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A method for drag reduction on bluff bodies Lesage, François 1983

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A METHOD FOR DRAG REDUCTION ON BLUFF BODIES by FRANCOIS LESAGE B.Sc.A., U n i v e r s i t e L a v a l , 1979  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in  THE FACULTY OF GRADUATE STUDIES Department Of Mechanical  We accept  Engineering  t h i s t h e s i s as conforming  to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA April  ©  1983  F r a n c o i s Lesage, 1983  In  presenting  this  requirements  for  British  Columbia,  freely  available  that  permission  scholarly  an  partial  advanced  degree  I agree  that  or  understood  that  the  for reference  purposes  gain  in  for extensive  Department  financial  thesis  by  may his  copying  shall  not  be or  and s t u d y .  this  granted  by  the  of  Mechanical  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5  Date:  April  2 5 , 1983  Engineering Columbia  Head  of t h i s  without  of i t  agree  thesis  representatives.  allowed  the  make  I further  of  or p u b l i c a t i o n be  shall  copying  her  of  at the U n i v e r s i t y  Library  permission.  Department  fulfilment  of It  for my i s  thesis for my  written  i i  Abstract This the drag small  thesis of t y p i c a l  circular  upstream  on  system  was  shedding various  reduced. the  typical and  from  main  defined  the main For measured  was  both  corresponds  to point  appearance  o f two  36%.  the  be  the f l a t d/D  = 0.33  The  < L/D  drag  D  overall  to  vortex  in  the  <  frontal  from  (d)  width  Reynolds  range  and  of  of  numbers  1x10"  to  the rod centre to  the c i r c u l a r at various  a t some c r i t i c a l elimination  the  body  points  the  showed This  a  change  usual  single  centre line  and  the  placed,  body.  s p a c i n g L/D  was  L/D  symmetrically  the optimum  the drag  cylinder,  spacing.  of  bluff  edges of the  reduction  circular  7.0.  coefficient  the  a  rod diameter  plate.  spacing L  plate  on  the  investigated for  front  i s the  or f l a t  D were  at a  of the  investigated:  The  where  stagnation  r e d u c t i o n (based  were  plate.  plate,  a  placed  cases,  due  on  diameters.  bodies  on  to the l a t e r a l For  drag  drag  "jump"  stagnation  to  and  the f l a t  overall  discontinuous  close  also  cylinder  0.4  drag  was  the l o n g i t u d i n a l  body  the  with  "rod")  most  main  using dimension  7x10", and  In  force  t o 0.5D  circular  a  side  flat  0.17D  and  body  bodies  called  Fluctuating  bluff  a  bluff  line.  beneficial  rod positions  cylinder  (here  stagnation  was  from  Two  varied  two-dimensional  cylinder  the  interaction  the  p r e s e n t s an e x p e r i m e n t a l i n v e s t i g a t i o n  configuration of  1.81,  of the due  to  and  plate  was  the  overall  alone)  a change  found  was  in front  pressure  only,  constant  and  d/D  that  over  observed  The vortex  the  flow  over  fluctuating  followed  size  and  Reynolds  significantly  suitable C l '  58%  Part  with  cases.  of the  configuration.  cylinder  plate.  force  being  The  reduction turbulent  CD  which  a  lower  effect  the  flat  was  a  was  plate, sensitive  for increasing  Re.  depending CI'  = 0.17 side  due t o  The v a r i a t i o n  but  fluctuating found  with  second  Unlike  trends  d/D  on  distribution similar to  investigated.  rod  drag  configuration  ( C I ' ) on t h e c y l i n d e r  number  was  the  critical,  pressure  different  The  number  overall  drag  the use of the f r o n t  f o r minimum minimum  best  for  decreasing  side  was a l s o  Reynolds  the c i r c u l a r cylinder  number, w i t h  shedding  most  No  the  coefficient.  on t h e f l a t  spacing  for  be  t h e main  with  in  to  change i n the f r o n t  Reynolds  L/D.  essentially  expected.  1.73.  of base p r e s s u r e  however, to  =  of  remaining  was d u e t o t h e r o d wake  made t h e f l o w  sudden  pressure  cylinder,  found  a n d L/D  cylinder  value  as  circular  was  = 0.33  the  found,  the  reduction  base  independent  d e p e n d e n c e was For  the  rod  increased  r o d a n d was  force.  t o depend  on t h e  never  seemed  of CI'  to The  reduced be  more  position  upon t h e p a r t i c u l a r  iv  Table  of  Contents  Abstract L i s t of Tables L i s t of F i g u r e s Nomenclature Acknowledgements Chapter I INTRODUCTION 1.1 M e t h o d s Of R e d u c i n g F l u i d 1.2 B l u f f B o d y I n t e r a c t i o n 1 .3 Objective  i i vi v i i x x i i 1 1 3 4  Forces  Chapter I I D E S C R I P T I O N OF A P P A R A T U S AND E X P E R I M E N T S 2.1 Smoke T u n n e l 2.2 W i n d T u n n e l 2.3 W i n d T u n n e l B a l a n c e 2.4 M o d e l s 2.5 P r e s s u r e D i s t r i b u t i o n M e a s u r e m e n t s 2.6 M e a n D r a g M e a s u r e m e n t s 2.7 F l u c t u a t i n g Side Force Measurements 2.8 D a t a A c q u i s i t i o n Chapter I I I R E S U L T S AND D I S C U S S I O N I : F L A T P L A T E 3.1 P r e s s u r e D i s t r i b u t i o n On F l a t P l a t e 3.2 P r e s s u r e D i s t r i b u t i o n On F l a t P l a t e Rod 3.3 F l o w R e g i m e A 3 . 4 Flow Regime B 3.5 D r a g 3.6 E f f e c t Of Yaw 3.7 E f f e c t Of R e y n o l d s N u m b e r 3.8 P o t e n t i a l F l o w M o d e l  6 6 6 7 7 9 10 11 13 ..14 14 With  Front 15 ...16 18 20 21 22 22  ;  Chapter IV R E S U L T S AND D I S C U S S I O N I I : C I R C U L A R C Y L I N D E R 4.1 P r e s s u r e D i s t r i b u t i o n On C i r c u l a r C y l i n d e r 4.1.1 Background 4.1.2 R e s u l t s 4.2 P r e s s u r e D i s t r i b u t i o n On C i r c u l a r C y l i n d e r F r o n t Rod 4.3 F l o w R e g i m e A 4.4 F l o w R e g i m e B 4.5 D r a g 4.6 E f f e c t Of R e y n o l d s N u m b e r 4.7 O p t i m u m C o n f i g u r a t i o n 4.8 E f f e c t Of Yaw 4.9 F l u c t u a t i n g Side Force 4.10 S i d e F o r c e On M o d e l W i t h F r o n t R o d 4 . 1 0 . 1 F r o n t R o d d/D = 0.17  27 27 27 28 With 30 30 32 32 34 34 35 36 36 37  V  4 . 1 0 . 2 F r o n t R o d d/D = 0.33 4 . 1 0 . 3 F r o n t R o d d/D = 0.50 4.10.4 G e n e r a l R e m a r k s Chapter V CONCLUSIONS 5.1 C o n c l u s i o n s 5.2 A r e a s Of F u r t h e r  38 39 40 41 41 43  Work  BIBLIOGRAPHY A P P E N D I X A - P R E S S U R E T A P L O C A T I O N FOR MEASUREMENT  45 SIDE  FORCE 89  vi  List  I.  of  Tables  C a l c u l a t e d wake v e l o c i t y d e f i c i t ( U ) c h a r a c t e r i s t i c wake w i d t h ( l ) 0  0  and 47  vi i  List  of Figures  1. C o o r d i n a t e s y s t e m a n d s y m b o l s (b) 2.  circular  plate;  cylinder  48  Smoke t u n n e l  3. O u t l i n e  48  o f t h e U.B.C.  4. S k e t c h o f a t y p i c a l 5.  f o r : (a) f l a t  aeronautical  model  inside  wind  tunnel  the wind  tunnel  End p l a t e s  6. C r o s s s e c t i o n  of models  showing  pressure tap 52  7. B a l a n c e c a l i b r a t i o n  curve  53  8. S k e t c h o f m a n i f o l d f o r p n e u m a t i c a v e r a g i n g 9. A p p a r a t u s f o r c a l i b r a t i o n o f t h e s i d e f o r c e measuring system against frequency d i s t o r t i o n 10. T r a n s f e r f u n c t i o n f o r t h e s i d e f o r c e m e a s u r i n g s y s t e m . The s o l i d Pressure  line  was u s e d  distribution  on f l a t  12.  P r e s s u r e d i s t r i b u t i o n on d/D = 0.33 ( R e = 4 . 0 x 1 0 " ) ; 13. P r e s s u r e d i s t r i b u t i o n on d/D = 0.33 ( R e = 4 . 0 x l 0 ) ; 4  14. 15. 16.  50 51  location  11.  49  to correct  plate  data  (Re=4.0x10")  flat plate with Flow regime A flat plate with Flow regime B  53 54 55 56  front rod 57 front rod 58  P r e s s u r e d i s t r i b u t i o n on f l a t d/D = 0.17 ( R e = 4 . 0 x 1 0 " ) ; F l o w  plate with regime A  front rod  P r e s s u r e d i s t r i b u t i o n on f l a t d/D = 0.17 ( R e = 4 . 0 x 1 0 " ) ; F l o w  plate with regime B  front rod  59  P r e s s u r e d i s t r i b u t i o n o n t h e f r o n t r o d d/D = 0.33 a t t w o d i f f e r e n t s p a c i n g s ( R e = 5.Ox 1 0 ) ; L/D = 3 . 