2  Spacing  B u r s t i n g  D i s c u s s i o n  of  a  6.3  149  P o s s i b l e  A  6 . 2 . 2  V i s u a l i z e d  6 . 2 . 3  The S c a l e s a c t i o n s  Continuum  Mechanism.  .  Approach Flow  Patterns  I m p l i c a t i o n s of  158  159 I n t e r 164 168  Aspects of Mechanism  6 . 3 . 2  the  Design AND  Drag:  Reduction 168  A p p l i c a t i o n  CONCLUSIONS  .  and  .  Eddy  .  158  C l o s u r e 6.3.1  7  146  Data.  6.2.1  Their  Data  to  Engineering  .  169  RECOMMENDATIONS  7.1  Summary  and  7.2  Recommendations  171  C o n c l u s i o n s  171 176  NOMENCLATURE  177  REFERENCES  181  APPENDICES A  P r e p a r a t i o n of  C h a r a c t e r i z a t i o n  Sol u t i o n s  B  Gross  C  F a b r i c a t i o n  D  and  Fringe  Flow  1  Data of  and the  A n a l y s i s ,  Computer  E r r o r Test  Data  Programs  A n a l y s i s  194  S e c t i o n  Sampling  8 8  206 Method  and 210  i x  APPENDICES  E F  Page  L i s t i n g Film  Data  Catalog  Motion G  of  and  225 Scenario  for  P i c t u r e  256  Pr.opos'edislimprovements to vthe ^Hdl o g r a p h i c Flow V i s u a l i z a t i o n Technique  x  261  LIST OF TABLES  Table  1.1  3.1  Page  Mechanisms  V B l o w d o w n  f o r  Flow  3.2  H o l o g r a p h i c  3.3  Steps  3.4  The  5.1  i n  of  5.2  Low-speed and  50  Pipe 5.3  Flow.  Burst f o r  5.4  .  Water  .  R a t i o s  of  Tests  .  50  .  .  f o r  .  Water i n  .  112 L i f e t i m e  Separan  T<.  AP30  Flow  119  L i f e t i m e  and  Streak  Spacing  6.1  Wall  140  Layer  P r e s s u r e  S t r u c t u r e  Gradient  Measurements  Flows  by  i n  Non-dimensional  Zero  D i f f e r e n t  I n v e s t i g a t o r s  6.2  57  H o l o g r a p h i c  S o l u t i o n  Streak  wppm  Streak  . . .  74  Data  AP30  and  Pipe  .  94  Spacing  .  Tg  and i n  D e t a i l s .  72  C o n d i t i o n s c f o r  Separan  P e r i o d  S o l u t i o n  Apparatus  Runs  Streak  wppm  54  P r e p a r a t i o n  Flow  Flow  V i s u a l i z a t i o n  25  D e t a i l s  V i s u a l i z a t i o n  Hologram  of  Reduction  Apparatus  Sequence  Summary  Drag  145  Sublayer  xi  P e r i o d  Data  156  Page  Table  A . l  A.2 A.3  V i s c o s i t y S o l u t i o n s  Reduced  Measurements  R e f r a c t i v e  Separan 190  V i s c o s i t y  Propylene  f o r  Index  -  C o n c e n t r a t i o n C o n c e n t r a t i o n  G l y c o l - W a t e r  Data Data  191 f o r  M i x t u r e s  193  B . l B.5  198 Gross Flow S o l u t i o n s  Data  f o r  Water  and  Separan  to 202 203  B.6B.8  E . l -  E.30  C a l c u l a t e d  „  c  . . - v  4.~  Data  ~-n  * s *  f o r  A-~a  Figure  *<  «  R e s u l t s from the A n a l y s i s Flow Interferograms  xi i  to 205  6.3  '  Of  H o l o g r a p h i c  22  5  to 255  LIST OF FIGURES  Figure  1.1  Page  Regimes and f e a t u r e s of d r a g - r e d u c i n g pipe flow of d i l u t e polymer s o l u t i o n s on a f r i c t i o n f a c t o r - Reynolds number p l o t .  1.2  (a)  8 V e l o c i t y  (b)  p r o f i l e s  ' E f f e c t i v e  s l i p '  1.3  Turbulence  2.1  (a)  Hologram  (b)  Holographic  View axes  I:  2.2  2.3  3.1  3.3  3.5  near  a  w a l l .  .  .  .  .  .  .  12  16  view  and  41  t h e  c o o r d i n a t e 42  Wall  edge  view  and  t h e  c o o r d i n a t e 43  blowdown  pipe  flow  and  h o l o g r a p h i c  apparatus  53  flow .  Total  r e f r a c t i o n  i n t e r n a l  the  pipe  r e f l e c t i o n  flow  and  wall  t e s t  56  61  The amplitude d i v i s i o n i n t e r f e r o m e t e r .  The  .  wall  The holography setup f o r pipe v i s u a l i z a t i o n and measurement  at  3.4  the  r e d u c t i o n  R e c o n s t r u c t i o n  plan  v i s u a l i z a t i o n  3.2  a t  drag  Recording  Wall  View I I : axes.  The  processes  during  h o l o g r a p h i c  s e c t i o n  64  64  xi i i  Page  Figure 3.6  4.1  4.2  4.3  S e c t i o n a l e l e v a t i o n of the wavefront d i v i s i o n hologram i n t e r f e r o m e t e r Summary o f o b t a i ned  the  experiments  data 77  R e f r a c t i v e index water mixtures Region of frame and  and  66  of  propylene  g l y c o l 81  flow r e c o r d e d on sampling method  82  An  5.1/ : -  Fanning f r a c t i o n f a c t o r - Reynolds number p l o t of gross flow of Separan AP30-water s o l u t i o n s i n a 2 . 6 3 cm p i p e . .  5.3  5.4  5.5  5.6 f i zh  curve  p i c t u r e  4.4  5.2  a u t o c o r r e l a t i o n  motion  p e r i o d i c i t y .  Holographic runs: gross "f.low.of;50wppm Separan AP30 s o l u t i o n and d i s t i l l e d water Streaks f l o w .  at  the  pipe  wall  i n  .  .  88  93  .  .  .  .  95  t u r b u l e n t 97  Laser l i g h t hologram  i n t e n s i t y  d i s t r i b u t i o n  at  the 100  Moire f r i n g e s d i s p l a c e m e n t .  R e a l - t i m e . f l o w  generated . .  by  hologram 102  i n t e r f e r q g r a m s  of  water  ? f (lowssshbwi fig*•*he If ormatnonzof s s « t r e a k s  z  at  5.7  A n a l y s i s of a t y p i c a l s t r e a k spacing  5.8  showing  the  pipe  wal 1  109 i n t e r f e r o g r a m  P h y s i c a l and non-dimensional streak spacing i n water and d r a g - r e d u c i n g Separan AP30 s o l u t i o n  XT.V  f o r 110  113  Fig ure  5.9  Page  R e a l - t i m e v a r i a t i o n the  5.10  pipe  flow i h t e r f e r o g r a m s showing the in spanwise c o n c e n t r a t i o n at wal 1  115  The e f f e c t of drag r e d u c t i o n on the r e l a t i v e i n t e n s i t y of spanwise concent r a t i o n f l u c t u a t i o n  117  5.11  B u r s t i n g  sequence  i n  a  121  5.12  B u r s t i n g sequence Separan f l o w .  i n  a  5.13  5.14  5.15  Streak l i f t u p n e a r - i n f i n i t e view  and  5.16  5.17  flow  d r a g - r e d u c i n g 123  and b u r s t i n g as seen with f r i n g e s and an o b l i q u e wall 124  Burst TSatfes i n Separan flows  Time  water  i n t e r v a l  water  and  d r a g - r e d u c i n g 126  between  d r a g - r e d u c i n g  bursts  Separan  Tg  in  water  flows  127  Wall l a y e r l o c a t i o n s for a u t o c o r r e l a t i o n s to determine s t r e a k l i f e t i m e  129  Autocorrelograms of c o n c e n t r a t i o n f l u c t u a t i o n at the pipe wall at s i n g l e l o c a t i o n  5.18  5.19  5.20  Autocorrelograms t i o n at the pipe  6.2  of c o n c e n t r a t i o n f l u c t u a wall at four l o c a t i o n s  Autocorrelograms  of  t i o n  wall  at  Streak  the  pipe  l i f t i m e  reducing  6.1  131  T~  Separan  c o n c e n t r a t i o n  in  at  water  streak  A  burst  of  f l u c t u a -  l o c a t i o n s  and  .  .  .  .  .  134  d r a g -  flows  Non-dimensional drag r e d u c t i o n  comparison  four  132  136  s p a c i n g  during 147  r a t e  xv  data  150  Figure  6.3  Page  Sublayer  p e r i o d  d r a g - r e d u c i n g  6.4  6.5  data  S t r e t c h i n g  and  wall  s t r e a k s  l a y e r  S t r e t c h i n g  in  flows  .  Newtonian  .  s h e a r i n g  and  and  .  152  zones  of 161  s h e a r i n g  zones  during  b u r s t i n g  Al  A2  Method  Reduced f o r  CI  Dl  165  of  D e t a i l s l o t  d i s p e r s i o n .  v i s c o s i t y  Separan of  AP30  the  vs.  c o n c e n t r a t i o n  flow  192  sectioneandvwal1 209  t r a c e  of  a  motion  frame  D2  D i g i t i z e d  Gl  A  211  f r i n g e  data  d o p p l e r - h o l o g r a p h i c  scheme.  189  s o l u t i o n s  M i c r o d e n s i t o m e t e r p i c t u r e  G2  Separan  -.  E l l i p t i c a l components  .  .  .  213 flow  v i s u a l i z a t i o n  .  263  arrangement of o p t i c a l in motion holography  xvi  265  ACKNOWLEDGEMENTS  I c o n t i n u e d to  b r i n g  wish  to  thank  encouragement, t h i s  p r o j e c t  ( d e c e a s e d ) ,  S h l e i n ment  provided  more  S.  Thompson an  c o u r s e s  and  into  h i s  t h e s i s ,  c o n c l u s i o n .  given  Gartshore  f o r  e a r l i e r  f r u i t f u l  i n s i g h t s  I  extend  my  -  to  Paddy  i n f i n i t e  the  flow  the  d e s i r e d  the  years  t e d i o u s  by  Dr.  Dr. D.  Zeev Joseph  t u r b u l e n c e  measure-  t h i s  of  many  the  machine  f a i l u r e s  superb  machining  wife  D a i s y ,  f o r  work  and  shop,  w h i l e  s k i l l  f o r  c o n s t r u c t i n g  f i n a l l y  gave  r e s u l t s . to  my  t h i s  to  my  and  f o r  her  her  f o r  f o r b e a r e n c e  e x t e n s i v e  h o l o g r a p h i c  p a r e n t s ,  help  through d u r i n g  p r o c e d u r e s .  t h e i r  p h i l o s o p h i c a l  input  s u p p o r t . -  to  Sharon  t h e s i s  i n  a  I Canada  g r a t i t u d e  J a r v i s  d u r i n g  His  p h o t o g r a p h i c  moral  s i n c e r e  p a t i e n c e  of  and  Mr.  s e c t i o n .  -  the  v a l u a b l e  g u i d i n g  and  Ian  W.  t e c h n i q u e s .  his  of  a  w i t h  Dr.  Donald  a f t e r  to  D i s c u s s i o n s Rotem  Dr.  wish  f o r  U n i v e r s i t y  s t y l i s t i c to  f o r  and  B r i t i s h  the  e x c e l l e n t  t y p i n g  of  f o r m a t .  acknowledge  r e s e a r c h of  H a l l e r ,  the  s p e c i a l Columbia  x v i i  National equipment f o r  a  Research g r a n t s ,  Graduate  C o u n c i l and  F e l l o w s h i p .  Chapter  1  DRAG REDUCTION WITH POLYMER ADDITIVES  1 .1  Preamble The  t u r b u l e n t  f l u i d  q u a n t i t i e s f i e l d  i n  of  i n  DNA  and  have  It  and  f i s h  been  i s  probes  to  the  and  has  t h e s e ,  the  most  w i d e l y  For  drag  r e d u c t i o n ,  show  an  the  anomalous  and  Nicodemo,  i n  small  researched  saving  due  to  f l u i d  the  pumping  p r o p u l s i o n .  and  i n  the  f i b r e  ( e . g .  d i l u t e  i n  presence  s u s p e n s i o n s ,  p o l y a c i d s , polymer  a l g a e ,  s o l u t i o n s  i n v e s t i g a t e d .  flow  important  very  l a r g e l y  observed  substances Of  of  i s  marine  been  r e d u c t i o n  a c t i v e l y  e f f e c t  p a r t i c u l a t e  other  that  an  i n t e r e s t  t h i s  drag  presence  been  t r a n s p o r t  s l i m e s ) .  plays  ( A s t a r i t a  of  polymers,  b e l i e v e d  boundary  f r i c t i o n a l  This  r e d u c t i o n  c e r t a i n  of  has  y e a r s .  p i p e l i n e  l o n g - c h a i n  soaps  due  a p p l i c a t i o n  Drag of  flow  a d d i t i v e s  recent  p o t e n t i a l power  phenomenon  the  flow  behaviour r o l e .  behaviour 1966;  i n Smith  1  has  to  near  be  the  turbulent. f l u i d - s o l i d  Conventional d i l u t e et  polymer  al.,  1967)  t u r b u l e n c e s o l u t i o n s and  a r e  2  d i f f i c u l t a  to  use  c l o s e  n o n - d i s t u r b i n g  measurement ( A c h i a ,  to  the  w a l l .  To  avoid  h o i o g r a m - i n t e r f e r o m e t r i c  technique  has  been  these  problems,  v i s u a l i z a t i o n  developed  i n  t h i s  and  l a b o r a t o r y  1971). E a r l i e r  work  of  Achia  (1971)  showed  that:  Under similar conditions, turbulent eddies in drag-reducing flow were observed (i) to show less small scale structure than those in the pure solvent and (ii) to 3  burst flow  from with  This  t h e s i s  experiments t a t i v e  to  and  d r a g - r e d u c i n g  1.2  H i s t o r i c a l  to  polymer  times  both on  i s  by  as  been  suggested  by  Savins  name  might  Mysels  pumping the  data  napalm  r e s u l t s  f i r s t  gave of  the et  al.  Toms;  Toms'  'MOT'  much  the  records  the  on  (1949), The  V i r k  who war  l a t e r ; f o r  drag using  e a r l i e r and  q u a n t i -  i n  Newtonian  that  d i s c o v e r e d  ' 0 ' drag  but  a f t e r  i n  a  i s i t  v a l i d  r e v e r s e ! ) : drag  unable  OOj'droyd  r e d u c t i o n  some-  has  more  reduced  were  due  polymethyl  However,  (T-O-M  years  r e d u c t i o n  phenomenon  (1970)  phenomenon  e x p l a n a t i o n 'T1.  to  s t r u c t u r e s  phenomenon.  and  (1945)  during  u n t i l an  Toms  work  monochlorobenzene. to  a f t e r  t u r b u l e n c e  p u b l i s h e d  r e f e r r e d  be  v i s u a l  bulk  f l o w s .  e a r l i e s t  in  the  refinements  c l e a r e r  w a l l  pipe  a d d i t i v e s  m e t h a c r y l a t e  layer into frequency.  presents  y i e l d  measurements  The  the wall a lower  to  (1 9 4 9 )  based  on  'M' w h i l e p u b l i s h who the  3  The u n t i l i t s  the  f i e l d  e a r l y  m i l i t a r y  expanded  of  '60s  when  with  d i v e r s e  f i e l d s .  s o l v e n t  c o m b i n a t i o n s ,  have  been  well  documented  1.3  r e d u c t i o n  the  a p p l i c a t i o n s .  r a p i d l y  (1969),  drag  A  The the  C h a r a c t e r i s t i c s  of  Newtonian the  same  pressure  (N)  and  flow  Hence, f a c t o r  f a l l s  number,  be  to  taken  (Q)  i n  under  below  Reynolds  t h a t  N  -  AP  AP  M  due  as  f l u i d s  the  for  shown  l i k e  in  workers  and  has i n  p o l y m e r s ,  polymermechanisms  phenomenon P a t t e r s o n  flow  to (DR)  flows  has  et  been  at.  trend  d e f i n e d  as  100  (1.1)  (AP) are  in  the  measured  at  p i p e . c o n d i t i o n s ,  Newtonian  Figure  t h i s  x  be  f r i c t i o n  same  the  may  DR  d r a g - r e d u c i n g  d i f f e r e n t i a t e  non-Newtonian  pipe  d r a g - r e d u c i n g  rate  by  i n  Reducers  in  drop  i n t e r e s t e d  (1972).  =  The  shown  of  dormant  l i t e r a t u r e  s i t u a t i o n s  works  Hpyt  AP DR(%)  the  r e d u c t i o n  Drag  r e d u c t i o n  became  1964,  flow  drag  and  r e l a t i v e l y  d r a g - r e d u c i n g  review  (1969)  Drag  of  Navy  being  p h y s i c a l  r e p o r t e d .  Lumley  S i n c e  i n t e r e s t  number  i n  U.S.  was  1.1. from  p s e u d o p l a s t i c s  flow  the  at  the  However, the ( e . g .  f r i c t i o n same  care  behaviour c l a y  must of  s u s p e n s i o n s ,  4  p o l y v i n y l f a c t o r s  a l c o h o l ) . by  But  w h i l e  the  f-Re  due  to  v i r t u e  t h e i r  polymer  of  drag  b l o c k  i n  s o l u t i o n s  extremely  DR).  At  those the  of  low  of  the  the  polymers  of  high  -  1  f o l l o w  This  by  been  l a r g e  to  100  s o l u t i o n s  d i l u t e  drag wppm  r e d u c t i o n c a n - g i v e  the  d e n s i t y  are  almost  and the  polymer  small  s o l u t i o n s  v i s c o e l a s t i c ,  used  i n  although  z e r o - i same  d i f f i c u l t  to  e l a s t i c  behaviour  becomes  to  a  with  measure  as  l o n g , i n  s t r u c t u r e .  drag  the  70%  r e d u c e r s ,  b a l l - l i k e  and  s u b j e c t e d  drag  to  c o n f i g u r a t i o n  clumped,  as  40  m o l e c u l a r  a  e f f e c t i v e  e f f e c t s  extended to  major  c o r r e l a t e  weight  p r e f e r r e d  on  trends  a  m o l e c u l a r  An  n  1.  p l o t .  c o n c e n t r a t i o n s ,  have  than  v a r i o u s  has  u n i v e r s a l l y  produce (5  c o r r e l a t e d  high  The i s  to  f-Re  polymer  c o n s i d e r e d  s o l u t i o n  n  less  a  D i l u t e  p r o p e r t y .  with  being  must  i s  i s  uniquely  behaviour.  d i l u t i o n  n  be  s o l u t i o n  component  the  index  f r i c t i o n  To  c h a i n s .  be  be  lower  s o l v e n t .  f l e x i b l e  may  can  attempts  can  e x h i b i t  power-law  reducers  on  t h e s e . l o w  v i s c o s i t y  f l u i d s  v i s c o e l a s t i c  Polymers at  the  p s e u d o p l a s t i c s p l o t ,  stumbling  These  r e d u c t i o n  ' e l a s t i c ' as  a  p h y s i c a l  important  i f  f l u c t u a t i n g  t u r b u l e n t  flow  of  the  may  the f i e l d  frequency. The  r e p r e s e n t e d  o v e r a l l as  rate  shear  on  f l u i d  then  be  5  dU  x  T  +  dy  elastic component  viscous component where  Equation  (1.2)  G  i s  may  the  be  shear  e l a s t i c  w r i t t e n  (1.2)  G  modulus.  as  (1.3)  where  The q u a n t i f i e s  from  the  as  measure  or  low  s o l u t i o n  number,  a  =  i s  u s u a l l y  time  De  of the  the  In the  f l u i d  The  s t r e t c h  may  theory  be  of  a d d i t i o n i s  v i s c o s i t y  De to  the  Zimm of  ( i )  e l a s t i c  ' f l u i d  as  of  At  f o r c e s ->  0  d e f i n e d  and  shearing  _e_  time  1/AT  or  dominate, v i s c o u s m o t i o n s ,  important  i n  of  Newtonian  f l u i d  (1.4)  AT  computed  i s  d i s s i p a t i v e  small  that  as  r e l a x a t i o n  also a  group  change  (1956). the  time.  time'  imposed  frequency  frequency;  elements  flow  taken  l i m i t s  -> ° ° a n d  eddy  of  r e l a x a t i o n  dimension 1 ess  c h a r a c t e r i s t i c  De  m o l e c u l a r  In quency;  Deborah  the  v i s c o e l a s t i c i t y ,  9  a  0,  high  taken  e d d i e s . eddy  ( i i ) f o r c e s  At  l a r g e  dominate.  s t r e t c h i n g  t u r b u l e n t i s  f r e -  of  f l o w s .  r e l a t e d  to  the  6  e l o n g a t i o n a l to  shear  s t r e s s ,  s t r e s s ,  j u s t  and  i s  as  the  given  shear  v i s c o s i t y  i s  r e l a t e d  by  du e£  For  a  r a t i o ,  Ug^/y,  and  for  by  De  has  the  Metzner  Newtonian a  (1970)  and  The  3y;  of  a  rod-shaped  (1  +  D e ^ l  or  the  r e l a t i o n  Trouton  between  element  i s  y  Q J l  given  as  e£  =  v i s c o e l a s t i c y ^ / y  0 0  O l i v e r have  l i q u i d  with  s o l u t i o n s For  and  =-2De)  (  De  =  0 . 5 ,  1  '  6  the  •  polymer  v i s c o s i t y .  experiment,  =  s t r e t c h i n g  D i l u t e e x t e n s i o n a l  ^  g  3.  a  r a t i o ,  y  of  l  Trouton  f l u i d  value  (1968)  For  e £ d x  M  example,  Bragg  roughly  may  Metzner  (1973),  estimated  e x h i b i t  using that  very  and  a  high  Metzner  j e t - t h r u s t  for  a  100  wppm  p o l y -  * a c r y l a m i d e to  s o l u t i o n ,  s t r e t c h i n g  c h a r a c t e r . the  This  s o l u t i o n  t r a i l s  from  due  the The  t e n s i l e  s t r e s s  220  s  and  s  and  _  1  _  1  (.15  .06 to  to i s  and  y  =  g £  high  500 y  drawn  o b j e c t  to  e l o n g a t i o n a l x  these 105  5-0)  a  an  The  s o l u t i o n o b j e c t  i s  t h r e a d - l i k e  r e s i s t a n c e a  ' p i t u i t o u s '  dipped  in  f i l a m e n t  s o l u t i o n .  experiments 105  y.  deformation  dynes/cm x  the  when  out;  the  10,000  g i v e s  n o t i c e a b l e  then  in  g J l  to  2  ;  were:  O l i v e r  dynes/cm  rate  2  .  &  and  the  Metzner Bragg,  &  522  a x i a l Metzner, to  12,000  )  7  1 .4  Features  of  The  Drag-Reducing  polymer  e x p e r i m e n t a l l y  at  (i)  by  Gross  as  flow  p o l y m e r i c  P a t t e r s o n  et  al.  i n  and  Figure  Hoyt,  e f f e c t s  a r e  seen  a r e  (a)  A  t u r b u l e n t  flow  regime  r e l a t i o n s h i p  obeyed  polymeric  parameters  as  A f t e r drag by  and a r e  polymer  a  does  u s u a l l y  r e d u c t i o n a  given  flow  polymer  of  of  i n  AP  i s  v a r i o u s f - R e  flow  p l o t  r a t e ,  observed:  without obey  which  the  the  drag  same  'onset  f r i c t i o n  depends Important  c o n c e n t r a t i o n ,  any  f r i c t i o n  s o l v e n t .  w e l l - d e f i n e d  parameters.  an  a  (reviewed  f o r  on  Newtonian  s o l u t i o n  f o r  experiment  i n c r e a s i n g  s o l u t i o n s  the  s o l v e n t s  r e a d i l y  flow  the  order  reported  The  measurement  turbulent  with  d e t a i l :  been  1972).  of  wherein  the  and  regimes  r e l a t i o n of  1969;  3  have  In  regime  s t u d i e d  s t r u c t u r e measurements by and (b) v i s u a l t e c h n i q u e s .  a d d i t i v e s  i n v o l v i n g  the  (b)  been  p r o f i l e s  1.1.  r e d u c t i o n f a c t o r  i n c r e a s i n g  r e l a t i o n s h i p s  of  v a l u e s ,  has  measurements  v e l o c i t y  number  three  a  flow  of  e f f e c t  Flow  s t r a i g h t f o r w a r d , Q  l e v e l s  Turbulence (a) pnobes  Gross l a r g e  three  Mean  ( M i )  1.4.1  d r a g - r e d u c i n g  Gross  ( i i )  Flows  type,  upon  a  among  p o i n t ,  1  f a c t o r v a r i e t y p o l y m e r i c  m o l e c u l a r  w e i g h t ,  8  -*  direction t  N:  of  shift  pipe  wall  increasing  value  C  polymer  decreasing  value  M  polymer  D  pipe  Newtonian,  DR:  (1)  Onset:  tC,  tM,  ID  (2)  DR  smooth:  tC,  tM,  Figure  e/D  1.1.  drag  reducing  ID  Friction  factor  features  of  -  concentration molecular  DR  (h)  Deviation  drag-reducing  rough:  number pipe  wt  diameter  (3)  Reynolds  roughness  plot  flow  of  t  e/D  from  asymptote:  t  E/D  showing  regimes  and  polymer  solutions.  9  l e v e l  of  polymer  parameters wall i n  are  d e g r a d a t i o n  pipe  roughness. Figure  The  l i m i t s  found  and  independent  the  onset  of  s h i f t s polymer  observed  to  f o l l o w  the  of  an  to  The  and  parameters  1.4.2  Mean  The  the  flow pipe  are  shown  (1966), P i t o t  e f f e c t  are  V i r k  drag  and  polymer In  t r a n s i t i o n  regime  These  of  the  a  some  s o l u -  w i t h  l i n e  an  are and  then  numbers.  method  s o l u t i o n s i s  s o l u t i o n s  s o l u t i o n s  l a m i n a r  V i r k  but  probably  i n v o l v e d  to  observe  have  due  and  an  to  not  the l e d  the  to  l a r g e  i n c o m p l e t e  P r o f i l e  v e l o c i t y et  many  p o s s i b l e .  i n t e r a c t i o n s .  V e l o c i t y  probes of  This  asymptote  parameters.  provide  that  t h e i r  mean  to  Reynolds  i n d i v i d u a l  parameters of  high  data  number  understanding  the  e x t e n s i o n  c o r r e l a t i o n s .  of  apply  p o l y m e r i c  u n i v e r s a l  the  number  r e d u c t i o n  c o n c e n t r a t i o n .  flow  c h a r a c t e r i s t i c s  drag  to  towards  asymptote  Gross  using  these  type.  determined  maximum  asymptote  i n  al.  of  experimentally  i n c r e a s e  et  s o l v e n t  Reynolds  e f f e c t s  the  (1971)  f o l l o w  the  1.1.  u l t i m a t e l y  t i o n s ,  d i a m e t e r ,  The  (c)  be  and  al.  p r o f i l e (1967)  and  hot-element  r e d u c t i o n  on  measurements  the  Wells  et  anemometers v i s c o u s  of  al.  E l a t a (1968)  have  s u b l a y e r .  shown These  ,  10  probe  measurements  anomalous  normal  of  Anomalous  Brobe  1 ayer Hot  a t  and  the  element  ( F r i e h e  and  s i d e r e d  w i t h  by  Schwarz,  i n  in  tube  polymer  drag  cm  w i r e  probes  l i q u i d s of  Smith  poorer and  than et  heat  be  i n al.  P i t o t  much  (1967)  abrupt  i n  tube  s o l u t i o n s .  l e s s  to  1967) .  t r a n s f e r  must  be  c o n -  the  d i s c r e p a n c y a b s o l u t e of  the  A s t a r i t a low  oxide  and  r e a d i n g s  i n  d i a m e t e r s .  (1966)  a l s o i n  observed  i n  measurements  c r o s s  s o l u t i o n s over  hot-  drag=-reducing  H o t - f i l m  c y l i n d e r s  t r a n s i t i o n s  that  give  s e n s i t i v e  polymer  boundary  heat  i n c r e a s i n g  small  et  As t a n " t a ,  c o n c e n t r a t i o n  l i q u i d s .  f o r  Smith  p o l y e t h y l e n e  diameter.  tubes at  and  with  with  w e i g h t ,  Nicodemo  Newtonian  t r a n s f e r  e x h i b i t e d  P i t o t  and  the  b e s t .  observed  i n c r e a s e d  found  to  a f f e c t e d  the  data  at  working  pipe  p a r t i c u l a r l y  to  of  poorer  probe  q u a l i t a t i v e  i . d .  d e c r e a s i n g  by  a r e  1966;  t h i c k e n i n g  Hence,  m o l e c u l a r  A s t a r i t a  Nicodemo,  a f f e c t e d  (1967)  readings  r e d u c e r s ,  and  a r e  and  3.21  due  polymer  tubes  l e a d i ngse'dge ^ M e t z n e r  al.  (1966)  doubt  d i l u t e  P i t o t  a p p r e c i a b l e  et  polymer  and  Nicodemo  a  m e d i a ,  1969).  c a u t i o n  i n  to  Behaviour  anemometers  s o l u t i o n  v e l o c i t y ,  an  s u b j e c t  probes  ( A s t a r i t a  probeis"  Smith  P i t o t  such  v i s c o e l a s t i c  s t r e s s e s  1967)  al.j  however,  behaviour  In by  a r e ,  flow  than  which  the  i n  i n d i c a t e d the  heat  s o l v e n t t r a n s f e r  11  c o e f f i c i e n t found ing  to  could  vary  t h r e e f o l d .  i n c r e a s e  with  i n c r e a s i n g  polymer  m o l e c u l a r  e x p e r i m e n t a l l y c o n i c a l  v e r i f i e d  h o t - f i l m  p o l y a c r y l a m i d e reduced  heat  v e l o c i t y  i n  c e r t a i n  use  Seyer  of  and  provided  and  1967;  s h i f t  y  +  law  (y  In  >  10).  in  d i l u t e  probe  number  and  r e v e a l e d  independent  of  probes  c a s t  data  reported  techniques  data  on  doubt  ( e . g .  mean  on  in  s e v e r a l  the  t r a c e r Rudd,  l i t e r a t u r e .  p a r t i c l e s :  1971)  v e l o c i t y  have  p r o f i l e s  i n  Profiles s o l u t i o n  from,  l o g a r i t h m i c +  (1969)  f l o w .  c o o r d i n a t e s  upwards  N u s s e l t  d e c r e a s -  c y l i n d r i c a l tubes  1 a s e r - d o p p l e r :  dependable  Polymer vs  P i t o t  Schwarz  c y l i n d r i c a l  p r o f i l e  Velocity  U+  of  n o n - d i s t u r b i n g  more  of  and  was  ranges.  v e l o c i t y  d r a g - r e d u c i n g  on  the  anomalies  Metzner,  and  t r a n s f e r  v e l o c i t y and  o p e r a t i o n  The  heat  flow  Friehe  anemomenteVs  t r a n s f e r  d r a g - r e d u c i n g  the  s o l u t i o n s .  These  The  weight.  The  of the  (Figure  but the  v e l o c i t y  remain wall  U+  =  1.2),  A  e x h i b i t  roughly  over  g e n e r a l i z e d  p r o f i l e s ,  the  when a  p a r a l l e l  outer  flow  p l o t t e d  c h a r a c t e r i s t i c to  the  s e m i -  r e g i o n  e q u a t i o n ,  %r\ y  +  +  B  (1.7)  12  u  0  10  1  0  io  2  101  y  1.  Viscous  2.  Newtonian  3.  Drag  k.  Drag R e d u c t i o n Asymptote a. Vi r k m o d e I b.  Sublayer  Reduction  profile  profiles  Seyer-Metzner  10 4  +  profile  wall-law  10 3  = y  +  u  +  u  +  - 2.5  In  y  +  + 5-5  u  +  = 2.5  In  y  +  + 5.5  + AB  <1  model  .  u  +  11.7 I n v + -• 17.0 = 2.5 I n y + 32.0  1.0  Newton ian sub 1ayer  R  Th i c k e n e d D r a g - R e d u c i ng sublayer  o u Figure  1.2.  V e l o c i t y during  p r o f i l e s  drag  and  r e d u c t i o n .  the  thickened  s u b l a y e r  13  the  mixing  length  constant  for  the  Newtonian  s o l v e n t .  to  i n c r e a s e  as  AB  as  [ F i g u r e  p r o f i l e s  a r e  1 . 4 . 3  drag 1 . 2 ,  i n  nised  as  ments  have  and of  mean  doubt  r e q u i s i t e been  and  using due  probes  1  has  made  More  V i r k  probes  et  and  1972) ,  the  e l e c t r o c h e m i c a l  w a l l  s t r e a k  and  p a r t i c l e - s t r e a k  photography  s t u d i e s  w a l l - s l o t  a r e  dye  d i s c u s s e d  of  the  of  probe  l a t e r  to  seen f o r  v e l o c i t y  Flow  was  e a r l y  This v i s u a l have  to  Spangler some  l i m i t a t i o n t e c h n i q u e s  come  from  dopplermeter  ( F o r t u n a , (Seyer, (Donohue,  s e c t i o n ,  flow  s t u d i e s  and  s u b j e c t  r e c o g -  measure-  gross  (1 9 6 7 )  been  l a s e r  v i s u a l i z a t i o n  i n 3. a  i s  accounted  flow  The  b e h a v i o u r .  developments  and  B  t u r b u l e n c e  al.  have  measurements  use  that  Drag-Reducing  compared  recent  1973)  and  i s  t u r b u l e n t  as  n o n - d i s t u r b i n g  r e l i a b l e  i n  measurements.  probe  f u n c t i o n  d e t a i l s  r e d u c t i o n ,  (1 9 5 9 ) ,  anomalous  of  sparse  c o n v e n t i o n a l  to  n e c e s s a r y .  Merri1  as  1 . 6 . 3 - 5 .  drag  p r o f i l e  same  and  Further  presence  extremely  the  i n c r e a s e s  ( 1 . 3 ) ] .  f o r  i s  i n t e r c e p t  Measurements  the  v e l o c i t y  Shaver  (1969)  of  a  The  s e c t i o n  Turbulence Although  (slope)  r e d u c t i o n Eqn.  given  A  1971), 1969; 1972).  1 . 5 . 2 .  the (Rudd, b u b b l e C a r p e n t e r , These  14  1.5  The  Nature  1.5.1  Wall  The boundary  of  has  Turbulence  Turbulence  importance been  in  to  be  a  ' l a m i n a r  of  t u r b u l e n c e  q u i s c e n t  s u b l a y e r 1956; by  the  ( s i n c e shown  each  p r o f i l e  c h a r a c t e r i s t i c s t r u c t u r e s  (y  the +  <  of  been  l a y e r  flow  by  long  term  of  v e l o c i t y  i n  the  (y  >  +  averages  i s  of  from  K l i n e  of  (10  d i f f e r e n t  from  mean  s i n g l e - p o i n t  doubt  coworkers have  has  The the  v i s u a l i z e d  the >  +  v e l o c i t y  a  outer  zones  s u b l a y e r  4 0 ) ,  that  probe  L i ,  non-dimensional  in y  and  They  i n  >  unsteady  beyond  l a y e r  However,  regions  b e l i e v e d  an  and  the  boundary  presence  of  1965).  measurements  e i t h e r  the  s i g n a t u r e ' .  40).  the  ( E i n s t e i n  boundary  ' v i s u a l  b u f f e r  s t r u c t u r e  taken  p o r t i o n s  probe  i n  e s t a b l i s h e d of  f l u i d - s o l i d  then  concept  ( s i n c e  t u r b u l e n t or  c o r r o b o r a t e  and  observed  the  pattern  boundary 10)  known  was  flow  experiments al.  a  proposed  even  The  now  the  of  f l o w .  et  at  l a y e r  s u b l a y e r ' ,  has  Brodkey  that  w a l l  outer  1959)  Flow  Prandtl  the  v i s u a l  Boundary  motions  with  1956)  and  The  outer  e x t e n s i v e  v e l o c i t y  of  the  i n t e r a c t i n g  H a n r a t t y ,  s i n c e  1904.  a  Newtonian  f l u i d  r e a l i z e d  hypothesis  in  i n  of  l a y e r  Near  the  suggested or  f l u c t u a t i o n s  measurements.  * R u n s t a d l e r ,  K l i n e  w a l l - s l o t  dye  i n j e c t i o n  nique  v i s u a l i z a t i o n  K l i n e for  and  (-0.0005"  d i a . )  pulses  to  produce  and  w a l l - n o r m a l  in  were  and  and  hydrogen  coworkers and  used  l i n e s .  d i r e c t i o n s  from The in  a  (1963),  bubble the  v e l o c i t y  r e l e a s e d  time  Reynolds  a  using  s h e e t s ,  hydrogen  bubble  measurements. f i n e  wire  w i r e  was  l a r g e ,  in  t e c h -  The  bubbles  sheets  placed  open  r e v e a l e d  water  in  or  in  spanwise c h a n n e l .  15  the  presence  of  w e l l  motions  w i t h i n  was  c o l l e c t i o n  the  by  'streaks' Figure wise  1 . 3 a ) .  spanwise  to  the  and  the  f l o w ,  the  nature  v i o l e n t l y  i n  form  i n  zero  the  value  streak  A+  s p a c i n g  Lumley,  1967;  The  p r e s s u r e  ^-  Streaks  z:-.  motion  at  the  Townsend  ( F i g u r e  l i n e s  at  the  regions  is  a f f e c t e d  ( e . g .  K l i n e  et  form  as  of  i n f l o w .  by  t h i s  is  the  9u/9y  there  r e s u l t s  a  to  al.  s t r e a m w i s e , of  vortex  The  spanwise  primary  spanwise  term  and  l i n e s  to  al.  a  f l u i d  was  hypothesised  compress are  near  and  1974),  3  eddy vortex  s t r e t c h e d (9v/9x  compressive  u  have  Bakewell  v o r t i c i t y ,  of  were  non-dimensional  c o n t r i b u t i n g  v a r i a t i o n  s h o r t e r  and  c o u n t e r - r o t a t i n g  w h i l e  s t r e a k s  Newtonian  found  motion  outflow  Schraub  were  ' i n f l o w - o u t f l o w '  c i r c u l a t o r y  s t r e t c h i n g  et  outwards  the  g r a d i e n t s  the  stream-  and  leap  of  1967;  3  Lee  the  Regions  [C]  for  1971;  3  This  1 . 3 b ) . w a l l  Since  due  w a l l .  (1956)  p a i r s  in  100  low  waver  s t r e a k s  been  (see  s p e c i f i c  gg'&aid.i*e;n:t;s..  have  long  v i o l e n t l y .  f l o w .  g r a d i e n t  al.  up  s p a c i n g  about  et  to  and  of  Gupta  of  r a t h e r  seen  breaking  adverse  pressure  at  i n t o w.  regions  f l u i d  f e a t u r e  dye  i n t e r m i t t e n t l y  s i z e  of  or  v e l o c i t y ,  are  were  and  t h e r e a f t e r  c h a r a c t e r i s t i c  by  w a l l  found  the  s t r e a k s  dependent  n o t i c e a b l e  of  which to  time  bubbles  qu.fe,$oe-rtt *-bnffa;.vj.oju,6.&b"lsepp-eesoiree  flows  z.  hydrogen  observed  and  most  component  The  at  space The  s t r e a k s ,  were  (1965)  with  the  spanwise  u,  mean  waved  more  of  These  w h i l e  K l i n e vary  s u b l a y e r .  s p a c i n g s .  o s c i l l a t e  and  the  v e l o c i t y  i n t o  the  organized  [S] -  9u/9y),  a c t i o n .  to  z - v o r t i c i t y ,  the  w a l l ,  g i v i n g  16  wall S:  s t r e t c h i n g  C:  compression  zone zone y  zone  element  St,  low-speed  growth; large  E,  s t r e a k ;  e j e c t i o n  t r a n s v e r s e  Figure  1.3.  L,  l i f t u p  and  vortex  in  C o u n t e r - r o t a t i n g  (b)  Vortex  s t r e t c h i n g  inflow  and  The  (d)  The (c  (e)  The  &  p r o c e s s e s  eddy and  o u t f l o w  at  the  mechanics  of  s t r e a k  ' c y c l e '  of  near  compression  ' s t r e a k '  from  0,  o s c i l l a t o r y  i n r u s h ;  LTV,  a  w a l l .  p a i r s  of  adapted  f l u i d  flow.  mechanics  d  s t r e a k ;  I,  mean  T u r b u l e n c e  (a)  (c)  of  breakup;  due  to  w a l l . f o r m a t i o n .  breakup:  Kl i n e  t u r b u l e n c e  et  al.  events  ' b u r s t i n g ' 1967).  3  at  a  w a l l .  18  r i s e  to  f l o w ;  h i g h - s p e e d  ( i n f l o w ;  compression)  1.3c.  Dye  c o l l e c t  i n  p r e s s i o n  or  bubble  the  growth  The  low-speed  to  of  s u b l a y e r s t r e a k s  ' b u r s t i n g '  f611ows Kim,  as  being  speed  b u r s t i n g made  i n f l e c t i o n a l  of  t h e  r a t h e r  w e l l  e j e c t i o n s .  the  c y c l e  low-speed was  r a t e .  K i m et  al.  low-speed  p a r t i c l e s in  a  2"  50,000. the  about  to com-  v o r t i c i t y  and  to  t h e of  (1968)  ( i )  w a l l  by  events  1971).  t h e  c a l l e d  t h e  thus  was  more a  p r o f i l e ,  showed be  of  an  ( i i )  and  motion by  growth  into  that  d e f i n e d n e a r l y  a t t r i b u t e d  of  breakup  c h a o t i c  r e g e n e r a t i o n """This  mean  70%  to  l o w -  ( i i i )  a  p e r i o d  u n s t a b l e  quieseent^f.Tow.  w e l l  d e t a i l s  b u r s t i n g  forming  f o l l o w e d  t h e  l i f t i n g  i n s t a b i l i t y  had  could  observed  t h e  o s c i l l a t o r y  but  the  t h e  and  d i a . g l a s s Thei r was  same  of  p i p e .  The showed  with  Corino  used  n e u t r a l l y  suspended  p i c t u r e s moved  t i m e ,  Brodkey  motions  ( 0 . 6 y d i a . )  camera  tend  r e p e t i t i o n  of  t h e  a l l  b u r s t i n g  s t r e a k s .  Corino observe  w a l l  and  and  d e s c r i b e d  the  and a  (1971)  1.3b  s t r e t c h i n g  from  v e l o c i t y  event  s t r e a k  t h e  sequence  l a y e r ,  d e f i n e d This  up  s t a g e s ;  from  p r o d u c t i o n  At  to  They  w a l l  i n t e r m i t t e n t  t u r b u l e n c e of  motion  Figures  (out-  1 . 3 d ) .  i n s t a n t a n e o u s  o s c i l l a t o r y  of  the  a  low-speed  ( M o l l o - C h r i s t i a n s e n ,  Reynolds  three  near  streamwise  then  and  i n  Vortex  l i f t e d  (Figure  of  from  an  f l u i d  a r e  and  shown  i n s t a b i l i t y  p r o c e s s .  up  s t r e a k s  zones.  and  K l i n e  as  p l a c e d  secondary  v o r t i c i t y  t h e  markers  a  streamwise  of  zones  low-speed  leads  the  f l u i d  s t r e t c h i n g )  the  in  buoyant  t r i c h 1 o r o e thy 1ene number  at  the  1  (1969)  photography  magnesium  ' c o n v e c t e d  flow  Brodkey  high-speed  Reynolds a  and  was view  mean  oxide f l o w i n g  about s i n c e  flow  v e l o c i t y .  19  v i s u a l l y of  the  flow  i n r u s h ' and  i d e n t i f i e d near  a  phases.  coworkers  two pipe  The  due  w e l l w a l l ;  l a t t e r  to  d e f i n e d  the  ' f l u i d  event  e j e c t i o n  corresponded  to  which  convects  low-momentum  f l u i d  w h i l e  t r a n s p o r t a  f l u i d of  complete  f l u i d are  c y c l e  b e l i e v e d of  of the  i n  w a l l .  Brodkey  major  f a c t o r s  and the  the  (1969)  but  moved  downstream,  f l u i d  elements  the  s i m i l a r w a l l  and  l a y e r  they the  i n  were wall  i n  the  streak  b u r s t i n g into  with  The the  the  the  w a l l .  Thus,  e j e c t i o n outer  g e n e r a t i o n  of  of  flow and  main-  (1973),  a  p l a t e ,  f l a t  to  two  f l o w ,  up  Offen dye  As  at  using  Corino  f l o w .  sweep  importance  b u r s t i n g  as  bulk  using  the  scheme  r e g i o n .  outer  i n t e r a c t i o n  i n f l u e n c e  over the  the  confirmed  Brodkey  seen  i n t e r a c t i o n s one  have  t h a t  and  flow  v o r t i c e s  from  s t u d i e s  experimental  with  the  K l i n e  1 . 3 e ) .  l a y e r s  Hershey  same  t r a n s v e r s e  at  inner outer  l a r g e  s t u d i e d  v i s u a l  in  by  t e c h n i q u e .  the  with  ' f l u i d  boundary  o b s e r v e d .  be  recent  the  towards  i n t e r a c t i o n  ( F i g u r e  and  a s s o c i a t e d  t h e i r  Nychas,  e s s e n t i a l l y  was-e  t h e i r  from  f e a t u r e s  observed  low-speed  were  f l u i d  events  t u r b u l e n c e  outer  events  of  the  not  of  and  to  More between  phases  high-momentum  elements  tenance  i n r u s h  e j e c t i o n '  was  l i m i t a t i o n  F l u i d  core  i n t e r m i t t e n t  and  observed these  v o r t i c e s  s m a l l - s c a l e and  K l i n e  (1974)  i n j e c t o r s ,  together  with  one a  20  w a l l - n o r m a l  hydrogen  bubble  them  that  t r a n s v e r s e  to  see  e j e c t i o n e a r l i e r  was  generated  b u r s t The  put  together  1.3e. the  The sake  o u s l y  Gupta i s  a  complete  3  from  probe  1.5.2  As as  y e t  phenomena. Shaver  and  core  t r a t e d  The  regions  p s e u d o p l a s t i c  of  an  ' c y c l e '  has  et  3  e r r o r  i n  as of  e . g .  and  Drag-Reducing  Newtonian  d e t a i l s v i s u a l  They  t u r b u l e n t  et  £ a r b o x y m e t h y l  1971;  3  there s t r u c -  r e c e n t (1973).  Flow  i s  f l o w s ,  flow  of  that  dye  into  a  f a i r l y  £ e l l u l o s e  l i t t l e  t u r b u l e n c e  probably  i n j e c t e d  pipe  al.  the  d r a g - r e d u e i n g  study  s i z e ,  s u p p o r t e d . t o  K l i n e  t u r b u l e n t  of  t h e i r  p h y s i c a l b y  f o r  c o n t i n u -  However,  evidenced Offen  in  Rap  deducing  Figure  f e a t u r e s  been  1 972 .  al..  i n  o c c u r s  p i c t u r e  measurements,  t u r b u l e n c e ,  shown  d i s t i n c t  This  (1959). in  as  i s  g r e a t l y  e a r l i e s t  M e r r i l l  s t u d i e s ,  w a l l  v a r y i n g  i n  w i t h  i n t e r a c t i o n  Newtonian  complete  of  a l l o w e d  a s s o c i a t e d  events  to  the  of  shown  experiments  of  vortex  of  measurements  compared  known  are  Wallace  Turbulence  technique  f l o w .  s e r i e s  probe  r i s k  This  upstream  p i c t u r e  the  1971;  p r o b e - c u m - v i s u a !  and  by  the  bulk  d u r a t i o n .  degrees al.  by  steps  i n d i v i d u a l  c o n s i d e r a b l e  tures  is  t h i s  c l a r i t y :  and  et  the  v a r i o u s  w i t h  varying  w i t h  from  of  v e l o c i t y  the  w i r e .  the  of w a l l  c o n c e n -  s o l u t i o n  21  (0.25%  CMC  in  t a t i v e  and  not  e x t e n s i v e .  of  t u r b u l e n c e  a c t e r i s t i c s  water,  o v e r a l l  r a d i a l  rate  formation  of  To Seyer for  and  measured and  of  (1969)  The  flow  i . e .  developed  t u r b u l e n c e  f l o w . s c a l e  This of  up  to  the  r a d i a l  was  nique  n e a r - w a l l  of  r a d i a l  f l u c t u a t i o n s  momentum  t r a n s p o r t  decrease  in  in  sublayer  a  -  showed  in  Roll in r e g i o n near  to  the  drag  the  a  w a l l .  