4 2 ( r e g i m e A ) a n d L/D = 1.42 ( r e g i m e B )  60  4  17. V e l o c i t y d e f i c i t regime A 18.  Base  pressure  (U ) versus spacing 0  f o r regimes A and B  61  (L/d) f o r flow 62 63  vi i i  19.  20.  F l o w v i s u a l i s a t i o n a t Re = 5 X 1 0 for front d/D = 0 . 2 1 ; ( a ) L/D = 1.36 ( r e g i m e A ) ; ( b ) L/D = 0.79 ( r e g i m e B) 3  Drag c o e f f i c i e n t of f l a t (Re=4.0xl0")  plate  21. Drag c o e f f i c i e n t of f l a t (Re=4.0xl0«)  plate  22.  with  rod 64  r o d d/D  =  0.33 65  with  r o d d/D  =  0.17 66  E f f e c t o f yaw o n t h e o v e r a l l d r a g ( p l a t e a n d r o d ) f o r r o d d/D = 0.33 a t L/D = 1.42 ( R e = 5.Ox 1 0 )  67  Separated flow source model  67  4  23.  24.  25.  26.  27.  28.  29.  30.  31.  32.  33.  past a normal  flat  S t r e a m l i n e s over p o t e n t i a l model s t a t i o n a r y p a i r o f v o r t i c e s ; Cpb  plate  from  wake  using condition = -1.24  Typical drag c o e f f i c i e n t versus Reynolds Achenbach  number  for 68 from 68  Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r at v a r i o u s R e y n o l d s n u m b e r s ; s o l i d l i n e i s f r o m ESDU for s u b c r i t i c a l range  69  Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r Re = 1 . 0 x 1 0 " w i t h f r o n t r o d d/D = 0 . 1 7 . ( a ) r e g i m e A; ( b ) r e g i m e B  at 70  Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r Re = 3 . 3 x 1 0 " w i t h f r o n t r o d d/D = 0 . 1 7 . ( a ) r e g i m e A; ( b ) r e g i m e B  at  Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r Re = 6 . 5 x 1 0 " w i t h f r o n t r o d d/D = 0 . 1 7 . ( a ) r e g i m e A; ( b ) r e g i m e B  at  Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r Re = 1 . 0 x 1 0 " w i t h f r o n t r o d d/D = 0 . 3 3 . ( a ) r e g i m e A; ( b ) r e g i m e B  at  Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r Re = 3 . 3 x 1 0 " w i t h f r o n t r o d d/D = 0 . 3 3 . ( a ) r e g i m e A; ( b ) r e g i m e B  at  Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r Re = 6 . 5 x 1 0 " w i t h f r o n t r o d d/D = 0 . 3 3 . ( a ) r e g i m e A; ( b ) r e g i m e B  at  Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r Re = 1 . 0 x 1 0 " w i t h f r o n t r o d d/D = 0 . 5 0 . ( a ) r e g i m e A; ( b ) r e g i m e B  at  71  72  73  74  75  76  ix  34.. P r e s s u r e d i s t r i b u t i o n a r o u n d a c i r c u l a r c y l i n d e r Re = 3 . 3 x 1 0 " w i t h f r o n t r o d d/D = 0 . 5 0 . ( a ) r e g i m e A; ( b ) r e g i m e B  at  35.  at  36. 37. 38.  Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r Re = 6 . 5 x 1 0 " w i t h f r o n t r o d d/D = 0 . 5 0 . ( a ) r e g i m e A; ( b ) r e g i m e B O v e r a l l drag d/D = 0.17  coefficient for cylinder  O v e r a l l drag d/D = 0.33  coefficient for cylinder  O v e r a l l drag d/D = 0.50  coefficient for cylinder  front rod  with  front rod 80  with  front rod 81  Rod s i z e  40.  C r i t i c a l spacing ranges f o r d i f f e r e n t R e y n o l d s numbers ( c i r c u l a r c y l i n d e r )  42.  with  78 79  39.  41.  77  f o r minimum  drag  (circular cylinder)  82  rod sizes  and 83  F l u c t u a t i n g s i d e f o r c e on a c i r c u l a r c y l i n d e r ; S t r o u h a l number v e r s u s R e y n o l d s number; (b) i n t e n s i t y C l ' v e r s u s R e y n o l d s number  (a) 84  F l u c t u a t i n g s i d e f o r c e on a c i r c u l a r c y l i n d e r r o d d/D = 0 . 1 7 ; C l ' i s from Fig.41(b)  with  Fluctuating side r o d d/D = 0.33  force  with  Fluctuating side r o d d/D = 0.50  force  85  f  43. 44. 45. 46.  S t r o u h a l number r o d d/D = 0.17  on a c i r c u l a r c y l i n d e r  86 on a c i r c u l a r c y l i n d e r  .86 on a c i r c u l a r c y l i n d e r  with  front 87  S t r o u h a l number on a c i r c u l a r c y l i n d e r w i t h front r o d d/D = 0.33 ( R e = 3 . 3 x 1 0 " ) ; p e r c e n t a g e s s h o w n represent percentage of ( C l ) due t o t h a t f r e q u e n c y  .87  S t r o u h a l number on a c i r c u l a r c y l i n d e r w i t h front r o d d/D = 0.50 ( R e = 3 . 3 x 1 0 " ) ; p e r c e n t a g e s s h o w n represent percentage of ( C l ) due t o t h a t f r e q u e n c y  .88  1  47.  with  1  2  2  X  Nomenclature CD  drag  CI'  fluctuating =  coefficient side  (rms o f s i d e  =  (drag)/(0.5pU, HD) 2  force  force  fluctuation)/(0.5pU, HD) 2  Cp  pressure  Cpb  base p r e s s u r e  coefficient  D  frontal  of the main  d  rod diameter  F(z)  complex  f  frequency  H  test  h L  p l a t e w i d t h ( p o t e n t i a l flow model) l o n g i t u d i n a l spacing from the rod center to t h e main body  1  0  coefficient  coefficient  width  potential  characteristic  wake  pressure  p,  static  Q  strength  R  circle  Re  Reynolds  number  S  Strouhal  number  U  free 0  2  body  shedding  (Hz)  height  p  U  (p-p,)/(0.5pU, )  i n the z-plane  of vortex  section  =  on m o d e l  half-width  surface  pressure of  sources  radius  i n $-plane  stream v e l o c i t y  characteristic  i n the z-plane  wake v e l o c i t y  U,  free  stream  V  free  stream  w(z)  complex  x  distance defining position of t h e f l a t plate  deficit  velocity velocity  velocity  i n the $-plane  i n the z-plane on t h e s u r f a c e  xi  z  complex  variable  defining  6  angular  position  of  T  circulation  p  density  4>  a n g l e d e f i n i n g p o s i t i o n on of the c i r c u l a r c y l i n d e r  ii  stream  $  complex  So  position  of  upper  vortex  i n the  $-plane  $"  position  of  lower  vortex  i n the  $-plane  0  of  the  flat  plate  plane  source  strength air the  surface  function variable  defining  the  circle  plane  Acknowledgement  The  author  gratitude  to  and  I.S.  valuable  are  also  Mechanical  Engineering  facilities,  and  their  valuable tunnel  his  sincere  Gartshore  direction  help  for his throughout  thanks  t o my  helpful advices  for  playing the role  the  use  the  their  members f o r the  experiments. students  and  Chantal,  t o my  wife,  of a student's  this  research  Council  of  Canada  Computing  of  of  fellow graduate  for  acknowledged.  the Department  the c o n s t r u c t i o n of  and d u r i n g  their  Support  to  for  during  for  Research  due  to the t e c h n i c a l staff  models  Special  by  express  study. Thanks  wind  to  Professor  encouragement this  wishes  wife  from  the U n i v e r s i t y Computing  Center.  the  i s  facilities  so  well.  National  gratefully  were  provided  1  I . The  purpose  of  reducing  in  a uniform  since  a of  steady  force  time The  and  this  largely  distribution  loading.  value  shed  from  mainly  a function  both  body.  importance  strength  of  a  to  force  boundary  i n the layer  whereas  the front  these  This  force  has  to  there  are usually  creates  be  are small  cylinder.  cylinder, a  the  unsteady  compared t o  here.  local  the  shedding time  a  pressure force  on  shedding.  the f l u i d  of t h e shape of  Each  time-varying  of vortex  a  designed to  i s due t o a l t e r n a t e  of the  i s rigid,  o f t h e body i s  difference  and a r e not considered  the  bluff  i s a steady due  i s altered, creating  the cylinder  a  i s of great  Although  side  t o reduce  on t h e b a c k o f t h e body,  c y l i n d e r , a t the frequency If  cylinder  i t s cost.  structure  fluctuating side  i s  on a  region,  pressure.  the  on  the required  the drag  flow  from each  forces  and t h e r e f o r e  to the drag,  averaged  vortices  vortex  the  force  reducing  of low pressure  components  the  dynamic  body,  to a higher  withstand  force  been d e v e l o p e d  side  The s e p a r a t e d  a region  subjected  of  fluid  bluff  separation.  the  shedding  i t s weight  direction  side  method  Forces  have  i t means p o s s i b l y  For  is  Fluid  methods  these  structure,  i s t o i n v e s t i g a t e a new  and unsteady  Of R e d u c i n g  and vortex  Reducing  work  flow.  Different drag  of t h i s  mean d r a g  1.1 M e t h o d s  INTRODUCTION  dynamic  body.  forces are  But  i f the  2  cylinder the  deflects,  fluid  structural case the  forces  damping  cases,  The  important  dynamic  turn  can  parameters  natural  cause in this  frequency  and  of t h e  and  are  due t o v o r t e x  as  associated  material  shedding  than  with  this  fatigue  and  frequency  with  the  structure.  b a s i c a l l y two methods  and v i b r a t i o n s  on a  t h e shape of  change  force  i n the design of a structure  vortex  - Altering  amplitude  in  fluctuating  such  of  are  forces  (1)  the  problems  force  frequency  There  the  important  synchronisation natural  -  Important  fluctuating  of reducing the f l u i d  cylinder: the  the frequency  body  to  reduce  of the force  the  applied  to  body. (2) - A l t e r i n g  structure of  which  with  of the s t r u c t u r e .  i s more  drag.  of the displacement  result  vibrations.  many  shedding  the  may  a r e t h e shape o f t h e body,  In  the  an i n t e r a c t i o n  to  the natural  reduce  frequency  the amplitude  o r damping  and change  of  the  the frequency  oscillation. A good  review  of a v a i l a b l e  methods  w a s made b y E v e r y e t  al. (1). The fairings, others. shape  first  class  splitter  of methods plates,  These methods  of the structure  separation vortices  points, and prevent  flags,  a r e based i n order  prevent the  includes  or  on  helical  perforated an  reduce  correlation  shrouds  alteration  t o change  and  of  the boundary the  of  strakes,  the layer  formation  vortex  of  shedding  3  along  the l e n g t h of the s t r u c t u r e . Some  increase  of  these  drag  expensive plates);  (helical  are  omnidirectional The  change  the natural  It  Body i s  uniform  stream  (2)  preceded  lower  than  in  the  drag  Morel  optimum  can lead,  of  but  efficient  (fairings),  methods  different  includes  are  (splitter others  the  materials  and damping  two b l u f f  in  are  use  of  order  to  of the structure.  that  flow  showed  in a  total  drag  alone.  two d i s k s &  They  Morel  of  both  &  unequal  Koenig  faced c i r c u l a r  disk.  from  in line  a  Roshko  a flat  circular  to body  over  and  over  reduction  & Bohn  cases,  of either  tandem  flow  bodies placed  i n some  (3)  cylinder found  a  the value of the reference  a drag  idea i s used  in this  could  be u s e d  on t w o - d i m e n s i o n a l  and  vortex  shedding  experiments,  side  the flow over  cylinder  investigated. plate  very  both  reduction of  81%  in  the  case.  This  circular  reduce  but  strakes).  the  by a c o n c e n t r i c  remarkable  shedding  Interaction  placed  investigated  not  frequency  investigated  diameter  body.  and  known t h a t  significantly Bohn  class  vortex  some  unidirectional  stiffeners  1.2 B l u f f  or  (helical  second  reduce  strakes);  (fairings) some  dampers,  devices  work  to design a device  structures  force.  typical  to  Through  bluff  bodies  reduce wind  and a c i r c u l a r  typical  bluff  cylinder.  bodies  drag tunnel  with a small  p l a c e d u p s t e a m on t h e s t a g n a t i o n  Two  that  line  are studied:  a  i s flat  4  Igarashi  (4)  characteristics ratio The  dl/d2  = 0.68, of  Zdravkovich  transfer  around  diameters  in  a l l  two  (5) i n v e s t i g a t e d t h e  circular  tandem.  varying  The  with  shown.  c y l i n d e r s o f t h e same  at the f l u i d  smaller  interaction  size  cylinders  as a t u r b u l e n c e  previous  dimensional identified has  bluff  works  bodies,  at different  y e t been done  overall  drag  cylinder, small  placed  flow of  cylinder  and  in heat  different was  placed  generator.  the  following  from  now  from  0.17  D t o 0.50  main  body. vortex  be  kept  of  force  Since  D,  flow  two-  patterns  were  shedding  spacing side  no  work  for least  force.  This  work. experiments,  where  the  the front  main  reduction  t o make i t c o s t  reduction.  of  However,  t h e optimum  D  body.  front  rod,  is  I t s diameter  i s the f r o n t a l  the f r o n t rod i s used  shedding  small  the  interaction  ratios.  vortex  on c a l l e d  to  the  different  to identify  or f o r least  compared  on  spacing  the o b j e c t i v e of t h i s In  or  patterns  downstream.  Objective In  is  flow  the  cylinders with  c y l i n d e r being  et al.(6) looked  upstream and used  investigated  two c i r c u l a r  n u m b e r was  two c i r c u l a r Hiwada  1.3  different  & Pridden  tandem.  over  the smaller  and Reynolds  between  already  of the flow  existence  spacing  has  circular relatively i s varied  width  as a method  on a b l u f f competitive  body, with  of  f o r drag  i t ssize other  the  must  methods  5  Experiments as  the main  The  body  results  Reynolds  the  system  time  the fluctuating  in  i s  is  using  out varying  expected  side to  a flat  circular  should  be  be  Re.  are defined a circular t h e same  an  independent side  The  of  force  L, t h e r o d flat  plate  in Fig.1(a).  c y l i n d e r as the main  parameters,  i s measured important  system  plate  cylinder.  significant  number  force  cylinder coordinate  Fig.1(b).  no  a  using  varied are the spacing  Reynolds  experiments  are carried  circular  there  plate  and symbols  body  number  flat  parameters  d and the  coordinate The  for  The  out, f i r s t l y  and secondly u s i n g  number a n d  present. diameter  are carried  but  this  and the Reynolds parameter.  and symbols  are  The  defined  6  II. 2.1  Smoke A  It  DESCRIPTION  an  a  test  cross  dimensional the  was  open  section was  used  circuit  section.  model  EXPERIMENTS  wind  I t s test of  29  placed  f o r flow  tunnel,  section  mm  by  150 mm  visualisation. with  i s 558  330  mm.  downstream  a  two-  mm  long  The  two-  of t h e end  of  s e r i e s of  29  contraction. S m o k e was  horizontal the  (Fig.2)  Elektron  dimensional with  A P P A R A T U S AND  Tunnel  smoke t u n n e l  is  OF  flow  burning  nozzles. pattern  pipe  The section  i n j e c t e d ahead of t h e model smoke,  visible.  tobacco and  maximum was  The  following the a i r flow,  The  smoke  was  i t s flowrate could  Reynolds  5X10 .  number  based  P i c t u r e s of d i f f e r e n t  3  by a  generated  be  on  made by  adjusted.  the model  cross  arrangements  were  taken. 2.2  Wind  Tunnel  The  quantitative  experiments  U.B.C.  low speed,  tunnel  i n which  the v e l o c i t y  with  inherent  undisturbed  an  0.1%.  The  section  i s less  Three settling improving The  test  low t u r b u l e n c e ,  spatial than  conducted return  varied  turbulence  from  level  type  wind  0 t o 46  of  o f mean v e l o c i t y  i n the  m/s  less  than  i n the  test  0.25%.  and a  the flow  7:1  i t s uniformity section  closed  c a n be  variation  s c r e e n s smooth  chamber  were  i s 2.74  m  at the  entrance  contraction accelerates as  i t reaches  long  with  a  the test  of the  the flow,  section.  cross-section  of  7  914  mm  by  the  u p s t r e a m t o 121 mm  effect  6 8 6 mm.  Four f i l l e t s at  of boundary l a y e r  The driving  tunnel  the  decreasing  downstream  end  growth i n the test  i s powered  a commercial a x i a l  by a  flow  f r o m 152 mm a t the  section.  15 HP d i r e c t fan  offset  with  current  Thyristor  motor speed  control. The  pressure  measured mm  of  differential  on a B e t z m i c r o m a n o m e t e r water.  The  the  outline  of the tunnel.  2.3 W i n d  Tunnel  Force  only  above  test  against  strain  the contraction i s  w h i c h c a n be r e a d  section  pressure  velocity  difference.  to  0.02  i s calibrated  Fig.3  shows  an  Balance  measurements  gauge  balance.  t h e mean d r a g  response  on m o d e l s were  taken  For the purpose of  was r e a d  of the balance  the measurement 2.4  across  on a n  this  from the balance.  experiment, The  i s much t o o l o w t o a l l o w  of f l u c t u a t i n g  side  Aerolab  frequency i t s use i n  force.  