for  reducers  was  made  time-averaged  of  f u l l y was  Newtonian  reducer  This  drag  and  core  i n c r e a s e  and  0.1%  t r a n s i t i o n a l  the  extended  pipe  and  c o n d i t i o n s i n  and d i l u t e  laminar  than  an  (1971) of  of  p r o f i l e  a t t r i b u t e d  t r a c e r s  with  s o l u t i o n  Under  d e v i c e s , as  (0.01%  c o n d i t i o n s  decreased  t u r b u l e n c e  pipes  patches  i n  probe  s o l u t i o n s  v e l o c i t y  poor  a  bubbles  g l a s s  105.  c h a r -  in  the  due  time  to  i t s  S e y e r ' s  found  a  t e c h -  r e d u c t i o n  decrease  in  r a d i a l  i n t e r p r e t e d  as  a  b u r s t i n g .  Rudd ments  i n v e s t i g a t e d  f l u c t u a t i o n s  p r o p e r t y .  the  They  d r a g - r e d u c i n g  e f f e c t  of  small  in  three  ( b u r s t s ) .  used  Re  and  v o r t i c e s '  a i r  q u a l i -  Newtonian:  l a y e r  u n c e r t a i n t i e s  were  observed  to  wall  p r o f i l e s  a  v i s c o e l a s t i c to  t h i c k e r  a l t e r n a t i n g  f l o w ,  they  compared  concentrated  t u r b u l e n t  under  as  p o l y a c r y l a m i d e  r e s p e c t i v e l y ) .  experiments  However,  the  v e l o c i t y  behaviour,  The  'horseshoe  photography.  mean  0 . 6 1 ) .  a  overcome  concentrated  f l a t t e r  =  m i x i n g ,  Metzner  streak  n  (1972)  square  was  duct  t h i c k e n e d  using and  a  l a s e r  s t a b i l i z e d  v e l o c i t y  measure-  dopplermeter. by  the  a d d i t i o n  The of  22  100  wppm  Separan  t u r b u l e n t between to  the  wall  AP30  to  water.  i n t e n s i t i e s  i n  the  the  d r a g - r e d u c i n g  c o n c l u s i o n  t u r b u l e n c e  the  spanwise  t h i s  was  that  with  b e l i e v e d  to  Fortuna array  of  p i p e .  due  observed  200  s o l v e n t .  wppm This  i n t e r p r e t e d speed  a  the  values were  the  a t  not  caused  as  by  the  i n c r e a s e  i n c r e a s e  same  i n  wall  i n  dye  5  701)  wppm  mixture  Polyox  f l o w i n g  i n  shear  as  the  i n  value  a  a  and  2 . 5 4  c o r r e l a t i o n  Newtonian was  spacing  of  of  which  ( X  and  the  that  i n  l o w -  +  r e d u c t i o n .  noted  cm  d i s t a n c e  value  with  decrease  i n  the  i n t e n s i t y  and  wall  )  They  the  shape  Newtonian these  pressure  changes drop  a d d i t i v e . et  pipe  al. flow  t e c h n i q u e . was a  i n  spanwise  r e d u c t i o n  the  of  spanwise  s p a t i a l  50% drag  t u r b u l e n t  drag  polymer  l a s e r - i n d u c e d  the  a t  a  Newtonian  non-dimensional  during  d i r e c t i o n  i n  l e d  near  probes  spanwise  over  s t r i k i n g  the  the  and  e d d i e s .  i n c r e a s e  i n c r e a s e  changes  the  of  Arunachalam normal  dramatic  d i f f e r e n c e  suppressed  used  d i s s o l v e d  the  s p e c t r a  (1972)  a x i a l  s u p p r e s s i o n  w a l l - l a y e r  AP30  f i v e - f o l d  compared  was  e l e c t r o c h e m i c a l a  no  However, w  of  flows  general  Separan  an  s t r e a k s ,  showed  of  as  no  v e l o c i t y  Hanratty  z e r o - c r o s s i n g s  to  i s  s t a b i l i z e  and  showed  Newtonian  a d d i t i v e .  of  wal1-embedded  They  between  there  component  measurement  s u b l a y e r  and  the  A  added  1.36  cm  (1972) using  v i s u a l i z e d a  a  p i p e .  w a l l -  n o n - d i s t u r b i n g  P o l y e t h y l e n e to  the  70-30 The  oxide  ( 0 . 5  to  a l c o h o l - w a t e r dye  t r a c e s  showed  23  a  t h i c k e r  low  wall  l a y e r  frequency that  A  frequency  reducing  higher  were  (1973), K l i n e  drag  measured  frequency  of  reducing  wall  i n  f l o w s .  the  wall  f l u c t u a t i o n s  e j e c t i o n s  Higher  was  r e g i o n  were  s u p p r e s s e d .  observed  i n  d r a g -  s o l u t i o n s . More  l a y e r s  the  i n t e n s i t i e s  suggested reduced  i n  d e t a i l e d  made  using al.  et  by  s t u d i e s  Donohue  experimental (1967)  and  of  et  d r a g - r e d u c i n g (1972)  al.  techniques  Corino  and  and  wall  Carpenter  s i m i l a r  those  of  v i s u a l i z a t i o n  i n  Brodkey  to  (1969)  r e s p e c t i v e l y . Donohue a  2-D  139  wppm  were An  channel  rate  compared  to  a  a t  f o r  streak  the  d u c t i o n  a  to  record  i n  water. view  the  flow  r a t e s , had  wall  k i n e t i c  motion  a  cm  and  and  The  drag time the  a  bursts  p i c t u r e s .  averaged  streak  b u r s t i n g  r e d u c e r .  When  i n t e r v a l same  as  decreased  d r a g - r e d u c i n g  i n d i c a t e d  p a r t i c l e  value  shear.  the  (1973)  the the  a  7.3  non-dimensional  s p a t i a l l y i n  of  Streaks  as  and  measured  i n  f l o w ,  t u r b u l e n t  i n  dye  diameter  wall  reducer  b u r s t i n g  used  p h y s i c a l  and  reduced  Carpenter graphy  the  mass  drag  Newtonian of  dual  decrease  the a t  h y d r a u l i c  a  both  equal  (1972)  s o l u t i o n  obsevered  water  speed  from  i n  and  were  bursts  a  Polyox-FRA  i n c r e a s e  spacing  for  with  recorded  al.  et  f l o w ,  s u p p r e s s i o n  between that  l o w as  i n  compared  the  pro-  energy.  used  high-speed  t r a j e c t o r i e s  a t  motion the  wall  photoof  a  24  2.54  cm  p i p e .  d i o c t o a t e  were  was  near  This  the  wall  and  a  d e t a i l e d  a v a i l a b l e ,  s l i g h t  n o t i c e d  a  r e d u c t i o n  d e t a i l e d  p r e s e n t l y  not  w i l l  to  complete  in  Mechanisms  of  and  together flow  The  e x p l a n a t i o n s  r e d u c t i o n  are  based  continuum  e f f e c t s ,  in  Table  1.1.  of  c o n f u s i o n  e l a s t i c i t y of  the  in  Table  in  This i n  the  a a  wide  drag  r e d u c e r .  b u f f e r  l a y e r  t h i c k n e s s ,  f l u c t u a t i o n s  and  a  t u r b u l e n c e  the at  have  f l o w , and  f u t u r e  the  in  i s  probe to  s t u d i e s  provide  w a l l .  Reduction  been  suggested  of  continuum  combination  of  the  two,  as  shown  r e f l e c t s  the  present  s t a t e  to  s o l u t i o n models  e x p l a i n drag  f o l l o w s  the  r o l e  r e d u c t i o n . the  and  for  range  attempts  and  process  e j e c t i o n  v i s u a l  Drag  that  d i v e r s i t y  polymer  mechanisms 1.1.  on  for  Newtonian  the  Newtonian  i n  events  a x i a l  b u r s t i n g  the  drag  s t r e s s e s .  D e t a i l e d  Models  or  i n  as  p r o d u c t i o n  the  w a l l - l a y e r  that  a v a i l a b l e .  p i c t u r e  of  i n  i n  v e l o c i t y  Reynolds  to  pieced  of  used  average  the  i n c r e a s e d  p i c t u r e  s i m i l a r  be  flow  aluminium  energy  that of  0.1%  were  the  r e d u c t i o n  the an  than  account  r a d i a l  r e d u c t i o n  r e d u c e r s ,  have  by  i n  and  t u r b u l e n t  lower  during  f l o w ,  the  general  accompanied  A  1.5  d r a g - r e d u c i n g  Although  was  coagulant  t r i c h l o r o e t h y l e n e  l e v e l  c o n s i d e r a b l e  a  i n  a  was  drag  Polyox  to  not  event  a  During  reduced  f l o w .  ppm  d i s s o l v e d  r e d u c e r s . v e l o c i t y  250  of A  sequence  drag  non-  v i s c o -  d i s c u s s i o n of  l i s t i n g s  25  Mechanisms  1.6.1  MOLECULAR 1.  Wall  and  Table  1.1  Models  f o r  Drag  Reduction  e f f e c t s a d s o r p t i o n  of  macromolecules  (Elperin  and  Smolskii,  1.6.2  2.  M o l e c u l a r  s t r e t c h i n g  (Tulin,  3.  M o l e c u l a r  aggregates  and  1965)  1965) entanglements  (Lumley, 1967)  COMBINED MOLECULAR-CONTINUUM e f f e c t s (Macromolecule-Eddy I n t e r a c t i o n ) 1.  Length  2.  Time  3.  S t r a i n  s c a l e  s c a l e  CONTINUUM  i n t e r a c t i o n s  energy  (Virk  et  at.,  1967)  (Astarita,  h y p o t h e s i s  1965)  (Walsh,  1967)  e f f e c t s  1.  Wall  2.  A n i s o t r o p i c  3.  Normal  4.  E x t e n s i o n a l  5-  Thickened  6.  i n t e r a c t i o n s  s l i p  theory  v i s c o s i t y  s t r e s s  1949)  e f f e c t  e f f e c t  (Metzner  v i s c o s i t y  e f f e c t  s u b l a y e r  -  e f f e c t i v e  -  m o d i f i e d  -  e l a s t i c  Surface  (Oldroyd,  s l i p  &  M e r r i l l , 1959)  & Park, (Gadd,  1964) 1965)  models model  e f f e c t i v e  s u b l a y e r  Renewal  (Shaver  models  (Eldta^et.  s l i p  model (Black,  model Metzner, (Virk, 1969;  al., (Seyer  1966) & 1969)  1971) Meek Baer,  and 1970)  26  1.6.1  Mo1ecular  E f f e c t s  Adsorption s o l i d by  i n t e r f a c e  Eltferin  in  was  (1971)  of  i n t e r p r e t e d pipe  monolayer  adsorbed  m o l e c u l a r  l o o p s ,  were  a l t e r  the  proof  of  i t  d i f f i c u l t  i s  such  pipe  an  of  to  pipe  i n t o  t u r b u l e n t  i n t e r a c t i o n to  w a l l .  the  p e r c e i v e  Bryson  by  a  polymer  Free  hanging  wall  a t  the  not  macro-  s p e c i f i c  s u b l a y e r  and  somehow  D i r e c t  a v a i l a b l e .  i n t e r a c t i o n  et.  r e s u l t s  eddies , t h e r e o n .  i s an  a d s o r p t i o n  (1971),  a f f e c t e d  f l u i d -  mechanism  the  d i s p e r s i o n  being  extend  on  F u l f o r d  t r a c e r  the  attached  behaviour  d r a g - r e d u c t i o n Based  and  as  to  a  ( 1965).  flow  on  b e l i e v e d  as  t h e i r  a t a  MacromoTecules  suggested  Arunachalam  d r a g - r e d u c i n g  s i t e s ,  Polymer  and Smols*kii  measurements al.  of  Moreover,  between  an  o  adsorbed  monolayer Hand  (~  and  was  formed  by  an  a l r e a d y  w a l l - a d s o r b e d  of  polymer  macromolecu 1es .  a  damping  e f f e c t  on  Molecular c i t e d by and  ( T u l i n ,  which  a  p o s t u l a t e d  a  means  (1973)  t u r b u l e n t  eddy  (~  suggested  that  an  present polymer  This  the  p h y s i c a l l y  aggregates  and  (Lumley,  1 967)  The  was  e n -  a t t a c h i n g  forming  o u t  f r e e  as  provide  a  a  to  ' m a t '  b e l i e v e d  flow  to  have  have  been  mechanism  ' m i c r o - v o r t i c e s '  t u r b u l e n t  a  has  p o s s i b l e  l i n k e d  entanglements to  w a l l .  mm).  f l o w .  1970)  damping  the  m o l e c u l e s  'mat'  i n  P e t e r l i n ,  a t  thus  t u r b u l e n t  stretching  of  a  monolayer,  macromolecule  provided  M o l e c u l a r  1 9 6 5 ;  the  and  was  layer  l a y e r  A)  W i l l i a m s  adsorbed-entangled tangled  100  f l u c t u a t i o n s .  a l s o  length  been  s c a l e  that  i s  27  of  the  order  of  led  to  and  continuum  t h e o r i e s  1 . 6 . 2  in  gross  a c t i o n s the  (i)  t h a t  have  eddy  t r i e d  to  Macromolecule-Eddy  s i z e s .  This  combine  both  has  I n t e r a c t i o n s  presence  and  abruptness  of  flow  s t u d i e s ,  has  s t i m u l a t e d  hypotheses  t h i s  length  idea  m o l e c u l a r  The  between  on  d i s s i p a t i v e  approaches.  t u r b u l e n t  based  the  polymer  macromolecules  flow  f i e l d  idea  may  s c a l e s ,  during  be  ( i i )  drag  s c a l e s  and  the  as  into and  i n t e r -  s c a l e s  of  Hypotheses  groups  ( i i i )  observed  of  r e d u c t i o n .  c l a s s i f i e d  time  ' o n s e t ' ,  based  s t r a i n  on energy  c o n v e c t i o n .  1 . 6 . 2 - 1 , 2  Length  The a c t i o n  between  comparing length the  scale  time  f i e l d  scale  and  by  by  an  and  Z a k i n ,  the  shown  wall The  the  i t s  rms  eddy  1967) shear  et  length  rate  as  of  of  the  a  the  and  u * / v .  Elata  et  t y p i c a l  al.  M e r r i l l c o i l e d  the  The  s o l u t i o n ' s  and  The  c h a r a c t e r i z e d  c o r r e s p o n d i n g  V i r k  by  s c a l e s .  g y r a t i o n as  i n t e r -  eddies  (1967)  taken  the  of  time  al.  1965;  employed  s c a l e  and  r a d i u s  c a l c u l a t i o n s  length  t u r b u l e n t  length V i r k  Hypotheses  c h a r a c t e r i z e  and  ( A s t a r i t a ,  hypotheses  parameters. have  of  hypothesis  S c a l e  hypotheses  r e s p e c t i v e  macromolecule  Hershey  two  Time  macromolecules  t h e i r  t u r b u l e n t time  f i r s t  and  3  1966;  r e l a x a t i o n s c a l i n g (1969) polymer  28  macromolecule than  the  time  s c a l e s  to  have  to  d i s s i p a t i o n  the  r e c i p r o c a l  1 . 6 . 2 - 3  The attempts  to  from to  the  the  energy  h i g h l y  of  of  drag  of  k i n e t i c  dependent  of  same  the  of Stated  onsets i s  when  g r e a t e r  than  t i m e .  of  Walsh  the  b a s i s  l i q u i d s .  s t r a i n e d  energy  b e l i e v e d  occur  d i f f u s i o n .  Walsh  number  parameter)  ('H'  proposed to  r e l e a s e moving energy  the  when  i s  to  and  from  becomes  energy  concept  to  d i f f u s i o n  c o n v e c t i o n  the  s t r a i n  a d d i t i o n  to  of  Eddies  convect  in  (1967)  s u b j e c t e d  r e l a x e d .  r e g i o n is  The  when  when  are  This  energy  on  s o l u t i o n ,  k i n e t i c  s t r a i n  the  Hypothesis  wall  i s  order  r e d u c t i o n  r e l a x a t i o n  s m a l l e r  hand,  a p p e a l i n g .  t u r b u l e n c e  energy  f l o w .  r e d u c t i o n  Deborah  the  drag  f o r c e s  s t r a i n e d  energy  have  r e d u c t i o n  store the  the  other  hypothesis  i n  magnitude  the  v i s c o e l a s t i c  t u r b u l e n t  drag  magnitude to  strain  of  On  more  s o l u t i o n  Energy  when  of  i n  S t r a i n  s t r e s s e s ,  core  process Onset  the  e x p l a i n  energy  to  (1965),  frequency of  orders  approach  macromolecules  t u r b u l e n t s t r a i n  t h i s  c a p a c i t y  the  found  A s t a r i t a  the  three  m i c r o s c a l e .  been  making  a c c o r d i n g  that  about  t u r b u l e n c e  magnitude,  s t o r i n g  be  normal  the  w a l l .  the  comparable a  c o n c e n t r a t i o n -  p r e d i c t  onset;  2 8  c  M[n] RT  T  w  _  s t r a i n  ~  k i n e t i c  energy energy  c o n v e c t i o n  /  d i f f u s i o n  *  29  H  -  0.01  at  onset  and  H  ->  1 .0  at  maximum  drag  r e d u c t i o n . Walsh's continuum  v i e w p o i n t s .  been  g e n e r a l l y  that  the  the  from  that  of  an  the  wall  abnormally  mobile  to  the  Toms  w a l l . the  would  f l o w i n g give  Both  wall  l a y e r  been  d i s c o u n t e d  the  c o n t r a r y .  i s  a  in  has  due  poor  to  not  the  f a c t  measure  s o l u t i o n s  p o l y d i s p e r s e  of drag  Oldroyd  of  that  are  samples.  and  t u r b u l e n c e  The  theory  w h i c h ,  a  by  than  of  the at  pure the  experimental  probably  t h i c k n e s s  caused  i t s  i d e n t i f i e d  e x i s t e n c e  s h e a r - t h i n n i n g  s h e a r - t h i n n i n g of  the  whose  which  v i r t u e  the  Oldroyd  proposed  and  was  s u p p r e s s i o n  sublayer  f a c t o r s  presence  (1949)  r e d u c t i o n .  suggested  and  the  very  polymer  dimensions  f r i c t i o n s l i p  of  laminar  s o l u t i o n  lower  [n]  theory  m o l e c u l a r (1949)  parameter  and  E f f e c t s  l a y e r  r o l e s .  'H'  m o l e c u l a r  probably  a v a i l a b l e  e x p l a i n  important  comparable  in  to  the  u n i f y  i s  time  w a l l - s l i p  attempt  both  played  r e l a x a t i o n  to  This  v i s c o s i t y  Continuum  The e a r l i e s t  However,  c o m m e r c i a l l y  1 . 6 . 3 - 1  attempts  a p p l i c a b l e .  i n t r i n s i c  m o l e c u l a r  made  theory  s l i p  wall  low  was at l a y e r  v i s c o s i t y ,  s o l v e n t . wall  have  f i n d i n g s  s i n c e to  30  1 . 6 . 3 - 2  A n i s o t r o p i c  Anisotropic M e r r i l l  (1959)  that  they  They  p o s t u l a t e d  a  p o s s i b l e  observed that  a  s h e a r - r a t e - d e p e n d e n t the when  core  to  the  a p p l i e d  Fortuna  d i l u t e  Hanratty  (1972)  e x p l a i n  of  i n c r e a s e d  v i s c o s i t y  i n  the  give  of  1 . 6 . 3 - 3  to  Metzner as  a  v i s c o e l a s t i c r e d u c t i o n  Newtonian  the  formation  t u r b u l e n t  S t r e s s  and  f l u i d s .  r a t i o  r a t i o  and  Park  the  of  Reynolds  e l a s t i c  i s  from  s p e c u l a t i v e  t h e i r  A  of  during  wall  i n  drag  eddy  could  d i f f e r e n t  r a t e ,  This  by  experimental  s p a c i n g  d i r e c t i o n  and  suggested  i . e .  a  i n  the  than c o u l d  lead  l a t e r a l  flow lower spanwise  to  a  o s c i l l a t i o n s  E f f e c t  were  a  moved  i t  a  b u r s t s .  measure  of  as  was  shear  (1964)  They  (0.3%  (x)  s o l u t i o n . encounter  v i s c o s i t y  l o c a l  CMC  and s u p p r e s -  would  f l o w .  d i r e c t i o n s .  q u a n t i t a t i v e  s o l u t i o n a  (y)  Normal  s t r e a k  Newtonian on  streak  r i s e  to  streamwise  w a l l - n o r m a l  s u p p r e s s i o n  spanwise  compared  depending  to  Shaver  s o l u t i o n s .  and  d i r e c t i o n s  number;  polymer  by  t u r b u l e n c e  theory  approach  a n i s o t r o p i c  t r a t e d  t h i s  d i f f e r e n t  encounter  effect  vortex  s l i g h t l y  as  that  the  g r a d i e n t  However,  very  for  p s e u d o p l a s t i c  v i s c o s i t y  r e d u c t i o n  or  a  suggested  A  f i n d i n g s  (z)  i n  cause  t u r b u l e n t  w a l l .  to  was  v i s c o s i t y  as  sion  V i s c o s i t y  used of  the  a b l e  to  number  polymer) f o r c e s ,  the  normal  e l a s t i c  stress property  c o r r e l a t e for  with  a  the  measured  as  the  f a i r l y  of  f r i c t i o n c o n c e n -  Weissenberg normal  s t r e s s ,  31  to  v i s c o u s  a c c u r a t e l y t h r u s t  f o r c e s .  Normal  measured  i n  method.  (0.005%  to  s i t u a t i o n s  are  1 . 6 . 3 - 4  t i o n s  i n  l e n c e  damping'  to  Bragg  Donohue Gadd's  of  was  the  damping  of  flows  of  at  Thickened v e l o c i t y  p r o f i l e  E l a t a  al.  the  et  v e l o c i t y  d i f f i c u l t i e s .  to  (1965,  the  l i k e  those  and  Metzner  f i n d i n g s  Metzner  Carpenter  d i f f e r e n t  Sublayer  have  The f o r  of  r e s i s -  i n  v o r t e x The  and  O l i v e r  t u r b u l e n t R o l l i n  have  d r a g -  (1971),  supported  d e t a i l .  Models  models  accounts a  (1973)  l e v e l s  He  (1 9 7 0 )  (1969),  ' t u r b u -  l a y e r .  i n  s o l u -  high  present  Metzner  and  or  1966).  s o l u t i o n ' s  n e a r - w a l l  v i s u a l  polymer  t u r b u l e n c e  the  and  as  of  Gadd  measurements.  p r o f i l e  j e t  d r a g - r e d u c i n g  of  v i s c o s i t y  by  sublayer  (1966)  the  s o l u t i o n s  most  i n  the  Thickened  d i l u t e i n  and  u s i n g  experimental  p r o d u c t i o n  f l u i d  Seyer  (1972)  s u g g e s t i o n  1 . 6 . 3 T 5  and  e a s i l y  V i s c o s i t y  s t r a i n s  by  in  i n t e r e s t  s e r i o u s  e f f e c t  of  y „  (1973),  al.  to  of  suggested  motions  et  are  extensional  e l o n g a t i o n a l  measurements  reducing  r o l e  the  s t r e t c h i n g  and  s u b j e c t  d e c r e a s i n g  a t t r i b u t e d tance  which  be  s o l u t i o n s  measurements  E x t e n s i o n a l  The  can  c o n c e n t r a t e d  However,  0.01%)  s t r e s s e s  based  e f f e c t i v e - s l i p  the  p h y s i c a l  been  upward  on  mean  model  d i s p l a c e m e n t  t h i c k e n i n g  of  the  of of  v i s c o u s  32  s u b l a y e r models  adjacent  of  Seyer  v a r i a t i o n s  of  a  basic  approach  the  ' B '  f u n c t i o n  the  non-dimensional  (eqn.  drag  4 b ,  d i f f e r e n t  observed  the  pipes than  regime  ( c ) ] .  )  +  d i d  b a s i s  of  the  l o s s  to  the  flow  Pipes  of  from  of  (1969)  based  showed  f u n c t i o n  of  0  s o l u t i o n . value  of  +  ,  A t  about  the  sublayer  t i o n  to  2 i  32  was  d e f i n e d  extending  of  equation  ( e q n . 4 a ,  reducing  c o n d i t i o n , v e l o c i t y  Figure V i r k ' s  p r o f i l e ;  <  of  the  y  model  +  <  r e d u c t i o n  e f f e c t  maximum  roughness  r e d u c -  v a l u e .  the  with  ' e l a s t i c  by  f o r  r e p r e s e n t i n g  i d e a ,  drag  a d d i t i v e  f o l l o w s  with  1 . 1 ,  t h i s  5CLand  Thus,  were  Reynolds  Using  polymer i n  lower  of  of  pipes  asymptote;  peaks  the  being  i n  [ s e e Figure  drag  Newtonian  1 . 2 ) .  PV  a  the  as 5  a t  pipes  t h i c k n e s s  hypothesized from  r e d u c t i o n  l i n e  was  roughnesses  s u b l a y e r .  times  i n t e r a c t i o n  t u r b u l e n c e  t h i s  p r o t r u s i o n  estimated  about  drag  (1971)  measurements  t h e maximum  V i r k  the  a r e  a n a l y s i s  Virk  a l l  smoother  t h i c k e n e d  for  a  of  gross  the  as  a  the  approached  maximum  r e l a t i v e l y  The  The  be  of  model  above  be  to  r e c e n t  scheme.  and Metzner  time  sublayer  d e p a r t i n g  a t t r i b u t e d  elements  B ( 8  (1971)  s i m i l a r i t y  (1.7)  more  1 . 2 ) .  f o l l o w  number  was  Seyer  The  sublayer  and,the  of  1 . 2 ) .  and V i r k  t h i c k e n e d  roughnesses.  to  rougher  (1969)  r e l a x a t i o n  elastic  on  (Figure  equation  r e d u c t i o n  The  of  of  Figure  p o s t u l a t e d  wall  measurements  continuum  maximum  the  and Metzner  the  The on  to  a  t h e the  the given l i n e  the s u b l a y e r ' ,  asymptote d r a g OP-PV-VP'  ' e l a s t i c  33  s u b l a y e r ' .  In  f o l l o w s  l i n e  the  Newtonian  c o n t r a s t  changes  to  a d d i t i o n in  of  A l s o ,  d e s i g n  to  a v a i l a b l e  1 . 6 . 3 - 6  for  ( E i n s t e i n  v i s c o u s  y  15  cm) of  these  p r o f i l e  They to  have  not  mean-flow  1956;  d a t e ,  the  of  pipe  i n  the  to  be  been  value  s i z e s  of  t e s t e d .  drag  reducers  models.  f o r  Drag-Reducing  developed  B l a c k ,  of  due  c o u l d  t u r b u l e n c e  models  t h i c k e n e d  understanding  but  Models  the  .  +  v e l o c i t y  d r a g - r e d u c i n g  unsteady  f l u i d s  t r a n s p o r t  in  to  =  +  model  for  1969)  flows  Newtonian  have  (Meek  Flow  been  and  m o d i f i e d  Baer,  1970,  1969).  The  The  >  Renewal  L i ,  r e p r e s e n t i n g  good  s c a l e - u p ;  renewal  and  a p p l i c a t i o n  B l a c k ,  from  a  Seyer-Metzner  r e d u c e r s .  mechanism  Surface  Surface flows  drag  and  U  'mean'  ( d i a .  the  by  provide  Newtonian  the  PSM  given  models  i n t e r e s t  c l u e s  not  and  polymeric  e m p i r i c a l  p r a c t i c a l  are  the  t h i s ,  OP-PSM-SMP';  s u b l a y e r These  to  and  theory t i m e ,  i s  much  was  based l i k e  p r e d i c t e d  with  a  t h i s  the  from  wall  boundary  r e p e a t i n g  p r o f i l e s  measurements.  s i o n a l  p e r i o d ,  T  =  i n The  171  of  of  the  l a y e r ,  b u r s t s  s e l e c t e d  process  so  reasonable model v / u * .  at  r e p e a t e d l y and  for  model  measurements  l a y e r  a r b i t r a r i l y  experimental burst  Einstein-Li  o b s e r v a t i o n s on  An  v e l o c i t y  layer  developed  v i s u a l  i n s t a n t a n e o u s l y . a s s o c i a t e d  wall  then  mass pipe  w a l l .  d e v e l o p i n g  c o l l a p s i n g  time  period  that  the  agreement  p r e d i c t e d ,  a  was  theory with non-dimen-  34  Meek v i s c o u s  and  f l u i d s  Baev  by  i n t r o d u c i n g  w a l l - l a y e r  'patchy'  a  value  constant  than  IO1*.  using  a  T  Extension  -  +  of  324  the  Maxwell  1  t u r b u l e n c e  as  motions  motions  break  'horseshoe/: l i k e  (1969)  DR  which  down  The  Meek-Baer  Reynolds  V  gave  move  that  non-dimensional  drag  horseshoe  During f o l d  v o r t i c e s  maximum  i n c r e a s e  drag i n  These d e t a i l s While a do  as  they  Newtonian  s o l i d  away time  +  v i s c o s i t y  governed  boundary.  and from  These  time  to  the  wall  between  the  generate much  e r u p t i o n 2  T  model  models  have  of  t u r b u l e n c e  polymer how  the  as  wall  =  116  v / u * .  i n d i c a t e s  a  t e n -  .  e m p i r i c a l l y  i n d i c a t e  p r e d i c t e d  r e d u c t i o n ,  two  p o s s i b l e  d r a g - r e d u c i n g not  T  was  r e d u c e r s  Re  +  of  g r e a t e r  r e l a t i o n ;  and  space  convect  p r e d i c t s  (1  DR  v i s u a l i z e s  i n  the  model  to  the  f  the  to  ! j l  =  DR  along  f o r  numbers  model  N  V  theory  d e t a i l s  time-dependent  p e r i o d i c a l l y  v o r t i c e s '  b u r s t s .  N  model  o r g a n i z e d ,  primary  f o r  equation  T  Black s  The  Meek-Baer  T  t h i s  a d d i t i o n a l  s t r u c t u r e .  f o r  convected  m o d i f i e d  (-.1970)  the  the  p r e d i c t on  sought  the  a r e  i n c o r p o r a t e  p r o c e s s e s  e f f e c t s  Newtonian  changes  to  wall  of  a t  the  the  about.  many  w a l l .  a d d i t i o n  t u r b u l e n c e ,  brought  as  they  of  35  1.7  C l o s i n g  A is  not  as  v a r i e d  d e f i n i t e  yet  more  As  to  that  i s  The  a f f e c t  F u r t h e r ,  the of  i s  the  s t u d i e s is  an  drag a  i n  the  have  reducers  boundary.  L e c t u r e ,  to  to  of  on  r e c e n t  and  1972)  on  view  the  of  for  the  f a c t  on  flow  of  two  continuum c h o i c e  approach  and  a  c o n -  y e a r s .  suggests  that  t u r b u l e n t  drag  f l o w .  c o m p l i c a t e s  the  turbulent  r e a s o n a b l y  be-  in  to  that  so to  flow  visualization  flow  of  use  the  (ASME up  1883  pipes,  t h i s  e f f e c t s  l i t t l e  recent  dye  streamer  methods solutions.  to  at  pipes  from  in  need:  a  dye laminar  is  perhaps effort  study  or  other the  of  process  of  used it  There  Freeman  d i s t i n g u i s h  in  V i s u a l  p r o d u c t i o n  sums  Newtonian  w e l l .  approach  who flow  about  review  pioneering  in  l a y e r s .  v i s u a l i z a t i o n  r e d u c t i o n  the  polymer  past  p r o d u c t i o n  energy  comprehensive  made  the  n e a r - w a l l  t u r b u l e n t  technique  been  energy  i n f o r m a t i o n  streamer surprising  during  number  the  many  s t r o n g l y  reducers  t h i s  Reynolds  has  or  r e d u c t i o n  s o l v e n t .  remarks  of  in  for  drag  l a r g e  i n d i v i d u a l  continue  drag  Osbourne from  of  t u r b u l e n t  drag  a  m o l e c u l a r  l a y e r s  e s t a b l i s h e d need  though  evidence  wall  polymeric  performed  matter  dynamics  The  In  the  Newtonian key  for  even  been  l i k e l y  the  immediate  Hoyt's  a  presence  The flows  i s  present  reducers  haviour  have  whether  appealing  t r o v e r s y  mechanism  e s t a b l i s h e d ,  experiments  decades. is  Remarks  S c h o l a r  . . . reported results in the flow visuali zation area with polymer fluids are unexpectedly sparse; clearly this is an experimental area which could yield important insights if a thorough investigation were carried out.  Chapter  2  HOLOGRAM-1NTERFEROMETRIC INVESTIGATION OF THE WALL REGION  2.1  Flow  V i s u a l i z a t i o n  The d e t a i l as  of  an  probes  was  a b i l i t y area  d o ,  has  s p e c i f i c a l l y  region  of  during  of  aimed  had  The  the  t u a t i o n s l e s s  flow  a t  than  i n 1  f r e q u e n c i e s flow  a r e  i n  Chapter  the  and and  to point  This of  provide  study  the  was  data  wall  r e q u i r e d  t h a t  quan-  to f e a t u r e s  f l o w .  s t r i c t e r  somewhat f o r  s t r u c t u r e s as  data  r e s o l u t i o n  a r e  time  1.  f i n e - g r a i n e d  f o r  r u l e  than  p i c t u r e s  F u r t h e r ,  s u f f i c i e n t the  techniques  r a t h e r  o b t a i n i n g  requirements  b a s i c  p h y s i c a l  f i e l d ,  r e d u c t i o n .  of  The  flow  o u t l i n e d  d i s p l a y  f l o w .  Requirements  could be o b j e c t i v e l y t i t a t i v e l y a n a l y s e d ,  ( i i )  reducing  i t s  v i s u a l i z a t i o n  the  been  drag  (i)  and  as  small  cm/sec,  i s  s m a l l .  The  the  flow  than  those  v i s u a l i z a t i o n  l a r g e as  v i s u a l i z a t i o n  as  p o s s i b l e  p o s s i b l e .  d e s i r a b l e  to  r e s t r i c t i o n s  t h a t :  37  keep  A  low the  posed  by  of  f o r  i s  to  and u * ,  d r a g Newtonian make  the  f l u c -  g e n e r a l l y  f l u c t u a t i o n d r a g - r e d u c i n g  38  (i)  Drag-  r e d u c t i o n  t h r e s h o l d  ' o n s e t s ' shear  I.I),  thus  r e q u i r i n g  to  done  at  be  the ( i i )  wall  onset  a Figure  experiments  v a l u e s  wall  at  (see higher  than  the  shear.  Drag-reducing flows are diameter s e n s i t i v e . As a r e s u l t , large s i z e ducts do n o t p r o d u c e as much drag r e d u c t i o n as would a small diameter pipe with the same p o l y m e r s o l u t i o n .  ( i i i )  The  s o l u t i o n  v i s c o s i t y  i n c r e a s e s  r a p i d l y with polymer c o n c e n t r a t i o n . In o r d e r to make c o m p a r i s o n s with the Newtonian s o l v e n t , i t is most d e s i r a b l e to keep the s o l u t i o n v i s c o s i t y as c l o s e as p o s s i b l e to that of the s o l v e n t .  These experiment  to  r e s t r i c t i o n s  r e l a t i v e l y  s e c t i o n s  and  150  r e s p e c t i v e l y ) .  wppm  with to  a  good  20,000  low  Reynolds  polymer  provide  For a  t h i s  number  sion  of  t h i s  were  f u r t h e r  pipe  up  the  f l u i d  and  r e a l - t i m e  r u l e d  out  i n t e r m i t t e n t  While  the  hydrogen  at  the  to  the  2.63  w a l l ,  methods  bubble  wall  cm  a  to  e n s u r i n g  f l o w cm  and  number be  to  about  was  observe  chosen  small  dimen-  s t r e a k  e s s e n t i a l .  in i t s  with  schemes  tagging  technique  10,000  60%.  the  s t r e a k  25-  range,  v i s u a l i z a t i o n  to  l i k e  t i m e l i n e  10  pipe  continuous  was  to  then up  d i a .  flow  d i f f i c u l t y  and  of  Due  order  diameter (3  would  15,000.  In  v i s u a l i z a t i o n  Reynolds  r e d u c t i o n s  r e c o r d i n g  p h y s i c a l  pipe  u s e f u l  a v a i l a b l e  a t . t h e  flow  e f f e c t i v e  polymer,  a  r e s t r i c t e d .  s t r u c t u r e s  wire  The  study, of  the  c o n c e n t r a t i o n s  drag  burst  c a n d i d a t e ,  small  d r a g - r e d u c i n g  to  l i m i t  and  of  This  the  n e c e s s i t y  photography. was  l o c a t i n g  a  a  prime  bubble  s a t i s f a c t o r y  o p e r a t i o n  39  made  i t  u n s u i t a b l e .  (Donohue, the  1973)  shedding  that  of  While i t  does  poor  not  was  is  and  decided  index  to  windows. ometry  to  has  i n j e c t i o n  dye a  as  an  wall  i t  2 .2  development  p o s s i b l e  t i o n  i s  stems  now  from  message.  d i s t r i b u t i o n phase a  f i n e  and  of  known  an  the  and  get  s m a l l .  of  To  of  a  c o n v e n t i o n a l f l a t  complex  presents  f o r  wall  improve i t  r e f r a c t i v e i n t e r f e r o m e t r y  and  h o l o g r a p h i c  study  has  a n a l y s i s ,  d i s p l a y  o p t i c a l l y  p r i n c i p l e as  of  p a r a l l e l  i n t e r f e r -  geometries the  p r i n c i p l e s  l a y e r  t u r b u l e n c e  wavefront  a  p a t t e r n .  The  r e c o n s t r u c -  word  complete  and  ' g r a m ' ,  r e c o r d s  the  l i g h t  hologram  wavefronts  wavefronts  of  holography.  meaning  o b j e c t ,  amplitude  that  scheme  q u a n t i t a t i v e  chapter  photograph  i n t e r f e r e n c e  r e q u i r e s  to  u t i l i z e d  (1948)  ' h o l o s ' , a  sampling  perform,  Holography  w i d e l y  While  to  measurements.  of  Gabor's  This were  and  P r i n c i p l e  with  a f f e c t  simple  scales of  a d v e r s e l y  q u i t e  However,  s e c t i o n s  that  v i s u a l i z a t i o n  means  l a y e r .  r e c e n t  holography  a  r e c e n t l y  w i r e s .  i s  i n t e r f e r o m e t r i c  i n t e r f e r o m e t r i c a l 1 y . of  p h y s i c a l  shown  may  from  q u a n t i t a t i v e  the  been  a d d i t i v e s  wall  use  made  has  bubbles  t e s t  The  i t  hydrogen  provide  enhanced  l i m i t e d  polymer  provide  r e s o l u t i o n  r e s o l u t i o n  F u r t h e r ,  coming  This are  r e c o r d s from  f e a t u r e  t e m p o r a l l y  of  hologram meaning  i n t e n s i t y both an a  the  o b j e c t  as  hologram  c o h e r e n t .  Thus,  40  i t  was  not  l i g h t  u n t i l  s o u r c e ,  Upatnieks f r o n t  the  and  advent  the  (1962,  the  f i r s t  s t e p ,  i n t e r f e r e n c e w a v e f i e l d In  the  beam  R  the  R'  f i e l d  in  i s  or  be  Study  r e g i o n  that may is  is  to  in  hologram.  in The  of  the  the  0  is  wave-  as  and  a  the the  In  r e s u l t  a  of  r e f e r e n c e 2 . 1 a ) .  recorded  p a t t e r n  r e c o n s t r u c t i o n  o r i g i n a l  o b j e c t  wave-  the  v i c i n i t y  study.  be  used  to  with  denote  p a t t e r n  is  f r i n g e  f r e q u e n c i e s  The  s p a t i a l  the  angle  R  that  to  is  and  is  f r i n g e 2000  given  —  0.  that by  was  of  s e c t i o n ' of  the  pipe  'primary'  macroscopic  emulsion  frequency  between  a  1000  photographic  ' t e s t  the  'primary'  of  wall  i n f o r m a t i o n .  p a t t e r n is  pipe  s e c t i o n  c a l l e d  the  which  a  term  that  h o l o g r a p h i c  work,  of  The  the  observed.  the  Region  Sin  where  of  ( F i g u r e  by  Wall  t h i s  t h i s  s p a t i a l  recorded  i l l u m i n a t e d  in  f r i n g e  v i s u a l l y  have  0  recorded s t e p ,  in  records  confused  r e f e r r e d  and  2 . 1 b ) .  w i l l  that  L e i t h  t e c h n i q u e .  p a t t e r n  w a v e f i e l d  r e c o n s t r u c t  This not  o b j e c t  order  ' o b j e c t '  of  wavelength  a s p e c t s  imaging  f r i n g e  i s  i n t e r e s t  p a t t e r n  two-step  hologram  The  or  s i n g l e  r e a l i z e d .  a  an  a  p r a c t i c a l  reconstruction  Holographic  primary  the  m i c r o s c o p i c  to  l a s e r ,  experiments  p h o t o g r a p h i c a l l y  (Figure  2.3  i s  between  second  c a l l e d  a  that were  Holography  a  p i o n e e r i n g  1964)  r e c o n s t r u c t i o n  of  it  f r i n g e must  g e n e r a l l y p a t t e r n p a t t e r n  fringes/mm forms  the  and  41  F i g u r e  2.1.  (a)  Hologram  (b)  Holographic_  (H,  hologram;  beam  R'  is  r e c o r d i n g ; 0.,  r e c o n s t r u c t i o n o b j e c t  i d e n t i c a l  to  beam. the  The  r e c o n s t r u c t i o n  r e f e r e n c e  beam  R.)  view I gure  2 . 2 .  Plan (C,  view  of  camera;  s l o t ;  BE-SF,  the D,  pipe  wall  d i f f u s e r ;  beam  F,  expander  and  the  t e s t and  c o o r d i n a t e  s e c t i o n ;  s p a t i a l  S,  axes. wall  f i l t e r )  pipe c/s F i g u r e  2 . 3 .  Edge (C,  view  of  camera;  the D,  pipe  wall  d i f f u s e r ;  F,  and  the  t e s t  c o o r d i n a t e  s e c t i o n ;  S,  axes. wall  CO  s l o t )  44  which  was  s i s t e d  of  recorded  on  the  hologram.  a  r e g i o n  of  the  pipe  Figure  3 . 5 ) .  photograph, d i r e c t i o n s  to  the  Figures geometries  of  the  w a l l ,  two  views.  hologram  plane  The  c o o r d i n a t e  rotated  system  (i)  the  I)  and  the  s e c t i o n  8  in  cm  were II)  two  views as  in  show  normal  the  each  the  are  seen  between  t h a t  and  (see  n e c e s s a r y .  (view  axes  con-  length  spanwise  the  90°  chosen  t e s t  views  c o o r d i n a t e  so  to  2.3  Since  through  was  6  separate  (view  p e r p e n d i c u l a r  wall  observe  two  2.2  mutually  i s  To  The  on  the  v i e w s . of  the  v i e w s ,  the x - a x i s is p a r a l l e l to and in the d i r e c t i o n of the mean f l o w ; the streamwise  ( i i )  the  d i r e c t i o n ; y - a x i s  is  normal  to  the  pipe  w a l l ;  and; ( i i i )  2.4  The  the z - a x i s is along the pipe w a l l , p e r p e n d i c u l a r to the flow and the hologram plane; the spanwise d i r e c t i o n .  Hologram  This  and  i t s  a n a l y s i s  the  frame  of  r e f e r e n c e  any  other  changed  i s of  P r o p e r t i e s  of  a  general  Figure  c o o r d i n a t e  2.2.  system  form It  and  can  without  be  i s  done  in  a p p l i e d  to  a f f e c t i n g  any  r e s u l t s . The the by  d i f f u s e l y a  complex  amplitude  of  t r a n s m i t t e d f u n c t i o n  as:  the  r e f e r e n c e  o b j e c t  wavefront  wavefront  may  be  and  of  d e f i n e d  45  1 A  R ( x , y )  =  a  R ( x , y )  * R ( x , y )  (2.1a)  6  and  A  where  the  d i s t r i b u t i o n  a  amplitude  modulus  <J>  phase  of  the  C a r t e s i a n r e f e r e n c e  0  o b j e c t  The  photographic  to  a  i n t e n s i t y  |0  *  beam  p l a t e  amplitude  the  o b j e c t  that  r e c o r d s  d i s t r i b u t i o n  beams,  A  R  +  Ag,  the of  hologram  the  which  sum gives  of the  R|  +  A  +  a  2  a nR  2 . 2  as  +  |AR  Figure  beam  l i g h t  and  wavefront  c o o r d i n a t e s ,  R  r e f e r e n c e  where  (2.1b)  O ( x , y )  a  amplitude  exposed  1ight  =  A  x , y , z  is  0 ( x , y )  | | A  Q  +  R  A ( J  2  denotes  Q  +  a  the  R  |  e  +  complex  c o n j u g a t e .  a  0  e  (2.2)  46  The  photographic  d i s t r i b u t i o n Hence,  the  developed  i s  exposed  amplitude and  when  r e c o n s t r u c t i o n  so  as  to  i l l u m i n a t e d  i s  given  r e c o r d i n g  give  t r a n s m i t t a n c e  a  l i n e a r  a f t e r  by  the  -  k l )  =  A  R  (1  R  "  a  f o r  o  I  and  -  2 )  k  ( i )  The  of  beam  and  ( i i i )  r e f e r e n c e  a r e  s t r u c t u r e t h a t  amplitude is  i n t e r e s t  of  the  the  real  i t the  and or  to  ( i )  beam  of  causes  r e p r e s e n t s  i n  R  the  conjugate  i s during  Q  -  l i k e  k  a  R  i(2(J>R-<j>0) a  the  unmodulated  The  terms  r e p r e s e n t  f r i n g e  pattern  d i f f r a c t i o n  i n t e n s i t y  v i r t u a l image  image  (2  e  Q  ( i i i )  they  a  photo-  gives  2  A  r e p r e s e n t  s i n c e  r e f e r e n c e i s  a  i n t e n s i t i e s .  ' p r i m a r y ' a c t  beam  the  expanding  (i i )  terms  emulsion  (2  2 k ( a  the  i n t e n s i t y  response.  r e f e r e n c e  a c h a r a c t e r i s t i c constant graphic e m u l s i o n .  S u b s t i t u t i n g  the  by  Aj  k:  emulsion  the of  coming  f i n e  the  by  the  o b j e c t .  into  focus  and l i n e  hologram  g r a t i n g .  modulated of  ( i i )  o b j e c t  Term  the  o b j e c t Term  i n  ( i i )  ( i i i )  f r o n t  47  of  the  hologram.  image  2.5  i s  Hoiographic  a c c u r a t e l y powerful  r e c o n s t r u c t  i t  at  of  wall  at  some  the  n e a r - w a l l  ponents,  (due  to  t e s t to  be  2.6  or  f r i n g e  recorded  by  Flow  a  v i r t u a l  p r o c e s s e s .  of  a  the  The  any  v i r t u a l  those or  These  f l e x i b i l i t y  i s  v i s u a l i z a t i o n  of  same w h i l e  r e -  o p t i c a l  comflow  P e r t u r b a t i o n s  r e f r a c t i v e or  as  could  an be  index  i n  change  d e n s i t y i n t e r f e r o observed-  and  hologram.  Holographic  a v a i l a b l e by  the  t r a n s m i t t i n g  appear  f r i n g e s  the  with  to  in  image  aspect  p e r f e c t  temperature  v i b r a t i o n  through  V i s u a l i z a t i o n  due  1965).  