Models Each model  bluff  body  models  used  frontal front  and  width  dimensionalised  was f i x e d  main  o f two p a r t s :  the upstream r o d .  (a f l a t  r o d were  The  consisted  of  and a c i r c u l a r  38.1  mm.  d/D  was f i x e d  t o a support  cylinder)  Three d i f f e r e n t  u s e d : 6 . 3 5 , 12.7 a n d  body  The two m a i n  plate  rod sizes  t h e downstream  19.1  mm,  main  bluff  body  had  same  diameters of giving  non-  o f 0 . 1 7 , 0.33 a n d 0 . 5 0 . to a stand  w h i c h was m o v a b l e  while on  the front rod the  stand  so  8  that  the  axis  direction  of  the  all  the  way  The  two  parts  the  mm  just  wind  were c o n n e c t e d was  The  and  together  the  would  stay  in  models v e r t i c a l l y  tunnel  p l a t e s were mounted  from  the  wind  outside  the  Stansby  (7)  this  total  extended  on  the  force  aspect  on  outside.  balance on  the  spanned  the  so  that  two  parts  roof  each model at  a distance  and  that  floor,  w a l l boundary  showed  circular  change  end  tunnel  tunnel  base pressure  when t h e  of  cylinders  stream.  the  measured  dimensional true  two  4)...  End 38  the  free  across  drag  (Fig.  of  that  the  over  ratio  the  was  effects  end  entire length  as  high  i n base pressure  as  they  were  layers. end  c y l i n d e r without  so  of  20,  could  be  work  on  on  a  two-  plates altered of  the  I t was  the  model,  even  shown  that  r e c t i f i e d by  the  use  plates.  Lee  (8),  concluded  doing  that  sharp corners,  in the  related the  case  of  square  sections,  two-dimensional  u t i l i s a t i o n of  end  models  p l a t e s was  with  of  little  sharp  corner  use. In  this  work, both c i r c u l a r  models were used. for  the  circular  consistency  on  balance  around roof  and  was  the  end  a  second  used  reason  from  where this  end  seem  the  end  drag,  a  through  a i r could  be  be  compulsory  were  flat  for using  i t passes gap,  to  plates  i n c l u d i n g the  t o measure  model  floor;  plates  cylinder,  a l l models  T h e r e was a  Since  c y l i n d e r and  used  for  plate. plates; gap the  because  was wind  sucked  left tunnel  i n or  out  9  due on  to the pressure  difference  and t h e pressure  t h e m o d e l c o u l d be a f f e c t e d .  minimize  this  The  distribution  End p l a t e s were assumed  to  effect.  end  plates  were  designed  recommendations  (Fig.5).  The f r o n t  various  to  different  sizes  suit  according  to  Stansby's  r o d end p l a t e s rod  were  spacings  of  and avoid  interference. 2.5  Pressure All  Distribution  m o d e l s were  span p o s i t i o n . distributed the  back.  across  fitted  The p r e s s u r e width  of  at the the  experimentally.  pressure  taps  near  constant span  on  were  the  12.7  plate, For  where  the  For the other  pressure location  distribution of pressure  Pressure differential pressure Betz The  two r o d s , was  taps  measurements pressure  transducer  taps  assumed  constant t h a t was  circular  cylinder,  20° i n t e r v a l s  a l l around,  i s  essentially  t a p was l o c a t e d a t m i d r o d , and pressure  made  by  measured.  rotating  the  diameter, the  Fig.6  shows t h e  on t h e m o d e l s . were  made  transducer  was c a l i b r a t e d  manometer and t h e c a l i b r a t i o n pressure  were  t a p was l o c a t e d a t  6.35 a n d 19.1 mm not  taps  assumption  front  were  a t t h e i r mid-  pressure  pressure  diameter  measurements a t v a r i o u s a n g l e s rod.  an  One p r e s s u r e  mm  taps  was  the  at  base  seven  back  located  (seeFig.29). the  plate,  a n d one p r e s s u r e  verified  except  with pressure  For the f l a t  on t h e f r o n t  the  Measurements  were c o n n e c t e d  in  using a  a  Setra  scanivalve.  against the  wind  was f r e q u e n t l y  237 The  tunnel checked.  t o the scanivalve through  1  10  m of tygon  tubing with  reference  pressure  internal  was  the  diameter static  of  1.68  mm.  pressure  The  i n the  test  section.  2.6  Mean D r a g The  rod  overall  frontal  was  area  o f t h e two p a r t s o f t h e  calculated  The  test  section  An  error  introduced plates.  due This  the t o t a l  between the  force  frontal  in to  error on  balance measured  distribution  area  (force  i n drag the  was  model.  reading by on  (total  which  later  balance  a calibration  coefficients  =  1.048  force,  the  pressure  height  coefficient on  t o be  force  on  the of the  was  were c o r r e c t e d  CD(balance)  the  end  proportional  different  1.048  was  was  made  the model)  of  section  of  D of the model.  calibration  curve, using  constant of  drag  the  friction  assumed  the mid-span  from  as  drag  A  A  the dynamic  taken  integration  shows t h e c a l i b r a t i o n  CD(true)  and  and  front  the balance.  the dimension  effects  model,  measured  measured  Fig.7  drag  was  by  by  the  cylinder  the  end  measured from  multiplied  drag  the  was  of the main  the flow.  the  to  drag  and main c y l i n d e r ,  coefficient  of  Measurements  and  pressure model). models,  deduced; a l l in this  way:  11  2.7  Fluctuating Side  A different  eight  cylinder  the  a  taps  way  that  pressure  tap  location  shown  averaging for  of  the  pneumatic  to  symmetrical  special  possible  internal  which  was  eight  The  expected  pressure  was  averaging  as  The  works w e l l  least  at  tubing  connections  low  and  the  frequencies used).  Fig.8  about shows  A. using  the  a  minimum  single of  by  connected  have  the  showed  frequency  (below  was  calculations  were  to  m a n i f o l d had  good  the  described  Stathopoulos  a  was  s i d e of  made  t o g i v e a measurement  has  taps  pressure  tubes  manifold designed  input pressures.  system  of  circular  i n Appendix  eight pressure  volume.  the  one  average  Details  (9).  the  l o c a t e d on  their  are  on  pressure  side force.  Stathopoulos  of  of  the  technique  tube  were  taken  to  The  a  Measurements  arrangement  pressure  i n such  proportional of  Force  f o r c e measurements were o n l y  cylinder. used;  Side  output average  that  this  response,  60  Hz  a  sketch  at  depending  on  of  the  and  the  mani f o l d . Because transducer of  the  system  cavity  pressure was  pressure  fluctuations,  created The  to a  to the  system,  the  introduce frequency  A  apparatus  was  diaphragm. connected  tubing  calibrated.  calibration  fitted  the  is in  diaphragm  frequency cylinder  shown the  distortion  force  measuring  representation Fig.9.  cylinder  was  so  side  in  by  activated  generator.  head  dependent  the  schematic  manifold  Nine  t h a t one  A  fluctuating a  pressure  c o u l d be  the  fluctuating  a by  of  vibrator taps  used  were as  a  12  reference  while  the  other  eight  were  connected  to  the  manifold. The  reference  pressure  through  a  short  length  pressure  of  the  the  system  s c a n i v a l v e on  (RMS/RMS f ) 8 Hz  function,  manifold other  in  value  was  In  left taken  case  value  reference  as if  of  was  half  of  There  source The  correct  averaging  high  as  i s around  the  of  solid  frequencies  the  transfer  240  the  the  pressure.  The  fluctuation  distortion left  due  to  open,  amplitude  even method  Hz.  resonant  The peak  at  only (~60  of  the  frequency  for  example,  read  high  works  two  head,  i s good agreement  the  a  by  ratios  s i x , f o u r and  ambient  inputs  shows t h a t  be  for  cylinder  average  no  four  tap.  to  the  which  results  output  amplitude  called  the  open  configurations  the  The  a l s o measured  frequency  to  different  as  was  where e i g h t ,  four  frequencies  scanivalve  mm).  The  result,  shown  inputs,  the  the  (50  calibrated  The  by  Fig.10.  being  reference  cylinder  Hz.  are  manifold  existed.  t o be  tubing  second channel.  240  cases  inputs  eight  of  i n p u t s were c o n n e c t e d  reference  the  and  i s shown  Four  measured  were p l o t t e d a g a i n s t  r e  between  a  was  at  the  between  the  frequencies,  well  even  at  inconsistency in Hz)  and  could  error. curve  fluctuating  in side  Fig.10 force  i s used readings  i n Chapter for  IV  to  frequency  distort ion. A the  Spectrascope  experiment  II  to measure  frequency the  analyser  frequency  was  spectrum  used and  during as  a  13  result 2.8  the  Data  dominant  transducer  The  from  signals  seconds. of  both  were t h e n  rate  was  From t h e s e the  The  the  were d i g i t i z e d by  sampling  value  of  vortex  shedding.  Acquisition  Signals  Digital  frequency  coefficient  form  as  Cp  =  (p -  CD  =  (Drag)/(0.5pU  processed  by  Hz  were  the  and  pressure  Acquisition  a PDP-11/34  4000 r e a d i n g s , t h e  would  and  a NEFF Data  s e t t o 400  fluctuation  program  balance  sampling average  System.  computer.  time and  was  10  the  RMS  values  into  calculated.  also  transform  these  follows:  p,)/(0.5pU, ) 2  2 1  DH)  i s given  by  the pressure  i s given  by  the  Betz  Drag  i s given  by  the  balance  DH  i s given  by  38.1  p  - Pi  0.5pU,  2  mm  transducer  manometer  x 6 8 5 . 8 mm  (model  frontal  width  by  tunnel height)  wind  multiplied  14  III. Tests of  front  R E S U L T S AND  were  conducted  r o d , d/D  numbers  (2.5x10",  number  dependence  were  conducted  Pressure In  to  was  tunnel, by  of  i n Fig.11.  Cp  using  a n d CD, Maskell's  This  the  balance CD  in  CD  reading =  1.90.  Johansen's base  source  CD  results  thickness  perpendicular  Plate  on  1.95  and  width  plate  tunnel  blockage  compared  with  for  blockage,  Numerical a  Fage  &  The  to width  of  and  calibrated  between  due  &  drag  Johansen's  model  ratio  Fage  of  the  results,  i s probably  4.1%.  integration  value  with  i s  values  is  discrepancy  ratio.  had a t h i c k n e s s  flat  being  the current This  pressure  the blockage  and w i t h a  the  f o r wind  compared  is  the  as w e l l as a l l l a t e r  gives  =  until  symmetrical.  distribution  value. to  aligned  3  corrected  as  tests  5x10 .  (12).  1.94  Reynolds  visualisation  model  There  pressure  experiment  =  No  for  was  (10) w i t h  Reynolds  tunnel  distribution  (11),  o n D.  t h e model  results,  at three  sizes  Similar  t h e p l a t e was  rotating  two  as expected.  Flat  distribution  pressure  based  been c o r r e c t e d  method  wake  coefficient  of  have  results  Parkinson's of  These  pressure  Johansen's  On  of  on t h e f r o n t f a c e  T h e mean p r e s s u r e shown  number  Distribution  a i r stream  distribution  smoke  PLATE  plate with  = 0.33,  5x10")  found,  the  I ; FLAT  the f l a t  a n d d/D  4x10" and  in  the wind  the  on  = 0.17  purposes at a Reynolds  3.1  DISCUSSION  mainly  value Fage in  & the  to a difference used 1/12  in while  this Fage  15  &  Johansen's  Data  (13)  ratio  3.2  1/12  i s about  Pressure The front  L/D  =  is  distribution b e t w e e n L/D Two  L/D  =  to  was the  used.  Flat  a  was  Plate  for  <» > l / D  >  other.  >  be  No  L/D  plate  rod  when  = 7.17  and  pressure  was  located  0.84. are  to  width  Rod  shows t h e  the  regimes  > L/D  flat  l o c a t e d between  =  to  Front  the  Fig.13  Science  here.  With  on  flow  1.97 found  L/D  thickness  observed  same m o d e l , w h e n and  results  Pressure  The two  are L/D  On  Engineering  observed.  1.97  0.84.  and  The  bistable,  experiments  The  first,  the  second,  at  spacing  flow  switching  from  one  w e r e d o n e w i t h L/D  less  0.84.  regime A and  at  1.81  for  Similar was  the  same a s  in Fig.12.  i s observed  1.97  than  =  B,  regime  on  of  distribution  = 0.33  different  r e g i m e A,  the  shown  edges.  effect  pressure  r o d d/D  1.97  sharp  Distribution  mean  the  had  shows t h a t t h e  of  regime  model  =  different  3.42  pressure  spacings  in Fig.16.  distribution  strong  interaction  case.  has  The  ( f l o w r e g i m e A)  flow.  At  are  f o r regime  distribution  uniform  pressure  distributions  in Fig.15  pressure  shown  w e r e o b t a i n e d when t h e  of  have a c o n s t a n t  on  the  i s very  the and  front  been measured  around  a =  in  =  0.17  Fig.14  for  B.  pressure  s p a c i n g L/D  shown  r o d d/D  two higher  and  to a  circular (flow  bodies value  =  the  distribution  similar  1.42  r o d d/D  0.33  results  at  spacing  subcritical  cylinder  in  a  regime  B)  the  makes t h e  rod  base  than  previous  the  16  3.3  Flow  Regime  The are  characteristics  that  with  A  the pressure  decreasing  decreasing  can  be  explained  that  reaches  velocity  stream mean  plane  velocity increasing width,  1 , 0  deficit l ocx  1 / 2  0  If  the  can  plate  the base  pressure  position. decreasing  spacing  with  mean  the  a circular  typical  cylinder.  cylinder in a  by  Townsend  wake  uniform  (14).  The  i s c h a r a c t e r i s e d by  U ,  decreasing  0  distance. that  i n the streamwise  a  with  a n d by a c h a r a c t e r i s t i c  a r g u m e n t s showed  does not have a s t r o n g  the stagnation  be  considered  centre  o f t h e wake.  to  be  the  wake c a n be  constant  the centre  decreases  flow  downstream  i s measured  14)  i t i s not a uniform  center,  distance  &  For a U o: x "  wake small  V 2  0  and  direction  from  interaction  with  origin.  the  at  the  the  (Figs.12  plate  that  a circular  in  similarity  when x  flow  studied  increasing with  r o d wake,  plate  at  downstream  wake, ,  profile  an a p p r o p r i a t e  the  wake b e h i n d  the  with  that  o f a wake b e h i n d  deficit  regime  of the rod  by t h e f a c t  has been c a r e f u l l y velocity  and  front pressure  the p l a t e , but a  profile  The  spacing  independent  The  flow  on t h e f r o n t o f  rod  remains constant,  of t h i s  across found  pressure  as a measure  The  static  the flow  from  of the p l a t e ,  at the centre of the t o t a l  pressure  c a n be  and t h e v e l o c i t y  the measured p(centre):  stagnation  of  the  head a t assumed  deficit  of  pressure  17  Cp(centre)  U  The  = u,  0  of  rod  (p(centre) -  =  (0.5pU(centre) )/(0.5pU, )  =  (U(centre)/U,)  of (1  =  0  I , and  shows  (1  This  2  deficit  should  on  are  be  the  centre  proportional to  to  L/d, the  i s a l s o shown and  1 / 2  the  line,  t a b u l a t e d f o r both  versus  respect  result  s h o w e d t h a t on  2  - VCp(centre))U,  Uo/U,  with  (L/d)'  well.  2  - \/Cp(centre))U,,  dimensonalised U /Ui  =  velocity  i n Table  Fig.17  p,)/(0.5pU, )  2  - U(centre)  values  calculated  =  x~  1 / 2  sizes  .  distance  rod  size.  f o l l o w s the  non-  The  data  as  curve points  i s i n good agreement w i t h Townsend  centre  line  of  a wake b e h i n d  a  who  circular  cylinder:  (Uo/U,)(L/d) This  last  figure  front  stagnation  to  velocity  the  The  second  supports  pressure  deficit  of  of  independent  of  coefficient  versus  regime  the  B,  rod p o s i t i o n .  some s c a t t e r  spacing  but  the  the  coefficient  characteristic  characteristic  is  well  = 1  1 / 2  wake of of is a  the  i s less  due  the  than  which  base p r e s s u r e shows t h e  two  base p r e s s u r e  one  rod.  r e g i m e A,  Fig.18  f o r the  explanation that  sizes  of  is also  a  essentially  base  pressure  rod.  coefficient  is  There fairly  18  constant  around  to  important  be  an  probably  because  possibility The  of  the  Turbulence  factor governing  of  the  fixed  velocity either.  f r o n t rod  I f the  i s consistent with then  1 ,  would  i n the  evaluated.  1  From are  the  always  =  0.4(Ld)  last  shown  exist  Townsend  0  showed  equation,  i n Table  smaller  1 /D  than  the  a  at  the  edge  of  the  that  the  3.4  Flow  Regime  This  flow  i n f l u e n c e on  flow  over  This  spacing,  Flow  seem t o a f f e c t  the  in  the  wake  Townsend's r e s u l t s  of  the  wake  as  i t  width,  plate,  width  of  to half  can  be  1 /D  depth)  were  0  calculated  smaller  than  p l a t e h a l f - w i d t h , except  plate  a  is  flat each  change that  we  visualisation  pattern  no  characteristic  weak e f f e c t .  