i n t e r f e r o m e t e r  i n t e r f e r o m e t r i c a l 1 y . as  a  r e c o n s t r u c t e d  This  l i g h t  and  provided  served  observed.  o b j e c t  (Horman,  c o n v e n t i o n a l  for  an  i n s t a n t  o b j e c t .  almost  p a t t e r n .  flow  and  record  c o n d i t i o n  being  mechanical  viewing  l a t e r  requirements  such  to  superimposing  c o n c e n t r a t i o n  Some f e r o m e t r i c  was  s t u d i e d  e i t h e r  real  i n t e r f e r o m e t r y  i n i t i a l  a l l o w i n g  s e c t i o n  g r a d i e n t s ) metric  flow  by  arm  s t r i n g e n t  thus  any  o r i g i n a l  r e f e r e n c e  the  s e c t i o n  done  the  as  l i e v e d  was on  way  a  h o l o g r a p h i c  hologram  performing  image  pipe  both  Interferometry a  the  of  a l l  of  Interferometry  the  of  a b i l i t y  means  v i r t u a l  presence  c h a r a c t e r i s t i c  This  the  The  the  use  Interferometry  in  hologram of  i n t e r -  48  (i)  double  or  m u l t i p l e  exposure  H.I.  and ( i i )  In more  Any  appears  as  ' f r o z e n '  t  0  so  by  o p t i c s .  This  i s  r e c o r d i n g  of  the  r e f r a c t i v e  recorded  i n  observed  at  when  setup  of  i n i t i a l  by  Moire  s e c t i o n The  the  time  on  made  d i s t u r b a n c e s o p t i c a l  on  the  hologram  o n - s i t e 1972).  i n  components v i r t u a l  the of  t e s t r e c o r d i n g  the  l i v e  f r i n g e  can  be  observed  the  some  caused  A  through  at  a c t u a l  p r o c e s s i n g  flow  exposures  r e c o n s t r u c t i o n .  exposure  and  h o l o -  the  r e c o n s t r u c t e d  the  commonly  r e f e r  r u l i n g s HI  hologram a  same  hologram p a t t e r n and  hologram.  Techniques,  Real-time  g r a t i n g ;  one  phase  viewing  s i m i l a r  t0>  only  enhanced  patterns  two  the  i n  superimposed  by  the  p a t t e r n  (Achia ,  index  superimposed. ' s t o r e d '  i s  on  between  r e l o c a t i n g  r e a l - t i m e  Moire  t e s t  achieved  A p p l i c a t i o n  recorded  two o r  method,  s i t u a t i o n s  r e c o r d e d .  wall  exposure  unwanted  the  p r e c i s e l y  the  a  i n  pipe  in  are  that  h o i o g r a p h i c a l l y the  the  r e q u i r e s  method  i m p e r f e c t i o n s  s e c t i o n  2.7  s e q u e n t i a l l y  f r i n g e  time  of  multiple  a  i n i t i a l  image  or  i n  time  are  are  H.I.  d i f f e r e n c e  real  by  time  t h e double  exposures  gram.  The  real  ' l i v e '  or  i s of  to  high  those  frequency  analogous the  g r a t i n g ;  patterns  to  v i r t u a l the  g r a t i n g s  superimposing image  a c t u a l  recorded t e s t  49  s e c t i o n . between ments  Small the  of  measure  t e s t  the  s e c t i o n  moire  extremely  Thompson,  changes  i n  and  image  f r i n g e s , small  i n t e r f e r e n c e c o n s i d e r i n g  hologram o f  o b j e c t  o n l y  the  wavefronts  At and  a t  the  a  The  time  and  path  appear  the  terms  ( e q u a t i o n  l a t e r  same  -  i n s t a n t  r e f e r e n c e  moire  of  t0>  as  l e n g t h l a r g e  t e c h n i q u e  u s e f u l  v a r i a t i o n s  (Achia  which  r e f e r e n c e  phase  <j>0  hologram  making  c o n c e n t r a t i o n  4>0  wave  i t s  o p t i c a l  moveto and  1 9 7 2 ) . The  f e r i n g  r e l a t i v e  -  the  i n as  <j>R  m-rr  =  of  beams, the  2 . 2 )  i s  be of  by  the  d e f i n e d two  i n t e r -  ( 2 . 5 )  wave  i s  <t>R  m'-ir  f r i n g e s  can  e q u a t i o n  t i m e t ' ,  =  produced  the  g i v e n  p e r t u r b e d  o b j e c t  by  .  observed  through  ( 2 . 6 )  the  i s  Ug  "  *  R  )  "  UQ  "  <f> R )  =  MTT  or  <j> 0 -  which  r e p r e s e n t s  d i f f e r e n t  t i m e s .  the  phase  <{>0 = MTT  d i f f e r e n c e  ( 2 . 7 )  i n  t h e  o b j e c t  beams  a t  50  Exact o p t i c s  g i v e s  resents A  a  n u l l  r a s t e r  d e s i r e d  alignment c o n d i t i o n  f r i n g e s  of  moire  2.7.1  of  the  the  u n i f o r m l y  t r a t i o n  changes,  is The  i n f i n i t e  t i o n s  and  hologram  1971,  be  the  a r e a . by  F i n i t e  d  The  mm.  =  With  =  0,  which  f i e l d  f r i n g e ' be  r e c o r d i n g r e p c o n d i t i o n .  f i e l d  generated  of  by  small  0)  c o n d i t i o n , the  appear  Figures  of  of  very  d i s t u r b e d  f i e l d  i n  of  the  2 1 a , b ) .  points i s  the  i n t r o d u c t i o n  l i n e s  92,  locus  Fringes  These  f r i n g e  s e l e c t i n g  hologram  can  f r i n g e  p.  e a s i l y  i n t e r f e r o m e t e r  s p a c i n g ,  M  the  f r i n g e '  ' f i n i t e  (M  c o n d i t i o n  C o n t r o l l e d the  d;^.  in  of  any  f i e l d  of  f r i n g e  c o n c e n t r a t i o n .  s e n s i t i v e apparatus  view  concen-  Each  equal  by  of  to  p e r t u r b a -  v i b r a t i o n  or  movement.  2.7.2  in  a  Fringes  f r i n g e  can  or  i n t e r f e r e n c e  as  =  ' i n f i n i t e  b r i g h t .  A c h i a ,  i n t e r p r e t e d  cf>0  frequency  i n f i n i t e  appears  ( e . g .  the  hologram  hologram.  I n f i n i t e  At  view  and  the  where  f r i n g e s  o r i e n t a t i o n  displacements  or  of  may  be  f  0)  d i s p l a c e m e n t r e s u l t s  in  f r i n g e s  form  d e n s i t y  s u i t a b l e  (M  (1/d,  i n t e r f e r e n c e  along  a  g r i d  fringes/mm)  d i s p l a c e m e n t s  d i s p l a c e d  o p t i c a l  or  of  the  r o t a t e d  component  l i n e s  a c r o s s can  the be  hologram. about  any  of  f r i n g e t e s t  a l t e r e d The axis  to  51  generate d e n s i t y shown what  a and  in  a  i n  r e p r e s e n t s t i o n s  on  movement  the  the of  these  a  of  the  o b s e r v a t i o n  over  l a r g e  flow terms  a p p a r a t u s . of  be  l i n e a r  flow  on  The  some-  an  i n f i n i t e  due  estimated not  b a s i s  f o r  to  Each  e f f e c t  is  are  is  g r a d i e n t  d e t e c t e d .  phase.  the  f r i n g e s  g r a d i e n t  a c c u r a t e l y  when  forms  wall  i n  due  f i e l d  f r i n g e s . path  f o l l o w i n g An  t u r b u l e n c e  to was  the  s t r e a k s  streaky  f r i n g e s  stream  o p t i c a l The  can  of a  and  of  the  f r i n g e v i b r a -  from  the  enhanced  by  some  wall to  d e s i r e d  the  enhancer  v i s u a l i z e d  F i n i t e length chapter  f r i n g e s  was  For  coded  Phase  with v a r i a t i o n  i n t r o d u c e d r e a l  r e t a i n  upstream  time high  burst  d i s t o r v i s i b i l i t y  v a r i a t i o n s . d e s c r i b e s  i n t e r p r e t a t i o n parameters  as  the 2 . 2 ;  spacing  was  w a l l .  For  (Figure  d i r e c t i o n .  r e g i o n  the  v i s u a l i z a t i o n  b u r s t s .  s t r u c t u r e  spanwise  p e r p e n d i c u l a r  f l o w i n g  these  f i n i t e  t h i s  constant  unperturbed  the  of  of  f r i n g e  d i s p l a c e m e n t s  s e n s i t i v e l y  spanwise  the  in  t i o n s  be  f i e l d  of  the  f r i n g e s  from  w a l l - l a y e r  the  on  o b s e r v a t i o n s , i n i t i a l  of  r a s t e r  superimposed  hologram  of  enhancer.  f r i n g e  of  to  r e s u l t s  c o n c e n t r a t i o n  can of  Some  e f f e c t  f r i n g e s  index  measurement I),  flow locus  measurement  view  The  apparatus  The and  due  D e v i a t i o n s  the  r e f r a c t i v e  5 . 5 .  f i e l d .  superimposed  f i e l d .  enhancer  f r i n g e  o r i e n t a t i o n  Figure  l i k e  f r i n g e  f i n i t e  i s  of  the  f r i n g e  provided  i n  h o l o g r a p h i c d i s t o r t i o n Chapter  in 4.  Chapter  3  EXPERIMENTAL APPARATUS AND PROCEDURE  The down  pipe  apparatus  flow  c o n s i s t e d  apparatus  and  a  of  two  major  h o l o g r a p h i c  p a r t s ;  flow  a  blow-  v i s u a l i z a t i o n  u n i t .  3.1  The  Blowdown The  t i c a l l y  i n  Pipe  Flow  blowdown  Figure  (i)  pipe  3 . 1 .  A a  l i t r e  flow  were  flow  about  25,000 pipe  g l a s s  f o r  The to  the  so  used  to  d i l u t e  F  tank  T  to  could provide  m l / s e c . time  At was  Reynolds in  was  long  the  number  2 . 6 3 cm  7  m  long.  pressure  and  flow  This  drop  s u f f i c i e n t  developed  tank  that  f l o o r  c o n s t a n t  components.  a t  entry the  l o c a t i o n .  c o l l e c t i n g  c a s t e r s  the  s e c t i o n f u l l y  v i s u a l i z a t i o n ( i i i )  515  schema-,  F.  3 . 0 5 m  measurement  head  water  p i p e l i n e a  major  blowdown  and  f o r  shown  n i t r o g e n  to  the  minutes  provided length  up  rate  5  The  with  of  about  d iameter  three  c o n s t a n t  rate  i s  apparatus  p r e s s u r i z e d  t h i s  ( i i )  flow  There  160  be  Apparatus  above  head  tank  reduce polymer  T'  was  s o l u t i o n s and  drained  T.  This  shear  be into  method  d e g r a d a t i o n  s o l u t i o n .  52  mounted could  of  on c a r r i e d the was the  Figure  3.1.  The  blowdown  pipe  flow  and  h o l o g r a p h i c  v i s u a l i z a t i o n  a p p a r a t u s .  Co  54  Table Blowdown  Flow  Code (Fig. 3.1)  Apparatus  D e t a i l s  Component  Tank:  T  3.1  -  D e s c r i p t i o n  Elco water b o i l e r , b r a s s , v e r t i c a l . 160 l i t r e c a p a c i t y , 40 p s i pressure t e s t e d . Connections: I n l e t for s o l u t i o n , compressed N2 and wash water from mains; a l l s o l e n o i d valve c o n t r o l l e d . O u t l e t to t e s t s e c t i o n via globe and s o l e n o i d v a l v e s .  G  Flow  F  Pipeline:  straightener: c o n i c a l i n l e t to s e c t i o n . Brass c o n s t r u c t i o n , thermowel1.  QVF pyrex g l a s s ; 2.63 cm diameter, about 7 m long in s e c t i o n s . Supported on D e x i o n a n g l e s and rubber c r a d l e s . Standard QVF f l a n g e s with rubber g a s k e t s . V i s u a l i z a t i o n c o n s t r u c t i o n (as  T  1  Collecting with  tc  Nalge  tank: l i t r e .  p.  Pressure  Open one  r e c .  water  for  Recorder:  Sargent  Q  Flow  rate:  s p e c i a l C).  p o l y e t h y l e n e , and  mounted  250 on  c a s t e r s ,  o u t l e t .  Statham  transducer: ing  top  s e c t i o n of in Appendix  d r a i n i n g  d i r e c t i o n a l .  AP  the flow with  Mounted  PM with  280-TC, a  b i -  c a l i b r a t -  manometer.  pressure Welch  measured  drop  SRG  with  s i g n a l  from  p . t .  s t r i p - c h a r t .  s t o p c l o c k  and  bucket.  55  The s p e c i f i c a t i o n s e c t i o n  was  components  of  the  are  in  Table  l i s t e d  l o c a t e d  over  the  flow  s t r a i g h t n e r  3.2  The  Holographic  The shown  in  the  same  for  s p e c i f i e d e a r l i e r  are  in  The  A e a r l i e r  15  weight,  the  separate  l a s e r  to  the  p r o t e c t i o n l a s e r set  i t  at  800  a f i r e  t h i s  Only  t e s t  downstream  of  Apparatus  i s  apparatus f o r  apparatus  (1971),  pp.  59-83  study.  The  components  the  major  and  m o d i f i c a t i o n s  and  are are  to  the  here.  a r g o n - i o n  l a s e r  away to  eyes  c o u l d  w i t h i n  15  i t s  the  s h i e l d  and  l a s e r  l a s e r .  and  from  holography  mW  t h e i r  Laser  used  for  diameters  c o n s i d e r a t i o n s  d e s c r i b e d  argon  was  and  h o l o g r a p h i c  visualization  Achia  of  helium-neon  t a b l e s  e n c l o s u r e  in  3 . 2 .  2-watt mW  The  V i s u a l i z a t i o n  Design  purpose  are  3.1.  pipe  flow  d e t a i l e d  Table  setup  3.2.1  Flow  3.2.  the  apparatus  G.  holographic  Figure  techniques  200  flow  s k i n  burn  a  Due  used to  i t s  supply  o p t i c a l  bench.  beam This  along was  exposure  hole  in  from  a the  place  l a r g e were A i t s  to  sheet s t a r t  of  the  s i z e  and on  t u b u l a r path  the of  of  mounted  necessary  from  seconds  in  power  the  setup.  was  from  to  provide  beam.  paper  the  The and  exposure.  Figure  3 . 2 .  The holography setup f o r f l o w v i and measurement. (ADHI, a m p l i t u d e d i v i s i o n h o l o g r ferometer; BS, beam s p l i t t e r ; B, bench; C, movie camera; E, R e f r a enhancer; F, flow t e s t s e c t i o n ; p l a t e h o l d e r and hologram.)  s u a l i z a t i o n a p h i c i n t e r o p t i c a l c t i v e index P-H, photo-  57  Table Holographic  (Figs  3.2  V i s u a l i z a t i o n  Code . 3 . 1 , 3 . 2 ,  Apparatus  Component  D e t a i l s  D e s c r i p t i o n  53C4,;-:3*5?.&33?6)  Spectra P h y s i c s a r g o n - i o n , Model 2W c o n t i n u o u s wave, water c o o l e d .  Laser:  164.  Mounted on a s e p a r a t e t a b l e from other o p t i c s . Shutter mounted on l a s e r output.  Laser  p. s  power supply & exciter: model 265. Contains f o r the lasjer.  Spectra P h y s i c s v a r i o u s c o n t r o l s  E t a l o n : Spectra P h y s i c s model mounted in the l a s e r , o p t i c a l to improve c o h e r e n c e .  Optical  ADHI  (1)  Bench: Ga t h i c k s t e e o p t i c a l co s p e c i a l l y i n s i d e ana v i b r a t i o n  Amplitude  ertner model 210. l s l a b with r a i l s mponents. Mounted c o n s t r u c t e d t a b l e e n c l o s u r e ; to i s o and air.movement.  D i v i s i o n (shown  in  Holographic Figure  3.4  #89, c a v i t y  5 cm f o r on a and l a t e  Interferometer and  used  i n  c o n j u n c t d o n i c w i t h . v i e w ' ! 11 . ' " F i g u r e -  WDHI  (2)  Wavefront  components  mounted  designed  v e r t i c a l  Division  Holographic  (shown  in  Figure  c o n j u n c t i o n  w i t h  3.6 view  on  a  2.3)  s p e c i a l l y  s t a n d .  Interferometer and I,  used Figure  CONTINUED  i n 2.2)  58  Table  3 . 2  Code ( F i g s . 3 . 1 , 3 . 2 , 3 . 4 , 3 . 5 & 3 . 6 )  Component  R  Reference  0  Object  Beam  BS  M  (Continued)  j  beam  :  f r o n t s u r f a c e i n v a r i o u s from Edmund S c i e n t i f i c C o .  Expander/s  (a)  :  | | ( 1 , 2 )  3  w  i  m  1 0  Spatial  SF  used  S p l i t t e r ^ ^: Jodon model VBA-200, with c o n t i n u o u s l y v a r i a b l e o p t i c a l d e n s i t y .  Mlrror/s^  Beam  These beams a r e formed using t h e components l i s t e d : in (1) or (2) above  beam  s i z e s  BE  D e s c r i p t i o n  u  '  with  t  h  Spectra 4  m  f  o  c  a  P h y s i c s i  l  (b)  Gaertner  lOx  o b j e c t i v e  (a) (b)  F i l t e r / s :  m  e  n  model  g t h  model  l e n s , R250-F-  l e n s .  6 . 8 micron 2 5 . 0 micron  p i n h o l e p i n h o l e  (all o p t i c a l components were mounted on r i g i d supports with magnetic b a s e s ) .  P  Fhotoplate  or  Hologram  designed and  water  ( A c h i a ,  H  f o r  recorded  Hologram: 0  and  R  on  r e s o l u t i o n  D  Diffuser:  immersion  1971  S p e c i a l l y  holder: o n - s i t e  ;  pp.  by  wet of  p r o c e s s i n g  holograms  7 6 - 7 9 ) .  the  i n t e r f e r e n c e  A g f a - G e v a e r t  10E56  photographic  p l a t e  t w o - l a y e r t i o n , to d i f f u flow v i s u a l i z a from f i n e l y gr  gro s e l t i o oun  of  h i g h -  und g l a s s c o n s t r u c y b a c k l i g h t the n s e c t i o n . Made d commercial g l a s s .  CONTINUED  59  Table  3.2  (Continued)  Code (Figs . 3 . 4 ,  3.1,  3.5  &  Component  3 . 2 ,  D e s c r i p t i o n  3.6)  Flow  Visualization  section:  The  region  of  the flow used for v i s u a l i z a t i o n study. S p e c i a l l y c o n s t r u c t e d as in Appendix C and shown in F i g u r e ' 3 . 5 .  Refractive  Index Enhancer i n f u s i o n s e t u p , with a small r e s e r v o i r connected to the i n f u s i o n port (see d e t a i l Appendix C).  Camera:  Red Lake Labs Hycam K20S4AE with t i m i n g l i g h t generator and a c c e s s o r i e s . Bblex H-16 camera. E l e c t r o n i c timer with LED d i s p l a y .  60  The  l a s e r  remotely  output  c o n t r o l l e d  double-stepped sec be  so  was  that  kept  m e t a l - l e a f  timing  the  c l o s e d  range  exposure  when  not  s h u t t e r .  from  time  use  This  1/120  f o r  i n  sec  a  s h u t t e r  to  hologram  with  1  sec  r e c o r d i n g  had  a  and  °°  c o u l d  s e l e c t e d . o  The (blue was  l a s e r  l i g h t ) .  mounted  frequency value  of  s u p p l i e d  A i n  about  could The able  v i s u a l l y  hologram  w h i l e  c o n s i d e r a t i o n s pp.  gave  monitor  i t  was  were  used.  the  the  water  This  emulsion  a  the  red  same  as  f i l t e r .  about  649-F  and  s a f e l i g h t .  other i n  maximum  was  d e n s i t y  The  a was  f l e x i b i l i t y  p r o c e s s e d .  e t a l o n  o r t h o c h r o m a t i c  Kodak  7W  photographic  e s s e n t i a l l y  micron  l a s e r ,  of  to  l a s e r  t h i s  a d d i t i o n a l  the  being  25  A  s i n g l e  tuned the  panchromatic  presence  the  s t a b l e ,  f o r  4880  a i r - s p a c e d  was  a  f o r  of of  being the  p r o c e s s i n g  A c h i a ,  1971;  70-79.  3 . 2 . 2  Flow  Pipe The due  than i n  f e a t u r e  were  #89  power  with  adjusted  provide  through  holograms  photoplates f a s t e r  output  mains  was  Model to  Cooling  water  processed  l a t t e r to  the  c a v i t y  The  mW.  wavelength P h y s i c s  l a s e r  record  times be  the  850  from  10E56  twenty  Spectra  o p e r a t i o n .  To Agfa  output  to  t o t a l  V i s u a l i z a t i o n  Wall wall  S e c t i o n  D e t a i l s  Refraction of  i n t e r n a l  a  round  pipe  r e f l e c t i o n .  i s  o r d i n a r i l y  Figure  3 . 3  not  shows  v i s i b l e the  e f f e c t s  F i g u r e  3.3.  Total pipe  i n t e r n a l wall  r e f l e c t i o n  and  r e f r a c t i o n  at  a  .  (a) unenclosed pipe (b) index-matched e n c l o s u r e around pipe (c) fI a t - w a I Ied p i p e [ W - w a t e r , n = 1.333; G - g l a s s , n = 1.474; A - a i r , n = 1.0; x: d i s t a n c e from w a l l a t t o t a l i n t e r n a l r e f l e c t i o n . ! pipe  i.d.= 2 . 6 3 c m  i ; light  path  62  of a  (a)  an  r e f r a c t i v e  the as  w a l l , the  The  a  pipe  5  a  square  of  the  The  d e t a i l s  pipe of  The  gram, the  flow  i s  in  14  mm  i t s  was  in  mounted  downstream f o c u s s i n g  block  shown m  in  i n  in  r e g i o n a f f e c t e d  the  f a b r i c a t i o n  m  of  Figure  the  the  3 . 5 .  The  outside  while  pipe  e x t e n t .  s l o t .  view  This  f a b r i c a t e d which  s e c t i o n  by  from  were  had  a  This  rate  in  diameter  3 . 3 c .  lengths  given  at  c o n s t r u c t e d .  was  flow  in  f l a t  f l a t t e n about  Appendix  1%.  C.  Port  enhancer C.  was  s t u d i e s .  bulk  are  a  i n s i d e  l e n g t h ,  0.125  enclosed  Figure  flow  spanwise  guide  wall  for  Appendix  the  same  the  Infusion  the  the  pipe  enable  c i r c u l a r  index  on  To  f l a t  as  0.5  v i s u a l i z a t i o n ,  of  a  a  The  wall  in  (b)  t o g e t h e r .  s e c t i o n  r e f r a c t i v e shown  about  pipe  shown  is  having  having  P l e x i g l a s  Enhancer  graphic  but  p i p e ,  formed  ing  pipe  and  medium.  c r o s s - s e c t i o n  a l i g n e d  which  p i p e ,  matching  p i p e ,  the  c a r e f u l l y  round  P l e x i g l a s  had of  cm  wall  index  g l a s s  p o r t i o n a  unenclosed  of  This  that  was  ' o b j e c t ' The  i s wall A  35  the  mm  S;  x  as  a  f r i n g e  the  d e t a i l e d  0.2  14  on  holoh o l o -  i n t r o d u c i n g a  was  f l a t t e n e d  served  photographing  for  at  s l o t  for  recorded  port  seen  used  mm  mm  by  'window'  pipe s c a l e  wide  view  w a l l , and  p a t t e r n s .  as  W j u $ t a  rough  63  Vibration The i n v e r t e d the  v i s u a l i z a t i o n  aluminium  o p t i c a l  e l i m i n a t i n g  3.3  Isolation  The  c h a n n e l ,  bench pipe  B.  which  This  Ci)  a  beam  ( i i )  a  means  and ( i i i )  I  &  to  with  I I , s u i t  3.3.1  (ADHI),  l a y e r  of  wall  edge  the  o b j e c t  s t e e r i n g paths  beams  d i f f e r e n t &  2 . 3 ) .  s p e c i f i c  needs  to  division  i n  3 . 4 ,  beam  Figure  (view to  the  e f f e c t i v e  beams  form  i n  along  r e f e r e n c e  and system. the l a s t  r e q u i r e d  o p t i c a l Two  path  designs  used  D i v i s i o n  amplitude  view  very  on  The f u n c t i o n .  two  separate  geometries  of  (views  i n t e r f e r o m e t e r s  wavefront  d i v i s i o n  and  r e s p e c t i v e l y .  Amplitude  shown  was  an  system  v i s u a l i z a t i o n  2 . 2  d i v i s i o n  The  was mounted  to  Design  a beam r e c o m b i n i n g hologram performed  Figures  amplitude  clamped  r e q u i r e d  d i v i d n g  t e s t  s l i g h t l y  these  r i g i d l y  turn  Interferometer  d i f f e r e n t  views  i n  arrangement  i n t e r f e r o m e t e r  Wall  was  v i b r a t i o n .  Holographic  The  s e c t i o n  be  I I ,  Holographic  Interferometer,  holographic was  Figure  p a r a l l e l  interferometer  designed 2 . 3 ) .  with  the  (ADHI)  f o r  This pipe  use  with  geometry w a l l  so  the r e q u i r e d  as  to  64  Figure  3 . 4 .  The  amplitude  ferometer (BS,  variabl.e  SF-BE,  Figure  3 . 5 .  o b j e c t  The  flow  (B,  h o l o g r a p h i c  t e s t  o p t i c a l flow  s p l i t t e r ;  f i l t e r  beam;  R,  i n t e r -  and  M,  beam  reference  m i r r o r ; expander;  beam.)  s e c t i o n .  bench;  r e f r a c t i v e  F, pipe p i p e . )  beam  s p a t i a l  0,  E,  d i v i s i o n  .  index  D,  d i f f u s e r  enhancer  s e c t i o n ;  W,  behind  pipe;  i n f u s i o n  port;  window  mounted  on  65  provide around  uniform and  over A  a  base  s p a t i a l  were  of  s p l i t t e r  that  f o r the  r e c o r d i n g  and  3 . 3 . 2  d e n s i t y  beam  c a r r i e d  a l l  i n  the  a  r e f e r e n c e  f o r  s p l i t t e r the  v e r t i c a l  r e l a t i v e  beams  provided  The  beam  was  s t e e r e d  p i p e .  f i l t e r s  provided  alignment  the  v a r i a b l e  u n i t i z e d  and  i l l u m i n a t i o n .  (see beam  was  m i r r o r s ,  beam  p o s i t i o n .  movement  Figure  of  i n t o expanders  S l o t t e d  r a i l s  components  3 . 4 ) .  i n t e n s i t y  b u i l t  The  during,  v a r i a b l e  adjustments  beam  during  r e c o n s t r u c t i o n .  Wavefront  D i v i s i o n  H o l o g r a p h i c  I n t e r f e r o m e t e r  (WDHI)  The shown  (WDHI),  wave front  division  i n  3 . 6 ,  Figure  to  observe  s t r e a k s .  an  o f f - a x i s  Fresnel  of  the  i n  pipe  a  Since expander, graphy  i t  and  is  that  be  a l t e r e d  hologram. R  to  0  i s  observing  s i n g l e , t h i s  very  During about the  beams  used  0  and  expanded  the  easy to  R  o b j e c t  by  used  a l i g n .  the  were  l a s e r  a v a i l a b l e  to  interferometer  w i t h  system  i n t e r f e r o m e t e r  r e f e r e n c e between  was  holography  conserved  was  the  The  holographic  beam  only  one  f o r  i n t e n s i t y  r e c o r d i n g ,  the  optimum  r e c o n s t r u c t e d  image  l o c a t i o n  beam  of  of  a l t e r  r a t i o the  photo-  the  r a t i o  i n t e n s i t y  i n t e n s i t y can  form  motion  drawback  r e c o n s t r u c t i o n  the  view  beam.  and  Changing  to  proper  r e c o r d i n g  4 : 1 .  plan  d i v i d e d  the  l i g h t The  wall  WDHI  cannot  the r a t i o w h i l e  r e l a t i v e  of  67  b r i g h t n e s s  between  o p t i m i z i n g  f r i n g e  had to  to a  be  Test  by  (25 on  150  these  t a i l e d  wppm)  t e s t s ,  were a  weight  water  s o l u t i o n s . during some  of  t e s t  the  s e c t i o n ,  WDHI,  development  of  thus  f r i n g e  the  c o n t r a s t  photoplate  d e n s i t y .  50  wppm  represented  used  i n  the  i s  a  Dow  and  a n i o n i c  This  due  to  CH2  -  a  whereby  n o n - i o n i c the  v a r i o u s  was  flow  c o n c e n t r a t i o n t e s t s .  Based  f o r  d e -  chosen  amide  CH2  Chemical (m.  wt.  i n  neutral  a n i o n i c groups.  2  -  the  The  medium-to-high 5  x  and of  carboxyl  g e n e r a l i z e d  -  Co.  =  m o d i f i c a t i o n  f o l l o w i n g  CH-  Newtonian  s t u d i e s .  s o l u b l e  by  the  g r o s s - f l o w  s o l u t i o n  p o l y a c r y l a m i d e  i s  f o r of  APSO  used  AP30  manufacture, the  was  Separan  v i s u a l i z a t i o n  m o l e c u l a r i s  the  water  of  Separan  It  the  L i q u i d s  S o l u t i o n s  to  and With  photographic  D i s t i l l e d t e s t s .  image  c o n t r a s t .  optimized  s p e c i f i c  3.4  the  1 0  6  ) .  a l k a l i n e  the  polymer  groups  polymer  r e p l a c e  may  be  s t r u c t u r e  CH-  C =0  C =0  NH2  0"  Na J y  x  =  y  ->  3 l a r g e  68  Separan  was  p o l y e t h y l e n e o x i d e s t u d i e s d a t i o n  ( A c h i a , by  t e r i z e d The  a  by  of  a  i n  of  50  and  by  the  (a.)  f l o w s .  when  A  very  would  In t i o n s  have  a  c o n c e n t r a t i o n  3.5  the  (see  Experimental The  z a t i o n  t e s t s  I  into  r e a c t  a  d e g r a -  Appendix  A.  measured  at  3 . 5 %  2 1 . 5 ° C . by  made  f o r  volume up  use  enhancer  w i t h was  flow  m l / s  at  of  would  or  the  Separan  with  index  i n f u s i o n a (Q  propylene  them.  enhancer  r e f r a c t i v e  the  10,000  i t  p r o p e r t i e s water  of  large  10%  v a r i a t i o n Figure  cP  was  c h e m i c a l l y  amount  0.02  to  t'he  d i s t i l l e d  about  0  i n  a  s o l u t i o n  p h y s i c a l  T y p i c a l l y ,  range  l i n e a r  the  smaI  of  to  r e q u i r e m e n t s :  or  about  was  the  produce  number  1.443  of  e a r l i e r  c h a r a c -  s o l u t i o n ,  The  the  change. was  AP30  c h o i c e  and  d e t a i l e d  was  i n  d r a g - r e d u c i n g  enhancer  introduced of  used s t a b l e  f l u i d  a f f e c t  (p,v)  more  d r a g - r e d u c i n g  f o l l o w i n g  l o n g - c h a i n  prepared  as  The  (a  C o . )  higher  Separan  g l y c o l . the  i s  were  index  s o l u t i o n ; (b)  a  v i s c o s i m e t e r ,  i n  not  Separan has  wppm  refractive  r e s p e c t i v e  governed  and  Polyox  Carbide  measurements  propylene  water  to  Union  s o l u t i o n s  Cannon-Fenske  s o l u t i o n  t h e i r  age  v i s c o s i t y  The  both  or  by  s i n c e  Separan  v i s c o s i t y  with  made  1971)  shear  e f f i c i e n c y .  p r e f e r r e d  rate  Reynolds -  225  m l / s ) .  g l y c o l - w a t e r  r e f r a c t i v e  index  s o l u -  with  4 . 2 ) .  Procedure  complete c e n t r a l  to  procedure t h i s  f o r  study  i s  the  s e t  of  d e s c r i b e d  flow here.  v i s u a l i -  69  The to  a u x i l i a r y support  t e s t s  the  and  c e n t r a l  gross study  flow use  t e s t s  parts  that  of  were  t h i s  done  complete  procedure.  3.5.1  Laser  The  flow  when  the  This  p r e c a u t i o n  on  the  b u i l d i n g  second  s t a b i l i z e e t a l o n  f o r  and  at  150  f o r  the mW.  s k i n  avoid  was  r e l a t i v e l y  about  i n  f r e e  from  v i b r a t i o n .  l a b o r a t o r y  was  The  l a s e r  was  allowed  warm  hours  output  power  before  m i r r o r s of  into  mW.  found  the  to  be  or  s i t u a t e d up  and  The  the  maximum  l a s e r  o p e r a t i n g  r e a s o n a b l y  was  a t  evening  alignment  the  care  beam  f o r  Beam  with  s p e c i a l  to  the  experiment.  tuned  done  was  However,  d i r e c t l y  850  was  l e v e l  an  were  about  i n t e r f e r o m e t e r s  l o o k i n g  done  the  12  exposure.  were  s i n c e  c a v i t y  This  runs  taken  f l o o r .  power  Alignment  v i s u a l i z a t i o n  was  l a s e r  a v a i l a b l e through  Beam  taken  i t s  safe  to  s p e c u l a r  r e f l e c t i o n . The WDHI  and  ADHI  the  c o l l i m a t e d  and  then  so the of The  that  a  beam  s p a t i a l  H  was  the  p o r t i o n  beam  was  s e p a r a t e l y  c o n f i g u r a t i o n s .  through  photoplate the  system  of to  f i l t e r  r e f l e c t e d  beam the form  i l l u m i n a t e d was  For  a l i g n e d the  from  expander. expanded the  the then  r e f e r e n c e pipe  WDHI two  The beam  R,  each  of  (Figure  alignment  the  a l i g n e d  the  d i f f u s e r i n  m i r r o r s  was  d i r e c t l y  w h i l e  the  3 . 6 ) ,  a u x i l i a r y  went  through  c a r e f u l l y  i n  the  done  to remainder D. beam  70  expander in  the  w h i l e  s o - a s ' t o expanded  a l i g n i n g  for  the  ADHI  the  presence  hologram the  the  of  was  two  Test  the  The  p i p e l i n e  i t s  o u t l e t  present  i n  be  recorded  c l o t h  and  the  t e s t  The  s o l u t i o n  t e s t s  so  that  time  of  use  index  the  were  case  for  (Figure  d i r e c t  t e s t  3 . 4 ) .  beam  on  the  through beam.  at  s e c t i o n  p i p e l i n e  or  upward  out  s o l u t i o n ) .  times  c u r v e .  due  to  Bubbles  i f  of  the  b a c k l i g h t i n g  pipe  s u r f a c e s  cleaned  with  was f i l l e d  Separan a l l  f l u s h e d  The  except  observed  e n t i r e  the  procedure  P r e p a r a t i o n  water  and  card  p i p e . d i f f u s e r  t h a t  a  were  to  l i n t - f r e e  water.  the  the  of  were  hologram  be  areas  white  r e f e r e n c e  the  l i q u i d  s l i g h t  s e c u r e n e s s .  the  the  to  the  of  supports  A.  by  a  of  a  WDHI,  t h i s  S o l u t i o n  with  l i q u i d  Appendix  up  and  in  on  alignment  the  could  ( d i s t i l l e d  having  Separan  flow  pipe  f u l l  The  beams  i l l u m i n a t e d  viewed  for  exposure  recorded  for  that  c o n d i t i o n  remained  on  the  eye  end  checked  was  f i l t e r .  to  S e c t i o n  pipe  beam  s p o t t i l y  i n c i d e n c e  t h a t  l i q u i d  The were  of  i n i t i a l  t e s t  the  separate  without  h o i o g r a p h i c a l 1 y with  The  s p a t i a l  angle  The  a l l  s i m i l a r  such  hologram  3 . 5 . 2  beam.  was  The  remove  enhancer  s o l u t i o n  was  mixing  any of  made  p r e p a r a t i o n  polymer  the up  was  i n  i s  commenced  clumps  s o l u t i o n . samples  d e t a i l e d  would  The of  a  both  day be  in before broken  r e f r a c t i v e water  and  71  polymer These  s o l u t i o n  samples,  batches  j u s t  3 . 5 . 3  i n  o n - s i t e  may  be  i n  3 . 2 .  f i l m  with  (850  mW).  However, the  Table  3 . 3  the  l a s e r  w h i l e  (i)  no  time  flow  t e s t  to  m o d i f i e d  of  some  i t s  the  steps  c o n d i t i o n i n - t h e  were  and  p l a t e h o l d e r  were  l a s e r  steps  design  was  kept  the  and a l t e r e d .  o p e r a t i o n ,  P  can  be  seen  .  immersed  t e s t  of  i n  s e c t i o n .  o r i e n t a t i o n  d i s p l a c e m e n t  f r i n g e  (1971)  Runs  d e s i r e d  o p e r a t i n g  flow  due  viewing  operated  f i r s t  Achia  o u t l i n e s  hologram  c o n t r o l l e d  r e a l  by  The  V i s u a ! i z a t i o n  The  the  used  a p p a r a t u s ,  of  from  f l o w s .  P r o c e s s i n g  d e t a i l s  (1972).  gate  drawn  and  as  Achia  micrometer  The  were  r e s p e c t i v e  r u n .  f e a t u r e s  p a t t e r n by  t h e i r  Recording  processed  water  f r i n g e  i t s  a  s t e p .  FIow  adjusted  using  to  b a s i c  The  was  m l ,  holography  3 . 5 . 4  moire  100  t h i s  found  d i s t i l l e d  about  c o n d i t i o n s ,  The  Figure  with  Hologram  photoplate  in  use  p r i o r  The r e t a i n e d  f o r  and the  the A  frequency p l a t e h o l d e r  t a b l e s . d i s p l a y at  was  maximum  f i l m e d  was  recorded  a v a i l a b l e a t  p i p e .  F r i n g e m o v e m e n t a t no f l o w g i v e s a measure of extraneous d i s t u r b a n c e s to the apparatus due to b u i l d i n g v i b r a t i o n and a i r movements in the I a bo r a t o r y .  on  16  power  mm  72  Table Steps  Step No.  in  3.3  Hologram  Process  P r e p a r a t i o n  S o l u t i o n  Normali z a t i o n photoplate  of  d i s t i l l e d  D e t a i l  water  Agfa 10E56 g l a s s backed p l a t e , 1/2 to 1 hr at l a b . temperature  Exposure  Prehardening  in  for  Kodak  SH-5  water  about t o t a l  3  to  ness  5  Development  in  Kodak  Stop  Kodak  SB-5  Fix  Kodak Fi xer  Rapid  minutes  min.  in  wi th  dark-  7W  red  ght  for 3-1/2 min. with s a f e l i g h t to observe p a t t e r n d e n s i t y  D-19  d i s t i l l e d  10  darkness  or  s a f e l i  Wash  darkness  1/120 s e c . with l a s e r output at 200  d i s t i l l e d  *  t o t a l  p l a t e immersed in d i s t i l l e d water  in Wash  in  1/2  water  to  4  1  3  to  2  washes,  min.  min. 5  min  each C l e a r i n g and f i n a l wash  A i r  burst  in Kodak S-13 and d i s t i l l e d water  a g i t a t i o n  The exposure time are interdependent o p t i m i z e d to o b t a i n the A  D3.  in  steps  4  min.  to  water  wash  9.  time, l a s e r power and development v a r i a b l e s . Their values are d e s i r e d photographic d e n s i t y .  A  S o l u t i o n D2,  used  5  formulae  given  in  Achia  (1971),  pp  mW  73  The c y l i n d e r ; constant  tank  then AP.  volumetric  was  the The  flow  p r e s s u r i z e d  flow AP  was  s t a r t e d  signal  rate  Q  was  with  was  and  nitrogen  from  allowed  t o ^ a t t a i n  c o n t i n u o u s l y  measured  with  a  a  r e c o r d e d .  bucket  The  and  s t o p c l o c k . The  second  ( i i )  c o n d i t i o n  flow  without  filmed  was  at  index  .refractive  g r a d i e n t s .  Fringe movement at flow without g r a d i e n t s gives a measure of the flow-induced v i b r a t i o n in a d d i t i o n to (i ) . The clamp-held r a i s e d the  to  flow  r e f r a c t i v e  r e s e r v o i r a  by  E  index (see  predetermined g r a v i t y  The  Figure  l e v e l  to  was  readied  3 . 2 ) .  This  i n f u s e  the  in  a  r e s e r v o i r enhancer  was into  f e e d .  t h i r d  ( i i i )  enhancer  c o n d i t i o n  flow  f i l m e d  was  r e f r a c t i v e  with  at  index  g r a d i e n t s .  Fringe movements at t h i s c o n d i t i o n show tho flow patterns and the e f f e c t s of (i) and ( i i ) . Conditions durations the  same  of  d e s i r e d  about flow  (i) 5  to  10  d u r a t i o n ,  The  sequence  A l l  of  s o l u t i o n .  and  the This  of  s i x  ( i i )  were  seconds about flow  and  70  experimental  ( i i i )  to  t e s t s  Separan  f i l m e d  runs  90  is  was  short f i l m e d  for  seconds.  shown  were  design  for  in  done  was  Table with  3.4. the  prechecked  Using a separate batch of 50 wppm S e p a r a n , , g r o s s flow t e s t s were conducted by p a s s i n g the s o l u t i o n through the system. Up to ten runs at Re 18,000 were p o s s i b l e with about the same d r a g - r e d u c i n g e f f i c i e n c y . The s i x flow t e s t s represent a much lower shear level ( 6 0 0 0 < Re < 15,000).  Table The  I n t e r f e r o m e t e r  Sequence No .  Sequence  of  3.4 Flow  F l u i d  Tests  Type  of  Run  Run  Wa t e r * I  (Newton i an)  Streak (as  in  o b s e r v a t i o n Figure  2.2)  No.  D e s i g n a t i o n  1 2 3  Wl s W2s W3s  4 5 6  Sis S2s S3s  7 8 9  S3b S2b Sib  WDHI  II  Separan (50wppm) (Drag Streak Reduc i ng)  Test  S e c t i o n  rotated  o b s e r v a t i o n  through  90°  Separan III  (50wppm) B u r s t o b s e r v a t i o n (Drag (as i n Figure 2 . 3 but v e r t i c a l l y inverted) Reducting)  ADHI IV  Water (Newtonian)  Burst  o b s e r v a t i o n  10 11 12  Wl b W2b W3b  (Sequences I and II were done a t predetermined flow c o n d i t i o n s . I l l a n d IV were done to match with the c o n d i t i o n s i n II and I r e s p e c t i v e l y . A new h o l o g r a m was made f o r each sequence.) 4*>  75  to  ensure  during  that  the  performed  was  to  were  w i t h i n  two  days  s o l u t i o n  Before  the  b u r s t  The  f l u s h e d that  zero  of  to  was  drop  r e d u c t i o n  runs.  with  times no  r e s i d u a l  p r e s s u r e drag  runs  three  there  due  The  A l l  due  to  the  runs  w a t e r ,  with  the  water.  polymer  of  flow  system  This  was  the  s o l u t i o n  checked  before  were  p r e p a r a t i o n ) .  p e r s i s t e n c e  was  shear  the  to  d r a g -  in  the  ensure  runs  in  that  sequence  conducted. The  f i l m  degrade  the  e f f e c t  was  not  between  apparatus. there  did  and  ensure  reducing  s o l u t i o n  t e s t s  c o m p l e t e l y  done  IV  the  type,  f i l m  speed  s c e n a r i o  f o r  c a t a l o g  and a  showing  c a l i b r a t i o n  r e p r e s e n t a t i v e  d e t a i l s  i s  given  f i l m  i s  of i n  the  r u n s ,  Appendix  a l s o  F.  i n c l u d e d .  Chapter  4  MEASURED QUANTITIES AND DATA ANALYSIS  This  chapter  (i)  the  gross  d e f i n e ( i i )  of  data  4.1  Gross  Flow  Q  and  the  Q  was  measured  bucket,  D  and  s o l u t i o n  used  to  and  from  the  experiments  and  the  them.  Measurements  basic  q u a n t i t i e s  three Q  =  flow  times  with of  were  drop a  l i q u i d  v  number was,  76  were  AP.  the  flow  During  s t o p c l o c k  and  Re  from  Q  based  and on  rate  each  a  12  c o l l e c t e d / t i m e .  c a l c u l a t e d  Reynolds  v i s c o s i t y  measured  pressure  volume  parameters The  q u a n t i t i e s  f l o w s ,  summarizes  c o r r e s p o n d i n g  g i v i n g  f o l l o w i n g  4.1  obtained  The  flow  the  the i n t e r p r e t a t i o n of the hologrammoire f r i n g e f i e l d to o b t a i n measurements of the v i s u a l i z e d f l o w .  Figure type  d e s c r i b e s :  r u n , l i t r e  The  AP. pipe  diameter  Flow 1.  2.  Water  Experiment  (Newtonian)  3a A u x i l i a r y Expts, dye, enhancer  r  1  Gross -  Flow  Data  M e a s u r e Q,  Hoiogram f o r r e a l time flow visualization  AP  Motion p i c t u r e records o f f r i n g e movements  S treaks Wall plan view Reynolds No: Re Friction factory f Mean v e l o c i t y : U Shear v e l o c i t y : % Drag R e d u c t i o n : • DR  compute  4.1.  Summary  view  count  •  Burst  Streak S p a c i n g , X, X+ S t r e a k l i f e t i m e , Tc  Figure  Bursts W a l l edge  of  Visual Observ a t i onsj motion pi cture  experiments  and  data  rate  F  Burst  time:  Interval  obtained.  3b Double-Exposure Holograms  78  where  the  bulk  v e l o c i t y  and  the  k i n e m a t i c  The  Fanning  U  =  v i s c o s i t y  f r i c t i o n  f  the  mean  w a l l  The  w a l l  shear  v  =  cm/s y/p  cm  2  /s  f a c t o r  (4.2)  =  2  where  4Q/TTD2  g„  shear  s t r e s s  <T  w  >  =  DAP/4L  dynes/cm  :  v e l o c i t y  (4.3) cm/s m  The  percentage  drag  r e d u c t i o n  AP  AP, DR%  These f l o w s w i t h  i n  which  the  *  DR  a  given  Q  100  (4.4)  AP,  q u a n t i t i e s  were  t u r b u l e n c e  used  was  to  c h a r a c t e r i z e  s t u d i e d  i n  the  g r e a t e r  d e t a i l  v i s u a l i z a t i o n . D e t a i l e d  q u a n t i t i e s below.  =  a t  The  a r e  e s t i m a t e s  presented  q u a n t i t i e s  i n  shown  of  e r r o r s  Appendix a r e  mean  f o r  B,  the  and  values  g r o s s  flow  summarized i n  the  '..  79  6000 The  <  Re  <  e r r o r  Appendix  4.2  i s  f u n c t i o n  i . e .  of  Q  the  for  flow  d e s c r i b e d  r u n s .  i n  rate  ± 1 . 3%  (1)  Flow  Q:  (2)  Pressure  (3)  Mean  (4)  Reynolds  number  Re:  ± 1 . 0%  (5)  F r i c t i o n  f a c t o r  f:  ± 5 . 0%  (6)  Wall  s h e a r - s t r e s s  (7)  Wall  shear  (8)  Drag  r e d u c t i o n  AP:  ± 3 .0%  U:  ± 1 .3%  drop  ve1oc i ty  ± 3 .0%  T..: w  v e l o c i t y  u  x  ±1  the  Reduction  of  i n t e r f e r o m e t r i c  on  the  s o l u t i o n given  flow of  Fringe  s t r u c t u r e  the  ± 2 .5%  :  DR:  of  S  v i s u a l i z a t i o n  reasons  I n t e r p r e t a t i o n  the  wave  a  range,  B.  formation on  15,000  i n t e g r a l  F i e l d  i n  the  for  data  to  wall  l a y e r s  the  phase  o b t a i n  of  i n -  i s  the  based l i g h t  by  S ( x , z )  =  ± .  An  (4,  dy  lightpath  The are  shown  c e n t r a t i o n very  t h i n  in  c o o r d i n a t e Figure  2 . 2 .  d i s t r i b u t i o n l a y e r  axes  adjacent  In of to  r e f e r r e d t h i s  the the  to  flow  t h i s  s i t u a t i o n ,  enhancer w a l l ,  in  i s  equation the  c o n f i n e d  e s s e n t i a l l y  i n  to  c o n a the  80  region  of  y  <  stream  of  the  +  10.  enhancer  the  w a l l - n o r m a l the  y  y  w  =  has  not  10,  had  so  equation  of  phase  of  r e f r a c t i v e  be  J L  n  index  v a r i e s  w  i s  i n f u s i o n  then  reasonable  d i f f u s e  i n  be  the  n  n(.x,z)  a c c o r d i n g  as  a n a l o g o u s l y  which  to  i s  so  that i n  to  assume  l a y e r , to  ( x , z f ]  t  i n t e r p r e t e d  or  down-  f a r  w a l l  s i m p l i f i e d  +  S ( x , z )  s l o t  to  only  can  immediately  time  |Tir(x-,z)  d i s t r i b u t i o n ,  determined  i s  ( 4 . 5 )  y  i s  enhancer  It  i n t e r f e r o g r a m  d i f f e r e n c e  c o n c e n t r a t i o n can  =  region  s u f f i c i e n t  index  S ( x , z )  The  index  y - d i r e c t i o n .  r e f r a c t i v e <  +  sampling  r e f r a c t i v e  the  that  The  as  ( 4 . 6 )  a a  d i s t r i b u t i o n d i s t r i b u t i o n  equation  the  ( 4 . 6 ) .  q u a n t i t y  of  The  i n t e r e s t ,  from  ACCx.z) - X , j i i p f s U . z ) or  expressed  f r i n g e  AC/AS.  c e n t r a t i o n that  the  f r i n g e t i o n the  as  the The  w i t h i n  c o n c e n t r a t i o n r e f r a c t i v e  the  c o n c e n t r a t i o n  s h i f t .  f i e l d  i n  Hence terms  measurement  of  of  i t  was  f l u c t u a t i o n s  i n  terms  the  between  was  e i t h e r  C  d i r e c t l y  two  or  of S  the i s  f r i n g e  to  adjacent  i n t e r f e r e n c e  Figure  with so  p r o p o r t i o n a l  to  i n  the  and  one or  the  c o n c e n t r a -  e q u i v a l e n t .  b r i g h t  c o n -  4.2)  t u r b u l e n t  measure  s h i f t ,  per  l i n e a r l y  (see  c o n c e n t r a t i o n  convenient of  v a r i e d  range  d i s c u s s i o n  enhancer  c a l i b r a t i o n ,  d i s t a n c e  f i e l d  a  d i f f e r e n c e  index  measuring  (4.7)  Since  flow  express  r e q u i r e d a l l  f r i n g e  width  dark  bands.  d  being  F i g u r e  4 . 2 .  R e f r a c t i v e  index  of  propylene  g l y c o l - w a t e r  m i x t u r e s .  CE denotes the enhancer c o n c e n t r a t i o n range used flow v i s u a l i z a t i o n experiments. C vs. n data in Appendix  A.H  in co  82  (a)  Fringe o r i e n t a t i o n with no g r a d i e n t s .  at  p o s i t i o n  f 1 ow  A  (b)  F i g u r e  Fringe o r i e n t a t i o n during flow g r a d i e n t s . A s i n g l e f r i n g e is c l a r i t y .  4 . 3 .  Region of frame and  L~f|3» b r i g h t  fringe;  notch; ' A , region.]]  samp I i n g  1  f  with i nd uce d shown for  flow recorded on a m o t i o n method of s a m p l i n g .  dark  fringe;  I i n e ; ——*,  p i c t u r e  W, w i n d o w ; N, a l i g n m e n t  low c o n e , r e g i o n ; — — ,  high  83  Figure the in  'window' the  are  W  f l o w ,  t i v e  from  d i f f e r e n t  4.3  i t s  The the  was  c e n t r a t i o n  l i n e  f l o w .  which  i s  the  s e l e c t e d one  d i f f e r e n t  f r i n g e  s h i f t s The  d e f i n e d  of  mean  l i n e s e t  i n s t a n t s was  at  1  s i n g l e A'  due  f r i n g e to  and  Time  axes  r e f r a c h i g h - s p e e d  i n s t a n t s  f o r  . ' " » t - .  2  f i e l d to  i n  C +  =  the the  of in  The  the  w a l l  t u r b u l e n t  l a y e r , flow  i n s t a n t a n e o u s  c o n -  c  (4.8)  about  space  and  c  the  mean.  z - d i r e c t i o n  time. to  This give  f r i n g e  i s  average  i n t e r f e r o g r a m s  average  in  the  c o n c e n t r a t i o n  averaged  space  g r a d i e n t s  c o o r d i n a t e a  by  as  c o n c e n t r a t i o n  a  the  framed  no  low-speed  t  r e l a t e d  regarded  be  ,  c o n c e n t r a t i o n  E x p e r i m e n t a l l y ,  at  x  C  i s  each  t  with  s p i k e s .  s t a t i s t i c a l l y .  t u a t i n g  from  The  flow  Readout  v a r y i n g  can  and  p o s i t i o n  by  the  c l a r i t y ,  a n a l y s e d  where  a  at V f o r  denoted  of  f r i n g e s  c o n c e n t r a t i o n  Fringe  of  the  C  along  The  shows  in  are  f l u c t u a t i o n  f i e l d ,  4.3b  as  frames  of  region  ' n o - g r a d i e n t '  seen  Method  the  3 . 5 .  sampling  enhancer  are  shows  Figure  Figure  index  s t r e a k s  in  the  shown.  s h i f t e d  4.3a  s e t  a  mean  s h i f t  s  z  )  the  f l u c -  f r i n g e  s h i f t  was  of  the  of  space  space at  any  determined  flow  taken  averaged  average  S.  i n s t a n t  i s  as S ( i = 1  Z 1  )  (4.9)  84  at  a  f i x e d  of  frames  value at  of  x  and  d i f f e r e n t  t.  into  a  t i o n  so  Az  was  sampling  number as  of  to  l i m i t e d  gram, which  i s  d.  In  mm  of  the  t h a t  was  0.38  mm.  by  the  t h i s  g e n e r a l l y  c e r t a i n  s p a t i a l  d e s c r i b e  the  flow  measurements, in  4.4  Appendix  the  (4.10)  in  Figure  4.3  Az  in  spanwise  s p a c i n g .  The  length  the  =  of  s h i f t s  r e g i o n . and  in  the  d  data  14  =  3  was  mm  about  compute  parameters D e t a i l s  of  f r i n g e  With  to  d i r e c -  i n t e r f e r o -  used  used  d i v i d e d  c h o i c e  r e s o l u t i o n  were  was  the  mm.  t u r b u l e n c e  programs  of  were  0.583  minimum  wall  the  o n e - e i g h t h  Az  the  Turbulence  Determination S p a t i a l  This  tended  number  that  of  f r i n g e  a n a l y s i s  are  given  D.  4.4.1  X  a  L  segments  temporal  in  'A'  width  24  g i v i n g  computer  W a l l - L a y e r  spacing  at  about  f r i n g e  and  over  S  I t=l  r e s o l u t i o n  used,  Measured  f  streak  work,  w a l l ,  =  of  the  t y p i c a l l y  spacing span  l i n e  segments  r e s o l v e  sampled  times  S  The  When  using  from  the  of  Streak  C o r r e l a t i o n  method a  Parameters  of  s p a t i a l  work  of  Spacing  X  from  of  C o n c e n t r a t i o n  o b j e c t i v e  d e t e r m i n a t i o n  c o r r e l a t i o n  Schraub  and  c o e f f i c i e n t  K l i n e  (1965).  the R£(5)  of  the  i s  ex-  They  streak  85  used  hydrogen  the  s p a t i a l  spanwise f r i n g e  bubble  s t r u c t u r e .  In  c o n c e n t r a t i o n  was used The  is  t i m e l i n e  defined  t r a c e s  t h i s  p r o f i l e  (Figure  work, as  spanwise  ( ? )  ( x  of  i n  c o r r e l a t i o n  0  ,  y o . A z j  t  0  t h e  terms  of  ( x  0  of  •  by  an  i n t e r f e r e n c e  c o n c e n t r a t i o n  R  ( 5 )  c  f r i n g e  Hence,  , y o , J A z ; t o )  c ( z  +  Az)  dz (4.11)  c ( z  d a t a ,  s h i f t  e q n .  N  •  2  experimental the  c o n c e n t r a t i o n .  c  instantaneous  )  1 R  determine  as  From c  an  to  4 . 3 b ) .  j"c(z)  R  v e l o c i t y  shown  J c ( z ) R  of  i t  S  -  A z )  i s  S (  to  i n  express  terms  m o d i f i e d  +  Z i  dz  than  c a n be  S  2  e a s i e r  rather  (4.11)  s(Zi)  +  j A z )  -  to  S  i=l  = N  r-  s(Zi)  2  -  S  i=l  1  N  N  ^  S (  Z i  +jAz)  -  S  i =l (4.12)  where  the  R  of  the  to  e x i s t  f i e l d  c  ( ? )  flow.  i s  s p a t i a l  when  s e p a r a t i o n  provides  A  d e f i n a b l e  t h e  i n f o r m a t i o n s p a t i a l  t u r b u l e n t  c o r r e l a t e d .  E, =  Thus,  Az  of  t h e  s t r u c t u r e  c o n c e n t r a t i o n at  s e p a r a t i o n  s p a t i a l c a n be  over  the  d i s t a n c e s  s t r u c t u r e thought spanwise where  86  the  c o r r e l a t i o n  i n f o r m a t i o n  of  The between can  be  the  i s  non-zero,  the  s p a t i a l  s i m p l e s t  o r i g i n  taken  as  a  for  a  number  50)  sampled  was  kept  t i m e .  at  long  The  o b t a i n  frames  enough  A  the  4 . 4 . 2  In  be  a  of  s i n g l e  the  d e f i n e d  R  where  c  of  each  X  flow  provides  f o r  the  flow  ,  z „ ;  x )  i n  s c a l e ( ? )  w  A  a  R  not  each  c  of  ( ? ) the  w a l l  computed  s  (40  between  two  c o r r e l a t e d frame  p o s i t i o n s  Sublayer of  was  to samples i n  was used  to  Period  the  s p a t i a l  i n f o r m a t i o n  f i e l d  T  to  from  C o n c e n t r a t i o n  s t r u c t u r e .  i n  c  d i s t a n c e  c o n d i t i o n .  provide  w a l l - l a y e r  ( ? )  i n t e r f e r o g r a m s  were  peak  manner  can  c  the  peak  i n t e r v a l  they  of  R  view  spacing  s i m i l a r  point  5 . 7 ) .  A u t o c o r r e l a t i o n  a u t o c o r r e l a t i o n  scales a  f o r  R  that  s p a t i a l  time  that  Determination the  the  so  i s  p o s i t i v e  the  plan  The  histogram X  of  of  streak  mean  f i r s t  Figure  random.  mean  determined.  the  see  of  s c a l e s .  measure  s t r e a k s . (e . g .  behaviour  i n t e r p r e t a t i o n  and  l a y e r  of  the  The  over  a  R  c  (x)  c o r r e l a t i o n , on  the  time  a u t o c o r r e l a t i o n period  of  time  a t  may  as  ( x  0  ,  the  y  0  time  l a g  x  =  =  i  c(t)  Jc  (t)  At.  •  c ( t  +  At)  c ( t  +  A t )  dt (4 2  dt  87  In m o d i f i e d  terms  of  f r i n g e  s h i f t ,  equation  4 . 1 3  can  be  to  R  c  ( x  rS ( t . )  i  N  0  ,  y o ,  -  S  - i  i—  z  ;  0  j A t )  S ( t .  2  l  +  j A t )  -  (4.14)  S  r  N  ^ i  2  (4.15)  where  A f i g u r e  t y p i c a l  d i s t a n c e  a u t o c o r r e l a t i o n the  s i g n a l  t r a c e  being  number  of  r e r i s e  p o s i t i v e  estimate  c y c l e s ,  of R  taken  curve  i s  shown  i n  time  u n i t s  of  4 . 4 . The  of  a u t o c o r r e l a t i o n  from  The  length  the  maximum  C  between may  be  t h e  d i s t a n c e  maximum  of  the  mean  p e r i o d  ( % )  was  computed  s t r i n g  of  the  l a g 3  of  as  the  In  the  absence  from  the  o r i g i n  R  C  ( T )  curve  i s  of  l a r g e  a the  as  f i r s t an  T^. s h i f t  s e q u e n t i a l  motion  p i c t u r e  was  s e c ,  p e r i o d -  max  p e r i o d  taken  f r i n g e  T  the  mean  to  from  sampling  t i m e ,  i n  i n t e r p r e t e d  c o r r e l a t e d .  the  a  peaks  0 . 5  20  s e c , of  the  measurements frames.  i . e .  40  times  a u t o c o r r e l a t i o n  88  F i g u r e  4 . 4 .  An  a u t o c o r r e l a t i o n  showing  4 . 4 . 3  I n t e n s i t y  The f l u c t u a t i o n  r e l a t i v e I  i s  I  The frames  the  runs  From were  T u r b u l e n t  i n t e n s i t y  d e f i n e d  c  t h a t  these  c  t u r b u l e n t  r  N  F l u c t u a t i o n  c o n c e n t r a t i o n  ~i  2  Kj,[ < i>- ] s  was  were  measured a l s o  samples  o b t a i n e d  of  i  C  I  C o n c e n t r a t i o n  as  4  mean  (40-50)  t i o n s .  of  curve  p e r i o d i c i t y .  of  used I  z  for to  D  each  the  and  14  of  o b t a i n  d a t a ,  (Appendices  ?  the  s p a t i a l  means E).  f o r  i n d i v i d u a l c o r r e l a each  of  89  4 . 4 . 4  The  The Table  3.4)  water  and  f l u i d  i s  f l u i d  edge  were  from  w a l l  and  p e r i o d  6  of  cm  30  to  frame-by-frame r e v e r s e  was  in  way,  t h i s  col 1 apse  in  the  60  due  to  j u s t  upstream  F  the  d i f f u s e d  i n t o  the  flow  r e a s o n ,  in  the  the  bulk  region  motion  of 14  i n  enhanced  f i l a m e n t s the  spanwise  counted  Running  of  f l o w .  i n  p i c t u r e s  would  during  were  run  a  both  the  f i l m  in  bursts  more  c l e a r l y :  come  of  f l o w ,  the  at  method  the  together  spanwise  a  and  the  are  width  the  can  be  two  tags  i s  a  x - d i r e c t i o n . x - s t a t i o n ; and  enhancer seen.  l i m i t s  (Schraub, that  counting  observed^,  the-.enhancer  wall  i n c o r p o r a t e d  d i s c r e t e  where  these  not  burst  to  at  bursts  between  the  of  bursts  s l o t  no  was  r e s p e c t  no  f u n c t i o n v b f « x ,  c o n d i t i o n  (x)  IV,  i n t e r m i t t e n t  mm  were  and  b u r s t i n g  index  i n  i d e n t i f y i n g  i n f u s i o n  s l o t  d i s t r i b u t i o n  only  wall  motion.  with  enhancer of  :  a  dimension  s i n c e  downstream  some-unknown  of  III  w a l l .  d i s t a n c e  marking  the  the  f i l a m e n t s  o b s e r v a t i o n  i s  r a t e  r e f r a c t i v e  d i r e c t i o n  slow  streamwise  This  i n  The  h e l p f u l  e j e c t e d  q u a n t i t y  nonuniform  in  (sequences  d i s t i n g u i s h a b l e  into  flow  s e c .  and  the  A  l a y e r  the  often  at  c a r r y  the  The  from  o c c u r r i n g  i n  p i c t u r e s  determine  away  bursts  the  motion  to  move  Bursts width  view  F  s o l u t i o n s .  to  These  Rate  used  Separan seen  b u r s t s .  Burst  some  has  The  burst  may  vary  as  i n f u s i o n  rate  and  1965). the  For  f l u i d  t h i s with  90  r e f r a c t i v e r a t e  F  as  index bursts  4 . 4 . 5  Time  Tg, r a t e  F  and  a  enhancer  i s  per  time  u n i t  I n t e r v a l  This et  al.  those  (1968), of  Newtonian  B  =  A,  based and over  on  w a l l  i n  e x p r e s s i n g  u n i t  spanwise  Bursts  using  given  the  burst  w i d t h .  Tg  values  by  the  of  b u r s t i n g  equation  i s / b u r s t y  f o r  t h e i r  K l i n e a  i s  FX  r e l a t i o n s h i p  Schraub flows  q u a n t i t y  spacing  T  per  Between  computed  streak  used  Tg  was  suggested  experimental  (1965)  for  (4.1  by  Kim  f i n d i n g s  and  z e r o - p r e s s u r e - g r a d i e n t  o f a a s r e c t a n g u l a r  c h a n n e l .  Chapter  5  EXPERIMENTAL RESULTS AND DISCUSSION  5.1  A  Note  on  Six three 50  with  wppm  p a r t s ; view  flows  water  Separan a  to  broad  P r e s e n t a t i o n  c o n s i d e r e d  (Newtonian) AP30  w a l l - p l a n observe  were  and  three  s o l u t i o n s .  view  to  b u r s t s .  d e t a i l with  Each  study  The  i n  r u n  s t r e a k s  r e s u l t s  t h i s  study;  d r a g - r e d u c i n g c o n s i s t e d  and  a r e  f o r  a  of  two  w a l l - e d g e  presented  i n  two  s e c t i o n s :  (i)  ( i i )  Gross  flow  measurements  l i m i n a r y  flow  followed  by  and  Turbulence  s t r u c t u r e  and  o b s e r v a t i o n s  v i s u a l  and  a l l  holography  p r e -  t e s t s ,  measurements of  the  wall  l a y e r s .  For are  provided  s i n c e  the  space, from for  a  Appendix  l a t t e r ,  wherever  t u r b u l e n c e true  motion t h i s  the  and  p o s s i b l e being  complete  p i c t u r e s .  purpose,  r e p r e s e n t a t i v e  the  A  as  s t i l l  observed  s c e n a r i o  F.  91  movie  f o r  i m p r e s s i o n s  p i c t u r e s .  changes  i m p r e s s i o n  d i s p l a y  v i s u a l  can  be  has  which  with  i s  However, time  obtained  been  and only  prepared  i n c l u d e d  i n  92  5.1.1  Gross  Gross the  Flow  flow  d r a g - r e d u c i n g  s o l u t i o n s wppm. flow  of  The  t e s t s  and  water  was  l i n e  f  A l l Fanning (data f o r  the  f r i c t i o n in  determined  i s  the  Separan  'onset' f o r  of  each  s o l u t i o n s  l i n e s  s t r o n g l y  centage order  of  to  s t u d i e s , ments  for  s e l e c t the  as  the  -  to  by  d e t a i l e d  v i s u a l i z a t i o n ,  on  are  The  more  were  flow  in  150  the  be  on  the  Figure  5.1  Reynolds that  was  (Appendix  5.1.  the  a l s o  Reynolds d e t a i l e d  Chapter  2.1,  a p p l i e d .  A). by  The  estimated  of  number  e x h i b i t e d  Figure  So  given  i n  shown  roughly  e x t r a p o l a t e d  t u r b u l e n t - s m o o t h  dependent.  for  and  Newtonian  v i s c o s i t y  may  Newtonian  s o l u t i o n  the  p l o t  B5).  i n t e r s e c t i o n  a  check  v i s c o s i m e t e r  which  100  (5.1)  number  r e v e a l e d  at  AP30-water 50,  a  with  d r a g - r e d u c i n g  are  the  as  measurements  s o l u t i o n  of  25,  e s t a b l i s h  2 0  on  r e d u c t i o n a  0  Bl  the  0,  to  e q u a t i o n ,  Tables  the  c r i t e r i a  flow  by  flow  r e d u c t i o n ,  with  Separan  agree  0 . 0 4 6 ( R e ) "  c o n c e n t r a t i o n drag  to  Cannon-Fenske  regimes  s o l u t i o n  s o l u t i o n is  based  drag  given  =  B,  a  of  conducted  served  f a c t o r - R e y n o l d s  using The  data  found  gross  Appendix  Separan  f i r s t  c o n c e n t r a t i o n s ;  d i s t i l l e d  t u r b u l e n t - s m o o t h  were  c h a r a c t e r i s t i c s  v a r i o u s  apparatus  Measurements  i s  l i n e , the  number.  perIn  v i s u a l i z a t i o n i . e . The  50  r e q u i r e wppm  Re (xio ) -3  Figure  5.1.  Fanning  f r a c t i o n  Separan  AP30  -  f a c t o r  -  d i s t i l l e d  (1 laminar l i n e , 2 r e d u c t i o n asymptote.)  Reynolds water  Newtonian  number  s o l u t i o n s  p l o t in  t u r b u l e n t  a  f o r  gross  smooth  smooth,  3  flow  2.63 -  cm  drag  of p i p e .  Table Summary  Run No .  F l u i d  WATER ( d i s t i l l e d ) v  =  =  0.0144  Flow  Reynolds Number Re  C o n d i t i o n s  F r i c t i o n Factor f  f o r  FI ow  Holographic  Q  Bui k V e l o c i t y U  ml/s  cm/s  Rate  V i s u a l i z a t i o n  Runs  Shear  Pressure Drop AP cm  H20/305  cm o f  V e l o c i  pipe  cm/ s  ty  DR  %  Wl  6,550  0.00745  135.0  24.9  1.10  1 .52  0  W2  10,900  0.00695  225.0  41 . 5  2.85  2.45  0  W3  14,500  0.00672  300.0  55.3  6.15  3.25  0  SI  7,400  0.00574  220.0  40.5  2.25  2.18  20  S2  9,750  0.00455  290.0  53.4  3.10  2.56  32  S3  14,800  0.00360  440. 0  81  5.65  3.45  44  cm2/s  SEPARAN AP30 50 wppm d i s t i l l e d water)  (in v  0.0100  of  5.1  cm2/s .1  Ap  U¥ Figure  5 . 2 .  H o l o g r a p h i c water  and  cm water 3.05 m pipe  cm/s  v i s u a l i z a t i o n  Separan  AP30  runs:  s o l u t i o n .  gross  flow  data  f o r  96  Separan  s o l u t i o n ,  w h i l e  provide  good  r e d u c t i o n  5000  to  drag  a  i n  v i s c o s i t y  the  of  Reynolds  1 . 4 4 3 ,  number  could  range  of  15,000. The  gross  shown  s e p a r a t e l y  as  provide  to  having  flow  in  flow  data  Figure  5 . 2 .  comparisons  Reynolds  (i)  of  the  v i s u a l i z a t i o n  The  runs  at  numbers  were  planned  approximately Re:  runs  are so  equal  SI-WI,  S2-W2,  S2-W3,  and  S3-W3, Flow  (ii)  the  runs in  flow  are  each  f i g u r e  q u a n t i t i e s  shown of  i n  the  of  SI,  AP  the  5.1. S2  P r e ! i m i nary  Figure  (wall  s h e a r ) :  h o l o g r a p h i c The  and  the  seen  to  shows  flow leave  is  at  the  v i s u a l i z a t i o n  percentage  S3  i s  drag  c a l c u l a t e d  the  wall the  I n f u s i o n  were  l a r g e the  done  r e d u c t i o n from  to  In  dye  s a t i s f a c t o r y .  in  who  the  form  showed were  no  the  o b s e r v a -  reported  t u r b u l e n t  s t r e a k y  laminar  t e s t s There  check  during  c h a r a c t e r i s t i c  s l o t  Tests  channels  wall  t u r b u l e n t .  F u r t h e r , was  Dye  t e s t s  using  formation  5.3a  when  dye  workers  burst  design  of  Table  runs  These  and  SI-W2,  5 . 2 .  5.1.2  t i o n s  Q:  Pressure drops W2-S2, W3-S3.  (iii)  A l l  rates  f l o w , of  a  that  s t r e a k f l o w .  s t r u c t u r e the  dye  uniform the  s h e e t .  flow  o b s e r v a b l e  was  s e c t i o n  corner  ^-flow (a)  streaks *  (b)  Figure  5 . 3 .  Streaks  at  the  (a)  as  v i s u a l i z e d  (b)  as  seen  index [The  pipe by  through  enhancer dotted  reg ion  in  a  in  s l o t  hologram  infused  l i n e (b ) . ]  wall  wall  on  (a)  at is  t u r b u l e n t dye with  the the  flow  i n j e c t i o n , a  r e f r a c t i v e  w a l l . framed  98  e f f e c t s  at  the  f l a t t e n e d . did or  not  When  appear  i n f u s i o n  5.2  points  where  observed  to  form  s t u d i e s  d e t a i l e d  107).  The  to  l i q u i d the  i n  be  e a r l i e r  t h e s i s  t e c h n i q u e s ,  were  time,  l o c a t i o n s  flow  s e c t i o n in  are  Density  the  of  and  was the  on  the  s t r e a k s pipe  and t h i s  Achia  the  (1971,  the  use  hologram work.  d i s c u s s e d  of  r e a l - t i m e  v i s u a l i z a t i o n  i n c l u d i n g  r e t a i n e d  making  c o n t r o l l e d  wall  h o l o f a c i l i t y  pp.  of  88-  d i f f u s e d  immersion  in  Improvements  here.  Hologram  hologram,  the  important  f a c t o r s  were:  the  exposure  time,  ( i i )  the development photopI ate .  These  two  d i s t r i b u t i o n  f r i n g e  test  scheme  Optical  (i)  of  an  holography  d e n s i t y  of  double-exposure t h i s  the  While to  s p e c i f i c  develop  of  gate,  5.2.1  length  to  b a s i c  i l l u m i n a t i o n a  at  a  s e c t i o n  Experiments  E x p l o r a t o r y  are  for  c i r c u l a r  s l o t .  Hologram  graphic  the  readout.  f a c t o r s which To  and  time  of  determined a f f e c t e d  a r r i v e  at  the  the  the  the  hologram  c l a r i t y  best  and  c o n d i t i o n s ,  o p t i c a l c o n t r a s t a  99  t r i a l - a n d - e r r o r guess  for  worked  the  of  the  i n t e n s i t y  d i f f u s e  (see and  beam  r e f e r e n c e  S t a r t i n g  the  other  with  f a c t o r s  i n s e t ,  the  from of  exposure  the  time  ' d e s i r e d '  s i m i l a r such  WDHI.  beams  was  s e c t i o n  of to  t h a t  that  shown  and.development d e n s i t y  a  rough  could  be  c o n i c a l  t e s t at  125  that  cm of  the  The  viewing used  passed  t h i s  of  were  plane  of  recorded  the  the  Figure  beam.  hologram  bundle  a d j u s t e d  hatched  was  aperture  that  i n  r a d i a l  r e f e r e n c e  through  hatched  0  area  c e n t r e  the  roughly  the 2  i n  The  beam  the  time  of  was  uniform  v i s u a l i z a t i o n  hologram,  o p t i c a l  the  The  i n t e n s i t y .  flow  t e s t  i n  5 . 4 ) .  photoplate  was  h i g h e s t  the  R  these  c o n s i d e r e d  v a r i a t i o n  for  a c r o s s  Figure  Thus,  the  beam  s e m i - c o n i c a l  be  hologram  p o r t i o n  and  alignment  recorded  rays  expanded  could  i n t e n s i t y  the  time,  ADHI  r e c o r d i n g .  The  used.  exposure  d i s t r i b u t i o n  Gaussian  an  was  out. The  case  method  at of  c e n t r a l  5.4. to  p o r t i o n  The  get  of  the  the  hologram. This determined While the  by  ' d e s i r e d ' viewing  developing  t r i a l  observed reached  the  f r i n g e s  holograms  hologram by  value  was  held  s a f e l i g h t .  The  d e s i r e d  o p t i c a l  for  o p t i c a l  through  for  the  a  flow  a l o n g s i d e photoplate d e n s i t y .  d e n s i t y  t r i a l  was  hologram.  v i s u a l i z a t i o n  and was  the  r u n s ,  darkening  f i x e d  when  was i t  o  xJL Inset: Intensity  F i g u r e  ER, H,  d i s t r i b u t i o n  5.4.  Laser l i g h t hoiogram.  r e f e r e n c e hologram;  along  beam P,  cone;  p i p e .  l i n e  i n t e n s i t y  V, f i ,  viewing f2,  f3  X-X  d i s t r i b u t i o n  aperture * * •  at  the  cone;  imaginary  aperture  l i n e s . ]  101  5 . 2 . 2  Moire  The d i s c u s s e d f r i n g e s gram  in  i s  was  normal  to  to  the  2 . 2 ) .  f r i n g e s  to  i n  to  2  chosen  flow  t i o n s  was  d i s p l a c e d  the  change  i n  t h i s  were  being  the  optimum  amounts i n  was  shown  a  hologram  in  d i r e c t i o n  (along  viewing  s t r e a k i n  the  d i r e c t i o n at  the  plane  A  i n  f r i n g e  the  For x-y  b u r s t plane  s p a c i n g  of  s e n s i t i v i t y  Both  a  z - d i r e c t i o n .  w a l l .  f r i n g e  o b s e r v e d .  measurements  the  pipe  a l i g n e d  w a l l .  h o l o -  e f f e c t s .  needed at  generated  p a t t e r n  o r i e n t a t i o n  a c c u r a t e  focus  pipe  and  f r i n g e  viewed  the  been  u n d i s p l a c e d  i n  to  were  f o r  are  the  and  f r i n g e s  phenomena  the  extreme  and  between to c o n d i -  of (i)  large e . g .  ( i i )  give  b a t i o n ,  high  were  f r i n g e F i g u r e  small e . g .  that  i n f i n i t e  make  f r i n g e s  p e r p e n d i c u l a r  the  an  p a r a l l a x  were  was  R1,  due  has  e x p e r i m e n t a l l y When  s p a c i n g  to  formation  5 . 5 .  f r i n g e s  A  the  mm  of  f r i n g e  order  p a r a l l e l  5  by  Formation  f r i n g e  set  s e c t i o n  o b s e r v a t i o n s ,  to  A  The  t e s t  wall  In  moire  Figure  f.  the  pipe  of  i n  P a t t e r n  hologram  a  change  These  2.  Figure  the  set  Chapter  The  5 . 5 ,  of  of  i l l u m i n a t e d  f i g u r e  would  theory  shown  o b s e r v e d .  y - a x i s ,  Fringe  and  found  f r i n g e Figure low to  s p a c i n g , 5 . 5 c ,  >  5mm,  s p a c i n g ,  d  <  2mm,  5 . 5 f ,  s e n s i t i v i t y be  d  and  r e s p e c t i v e l y  u n d e s i r a b l e .  to  p e r t u r -  102  Ax  =  0, d  Figure  5.5.  Moire di  Ay =  f r i n g e s  =  7.1,  - 0 . 2 0 , f  =  Az  =  0  1.k  generated  by  hologram  splacement.  (The  c o o r d i n a t e  At  the  Az  =  0.  spacing  axes  i n f i n i t e A, in  hologram mm;  are  f r i n g e f,  shown  in  F i g u r e  adjustment,  Ax  d i s p l a c e m e n t ;  d,  f r i n g e s  per  cm.)  =  2.2 Ay  =  f r i n g e  103  5 . 2 . 3  Speckle  The a  speckle, This  E f f e c t  g r a n u l a r  problem  nature  common  to  problem  was  compounded  to  b a c k l i g h t  the  t e s t  to  e l i m i n a t e  the  s c a t t e r i n g  p a r t i c l e s 1971,  and  p.  by  s u r f a c e s  A  are  g i v e s  d e t a i l e d  C o l l i e r t h i s  seen the  t h a t  and/or  The  of  a  due  coherent in  the  to o b j e c t s .  d i f f u s i n g  d i f f u s e r  was  l a s e r g l a s s  an  eye,  s u r f a c e  a  screen  e s s e n t i a l  l i g h t pipe  by  dust  ( A c h i a ,  pp.  203  &  d e g r a d a t i o n  pipe  and  mechanism  p a t t e r n appearance.  i s  347).  For  of  q u a l i t y  the  d i f f u s e r  s p e c k l e  s c i n t i l l a t i n g  (1971, the  the  annoying  s p e c k l i n g  s p e c k l e are  F-5).  The  the  viewing  s u r f a c e  s i z e the at  gets  and  minimized that  g r a i n  the  s i z e  l a r g e r  the as  gets  r e a s o n a b l y  by  the  and  point  i n  The  two  given  by  purpose  of  of  the  moire  By  The  a p e r t u r e  opening  a l s o  d i s t a n c e  keeping (f  4 . 0  of  due f i n e -  ( A c h i a ,  i s  v i e w i n g .  viewing  f r i n g e  s p e c k l e  together  the  the  l a y e r s  s p e c k l e  on of  l a r g e r . l a r g e  using  pasted  of  the  g r a i n i n e s s  r e c o r d e d .  were  aperture  from  d i s t a n c e a  i n t r o d u c e s  observed  g l a s s  a p e r t u r e  by  the  the  ground  observed g r a i n  use  of  was  on  with  covered  d i f f u s e r  grained  dent  i s  1 a s e r - i 1 1 u m i n a t e d  the  of  f r i n g e s  d i s c u s s e d . The  Figure  by  s t r i a e  observed  only  i s  p a t t e r n s  observed  al.  work,  the  a l l  s e c t i o n .  o p t i c a l  account  et  f r i n g e s  to  the  69). When  which  of  of  depenthe  s p e c k l e  gets  the to  1971,  s m a l l e r  camera f  5.6)  104  the  f r i n g e  c l e a r l y  p a t t e r n  viewed  5 . 2 . 4  on  recorded a  E f f e c t  l a r g e  of  f1ow-induced,  p a t t e r n  due  and  hologram.  the  both  types  to  of The  i t s  ever,  s i n c e  o p t i c a l  was  the  b u i l d i n g ,  to  the had  the  o p t i c a l  The  t e s t  t a b l e  as  the  other  v i b r a t i o n  movement  between  the  at  ' n o . f l o w '  ment. at  a  The  showed f r i n g e  maximum  f r i n g e spacing  s h i f t d.  of  the  s h i f t  1%  during  of  d,  flow  be  on  a  was  be  f r i n g e  t e s t  s e c t i o n  of  flow  p a t t e r n s ,  was  the  clamped in  turn  l i t t l e  the  In no  t h i s  40%  to  f i l m s  the 80%  was  to  to  an the way,  r e l a t i v e keeping of  a r r a n g e -  estimated  e n h a n c e r - i n f u s e d of  the  the  f r i n g e s  experimental  v i b r a t i o n to  thus  How-  to  t h i s  by  bench  and  clamped  hologram,  of  base.  r i g i d l y  or  p i c t u r e  designed  o p t i c a l  equipment  components.  to  or  the  pneumatic  of  was  compared to  of  3.2  beyond  Motion  due  Pattern  i s o l a t e d .  p i e c e s  success S  could  the  a n a l y s i s  caused  movement.  movement between  far  and  Fringe  Figure  f l o a t  o p t i c a l  induced  of  in  s e c t i o n  pipe  f i l m  b u i 1 d i n g - i n d u c e d  be  t a b l e  b u i l d i n g  f r e e  B  v a r i o u s  frame.  f r i n g e s  to  extended  to  movie  the  b o d i l y  bench  outer  were  (i)  proper  f r e e l y  pipe  connected  a  on  movements  v i b r a t i o n  the  and  caused  For  mm  s c r e e n .  e i t h e r  r e l a t i v e  manufacturer  16  V i b r a t i o n  V i b r a t i o n s , ( i i )  on  f r i n g e  105  When the  f r i n g e  The  p a t t e r n  t i o n  ment of  would the  the  5 . 2 . 5  of  the  The  i s  The  of  other  t i o n ,  are  streaks This  of  marked  observer  the  marked  f l u i d  5.3b  dye by  or  from  not  a  the  new  the  to  p i p e ,  p o i n t .  and  p o s i -  ' r o c k i n g '  the  mover e a c t i o n  l o c a t e d  Higher  about  flow  of  the  f r i n g e s .  of  the  wall  shows  flow  s t r e a k s ,  can in  be  due  c h o i c e  to  c h a r a c t e r i s t i c s . are  a l s o  enhancer that  measure  or  the  correspond  seen  pictures".  to  f l o w .  marking  to  movement  the  which  index  the  i n t o  directly  s t r e a k .  i n t e r f e r o m e t r y .  p o s i t i o n  n e a r - w a l l  dye-marked  as  due  enhancer  d i f f i c u l t  i n f l u e n c e s  element  the  p o s i t i o n .  b o d i l y  h o l o g r a p h i c  index  It  t h i s  The  appearance  s u b s t a n t i a l l y i t  of  r e f r a c t i v e  a r r o w s .  makes  being  'window'  low-speed  new  i n f u s i o n ,  1 i z a t i o n  w i t h  do  a  about  as  n o - g r a d i e n t  s i m i l a r  the  d i f f e r  of  the  the  show  spacing  shows  the  to  d i s p l a c e m e n t s  Visua  by  and  end  Dye  r e f r a c t i v e  5.3a  streak  b o d i l y  enhancer  T h e r e a f t e r ,  o b s e r v a t i o n  v i s u a l i z e d  from  v a r i a t i o n  the  b o d i l y  v s .  higher  may  the  5.3b  the  e x p l a i n e d on  l a r g e r  but  of  i s  of  as  p o s i t i o n s  regions  t o - a n d - f r o  framed  p i c t u r e s  each  move  f l u i d  f r i n g e s  i n f u s i o n  then  Fringe  s t r e a k s  move  i n d i s c e r n a b l e .  Figure  scene  to  almost  downstream  The  seen  without  was  m  l a y e r  was  f r i n g e s  produced  on  steady.  e x i t i n g :  r a t e s  turned  became  the  1.5  was  flow  movement  of  flow  p a t t e r n  u n t i l  f r i n g e  the  The  c o n c e n t r a i n d i v i d u a l  i n t e n s i t y . the  spanwise  s u b j e c t i v e n e s s  r e j e c t i o n  of  a  dye-  106  The Figure  5.3b,  r e l a t i o n In A  were  of  t h i s and  f r i n g e  p a t t e r n s ,  analysed  c o n c e n t r a t i o n  way  a  streak  more  R  T  t y p i c a l  using c  the  ( £ )  o b j e c t i v e  l i f e t i m e  a  s p a t i a l  and  be  shown  i n  spanwise  a u t o c o r r e l a t i o n  measure  could  frame  of  the  streak  c o r -  Rc(  ).  s p a c i n g  o b t a i n e d .  s F u r t h e r , f u n c t i o n  of  i n j e c t e d  s o l u t i o n .  as  p o s s i b l e  ferometer  dye  to  set  r e f r a c t i v e  at  1/3  s o l u t i o n . the  i n f u s i o n  rates  flow  rate  spacing  of  1/4  needed  that  higher  s e n s i t i v i t y are  r e s o l u t i o n  the  of  the  l e s s e r  marking  must  be  With  d  -  3  with  a  kept the  mm,  10%  spacing  flow  f r i n g e s  f e a t u r e  of  the  as  small  3.5%  rate  was  food  c o l o u r i n g  which  would  even  lower  demonstrates  d i s t u r b a n c e provide  a  i n t e r -  the  i n t e r f e r o m e t e r ,  This  i s  d i l u t i o n  i n f u s i o n  f r i n g e  p o s s i b l e . and  and  d i s t u r b a n c e s .  s o l u t i o n  a  streak  rate  enhancer  h o i o g r a m - i n t e r f e r o m e t r i c techni  of  i n j e c t i o n  f r i n g e  With  i n c r e a s e  higher  The  a  to  i n t e n s i t y  i n j e c t i o n  avoid  index  t y p i c a l l y dye  the  the  over  that the  the  the dye  que.  5 . 2 . 6  Double-Exposure  The  technique  i n t e r f e r o m e t r y  i s  t h r e e - d i m e n s i o n a l p o s s i b l e . i d e n t i f y  This and  viewing was  bursts  Interferograms  double-exposure  d i s c u s s e d  aspect  study  of  Flow  in  of  a  s e c t i o n scene  c o n s i d e r e d using  an  h o l o g r a p h i c  2 . 6 .  By  t h i s  ' f r o z e n  in  time'  e s p e c i a l l y  o b l i q u e  view  method,  useful of  the  i s to w a l l .  107  However, t h i s  due  to  technique The  flow  i n  the  t i o n  of  a  There of  was  p i p e .  no  at  some  l e v e l s  The  of  present thus  at  t h i s  the  recorded An  dynamic  motion  w i t h  that  time  event was of  p i c t u r e s  r e s u l t s  with  of  provide  second  s e c t i o n  a l l  s t u d i e s  at  with  no  the  hologram.  exposure  a  means  had  to  be  However,  at  the  was  any  l i k e l y  i n s t a n t  to  be  and  exposure. a  one  doubly-exposed  h o l o g r a p h i c  i n s t a n t  in  t i m e ;  l o s t .  In  c o n t r a s t ,  was more  g r e a t l y  r e a l - t i m e  these  b u r s t  to  t e s t s .  s y n c h r o n i z a -  of  event  f a r  was  r e q u i r e d  b u r s t i n g  bursts  w h i l e  hologram  f l o w .  at  gave  p r e l i m i n a r y  the  as  e x p e r i m e n t s ,  exposure  second  f r o z e n  technique  done  the  recorded  Subsequently, were  a  the  the  a  a c t u a l  some  exposure  during  study,  in  the  that  v i s u a l i z a t i o n  nature  r e a l - t i m e  second  so  during  i n t e r f e r o g r a m  of  d e t e c t i n g  random  of  a f t e r  exposure  event  way  u t i l i t y  abandoned  f i r s t  burst  was  marginal  s y n c h r o n i z a t i o n ,  made u*  i t s  i n f o r m a t i o n  r e d u c i n g  streak  and  h o l o g r a p h i c  i n  hence  the  the  form  experimental burst  the  of  c o m p l e x i t y .  o b s e r v a t i o n s  i n t e r f e r o m e t r y .  are  presented  in  the  and  S t r u c t u r e  Measurement  The  f o l l o w i n g  s e c t i o n s .  5.3  V i s u a l the  Observations  Mall  Layer  D e t a i l s the  s t r e a k y  in  of  s t r u c t u r e  the and  flow ( i i )  s t r u c t u r e the  are  b u r s t i n g  presented  as  phenomenon.  (i)  108  5.3.1  The A  s t r u c t u r e and in  d e t a i l e d  i s  given  d r a g - r e d u c i n g Table  shows  3.1  the  with  dye  water  (b)  and  w a l l  to  This  in  are  (a)  of  f r i n g e  or  a  i s  the  the by  1.  with  flow  wall  with  i n  made  with  the to  Figure at The  frame  5.7.  b a s e l i n e  of  t h i s  c o r r e l a t i o n (c).  peak  of  mean  Frames  edge  'A'. of  the  the streak  the  kind  The  a n a l y s i s  'A',  shown  index  the  superimposed  s t a t i o n  e i t h e r  i s  three  shown.  lower  of  a  f r i n g e  in  f r i n g e  d i s t a n c e  the  c o r r e l a t i o n  mm  s h i f t ,  t r a c e i s  the Trace  s h i f t .  Rc(?)  from  20  m i c r o d e n s i t o -  g r a d i e n t s .  The  shown  l o c a t e d  t r a c e  c o e f f i c i e n t  6  5.3  the  determine  D)  about  at  s t a t i o n  u s i n g  to  c o n d i t i o n .  instantaneous  r e f r a c t i v e  t r a c e  p o s i t i v e  were  1  r e a l - t i m e of  c o n d i t i o n s  (Appendix  f l u c t u a t i o n s p a t i a l  enhancer'  water  v i s u a l i z e d  p a t t e r n  i n t e r f e r o g r a m ,  f i l m  no  p i c t u r e s  a n a l y s i s  s l o t .  The  motion  0,  in  as  shows  f r i n g e  in  F i g u r e  s t r e a k s  flow  s t r e a k y  Runs  5.6  no  measurements  5.7.  shown  =  d e s c r i b e d  p r o j e c t i o n  the  x  The  movie  flow  f i r s t  =  t y p i c a l  of  spanwise  the  z  s h i f t  The  to  ' f l o w  r e p r e s e n t s  5 . 6 ,  shows  i s  the  here.  Figure  the  Rc(5)  (b)  frame  shows  of  Figure at  (a)  the  l a y e r  s e c t i o n .  w a l l - l a y e r  from  wall  Measurements  t h i s  p a t t e r n s .  Frame  the  presented  of  Measurements  downstream  meter  b a s i s  the  f r i n g e  from  are  at  in  Figure  read  the  of  1 . 5 . 1 .  samples  denoting  uses  Chapter  picked  at  (d)  spacing  i n  f r i n g e  l o c a t i o n  frame  d e s c r i p t i o n  c h a r a c t e r i s t i c  f l o w s .  the  S t r u c t u r e  s o l u t i o n  form  i n t e r f e r o g r a m s  on  Streaky  the  for  t h i s  o r i g i n  f u n c t i o n  1  $, E £  J  109  Flowjx]  No gradients  (a)  Re= 6550 r 1.52 cm/s  Re = 10900 : 2.45 cm/s  «  •• • • • *" J* J* A\  : 3.25 cm/s  > * *1 % t X &"v i % 4* "ll  >£ >  Re = 14500  3f* *f * 3 K - 'f^- <*£ '^r" J: " *'  v "  (d)  Figure  5 . 6 .  Real time flow i n t e r f e r o g r a m s of showing the formation of s t r e a k s wall . [ " " • » approximate l o c a t i o n s t r e a k s . Z+ = I 00 b e t w e e n  water at the  flows pine H  H  of low-speed s c a l e m a r k i n g s . ]  1 1 0  1 -)  5 1  1  10 1  1  1  1  1  1  1  15 1  1  1  1  25  20  1  1  1  1  1  1  1  1  1  H  (a) + 1.0+ s  no-grad. fringe position—»  o  +1.0 -  (b)  1.0f  +  1  0  \*—k  f  25  -1.04-  cm/s]  Az=  run 0.583mm  Z" 190  95  380  285  H  - I — i — i — i — i — | — i — i — i — i — | — i — i — i — i — i — i — i — i — i —  0  5 Figure  5.7.  10  Spanwise A n a l y s i s streak  of  Width a  t y p i c a l  s p a c i n g  15  1  20  -jAz  i n t e r f e r o g r a m  for  X.  (a)  instantaneous  (b)  f l u c t u a t i o n  (c)  s p a t i a l  f r i n g e  about  the  c o r r e l a t i o n  s h i f t  S  mean  s  c o e f f i c i e n t  R^($)  h  Ill  gives t i o n to  a a  measure l a r g e  a r r i v e  is  due  f i l m  of  at  a  X  It  i s  an  to  the  provides  as  a  used  Separan to  (d)  o b t a i n  s t r e a k The u * . to  i n  have  a  of  only  the  are  f o r  the  c o n s t a n t  Figure  5 . 8 ) .  the  frames  i n  The  Figure  s c a l e s 5.6  are  a p p r o x i m a t e l y  arrows  l e f t  the  the  low-speed  t h i s  s i d e  s t r e a k s .  one  s t r e a k s  s p a t i a l  or  set  i s  of  more  c o r r e l a -  d e t e r m i n i n g  frame  spacing in  the  then  t r e a t e d  samples  i s  X  measurements  Table  s e l e c t e d  flows  f o r  of  any  This  o b t a i n e d .  20  the  frame.  i n  i s  a  mean.  been  corresponding on  and  c o n s t i t u t e  data  Each  at  the  the on  the  marked to  100  i n d i c a t e  f o r  Frames  (b)  i l l u s t r a t e  the  u*  v a l u e s .  with  an  i n c r e a s e  spacing  flows  r i g h t at  i n  three  streak water  5 . 2 .  