regime  strong  typical  and  Therefore,  i s expected is also  to  0.5  or  when  the  and 1  0  the  velocity  keep a  constant  constant.  B  flow  field.  seem  value,  points  profile  absence  base p r e s s u r e  typical  flow  base p r e s s u r e  not  i s always  0  has  the  values  I.  i s f a r and  so  does not  that:  (half  1 / 2  rod  value  does  velocity  from F i g . 1 7 ,  which  the  flow  separation  profile  s e e m s t o be 0  i n the  reattachment.  wake  base p r e s s u r e of  -1.24.  completely  plate alone. other,  different The  substantially  in  flow  will  call  pattern the  =  1.36  bodies  the  have  affecting  begins  critical  p i c t u r e s (Fig.19)  o c c u r r i n g b e t w e e n L/D  two  from  at  the one  spacing.  show a c h a n g e and  a  L/D  =  in  0.79.  19 The  pattern  circular plate  f o r L/D  the  rod  of  lower  wind  helpful  of  regime at  the  symmetrical plate.  B  rod  shear  layers  recirculation  from  than  Cp  occurs.  plate  The  two  plate  very  strong blockage  and  the  two-dimensional  the  plate.  smoke t u n n e l , t h e critical  the  (Figs.13 &  represent  1  the  in  the  visualisation  spacing  Nevertheless,  the  the  reach  centre,  of  and  f l o w p a t t e r n i s shown  the  than  15),  the  in  flow v i s u a l i s a t i o n s  are  regimes.  i n s t e a d of  pressure  rod  because  the  one  of  stagnation  distributions  reattachment  onto  results  shown  different  that  n e a r - s t a g n a t i o n p o i n t s c l o s e to the  They  =  the  a  rod  of  tunnel.  wake b e h i n d  the  the  value  typical  between  different  layers  the  a  A c l o s e d r e g i o n between  in understanding  In point  A  edges of  section  the  region  = 0.79.  shear  Because  show a  1.36.  shows  i s formed where  to the  test  =  i n the  f o r L/D  separated close  Fig.19(a)  cylinder  Fig.19(b) and  in  the  plate.  losses  in  of  show  two  edges of  the  the  separated  Their value the  shear  is  less  layers  and  unsteadiness. The  exact  stagnation located tap.  m u s t be plate the  points  between  But  location  from  could  the the  pressure  not  edge of pressure  be  the  first  pressure pressure  by  plate  and  distributions  the  base  of  measured  a p o i n t o f maximum p r e s s u r e (pressure given  The  and  these  because the  first  i n regime  between pressure  the  near-  they  were  pressure B,  there  edge of  measurement)  the and  tap. distribution  on  the  central  p o r t i o n of  the  20  plate, d/D  s a y 0.3  = 0.33  < x/D  at spacing  approximately  Cp  base p r e s s u r e the  idea  the  plate,  pressure  i s an The  front As  fairly 3.5  fact  constant  i s  i s t h e same a s t h e f r o n t  rod  (Fig.16).  This  i s formed between  supports  t h e r o d and  i s small  and  where  the  distribution  with  spacing for  with  decreasing  constant.  pressure  that  pressure  the closed region  suggests  that  at smaller  gets  smaller  less  dissipation  spacing  and hence an  with  due  to  increase  pressure. already  constant  pointed  out,  the  plate  whatever the p o s i t i o n  t h e two  a n d 21 rods,  graph balance  show d r a g  d/D  shows  = 0.33  base  pressure  i s  of the rod (Fig.18).  by  distribution.  The  minimum  spacing.  drag  alone;  drag  this  at is  L/D a  =  d/D drag  t h e two  drag  spacing  the of  measured plate  the  of the rod i s  by  only,  pressure given  by  curves.  coefficient = 0.33  1.81,  of  rod  respectively.  coefficient  integration  coefficient  versus  = 0.17  coefficient  F o r t h e r o d d/D  occurring  and  numerical  d i f f e r e n c e between A  coefficient  the o v e r a l l  and t h e drag  calculated  the  region  this  For the rod  Drag  Each the  and  constant.  value  increasing front  occurs  Fig.20 for  in  spacing  turbulence  1.42,  t h e mean v e l o c i t y  change  smaller  =  = -0.10  i s essentially  B,  is fairly  a t t h e same s p a c i n g  where  spacing.  in  L/D  that a closed  The regime  < 0.7,  i s reached the  as compared  reduction  of  at the  minimum t o 1.94 36%.  CD  critical is  1.25  f o r the plate For  the  rod  21 d/D  =0.17  the  critical The  line  a  maximum  s p a c i n g , L/D  change  because  the drag  pattern  point  t h e f l o w was  each rod  from  found  regime  At  this  s m a l l e r than  constant the drag  value  in  o f t h e same  drag  coefficient  decreases  with  decreasing spacing i n  B. Of  Since  Yaw the  unidirectional  Fig.22  L/D = 1.42 divided  the  at  drag rod  (regime  by C D  r e  ^  zero  B).  which yaw.  d/D  the flow,  = 0.33 The  The d r a g  The e f f e c t  and  the  should  i f a large drag  investigated  the  structure  i s may  i t i s of interest  to  on t h e d r a g . versus  was  measured  i s the drag  17% a t 12°.  possible  cases,  coefficient  only  device  device  o f s m a l l yaw a n g l e  overall  when  reduction  aligned with  the effect The  drag  and, i n p r a c t i c a l  be p e r f e c t l y  alone  when t h e  bistable.  i n regime A and i n c r e a s e s w i t h d e c r e a s i n g  3.6 E f f e c t  study  dotted  flow.  overall  spacing  a  d r a s t i c a l l y drops  of t h e r o d keeps a f a i r l y  i n a uniform  by  r e g i m e A t o r e g i m e B.  t o be  regime and i s always  The  not  = 1.64.  coefficient  switches  drag  r e d u c t i o n of 24% i s a c h i e v e d a t  i n flow pattern i s represented  flow  The  drag  yaw  located drag  coefficient  i s shown i n at  spacing  coefficient i s of the  plate  r e d u c t i o n i s 3 4 % a t 0° a n d i s  o f yaw  i s  therefore  important  be a l i g n e d w i t h t h e f l o w a s much a s r e d u c t i o n i s t o be  achieved.  22  3.7 E f f e c t As on  Of R e y n o l d s  expected,  pressure  fixed  coefficient  results  2.5x10", accuracy  Flow  points are  and  In circle  B.  I t represents The b l o c k a g e  importance,  this  numbers,  Consider  developed  the flow  over  as  flow a  effect  point  model  numerical  the f l a t  plate  due t o t h e r o d was a s s u m e d  model,  the normal  and c r e a t e  a wake  flat  i s mapped  in  t o be o f  of the r o d being  flow  wake  behind  source  pair  of  the  model  The  plate  i s  (12).  The  the flat  to f i x  independant  plate  model  a  representation obtained  using  separated  flow  i s represented  f o r a normal  The c o m p l e x p o t e n t i a l  i n t h e $-plane i s :  F(0 = V(?+| ). Q{1n(^Re )+ln(^-Re-' )-lnU i6  +  from  by  vortices.  t h e wake s o u r c e  shown i n F i g . 2 3 .  plate  transformation.  by t h e r o d u p s t r e a m  symmetrical  potential  size.  by t h e J o u k o w s k i  Parkinson's  was  t h e main  stagnation  the separated  created  Reynolds  Model  here  r o d shape o r  flow  effect  a n d 5 x 1 0 " , w e r e e x a c t l y t h e same w i t h i n t h e  presented  upstream  as  differents  incompressible  little  a  the separation  A two-dimensional  regime  of  because  much  of measurements.  experiment.  of  number d i d n o t h a v e  at the three  4x10"  3.8 P o t e n t i a l  the  Reynolds  a t t h e edges of t h e p l a t e . The  is  Number  ,6  flat  plate  of the r e s u l t i n g  23  and  the  complex  velocity i s :  •«> • ^ • s t b ^  -&  +  The at  Joukowski  infinity,  z  The  transforms  $-R /S  conditions  stagnation the  and  flow  w($)  (2)  the  w(z)  leaves  =0  From  these  the  to (at  have  to  $  0  plate:  points  the  are  doubled  there  angles  tangentially:  ±iR  is specified.  At  the  critical  points,  : at  V 2  a  and  symmetrical  and  add  Q  $ ) 0  z  images  pair  inside  (D.  the  pair  The  complex  of  =  ±h/2  6 are  in order  strength  bubble.  flat  critical  conditions.  the  normal  the  boundary  of  a  $-plane at  circle  of  into  velocity  h/4  plate  conditions, add  =  that  J =  - Cpb)  two  circle  also  and  = U(1  Now the  so  base p r e s s u r e  w(z)  circle  i n the  at  is finite  which preserves  are:  points  transformation  the  the  where R  2  boundary  (1) of  =  transformation,  determined.  