to  decreases  non-dimensional value  from  l e a s t  method  frame.  spacing  e x t r a c t e d  s t r e a k s  Thus,  summarized have  c o n d i -  used  not  7  at  frame.  streak  water  streak  and  of  X  s h i f t  mean,  p o p u l a t i o n  flow  was  p a r t i c u l a r  to  f r i n g e  given  5.6  that 3  any  frames)  that does  o b j e c t i v e  r e s u l t s  p a t t e r n s  a  for  s t a t i s t i c a l  Figure  However,  method  each  a  a  water  p h y s i c a l  frame  For  5 . 2 ) .  note  each  an  for  from  and  in  only  spacing  The  to  X .  (40-50  (Table  s t a t i s t i c a l  a v a i l a b l e  sample to  f o r  s p a c i n g  v a l u e s  value  which  adequate  t i o n  X  presence  from  be  streak  important  s t a t i s t i c a l  must  streak  mean  peaks  frame  For  the  sample  c o r r e l a t i o n r i g o r o u s  of  (see  hand  X  +  Table  i n t e r v a l s  of  each  and  approximate  appears  s i d e s  flow  i n  5.2  of X  +  l o c a t i o n s  the of  Table Low-speed  Streak  Spacing AP30  Run  F l u i d  No .  DR .  %  Shear u*  V e l o c i t y cm/s  Data  S o l u t i o n  5 . 2  f o r in  Water Pipe  Phys ic a l s treak s p a c i n g , X ,  and  50  wppm  Separan  Flow  Non-dimensional  R e l a t i v e  streak  I n t e n s i t y  spacing  cm  l  c  Wis  0  1 .52  0.58  88  0.428  W2s  0  2.45  0.32  79  0 .429  W3s  0  3.25  0.29  9 3  0.432  Sis  20  2.18  0.75  114  0.404  S2s  32  2 .56  0.96  170  0.400  S3s  44  3.45  0.98  235  0.362  WATER (Newton i an )  SEPARAN AP30  -  s o l u t i o n  (Dragreducing)  113  O  Water  © Separan  200  h-  A  100 .O.  U  I  o l  0 Figure  1 5 . 8 .  P h y s i c a l spacing AP30  cm/s  #  (A) in  and  water  s o l u t i o n .  n o n - d i m e n s i o n a l and  d r a g - r e d u c i n g  (A  )  streak  Separan  114  While  the  non-dimensional shows  an  streak  i n c r e a s i n g A l l  these  u * ,  the  data  i n  X+  w h i l e  of  d r a g - r e d u c i n g that  the  i n c r e a s i n g  wall  s h e a r ,  The  l i m i t i n g  from  these  z a t i o n rate The  decrease  r e s u l t  is The  water  flow  dramatic F). at  when  almost  same 2A  1A  and  frames  IB  to  p a t t e r n s . elapsed were those  from  s e l e c t e d of  IE  The  of  which  are and  to  Separan.  X  changes  2B  s t a r t  to  seen  S3s  of  X  r e d u c e r .  not  by  the  2.1.  of  +  water W3s  i n  and  Separan  +  The w i t h  a v a i l a b l e flow In  v i s u a l i -  water,  w a l l  the  shear.  87.  i n  the  n e a r - w a l l  reducer  are  ( s c e n a r i o , flow  enhanced frames  in  r a t h e r Appendix  patterns  Table  water  a p p r o x i m a t e l y  X  l i n e a r l y .  p a t t e r n s  g r a d i e n t  the  X  known.  are  drag  f r i n g e  the  with  drag  almost  occur  and  The  decreases  p i c u t r e s  f i l m i n g ;  correspond  not  X  +  of  i n c r e a s i n g  the  and  are on  X  mean  of  Separan  2E  of  with  motion  runs  are  Chapter  t h a t  the  trend  l i m i t e d  i n  s h e a r .  5 . 8 .  and  are  n o - g r a d i e n t  numbers  the  of  c o n s t a n t  s o l u t i o n  s m a l l e r  i n  i n c r e a s e s  c o n s t a n t  the  u * ;  happens  i n c r e a s e +  almost  wall  becomes  s o l u t i o n  X  an  polymer  i n c r e a s i n g  a d d i t i o n  in  the  Figure  decreases  compares  the  Frames  X  the  seen  5.9  the  almost  to  in  o u t l i n e d  p h y s i c a l  due  Figure  of  an  r e v e r s e  values  c o n s i d e r a t i o n s  of  in  w h i l e  experiments  ,  water  rate  maximum  +  X  Separan  shows  X  have  i n c r e a s i n g  shown  l i m i t s  flows  with  the  are  water  spacing  spacing  trends The  in  streak  i n c r e a s e  p h y s i c a l  three  5 . 2 . w h i l e flow mark  time  flow  frames  time  with  115  Figure  5 . 9 .  Real  time  v a r i a t i o n p i p e wal1 (1) (2)  flow in in  interferograms  spanwise  Separan,  u*  =  3.43  water,  u*  =  3.25  [The  s p a t i a l  s c a l e  showing  c o n c e n t r a t i o n  the  at  the  cm/s cm/s is  same  as  for  Figure  5 . 6 . ]  116  A wall  flow  s c a l e  of  n o t i c e a b l e  s t r u c t u r e the to  to  Frames  show  the  the  water 1C  This  motion  p i c t u r e  i s  whether  same  flow  c h a r a c t e r i s t i c  the  drag  streaks  was  in the  water  with  an  was  The of  in  5.10.  mean taken  I  c  at  and  at  near-  d i s t r i b u t i o n  with  2C  and  p e r s i s t i n g  over  a  e a s i l y  the  spanwise  compared  X  and  2B  2D,  longer  observed  when  time the  s t r e a k s  spanwise than  Reynolds  a l l  rare  and  became  of  drag  of  p e r s i s t e n c e  In  i n  a d d i t i o n ,  the of  the  O c c a s i o n a l l y ,  flow  2E  the  The  waving  water.  and  flow  t i m e s .  g r e a t e r  Separan  number,  s t r e a k  ' f l a g - l i k e ' in  are  v e l o c i t y .  IE  the  Separan  g r e a t e r  was  r e l a t i v e l y  Each  the  of  the  and  f r i c t i o n  at  frames  spanwise  same  n o t i c e a b l e  frames,  i n  water  the  and  reduced  i n  of  same  i n  the  e f f e c t  i n t e n s i t y Figure  extent  as  i n c r e a s e  frames  the  ID  flows  the  was  movie  flow  occurrence  or  markedly  i n d i v i d u a l  in  to  more  compared  reducer  s o l u t i o n  i n c r e a s e  on  IB  when  i s  reducer  c o n c e n t r a t i o n  Separan  i n c r e a s e  Separan  an  drag  viewed.  rate  l o n g i t u d i n a l  as  the  (compare  ID,  w a l l - l a y e r  d i f f e r e n t  the  flow  in  of  l i k e  p e r s i s t e n c e  The  mass  seen  and  s t r u c t u r e  span.  in  i s  ' s a w - t o o t h '  compared 2D).  e f f e c t  appears  Figure even  l i k e  5 . 9 . l e s s  This frequent  r a t e . r e d u c t i o n  c o n c e n t r a t i o n on  Figure  sample  of  40  from  a  t h a t  flow  c o n d i t i o n .  The  the  r e l a t i v e  f l u c t u a t i o n  p o i n t  value  on  to  5.10 50  i s  r e p r e s e n t s  flow  v i s u a l  I  shown a  i n t e r f e r o g r a m s  o b s e r v a t i o n s  are  F i g u r e  5.10  The e f f e c t of drag r e d u c t i o n on the i n t e n s i t y of spanwise c o n c e n t r a t i o n a t i o n . water:  Separan;  I  ^ c  r e l a t i v e f l u c t u 2  / C ]  118  q u a n t i f i e d reduced  as  a  d r a g .  reducing  small I  but  d e f i n i t e  ranges  s o l u t i o n  from  flows  and  The  small  percentage  able  the  l a r g e  percentages  40%  to  r e s p e c t i v e l y  5 . 3 . 2  The  for  i n v o l v e the of  the  wall  b u r s t i n g  comprising side  was  recorded  e r r o r E  and  view  burst  ranges  7  of on  to the  r a t h e r  i n d i v i d u a l the  drag  with  the  i n  the  I  i s  drag water  not  r e d u c t i o n  compar-  (15%  v s .  to  the  sequence  12  in  w a l l - l a y e r p i c t u r e s  A  to  D e t a i l s of  d e t a i l e d The  3.1,  i s  flow  as  data  are  in  burst  f i l m i n g  from  d e s c r i p t i o n  data  shown  t h a t  f l u i d  on  d e t a i l e d  o b t a i n of  events  enhanced  1 . 5 . 1 .  Table  l i s t i n g  index  f l o w .  Chapter  of  i n  b u r s t i n g , Table  Figure counts  2.3 and  c o n d i t i o n s ,  given  i n  Appendices  F.  The the  in  I  B u r s t i n g  bulk  s t r u c t u r e . a  of  i n  0.43  r e d u c t i o n  i n  motion  and  0.40  about  r e f r a c t i v e  the  Physical  by  of  given  runs  The  observe  into  i s  of  r e f e r s  e j e c t i o n  l a y e r  to  of  S3).  Nature  B u r s t i n g  0.36  i s  f l o w s .  r e d u c t i o n  t e r i s t i c s  d e s c r i p t i o n l a r g e  bursts  b u r s t i n g i s  Structure  of of  b u r s t i n g  v a r i a t i o n s  and  the  Bursts  i n  c h a o t i c  p r o c e s s .  A  attempted  with  s i z e  made  and  motions  d e s c r i p t i o n the  i s  a i d  of of  d i f f i c u l t  i n t e n s i t y a s s o c i a t e d  the  general  frames  from  of with c h a r a c the  5.4.  Burst  Period  T  R  and  Run No .  F l u i d  Streak  DR %  Shear  L i f e t i m e  V e l o c i t y u*  T~  f o r  Table  5 . 3  Water  and  Burst F  Rate  cm/s  b u r s t s / c m . s  4.2  50  wppm  Time between b u r s t s , Tg s / b u r s t  Separan  AP30  S o l u t i o n  Non-dimensional burst T  =  in  Streak  Pipe  L i f e t i m e  time T  B  u * / v  from R  c  ( T )  0.41  95.  0.300  22.  0.14  84.  0.098  3.25  45.  0.077  81 .  0.128  20  2.18  10.  0.13  43.  0 . 31'3  S2b  32  2.56  0.21  96.  0.285  S3b  44  3.45  0.057  47.  0.255  Wlb  0  1.52  W2b  0  2.45  W3b  0  Sib  Water (Newton i an) v  =  0.010  cm2/s  Separan AP30 50 wppm s o l u t i o n (drag reducer) v = 0.014 cm2/s  5.1  18.  Flow  120  motion  p i c u t r e s  5.11.  The  into  (i)  ( i i i ) t h i s  and  three  streak  breakup,  stages l i f t u p ,  by  three  There  s e r i e s at  flow  et  s k e t c h e s ,  b u r s t i n g ,  as  b r o a d l y  o s c i l l a t o r y (1967),  al.  i s  no  sharp  shown  Figure  c l a s s i f i e d  motion  are  in  and  r e t a i n e d  demarcation  to  ease  between  s t a g e s .  A water  of ( i i )  K l i n e  d e s c r i p t i o n .  these  s i m p l i f i e d  u n d i s t u r b e d  u*  of  =  c o n s e c u t i v e  2.45  f r i n g e  cm/s  p a t t e r n  i s  i s  frames  shown  shown  of  in  in  bursting  Figure  in  a  5.11.  f r a m e - ( O ) .  The The  * p i c t u r e s  are  r e f e r e n c e speed  v e r t i c a l l y  shown  streak  arrows  in  sketches stream  the  with  of  the  that  the  wise  d i s t a n c e .  the  a  way  in  with  e j e c t e d  off  and  motion of  seen i s the  r e g i o n  The  i n  seen  the f l u i d  from  the  the  as  i t  w a l l .  i n  (2)  and  seen 150  the  down-  An  f u r t h e r  frames  The  moves  and  a m p l i f i -  (3).  The  to  have  grown  r a p i d l y  a  very  short  stream-  in  l i f t e d - u p  Frame-(5)  complete with  c o r r e s p o n d i n g  element  w a l l .  low-  the  *  f r a m e - ( 4 ) .  a  and  to  of  p i c t u r e ,  f r a m e - ( l )  +  of  pipe  i s  breakup  frame  the  burst y  t h i s  a  from  f l u i d  outward  provide In  p i c t u r e s  d i s c r e t e  i s  to  s k e t c h - ( O ) .  l i f t i n g  flow  n e a r - w a l l  a s s o c i a t e d of  to  extent  from  under  j u s t  motion  w a l l - n o r m a l  is  the  subsequent  point  o s c i l l a t o r y c a t i o n  i s  by  i n v e r t e d  shows  f l u i d the  element  f i n e  breakup  and  v i o l e n t  outer  f l o w .  The  s c a l e s  mixing  d i s t o r t i o n  —  o r i g i n a l present y-ax i s .  V e r t i c a l i n v e r s i o n gives a m i r r o r image of the p i c t u r e . There i s no c h a n g e in the i n f o r m a t i o n but only a r e o r i e n t a t i o n in the d i r e c t i o n of the  of  Figure  5.11.  B u r s t i n g  sequence  in  a  water  f l o w .  (u* = 2.45 cm/s; y+ at 100 0.40 cm S i n d i c a t e s the l o c a t i o n of the wall s l o t . ) At = .016 s  122  the  f r i n g e s  b u r s t  shows  s t r u c t u r e  a s s i g n  a  motions  250.  i s  not  p o s s i b l e  to  s i n c e  the  p i c t u r e s  are  a  d i r e c t i o n  to  the  an  the  f i n e s t  the  l a s e r  and  the  i n t e g r a t i n g  s t r e t c h e d  scales l i g h t  't'  i n  are  and  b u r s t i n g  away  of  process  t r a v e r s i n g  the  spanwise  by  5 . 2 . 3 ) . from  The  mean  e f f e c t  beam in  (5).  the  It  v o r t i c e s  obscured  ( s e c t i o n  with  =  +  o b j e c t  frame  The  y  e f f e c t  outwards  downstream  the  v o r t i c a l  to  has  on  strong  up  dimensional  marked  the  w i t h i n  the  g r a n u l a r  The  burst wall  e j e c t e d  f l u i d  A l s o ,  s p e c k l e  appears  along  a  i s  two-  s e c t i o n  d i r e c t i o n .  the  the  t e s t  the  to  of be  t r a j e c t o r y  then  convected  f l o w . the i s  d r a g - r e d u c i n g shown  in  the  polymer  frames  a d d i t i v e  of  Figure  * 5.12.  The  those  a l r e a d y  tory  growth  (2),  and  't' of  along  the  s c a l e  e j e c t e d  burst  of  a  the  f l u i d  However,  l i n e A  scales  d e s c r i b e d  (3)].  water.  small  s p a t i a l  more  reduced  f l u i d  i s  for  sketch  Figure  element the  as  absence  to  markings  5.11.  f l u i d  p a r a l l e l  n o t i c e a b l e and  and  i t  There bursts  element the  of  w a l l - n o r m a l  c h a r a c t e r i s t i c  the  conform  wall  i s  an  [frames  has  a  than  h i g h l y  to o s c i l l a (1),  t r a j e c t o r y in  the  case  v o r t i c a l  extent  (y  of  d r a g - r e d u c i n g  the  +  =-  100)  of  s t r u c t u r e .  While the p i c t u r e s in Figure 5-11 were taken from B/W Kodak 7224-4X n e g a t i v e f i l m and p r i n t e d on F-5 paper, the p i c t u r e s in Figure 5.12 were taken from c o l o u r p o s i t i v e Ektachrome EF7241 and p r i n t e d on Kodak Panalure paper. Thus, there is a r e v e r s a l in zone c o l o u r a t i o n and some loss of c o n t r a s t in Figure 5-12 when compared with Figure 5-11. However the general burst f e a t u r e s being d e s c r i b e d are not a f f e c t e d .  Figure  5.12.  B u r s t i n g Separan  sequence f l o w .  in  a  d r a g - r e d u c i n g  (u* = 2.56 cm/s; y+ at 100 = 0.55 cm. S i n d i c a t e s the l o c a t i o n of the waI I s l o t . ) At=  .016 s  124  Figure  5.13.  Streak l i f t - u p and b u r s t i n g near- • i n f i n i t e f r i n g e s and an v i ew  (a)  Newtonian  (b)  d r a g - r e d u c i n g  flow flow  as  seen  with  o b l i q u e  wall  125  Figure i n f i n i t e  f r i n g e  a v a i l a b l e  as  5.13  s p a c i n g .  i n  Figure  appearance  of  of  5.13(a)  Figures  r e s p e c t i v e l y d i m i n i s h e d f l u i d the  the  elements.  d e t a i l  and  out  to  a  b u r s t  break i s  i s  f o r  shown  but  the  into i n  view the  the  a t  and  drag  neari s  not  f i n g e r - l i k e Comparison  drag  r e d u c e r  reducer  f i n g e r - l i k e  the  a  b u r s t  n o t i c e a b l e .  water  i n  up  wall  w i t h i n  5 . 1 2 ,  burst  5.13(b)  that  This  The  o b l i q u e  sketches  has  a  e j e c t e d accompanying  photographs.  only  the  f l o w s .  p i c t u r e s  general  a  general to  obtained s e c t i o n number  by  i n  may  attempted  water  and  to  show  d r a g - r e d u c i n g  vary  q u i t e  s u b s t a n t i a l l y  making  b u r s t  c h a r a c t e r i s t i c s  Sublayer  i s  of  s e c t i o n s shown  i n  Frequency  from  counting  number  bursts  Figure per  5.14  second  2,  Table  and  4,:  of and  bursts 5 ,  are  and d e s c r i b e d  5 . 3  Period  of of  shows per  Period  p e r i o d  4 . 4 :  measure  the  Flow  the  q u a n t i t a t i v e  4 . 4 . 4 . of  the  i n  Burst  A  b u r s t i n g  measurements  data  5.4.1  of  events  of  d e f i n e d  The  have  q u a n t i f y .  The  here.  sketches  d e s c r i p t i o n ,  Measurements  s t r e a k s ,  and  f e a t u r e s  I n d i v i d u a l  d i f f i c u l t  5.4  and  tendency  an  5.11  drawn  shows  These  such  shows  cm  burst bursts  the  frequency as  burst  spanwise  was  d e t a i l e d rate  F;  marking  i n  the w i d t h ,  126  0 2  5  1 U*  igure  5.15.  Time and  i n t e r v a l  cm/s  between  d r a g - r e d u c i n g  10  b u r s t s  Separan  (  in e  )  water f l o w s .  (  O  )  128  as  a  f u n c t i o n  f l o w s . F  The  u * .  a  of  water  burst  rate  i n  water  u *  i s  Separan  Newtonian between  shown  l i n e  equal  t i o n  from  s e c t i o n  when  view r u n s ,  Separan  the as  l a r g e  r e d u c t i o n  compared  to  that  from  2  ) ,  the  The  Tg  that  d r a g - r e d u c i n g i s  f o r  b u r s t s  both  water  z e r o - p r e s s u r e - g r a d i e n t  i n d i c a t i n g  and  between  made  at  the  time  flows  equal  i n t e r v a l  may  wall  be shear.  L i f e t i m e  be  i n t e r p r e t e d  as  et  al.,  1967).  A  estimate  the  of  s t r e a k  view  of  of  average  more  l i f e t i m e  a u t o c o r r e l a t i o n s  plan  the  l i f e t i m e  d i r e c t  T<.  was  and  obtained  c o n c e n t r a t i o n  w a l l - l a y e r  s t r e a k s  F-Xi n  f l u c t u a -  ( d e t a i l s  i n  4 . 4 . 2 ) .  at  a  W2s  5.17(a)  and  point  along  s i n g l e  [ F i g u r e  p i c t u r e  i s  i n t e r v a l  5 . 1 5 .  comparison  might  Figure taken  and  p r o p o r t i o n a l i t y ,  flows  time  about  water  ( K l i n e  independent study  i n  of  Figure  u *  a  Streak  streak  t h i s  i n  (Tg  b u r s t s  Tg a  water  the  f e a t u r e  Separan  c o r r e l a t i o n  d i s t r i b u t e  5 . 4 . 2  of  the  f o r  f l o w s . The  almost  approximates  n o t i c e a b l e  in  and  data  v e l o c i t y  most  the  and  shear  The  of  Tg  wall  5 . 1 6 ( a ) ]  and  frames  S 2 s . (20s  r  f o r c  of  ( T )  (b)  each w  a  s  motion  the of  show  a u t o c o r r e l a t i o n s  m i d - l i n e the  water  determined p i c t u r e  of  at  and  from 60  the  w a l l  plan  Separan  1200  motion  f r a m e s / s ) .  129  The  t o t a l  f i l m i n g  d i f f e r e n t  (a)  time  v a r i e d  between  70  and  point  on  the  mid-  (b)  four  I i ne  the  5.16.  Wall  l a y e r  determine (a s t r e a k eIement)  To l a y e r ,  the  time  R  determine  ( T )  from  for  each  t r a c e s  of are  l o c a t i o n s the s t r e a k r e p r e s e n t s  T^  a u t o c o r r e l a t i o n s  5 . 1 6 ( b ) ]  f o r  the  r u n s .  s i n g l e  F i g u r e  90s  the  f o r  made  runs  shown  in  The  streak  l i f e t i m e  the  o r i g i n  to  the  at  Wis,  f i r s t  was  a c r o s s  a u t o c o r r e l a t i o n s  a c r o s s  four  S i s ,  Figures T<.  p o i n t s  l i f e t i m e , l o w o_r h i g h - s p e e d  d i s t r i b u t i o n  were  z  wa1 1  p o i n t s  W3s  5.17  and to  e s t i m a t e d  p o s i t i v e  the  to  f l u i d  w a l l [ F i g u r e  S3s.  A l l  5.19. as  maximum  the  lag  a f t e r  a  130  zero at  c r o s s i n g  u *  =  of  the  water  (b)  and  a t  u *  =  narrow  at  z - p o s i t i o n  The  (  s o l i d  l i n e  comparison  5 . 4 . 3  T<.  A l l  the  the  t h e  T<.  R  a  T<.  each  of  showing  the  that  i s i s  shown f o r  Separan  the  value  Figures  f a l l  e s t i m a t e  data  5 . 1 7 ,  times  ( T ) peaks  c  figure,  of  Figure  three  good  data  f o l l o w i n g  In  T^,  same  In  about  four  f o r  Comparison  The  t r a c e .  may g i v e  on  with  )  a  the  timeband  c o n d i t i o n .  T  2 . 4 5 c m / s .  5 . 1 9 ( a ) , ( b ) ,  r a t h e r  flow  C  2 . 5 6 c m / s shows  f o r  any  R  5 . 1 8 ( a ) ,  w i t h i n  s t r e a k s of  i n Tg  T  sampled  f o r  $  Figure d a t a ,  a  that  5 . 2 0 .  shown  f o r  p o i n t s .  T^  and  a s p e c t s  T^  a r e  r e a d i l y  seen  on  Figure  5.20  (i)  Tg  i s  T  f o r  n  a p p r o x i m a t e l y t h e  three  t h e  same  water  as  f l o w s ,  D ( i i )  Tg  in  drag  reducing  Separan  f  ow  T  p m n , i s ga r e a t e r than t h e S(DR ) c o r r e s p o n d i n g value f o r water  "'"s(N)  ( i i i )  w  ^  e  i s  f l o w ,  i . e .  has an  n  D  ,  S \ UK )  S(N)  exact  n o t  known.  ~  T  P  a  same  p e r i o d  r  e  d  u * ,  - 0 5) u# * > , •2  of B ( N )  a t  a p p r o x i -  and  approximate  ^  q u a n t i t a t i v e  e s t i m a t e s t h e  m  T . ,  The  approximate  o  t h e  T  Tg  c  mately  t i o n a l i t y  and  n  U  whereas  *  correspondence  Q u a l i t a t i v e l y , same  propor-  of  t h e  of  w a l l - l a y e r  they  q u a n t i t y flow  appear f o r  between to  be  Newtonian  d i s t u r b a n c e .  T<.  131  0.60  F i g u r e  5.17.  Autocorel1ograms f l u c t u a t i o n s i n g l e  (a)  Water,  (b)  Separan,  run  W2s,  run  S2s,  at  of the  c o n c e n t r a t i o n pipe  w a l l  at  a  l o c a t i o n . u*  = u#  2.45 =  cm/s  2.56  T =0.098 s  cm/s,  DR  =  32$.  T = 0.285s  133  Rio  T  0.15 F i g u r e  5.18(b)  0.30  0.45  0.60  s  A u t o c o r r e l o g r a m s of c o n c e n t r a t i o n t i o n at four w a l l l o c a t i o n s . Separan,  run  S i s ,  U*  =  2.18  cm/s,  f l u c t u a -  DR  =  20%  T = 0.3l3s  134  V  0  1  1  V  o  FL(T)  3  0  V J  1  1  0.15 F i g u r e  5 . 1 9 ( a ) .  T  i  0.30  0.45  S  Autocorrelograms of c o n c e n t r a t i o n t i o n at f o u r w a l l l o c a t i o n s . Water,  run  W3s,  u*  =  3.25  0.60 f l u c t u a  c m / s . 7 = 0.128  s  135  IT)  h  T *  0.15 gure  5 . 1 9 ( b )  Autocorrelograms tion  at  Separan,  0.45  0 30  of  0.60  c o n c e n t r a t i o n  f o u r  wall  l o c a t i o n s .  run  S3s ,  u.  3.45  cm/s,  f l u c t u a -  DR  =  44$,  T =0.255 s  Figure  5.20.  Streak  l i f e t i m e  d r a g - r e d u c i n g  in  water  Separan  (  ( A  A )  )  and  f l o w s .  137  Some Tg  e x p l a n a t i o n s  data  as  seen  are  on  Figures  Scanning analogous f l o w ; a  to  streak  to  for  at  d e t e c t  the  estimate  i s  assumed  the  "*"B"  period  (b)  e f f e c t i v e  were  streak ^  E  C  the  three  water  for  these  water  that  the  spanwise  is  l a r g e r  '  zone) a  i s  1  "runs  the  than  the  N  T  the  time  scanning  for  which  point  that  can  point  T<~  in  i s  the  as  decrease  in  T<,  shows  T<~  <  5.3).  below  the  water  cases  of  the  d r a g - r e d u c i n g  y  a  f  a  c  t  o  r  ° f  flows  I-  i  5  to  i s  the equal  tend c  to  ( T ) ,  for  g i v i n g  two  and  This  may  value  of  T<» i n d i c a t e due  s m a l l . r u n s ,  3.  /  of  Tg  Tg  the  R  Tg  between  c o r r e c t  almost  from  in  ^  a  and  would  waving  $(N)  be  (a)]  detected  (Table  i s  f l o w s ,  would  d i f f e r e n c e  small  Tg  d e t e r m i n a t i o n  [reason  5.20  U R E  .The  computed  estimate  T^  line  low-speed wall and  Newtonian  waving  "19  R  runs.  streak  in  i s  c o n t i n u o u s l y  passing  the  i n  l i f e t i m e  A T A  apparent  In  that  sublayer  However,  and  point  point  l e n g t h , of  if that s t r e a k , being a zone, l i f t s up f r o m the d i sa ppea r s .  of  s i n g l e  that  the  However,  a  (b)  streak  <  at  if that streak waves out of with the sampling point or  i t  T<-  5.20.  at  streak  of  reasons:  to  S  then  particular  then  T  probe  i s  p o i n t .  a u t o c o r r e l a t i o n ,  reduce  and  trends  (a)  reason  Tg.  the  high-speed  or  f o l l o w i n g  If  only  a  5.15  s i n g l e  l i f e t i m e '  that  for  interferograms  a  (low-speed  d e t e c t a b l e f a i l  the  having  'Streak  provided  This  s  (DR) trend  to  138  is  c o n s i s t e n t  streak water  with  p e r s i s t e n c e flow  at  the  motion  p i c t u r e s  streak  waving  data  p o i n t s  showing trend  -0 u*  for  o b s e r v a t i o n s  which  i n  drag  as  of  An  d r a g - r e d u c i n g in  d r a g - r e d u c i n g  appear drag  with  v i s c o s i t y  j o i n e d  than  by  a  with  from  the  i n d i c a t e  f l o w s .  T  l e s s e r  $(DR)  dotted  i s  only and  the  the  streak  e x h i b i t 0  which  to  l i n e  a  d i f f e r e n t  S u b l a y e r  s e c t i o n  p a t t e r n s that  5 t a b i l i t y  1.44  the  cP. a  the The  ^QRM^;  the  i s  many z e r o -  w a l l - l a y e r  l i f e t i m e  may  with  s o l u t i o n  observed  reducer  the  compared  s o l u t i o n  longer  This  5 . 3 . 1 ,  when  although  have  drag  form,  s t r e a k s  i n  the  ' i n c r e a s e d be  r a t i o  accounted of  the  f o r  non-  s p a c i n g s .  r a t i o n a l e  f o l l o w s .  compared  Increased  water;  i n  of  as  appearance  e f f e c t '  v  a l s o  water  e a r l i e r  flow  water.  as  can  an  in  The  t i o n s  the  s t a b i l i z e d  f a c t o r  i s  are  for  than  dimensional  term  from  v i s c o s i t y  reducer  a  of  compared  i m p r e s s i o n s  flows  g r e a t e r  Reduction  w a l l - l a y e r  give  more  v i s c o s i t y  5.20  Drag  v i s c o u s  s h e a r - r a t e  case  Explanation  R e c a l l i n g  more  the  Figure  During  times  V i s u a l  p r o p o r t i o n a l i t y , - 2 « u* .  5 . 4 . 4  flows  u * .  reducer  show  5  Tg  water  the  same  than  in  v i s u a l  It  i n  forming  is  known  t h i s  that  v i s c o s i t y  d i l u t e  e f f e c t  polymer  s o l u -  stretch-rate-dependent.elDngational is  l a r g e r  than  the  v i s c o m e t r i c a l l y  139  measured  v i s c o s i t y  v  f l u i d  subjected  to  in  i s  the  1.5),  formation the  t i o n s ,  s o l u t i o n  i . e .  *  t i o n .  the  the  were  increased  measure  of  w a l l - l a y e r may  i n  v  may  be  streaks i n  z - d i r e c t i o n  x  and the  s i n c e  was  used  drag  Newtonian  a v a i l a b l e .  Thus,  present (Chapter d i r e c -  streak  formaf o r  A U * / V )  was  r e d u c t i o n  constant  those  the  s t r e t c h i n g  + ^[)R(=  v  When  bursts  during of  0  -»- 0 .  l i k e  c a l c u l a t i o n  during the  as  a c t i o n s  e x h i b i t  the  X^ to  s o l u t i o n  s t r e t c h i n g  s o l u t i o n ,  normalized  the  spanwise  However,  d r a g - r e d u c i n g If  of  of  0  unknown.  (Figure value  the  the  5.8) a  Ajj,  r a t i o  B 36  *DR v  e £  ^  may  N  / X  n  t  ^  give  d r a g - r e d u c i n g  i e  s h e a r - r a t e  s o l u t i o n Table  and the in u*  ApR/XjJj streak the drag  u  5.4  measure  of  flow  greater  i s  the  v i s c o s i t y  v  shows  r a t i o s ,  They  reducer  Newtonian  Table  .  5.4  l i f e t i m e  The of  some  are  and i s  the  0  than  T  S ( D R )  the  which  the  over  the  / T  zero-  S ( N )  f a c t o r  non-dimensional  increased  by  -  r e s p e c t i v e l y  the  f a c t o r  streak  by  which  spacing  corresponding  v a l u e . almost  equal  i n d i c a t e  the  values  i n  the  l a s t  two  columns  r e l a t i o n s h i p  A more d e t a i l e d d e s c r i p t i o n of s t r e t c h i n g motions at the wall and the e f f e c t s of s o l u t i o n e l o n g a t i o n a l v i s c o s i t y is given in Chapter 6 . 2 from the point of view of a drag reduction mechanism.  140  Table Ratios  Streak  l i f e t i m e ,  sStrea k  T  of  S(DR)  L i f e t i m e  DR  line 5.20  114  0.285  0.1 50  170  0.255-  0.080  235  2 3  3  Streak  Spacing  Streak spacing non-dimensional  s  0.20  0.31  and  S(N)  T  from on Fig. 1  5.4  constant mean =  87  T  S(DR)  T  S(N)  • DR X+  1 .6  1.3  1 .9  1.9  3.2  2.7  DR T  at  u *  (  D  R  -  )  u *  This points  that  l i n e  p o l a t e d u*  -  shows 1.7  an  )  to  c m / s .  r e s u l t an  i s  a s i d e ,  the  T  D  R  on  i s j  Figure  c m / s .  The  dotted onset  5.2 of  a  of  l i m i t e d about  i n t e r e s t i n g  p o i n t s  T^-Newtonian  'onset'  s i m i l a r  (5.2)  S(N)  range  i t  5 (  the  a  based  e r r o r  that  gives  T  .  j o i n i n g  back  1.7  N  have  As dotted  (  S(DR)  f o r drag  l i n e  f o r  u * .  It  i n  mean.  to  that  the  note 5 . 2 0 ,  s o l u t i o n  r e d u c t i o n  occurs  F  on  <r u ] . - ^  5  data  the  i n t e r s e c t s  Separan  appears  of  ±15% of  Figure  l i n e ,  s e t  from  when i t  extraat  gross  flow  at  -  Figure Figures  u *  5.14 5.14  and  141  5.20  that  for  g r a d u a l l y v a t i o n s a  the  from  d r a g - r e d u c i n g  the  Newtonian  f l o w ,  l i n e  suggest  that  the  burst  d r a g - r e d u c i n g  flow  may  f o l l o w  laws  with  u*  5.5  Summary  than  of  they  would  W a l l - l a y e r  F  a f t e r  rate  and  a  and  (  D  )  R  depart  These  streak  o b s e r -  l i f e t i m e  i n  p r o p o r t i o n a l i t y  Newtonian  S t r u c t u r e  S  o n s e t .  d i f f e r e n t  i n  T  f l o w .  Changes  During  Drag  Reduction The 50  wppm  water  e f f e c t s  Separan  are  AP30,  The  %  drag  (DR  =  w a l l - l a y e r  d r a g - r e d u c i n g  The  water  flows  p h y s i c a l  ( i i i )  ( F i g u r e  a  The  f l u c t u a t i o n  u * .  with  flow  a d d i t i v e ,  s t r u c t u r e  i n c r e a s e d  constant  r e l a t i v e I  c  In  streak  of  i n t e n s i t y with  X  of  i n c r e a s e d  c o n t r a s t ,  almost  value  decreased  5 . 1 0 ) .  s p a c i n g  i n c r e a s i n g  non-dimensional  flows  had  s t r e a k  and  decreased  The  the  r e d u c t i o n  the  r e d u c t i o n  0)  ( i i )  t r a t i o n  on  p o l y m e r i c  Measurements (i)  water  d r a g - r e d u c i n g  S t r e a k y " S t r u c t u r e  (A)  f o r  the  summarized.  5.5.1  i n c r e a s i n g  of  u*  the  l i n e a r l y X  +  of  -  87  X  +  w i t h  ( F i g u r e  spanwise  i n c r e a s i n g  X  (Figure  s p a c i n g  %  with  5 . 8 ) .  in u * . 5 . 8 ) .  c o n c e n drag  142  (iv)  The  c o r r e l a t i o n s  of  drag  than  reducer  v i s u a l the  (B)  showed p r o f i l e  ( i i )  a x i a l l y  o r i e n t e d  a  obtained  g r e a t e r  c o r r e s p o n d i n g  u*  value  water  from in  auto-  the  v a l u e .  a  flow  wider  when  i n t e r f e r o g r a m s  s p a c i n g  compared  The  s t r e a k s  had  The  spanwise  of  the  w i t h  the  longer  of  the  d r a g -  s a w t o o t h - l i k e water  a x i a l  f l o w s .  extents  during  s t r e a k s  was  o s c i l l a t i o n reduced  by  or  the  waving  of  presence  the of  a d d i t i v e .  (iv) n o t i c e a b l y  Burst  (A)  drag  l i f e t i m e in  the  of  the  s t r e a k y  d r a g - r e d u c i n g  s t r u c t u r e  was  f l o w s .  S t r u c t u r e  Measurements (i)  during  The  i n c r e a s e d  5.522  The  r e d u c t i o n  ( i i ) from  had  T^,  r e d u c t i o n .  ( i i i )  the  d a t a ,  R e a l - t i m e  flows  c o n c e n t r a t i o n  drage  l i f e t i m e  Visualization (i)  reducing  s t r e a k  measurements  The of  b u r s t i n g  rate  (Figure  time burst  was  d r a s t i c a l l y  reduced  5 . 1 4 ) .  i n t e r v a l rate  F  and  between  bursts  p h y s i c a l  Tg,  s t r e a k  computed s p a c i n g ,  143  had  s i m i l a r  compared  values  at  the  i n  same  (B)  w i t h i n  A a  ( i i ) in  the  bursts case  of  a  reducing the  observed  f l u i d  d i r e c t i o n  t r a j e c t o r y  water  flows  when  the  strong  during  elements  during  more  in  did  drag  p a r a l l e l  drag  to  v o r t i c a l r e d u c t i o n .  not  move  as  r e d u c t i o n . the  w a l l  f a r  The  than  in  the  water.  to  to  Bursts  break  The changes  and  5 . 1 5 ) .  r e d u c t i o n  was  Ejected  ( i i i ) tendency  ( F i g u r e  marked  b u r s t  w a l l - n o r m a l had  u*  d r a g - r e d u c i n g  Visualization (i)  motions  the  the  and  to  i m p l i c a t i o n s n e a r - w a l l  a d d i t i v e  f o l l o w i n g  up  in  in  a  c h a p t e r .  the  drag  form  of  had  s m a l l - s c a l e  these  t u r b u l e n c e ,  Newtonian  reducer  f l u i d  measured caused  s o l v e n t ,  a  and by  are  a  reduced elements.  v i s u a l i z e d d r a g -  d i s c u s s e d  i n  Chapter  6  DISCUSSIONS OF RELATED EVIDENCE AND A DRAG REDUCTION MECHANISM  This the  evidence  c l o s e l y t i n e n t In  chapter  c o l l e c t e d  r e l a t e d t h e o r i e s  s e c t i o n  presents  6 . 3 ,  during  a  t h i s  experiments  of  i s  from  a  provided p o s s i b l e  c r i t i c a l  e v a l u a t i o n  study.  other  A  comparison  workers  the  and  p e r s p e c t i v e  mechanism  f o r  of  drag  with of  with per-  t h i s  work.  r e d u c t i o n  i s  d i s c u s s e d .  6.1  Related  Evidence  Table v e s t i g a t i o n s are  6.1  of  comparable  with  v i s u a l i z a t i o n  data  that of  cover the  p r o c e d u r e s . (P) are  i n  Streaks  summarizes  w a l l - l a y e r  flow  r e s u l t  on  a  t h i s  experiments range  time-consuming Many  Newtonian  only  Bursts  f i n d i n g s and  The (V)  burst  t a b l e  of  flow  have  some  l i s t e d .  144  been  of  other  i n -  s t r u c t u r e s  shows  provide  small  t h a t  and made  i l l u s t r a t i v e  data using  t h a t  the  sets  parameters;  experimental  measurements f l o w s ;  the  streak  work.  l i m i t e d  and  of  a  d i r e c t  a n a l y s i s probes  examples  Table Wall  Layer Structure  Measurements  6.1  in Zero-Pressure-Gradient  Flows  by D i f f e r e n t  Investigators  NEWTONIAN FLOW INVESTIGATORS Kline  Runstadler  2.  Schraub  3.  Kim et al. ( 1 9 6 8 )  4.  Bakewell 0967)  5.  Corino (1969)  & Brodkey  6.  Gupta, Kaplan  Laufer & [1971)  l.  TECHNIQUE  & co-workers  1.  DRAG - R E D U C I N G  FLUID  et al. (.1963)  Water  et al., 0 9 6 5 )  &  Lumley  V  Dye a n d h y d r o g e n bubble v i s u a l i z a t i o n channel flow  V V,P  FLOW  and h o t - w i r e  Re = 2 0 0 0  V F  •  cc  autocor.  Glycerine water mix.  P.  Hot-wire autocorrelations - p i p e , D = 2 8 . 4 cm  Re = 8 7 0 0  Tri chloroethylene  V  P a r t i c u l a r t r a c e r s , pipe f l o w , D = 2 . 5 4 & 5 . 0 cm  Re = ( 2 . 0 t o 5 . 5 ) * 10"  P  Hot w i r e a r r a y , v a r i a b l e time c o r r e l a t i o n s - wind tunnel  Re = 2200 6500  Array of wall-mounted e l e c t r o c h e m i c a l probes long time a u t o c o r .  Re = ( 4 t o  " , pipe flow, D = 2.54 cm instantaneous patterns  DR up t o 60%  Ai r  X+  = 100  u* = 0 . 2 5 to 1 . 0 cm/s  •I  11  CONDITIONS  90  --  to  --  t o 100 T+  = 256  --  = 95  FLOW  F o r t u n a and H a n r a t t y (1972)  Electrolyte s o l u t i on P  2.  Eckelman, Fortuna & H a n r a t t y (1972)  + 2 0 0 wppm Separan  3.  Donohue, Tiederman & Reischman (1972)  Wa t e r + 139 wppm Polyox  V  V i s u a l c o u n t s o f dye s t r e a k s & b u r s t s , 2-D c h a n n e l , D^ = 7 . 3 cm  Re = ( 1 0  10)*10"  to  DR up t o 52%  = 100 in e l e c trolyte Variable i n DR; F i g . 6.1  18)*103  •  = loo  Variable, F i g . 6.1  T  B(DR  =  at  T  B(N) same u *  146  6.1.1  Streak  The water 87  ±  75  to  flows 20  was  for f l o w .  by  and  f o r  found  and  (see  Table  5 . 8 ) .  A  The  flow  s e c t i o n  three  i n v e s t i g a t i o n s  et  al.  %  drag  in  A  1972;  t h i s  (Figure  6.1).  sets  of  p a r a m e t e r s . s u c h the  data  i n c r e a s e d  the  A  value  s i g n a l s  f l u s h  on  -  +  of  a  +  at of  A  zero  100  was  s i z e )  the  a  value  +  ranges  f i r s t  of  i s  for  three of from  p r e s s u r e o b t a i n e d  t h i s  parameters  and  the  the  to  a  an  an  A  (Re,  value  +  u * ,  well  i n c r e a s e  been  f l u i d  e s t a b l i s h e d  s h o w ;a  (Fortuna,  modest  the  to  p o l y m e r - s o l vent  spacing  a f f e c t e d  array The  of  with  an  trends Donohue  i n c r e a s e  form  type  Hanratty  +  The  l a r g e  to  of  A  1971;  appears  of  by  the  other combination  employed. (1 9 7 2 ) ,  in  who  f i r s t  d r a g - r e d u c i n g  l o n g - t i m e - a v e r a g e d  w a l l .  a  f u n c t i o n a l be  in  o b s e r v e d .  date  technique  and  streak  from  has  However,  as  from  f l o w s ,  done  work)  a n a l y s i s  the  of  A  in  u n i v e r s a l i t y  r e d u c t i o n  data  Fortuna  +  of  range  d r a g - r e d u c i n g  of  or  l a y e r s  A  6.1).  in  d i f f e r e n t  values  geometry  i n c r e a s e  +  r e p o r t e d  The a  s p a c i n g  c o n s t a n t  value  over  s t r e a k  almost  wall  mean  flow  In  ,  be  coworkers.  Newtonian  type  to  Newtonian  g r a d i e n t K l i n e  Data  non-dimensional  (Figure  120  Spacing  d i s t a n c e  f l o w ,  s p a t i a l  e l e c t r o c h e m i c a l between  hypothesized  c o r r e l a t i o n  probes  zero  obtained  mounted  c r o s s i n g s  was  * used  as  a  measure There  and  r e p o r t i n g  of  of is A  +  A / 2 . some in  However,  c o n f u s i o n  Fortuna1s  very  w i t h  (1971)  f l a t  the d a t a .  peaks  of  i n t e r p r e t a t i o n The  t h e s i s  600  500 h  400  300 h  200 h  100  r-  DR Figure  6.1.  Non-dimensional  streak  ( © ) t h i s work , ( O ) Eckelman et al. ( 1 972),  % s p a c i n q  during  Donohue a L ( Q ) Fortuna  drag  r e d u c t i o n .  (1972), ( v ) & Hanratty ( 1  _ 972).  148  the  c o r r e l a t i o n  smear  out  l a r g e s t aspect  s h o r t e r  s c a l e s has  a r r a y  of  averaging  i n c r e a s e d . no  phenomena,  thus  most  p e r s i s t e n t  s t r e a k s  a  w a l l .  Beyond  a  e s t i m a t e s  of  r e a l i s t i c .  of  record  can  of  was  be  the  dye  shown  i n  of  at  Figure  an  the  measurements  al.  (1972)  s h o r t  averaging  t i m e ,  there  X  a  'from  the  zero  Thesis  of  Donohue l a t e r of  the  et  of  et  to  report  X  +  o b t a i n  measure the  Fortuna, a Z .  an  s p a t i a l  Jnme  s p a t i a l  the  time  i s  averaging  Fortuna's  data  v a r i a t i o n s  w a l l .  These  appear (1972)  al.  of  the  new  to  be  a r e  p i c t u r e s ,  almost  or  second  how  of  motion  p r i n c i p l e  as  ordered  averaging  6 . 1 ,  et  uniform  1  the  the  Donohue  +  shown  spanwise  (1972),  reports  u s i n g  more  d i r e c t  a  frame  instantaneous  p a t t e r n .  Although  very  d e t e c t  re-examined  from  as  (1971)  This  e x i s t .  Donohue  s t r e a k s  the  d e t e c t a b l e .  al.  value  with  g r a d i e n t  to  only  to  v a r i a b l e-i_nterval  as  to  tends  making  et  have  (1972)  c o n s i d e r e d  flow  a  small  patterns  r e s u l t s  of  a i r  out  seen  al.  a l s o  ,  +  The  counts  which  smear  v e l o c i t y A  i n  they  c e r t a i n  et  eddy  instantaneous  v i s u a l  (VITA),  c o r r e l a t i o n  a s s o c i a t i n g  Gupta  Employing  g r a d u a l l y  Eckelman by  by  anemometers  technique  c o r r e l a t i o n s  l o n g - t i m e - a v e r a g i n g  demonstrated  h o t - w i r e a t  that  s c a l e  and  been  s t r u c t u r e s  time,  showed  1971)-  as  This  Figure  ' t w i c e This  the  t h i s  i . e .  X,  c o r r e l a t i o n  ( l 9 7 2 ,  c o r r e l a t i o n .  and  of  is  i s  al.  work  an  almost  no  o r i g i n  use  how  of  to 37,  that  the p.  +  is  z  +  112,  data  and  between  X  p a t t e r n s  u n i v e r s a l  Fortuna  d i s t a n c e  measure  et  instantaneous  (Figure  7)-  Eckelman  i s  a t  shown  Hanratty zero  shown  in  the  P h . D . by  (1972)  c r o s s i n g s ' Figure  6.1  149  r e l a t i o n  between  p o s s i b l y  due  a c t i o n ,  as  to  of  et  data  water  w e l l . the  An  gets  by  to  or  that the  f o r  span  may  l i e  in  l i n e  other  with  during  i n c r e a s i n g  u*  (>  c o r r e l a t i o n as  v a r i a b l e s ,  to U  b u r s t  l i n e 1.0  of  whether  proper  s i g n a l to  w i t h  s c a l e  b u r s t s ,  with  outer  peaks have  F  rate  v i s u a l  -  p o i n t .  <*  u * ,  data  p a r t i a l  1.5 The  q u i t e  p o i n t s  from  o b s c u r i n g  of  problem  that  a  of  shown  v a r i a b l e s  intended  would  et  (mean  (1971),  a s s o c i a t i n g  presents  data  the  not  the  5  Rao  and  of  cm/s)  and  F  al.  z e r o - p r e s s u r e -  burst  c o u n t i n g ,  i s  K l i n e  the  et  of  form  the  a  c o r r e l a -  u * .  e x t r a p o l a t e d higher  i n  previous  s h i f t  Tg.  i s  i n t e r -  the  t h e s i s  range  the  a t  c o r r e l a t i o n  shows  u *  This  a  h i g h e s t  c o n s t i t u t e  a i r ,  vs  f l o w .  t h i c k n e s s ) and  F  l i n e  f o r  c o n t r o v e r s y  outer  (1967)  s o l i d  e x p l a n a t i o n  e s t a b l i s h e d some  the  f u n c t i o n a l  worse  of  p o l y m e r - s o l v e n t  the  each  data  some  l a c k  f o l l o w  The t h a t  of  channel  than  e x t r a p o l a t e d  bursts  6 . 