of  to  vortices  create  the  circle  The  vortices potential  of  bubble,  we  to  satisfy  the  ($ )  determine  becomes:  front  a  location  will  in  0  the  and size  24  F(?)  2  =  )+?{ln(;-Re )+ln(c-Re' )-1n?}+ l5  l6  g{ln(r;-c )+ln(c-R /^)-1n(S-" )-ln(c-R /C )} 2  2  0  and  the v e l o c i t y -<<> • v  . - 5  (  ,ir  0  potential: ^  +  ^  1  r  0  l  - D  l  +  _  l  -i  with again the Joukowski t r a n s f o r m a t i o n and the c o n d i t i o n s :  =0  (1) w(I)  at  (2) w(z) = U(1 and  extra  - Cpb)  and  was used  here.  stationary,  = ±iR  A  at z = h/2  172  conditions  s t r e n g t h of v o r t i c e s . location  5  to  condition  The  condition  means  determining  l  T^—\ e-R  K  0  —  positions  is  that  itself,  ~ ZT^  c - R /Co  From these c o n d i t i o n s , we  each  was  vortex  be  =  °  at c = 5  4  0  can  determine  a  locus  of  where Q, T and 5 can a l s o be determined.  with the f r o n t s t a g n a t i o n p o i n t  experimentally  the  i s zero:  Fig.24 shows the s t r e a m l i n e s of the flow over  pressure  both  that the v e l o c i t y at i t s l o c a t i o n  due to a l l s i n g u l a r i t i e s except  vortex  the l o c a t i o n and  the s t r e n g t h of the v o r t i c e s at the same time  which  ^  determine  specified  at as  the f l a t p l a t e  L/D = 0.87. Cpb = -1.24  i n a previous s e c t i o n .  The as  base found  25  It too  i s noticed  large  plate  and,  quite  expected.  plate  over  compare  vortex  this This  result,  much  the  poor  very  downstream very  wake  than  smooth  when  rapidly.  simulation of the streamlines flow  result  could  be  visualisation improved  position that  c o n d i t i o n s and  also  by  would  give  be  \p = 0 l e a v e s t h e  streamline  the  and  look  to  go o v e r t h e  narrower  the streamlines  plate,  seems  the streamlines  with  strength  boundary  of the bubble  creating a  i s a rather  Fig.19(b).  two  a  though the  the size  t a n g e n t i a l l y and curves This  we  as  smoothly, Even  passing  that  p i c t u r e of choosing  satisfy  a  i f  the  good  a  first  streamline  representat ion. One m i g h t present inside  model. the  use  i s fairly  If  near which  pressure  i t would  would  pressure  i s  not change  conclusion,  and, i n i t s  improve  the total t h e model  A  not p o t e n t i a l be  prescribed  the pressure  inside the  therefore  specified  i s also  present  shape.  must  from t h e  make  sense  to  pressure.  t h e edges of the p l a t e can  streamlines  this  of  the drag  i s obviously  the experiment,  constant,  value  flow  the  t h e base pressure  In drag  the  real  and  From  a constant  since  The  bubble  empirically. bubble  be i n t e r e s t e d i n e v a l u a t i n g  form, better  i n s i d e t h e bubble, and  specified, be  only  varied  drag  the  by  pressure  the  model,  significantly.  i s not useful t o predict the does  not  condition  t h e model as f a r as s t r e a m l i n e s  " b e t t e r " c o n f i g u r a t i o n would have  give  realistic  f o r T and $  0  could  are concerned.  But  t o be f o u n d  by  trial  26  and  error. This  model  representing representing  shows  the l i m i t a t i o n s  separated how  base p r e s s u r e ,  flow  much a c h a n g e  can a f f e c t  but  of p o t e n t i a l i t  may  i n parameters,  the outer  flow.  be  flow  in  useful  in  such  as  the  27  the  IV.  R E S U L T S AND  DISCUSSION  The  flat  was  plate  same f r o n t a l  measurements flat  plate,  the  important side  numbers  Reynolds  in  the  4.1  out  was  flow.  case,  was  smoke  of  case, unlike  the  to  The  an  fluctuating  also  measured. for  7.0x10".  tunnel  be  at  Reynolds Similar  a  Reynolds  3  the  range  aerodynamicists, circular  On  Circular  of  Reynolds  between  cylinder  10  Cylinder  number  and  3  10 ,  shows t h e d r a g c o e f f i c i e n t ,  taken  from  CD,  (15).  subcritical,  critical,  supercritical  In  subcritical  surface  i s due  turbulent  range,  roughness  essentially  and  constant. to the  At  the  and  flow  boundary  layer,  i s not  Re,  occur  downstream.  It results  over  a  patterns.  range  of  Re,  specified:  suddenly  separation  final a  by is  drops. and  re-energizes  the in  influenced  coefficient CD  layer  making  for  transcritical.  Turbulent mixing  decelerating  flow  are  drag  higher  flow  in this  ranges  the  l a m i n a r boundary  reattachment.  further  Four  interest  the  7  Achenbach  the  of  i s subjected to different  Fig.25  This  type's  tunnel  to  of  Background In  the  same  expected  the  1.0x10"  cylinder  5x10 .  Pressure Distribution  4.1.1  the  i n the wind  i n the  CYLINDER  a circular  In t h i s  number  range  e x p e r i m e n t s were done number o f  out.  in this  were c a r r i e d  by and  governing  significant  Experiments  mm,  carried  parameter  force,  replaced  w i d t h , 38.1  were  I I ; CIRCULAR  the the  separation  narrower  wake  28  (low  pressure  coefficient. the  drag  range  region) Exceeding  the  coefficient  and  reaches  transcritical Near known t h a t  a  nearly  flow pattern i s  level the  of  Re,  t u r b u l e n c e was  the  left  that  mainly  the  in  CD  i n the  drag  minimum,  supercritical  value  which  CD  drops  strongly  in  the  approaching Achenbach to s h i f t  sharply, i t i s  dependent stream  showed  the  CD  at a  on  and  that  curve  f l o w becomes c r i t i c a l  the  on  the  the  effect  versus  Re  to  lower  Re.  Results Measured pressure  cylinder  alone  range are  represents  the  cylinder  i n the  Science  Data  solid  for  blockage  and  distributions  solid The  3.3x10" found  shown  Fig.26.  The  range, data  because  second,  the  in  distribution  The  as  shown  they  have not  because  they  the line  circular  Engineering  follow been  represent  numbers.  points are  in  a  in  not  circular  solid  around  p o i n t s do  Reynolds  data  exactly  corrected pressure  Despite  i n good agreement  some with  line. uncorrected  < Re  t o be later  numbers  at various  discrepancies,  the  Reynolds  subcritical  first,  around  different  pressure  (16).  line,  distributions  at  subcritical  used  fall  number o f  constant  at  the  surface.  of  the  a  range.  the  so  to  increases again  critical  roughness of  the  Reynolds  the  turbulence  4.1.2  corresponding  value  < 7.1x10", constant  as  the  as  w i t h CD  reference  of  drag  measured  by  =  This  1.19.  value.  coefficient the  balance,  value  will  for was be  29  As  mentioned  corrected  f o r blockage  this  chapter.  Apelt  (17)  circular  I t  that  correction, a  cylinder  On  the  other  suggested  changed  which curve  i s  this has  two  hand,  i s very  such  made  only  &  f o r blockage  (10), are applied t o of drag  coefficient  of blockage  effects.  f o r base  As  values  of the s e p a r a t i o n  a  result  of  drag  the  the pressure  i t s shape,  pressure value.  and pressure  Maskell's  method  i n order  values.  For  corrected  base p r e s s u r e  the  value  base  i n previous pressure t o compare  circular  distribution an  error.  coefficient in even  though  i t  here  by  works.  i s  corrected  i t with  cylinder  coefficient  points,  correction,  introduces  were n o t c o r r e c t e d f o r b l o c k a g e  of  numbers.  West  close t o the expected  by r e s i z i n g  changing  the  ESDU's  free  as the l o c a t i o n  value  with  n o t been  by  known m e t h o d s  the corrected value  b e e n a common p r a c t i c e One  recently  Maskell's  to the values  have  f o ra l l the results i n  shown  well  by t h e b l o c k a g e .  chapter  points  e x p l a n a t i o n was t h a t t h e s h a p e o f t h e p r e s s u r e  without  Therefore  data  the corrected values  M a s k e l l ' s method  distribution, is  been  one o f them b e i n g  not any c l o s e r  The  the  as i s t h e case  has  when  are  using  above,  i s  other  quoted  a t Re = 6 . 