2 ,  flows  higher  appear  This  Data  al.  Newtonian  data  DR.  unknown.  g r a d i e n t  decades  %  e f f e c t  Figure  K l i n e  f o r  and  B u r s t i n g  In t i o n  +  the  y e t  6 . 1 . 2  A  al. wall  f o l l o w  l a y e r  using the the over  a  of  There  i s  v a r i a b l e  u *  boundary b u r s t  h o t - w i r e  a  between  l a r g e  range  l a y e r  parameters,  probe  d i f f e r e n t i a t e d time  suggest  the  (1967).  v e l o c i t y , s c a l i n g  to  i n  v e l o c i t y b u r s t s of  Tg  Reynolds  u#  F i g u r e  6 . 2 .  A (  cm/s  comparison of b u r s t O ) t h i s work, (  ( 1 967)  .  )  rate data K l i n e et  al.  151  number. be  By  almost  boundary  t r a v e r s i n g  c o n s t a n t l a y e r .  o b s e r v a t i o n b u r s t the  i s  et  K l i n e that  flow  (1974) streak  the  ( e . g .  have  wall  to  d i s t u r b a n c e s  -  ' LTV1  see  ,  be  that  of  the  may  be  as  f l o w  to  the a  p r e s e n t  1 . 3 e ) .  with  to  leads  v o r t i c e s  w i t h  a s s o c i a t e d  edge  a l r e a d y  Figure  demonstrated  Tg  f i n d i n g  l i f t i n g  t r a n s v e r s e  found  outer  t h i s  l a r g e  may  a l s o  the  f o r  streak  l a r g e  a l s o  l i f t u p  they  e x p l a n a t i o n  by  (1 9 7 3 )  al.  probe,  low-speed  t r i g g e r e d  outer  Nychas  from  The  that  the  i n  shown Offen  by and  v i s u a l i z a t i o n  o u t e r - l a y e r  d i s t u r b a n c e s . A between  d e t a i l e d  inner  a v a i l a b l e  at  and  to  Re  S c a l i n g  of  b u r s t  u*  between  s i n g l e  <  range  and  l i n e  in  study  r e s u l t  i s  made  (1973).  Both  ments  the  at  the  flows at  from  the  u*  et  data  The  v i s u a l  T<.  b u r s t s  t h i s  time  data  f o r  d i s t r i b u t e s  a  higher  value  same  u * .  P a r t i a l  support  have  made  with  a  and  of  value  when  com-  for  t h i s  Thomas  a u t o c o r r e l a t i o n  h o t - f i l m  the  model.  Newtonian  (1968)  in  both  about  the  workers  work).  measurements  i n d i c a t e  Meek  is  i n t e r v a l  over  of  not  s a t i s f a c t o r i l y  a u t o c o r r e l a t i o n  l i f e t i m e  i s  on  1972;  al.,  6 . 3 .  f l o w s ,  i n t e r a c t i o n s  reducers  v i s u a l  from  work  wall  drag  works  the  pipe  the  K i m - K l i n e - R e y n o l d s  d i r e c t  streak  the  Figure  computed  by  more  for  comes  in  of  in  (Donohue using  seen  given  d r a g - r e d u c i n g  p a r i s o n  l a y e r s  d r a g - r e d u c i n g  The t h i s  data  Tg,  study  A l s o ,  18,000  as  b u r s t s  Newtonian  outer  p r e s e n t .  l i m i t e d  lower  v i s u a l  anemometers.  et  al.  measureAlthough  152  10  10  10 U*  F i g u r e  6 . 3 .  Sublayer  cm/s  period  d r a g - r e d u c i n g  10  data f l o w s .  in  Newtonian  and  Legend  f o r  Sublayer No.  1  et  al.  Period  (1971  )  Stanford w a t e r , T  2  3  Donohue  This  et  al.  (1972)  work  O •  —  a  •  A •  B  "  Thomas  et  &  al.  Greene  (1973)  (1973)  data  u  *  Data  (1962-68)  channel  flow  50 s  wppm -  u  V i s u a l *  [2]  h o t - w i r e  auto-  c o r r e l a t i o n * *  D  =  Separan  [8]  D  =  V i s u a l *  2 . 6 3 cm  AP30  [6]  Visual  [6]  wall c o n c e n t r a t i o n a u t o c o r r e l a t i o n Signal 1ength/x^=40  [6]  h o t - f i l m probe a u t o c o r r e l a t i o n s 10<Signal length/x^<35  [14]  as  *  f1ow,  Type  [7]  •  2  Pi pe f 1 o w , water  Pi pe Thomas  D e t a i l s  2-D c h a n n e l , DH = 7 . 3 cm water 139 wppm Polyox-FRA c o r r e c t e d f o r p r e s s u r e gradi ent  — - . - T  4  6 . 3 Data  Experimental  Reference Kim  Figure  and  0 . 3 0 cm  V T  water 20 wppm  Separan  AP30  o •  0 . 9 % wt 40 wppm  s a l i n e Separan  AP273  above  Signal  1ength/x  £  >l000  CONTINUED  GO  No .  5  Experimental  Reference Meek  (1968)  Pipe o •  (numbers  in  square  brackets  indicate  D e t a i l s  f l o w ,  D  =  2.42  data  •points  available)  Time  i n t e r v a l  T<-:  Streak  x0:  Maximum  between  b u r s t s ;  computed  ** l i f e t i m e ;  lag  time  a u t o c o r r e l a t i o n  for  peak.  a u t o c o r r e l a t i o n  =  1/FX  Type  cm  t e t r a l i n 2 0 0 wppm p o l y i s o b u t y lene in t e t r a l i n  * Tg:  Data  [6]  h o t - f i l m  probe  a u t o c o r r e l a t i  * * ons  155  q u a n t i t a t i v e to  some  found than  values  doubt  the the  due  f o r  to  sublayer  d r a g - r e d u c i n g  the  use  period  Newtonian  value  of  h o t - f i l m  d u r i n g at  flows  the  drag  may  be  probes,  both  r e d u c t i o n  c o r r e s p o n d i n g  s u b j e c t  to  workers  be  l a r g e r  Reynolds  number. To et  (1973)  al.  c a l c u l a t e d on  l a y e r  period  a l r e a d y the  s  Newtonian  Black  data  of  and  ( 3 ) ,  (1969) t h i s  and  v i s u a l  r e s u l t s  a s s o c i a t e d  f a l l  i s  near  and  (5)  when  i s  the  the  extended  and  Meek  and  Rows  1  s u b l a y e r  Baer  and  2  p e r i o d  of (=  a l l  the  u * .  renewal done  6 . 2  T u ^ / v ) ,  f o r  from  same  was  Table  have  d r a g - r e d u c i n g  s u r f a c e  (1970)  legend  K i m - K l i n e -  the  the  (see  trend  departure  d r a g - r e d u c i n g  sub-  u * .  that  n o t i c e a b l e  a t  of  shear  problems  t h e i r  p l o t t e d  a u t o c o r r e l a t i o n  wall  of  r e -  and  techniques  trend  Thomas  decades  and  of  and  were  u *  a  compared  of  of  four  (Tg)  measurement  there  (1968)  basis  decades  (4)  work.  Meek  c o r r e l a t e s  s i g n i f i c a n t  with  the  T  the  show  based  models  +  on  ,  both  T^. B l a c k ' s  f l o w .  the  The  t e s t  non-dimensional Tg  to  of  t h e i r  on  three  t h e i r  c o r r e l a t i o n A  of  and  data  of  from  d i f f e r e n t  l i n e .  data  B)  d i s c u s s e d ,  Newtonian  d a t a ,  f i g u r e  obtained  the  been  Reynolds T  This  6 . 3 )  r e s u l t s  v i s u a l  measurements,  Figure  the  Appendix  6 . 3 .  C o n s i d e r i n g to  with  (see  Figure  (T<«)  compare  The  model  a d d i t i o n  s t a b i l i z a t i o n ,  of  p r e d i c t s a  r e s u l t i n g  T  +  -  drag  reducer  i n  t e n - f o l d  a  115  f o r  leads  a  to  i n c r e a s e  Newtonian s u b l a y e r of  T  +  to  Table Non-Dimensional  S u b l a y e r  P e r i o d  Data  6.2 and  C a l c u l a t e d  RUN  Row  Quanti  No.  Ratios  to  Test  Models  NO.  ty Water  Separan  (N)  (DR)  Wl  W2  W3  SI  S2  S3  1  95.  84.  81.  43.  96.  47.  2  69.  59.  135.  103.  130.  211.  Wl Re f  3 f  ->  T+  =  T  v  =  0.010  N  u  2  S(DR)  T  S(N)  T  B(DR)  T  B(N)  / v ,  -  W2  SI 7,000  Re  *  -  W3  S2 10,300  Re  -  -  S3 14,700  1 .30  1 .53  1.87  0.85  1.42  1.17  0.47  1.01  0.71  DR  T  4  5  N  *  Tg  V  V  =  g / c m . s ,  DR  V  V  N  N  DR  1/FA, v o  T$: D R  =  a u t o c o r r e l a t i o n  0.0144  g/cm.s  measurement _ CT)  157  about Tg  1150  for  at  water  maximum i s  c o n s t a n t  drag  r e d u c t i o n .  during  both  with  i n c r e a s i n g  %  for  the  during  drag  not  l a r g e  as  to  the  Re  Separan  during  for  f  i s  f a c t o r  the  drag  r e d u c t i o n  as  B l a c k ' s  in  the  v  DR  but  i n c r e a s i n g s t a b i l i z a t i o n  i n c r e a s e  in  model  d r a g - r e d u c i n g  ( i . e .  reduced  of  data  Reynolds  t h i s  number.  numbers;  in  runs  rows  3  T^  i s  p r e d i c t s .  flow  reduces  (T<.) and  3  than  shows  does  T<~  in  DR  with  Re  model a  i n d i c a t e s  decrease  comparisons  Rows  3,  i s  at  4  and  and  of  f r i c t i o n  Table  at 6.2  the  the  agreement  using  an  made  W3-S3.  Row  show  same 4  uses  of  the  for  the  good. Tg  correspondence More  in  and  reasonably 5,  5  are  approximately  W2-S2  row  poorer d a t a .  (6.1)  The  data 4  N  when  W l - S l ,  Values comparison,  DR  f  compared  a u t o c o r r e l a t i o n s r a t i o s  f  period  drag)  work  N  f a c t o r .  s u b l a y e r  the  row  for  t h a t  s l i g h t l y  s u b l a y e r the  model  95  with  by  f r i c t i o n  Reynolds  in  and  i n d i c a t e d  Meek-Baer  constant  same  flows  shows  form:  i n c r e a s e  two  and  i n c r e a s e s  However,  V  only  T^  80  6.2  as  T  where  Table  between  water  f l o w s .  r e d u c t i o n  The  r e d u c t i o n .  almost  decreases  DR  drag  e x t e n s i v e  data with  the  support  of  values the  158  Meek-Baer Thomas  model  and  Greene The  Baer take  to  hold  has in  in  for  the  the  d r a g - r e d u c i n g  6.2  6.2.1  A  The  r e d u c t i o n  a  the  v i s u a l i z a t i o n  have  to  with  a  be  X  would  i s  (1968)  100,  (1969)  that  s t r e a k -  +  f l o w .  streak  and  the  of  both  to  . s p a c i n-g  Meek-  do  not  with  drag  Newtonian  v a l u e ,  v i s u a l i z a t i o n  s t r e a k s A  and  they  spacing  W a l l - l a y e r  P o s s i b l e  1.5  and  bursts  r e a l i s t i c  model  i n c o r p o r a t e  both  changes  the  and  the changes  Approach  has  of  provided  in  polymer  by  to  a  and  have  overview  d r a g ,  shown  due  Newtonian 'what'  'why'  i s  these the  of  the  t u r b u l e n t  t u r b u l e n c e  a s s o c i a t i n g  mechanism.  an  Newtonian  5  wall  i n d i c a t e  'How'  i n f e r r e d  of  f r i c t i o n a l  s t u d i e s  r e g i o n .  of  Chapter  s t r u c t u r e  s p e c i f i c  Mechanism  s i g n a t u r e s '  d r a g - r e d u c i n g  n e a r - w a l l  assume  in  have  of  Black  reducers  importance  r e s u l t s  a  a  the  flow  ' v i s u a l  in  of  drag  Continuum  changes l a r g e  of  p r o c e s s .  of  Chapter  l a y e r s .  Meek  p e r i o d .  D i s c u s s i o n  important  of  p r o d u c t i o n  f i n d i n g s  sublayer  data  i n c r e a s e  models  t u r b u l e n c e  important  for  d r a g - r e d u c i n g  e s t a b l i s h e d the  in  The  the  c r i t i c i s m  models  account  r e d u c t i o n .  from  (1973).  major  (1970) into  stems  to  the  boundary  remarkable  accompanied the  a d d i t i o n  s o l v e n t .  The  happening changes  observed  by  in  take flow  the p l a c e p a t t e r n s  159  The easy  task  v a r i a n t .  i n t e r p r e t a t i o n  s i n c e  t u r b u l e n t  A l s o ,  many  v i s u a l  p a t t e r n s .  e a s i e r  by  time  of  a  The e x p l a i n tinuum s i n c e  drag  study with  p r o p e r t i e s  of  the  i s  a  weight,  f l u i d  s t r u c t u r e s ,  c h a i n  of  i t  s i z e  An  c o u l d ,  however,  u s e f u l  a d d i t i v e s  6 . 2 . 2  s t r u c t u r e summarized  in  in  by  the  s e c t i o n s flows  w a l l - l a y e r  a  Thus,  i f  necessary  in the  the  s y n t h e s i s  Patterns  changes  to  5.5.1  and  the  v o r t e x  and  of  the  elements  to  the  new  parameters  I m p l i c a t i o n s  w a l l - l a y e r  have  d r a g -  ones.  Their  of  t u r -  d i f f e r e n t  The  importance  about  m o l e c u l a r  a d d i t i v e  5 . 5 . 2 .  o g i c a l )  observed  ( e . g .  for  and  d r a g - r e d u c i n g  (rheol  m o l e c u l a r  search  con-  i n q u i r e  conformation) of  A  s c a l e s  the  to  to  a p p r o a c h ,  continuum  parameters  and  1.  time  for  s i m i l a r  somewhat  forward  Chapter  and  to  present  m o l e c u l a r  length  not  Flow  v i s u a l i z e d  caused  wal1 - t u r b u l e n t on  or  in  to  i n v e s t i g a t i o n  V i s u a l i z e d  The  e f f e c t s  be  put  been  r e s p o n s i b l e  i s  p r o c e s s e s .  have  here  m o l e c u l a r  l e n g t h ,  1.5).  with  are  b u l e n t  reducing  the  continuum.  the  r e l a t i o n s h i p  at  an  time-  lead  understanding  d i s c u s s e d  d e a l t  may  (Chapter  not  and  made  p r e f e r r e d  has  i s  is  that  are  complex  mechanisms  l a y e r s  r e d u c t i o n  a s s o c i a t e d  t u r b u l e n t  wall  are  p i c t u r e s  i n t e r p r e t a t i o n  good  mechanisms  approach t h i s  d i f f e r e n t  reasonably  v i s u a l  motions  However,  Newtonian  of  to  flow water  dynamics  are of  s t r e t c h i n g been  d i s c u s s e d  160  in  chapter  1 . 5 . 1 .  complex  and  a c t i o n s  on  T u r b u l e n t  impose f l u i d  a  motions  combination  elements.  of  For  i d e n t i f i a b l e  w a l l - l a y e r  c l a s s i f i e d  s p a t i a l l y  s t r e a k s  spans  of  t h e i r  d e f i n e d . of  e x i s t e n c e  Thus,  r e l a t i v e l y To  and  s t r e a k s  the  dominant  Figure  6.4  motions  the  as  a  i l l u s t r a t e s  the  r e f r a c t i v e  to  the  nature  zones  H  r e g i o n  p r o f i l e 5.9)  p r o f i l e in  the  suggests the  drag  in  l a t t e r .  reducer  The the  i n  drag l e s s e r The  could  6.4  a  drag  provides in  [(a)  time  made  up  s c a l e s . of  bursts  r e d u c t i o n , are  (see  examined. and  s h e a r i n g  d i s t r i b u t i o n  d i r e c t  i s  zones and  from A  a  s t r e t c h i n g  and  an  by depleted  c l o s e l y  spaced  expanded  in  Figure  compression  s t r e t c h i n g of  the  f l o w ,  the  more  photographs  r e s u l t  W i t h i n  d e p l e t e d  L.  c l u e  f l o w .  Newtonian  spanwise  d i r e c t  a  the  removed  flows  spanwise  be  the  temporal  s t r e t c h i n g  enhancer  water  lowered  been  roughly  be  c o n c e n t r a t i o n  enhancer  reducer  to  the  f o r m a t i o n .  low-speed  the  been  impressions  s t r e t c h i n g  the  have  stretching  for  important  Figure  f l o w ]  motions.  c o l l e c t s  sawtooth  in  to  enhancer  spanwise  d r a g - r e d u c i n g  t r a n s v e r s e  in  of  v i s u a l  spanwise  index  and  s t r e t c h i n g  A l s o ,  seen  r a t h e r  s i m p l i c i t y ,  have  i s  s p a t i a l  streak  observed  wall  mechanism  the  accompany  of  (b)  and  of  are  and  b u r s t s .  resistance  p o s s i b l e  motions  The  high-speed  the  sake  and  hash  w e l 1 - o r g a n i z e d  w a l l  s t r u c t u r e s  the  t u r b u l e n t  i d e n t i f y  that  near  the  s h e a r i n g  the  s e p a r a t e l y  as  at  in  i n c r e a s e  the in  the  1  IwalK  X  (b)  (a) L : H :  low-speed f l u i d h i g h - s p e e d f l u i d  zone zone  lUHIIII 11  n  element zone  being  being  f r i n g e ,  s t r e t c h e d  sheared  showing  c o n c e n t r a t i o n  F i g u r e  6 . 4 .  S t r e t c h i n g (a)  and  Newtonian,  s h e a r i n g (b)  zones  of  Drag-reducing  w a l l - l a y e r f l o w s .  s t r e a k s  enhancer d i s t r i b u t i o n  in  162  value  of  i t s  Newtonian which  e l o n g a t i o n a l  value  v  i n c r e a s e s  v a l u e ,  could  ^ ( ^ ) -  e  Thus,  during  be  a  drag  d i r e c t  Assuming  v i s c o s i t y  that  xjlj  (an  almost  c o n s t a n t  if  the  proper  viscosity  the  £ ( p R )  e  spanwise  r e d u c t i o n  measure  of  A^R  would  value  f o r  value  A  v  +  DR  the  have  A  ~  A  the  change  in  Newtonian  w a l l  in  i t s  s p a c i n g ,  Newtonian  same  used  the  s t r e a k  the  were  =  over  over  v  ^.  value  as  l a y e r s ) c a l c u l a t i o n ,  (6.2)  +  N  or  X  DR v  When s h e a r ,  u * ^  D R  j  U  ,  A  =  e £ ( D R )  comparison =  *(DR)  u * ^ ,  is  [6.3)  made  at  with ing  i n c r e a s i n g u*  ( e . g .  see  same u*  or  u * , %  Figure  k  DR  *(N)  (6.3)  e £ ( N )  equal  value  of  w a l l  becomes  DR  the  U  v  v eil(N)  'eft(DR)  At  N  D  >  w h i l e  5.8)  A. A^  A l s o , decreases  (6.4)  i n c r e a s e s with  i n c r e a s -  163 In  another  form  v  e £ ( D R ) v  is  when on  i t s  x  c a l c u l a t e d  -»- 0  Thus,  the  streak  spacings  of  d r a g - r e d u c e r  the  + A  D  ^DR  \J  vN  the  (  d r a g - r e d u c i n g  s o l u t i o n  g  based  v0.  r a t i o  could  be  due  of a  the  non-dimensional  measure  to  of  the  s t r e t c h i n g  spanwise  change  in  motions.  v i s c o s i t y  The  r a t i o  + R  i s  / A ^  used  in  the  water  was  wise  to  of  in  a c t i o n flow be  the of  the  the  the  longer  s t a b i l i t y  (du/dx  t  strong  the  may  a l s o  streak  the  s o l u t i o n s streak  e x p l a i n  length  over  l i f e t i m e  the  term  i n c r e a s e d  d r a g - r e d u c i n g  a x i a l  regions  from  rates  in  t h a t  and  p o s s i b i l i t y  in  Figure  two  v  =  f l o w s .  that  of  or The  q u a l i t a t i v e l y  and  reduced  wal1-1ayer  6.4  are  the  span-  In  z - d i r e c t i o n  d i r e c t i o n s  being f1ow.  s t r e t c h e d  'drawing-out'  the  d r a g - r e d u c i n g  x - d i r e c t i o n  f n ( s t r e t c h  of  by  zones. the  the  the g £  in  d i r e c t i o n  of  i n  d r a g - r e d u c i n g  (x)  L  high-speed  magnitude  dw/dz)  in  e f f e c t '  s t r e a k .  adjacent  s t r a i n  e q u a t i o n ,  e x p l a i n  streamwise  d i f f e r e n t  t h a t  Separan  Low-speed out  In  v i s c o s i t y  the  in  a  ' i n c r e a s e d  of  e f f e c t  i n c r e a s e  waving  the  ( 5 . 2 ) .  sublayer  v i s c o s i t y  observed  of  v i s c o s i t y  used  increased same  form  equation  e l o n g a t i o n a l  a  ^DR  e £ ( N )  for  viscosity  =  v  e  ^ ^ (  would  e  z  £ (  x  ) ^  be  r a t e ) .  Thus  a n i s o t r o p i c  at  ) >  could  s i n c e d i f f e r e n t t h e r e - i s a  point  in  5  )  164  S t r e t c h i n g streak  l i f t u p  and  Figure  6 . 5 ) .  Streak  v o r t i c e s et  by  e f f e c t  the  s i n c e  f l u i d to  of  intense  burst The  to  6 . 2 . 3  useful of  in  of  r e s u l t s  phenomenological 1965;  Hershey  computing i t  has  the  been  and  in  be  models Zakin,  Deborah  customary  the  1973;  Nychas  wall  l a y e r .  than  that  caused  the  roughly  d i s c u s s e d ,  slower  f l u i d .  The  along  tend  to  motions  could  be  due  burst t h e i r  f l o w s . lead  drag  to  d i r e c -  lose  that  the  w a l l  the  d r a g - r e d u c i n g  in  l a r g e  the  from  flows  (see  by  p r e v i o u s l y  the  i n h i b i t e d  Eddy  the  the  have  from  during  to  r e d u c e r .  the  s o l u t i o n ' s  motions.  of  of  of  s t r e t c h i n g  b u r s t i n g  Scales  that  bulk  occur  b u r s t i n g  K l i n e ,  s t r e a k s away  to  t r i g g e r e d  s t r e t c h i n g  water  than  r e - e x a m i n i n g  t u r b u l e n c e  in  to  and  o r i e n t e d  s t r e t c h i n g  The  The  be  of  probably  moving  and  stages  b u r s t s  of  moving  r a p i d l y  s u p p r e s s i o n  v i s u a l i z e d  (Offen  r a p i d  B u r s t s  appear  i s  out'  are  may  s h e a r i n g  breakup  r e s i s t a n c e  more  f a s t e r  ' t ' .  more  flow  'draw  elements  be  subsequent  s t r e t c h i n g  s t r e t c h i n g  i d e n t i t y  a l s o  l i f t u p  mean  causes  the  t r a j e c t o r y  The  the  that  spanwise  l a y e r s t i o n  the  1973)  al.,  This  in  can  I n t e r a c t i o n s  v i s u a l i z a t i o n  b a s i s  been for  space  a s s o c i a t e d  and  in  d r a g - r e d u c i n g  1966;  A s t a r i t a  number  (De  to  a  use  of  =  0/AT,  experiments time  the flow  et  al.,  see  t h e o r e t i c a l  past  are  s c a l e s with  ( e . g .  A s t a r i t a ,  1969).  eqn. ' f l u i d  1.4),  In  165  -t  F i g u r e  6 . 5 .  I i iliDi'l): :  element being s t r e t c h e d zone being sheared  S t r e t c h i n g streak (a)  and  s h e a r i n g  zones  1i f t u p  and  b u r s t i n g  Newtonian  and  (b)  f1ows.  d u r i n g  in  d r a g - r e d u c i n g  166  r e l a x a t i o n  time'  for  s c a l e  d i s s i p a t i v e  time'  AT.  De  ~  Drag  1.0  (see  mentioned  m o l e c u l a r has  been  in  1966) drag  s e c t i o n are  f l u i d  assumed  range  for  many  by  Darby  of  d i l u t e  shown  9  10  to  0.1  in  the  -  to  d i l u t e On of  to  3  6 10"  6  other  a  has  been  sec  ( e . g .  s e c "  1  low  .  These  shear  the  a  constant  9  decreases  sec  f l u i d  rate  range,  time  with  of  9  a  recent  6 ,  are  than  F u r t h e r ,  which  i n c r e a s i n g • J  is  500  rate  range  leads  hypotheses  have  turbulence  t i m e . '  from  a p p r o x i -  p r e d i c t that  from  -  This  of  r e p r e s e n t a -  experience  v ~ 0 * 4 'max  1970).  about  although  more  to  have  of  t h e o r i e s  [ 9  Z a k i n , in  wppm)  c a l c u l a t e d  c o n t r a r y  s t r a i n  and  measurements  v a l u e s ,  the  to  i n t e r e s t  probably  those  (1956),  c h a r a c t e r i s t i c s  to  9  the  d r a g - r e d u c i n g  hand,  shear  from  Zimm  of  the  above-  c r i t i c i s m .  s o l u t i o n s  experimental  t h e o r i e s .  value  for  the  Hershey  (100  1.4  in  c a l c u l a t e d  s o l u t i o n s  to  when  or  P o l y h a l l - 2 9 5 0.3  occur  (1953)  r e p r e s e n t  polymer  the  to  9 , estimated  Rouse  s m a l l -  imposed  f o l l o w i n g  time  property. 10"  the  the  ' f l o w  defined  response  m o l e c u l a r  s c a l e s  s u b j e c t  A?  t r a n s i e n t  mate  scale  and  of  the  hypothesized 9  e i t h e r  of  the  of  Darby,  i s  frequency  measure  adequately  of  (1970)  t i v e  ' f l o w  to  r e d u c t i o n .  a  1.6).  of  e l a s t i c  the  as  i n v e r s e  r e l a x a t i o n  t h e o r i e s  s o l u t i o n ' s be  eddies  the  r e d u c t i o n  manner The  and  9  The  to  the  q u e s t i o n  c o n s i d e r e d to  v i s u a l  a r r i v e  at  r e s u l t s  the AT, of  as  to  proper the t h i s  whether s p a t i a l  time eddy  c h a r a c t e r i s t i c work  and  those  167  of  Donohue  in  the  et  wall  s t r e a k s  (1972)  al.  l a y e r  and  i n  i n d i c a t e  d r a g - r e d u c i n g  b u r s t s .  Bursts  are  (Kolmogorov)  s c a l e ;  nor  of  of  Instead,  the  order  medium-sized in  t h i s  It  i s  small the by  that  burst  time  streak  'flow  s c a l e s  of  l i f e t i m e  T<.  the  small  the  may  scale  be (£  t u r b u l e n t that  time'  may  be  v i s u a l i z e d the  time  of  the  s c a l e s  c o n s i d e r e d ~  gives  Figure  s c a l e s  ' d i s s i p a t i v e '  0.1  to  energy  see  or  those  l a r g e - s i z e d  ( e . g .  the  important  are  bursts  process  scales  c h a r a c t e r i s t i c  the  they  t r a n s p o r t  breakup  d i s s i p a t i v e  the  a r e  the  flows  not  ' e n e r g y - c o n t a i n i n g '  study)  the  D.  that  0 . 4  from  r i s e  to  a  D  the  w a l l .  the  5.11).  Thus,  p r o p e r l y  represented  w a l l - l a y e r  i n t e r v a l  as  s t r u c t u r e ;  between  bursts  V For  the  s i g n i f i c a n t l y d u r a t i o n of  the  of  A  measured and  l a r g e r  t r a n s i e n t  same  1971).  order  rough  2.1  <  1.3  s ;  of  sublayer  v i s u a l i z a t i o n u *  <  0 . 6  9  the  ( 0 . 3  periods  <  0 . 9  Newtonian  magnitude  cm/s) and  u *  v i s c o s i t y  e l o n g a t i o n a l  experiments  3 . 6 <  of  than  comparison  values  the  e l o n g a t i o n a l  as  of <  6  of  cm/s)  £(rjR)  must  (Denn  (1970)  <  f o r  1.4 drag  t h i s  s  6  Donohue  et  shows  and  e  £(n)>  the  general  be  Marrucci ,  >  ( 0 . 3 5  >  i  >0.1  s  -  from  the  Tg  0 . 0 6  (1972)  the  D  e x p e r i m e n t a l l y  10  al.  to  i n  r e d u c t i o n  work  0  v  and  Darby's  during of  e  value  flow 0  v  >  ( 3 . 4  sublayer  >  1  )  s ; T  g  >  period  * to  be  wall nitude  of  almost t h e same o r d e r of magnitude. The s t r a i n The s t r e t c h rates and a x i a l s t r e s s e s encountered  layer  s t r u c t u r e s  lower  experiments  could  r e s p e c t i v e l y (see  page  6 ) .  be  than  three  and  s i x  those  present  orders in  j e t  of  mag-  thrust  by  168  rates an  in  the  flow  experiments  order  of  magnitude  rate  of  decrease  the  comparison  c h a r a c t e r i s t i c the  to  be  from f l u i d  length  t h a t a  with  9  use  'flow scales  the  those i s  y  Re  < of  very  the  s u b l a y e r  time'  and  the  a s s o c i a t e d It  combination times  of  has  18,000)  could  Darby.  low,  be  However,  making  appear  of to  be  the  t h i s  as  t h i s  u*1.. proper  t i m e ,  (Donohue  time'  This  the s t r u c t u r e  flow  suggested  ' f l u i d  and  p e r i o d  s t r e a k - b u r s t  with  been  c h a r a c t e r i s t i c  d r a g - r e d u c i n g  6.3  the  a p p r o p r i a t e .  1972)  of  than  <  v a l i d . Thus,  as  higher  (6000  may  be  c h o i c e  of  s c a l e s  in  seem  et  al..  3  d e r i v e d flow  and  d e s c r i b i n g  f l o w s .  CIosure  6.3.1  Aspects  From tant  aspects  t h a t  i s  a  to  based  on  of  the  Drag  Reduction  phenomenological be  c o n s i d e r e d  the  p o i n t  in  s o l u t i o n ' s  a  drag  Mechanism  of  view,  the  r e d u c t i o n  r e s i s t a n c e  to  impor-  mechanism  s t r e t c h i n g  are: (i)  ( i i )  flow  c h a r a c t e r i s t i c s  space  and  layer  s t r e a k - b u r s t  the by  f l u i d the  rate  time  s c a l e s  of  c h a r a c t e r i s t i c  r e l a t i o n s h i p  the  s t r u c t u r e ,  e x t e n s i o n a l  s o l u t i o n .  defined  by  the  wall and  defined  v i s c o s i t y - s t r a i n of  the  d r a g - r e d u c i n g  169  6 . 3 . 2  A p p l i c a t i o n  One has  been  to  f r i c t i o n  the  clues  provide  for  such  s u b l a y e r  reducing  drag  a b i l i t y  to  p r e d i c t  a  present by  to  r e d u c t i o n  perform  flow  amount  and  the  t e s t s .  mechanism'  in  r e s e a r c h of flow  The  6.3.1  aspects provide  method.  the  i n d i c a t e  a d d i t i o n  has  been  r e s i s t a n c e  of  a  an  d r a g - r e d u c i n g  a t t r i b u t e d  to  i n c r e a s e d  to  s t r e t c h i n g  the  polymer.  d r a g -  motions  and  as  DR  =  v  e £ ( D R )  __N  'e£(N)  A for  the  s o l u t i o n  experiments  s t a b i l i t y  s o l u t i o n ' s  polymer  s t r e t c h i n g  design  s t a b i l i t y  i n c r e a s e d  s t a t e d  a  of  having to  Design  aims  given  ' r e s i s t a n c e  Engineering  major the  without  The  The  the  r e d u c t i o n  s i t u a t i o n , of  of  to  drag  t e s t  reducers  of  the  shows  Meek-Baer that  s u r f a c e  (6.6)  DR  renewal  model  From to  p r e d i c t  given  Re  these  the  and  f r i c t i o n  pipe  c h a r a c t e r ! ' s t i c The technique  The  the  not  equations  in  e n g i n e e r i n g  of  6.6  design  for  of  such  and  i f  the  a  6.7 for  the  drag  drag  be  d i l u t e  p o s s i b l e  r e d u c t i o n  at  a  v i s c o s i t y  known. present  p r e c i s e  technique might  would  e x t e n s i o n a l  were at  very  i t  during the  block  e x i s t  v i s c o s i t y  of  f a c t o r  s o l u t i o n  stumbling  development  e q u a t i o n s ,  diameter  'of  does  e x t e n s i o n a l  two  provide  a a  r e d u c e r s .  i s  measurement  polymer and  time  t h a t of  s o l u t i o n s .  r i g o r o u s v i a b l e  t e s t  approach  Chapter  7  CONCLUSIONS AND RECOMMENDATIONS  Flow measurements using  a  v i s u a l i z a t i o n  i n  Newtonian  r e c e n t l y  and  and  developed  w a l l - l a y e r  s t r u c t u r e  d r a g - r e d u c i n g  l a s e r  flows  were  done  h o i o g r a m - i n t e r f e r o m e t r i c  t e c h n i q u e .  7.1  Summary  7.1.1  and  Gross  Gross Separan  t i o n ,  drag the  f a c t o r s  flow  Experiments  experiments  There  onset  lower  percentage s o l u t i o n  water  of  than  drag  three  t u r b u l e n t  drag  the  a f t e r  r e v e a l e d  with  and  smooth  onset  r e d u c t i o n  d i s t i l l e d  d i s t i n c t  flow  r e d u c t i o n ,  Newtonian  Both  using  s o l u t i o n s  e x i s t e d  r e d u c t i o n ;  ( i i )  on  Flow  A P 3 0 - d i s t i 1 1 e d  (i) during  C o n c l u s i o n s  a  c o n c e n t r a t i o n .  171  the  flow  no  f o l l o w i n g :  regimes  drag  regime  and  reduc-  w i t h  f r i c t i o n  v a l u e s .  Reynolds onset  water  number  were  and  s t r o n g l y  the dependent  172  7.1.2  E f f e c t s  The  e f f e c t s  wall  l a y e r  drag  r e d u c t i o n ,  a l t e r e d  flow  in  compared  Drag  of  a  s t r u c t u r e both  t h e i r  to  of  the  50  wppm  were  and  f l o w s .  A d d i t i v e  Separan  s t u d i e d  s t r e a k s  s p a t i a l  water  Reducing  and  temporal  These  .  s o l u t i o n  in  on  d e t a i l .  bursts  the  During  were  s u b s t a n t i a l l y  c h a r a c t e r i s t i c s  e f f e c t s  are  as  summarized  as  f o l l o w s :  Streaky  (A)  Measurements (i)  with X  i n c r e a s i n g  for  water  (DR  The  u * .  the  drag  =  0)  Figure  The  d r a g - r e d u c i n g  The  water  p h y s i c a l  %  ( i i ) in  S t r u c t u r e  flows  streak  r e d u c t i o n  decreased  and  with  s p a c i n g  X  u * .  c o n t r a s t ,  In  i n c r e a s e d  i n c r e a s i n g  u*  ( F i g u r e  non-dimensional  streak  spacing  flows  i n c r e a s e d  almost  l i n e a r l y  had  constant  a  value  of  X  +  the  -  X  +  with  87  5 . 8 ) .  ( i i i ) c e n t r a t i o n r e d u c t i o n  The  r e l a t i v e  f l u c t u a t i o n (Figure  I  5 . 1 0 ) .  c  i n t e n s i t y  decreased  with  of  spanwise  i n c r e a s i n g  con%  drag  5 . 8 ) .  173  (iv)  The  a u t o c o r r e l a t i o n s drag  reducer  of  than  streak v i s u a l  the  l i f e t i m e d a t a ,  had  c o r r e s p o n d i n g  T  ,  a  greater  u*  estimated  water  from  value  value  in  the  ( F i g u r e  5 . 2 0 ) .  (B)  Visualization (i)  reducing  Real-time  flows  c o n c e n t r a t i o n  showed p r o f i l e  ( i i ) drag  wider  when  i n t e r f e r o g r a m s  spacing  compared  The  s t r e a k s  had  The  spanwise  of  the  with  the  longer  of  the  drag-  s a w t o o t h - l i k e water  a x i a l  f l o w s .  extents  during  r e d u c t i o n .  ( i i i ) a x i a l l y the  a  flow  o r i e n t e d  s t r e a k s  was  o s c i l l a t i o n reduced  by  or  the  waving  of  presence  the of  a d d i t i v e .  (iv) n o t i c e a b l y  i n c r e a s e d  Burst  (A)  drag  l i f e t i m e in  the  of  the  streaky  d r a g - r e d u c i n g  s t r u c t u r e  was  f l o w s .  S t r u c t u r e  Measurements (i)  during  The  The  r e d u c t i o n  b u r s t i n g (Figure  rate  F  5 . 1 4 ) .  was  d r a s t i c a l l y  reduced  174  ( i i ) puted  from  s p a c i n g , flows  The  time  measurements  had  when  s i m i l a r  compared  w i t h i n  A a  at  The  bursts  in  the  the  had  a  to  rate  the  b u r s t s  and  Tg,  p h y s i c a l  d r a g - r e d u c i n g  u*  ( F i g u r e  of  r e d u c t i o n observed  f l u i d  in  com-  streak  and  water  5 . 1 5 ) .  the  more  strong  during  elements  d i r e c t i o n  t r a j e c t o r y  drag  d i d  d u r i n g  p a r a l l e l  r e d u c t i o n .  not  drag  v o r t i c a l  move  as  r e d u c t i o n .  to  the  w a l l  than  water.  ( i i i ) tendency  in same  was  Ejected  w a l l - n o r m a l  case  the  marked  burst  ( i i ) in  burst  between  Visualization (i)  f a r  of  values  (B)  motions  i n t e r v a l  Bursts  break  up  and  in  the  to  drag  form  reducer  had  s m a l l - s c a l e  a  reduced  f l u i d  elements.  These reducing or  the  same  a l t e r e d leads  and  o b s e r v a t i o n s  water w a l l  shear.  w a l l - l a y e r  to  f r i c t i o n a l  reduced d r a g .  flows  flow  were  were These  compared r e s u l t s  s t r u c t u r e  t u r b u l e n c e  v a l i d  when at  the  drag  and  d r a g -  same  suggest  d u r i n g  g e n e r a t i o n  the  thus  that  flow the  r e d u c t i o n reduced  rate  175  7.1.3  A  A s o l u t i o n ' s e x p l a i n  Mechanism  mechanism  to  v i s u a l i z e d  The  i n c r e a s e d  streak  the  Newtonian  value  streak  for  r e s i s t a n c e  the  s p a c i n g  for  Drag  drag  and  was  streak be  spacing  accounted  for  v i s c o s i t i e s  A  Q  is  R  7.1.4  changes.  r e d u c t i o n  over  non-dimensional  the  (7.1)  r a t i o  and  of  non-dimensional  Newtonian  c o r r e s p o n d i n g  r a t i o  flows  of  can  e l o n g a t i o n a l  as  evaluated  Streak  The s u r f a c e  to  N  the  d r a g - r e d u c i n g by  used  DR l  t h a t  DR  when  _  S(N)  suggested in  the  s t r u c t u r e  drag  the  was  on  as  S(DR)  i s  flow  during to  based  motions  measured  r e l a t e d  T  It  r e d u c t i o n ,  s t r e t c h i n g  l i f e t i m e  r a t i o  Reduction  l i f e t i m e  model,  e £ ( D R )  '_^N_  'eH(N)  DR  s o l u t i o n  L i f e t i m e  streak  renewal  at  v  stated  (7.2)  z e r o - s h e a r - r a t e  v i s c o s i t y .  Data  data as  supported  the  Meek-Baer  176  S(DR)  T  V  S(N)  T  N  .  4  f  N  (7.3)  f  ^DR  DR Re  7.2  Recommendations 7.2.1  Ho!ogram-Interferons  The developed  to  in  7.2.2  a  s t a t e  r e q u i r e d and  rates  during  d i r e c t  to  outer  s o l u t i o n s .  The  of  e x t e n s i o n a l  to  v e r i f y  mechan i sm.  in  has  the  l a y e r s .  to  as  t h i s  a  has  been  useful  flow  technique  are  In  and the  Experiments  experiments  d e t a i l s s i t u  burst  of  v i s c o s i t y the  of  of  in  s t r e t c h i n g  to  reducers between  s t r a i n provide  of  for  s o l u t i o n s  ' r e s i s t a n c e  of  could  behaviour  techniques  d i l u t e  drag  i n t e r a c t i o n s  measurement  s t r e t c h i n g  development  d e t a i l ,  served  V i s u a l i z a t i o n  study  on  technique  G.  v i s u a l i z a t i o n  streak  evidence  i t  Improvements  Appendix  Further  inner  where  t o o l .  F u r t h e r are  Technique  h o i o g r a m - i n t e r f e r o m e t r i c  v i s u a l i z a t i o n suggested  t r i e  d i l u t e the  i s  polymer  measurement  e s s e n t i a l  s t r e t c h i n g '  N O M E N C L A T U R E  Symbol  D e s c r i p t io n  A  C r o s s - s e c t i o n a l  A  i n  e q n .  ( 1 . 7 ) ,  mixing  B  i n  e q n .  ( 1 . 7 ) ,  i n t e r c e p t  C  •>  pipe  area length  c o n c e n t r a t i o n  C  Average  c o n c e n t r a t i o n  c  Polymer  c o n c e n t r a t i o n  De  Deborah  Number  D  Pipe  d  Fringe  constant  f u n c t i o n of  enhancer  f l u c t u a t i o n  wppm  diameter  cm  s p a c i n g ;  s u c c e s s i v e ference DR  cm'  Instantaneous c o n c e n t r a t i o n in wall l a y e r Turbulent  Uni t s  d i s t a n c e  b r i g h t  o r  between dark  two  i n t e r •mm  bands  Drag  r e d u c t i o n  F  Burst  rate  f  Fanning  f  Fringe  G  Shear  per  cent  b u r s t s / c m . s  f r i c t i o n s p a t i a l  e l a s t i c  i , j ,k  Integers  M  M o l e c u l a r  N  Number  of  I  Length  scale  f a c t o r frequency  modules  f r i  nges/cm  g/cm  weight sampling of  p o i n t s  eddy 177  cm  s  2  178  Symbol  D e s c r i p t i o n  n  R e f r a c t i v e  AP  Pressure Flow  Q Re Rc(  ml / s number  l a y e r  c o e f f i c i e n t  Instantaneous  s  Mean  s  F I u c t u a t i o n  f r i n g e  t,T  (  T  ),  wall  temporal  f r i n g e  s h i f t  s h i f t  b u r s t i n g  Streak  of  c o n c e n t r a t i o n :  s p a t i a l ;  S  Mean  dynes/cm  rate  C o r r e l a t i o n (.£),  ts  index drop  Reynolds )  Uni  period  s / b u r s t  l i f e t i m e  Time Non-dimensional  s u b l a y e r  period  u*  Wall  shear  v e l o c i t y  U  Mean  flow  x  c o o r d i n a t e  a x i s ,  streamwise  y  c o o r d i n a t e  a x i s ,  w a l l - n o r m a l  z  c o o r d i n a t e  a x i s ,  spanwise  cm/s  v e l o c i t y  cm/s d i r e c t i o n d i r e c t i o n  d i r e c t i o n  +  Dimensionless  d i s t a n c e  =  - — ^  v  L  2  179  Greek  L e t t e r s  Units  A  Di  A  P h y s i c a l  A  +  f f e r e n c e spacing  Non-dimensional  h  Wavelength  Y  S t r a i n  Y  Rate  T  Shear  X  Rate  of  of  streak l a s e r  of  s p a c i n g  l i g h t  y  Dynamic  [p]  I n t r i n s i c  c "  s t r a i n lag  v i s c o s i t y  g/cm  v i s c o s i t y  between  9  F l u i d  r e l a x a t i o n  beams  Non-dimensional  el r t  Drag  r e l a x a t i o n  Reference  or  time  s e p a r a t i o n  Reduction  E l o n g a t i o n a l  s  time  C o r r e l a t i o n  cP  3  degrees  Newtonian  Test  or  d l / g  S u b s c r i p t s / S u p e r s c r i p t s DR  s  g/cm  Angle  S p a t i a l  i  em2/s  Density  £  s  time  v i s c o s i t y  0  N  nm  g/cm  shear  Kinematic  +  cm  s t r e s s  v  9  s t r e a k s  s t r a i n  A u t o c o r r e l a t i o n  p  between  e x t e n s i o n a l  mm  180  S u b s c r i p t s / S u p e r s c r i p t s  0  I n i t i a l  w  Wall  +  Non-dimensional  REFERENCES  A c h i a ,  B.U.  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Dry a  master  Separan  g l a s s was  500  Small  amounts  This  l i q u i d  w e t t i n g  to  a c t i o n  the  amount  of  same  steps  were  concen-  drag  p r e p a r a t i o n  AP30  batches  powder  beaker  water  s w i r l i n g  of  r e d u c t i o n ,  and  h a n d l i n g .  f o l l o w e d  i n  the  i n  d i s t i l l e d  made  was  as  water  were  f o l l o w s :  weighed  a c c u r a t e l y  to  b a l a n c e .  d i s t i l l e d rpm.  batch  Separan  M e t t l e r  A  of  same  c a r e f u l  of  d i l u t i n g  1.  the  s o l u t i o n  b a t c h .  S o l u t i o n s prepared  S o l u t i o n s  polymer  produce  on  p r e p a r a t i o n  of  not  depending l e s s e n  Separan  s t i r r e d of  d i s p e r s e g r e a t l y  c o n t a i n i n g by  the the  a  about  magnetic  powder  were  p a r t i c l e s  reduced  c o a g u l a t e .  188  t h e i r  200  s t i r r e r dusted (Figure tendency  ml  of  a t  about  into A . l ) . to  189  3. gm  of  Separan  batch  per  s o l u t i o n  4. rpm  These  u n t i l  to the  run  mix  batch  were  s o l u t i o n s t r a n s f e r r e d  The  d i s p e r s i o n  complete  batch  r e s e r v o i r  d i s s o l u t i o n  batches  q u a n t i t y  thoroughly  was  for  thus (153  about  g e n t l y  in  2.5  into  a  &/run). 12  hours  s t i r r e d  about  2.5  £  at  1  master  about  of  d i s t i l l e d  were  d i l u t e d  I  prepared  The with  s o l u t i o n a i r  60  water.  to was  the allowed  a g i t a t i o n  in  tank.  E r r o r  in  d e s i g n a t i n g  batch  s o l u t i o n s  i s  estimated  at  l e s s  a r i s e  from  d i f f e r e n c e s  in  the  the  c o n t a i n i n g  b o t t l e .  Master test  d i s p e r s e d  small  c o n c e n t r a t i o n than t o t a l  ±  values 2  to  wppm.  volume  t e s t  It  of  water  b a t c h . Separan  AP30  powder  7  h—1000ml  beaker  - d i s t i l l e d -magnetic  Figure  A . l .  Method  of  Separan  water s t i r r e r  d i s p e r s i o n .  may in  190  A.2  V i s c o s i t y  Measurements  Separan The was  AP30  Separan  c h a r a c t e r i z e d  from  v i s c o s i t y  -  by  Water  Solutions  AP30-water i t s  s o l u t i o n  i n t r i n s i c  used  v i s c o s i t y  in  t h i s  study  obtained  [n]  measurements.  Cn]  1 im 'sp  0 0 x-*0  Table V i s c o s i t y Water  Data  for  F r e s h l y  S o l u t i o n s  in  Prepared  5 0 - S e r i e s  V i s c o s i m e t e r s  in  Separan water,  A . l  at  AP30 c o n c e n t r a t i o n C, parts per m i l l i o n  0  (water)  t  0  =  12  S e p a r a n - d i s t i 1 1 e d Cannon-Fenske  2 0 . 5 ° C  * D r a i n i n g t i m e , t, s e e s . V i s c o s i m e t e r 5 0 - s e r i e s #E463 #98 #1262  280.0 311  328.5  .0  --  404.6  50 62  454  103  707.5  .4  --  155  -- .  310  -- .  d r a i n i n g  282  --  .5  24  The  262.8  time  is  an  average  of  3  995.0 2351  measurements.  .0  Table R e l a t i v e  and  Reduced  V i s c o s i t y  AP30-Water  Concn. C wppm.  of  Separan  S o l u t i o n s  R e l a t i v e . Vi scos i t y ' ' '  Reduced/ V i s c o s i t y ^  2  > '  n  r  1  0  (1)  A.2  —  .000  12  1.112  24  1  .250  104.16  50  1  .445  114.10  62  1  .729  130.17  93.33  103  2.527  148.25  155  3.528  163.  310  8.337  236.  R e l a t i v e V i s c o s i t y or V i s c o s i t y Ratio  _  n  s o l u t i o n  _  t  water S p e c i f i c r  (2)  V i s c o s i t y  n 'sp  =  Reduced V i s c o s i t y or V i s c o s i t y Number  The Figure  A.2  as  i n t r i n s i c 112  dl/gm.  n  'r  -  1  sp  v i s c o s i t y  [n]  was  obtained  from  250  "»  •  r  200  •nsp c  150  ®  [n] =CI +i0m  dl/gm  4  100 h  /  /  sp  =  122 dl/gm  / •  /  / 8 0 1  J  L  1  100  0  C Figure  A2.  _l  L  200  300  wppm  Reduced v i s c o s i t y vs. c o n c e n t r a t i o n d i s t i l l e d water s o l u t i o n s .  for  Separan  AP30  -  193  A.3  P r o p e r t i e s  of  the  R e f r a c t i v e  Table R e f r a c t i v e  Index  and  selected  at  Propylene  C o n c e n t r a t i o n %  D-203  intervals)  =  R e f r a c t i v e  3  76.09  Index  n  (water)  Densi ty 2 0 P20  1 .3330  1 .0000  1 .0  1 .3340  1 .0008  2.0  1 .3351  1 .0016  3.0  1 .3361  1 .0024  4.0  1 .3372  1 .0031  5.0  1 .3382  1 .0039  6.0  1 .3393  1 .0046  7.0  1 .3403  1 .0054  8.0  1 .3414  1 .0061  9.0  1 .3424  1 .0068  10.0  1 .3434  1 .0075  CRC P.  weight  Handbook  (1970),  ed.  of R.C.  Chemistry Weast.  for  Water  CH20HCH0HCH  wt  0.0  in  concentration  g l y c o l :  M o l e c u l a r  C h a r a c t e r i s t i c s  Glycol  unit  Enhancer  A.3  Density  Propylene (data  Index  and  Physics,  51st  e d . ,  APPENDIX  B  GROSS FLOW DATA AND ERROR ANALYSIS  B. 1  E r r o r  Ranges  Q f l o w .  The  and  AP  Flow  volume  f o r  of  a  to  0.5%  the  ( i )  ( i i ) and  r e a d i n g  seconds as  the  5  volume  e r r o r s  q u a n t i t i e s  during  d e f i n e d  Cahpter  was  of  g i v i n g  l i q u i d  about  measured  m l ,  i n  gross 4 . 1 .  12  w i t h a  a  t o t a l  c o l l e c t e d  l i t r e s . 1000  i n  This  ml  maximum  graduated e r r o r  of  c o l l e c t e d . of  response the  a r e  Data  Q  then  i  C a l c u l a t e d  measured  measurement was  and  q u a n t i t i e s  accuracy  of  the  r u n ,  volume  operator  reading  range  Q  w i t h i n  The by  a  l i q u i d  c y l i n d e r f o r  were  Rate  During bucket  Measured  c a l c u l a t e d  B . l . 1  a  f o r  timing to  c l o c k were  r e s p e c t i v e l y .  s t a r t  d i a l .  estimated The  the and The as  percentage  f o l l o w s :  194  l i q u i d stop  was the  maximum ±  0 . 3 e r r o r  determined c l o c k ,  t o t a l  and  ±  would  and  response 0.1 then  195  Q, m 1 / s e c  Re  maximum  475  23,000  minimum  35  The  1 ,  estimated  tota1  700  e r r o r  A  with  the  Using  p o s i t i v e  the  s i g n  extimated  time,  Q  values  AV  =  used  in  for of  V  sees  e r r o r  in  25  3. 2  342  0. 2  Q  (=  t j  V / t ) ,  !4t  +  ( B 1 )  maximum and  t,  p o s s i b l e Q  =  e r r o r .  *  and  0.6%  ma x  B . I . 2  Pressure  The as  d e s c r i b e d  drop  AP  e r r o r in and  was  of  t h i s  AP  d i f f e r e n t i a l by  Achia  read  about study,  decreased  Drop  from  the  mm  Re  4000,  with  H20  pp.  t r a n s d u c e r  A . 1 - 2 ) . and  column.  At  flow  in  AP  the  i n c r e a s i n g  e r r o r Re.  A  to  Sherwood,  Using equations (2.3) and T.K. and Reed, C.E., 1968,  Chemical  had  mean  was  The  r e c o r d e r  estimated  in  be  (1971,  0.50 >  pressure  a  c a l i b r a t e d  pressure constant  r a t e s  was  of  about  value  of  i n t e r e s t 5%  2%  was  s a t i s f a c t o r y .  Engineering,  2nd  ed .  ( 2 . 4 ) , Applied  M i c k l e y , H.S., Mathematics  196  Estimated and  measurement  i . e .  D  =  e r r o r  possible mean  2.63  value  of  of  temperature  is  assumed  d e v i a t i o n  e r r o r  ±  for  0.04  cm.  ranges Re  =  the  the  10,000 a  roundness  pipe  diameter  From  for  during  from  these  flow  was  rate  Pressure Mean  at  a  v a r i a t i o n  n e g l i g i b l e ,  hence  +  1 . 3%  AP:  +  3 . 0%  U:  +  1 . 3%  Q: drop  v e l o c i t y  Re:  +  1 . 0%  Fr i c t ?on  f a c t o r  f:  +  5 . 0%  +  3 . 0%  +  2 . 5%  +  1 . \%  shear  s t r e s s  Wall  shear  Drag  r e d u c t i o n  The  B . l  maximum  Number  Computed  Tables  the  (The  T  : w  Chapter  1.5%,  Reynolds  Wa 1 1  in  ±  pipe  v  c o n s t a n t . )  Flow  B.2  the  q u a n t i t i e s  c a l c u l a t e d .  t e s t  was  e s t i m a t e s ,  f o l l o w i n g  were  of  4.1 to  Values  v e l o c i t y  and  f o l l o w i n g to B.5  DR:  Data  T a b u l a t i o n s  computer  c a l c u l a t e l i s t  u*:  the  the gross  program gross flow  used  flow d a t a .  the  equations  q u a n t i t i e s .  197  $LIST  SEP 1  C  PROGRAM  2  10  3  101  4  TO  CALCULATE  102  END=99)  IAB.CONCVIS  IF(IAB.EO.l)  GO  TO  1  7  IF(IAB.GT.1)  GO  TO  2  1  9  103  WRITE16.103)  IAB  F O R M A T ! / / / / / / / 1 6 X , ' T A B L E  10  1,38"( • - • ) / / 1 0 X ,  11  2*(PIPE  12 13  DIA.=  2.63  CM  ;  ,.  121  PRESSURE  122  16  FORMAT I 81 ( * - •  FOR  305  CM  DATA OF  FOR  WATER'/16 X  PIPE)'/)  )/)  'F • , 8 X t  *  * / 5 X , ' M L / S E C , 3 X , ' C M  WATER',1X»'DYNES/CM2',2X,  2 ' C M / S E C , 3 X , ' C M / S E C , 1 3 X , ' T H E 0 R E T . ' , 4 X , ' W A T E R ' / 8 l ! • - • ) )  18  GO  19  2  20  107  21  TO  3  WRITE(6,107)  IAB.CONCVIS  FORMAT'<///////23X,'TABLE 1 3 0 ' / / 2 9 X . F 5 . 0 , '  22  2'SOLUTION  23  3'tPIPE  24  WT.  VISCOSITY  DIA.=  2.63  B - ' , I 2 , ' .  PPM =  CM  IN  ' , F 7 . 5 , ' ;  GROSS  DI ST I L L E D  FLOW  WATER  DATA  FOR  SEPARAN  •/ , 2 3 X , 4 5 ! • - •  AP  J//29X,  CM2/SV/19X  PRESSURE  DROP  FOR  305  CM  OF  PIPE)'/)  WRITEI6.109)  25  109  26  FORMAT(90!•-•)/> WRITE!6,106 )  27  F O R M A T ( • N O . • , 5 X , ' Q ' , 8 X , • D P • , 7 X , • T W • , 7 X , • U • , 8 X , ' U * ' , 8 X , • R E ' , 8 X , • F • ,  106  28  110X,  29  2 ' " C M / S E C , 3X, ' C M / S E C , 13X,  30  3  31  11  32  104  *F',8X» *DR'/5X,'ML/SEC',3X  READ(5t104,END=10) FORMAT(2F10.5 VEL=Q/5.4286 RE=Q*0.4843/VIS IFIRE.LE.2500.)  GO  TO  14  36  IF(RE.GT.2500.)  GO  TO  15  14  FFS=16./RE GO  39  15  i*0  16  41  IX,•DYNES/CM2•,2X,  Q.DELP  35  38  WATER' ,  )  33  37  , 'C M  ' S O L U T I O N ' , 4 X , • WATER ' , 6 X , ' % • / 9 0 t  N=0  34  TO  16  FFS=0.046/RE**.2 F F F = 4.  1885*DELP/1VEL**2)  TAU=2.11*DELP  42  DRO=FFF/FFS •  DRAT=(  44  1.0-DRO)*100.  N=N+1 .  USTAR=TAU**0.5  46  IF!  47  WRITE(<6, 105) 105  49 13  51  123  IAB.EQ.l)  GO  TO  13  N,Q,DELP,TAU,VEL,USTAR,RE,FFF,FFS,DRAT  FORMAT(I3,5F9.2,F11.0,2F11.6,F8.1,//) GO  50  TO  12  WRITE(6,123)  N,Q,DELP,TAU,VEL,USTAR,RE,FFS,FFF  FORMAT(13,5F9.2,F11.0.2F11.6,/)  52  12  GO  53  99  STOP  54  DROP  FLOW  F O R M A T ( • N O . « , 5 X , ' Q ' , 6 X , • D P * . 7 X , • T W « , 7 X , • U • , 8 X , • U * ' , 8 X , • R E • , 8 X , • F ' • , 110X,  17  48  GROSS  WRITE!6,122 )  15  45  B - ' , I 2 , ' .  WRITE!6,121)  14  43  QUANTITIES  FORMAT!13,2F10.0)  6 8  FLOW  FORMAT!'!') READ15, 102,  5  GROSS  WRITE(6,101)  END  TO  11 .  •-')/)  ( P I P E  N O .  T A B L E  B -  D I A . =  2 . 6 3  Q  D P  M L / S E C  C M  1.  G R O S S  C M  ;  TW  W A T E R  D Y N E S / C M 2  F L O W  P R E S S U R E  U C M / S E C  D A T A  F O R  D R O P  F O R  U *  W A T E R  3 0 5  C M  O F  R E  C M / S E C  P I P E )  F T H E O R E T .  F W A T E R  1  3 7 . 0 0  . 1 0  . 2 1  6 . 8 2  . 4 6  1 7 9 2 ,  . 0 0 8 9 2 9  . 0 0 9 0 1 6  2  5 0 .  . 2 0  . 4 2  9 . 2 1  . 6 5  2 4 2 1 ,  . 0 0 6 6 0 7  . 0 0 9 8 7 5  3  7 0 . 0 0  . 3 5  . 7 4  1 2 . 8 9  . 8 6  3 3 9 0 ,  . 0 0 9 0 5 1  . 0 0 8 8 1 7  4  1 0 0 . 0 0  . 7 0  1 . 4 8  1 8 . 4 2  1 . 2 2  4 8 4 3 .  . 0 0 8 4 2 8  . 0 0 8 6 4 0  5  1 1 5 . 0 0  .  9 0  1 . 9 0  2 1 . 1 8  1 . 3 8  5 5 6 9 .  . 0 0 8 1 9 6  . 0 0 8 4 0 0  6  1 3 5 . 0 0  1  . 1 0  2 . 3 2  2 4 . 8 7  1 . 5 2  6 5 3 8 .  . 0 0 7 9 3 7  . 0 0 7 4 5 0  7  1 7 7 . 0 0  1 . 9 5  4 . 1 1  3 2 . 6 1  2 . 0 3  8 5 7 2 ,  . 0 0 7 5 1 9  . 0 0 7 6 8 3  8  2 2 5 . 0 0  2 . 8 5  6 . 0 1  4 1 . 4 5  2 . 4 5  1 0 8 9 7 ,  . 0 0 7 1 6 6  . 0 0 6 9 4 9  9  3 0 0 . 0 0  4 . 9 0  1 0 . 3 4  5 5 . 2 6  3 . 2 2  1 4 5 2 9 .  . 0 0 6 7 6 6  . 0 0 6 7 2 0  3 4 0 . 0 0  6 .  1 2 . 9 8  6 2 . 6 3  3 . 6 0  1 6 4 6 6 .  . 0 0 6 5 9 8  . 0 0 6 5 6 7  1 0  0 0  15  T A B L E  8 -  2 .  2 5 .  G R O S S  W T .  S O L U T I O N  ( P I P E  N O .  Q M L / S E C  D P C M  W A T E R  D I A . =  2 . 6 3  TW D Y N E S / C M 2  F L O W  P P M  I N  V I S C O S I T Y  C M  D A T A  S E P A R A N  D I S T I L L E D  =  ;  P R E S S U R E  C M / S E C  C M / S E C  U  F O R  U *  W A T E R  . 0 1 2 4 7  D R O P  A P 3 0  F O R  R E  C M 2 / S  3 0 5  CM  O F  F S O L U T I O N  P I P E )  F W A T E R  D R %  1  1 4 7 . 0 0  1 . 2 5  2 . 6 4  2 7 . 0 8  1 . 6 2  5 7 0 9 .  . 0 0 7 1 4 0  . 0 0 8 1 5 5  1 2 . 4  2  2 6 6 . 0 0  3 . 0 0  6 . 3 3  4 9 . 0 0  2 . 5 2  1 0 3 3 1 .  . 0 0 5 2 3 3  . 0 0 7 2 4 3  2 7 . 7  3  3 7 5 . 0 0  4 . 8 0  6 9 . 0 8  3 . 1 8  1 4 5 6 4 .  . 0 0 4 2 1 3  . 0 0 6 7 6 2  3 7 . 7  1 0 . 1 3  T A B L E  B -  3 .  G R O S S  5 0 .  W T .  S O L U T I O N  ( P I P E  N O .  Q M L / S E C  D P C M  W A T E R  D I A . =  2 . 6 3  TW D Y N E S / C M 2  F L O W  P P M  I N  D A T A  ;  U C M / S E C  S E P A R A N  D I S T I L L E D  V I S C O S I T Y  C M  F O R  =  P R E S S U R E  U *  W A T E R  . 0 1 4 4 3  D R O P  A P 3 0  F O R  R E  C M / S E C  C M 2 / S  3 0 5  C M  O F  P I P E )  F S O L U T I O N  F W A T E R  D R %  1  2 1 3 . 0 0  2 . 2 0  4 . 6 4  3 9 . 2 4  2 . 1 5  7 1 4 9 .  . 0 0 5 9 8 5  . 0 0 7 7 9 7  2 3 . 2  2  2 2 0 . 0 0  2 . 2 5  4 . 7 5  4 0 . 5 3  2 . 1 8  7 3 8 4 .  . 0 0 5 7 3 8  . 0 0 7 7 4 6  2 5 . 9  3  2 6 1 . 0 0 .  3 . 0 0  6 . 3 3  4 8 . 0 8  2 . 5 2  8 7 6 0 .  . 0 0 5 4 3 6  . 0 0 7 4 8 6  2 7 . 4  4  2 9 0 . 0 0  3 . 1 0  6 . 5 4  5 3 . 4 2  2 . 5 6  9 7 3 3 .  . 0 0 4 5 5 0  . 0 0 7 3 3 0  3 7 . 9  5  3 4 7 . 0 0  4 . 1 0  8 . 6 5  6 3 . 9 2  2 . 9 4  1 1 6 4 6 .  . 0 0 4 2 0 3  . C 0 7 0 7 2  4 0 . 6  6  4 1 4 . 0 0  5 . 5 0  1 1 . 6 0  7 6 . 2 6  3 . 4 1  1 3 8 9 5 .  . 0 0 3 9 6 1  . 0 0 6 8 2 6  4 2 . 0  7  4 4 0 . 0 0  5 . 6 5  1 1 . 9 2  8 1 . 0 5  3 . 4 5  1 4 7 6 7 .  . 0 0 3 6 0 2  . 0 0 6 7 4 4  4 6 . 6  8  4 6 1 . 0 0  6 . 0 0  1 2 . 6 6  8 4 . 9 2  3 . 5 6  1 5 4 7 2 .  . 0 0 3 4 8 5  . 0 0 6 6 8 1  4 7 . 8  T A B L E  B -  4 .  G R O S S  1 0 0 .  W T .  S O L U T I O N  ( P I P E  N O .  Q M L / S E C  DP C M  W A T E R  D I A . =  2 . 6 3  TW D Y N E S / C M 2  F L O W  P P M  I N  V I S C O S I T Y  C M  ;  U C M / S E C  D A T A  F O R  S E P A R A N  D I S T I L L E D  =  P R E S S U R E  U *  W A T E R  . 0 2 5 2 7  D R O P  A P 3 0  F O R  R E  C M / S E C  C M 2 / S  3 0 5  C M  O F  F S O L U T I O N  P I P E )  F W A T E R  DR %  1  2 8 6 . 0 0  3 . 6 0  7 . 6 0  5 2 . 6 8  2 . 7 6  5 4 8 1 .  . 0 0 5 4 3 3  . 0 0 8 2 2 2  3 3 . 9  2  3 2 3 . 0 0  3 . 9 0  8 . 2 3  5 9 . 5 0  2 . 8 7  6 1 9 0 .  . 0 0 4 6 1 4  . 0 0 8 0 2 4  4 2 . 5  T A B L E  B -  5 .  G R O S S  1 5 0 .  W T .  S O L U T I O N  ( P I P E  N O .  Q M L / S E C  DP C M  W A T E R  1  2 7 9 . 0 0  4 . 2 0  2  3 6 2 . 0 0  5 . 4 0  3  4 5 7 . 0 0  7 . 1 0  D I A . =  2 . 6 3  TW D Y N E S / C M 2  8 . 8 6  1 1 . 3 9  1 4 . 9 8  F L O W  P P M  I N  D A T A  =  ;  P R E S S U R E  C M / S E C  C M / S E C  U  S E P A R A N  D I S T I L L E D  V I S C O S I T Y  CM  F O R  U *  W A T E R  . 0 3 5 2 8  D R O P  A P 3 0  F O R  R E  C M 2 / S  3 0 5  C M  O F  F S O L U T I O N  P I P E )  F W A T E R  D R %  5 1 . 3 9  2 . 9 8  3 8 3 0 .  . 0 0 6 6 6 0  . 0 0 8 8 3 3  2 4 . 6  6 6 . 6 8  3 . 3 8  4 9 6 9 .  . 0 0 5 0 8 6  . 0 0 8 3 8 5  3 9 . 3  8 4 . 1 8  3 . 8 7  6 2 7 3 .  . 0 0 4 1 9 6  . 0 0 8 0 0 3  4 7 . 6  203  B.3  C a l c u l a t e d  Data  f o r  Figure  6 . 3 :  Table Data  20  wppm  p i pe  Separan  d ia .  W:  =  from  AP  0.302  Thomas  30  in  et  Tables  B.6  to  B . 8 .  B.6 (1973)  al.  -  Data  Set  (1)  water  cm  water  S :  so Iut io n  water  so  Re  3800  6000  7500  Iution  f/2  w s  w s  w s  uu  *  s  0.0048 0.0038  8.71 7.75  0.0045 0.0032  13.32  0.0042  16.09 13.14  0.0028  A u t o c o r r e l a t i o n ;  11  10  Sublayer  ^  T  1 .66  0.037  1 .93  <  < T  l a g  0.024 0.040  0.017  2.19  .23  P e r i o d s  35.  0.011 0.021  204  Table Data  40  wppm  pipe  from  Separan  d ia.  =  Thomas  AP  0.302  A u t o c o r r e l a t i o n ;  273  and  in  B.7  Greene  0.9  wt.  (1973)  %  -  Data  Set  (2)  s a l i n e  cm A T / T ,  >  1000  I ag  Re  w  s  f/2  u*  cm/s  T  s  4,400  0.0053  10.60  0.040  5,400  0.0050  12.63  0.031  6,800  0.0045  15.09  0.014  7,500  0.0043  16.27  0.01  9,200  0.0041  21  0.0066  13,500  0.0038  27.54  0.0055  22,500  0.0032  42.26  0.0032  6,800  0.0036  13.50  0.045  8,200  0.0033  15.47  0.024  14,000  0.0025  23.26  0.014  16,000  0  26.10  0.011  20,000  0.0021  30.48  0.0072  24,000  0.0021  36.40  0.0070  36,500  0.0016  47.56  0.0030  .0024  .19  3  205  Table Data  200  wppm  P i pe  d ia.  PoIyisobuty =  2 . 42  I ene  from  in  B.8  Meek  TetraI  (1968)  in  cm  Tetralin =  y  2.11  eP,  p  FIB •• in =  0.972  gm/cm  Re i\ c T  f  S  ms  3  11* T+  u  Tetralin  =  2.13 cP, p 3 9 7 2 g m / c m 0-  =  T  cm/s  s ms  T  +  cm/s  58,700  0. 0054  16  22.5  26. 2  28  30  26.5  64,400  0. 0050  10  20  29.5  18  25  27.6  74,400  0. 0049  8.5  20  32.0  19  30  32.2  T  +  Tq:  Is V  s u b l a y e r  period  from  a u t o c o r r e l a t i o n s  206  APPENDIX  C  FABRICATION OF THE PIPE  The  0 . 5  m  o p t i c a l  bench  was  s p e c i a l l y  s e c t i o n  d e s i r e d  in  the  order  of  I.  i n  C.1  of  i n c r e a s i n g  the  pipe  f a b r i c a t e d  v i s u a l i z a t i o n  2 .  B r o a c h i ng  3.  Mach i n i ng  t h e s e ,  greater  to  give  s t u d i e s .  complexity  t r a v e r s i n g  were  the  the  c r o s s -  Three  methods  t r i e d . -  only  the  l a s t  was  s u c c e s s f u l  and  d e s c r i b e d  d e t a i l .  Casting The  r e s i n  #2200  Vancouver, the  s e c t i o n  C a s t i n g  Of here  f o r  long  pipe  (made  by  B . C . ) .  A  method  was  T a y l o r ' s smooth  t r i e d  Arts  with  and  machined  ' C r y s t a l  C r a f t s  mandril  c a s t '  L t d . , was  used  f o r  bore. The  s e c t i o n ,  c a s t i n g  t r i a l s  gross  showed  inhomogeneity  e x c e s s i v e when  shrinkage  viewed  of  a g a i n s t  the a  l i g h t  207  source  and  Removal rough  C.2  of  b r i t t l e n e s s  t h a t  the  was  mandril  Broachi  cm  f a b r i c a t e d  to  give  diameter  A  from  aluminium bore  change  of  per  b e t t e r .  and  gave  an  u n d e s i r a b l e  d e s i r e d  cm (3  cm  long)  a  broach  technique  p i l o t gave  P l e x i g l a s  with  more  might  broke bore  have  due  to  and  2.63  cm  Although  e x c e l l e n t  blanks  abandoned  of  h o l e .  gradual  length  was  designed  c r o s s - s e c t i o n  diameter  s i m i l a r  of  s p e c i a l l y  smoothness in  the  p r e s s .  diameter  p o s s i b l y the  t e s t s  worked  complexity  manufacture.  M a c h i n i ng  produce  ness.  2.30  was  broach  the  blanks  u n i t  The  This  long  broaches  The  broach  C.3  a  shape,  s e r i e s  of  d i f f i c u l t  i m p o s s i b l e .  ng  30  and  machining  s u r f a c e .  A  on  made  machining  steps  the  test  s e c t i o n  method  gave  the  Four  u n i t s  are  d e s i r e d  were  made  t h a t shown  were in  f i n a l l y the  c r o s s - s e c t i o n and  connected  used  f o l l o w i n g and  to digrams.  wall  e n d - t o - e n d .  smooth-  208  D e s c r i p t i o n  Machined  block  d i m e n s i o n , h  =  50;  d  Fastened (14; 4mm bore  Uni to d r i h o l  mm, =  12  and I = 5  f l a t 350;  to b  des i red =  f l a t to block with d i a . ) and s c r i b e d  U J  t>/ock  50;  b o l t s pipe  t p r e c i s e l y a l i g n e d and fastened lathe c a r r i a g e ; then fed into l l mounted in the c h u c k . P i l o t e ; 1.2 cm. Final bore; 2.63 cm  chyck  V//////////A e  Inside surface p o l i s h e d in s t a g e s : Final bore with reamer. F i n i s h ing with dental a b r a s i v e .  F l a t  turned  give  d e s i r e d  h o l o g r a p h i c outer p o l i  Ends  over  and  r e b o l t e d  c r o s s - s e c t i o n . test  s u r f a c e  block  m i l l e d  had  f l a t  to The  i t s and  shed.  faced  1"-QVF  pipe  chuck  and  machined  f l a n g e s  to  take  carnage  209  1.  P l e x i g l a s  block  2 .  P l e x i g l a s  f l a t  3.  Cover  h.  Enhancer  5.  S l o p i n g  6.  Wa11  s l o t  7.  F1ow  s e c t i o n  8.  Figure  C.1  p l a t e i n f u s i o n  l i n e  d i s t r i b u t e r  channel  b l o t s  Detai 1 s l o t .  of  the  flow  s e c t i o n  and  wall  APPENDIX  D  FRINGE ANALYSIS, DATA SAMPLING METHOD AND COMPUTER PROGRAMS  D.1  Determination  The out  and  4.3a  the  and  The  MDM  Fringe  r e a l - t i m e  data  4 . 3 b  d i r e c t i o n s .  of  the  was  by  f r i n g e  I n i t i a l l y  technique  f r i n g e s  processed  show  Displacement  a  r e c o r d e d • o n > ' f i 1m  d i g i t a l  computation.  o r i e n t a t i o n  and  m i c r o d e n s i t o m e t e r  r e p l a c e d  by  a  were  more  read Figures  c o o r d i n a t e  (MDM)  was  e f f i c i e n t  used.  p r o j e c t i o n  techni que. A U . B . C . ) e a r l y  was  Joyce used  m i c r o d e n s i t o m e t e r f o r  experiments.  f r i n g e A  Figure  4 . 3 a  i s  of  the  scan  r e p r e s e n t  To  obtain  a  shown  a v a i l a b l e f e r e n t frame  z  i n  the  had  could  dark  be  to  the  D . l .  and  b r i g h t  t r a c e , be  instrument  p o s i t i o n s ,  x-scan  Figure  s a t i s f a c t o r y  m i c r o d e n s i t o m e t e r  p o s i t i o n  t y p i c a l i n  manual. f r i n g e  determined.  210  Mech.  readout a t  a  The  Eng. i n  of  z - p o s i t i o n  of  peaks  and  These  f i e l d  troughs  of  d e t a i l s  scans of  the  r e s p e c t i v e l y .  parameters  From  D e p t . ,  some  f r i n g e s  v a r i o u s  a d j u s t e d .  whole  a c c u r a t e l y  (of  a  the are  along s i n g l e  d i f -  211  Figure  D . 1  M i c r o d e n s i t o m e t e r frame.  trace  of  a  motion  p i c t u r e  212  Since (each t i o n  trace  =  f r i n g e  f i g u r e s of  the  in  2  to  4.3  and  f i l m . 3  of  s ,  method  each  l o c a t i o n  5.6)  was  t h i s  was  frame  adopted.  the  In  -  25  mts .)  By  t h i s  of  i n t e r e s t  t r a c e d  way,  extremely  the  from  time  a  s i m p l e r  method,  a  a  s i n g l e  t r a n s -  'A1,  m a g n i f i c a t i o n  t r a c e  could  be  MDM  trace  The  l a t t e r  MDM-measured  was  useful  as  a  found  to  be  was  f r i n g e  check  d i s p l a c e m e n t s  on  w i t h i n on  the ±  the  0.1  obtained  Steps  in  1.  Fringe  The ment  A n a l y s i s  negative  using  the  was  c a r e f u l l y  framing  notch  (N  in  window Figure  a l i g n e d  and  a l i g n -  D.2).  2.  A frame at ' z e r o ' time, with flow but with no g r a d i e n t s was chosen. Fringes at and downstream of 'A' were t r a c e d . The mean f r i n g e width along each z l o c a t i o n was measured to account for non-uniform f r i n g e w i d t h , if any.  3.  Frames flow The  at  and new  A l l  the  f r i n g e data  described  in  i n s t a n t s  g r a d i e n t s  p o s i t i o n  enhanced 4.  d i f f e r e n t with  of at  the 'A'  with  were  a l i g n e d .  g r a d i e n t was  t r a c e d .  was  d i g i t i z e d  as  the  f o l l o w i n g  s e c t i o n .  p r o j e c mm  unmagnified  f i l m .  D.2  p r o j e c -  ( p o s i t i o n  lOx  d e s i r e d  consuming  mts.  method.  the  MDM  was  at  The t i o n  60  technique  verse  the  X,tn ?25 - . 1 0 . o1r4, . 3 0 . 2- 6o. 1 4 . ~1 4 . . . • ^ - 3 0 . 1 9 .  'i  x  16.22.S3.27.36.23.24'.27.30.25.17. 32.1?.25.3*  r.°:i J . : : " ? : o l : c d . : c l ; ^ « - 3 4 • S 9 - 2 3 • e s . 3 1 . 3 6 . s o . 2 5 , £ 9 . 3 4 . 3 0 . 2 9 . 2 3 . ? 4 . sr.. 3 c 1W. 2 2 . £ 7 . 2 8 . 2 0 . 1 9 . £ £ . £ 5 . £ 8 . 2 0 . 1 7 . 1 9 . 2 3 . 3 5 . 3 6 . 2 7 . £ 5 . £ 6 . 2 3 . 2 6 , 2 4 . 3 2 . 2 0 . 3 f i . " 4 ? ' . " " ' t • \ e fj ( -1 ft it |f B J is i f . r w . JO j n £ j . irjs nfft i i - i ii q a *••.» ! 5 - •„ » - > „ , • « , . «, „ * «, , o s « s u „ • 5 M „ „ «  t  GENERAL DATA CARD 4.  38.39.40.40.41.41 5. 5. 6, . 7.  ~m:-  FSOM —sr.-  U. B . C . C O M P U T I N G  ,43. ft,  'V.  1 * 1; 1^ >t iQi* i ; | » IT y o ,^  a i B • 3> e  1  ;^rs z. p : i  1 . < :"•  1  ' p . 13  ?• : 139 1 a i i u »  1  ) »:  3, nt  \f.  1 fi  r  1,.-,  17  62 6} C  65 U  61 CI 63 . 0 II l i I ) 4  ; II  1? m : a 51 M to  «i « u «» > «. • <» * « >i ^ JJ il  CENTRE  14 , l \  t  Ii P  «  l  3  i  I t  s  t  i  i I  ii ii !! ii ;i ii ii i) ii ii :J ii y  ; i it  :s;:  :J  z:zi :i  21 « 3 4 :s3t u  -  33 •': <:  II I 11111111 I I I 11 11 i 1  43 u a <s 1: 13  u  si  si si <i  K S;5)  u  53  *,  1 x,ly^ A  u !>  u  O  illll  ii  2  3 33 2  «  * Iz  5  n  § 5555 5  %C G C2G 44444444444444444 7 5 5 5 5 5 5 5 5 5 5 5 5 J9S929 55G55 GD 660 G 6GG 5G66G 6G G 7 7 7 7 7 7 7 0 7 7 CEPH 7 2> OJWJ--:.  5055055555 5 5 5 5 5 5 5 5 5 5 !  it J I ' s i i i i  S C6GS653 8 53 5 SSGE 665S I 7 7 7 7 7 7 7 ? 7 7 7 7 7 1 7 1 j] 7 7 7! 9 9 9 9 9 9 9 9 9 S S 9 9 9S 3 3; 3 n -j 93 9 a39 3 i ;9 3 is) 3 i 3 i :ni = ; 9 39• !  : SSD88088Q8 8V?4  9 ] i ] ] i : i  33  i  2 G 8 9 9 9 S 9 9 9.9 9 S 9 9 S 9  ) t I ID II 11 43 14 U It » 41 II 23 21 22 : J 2 ' 25 23 2> 21 11 S3 31 32 33 34 J j i t J> 31 31 41 I' <! 43 44 43 4; 41 (? 13 : J SI ; ! 53 S i ' i j i i i l 33 S3 tg El (2 [3 SI (5 ii U El £3 19 II |2 13 14 ~:i I i II '! II . ' i  F i g u r e O n s e t atioin  13  11  11  33333Q33G33033333  444444444 4 4444444444:  1 2 3 » i t  p.  22222222222222222  33l33g33@33B33l33B33|  3  r  I  a ti ts « ci o :i u ii ii it ;i u :i(! 54444 Q HQ 1 li] 1 J0 11J1! 11  a ii a  !  22222222222222222222: I  :i  '] JJ  •2222  IS 8 3  0 o o o o a o o o o o o o o o o o o o o o a o o a c o u u o o i] G u ^ o o o 3 0 a o o a o y • • o o o o c c e o o o o o o o o o c o a o c (j c o o o o s o o o o o 1  «  0 1 , C 0 Gr, 0 o 1  4 5 . 43.41-.. 46. 4 7 . 4 7 . 43. 48. 49. 5 0 . 5 u , 5 1 . 5 1 ,  0. t J .  GENERAL DATA CARD f « O M O. B . C . C O M P U T I N G  62 61 6 « 6 5 Dt 67 61 $3 10 i l 12 Ti '« f, Ii n  «l  CENTRE  ''-4. 4 4 .  <*, 1 H .  10 40  0.2.  D i g i t i z e d  Fringe  shows F i g u r e 4.3. i N u i B i i b e r s o.n c a r d s .i in mm from x<>, t « o n a I G x im-a : g OTI i if J e d  Data. denote s c a l e . ]  fringe  devii-  214  D.3  D i g i t i z i n g  c o n d i t i o n (x)  D.4  Computer  t r a v e r s e  f r i n g e  was  taken  the  each  d a t a ) .  and  The  f r i n g e s  along  Data  were z  The  Program  used  scan data  f o r  as  to  (see was  through  datum.  determine  Figure  D.2  processed  Computing  a t  the  s u c c e s s i v e  the  mean a  n o - g r a d i e n t downstream  f r i n g e  sample  of  width d i g i t i z e d  summarized.  C o r r e l a t i o n s  D e s c r i p t i o n  (Letters describe  No.  of  in paranthesis function in  (N),  data  no.  ( i )  a t  ( i i ) -  Mean  f r i n g e  x-scan -  -  -  -  are the  i n t e r f e r o g r a m s  s e p a r a t i o n s Fringe  COMPUTE BASIC QUANTITIES  'A'  Two  f o r  as  Step  READ  Program  f o r  ( K ) , of  s p a c i n g s e t  z - s c a n s  Instantaneous  f r i n g e and  along  f r i n g e  ( J ) ,  (I) flow  (1=3, K=l) [ ( I ) , K= 2 - • - I K ]  each  1  (AFHW) s h i f t  t r a n s v e r s e f r i n g e i n t e r f e r o g r a m  Residual  to  x - s c a n s  flow  between  n o - g r a d i e n t  f r i n g e  used  of  w i t h - g r a d i e n t  data  O v e r a l l mean t o t a l sample  no.  n o - g r a d i e n t  w i t h - g r a d i e n t Mean each  those program)  width  flow  (FF)  f o r (MFW)  width  f o r (OMFW)  s h i f t  Instantaneous-mean  = (R)  215  of  residuals:  Squares  COMPUTE CORRELATION QUANTITIES  Squares z i ( 0 ) ,  a t  Z  l o c a t i o n  Z i ,  z  • • •  2  a t l o c a t i o n with ( l ) . . . . Z l ( N )  Products  a t  Sums  square  and  v a r i o u s  s e p a r a t i o n (RNR)  s e p a r a t i o n s  root  of  (SRR, C o r r e l a t i o n  PRINT  mean  f o r  SRNR,  each  Turbulent  I n t e n s i t y  Mean  Turbulent  I n t e n s i t y  Mean  f r i n g e  of  sign  C  and  program  t i o n s , R  U)  R i n  i)  SPR,  C  f o r  ( T )  computing  d i f f e r s  from  d i r e c t i o n  of  The  A n a l y s i s and  standard  of  d e v i a t i o n  I  (COR)  of  c o r r e l a -  that  f o r  i s  as  shown  i n  D.2  p i c t u r e  are  s u c c e s s i v e  frames.  Data  and was  time  c o r r e l a t i o n  i n t e r f e r o g r a m s  motion  Samples  QSRNR)  that The  i i )  of  QSRR,  value  Figure  A n a l y s i s  MSPR,  (MTINT)  measurement  D.5  the  q u a n t i t i e s  s h i f t  C o r r e l a t i o n  The  ( P R )  i n t e r f e r o g r a m  Mean  Note:  (RR)  l  sum o f s q u a r e s of the above at v a r i o u s s e p a r a t i o n s  COMPUTE  Zj  A  done  samples u s i n g  f o r a  the  mean  separate  value  program.  216  l  C  2  c c c c c c c c c c c c  3 4 5 6 7 8 9 10 11 12 13  PROGRAM  FOR  COMPUTING  FLOW  QUANTITIES  OF M O T I O N P I C T U R E F R A M E S FROM K E A L K IS T H E N U M B E R OF S E T S OF D A T A M l ) J  IS  IS  THE  THE  SEPARATION I  IS  SAY AND  N O - M O U U L A T ION  NUMBER  THE  OF  SCANS  IN  OR  FROM  T I ^E  REFERENCE  THE  REAL  15  DIMENSION  16  D I M E N S ION  CONDITION  TRANSVERSE  SET  DIRECTION  AT  THE  NUMBER  OF  COLUMNS  CORRESPONDING  TO OR  A  FRINGE  TRANSVERSE  POSITION SCANS,  MINUS  17  DIMENSION  18  DIMENSION  19  DIMENSION  20  DIMENSION  XI100,25,3),FF( 100,25,1),F( 100,25,1),R(100,25,11 AFHW(25),SFW(25),FW(25) TRMFS(100),MFW(100),MTINT(100) P R ( 1 0 0 , 2 5 , 2 5 ) » RNR( 1 0 0 , 2 5 , 2 5 ) , R R 1 1 0 0 , 2 5 ) SPR 1 1 0 0 , 2 5 ) , S R R ( 100,25),SRNRfICC,25),A(100,25) MSPR1100,25 ),OSRR{ 100,25),QSRNR( 100,25),COR(100,25)  21 22 23  DATA  24  DIMENSION  PLUS,MINUS/'  25  REAL  MTINT  26  REAL  MSPR  27  REAL  MFW  +  • , •  -  • /  ISEP(25)  28 29 30 31  2  READ IN V A L U E S FOR IK.IR.IC READ(5,2)IK,IR,IC, IS FORMAT C 4 1 3 )  32 33  READ  34 35  IN  DATA  DO  4  K = l , l  DO  4  1=1,3  36  4  RE A D ( 5 , 1 ) ( X f K . J , I ) , J = 1 , I R )  37  1  FORMAT(25F3.0) DO 5 K = 2 , I K  38 39 <V0  5  41  C  <t2  c c  *3 44 45 ^•6  c  FRINGE  WIDTH  FOR  DATA  SET  1,  NO  GRADIENT  J=1,IR IS  THE  SUM  OF  THE  FRINGE  WIDTHS  ALCNG  A  SCAN  SFW(J)=0.0 DO  c  51 52  c  53  c  11  1=1,2  FW IS T H E F R I N G E WIDTH BETWEEN FW(J) = X ( 1 , J , 1 + 1 ) - X ( l , J , I )  50  SFW(J)=SFW(J)+FW(J) 11  CONTINUE AFHWtJ)=SFW(Jl/DIFF  10  CONT INUE  55 56  10  SFH(J)  48  54  AVERAGE  DIFF=2.0 DO  47 49  DO 5 1 = 1 , I C R E A D I 5 , 1 ) ( X I K , J , I ) , J = 1 , IR ) CALCULATE  SCAN  I NTERFEROGRAMS  DISTANCE  T H E R E A R E K = 5 0 D A T A S E T S , J = 2 5 ROWS 1= . C O L U M N S OR F R I N G E POSITIONS  14  MICRODENSI TOMETER  HCLOGRAPHIC  TWO  SUCCESSIVE  FRINGES  217  57  C  5B  c c  59  CALCULATE DATA  60  AMF=0.0  61  DO  21  INS TANTANEUUS  c c  65 66  IS  T H E SUM ALONG  FRINGE SHIFTS T R M F S l K )= 0 . 0 DO  70 71 72 73 74  c c c  76  29  AVERAGuD  THE TRANSVERSE IN  c  80  c c c c  20  81 82 83 84  IS  THE I N S T A N T A N E O U S  c  88 B9  DO  102  DO  40  J=1,IR  DO  40  1=1,IC  94 95  96  C  97  c  R(K, 40  100  POINT  MEAN  FRINSE  SHIFT  ;  IS  •  THE RESIDUAL  102  DO .1  AT  EACH  POINT;  RR(K,J,I)  THE SQUARES  OF R  J,I)=FF(K,J,IJ-OMFW  CONTINUE CALCULATION CALCULATION  101  61  O F T H E P R O D U C T OF R E S I D U A L S oF T H E SPATIAL CORRELATIOM  AT  SEPARATION  DISTANCES  J=1,IR  1=1  102.2  RR(K,J)=R(K,J,I)*R(K,JtI)  103  DO  104  1= I  105  60  N=l,IS  IF((J+N-l).GT.IR)  106  PR(K,J,N)=R(K,J  107 108  f  GO T O  110  60  CONTINUE  61  CONTINUE  61  I ) * R I K t J + N—l11 I  RNRt K , J , N ) = R « K , J + N - l ,  109  124  EACH  I )  K=2,IK  R(K,J,I)  98 99  123  AT  c c  93  122  SHIFT  OMFW=AMF/FLO AT( I K - 1 )  92  120  FRINGE  CONTINUE  91  121  AXIAL  AMF=AMF+MFW(K) 21  90  119  MEAN  CONTINUE MFW I S T H E T R A N S V E R S E MFW(K)=TRMFS(K)/IR  87  117  OF  CONTINUE  TRMFSlK)=TRMFS(K)+FFCK,J, 29  85 86  118  DIRECTION  DIRECTION  FFtK.J.I)=F(K,J,I)/AFHW(J)  78 79  116  T H E FLOW  J=1,IR  F F ( K , J , I )  77  114  TIME  DO 2 0 1=1,IC F(K,J, I ) = X ( K , J , I ) - X t i , J , l J  75  115  REAL  c c c c  69  113  FOR  K=2,IK  TRMFS  67 68  112  SHIFTS  I D A T A= K - l  63 64  111  FRINGE  c  62  102  INDIVIDUAL  I>*R(K,J+N-l,I)  c c C  c c c c c  SUMMATION FOR  N=l ,  OF  THE P R O D U C T  OF  RESIDUAL  SEPARATIONS  AT  SEPARATION  N=X,  =0,1,2,3..IS  SEP=X-1  N=l  c c  INITIALIZE 63  THE  SPR(K,N)=0.0 SRR(K,N)=0.0 SRNK(K,N)=0.0  SUMMATION  COUNTER  FOR EACH  SEPARATION  N=1,2,3..IS  N  125  00  126  IF((J+N-l).GT.IR)  127  SPR(K,N)=SPR(K,N)+PR(K,J,N)  128  SRR(k,N)=SKR(K,N)+RR(K,J)  129  J=1,  IR GO  TO  64 218  SKNRIK,N)=SRNK(K,N)+RNR(K,J,N)  130  C  131  C  132  C  133  C  134  65  135  64  CONTINUE MSPR(K,N)=SPR(K,N)/(IR-N*1)  136  OSRR(<,N)=(A8S(SRRIK,N)/(IR-N+1)))**0.5  137  OSRNR(K,N) = IAt3S(SRNR(K,N)/(IR-N4-l  138  N=N+1  139  IF(N.GT.IR)  140  GO  141  C  142  C  143  C  144  C  1*5  C  1*6  C  147  C  148  TO  THE  66  DO  149 68  151  TO  )**0.5  66  63 RESIDUALS  68  SQUARED  AT  SEPARATION=0  ARE  THE  SAME  AS  PR(K,J,0)  N=1,IS  CONTINUE  C  152  MTINT(K)=(MSPR(K,1)**0.5)/OMFW  153  DO  154  12  N=1,IS  IF(COR(K,N)J  155  13  GO T O  157  14  158 159  13,13,14  A(K,N)=MINUS  156  12  A(K,N)=PLUS  12  CONTINUE  102  CONTINUE  C  160 161  DO  162  80  N=1,IS  80  ISEP(N)=N-l  82  F O R M A T C l ' , '  163  WRITE16.82)  164 165  * , /»9X» 'RESULTS  FROM  THE  ANALYSIS  OF  FLOW  INTERFEROGR  1AMSV9X,•================================================«,//,9X,  166  2*RUN  167  3'SIGN  168  NUMBER OF  : • , / / 1 0 X , • S . N O . ' , 2 X , • M T I N T • , 5 X , • M F W • , 2 0 X ,  SPATIAL  CORRELATION  AT  SEPARATION  0 F : » )  WRITE(6,81)( I SEP(N),N=1,IS)  169  81  FORMAT(35X,25I3)  170  WRITE(6,83)  171  83  172  FORMAT(37X,' 1  173  • , / 00  103  IDATA=K-1  175  WRITE(6,84)  176  84  177  I DATA,MTI NT(K),MFW(K),(A IK,N),N=1,  IS)  F0RMAT110X,I4,3X,F5.3,4X,F5.3,5X,25A3)  103  178  )  K=2,IK  174  CONT INUE  C  179  WRITE<6,86)  180  86  181  OMFW  FORMAT(•1 • , / / • (RESULTS 1 / / / , ' S . N O . ' .45X,'VALUE  182  CONTINUED)'//'MEAN OF  SPATIAL  87  FORMAT(7X,2515,/,7X,•  184  1  185  2  186  ') DO  104  K= 2,  187  IDATA=K-1  188  WRITE(6,89)  189  89  190  104  191  CONTINUE  C  192  WRITE«6,85)  193  85  FORMAT('l')  194  STOP  195  END FILE  IK I DATA,(COR(K,N) ,N=1,1S)  FORMAT<I3.4X,25F5.2)  FRINGE  CORRELATION  WRITE!6,87)<ISEP(N),N=1,1S)  1B3  OF  GO  ))  COR(K,N)=MSPR(K,N)/(USRR(K,N)*QSRNR<K,NI)  150  END  65  AT  SHIFT  = ' , F 7 . 3 ,  SEPARATION  O F : ' )  219  98  C  99  C  CALCULATION ICALCULATION  100  DO  102  101  DO  61  101.1  1= 1  OF OF  THE PRODUCT THE TIME  101.2  R R ( K , J ) = R ( K , J , I ) * R ( K , J , I ) 00  103  1=1  104  C  IF  C  THIS  NO.OF  DATA  SETS  CALCULATION  •  SEPARATION  A N D GO TO  GO T O  IS  IFt(K+N-2).GT.(IK-1))  PR(K,J,N)=R(K,J,I)*R(K+N-1,J,I)  60  CONTINUE  111  61  CONTINUE  C  SUMMATION  113 114  C C  OF T H E PRODUCT  OF RESIDUAL  FOR N = l , ZERO  AT  SEPARATIONS  THE SUMMATION  TOTAL  SCANS;  STOP  SCAN  SEPARATIONS=  0,1,2,3  . . I S  AND FORN = X ,  C  SRR  :  IS  T H E SUM OF  THE  C  SPR  :  IS  THE  THE PRODUCTS  118  63  SUM OF  SQUARE  OF T H E OF  RESIDUALS  THE  RESIDUALS  SPR(J,N)=0.0  119  SRR(J,N)=0.0  120  SRNR(J,N)=0.0  121  DO  122  IF( <K+N-2).GT.( I K - D )  123  SPR(J,N)=SPR(J,N)+PR(K,J,N)  124  SRR(J,N)=SRR(J»N)+RR(K,J )  125  SEP=X-1  COUNTERS  116  65  K=2,IK GO TO  64  SRNR(J,N)=SRNR(J,N)+RNR(K,J,N)  126  65 C  128  CONTINUE MSPR  64  129  :  IS  T H E MEAN  OF  T H E SUM O F  THE PRODUCTS  OF  THE  RESIDUALS  MSPR(J,N)=SPR(J,N)/(IK-N) OSRRIJ,N)=(ABStSRRIJ.N)/(IK-N)J)**0.5  130  QSRNR(J,N)=(ABS(SRNR(J,N)/(IK-N))1**0.5  131  N=N+l  132  IFIN.GT.IS.OR.N.GT.(IK-1))  133  GO  134  138  THAN  STREAMWISE  61  117  137  N  SCAN  N=l  115  136  DISTANCES  STREAMWISE  RNRIK,J,N)=R(K+N-1,J,I)*R<K*N-1,J,I )  110  135  FROM  C  109  127  GREATER  THE NEXT  107  112  SEPARATION  N=1,IS  106 108  AT  COR(J.M)  IK  102  1D5  RtSIUUALS  J=1,IR K= 2,  60  OF  CORRELATION,  66 C  TO  DO 6 8  GO  TO  66  63 N=1,IS  CALCULATE  TIME  CORRELATIONS  AT  VARIOUS  TIME  COR(J,N)=MSPR(J,N)/(QSRR(J,N)*QSRNR(J,N)) 68  CONTINUE  102  CONTINUE  S E P . ALONG  EACH  J  220 194  CoSRF 1.AT1OM  C  195  DU  196  CALL  197  107  J=1,IK  S Y M B O L ( X P ( J ) , 0 . 0 , 0 . 0 7 , 1 3 , 0 . 0 , - 2 )  CONTINUE  198  CALL  199  CALL  200  CALL  201  CALL  202  CALL  S Y M B O L d . 4 , - 0 . 3 , 0 . 1 4 , • SPANWISE PLOT(0.0,10.0,+2) PL0T(XP(IR),10.0,+2) PL0T(XP(IR),0.0,*2J  203  C  DRAW  C  DATUM  LINE  CALL  PL0T(0.0,8.0,+3)  206  DATUM  CALL  207  C  209 210  C  LINE  P L O T ( X P ( IR 1 , 6 . 5 , + 2 )  CALL  213  C  CALL  215  C  217  CALL 105  219 220  C  221  COEFFICIENT  FUNCTION  POSITION  AND PLOT  THE INSTANTANEOUS  FRINGE  SHIFT  FROM  THE ZERO  POSITION  J=1,IR  SYMBOHXP(J) ,PFF(K,J)  , 0 . 0 7 , 3 , 0 . 0 , - 2 )  CONTINUE CALL  PL0T(XP(1),PMSUMR(K, l),+3)  PLOT  THE RESIDUAL  FRINGE  SHIFTS  J = l , IR  CALL S Y M B O L ( X P < J ) t P M S U M R ( K , J ) , 0 . 0 7 , 4 , 0 . 0 , - 2 )  223  104  224  CONTINUE CALL  225  C  PLOT(XPI  PLOT  226  DO  227 103  229  C  230  C  103  COEFFICIENTS  J=l,20  S Y M B O L ( X P ( J ) » P C O R ( K » J ) , 0 . 0 7 , 2 , 0 . 0 , - 2 )  CONTINUE LABEL  231  CALL  232  CALL  233  1),PCOR(K,1),+3)  THE CORRELATION  CALL  228  THE V E R T I C A L  AXIS  A N D MARK  SYMBOL I - 0 . 7 , 8 . 0 , 0 . 1 4 , ' F L O W  THE SCALE  POINTS  0IRECTION•,90.0,14)  S Y M B O L I - O . 7 5 , 9 . 8 , 0 . 1 4 , 2 , 0 . 0 , - 1 )  C  234  CALL  235  CALL  S Y M B 0 L ( - 0 . 5 0 , 2 . 9 5 , 0 . 1 4 , • - 1 . 0 - « , 0 . 0 , 5 ) S Y M B O L I - O . 4 0 , 3 . 9 5 , 0 . 1 4 , ' C O - ' , 0 . 0 , 4 )  236  CALL  S Y M B O L ( - 0 . 5 0 , 4 . 9 5 , 0 . 1 4 , ' + 1 . 0 - ' , 0 . 0 , 5 )  237  CALL  S Y M B O L ( - 0 . 5 0 , 5 . 4 5 , 0 . 1 4 , * - 1 . 0 - ' , 0 . 0 , 5 )  CALL  S Y M B O L I - O . 4 0 , 6 . 4 5 , 0 . 1 4 , « 0 . 0 - ' , 0 . 0 , 4 )  238 239  CALL  240  ;  241 242  0  243  C  S Y M B O L ( - 0 . 5 0 , 7 . 4 5 , 0 . 1 4 , ' + 1 . 0 - ' , 0 . 0 , 5 )  CALL  S Y M B O L ( - 0 . 4 0 , 7 . 9 5 , 0 . 1 4 » * 0 . 0 -  CALL  S Y M B O L ( - 0 . 5 0 , 8 . 9 5 , 0 . 1 4 , ' • 1 . 0 - * , 0 . 0 , 5 )  LABEL  EACH  PART  OF T H E PLOT  , I  0 . 0 , 4 )  AND INDEX  244  CALL  S Y M B O L U . 6 , 5 . 3 , 0 . 1 4 , 2 , 0 . 0 , - 1 )  THE POINTS  245  CALL  SYMBOL( 1 . 8 , 5 . 2 , 0 . 1 4 , ' C O R .  246  CALL  S Y M B O L ! 1 . 1 , 7 . 5 , 0 . 1 4 , 4 , 0 . 0 , - 1 )  247  CALL  S Y M B O L ! 1 . 3 , 7 . 4 , 0 . 1 4 , ' R E S I D U A LFRINGE  248  CALL  SYMBOL! 1 . 8 , 7 . 8 5 , 0. 0 7 , ' N O - G R A D .  249  CALL  S Y M B 0 L I 1 . 3 , 9 . 8 , 0 . 1 4 , 3 , 0 . 0 , - 1 )  250  CALL  251  C  252  C  253  C  CALL C  256  C  257  102  CALL  259  STOP  260  END FILE  THE ORIGIN  TO T H E NEXT  P L 0 T ( 8 . 0 , 0 . 0 , - 3 )  CONTINUE  258  C O E F F . • , 0 . 0 , 1 1 )  FRINGE  S Y M B O L ( 1 . 5 , 9 . 7 , 0 . 1 4 , ' M E A N FRINGE  SHIFT  254 255  3F  THE FUNCTION  P L O T t X P t l ) , P F F ( K , 1 ) , + 3)  DO 1 0 4  222  SHIFT  IR),4.0,+2>  TO F I R S T  DO 1 0 5  218  FRINGE  FOR THE CORRELATION  PLOTIXPI  PLOT  216  POSITION  PLOT!0.0,4.0,+3)  MOVE  214  FRINGE  RESIDUAL  CALL  LINE  FUNCTION  ),8.0,+2)  FOR ZERO  P L O T I O . 0 , 6 . 5 , O l  CALL  212  FOR E A C H  CALL DATUM  211  LINE  FOR THE NO-FLOW  P L O T ( X P ( IR  DATUM  208  SEP ARAT ION• , 0 . 0 , 19 )  P L O T I O . 0 , 0 . 0 , 0 )  204 205  ENO  107  PLoTTgR  PLOTND  PLOT  .  SHI F T • , 0 . 0 , 2 1 ) POSIT I  ON',0.0,24)  SHIFT',0.0,17)  1  C  A PROGRAM D I M L U S 1 UN  FC-< A N A L Y S I N G CM I 1 0 )  3 4  DIMENSION 0 1 MENS ION  AI 10I.FJ 10),FCM( 10)tFSUCM<10),SI MTINT(69)  5 6  REAL  c  15  20  F0RMATI2I  50  F0RMATI25F3.0) IA  30  c c c 31  c  24  ANALYSED  32 C  31  THE  BOUNDARIES K=l,  32  NUMBER  OF  FREQUENCY  ARE SET  CELL  DIVISIONS  COUNTER  UP  USING  A l l )  VALUE  IA LOCATED  K=1,IA  CM(K)=(A(K)+A(K+l))/2.0 SQCMIK)=CM(K)*CM(K> INTENSITY  28  INT(K),K=1,IK)  A(K+1)=A(K)+0.010 C E L L MIDPOINTS ARE DO  25 26 27  BEING  3.3F7.3)  INITIALIZE THE DO 3 0 K=1,IA Ft K ) = 0 . 0  DO  22  DENOTES  CELL  21 23  SAMPLES  20  c c c c  16 17 18 19  NT<60),SOCM(10)  IK,IA,A(l),STEP,USTAR  R E A D ( 5 , 5 0 ) (MT  11  14  CF  c  10 12 13  3F  READ(5,20)  B 9  SAMPLE  M TINT,STR.LAMDA  IK=NUMBER  7  A  M FA SUP. bMF N T S  2  SUMMATION  COUNTER  IS  SET TO  ZERO  SUM3=0.0  29  SUMF=0.0  30  00  31  IF(MTINT(K).GT.A(9).OR.MTINT(KJ.LT.A(1))  33  K=1,IK  32  I F ( M T I N T ( K ) . G £ . A ( 1 ) . A N D . M T I N T ( K ) . L T . A < 2 ) )  GO  TO  41  33  IF(MTINT(K).GE.A(2).AND.MTINT(K).LT.A(3))  GO  TO  42  TO  43  GO T O  33  34  IF(MTINT(K).GE.A(3).AND.MTINT(K).LT.A(4))  GO  35  IF(MTINT(K).GE.A(4).AND.MTINT(K).LT .A(5 ) )  GO T O  44  36  I F t M T I N T ( K ) . G £ . A ( 5 ) . A N D . M T I N T ( K J . L T . A ( 6 ) )  GO T O  45  37  IF(MTINT(K).GE.A(6).AND.MTINT(K).LT.A(7))  GO  46  38  IF(MTINT(K).GE.A(7).AND.MTINT(K).LT.A<8))  GO T O  47  39  IF(MTINTIK).GE.At8).AND.MTINTIK).LT.A(9))  GO T O  48  40 41  C 41  42 43  42  44 45  44  50 51 52 53  TO  54  34 34  F(6)=F(6)*1.0 GO  47  TO  34  F(7)=F(7)+1.0 GO  TO  34  55  48  F(8)=F(8)*1.0  56  34  SUMF=SUMF+1.0  33  CONTINUE  57 58  ""  34  F(5)=F(5)+1.0 GO T O  46  34  F(4)=F(4)+1.0 GO  45  34  F(3)-F(3)+1.0 GO T O  48 49  TO  F ( 2 ) = F « 2 ) + 1 . 0 GO T O  43  46 47  F(1)=F(1)+1.0 GO  SUM3=SUM3+MTINT(K)  TO  221  C  ARITHMETIC  MEAN  OF  T U R E U L ENT  INTENSITIES  AMINT=SUM3/SUMF C  CALCULATION  OF  VARIANCE  AND  STANDARD  DEVIATION  SUM1=0.0 SUM2=0.0 DO  35  K=1,IA  FCM(K)=F(K)*CM(K) FSQCM(K)=F(K)*SCCMIK) SUM1=SUM1+FCM(K) SUM2=SUM2+FSQCM(K) 35  CONTINUE  C C VAR=(SUM2-(SUM1*SUMX)/SUMF)/(SUMF-1.0) DEV=SQRT(VAR) CI=DEV*2.0 WRITE(6,36) 36  F O R M A T l ' l ' , / / / / / , 1 0 X , ' A N A L Y S I S OF A S A M P L E OF I N T E R F E R O G R A M S ' , / / , 110X,'FOR TURBULENCE INTENSITY MEASUREMENTS', 2/,10X, • * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * , / / , 310X,'RUN  NO.  : ' , / / / , 1 0 X , '  4 • , / , 1 0 X , ' C E L L BOUNDS',5X,'CELL 5' FREQ. ' ,4X, « F * C M ' , 5 X , ' F * S Q C M ' , / , 10X, • 6 • •,//)  DO  37  MIDPT.',5X,  K=1,IA  38 37  WR1TE(6,38)A(K) ,A 1K+l),CM IK),FIKJ,FCMIK),FSQCMIK) F O R M A T ( 1 0 X , F 5 . 3 , • - • , F 5 . 3 , 8 X , F 5.3 , 9 X , F 3 . 0 , 4 X , F 6 . 3 , 4 X , F6 CONTINUE  52  FORMAT!/,42X,'  WRITE(6,52)  SUMF,SUM1,SUM2 - » , 4 X , '  ' ,4X, '  •  , / ,  130X,'SAMPLE S I Z E = ' , 1 X , F 3 . 0 , 3 X , F 7 . 3 , 3 X . F 7 . 3 , / , 2 42X, ' • ,4X,' «,4X, • ' , / / / / / / ) WR I T E I 6 , 5 3 ) V A R HR I T E ( 6 , 5 4 ) D E V WRITE(6,55)AMINT WRITE<6,56)CI 55  FORMAT(21X, 'MEAN  53  F0RMAT121X,'VARIANCE  OF  54  F0RMAT(21X,'STANDARD  DEVIATION  56  FORMAT(21X,'95S WRITE(6,57) FORMAT('l') STOP  57  END  TURBULENCE  INTENSITY  SAMPLE  CONFIDENCE  INTERVAL  S  =  « , F 6 . 3 , / / / I  =  ' , F 8 . 5 , / / / )  =  ' , F 7 . 4 , / / / )  =  •  ,  , F 6 . 4 )  .3)  223  A  sample  were  picked  each  i n t e r f e r o g r a m ,  t u r b u l e n t  from  c o n s i s t i n g  the  i n t e n s i t y  motion a  value  I  was  of  40  to  50  p i c t u r e  for  for  streak  the  o b t a i n e d .  i n t e r f e r o g r a m s  each  r u n .  From  spacing  The  sample  and  X  of  the  and  X  * I  values  were  analysed  A f t e r I the  values ranges  w i t h i n of  a  that  the  c e l l of  the  of  c e l l ' s  for  i n s p e c t i o n e i g h t  and  X  boundaries the  was  .  t a l l i e d  range  a  measurement  value as  the  the  of  chosen  approximated  on as  the were  Each  that  f e l l  t h i s mean  sample x  of  of  a  to  f e l l  upper  of  f e l l  midpoint c e l l c o n v e n t i o n ,  boundary.  frequency  and  that  a of  X  w i t h i n  the  on  matter  f..  The  is  the  number  standard  Guttman, I., Engineering  approximated  the  x  Introductory N . Y .  I  a s s i g n e d ,  i t  of  ' c e l l s '  was  case  which were  a r i t h m e t i c  where  f o l l o w s .  The  o c c u r r e n c e  v a l u e . For  the  of  value  midpoints that  sample,  In  that  c e l l  c u r s o r y  each  c e l l .  boundary, to  in  a  as  *  sample  1  of  I  i s  f.  m.  measurements  d e v i a t i o n  s  measurements,  of  the  (D.l)  approximated  sample  W i l k s , S.S. and Hunter, S t a t i s t i c s , John Wiley  by  i s  J . S . , 1971, and Sons,  m..  The the  standard  v a r i a n c e  of  d e v i a t i o n .  the For  sample a  s  2  normally  i s  the  square  d i s t r i b u t e d  of sampl  about 95%  of  the  w i t h i n  and  (x  +  2s,  68%  "  (x  +  s ,  50%  "  (x  +  | s ,  Appendix  data E.  of  the  f a l l  i n t e r v a l  The in  measurements  R  c  ( z ) ,  Ic,  X  and  Rc(t)  are  x x  -  x  2s) s)  -  | s )  l i s t e d  APPENDIX  E  LISTING OF DATA FOR HOLOGRAPHIC VISUALIZATION RUNS  Table B u r s t  Length  RUN W:  Water  S:  Separan  of  count t i me  Wlb  Data  El  Range  Total  and  b u r s t s  c o u n t e d - * * s  range  to 1*50  E r r o r  Mean  b u r s t  rate b/cm.s  h.2  F  * E r r o r % ±  6 0  3 0 6  W2b  6 0  ikhO  to 2520  2 2 .  2 1  W3b  3 0  li+85  to  2 5 6 5  h5.  2 0  Sib  6 0  7 6 5  to  1 0 8 0  1 0 .  Ik  S2b  6 0  378  to 5I+O  S3b  3 0  6 3 O  to  E r r o r  range  i n d i c a t e s  95%  c o n f i d e n c e  9 9 0  5 . 1  1 8 .  1 9  1 2  11+  i n t e r v a l .  Range of four counts. ro ro en  RC S U I T S FROM  RUN  NUMBER NO.  1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 IS 19 20 21 22 23 24 25 26 27 28 29 3C 31 32 33 34 35 36 37 3>3 39 40 4 1 42 43 44 45  E2.  THE A N A L Y S I S  OF FLOW  I NTERFEROCRAf.S  : Wl  MT I NT  .393 .425 .405 .429 .403 .452: .405 .411 .443 .436 .443 .450 .430 .473 .422 .418 .439 .441 .447 .439 .422 .429 .398 .42 2 .453 .426 .418 .408 .44 1 .44 1 .45 7 .44 1 . 39 4 .430 .443 .4 36 .474 .422 .418 .413 .439 .411 .413 .44 0 .439  KFW  . 522 .489 .4 77 .533 .454 .5 11 .477 .452 .^47 .459 .4 47 .5 39 .440 .281 .453 .523 .511 .446 .451 .511 .5 13 .332 .522 .441 .517 .528 .525 .454 .290 .4 60 .447 .461 .463 .440 .459 .459 .443 .513 .525 .457 .4 83 .506 .457 .517 .483  +  -  -  -  -  +  2  +  +  +  +  +  +  +  +  +  +  +  +  +  +  -  -  -  -  -  -  -  -  -  +  +  +  +  +  +  +  -  +  +  +  -  +  -  -  +  -  +  +  +  +  +  +  +  +  +  +  +  + ,  +  +  +  +  +  +  +  +  +  +  © -  + +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  -  -  -  -  -  +  +  -  -  -  -  -  +  -  +  +  +  -  -  © ©  -  -  +  -  +  -  -  +  -  -  +  +  -  -  © +  -  + +  +  +  +  -  -  -  +  +  +  +  -  -  -  -  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  +  -  +  ©  +  +  +  -  -  -  +  +  +  -  -  +  -  -  -  +  +  -  -  -  +  +  +  ©  +  +  +  +  +  -  +  -  -  +  +  +  -  -  +  +  -  -  +  +  +  +  * +  +  +  -  -  -  -  +  +  +  +  +  +  -  -  -  +  +  +  +  +  +  +  -  -  -  +  +  +  +  +  +  +  -  -  -  -  +  +  +  -  -  -  -  +  +  +  +  -  -  -  -  +  -  -  -  +  +  +  _  ©+ ©  -  -  +  +  _  -  +  +  +  +  +  -  -  +  +  +  +  -  -  ©  ©  ©  +  ©  -  +  -  -  -  +  +  ©  -  —  +  . +  +  + +  -  +  i  ©  + +  -  +  0  -  -  +  +  + -  -  +  +  -  ©  -  + +  -  ©  -  +  +  -  +  ©  +  +  +  +  ©+  +  +  ©  +  -  +  0  ©+  -  -  + +  -  +  +  -  +  +  -  +  -r  +  +  -  +  +  +  +  0  -  +  +  +  +  +  +  +  +  +  +  -  -r  +  ©  +  © © © ©+ © © ©  20  +  +  +  +  +  +  SEPAR AT I ON CI F : 15 16 17 18 19  +  +  +  ©  +  + +  +  ©  AT 14  +  +  +  -  0  +  +  SPAT IAL CORREL AT I CM 7 9 10 11 12 13 13  4  1  +  c I G.N OF 5 6  3  ' 0  +  + -  ©  -  +  +  +  +  +  -  -  -  -  +  +  +  +  -  -  -  -  +  +  +  +  +  +  +  +  +  + +  +  +  +  +  -  -  -  -  +  +  —  -  -  +  +  +  -  -  +  +  +  +  ©  +  +  © © +  +  +  +  +  ©  -  +  +  0  + -  + +  +  +  -  .  -  —  _  _  —  +  + +  _  +  +  +  -  -  +  L i s t i n g of c o r r e l a t i o n signs f o r the samples i n Run w l . C i r c l e s indicate peak positions. ( One separation u n i t = O.O583 cm)  +  S.NO.  1 2 3 4 5 6 7 8 9 IC 11 12 13 14 15 16 17 13 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45  0  1  2  3  1.00 1.00 1.00 1.00 1.00 1.00 1.0 0 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.0 0 1. 00 1.0 0 1.00 1.00 1.00 1.00 1.0 0 1.00 1.00 1.00 1. 00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1. 00 1.00 1.00 1.00 1.00 1.00 1.00  .58 . 66 .44 .45 .61 .64 .44 . 54 .58 .66 .58 .59 .61 . 69 .59 .60 .71 .46 .58 .71 .63 .65 .53 .43 .62 . 57 .59 .61 •66 .65 .47 . 54 .46 .6 1 . 72 .63 .43 . 63 . 59 .71 .61 .75 .71 .62 .61  . 17 . 07 . 04 - . 11 . 13 -.09 .04 - . 14 -.00 .24 -.00 . 32 .04 . 15 .01 .25 . 2.4 .21 .03 . 24 - . 12 .CO . 17 .20 -.12 . 24 . 19 . 13 .11 .22 . 22 . 03 . 06 .04 .29 .24 . 19 -.12 . 19 .26 . 14 . 27 .26 -.13 . 14  - .13 - . 14 .07  - .36 .01  - .52 .07  - .23 - .21 - .09 - .21 .11  - .18 - .19 - .21 .22  - .06 - .04 - . 15 - .06 - .55 - .53 - . 13 .01 53 .20 - .13 .01 - .25 - .01 - .00 .01 .07 - . 18 - .07 - .09 .02 - . 55 - .13 - .09 - . 17 - .05 - .09 - .55 - .17  -.  E2  4 -.28 -.09 .2 1 -.33 -.11 -.52 .21 -.09 -.11 -.26 -.11 -.15 -.08 -.19 -.11 .05 -.17 - .26 - . 24 -.17 -.54 -.62 -.28 - . 19 -.50 •06 - .28 -.11 -.23 - .06 -.21 -.11 .19 - .08 -.2 8 -.26 - .22 -.54 -.28 -.29 -.20 -.IS - .29 -.52 -.20  5 -.37 - . 14 - . 19 -.11 -.18 -.31 -.19 . 00 -.01 -.43 -.01 -.32 -.03 .02 -.02 -.16 -.24 -.41 -.09 -.24 -.26 -.37 -.37 -.37 -.24 -.15 -.36 - . 18 -.02 -.06 - . 39 -. 1 3 -.17 -.03 -.47 -.43 -.39 -.26 -.36 -.46 -.16 -.26 -.46 -.25 -.16  6 -.29 -.14 -.37 -.00 -.25 -.16 -.3 7 .32 -.11 -.57 -.11 -.32 -.13 .26 -.12 -.37 -.36 — .54 .16 -.36 -.12 .23 -.29 -.4 7 - . 11 -.36 -.29 -.25 .26 -.16 -.54 -.2 1 -.35 -.13 -.60 -.57 -.47 -.12 -.29 - .60 - . 16 - . 37 -.60 -.12 -.16  7 -.26 .03 - . 17 -.01 -.27 -.14 -.17 .38 -.09 -.55 -.09 -.16 -.12 .35 - . 11 -.35 -.40 - . 53 . IS -.40 - . 13 .72 -.26 -.53 -.13 -.32 -.26 -.27 .34 -.20 -.59 -.20 - . 19 -.12 -.58 -.55 -.51 - . 13 -.26 -.56 -.07 -.42 -.56 - . 14 - . 07  VALUE OF S P A T I A L C O R R E L A T I O N 8 9 - 10 11 12 13 .13 -.15 .00 .12 -.24 -.34 .29 - . 0 7 .02 - . 13 .08 -.11 -.24 - . 34 -.03 -.43 .32 . 11 .59 -.12 .11 .32 .02 - . 1 5 .09 .26 .15 - . 4 5 .27 .12 —. 3 8 -.37 .28 -.2 7 - . 42 - . 1 0 -. 15 -.47 -.27 . 28 -.15 .07 . 19 .64 — .15 . 13 - . 4 2 - . 16 - . 16 .00 - . 3 4 -.31 . 10 - . 19 - . 13 .02 .17 -.44 -.02 .02 -.44 -.12 . 01 -.13 - . 24 - . 3 5 .09 .26 - . 13 . .56 .59 - . 12 - . 4 0 - . 14 .07 -.15 - . 19 . 10 -.09 .56 .09 .11 -.28 .19 -.09 . 56 -.16 .06 .09 . 11  .53  - . 15 - .21 - .20 .CO .39 - .21 - .57 - .03 .65 - .03 - .39 - .06 - .72 - . 08 - .32 .47 .23 - .39 .47 .42 - .48 .53 . 16 .36 - .32 .53 .CO - .72 - .29 .20 .02 - .20 - .06 .65 .65 . 13 .42 .53 .66 .03 .48 . 66 .43 .03  . 26 -.26 . 12 -.0.3 .09 .58 . 12 -.51 - . 53 .45 - . 53 -.49 -.51 -.71 -.53 - . 12 .17 . 36 - . 22 . 17 . 61 - . 78 . 26 . 33 .62 - . 13 .30 . 09 -.69 - . 51 . 38 .09 .11 -.51 .50 .45 .31 .61 .30 . 47 -.23 .21 .47 .65 -.28  .01 -.4 8 -.20 .21 .12 .22 -.20 -.38 -.69 .26 -.69 -.62 -.62 -.42 -.63 .09 - . 19 .26 -.06 - . 19 .21 -.72 .01 .09 .25 . 11 .01 .12 -.38 -.47 .17 .16 -.26 -.62 .27 .26 .16 .21 .01 .28 -.69 -.24 .28 .23 -.69  -.25 -.59 -.32 .39 -.33 -.39 -.32 . CO -.47 . 05 -.47 -.53 -.41 -.13 -.44 -.24 -.43. .49 -.01 -.48 -.43 - . 19 -.25 .42 -.39 -.28 -.22 -.33 -.11 -.38 .49 -.29 -.40 -.41 .07 .05 .42 -.43 -.22 . C7 -.82 -.57 . C7 -.44 -.82  AT SEPARATION 14 15 • 16  - . 4 2 -.43 - . 4 6 -.19 .47 -.21 - . 13 - . 4 0 -.69 -.80 - . 5 6 -.12 .47 -.21 - . 0 4 -.41 -.08 -.39 -.67 -.23 -.08 -.39 - . 4 4 -.15 - . 20 - . 53 -.12 -.27 - . 1 6 -.50 .02 -.21 -.61 -.63 .17 .62 -.23 -.43 -.61 -.63 -.62 -.17 . 32 .63 - . 4 2 -.43 .60 .12 - . 5 7 -.12 -.26 .00 -.39 -.41 -.69 — . 30 - . 0 5 - . 16 - . 4 5 -.62 .20 .63 - . 6 6 -.77 .45 •-.29 - . 20 -.53 -.27 -.66 -.23 -.67 .62 .08 -.62 - . 17 -.39 -.41 -.28 -.70 -.64 -.23 -.68 -.63 -.28 -.70 - . 6 5 , . -.20 - . 6 4 -.23  -.33 -.22 .41 -.34 -.62 .57 .41 -.48 -.54 -.91 -.54 .64 -.59 -.34 - .54 . 17 -.57 - . 35 -.77 -.57 .66 .41 -.33 -.31 .62 .18 -.33 -.62 -.21 -.56 -.30 -.62 .43 -.59 -.93 -.91 -.34 .66 -.33 -.93 .05 -.53 -.93 .65 .05  (contd.) L i s t i n g of s p a t i a l . c o r r e l a t i o n values f o r Run Wl.  OF: 17  18  19  20  -.39 -.63 .16 -.23 -.09 .55 . 16 -.13 .04 -.84. .04 .85 -.02 -.62 . 11 -.04 -.62 -.54 -.44 -.62 .75 -.26 -.39 -.42 .69 -.03 -.37 -.09 -.55 -.00 -.49 -.04 . 17 -.02 -.8 8 -.34 -.45 . 75 -.37 -.33 . 13 -.56 -.83 .74 . 13  -.40 -.58 .39 .07 .27 .03 .39 -.09 .28 -.47 .28 . 50 .21 -.64 .33 -.33 -.00 -.29 .59 -.00 . 16 -.81 -.40 -.13 .15 -.33 -.45 .27 -.61 .72 -.26 . 36 .44 .21 -.56 -.47 -.16 . 16 -.45 -.48 . 13 -.02 -.43 .13 . 18  -.28 -.15 .63 -.21 .13 -.57 .63 -.07 .02 .01 .02 .59 -.02 -.26 .04 .07 .72 -.2 9 .61 .72 - . 66 -.33 -.23 -.13 -.5 8 .07 -.35 .13 -.22 .80 -.25 .26 .5 9 -.02 -.02 .01 -.15 -.66 -.35 .00 .54 .78 .00 -.71 .54  .25 . 11 .66 -.44 .39 -.79 .66 .01 -.29 .45 -.29 .23 -.26 .53 -.22 .24 .75 . 14 .59 .75 -.95 -.35 .25 . 20 -.9 2 .33 . 19 . 39 .57 .73 . 11 .41 .61 -.26 .41 .45 .24 -.95 . 19 .46 .82 .77 .46 -.94 .82  S  229  ANALYSIS FOR *  *  *  OF  A S A M P L E OF  SPANWISE STREAK *  *  *  *  RUN NO.  CELL  *  *  *  *  *  INTERFEROGRAMS  SPACING  * * * * * ^ * * j { i : * < c 3 j t ) j c * *  : Wl  BOUNDS  CELL  6 . 5 - 7.5 7.5- 8.5 8.5- 9.5 9 . 5 - 10.5 10. 5 - 1 1 . 5 11.5- 12.5 12.5- 13.5 13.5- 14.5  MI D P T .  FREQ.  7. 8. 9. 10. 11. 12. 13. 14.  .  SAMPLE  SIZE=  F*CM  F*SQCM  4. 4. 8. 13. 9. 5. 0. 2.  28.0 32.0 72.0 130.0 99.0 60. 0 0.0 28.0  196.0 256.0 648.0 1300.0 1089.0 720.0 0.0 392.0  45.  449.0  46 0 1 . 0  (NOTE: UNIT SEPARATION J = l REPRESENTS A S P A N W I S E D I S T A N C E OF 0 . 0 5 8 3 CM CELL MIDPOINT IS IN J U N I T S . )  VARIANCE  OF  STANDARD  DEVIATION  MEAN S T R E A K  95*  SAMPLE  SPACING  CONFIDENCE  NON-DIMEN.  S  INTERVAL  STREAK  .009  CM  .097  CM  .582  CM  = + .193  CM  SPACING = 8 0 .  2 30  H I S T O G R A M  S T R E A K  R U N  O F  A  S P A C I N G  S A M P L E  O F  M E A S U R E M E N T S  :W1  N O .  0 . 3  F  0 . 2  0 . 1  0 . 0  . 4 0 8  . 4 6 6  . 5 2 5  S T R E A K  ( F  :  F R A C T I O N  O F  T H E  . 5 8 3  S P A C I N G  T O T A L  . 6 4 1  -  C M  S A M P L E )  . 7 0 0  . 7 5 8  . 8 1 6  231  ANALYSIS FOR  A SAMPLE  TURBULENCE  RUN N O .  CELL  OF  INTENSITY  MEASUREMENTS  : Wl  BOUNDS  .390.400.410.420.430.440.450.460-  OF ' I NTERFEROGRAMS  CELL  .400 .410 .420 .430 .440 .450 .460 .470  MIDPT.  FREQ.  . 395 . 405 .415 .425 . 43 5 .445 .455 . 465 SAMPLE  3. 4. 7. 7. 8. 9. 4. 0. SIZE=  VARIANCE  OF  STANDARD  DEVIATION  *  42,  CONFIDENCE  .00031  S =  INTENSITY  INTERVAL  1 . 185 1 . 62 0 2 . 9 05 2. 975 3. 480 4.005 1. 820 0. 0  17.990  SAMPLE  MEAN T U R B U L E N C E  95%  F*CM  .0175  =  .428  = +  .0350  F*SQCM  .468 .656 1.206 1.264 1.514 1.782 .828 0.0 7.718  232  HISTOGRAM TUR8  RUN  OF  A  INTENSITY  NO.  SAMPLE  OF  MEASUREMENTS  : U1  0 . 0  395  .405  .415  .425  TURBULENT  (F  :  FRACTION  OF  THE  TOTAL  .435  INTENSITY  SAMPLE)  .445  .455  .465  ANALYSIS  OF  A SAMPLE  OF  I NTERFEROGRAMS  FOR S P A N W I S E S T R E A K S P A C I N G * * * * * * * * * * * * * * * * * * * * * * * * * * * RUN N O .  CELL  :  W2  BOUNDS  2.53.54.55.56.57.5-  CELL  MI D P T .  3.5 4.5 5.5 6.5 7.5 8.5  FREQ.  3. 4. 5. 6. 7. 8. SAMPLE  SIZE=  F*CM  F*SQCM  7. 0. 16. 11. 5. 5.  21.0 0.0 80.0 66.0 35.0 40.0  63.0 0.0 400.0 396.0 245. 0 320.0  44.  242.0  1424.0  (NOTE: UNIT SEPARATION J = l REPRESENTS A S P A N W I S E D I S T A N C E OF 0 . 0 5 8 3 C M C E L L MIDPOINT IS IN J U N I T S . )  VARIANCE  OF  STANDARD  DEVIATION  MEAN S T R E A K  95%  SAMPLE  NOM-DI M E N .  INTERVAL  STREAK  C M  .086  C M  .321  CM  = + .172  CM  S  SPACING  CONFIDENCE  .007  =  SPACING = 7 9 .  234  HISTOGRAM STREAK  OF  A SAMPLE  SPACING  RUN N O .  OF  MEASUREMENTS  :W2  0.4  0.3  -I  0.2  -I  0.1  0.0 175  .233  .291  STREAK  (F  :  FRACTION  OF  THE  .350  .408  S P A C I N G - CM  TOTAL  SAMPLE)  .466  235  ANALYSIS  OF  A SAMPLE  OF  INTERFEROGRAMS  FOR T U R B U L E N C E I N T E N S I T Y MEASUREMENTS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * RUN N O .  CELL  :  W2  BOUNDS  .390.400.410.420.430.440.450.460-  CELL  .400 .410 .420 .430 .440 .450 .460 .470  MI D P T .  FREQ.  .395 .405 .415 .425 .43 5 .445 .455 .46 5 SAMPLE  SIZE=  VARIANCE  OF  STANDARD  DEVIATION  CONFIDENCE  F*SQCM  8. 4. 11. 9. 3. 5. 2. 0.  3. 160 1.620 4. 565 3. 825 1.305 2.225 .910 0.0  1.248 .656 1 .894 1 .626 . 568 .990 .414 0.0  42.  1 7. 610  7 .39 6  SAMPLE  MEAN T U R B U L E N C E  95?  F*CM  .00031  S =  INTENSITY  INTERVAL  .0176  =  .429  t  .035 1  236  HISTOGRAM TURB  RUN  OF  A  INTENSITY  NO.  SAMPLE  OF  MEASUREMENTS  : W2  0.4  -a  0.3  0.2  0.1  4  0.0  I.  .395  .405  .415  .425  TURBULENT  (F  :  FRACTION  OF  THE  TOTAL  .435  INTENSITY  SAMPLE)  .445  .455  .465  ANALYSIS  OF  A S A M P L E OF  INTERFEROGRAMS  FOR S P A N W I S E S T R E A K S P A C I N G * * * * * * * * * * * * * * * * * * * * * * * * * * * RUN N O .  CELL  :W3  BOUNDS  2.53.54.55.56.5-  CELL  MIDPT.  3.5 4.5 5.5 6.5 7.5  FREQ.  3. 4. 5. 6. 7. SAMPLE  F*CM  F*SQCM  8. 8. 16. 9. 5.  24.0 32.0 80.0 54.0 35.0  72.0 128.0 400. 0 324.0 245.0  SIZE= 4 6 .  225.0  1169.0  (NOTE: UNIT SEPARATION J = l REPRESENTS A S P A N W I S E D I S T A N C E OF 0 . 0 5 8 3 CM CELL MIDPOINT IS IN J U N I T S . )  VARIANCE  OF  SAMPLE  =  STANDARD  DEVIATION  MEAN S T R E A K  95?  SPACING  CONFIDENCE  NON-DIMEN.  INTERVAL  STREAK  .005  CM  S =  .072  CM  =  .285  CM  = +  .144  CM  SPACING = 9 3 .  HISTOGRAM STREAK  RUN  OF  A  SPACING  NO.  SAMPLE  OF  MEASUREMENTS  : W3  0.4  0 . 3  F  0 . 2  0.1  0 . 0  L — .175  — . 2 3 3  .291  STREAK  (F  :  FRACTION  OF  THE  . 3 5 0  SPACING  TOTAL  . 4 0 8  -  CM  SAMPLE)  239  ANALYSIS  OF  A SAMPLE  OF I N T E R F E R O G R A M S  FOR T U R B U L E N C E I N T E N S I T Y MEASUREMENTS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * RUN  CELL  NO.  :  W3  BOUNDS  .390.400.410.420.430.440.450.460-  CELL  .400 .410 .420 .430 .440 .450 .460 .470  MI D P T .  FREQ.  . 395 .405 .415 .42 5 . 435 .445 .455 . 465 SAMPLE  0. 9. 3. 9. 2. 4. 5. 6.  0.0 3 . 645 1.245 3 . 825 . 870 1.780 2.275 2.790  SIZE= 3 8 .  VARIANCE  OF  STANDARD  DEVIATION  16.430  SAMPLE  00048  S =  MEAN T U R B U L E N C E I N T E N S I T Y  =  95?  = +  CONFIDENCE  INTERVAL  F*CM  .0219  .432  .0438  F*SQCM  0.0 1.476 .517 1.626 . 378 .792 1.035 1.297 7 . 122  240  HISTOGRAM TURB  RUN  OF  INTENSITY  NO.  SAMPLE  OF  MEASUREMENTS  : W3  0.4  F  A  i  0 . 3  -  0 . 2  -  0. i  -  i  0 . 0  | .395  I . 4 0 5  . 4 1 5  . 4 2 5  TURBULENT  (F  :  FRACTION  OF  THE  TOTAL  . 4 3 5  INTENSITY  SAMPLE)  . 4 4 5  . 4 5 5  . 4 6 5  241  ANALYSIS FOR  OF  A SAMPLE  SPANWISE STREAK  OF  INTERFERGGRAMS  SPACING  ************** ************* RUN N O .  CELL  10.5 11.5 12.5 13.5 14.5 15.5  :  SI  BOUNDS  CELL  MI D P T .  -11.5 -12.5 -13.5 -14.5 -15.5 -16.5  FREQ.  F*CM  F*SQCM  7. 14. 9. 5. 4. 3.  77. 0 16 8 . 0 117.0 70. 0 60.0 48.0  847. 0 2016.0 15 2 1 . 0 980. 0 900. 0 768.0  42.  540.0  7032.0  11. 12. 13. 14. 15. 16. SAMPLE  SIZE=  (NOTE: UNIT SEPARATION J = l REPRESENTS A S P A N W I S E D I S T A N C E OF 0 . 0 5 8 3 CM C E L L M I D P O I N T IS IN J U N I T S . )  VARIANCE  OF  STANDARD  DEVIATION  MEAN STREAK  95%  SAMPLE  SPACING  CONFIDENCE  NOM-DI ME N .  S  INTERVAL  STREAK  SPACING =  .007  CM  .086  CM  .750  CM  + .172  CM  113.  242  HISTOGRAM STREAK  Run  F  OF  A  SPACING  SAMPLE  OF  MEASUREMENTS  S1:  0 . 4  -  0.3  -  0 . 2  -  0.1  I  -  0 . 0 .641  .700  .758  STREAK  (F  :  FRACTION  OF  THE  .816  SPACING  TOTAL  .874  -  CM  SAMPLE)  . 9 3 3  243 ANALYSIS  OF  A  FGR  TURBULENCE  RUN  NO.  CELL  :  SAMPLE  OF  I  INTENSITY  NTERFEROGRAMS MEASUREMENTS  SI  BOUNDS  CELL  MI D P T .  FREQ.  . 3 6 0 -  .370  .370. 3 8 0 . 3 9 0 -  .380 .390 .400  .365 .375  2 . 2.  .38 5 .395  5 . 6 .  .400.410. 4 2 0 -  .410 .420 .430  .40 5 .415 .425  12. 7. 5 .  . 4 3 0 -  .440  .435  3 .  SAMPLE  SIZE=  VARIANCE  OF  STANDARD  DEVIATION  MEAN  952  F*CM  .730  4 2 .  TURBULENCE  CONFIDENCE  .266 .281 .741 .936  4. 860 2.905  1 .968 1 . 206  2. 125 1. 3 0 5  .903 .568  .00032  S  INTENSITY  INTERVAL  .750 1.925 2.370  16.970  SAMPLE  =  .0178  =  .404  ±  F*SQCM  .0356  6 .870  244  HISTOGRAM TURB  RUN  F  OF  A  INTENSITY  NO.  SAMPLE  OF  MEASUREMENTS  : S 1  0 . 4  -  0 . 3  •  0 . 2  -  0. 1  -  .365  . 3 7 5  . 3 8 5  . 3 9 5  TURBULENT  (F  :  FRACTION  OF  THE  TOTAL  . 4 0 5  INTENSITY  SAMPLE)  . 4 15  . 4 2 5  . 4 3 5  245 ANALYSIS FOR  OF  A  SPANWISE  SAMPLE  OF  STREAK  INTERFEROGRAMS  SPACING  * * * * * * * * * * * * * * *******;£**$££ RUN  CELL  NO.  :  S2  BOUNDS  CELL  MIDPT.  13. 5- 14.5 14. 5 - 15.5 15. 5- 16.5 16. 5- 17.5 17. 5 - 1 8 . 5  FREO.  14. 15.  3 . 5.  16.  16.  17. 18.  12. 9 .  SAMPLE  SIZE=  F*CM  4 5 .  F*SQCM  4 2 . 0  5 8 8 . 0  75.0 256.0 2 0 4 . 0  1125.0 4096.0 3468.0  162.0  2916.0  739.0  12193.0  (NOTE: UNIT SEPARATION J=l REPRESENTS A SPANWISE DISTANCE OF 0 . 0 5 0 3 CM CELL MIDPOINT IS IN J UNITS. )  VARIANCE  OF  STANDARD  DEVIATION  MEAN  953  STREAK  SAMPLE  SPACING  CONFIDENCE  NON-DI MEN.  S  INTERVAL  STREAK  SPACING  =  =  +  .004  CM  .066  CM  . 9 57  CM  . 1 3 3  CM  170.  HISTOGRAM STREAK  RUN  F  OF  A  SPACING  NO.  :  SAMPLE  OF  MEASUREMENTS  S2  0 . 4  -  0 . 3  -  0 . 2  -  0.1  -  J  o.o .016  .874  j . 9 3 3  STREAK  (F  :  FRACTION  OF  THE  L-  —I .991  SPACING  TOTAL  1.049  -  CM  SAMPLE)  247 ANALYSIS  OF  A  SAMPLE  OF  I NTEKFEROGRAMS  FOR TURBULENCE INTENSITY MEASUREMENTS * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * RUN  CELL  . . . . . . . .  NO.  :  S2  BOUNDS  3 5 0 3 6 0 3703 8 0 3 9 0 4 0 0 4104 2 0 -  CELL  . 3 6 0 .370 . 3 8 0 . 3 9 0 . 4 0 0 .410 .420 . 4 3 0  MI D P T .  FREQ.  . 3 5 5 . 3 6 5 .375 . 3 8 5 . 3 9 5 . 4 0 5 .415 . 4 2 5  SAMPLE  SIZE=  VARIANCE  OF  STANDARD  DEVIATION  MEAN  951  2 . 2. 3 . 4. 10. 9 . 8 . 7.  .710 . 7 3 0 1.125 1 . 5 4 0 3.950 3.645 3.320 2.975  4 5 .  17.995  SAMPLE  TURBULENCE  CONFIDENCE  =  S  INTENSITY  INTERVAL  F*CM  .00036  =  . 0 1 9 0  =  . 4 0 0  =  +  .0380  F*SQCM  . 2 5 . 2 6 . 4 2 . 5 9 1 . 5 6 1.47 1.37 1.26  2 6 2 3 0 6 8 4  7.212  248  HISTOGRAM TURB  RUN  F  OF  A  INTENSITY  NO.  SAMPLE  OF  MEASUREMENTS  : S 2  0 . 4  -  0 . 3  -  0 . 2  -  0.1  -  o.o '  j .355  . 3 6 5  . 3 7 5  . 3 8 5  TURBULENT  (F  :  FRACTION  OF  THE  TOTAL  . 3 9 5  INTENSITY  SAMPLE)  . 4 0 5  .415  . 4 2 5  ANALYSIS  CF  A  FOR  SPANWISE  RUN  NO.  CELL  :  SAMPLE STREAK  INTERFEROGRAMS  SPACING  S3  BOUNDS  1 4 . 5 - 15 1 5 . 5 - 16 1 6 . 5 - 17 17. 5 - 18 1 8 . 5 - 19  OF  CELL  MI D P T .  FREQ.  F*CM  .5  15.  4 .  .5 .5  16.  17.  17. 18.19.  12. 12. 2 .  6 0 . 0 272.0 204. 0 216.0 3 8 . 0  47.  790.0  .5 .5  SAMPLE  (NOTE:  UNIT  SIZE=  SEPARATION  A SPANWISE DISTANCE CELL MIDPOINT IS IN  VARIANCE  OF  STANDARD  DEVIATION  MEAN  9b%  STREAK  NON-DIMEN.  13330.0  REPRESENTS OF 0 . 0 5 8 3 CM J UNITS. )  S  SPACING  INTERVAL  STREAK  900. 0 4352.0 3468.0 3888.0 722.0  J=l  SAMPLE  CONFIDENCE  F*SQCM  SPACING  =  .004  CM  .062  CM  . 9 8 0  CM  .123  CM  =  +  =  2 3 5 .  HISTOGRAM STREAK  RUN  F  OF  A  SAMPLE  SPACING  NO.  :  OF  MEASUREMENTS  S3  0 . 4  -  0.3  -  0 . 2  -  0.1  -  o.o  '  I .874  f  I  )  . 9 3 3  . 9 9 1  STREAK  (F  :  FRACTION  OF  THE  1.049  SPACING  TOTAL  1.108  -  CM  SAMPLE)  251 ANALYSIS FOR  OF  A  SAMPLE  TURBULENCE  OF  INTERFEROGRAMS  INTENSITY  MEASUREMENTS  ************************************* RUN  CELL  NO.  : S3  BOUNDS  CELL  MI D P T .  FREQ.  . 3 2 0 .330-  .330 .340  .325 .335  1. 6.  . 3 4 0 . 3 5 0 . 3 6 0 -  .345 .355  6. 10.  .370. 3 8 0 -  . . . . .  350 360 370 380 390  .365 .375  6. 6.  .385  5 .  . 3 9 0 -  .400  .395  5 .  SAMPLE  VAR  IANCE  STANDARD  MEAN  95S  OF  SIZE=  F*CM  .325  TURBULENCE  CONFIDENCE  2. 070 3.550 2. 190  1.260 .799  1 6 . 2 9 5  .00039  S  INTENSITY  INTERVAL  .106 .673  2. 250 1.925 1.975  SAMPLE  DEVIATION  010  2.  4 5 .  =  .0197  =  .362  t  F*SQCM  .0395  .714  . 844 .741 .780  5.918  252  HISTOGRAM TURB  RUN  F  OF  A  INTENSITY  NO.  SAMPLE  OF  MEASUREMENTS  : S3.  0 . 4  -  0 . 3  -  0 . 2  -  0.1  -  I  o.o  .325  — . 3 3 5  . 3 4 5  . 3 5 5  TURBULENT  (F  :  FRACTION  OF  THE  TOTAL  . 3 6 5  INTENSITY  SAMPLE)  . 3 7 5  . 3 8 5  . 3 9 5  s .r.o.  (Y,  (D  (5)  0  AT  SEPARATION  OF:  4  5  20  21  22  23  24  25  26  27  28  29  30  .686 .105  .640 .223  .568 .050  .547 .068  .525 .178  .422 .281  -312 .155  .295 .166  .264 .080  .170 .152  .703  .563  .344  .272  .194  .205  .183  .214  .040 - . 0 8 8 - . 1 4 4 - . 3 3 2 - . 3 3 0 - . 2 9 4 - . 2 8 4 - . 1 7 0  l.CCO  l.CCO -.C04  l.COO -.007  Run  8  CORRELATION  3  -.102  7  TIKE  2  l.COO .094  6  OF  1  Run  .  VALUE  0  y  10 .  11  12  13  14  15  16  17  13  19  31  32  33  34  35  36  37  38  39  W1 :  -.026 -.062  .591 .159  .664 -.037  .486 -.073  .427 .151  .574 -.064  -.071 -.156 -.086  .360 .177  .177 .235  .564  .081 .167  .560 . 4 9 6  .009 - . 0 4 7  .084  .091 - . C 6 9 - . 1 3 1 - . 0 6 1  .069 - . 0 3 0 .256 .336  -.116 -.123 -.134 .257 .244 .241  .133 .058 .023 - . 1 6 8  -.181  -.165  - . 0 1 3 -.001 .011 .048 .055 .027 -.204 -.263 -.370 -.461 - . 4 7 8 -.581  -.109 -.084 -.003  .192  -.164  .024 - . 0 2 6 .151  -.196 -.183 -.225 -.191 -.168 -.236 - . 2 0 6 -.061 .159 .253 .102 - . 0 9 1 - . 2 1 7 - . 2 3 2 - . 3 6 3 - . 2 4 6  .153  .120  .059  .169  .077  .014 -.625  .553  .423  .399  .382  .362  .229  .083  .038  .083  .044  .034  .068 - . 0 1 4 - . 0 8 9 - . 1 1 5 - . 1 4 0 - . 2 3 4 - . 2 0 0 - . 3 1 6  ..257  -.057-.027  . 0 0 4 - . 0 2 3 .021 -.529  'ill:  ® - : 3 « - : 2 ; j - : J 2 i " : S  9  2  8  i - . 1 L  6  - : ^  : i ; r : ^ -  0  4  9  -  0  2  3  >™-™-™-™-™  . m  .o  8 2  - .  2 5 6  - . 3 3 9  Autocorrelation data: Run Wl ( f i g . 5.l8a) & Run W2 ( f i g . 5.17a). (One separation unit = 0.016 s) no tn Co  r,  ,  VALUE  1  20  21  Run  *  -  :  S  .  2  22  23  -  »  -  •  '  24  6  25  OF  3  7  .26  TIME  C L1RR.E L AT I fiN AT  <>  27  28  10  11  29  30  "LU  (3) l.COO -.C20  .576 -.050  .365 -.011  .14  -  :  .J>-JO  0  3  »  .>i i .2 "0 "3 ^  -  4  SEP ARATI DM  12  L3  31  32  OF:  14 33  15  16  17  -«  -;8i  18  19  34  W3:  ^ -*^9  ^ j . . v , v w .029  3  0  .C94 " i l t " H ..' 0U°2539 -~* < ..'00°00 66 .055  .Lft> . l<< f .081" - . 0 2 1  .124 -.053  -.062 -.095  l.COO .348 .076 .032 -.136 -.249 - . 3 9 1 - . 1 7 5  .035 .071  7  5 9  -.088 -.252  09  r  -.004 -.109  *  4 6  023  ^  --  -'°  081  -3? 117  -. .0 01 10 0  .0 13 -. 013 -. .0 06 65 5  .128 .168  .106 .260  .117 - . 0 3 6 .103 - . 0 6 7  -  a  :  . _ . _ .037 . . ,^w^ -078 ..056 .066 068 L ..073 , 1, 7« 159 .076 162 ., 140 .21 1  -- .235 -0 .093 .093  2 9  -. .0 03 31 1  .070 -.045  ::St;  " 3 8  6 5  , * o  .194  .C61-.010 .061 .008 - . 0 0 0 -.230 -.509 -.378 -.284 -.162  .029 .057 - . 1 0 5 .062 .359 .295 .113 - . 0 2 0 - . 1 1 3 .110 - . 2 2 1 -.301 - . 1 7 5 -.065 -.397 -.317 - . 2 6 9 -.010  .099 .220  .010 .045 -.102 -.103  .084 - . 2 4 7 .064 - . 0 4 3  -.227 .051  -.183 .072  O i l -.211  .CC4 .036  Run S I :  (D 1.00 3  .013  $70  0  1.0c:  .573  :Hl  :Si  .614  .2 75  .425  ,36:  _ »;  ::JS?  :  o,3 mi -.IS -:JSJ  .:{»_rltf :SS  « . .915 .081  : f j ;  'HI •06o  *033 .033  '111 .149  -  -.lit  '^1 .^14  - ? .160 7  9  :  " .046 - . 2 4 7 4  3  7  3  6  9  » s  -.378 3  0  9  :  » »  - « -.361 2  :  » j  '186 .395  :  -  » ;  --if: - 2 1 4 :  - _  .099 -.292  :  » ;  .077 -.606  - ~ —  • » »  .044 .108  .024  . . . .  .012  -.002  Autocorrelation data : Run W3 ( f i g . 5.19a) & Run SI ( f i g . 5.l8b) (One separation unit = 0.016 s)  . «  — . 366  .009  .014  £  S \'G * ~  l  o  5  ?  2  2  0  2  1  2  2  3  2  ,  VALUE  4  5  ^  3  2=  6  26  7  27  8  28  flF TIME CORRELATION « 1 0 — U 29  30  31  AT S E P A R A T I O N OF: 12 13 IT 15 32  33  16  17  13  19  34  Run S 2 :  l.COO .803 .103 - . 0 0 9  . 6 6 1 -.050  .522 .411 -.003 - . 0 7 9  .321 .241  .248 .224  .197 .113  -153 .121 .048 - . 0 1 4  .094  .058  .002  -.061  -.074  -.042  .003  .081  .126  .201  .221 .136 .013 - . 1 7 3 -.292 - . 2 9 5 - . 2 5 9 -.200 - . 104 - . 1 3 0 -.102 - . 0 8 6 .092 - . 2 7 9 - . 4 2 7 - . 6 8 3 - . 8 5 6 - . 7 3 1 - . 5 2 9 - . 4 8 9 - . 564 .018  .190  .211  .427  Run S 3 :  0  1.003 • •>75  .722 .413  .592 .274  .379 .439  -J8 :S  ® 01.000 .c74  -.-72  .391 .462  .732 .71  "*?o -  .  0  6  9  .517  .249  •632  .341  38 :?g 7S&  -.048 - . 1 4 6 - . 1 7 3 - . 2 0 4 - . 0 7 4 .047 -.238 -.377 -.314 -.177  -:J8 :!K  .007 -^23  MfJ  * ' ° - 0 ^ -.029 -.017 .035 .092 . 162 .276 .283 .063 - . 0 9 0 - . 4 , 1 - . 4 3 9 - . 5 7 1 - . 2 6 2 - . 3 6 2 - . 6 3 1 - . 4 9 7 - . 2 5 2 K  -.no  :iS  3  5  1  -220  •  3S2  " l 2 7 - 0 9 8 «223 .182 - . 0 4 2 .053 .217  .101 - . 1 9 6 - . 4 3 4 - . 5 8 3 - . 4 4 8  Autocorrelation data : Run S 2 ( f i g . .5.17b) & R u n S 3 ( f i g . 5.19b) (One separation unit = 0.016 s)  ro on on  APPENDIX  F  SCENARIO- FOR MOTION PICUTRE  TITLE  :  Flow -  CREDITS  :  V i s u a l i z a t i o n  with  Laser  Holography  A study of pipe wall turbulence i n Newtonian and d r a g - r e d u c i n g f l o w s .  by  B.U.  Achia  and  D.W.  Thompson  made from the M.A.Sc (1971) and Ph.D. (1974) r e s e a r c h f i l m s of B . U . Achia Research A d v i s e r : Dr. D.W. Thompson Department of Chemical Engineering The U n i v e r s i t y of B r i t i s h Columbia Vancouver, CANADA V 6 T 1W5  RESEARCH  TYPE  SUPPORT:  :  National Research grant A4936  16  mm,  c o l o r ,  Running  CONTENT  :  Time  8  speed  The  o u t l i n e s  f i l m  the at the  mts  of  pipe  the of  i n  It the  s t r u c t u r e  (streaks  flows  to  due  reducing  Canada  18  under  pps  scenes  the  polymer  256  vary)  p r i n c i p l e  i n t e r f e r o m e t r y  w a l l .  changes  at  flow  v i s u a l i z a t i o n a  of  s i l e n t =  (framing  h o l o g r a p h i c  Council  as  of  l a s e r  a p p l i e d  turbulence  to  s t r u c t u r e s  f u r t h e r  demonstrates  n e a r - w a l l  turbulence  and  bursts) of  (50  Separan  wppm  a  of  a d d i t i o n  Newtonian  d r a g AP30).  257  comprising  The  f i l m  i s  broadly  of  many  s c e n e s .  d i v i d e d  Section  into  s e c t i o n s ,  each  D e s c r i p t i o n  1.  Principle of holography: a 2-step technique with hologram r e c o r d i n g and image r e c o n s t r u c t i o n s t e p s . R e a l - t i m e h o l o g r a p h i c i n t e r f e r o m e t r y is performed by superimposing the r e c o n s t r u c t e d v e r t u a l image of the t e s t s e c t i o n on the pipe under t e s t . Flow i s v i s u a l i z e d as the r e a l time d i s t o r t i o n s of hologram moire f r i n g e s due to a r e f r a c t i v e index enhancer induced into the flow (3.5% propylene g l y c o l s o l u t i o n made up in water and d r a g - r e d u c i n g l i q u i d ) .  2.  Apparatus:  a)  The  flow  constant head tank, a n d AP r e c o r d e r .  t e s t  pipe  stand  l i n e ,  views  show  pressure  b) The h o l o g r a p h i c i n t e r f e r o m e t e r the argon l a s e r output end, o b l i q u e view of hologram and t e s t s e c t i o n .  the  to  3.  Hologram and  viewer  to  the  transducer  shows  The view through the hologram the r e g i o n of o b s e r v a t i o n .  o r i e n t s  The  r i g h t  d i r e c t i o n  of  flow  i s  from  l e f t .  moire with  at  fringes:  flow;  a)  without  No  flow,  v i b r a t i o n  of c)  Moire  with  no  This f r i n g e focus at the pipe wall ( movement, i f any, is cau the s u r r o u n d i n g s . It pr a s s e s s i n g the s t a b i l i t y b)  conditions  and  no  flow g r a d i e n t s .  gradients pattern i s brought into in plan view). Its s e d by v i b r a t i o n s from ovides a means of of the a p p a r a t u s .  f r i n g e s :  with  flow,  The  movement  of  the  the  pipe  to  f l o w i n g  Moire  of  induced  due  f r i n g e s :  with  no  f r i n g e s  flow,  gradients shows  f l u i d . with  The n e a r - w a l l flow i s seen as r e a l time modulation of the f r i n g e s due to s p a t i a l d i s t r i b u t i o n of the r e f r a c t i v e index enhancer.  gradients  258  S e c t i o n  D e s c r i p t i on  4.  Flow  The  tests: separate  4A.  Five . •  ,.  flow  p a t t e r n s  are  observed  a)  Plan  view  to  observe  ' s t r e a k s '  b)  Edge  view  to  observe  ' b u r s t s '  scenes  in  two  v i e w s .  of  streak  in  observations  Newtonian  (Water) and d r a g - r e d u c i n g (Separan AP30; 50 in water) are shown. Refer to Figure 5 . 2 .  wppm  4A  Run  SI  DR  %  Re  FI  ow  Rate  ml/s  11*  f  cm/s  p/s  Remarks  20  7,400  225  2.18  24  The f r i n g e m o d u l a t i o n in a 20% d r a g - r e d u c i n g flow i s seen. Note the p e r s i s t e n c e of s t r u c t u r e s .  W2  0  10,900  220  2.45  24  -  S2  32  9,730  300  2.56  24  A 32% d - r flow at almost same u * as W2. Note the i n c r e a s e d s t r e a k s p a c i n g .  W3  0  14,500  305  3 .2 5  32  The  S3  44  14,800  440  3.45  32  at almost same Q as SI . Note the r e l a t i v e l y s h o r t e r l i f e t i m e s of p a t t e r n s .  f r i n g e s  are  than  the  same  f e a t u r e s  i n h i b i t i o n are  of  and  observed  p h y s i c a l  spaced  p r e v i o u s  i n  s t r e a k  i n c r e a s e d .  c l o s e r  r u n .  The.  s t r e a k p e r s i s t e n c e S3.  The  s p a c i n g  i s  259  4B  Three  (The  Run  Scenes  of  Burst  Observations  The geometry of the scene is difference in framing rate between taken into account when comparing  f  F l ow  Re  Rate  ml/s  cm/s  p/s  shown. scenes must the scenes)  be  Remarks  W2  10,900  220  2.45  .32  S2  9,730  300  2.56  64  A 30% d r a g - r e d u c i n g flow at a p p r o x i m a t e l y same u* as W2. The b u r s t i n g rate is d r a s t i c a l l y r e d u c e d . (Note that the framing speed is doubled and the f i e l d of view i s s m a l l e r )  W3  14,500  305  3.25  120  A water flow at about the same Q as S 2 . The s p a t i a l l y averaged b u r s t ing rate i s i n c r e a s e d ei g h t f o l d .  THE  The on  the  b u r s t s )  nature are  e f f e c t s of  of  END  d r a g - r e d u c i n g  wal1 - t u r b u l e n c e  summarized  in  The scene shows the movement of b u r s t s of f l u i d away from the pipe w a l l . N o t e how the b u r s t s break up into blobs as they move downstream.  f i g u r e s  Separan  s t r u c t u r e s 5.8  and  AP30  ( s t r e a k s 5.11.  s o l u t i o n and  260  F.2  D e t a i l s  1.  of  Cameras:  Motion  16 16  P i c t u r e  mm H y c a r r / ^ , (2) mm B o l e x v ,  Film  Recording  1/2.5  s h u t t e r  v a r i a b l e  s h u t t e r  (1)  used f o r speeds 1i gh t g e n e r a t o r  >  64  p p s ;  c a l i b r a t e d  w i t h  a  timing  (2)  used f o r speeds > e l e c t r o n i c c l o c k .  64  p p s ;  c a l i b r a t e d  with  a  LED  2?  Lens:  75  3.  F i l m s :  mm,  f  ( i ) ( i i ) ( i i i ) Civ)  1.9  Cosmicar  +  20  mm e x t e n s i o n  Kodak Kodak  7224 7241  4x N e g a t i v e B/W & 7242 Ektachrome  Kodak Kodak  7277 2485  4x R e v e r s a l B/W High Speed Recording  exp. Run  type  P r e ! i m i Dye  nary  Camera  1m  ASA  (iii;  160  Fi  2  f.  no.  t i me s  ll  tube.  C o l o r  f i l m  Length run s  Frames per second pps  l/6o  Reversal  & r  30  60 20  t e s t s  S treak Runs Wls,W2s,W3s) S l s , S 2 s , S 3 s /  2  B u r s t Runs Wlb, W2b \ S i b , S2b f W3b & S 3 b  2  Hycam LED  |(ii)  1  s e t t i n g  1/60 1/60  2k to 32  320  k  l/6o  60  500  k  60 60  120  30  H  5.6  ( i v ) 1000  and  superimposed  ( i i )  320 k 500"1 • 5.6  c a l i b r a t i o n on  f i l m  at  24  1/300  showed &  16  < pps  1%  20  d i f f e r e n c e .  f o r  ( i )  and  r e s p e c t i v e l y .  t Bolex  s e t t i n g  at  64  pps  was  Pushed 2 stops while processing.  c a l i b r a t e d  at  60  ±  1  p p s .  of  APPENDIX  G  IMPROVEMENTS TO THE HOLOGRAPHIC FLOW VISUALIZATION TECHNIQUE  The  v i s u a ! - q u a n t i t a t i v e  i n t r o d u c e d  i n  other  s e c t i o n s  the  flow  r e g i o n  sion dye.  of  of  t h e  away  too  mass  o r  of  heat  G.1  about  1  dependent  the  s u i t a b l y i s  cm/s s i n c e On  extremely sources  on  f o r  much  v i s u a l i z a t i o n  a d d i t i o n  mainly  where  here  d e t e c t i o n .  tagging i n  s u i t a b l e  f l u i d s  used  flow  f o r  i s  c a n be  dye  can d e t e c t  i n f o r m a t i o n  t i o n  and  enhancer  soon  ferometer  t h e s i s  i n t e r e s t  However,  v e l o c i t i e s  is  t h i s  h o l o g r a p h i c  to the  at the  small and  flow  r e f r a c t i v e  l i k e i s  the  other  u * ,  can provide  index  The  to  dye  hand,  g r a d i e n t s  with of  i n f u -  i n f u s i o n  l i m i t e d  higher  l i g h t  s t u d i e s  enhanced.  v i s u a l i z a t i o n . l a s e r  technique  of  shear i s  the  from  washed i n t e r -  e i t h e r  q u a n t i t a t i v e  The:1! i m it i ng  i n t e n s i t y  and  u *  v i b r a -  e f f e c t s .  Improved  One c e n t r a t i o n  Flow  Tagging  p o s s i b l e  changes  method  would  be  of  the  261  tagging use of  an  t h e  f l u i d  e l e c t r o d e  with i n  c o n the  262  form  of  the  a  wall  f i n e or  hydrogen  bubble  with  convected  w i r e .  f r i n g e s . with  a  flow  be  Data  s e c t i o n  time  p r e s e n t ,  consuming of  s u i t e d  due  automated  densitometer to  c o n t r a s t  zones  apparent  dye  by  d i f f e r e n t lack  to  i s  than  T r a n s l a t i n g  s i t o m e t e r . to  the  would  would  would  flow  c o n v e n t i o n a l  then  be  an  e l e c t r o l y t i c  would  be  the  on  produce appear  f r e e  from  c e l l , e q u i - c o n -  as  t i m e l i n e s  i n e r t i a l  v i s u a l i z a t i o n  or  c o n d i t i o n s ,  that  used  i n  t h i s  study  data  r e d u c t i o n  i s  very  l a b o r i o u s  of  f r i n g e  manual  of  readout  scanning  coupled  i n t e r f e r o m e t r i c  would  do  d a t a .  most  F r i n g e  from  F i e l d  Figure  example,  measuring He zones  could  s u f f i c i e n t  a  computer,  would  The  f r i n g e s  provide  to  flow  between  5 . 9 .  photographic  that not  the be  (1963)  m i c r o be  of  w e l l higher  schemes.  and  w i t h  dye  v e l o c i t y  c a l i b r a t i o n  attempted  d e n s i t y  s a t i s f a c t o r i l y  c o n t r a s t .  s h i f t  r e a l - t i m e  c o n t r a s t  a  F i e l d  f r i n g e  I n s i t u  The  v i s u a l i z a t i o n  V e l o c i t y  Runstadler  the  found  e . g .  other  and  d a t a .  t e c h n i q u e s ,  with  correspondence  For of  of  e i t h e r  than  o p t i c a l  that  The are  l i k e  medium  f i e l d ,  b e t t e r  placed  Reduction At  G.3  For  much  f r i n g e s  and  be  d e s i r a b l e .  G . 2  use  i t ,  f r i n g e  flow  may  flow  These  the  e f f e c t s .  to  o p e r a t i o n  i n f i n i t e  buoyancy l a r g e r  wire  The  Pulsed  an  c e n t r a t i o n  This  p e r p e n d i c u l a r  e l e c t r o l y t e . used  w i r e .  a  an  a n a l y s i s  m i c r o d e n -  marking  determined  in due  263  with of Any  a  l a s e r  doppler  t r a n s f o r m i n g one  spanwise  c o n c e n t r a t i o n High-speed r e g i o n s  f r i n g e  f r i n g e  and  ( F i g u r e  low-speed  r e s p e c t i v e l y i s  ( i n s e t ,  a  of  F i g u r e  of  zones the  m i r r o r  c o u l d  f i e l d  d i s t r i b u t i o n  d i s t r i b u t i o n b u t i o n  the  v e l o c i m e t e r  to  one  5.9)  the are  of  of  i s  a  l i n e  d e p l e t e d  the  the  2-D  r e f r a c t i v e  enhancer.  image  p r o v i d e  Thus,  p o s s i b i l i t y  v e l o c i t y . of  spanwise  index and  enhancer.  e n r i c h e d  the  v e l o c i t y  c o n c e n t r a t i o n  d i s t r i -  G . l ) .  £teettonttS  IN  F i g u r e  ser  G . l .  A d o p p l e r - h o l o g r a p h i c f l o w v i s u a l i z a t i o n scheme. (I) P h o t o g r a p h i c r e c o r d i n g of flow p a t t e r n s and  (2)  dopper  O s c i l l o g r a p h i c frequency  r e c o r d i n g  s i g n a l .  of  264  A  schematic  G . l .  The  flow  p o i n t  v e l o c i t y  frequency are of  a  pattern i s  s h i f t  recorded Hycam  t r a c e .  means  s t r u c t u r e s  both  of  s h i f t s  h o l o g r a p h i c on  i n  and  instantaneous  f i l m  presented are  which  and  using  here  foreseen  F i g u r e the  doppler  doppler  the  i s  s i g n a l s  p r o v i s i o n s  o v e r s i m p l i f i e d ;  due  and  to  problems  l a s e r - h o l o g r a p h i c  problem  i s  one  mechanism t h a t  s t a t i o n a r y wavefront  in  of  o b j e c t  i n  motion.  recorded  on  f r i n g e s  i n  an  which  Thus,  get  the  i f  l i t t l e  the  as  has  A  o b j e c t  and  to  of use  motion  i s  the  In  are of  2 . 2 ,  The  ' p r i m a r y '  produced the  by  o b j e c t  r e c o r d i n g , f a i l s  t h i s  hologram a l i g n e d  h o l o -  Chapter  hologram  reducing a  At  r e c o r d i n g  A ^ / 2during  method  been  phase  much  t u r b u l e n c e  o u t l i n e d .  hologram  'smeared'  image.  motion  the  was  a  n a t u r e .  s u c c e s s f u l l y  are  as  of  t h r e e - d i m e n s i o n a l  r e c o r d i n g  by  provide  i n t e r a c t i o n s  hologram  changes  o b j e c t s  could  of  r e c o n s t r u c t  geometry  an  w a v e f r o n t s .  primary  the  a  of  V i s u a l i z a t i o n  holography  of  r e a l - t i m e  f r i n g e s  of  are  grams  i n  Flow  o b s e r v i n g  the  f o r  the  1 a s e r - d o p p l e r  aspect  p r e s e n t ,  to  as  Three-Dimensional  b e t t e r  the  f r i n g e  shown  ques.  This  the  is  o s c i 1 1 o g r a p h y .  c o m p l e x i t i e s  with  setup  as  from  Both  for  concept  experimental  G . 4  seen  s i m u l t a n e o u s l y  The  techni  i s  measured  camera  a s s o c i a t e d  experimental  problem  r e c o r d i n g  along  an  265  ' i s o p h a s e ' beam  p a t h ,  s p l i t t e r  ( F i g u r e  e . g .  and  along  hologram  the  r i m  l o c a t e d  of at  an the  e l l i p s e , f o c i  of  w i t h the  t h e e l l i p s e  G.2)  M  F i g u r e  G . 2 .  E l l i p t i c a l in  The and  t h a t  due  to  0  =  R.  In  t h r e e - d i m e n s i o n a l  each  A  frame  could  be  where  ( A c h i a ,  i s  f l o w  made.  of  way,  o p t i c a l  a  e l l i p s e  the  beam  minimum.  motion a  D e t a i l s 1974).  the  components  such  path  and  p i c t u r e ,  photograph of  p r o v i d e  Using  v i s u a l i z a t i o n  holographic  i n s t e a d  of  t h i s  motion  of  h o l o g r a p h y .  p r o p e r t i e s  o b j e c t  p o s s i b l e .  arrangement  motion  a  of  the  scheme  t h a t  l e n g t h  t h i s  0  p r i n c i p l e ,  a  i s  hologram  v i r t u a l a r e  0 '  change  measurement w i t h  =  i n  image,  proposed  e l s e -  

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