5 x 1 0 " , t h e -1.30  (16) of -1.23 f o r t h i s  range  as of  compared Reynolds  30  4.2  Pressure  Distribution  On  Circular  C y l i n d e r With  Front  Rod The  pressure  when  a r o d was  sizes  of f r o n t  d/D  = 0.50.  Reynolds  r o d were The  (b).  The  nine  will  spacings.  = 0.17,  3.3x10" and  graph  measured  d/D  A and  occurred  The  nine  t o 35.  i s presented  regimes,  and  different  6.5x10".  i n Figs.27  Three  = 0.33  were done a t t h r e e  (a) r e p r e s e n t s  B  i n two p a r t s , described  f o r the c i r c u l a r  regime A w h i l e  (b)  g r a p h s h a v e t h e same g e n e r a l  be d i s c u s s e d  rod  spacing where  i n the following  except  (a)  in  the  cylinder. represents  show  Flow  Regime  A  The  effect  of the  pressure  distribution  flat  plate.  The  front  less  than  one  and  spacings.  This  r o d wake a n d UQ/U,  i s due  some  the  low  In  Reynolds  of the pressure  rod  on  i s similar  most  number,  measurements  the  cylinder  to that described  stagnation  pressure  decreasing  with  to the v e l o c i t y  i t w o u l d be p o s s i b l e  versus  sections.  scatter.  front  is  characteristics  d i s t r i b u t i o n are progressive  for  the inaccuracy  makes t h e r e s u l t s  of  d/D  the changes i n pressure  1.0x10",  4.3  still  at various  was  B.  cases, with  each flow  chapter,  The which  1.0x10",  two  each graph,  regime  used,  experiments  clarity,  previous  upstream  graphs are presented  For  For  located  numbers,  resulting  and  d i s t r i b u t i o n on t h e c y l i n d e r  L/d as f o r t h e f l a t  plate.  f o r the  coefficient decreasing  deficit  to present  front  of the  a similar  is rod  front graph  31  Unlike  the  flat  plate,  the  pressure  i s a f f e c t e d by t h e p o s i t i o n  creates  turbulence  mentioned points  i n the stream  circular of the  reaching  i n s e c t i o n 4.1, t u r b u l e n c e  occur  further  downstream  cylinder rod.  the  the  p e r m i t t i n g a more c o m p l e t e p r e s s u r e  proximity  of the r o d  therefore  t h e base  For  at  point,  i s  Cpb = - 1 . 3 2 .  closer  to  the At  becomes almost  constant  The  from  solid  distribution taken  certain  base  at small  stagnation turbulence The  line  in  r o d d/D  the  toward  spacings point.  larger  Data  a  and  remains  to  regime.  have  been  of the s o l i d  (L/D < 2 . 4 ) , This  base  pressure numbers.  the pressure  circular  cylinder,  ( 1 6 ) . Good agreement i s curve  and the  present  except  for  the  that  the  effect  of  in  regime  A,  suggests  front  critical.  of the group of curves  Reynolds  0.17  pressure  i n flow  represents  flow around  i s t o make t h e f l o w  a larger  =  increases  base  spacing  t h e change  Fig.28(a)  Science  t h e shape  trends  stagnation  pressure  spacing,  until  the rod i s absent  the  with decreasing  for critical  between  and  by b r i n g i n g t h e r o d c l o s e r .  from E n g i n e e r i n g  found  The  level  the front  bringing  the  Cpb = -0.83  downstream  The  and  when  separation points are therefore expected  shifted  data  a  180°  By  cylinder,  (Fig.28(a)).  at  of the  recovery.  turbulence  Re = 3 . 3 x 1 0 "  the base p r e s s u r e ,  constant  As  pressure.  example,  (Fig.26),  the  rod  separation  surface  cylinder,  increases  The  the cylinder.  makes on  base  value  are,  for larger  rod  diameters  32  4.4  Flow A  Regime  B  different  flow  regime  interaction  between  the  spacings.  Again,  like  stagnation roughly flat by  p o i n t s are  constant  plate the  results  rod  earlier  base p r e s s u r e  of  regime  diameters 4.5  toward  the  total  main  closer  in  is  B  group of  are  Reynolds  similar  base p r e s s u r e  of the  influenced occurs  because  spacing.  larger  with  separation  with decreasing  a  smaller  region  difference  regime  curves  strong  symmetrical  a closed  I t seems t h a t t h e  this  larger  at  known  from of  almost  i n the  the  drag  the  balance  of  Fig.36 6.5x10" similar  very  the  of  of  flat itself  to  the  those  for larger  rod  numbers.  the  the  was  results  front f o r d/D  Reynolds balance small.  the  and  =  number, readings  0.33  was  i t  was  that  the  value  was  smaller  than  Therefore,  only  always  plotted.  overall r o d d/D  3.5)  Its  flow.  model  since  (section  important. regime  the-  cylinder,  i n a uniform  measurements were shows  p a r t s of  results  not  flow  same r o d  two  circular  plate  i n each  f o r the  third  because  the rod  drag  case  constant  the  was  as  at  two  base p r e s s u r e  and  looked  The  well  the  Drag Only  drag  plate,  i s t h a t the  gets  of  cylinder  The  decreases  A,  the  flat  formed as  because  pressure.  rod  t r e n d s of  and  the  position.  when t h e  The  rod  occurs  drag = 0.17. and  d/D  1.0x10", were v e r y  at  Re  =  Figs.37 = 0.50  i s not  3.3x10" and  38  and shows  respectively.  represented  i n a c c u r a t e as  the  here force  33  The  shape of  each p l o t  results.  In  decreasing  spacing.  curve  the  flow  at  The  Then,  drag  main  important  drag  plate. due  to  flow  enter An  when  the  extra  the  reduction  base pressure the  critical For  (Fig.37),  the  at  in  the  change  in  that in  critical  regime  B,  p l a t e and  the  already  an  c y l i n d e r when  the  flat  there  circular 7,  is  whereas  there  at  that  the  cylinder in  created  by  to  spacing  the  rod;  decreasing  i s obtained  to a change  example, the  critical  spacing  pressure.  to a  with  at  regime in  essentially  the  this  no flat  regime  A  is  makes  the  drag.  critical  B.  front  f o r the  its  the  was  spacing  This  extra  drag  pressure  only,  the  same a s  that  just  before  spacing.  (regime  is  =  on  switches  being  spacing  24%,  L/D  region,  reduction  i s due  plate  jump  closer  that  f o r the  reduction  critical  flow  flat  decreases  sudden  i s obtained  is  reduction  turbulence  the  drag  corresponding  between  results  reduction  drag  the  again.  drag  The  a  i s brought  d i s t a n t , say  significant  is  spacing  rod  to  overall  there  difference  cylinder  is quite  the  minimum d r a g  i f the  circular  rod  Then  increases  The  A,  critical  pattern.  spacing. the  regime  is similar  mainly  i n the  drag A) i t is due  case  of  reduction is  d/D just  already 58%  to  (CD a  34% =  =  0.33 before  (CD  0.50).  change  at  in  =  Re the  0.78) The  the  =  6.5x10" critical  and  at  the  difference,  cylinder front  34  4.6  Effect In  effect  Of R e y n o l d s  t h e range of of  the curve  to  This  Reynolds the  number  pressure  Re  around  the cylinder  It  reducing  corresponding parameters  giving to  the  governing  (1)  - size  (2)  - spacing  (3)  - Reynolds  Fig.39  downwards  drag  58% i s achieved  At  lower  Reynolds  Re = 3 . 3 x 1 0 "  base  in  Reynolds  turbulence  number  around  number  there i s  drag,  this  position  spacing.  The  important  L/D number  Re  A t Re  rod  must  t h e r o d d/D  be a c h i e v e d  be  reduction  small  larger  = 0.50  44%  for i s  i s  = 0.33. less  and  maximum  drag  achieved  at  but a lower  larger rod.  drag  reduction  r o d , d/D  reduction  of  w i t h an even  on t h e minimum  = 6.5x10", a drag  numbers, the drag  drag with  of rod size  with a relatively  the A  the  t h e optimum c o n f i g u r a t i o n a r e :  numbers.  of  reduction.  the  coefficient.  increase  minimum  shows t h e e f f e c t  of  (Figs.36 that  improving  the  critical  drag,  o f r o d d/D  two R e y n o l d s  size  a  main  the overall  h a s been shown t h a t a t any R e y n o l d s position  the  i s increased, bringing  range,  due t o a h i g h e r  Optimum C o n f i g u r a t i o n  probably  spacing  p o s s i b l e e x p l a n a t i o n i s an  4.7  the  lower  the cylinder  and  front rod.  for  versus  to the c r i t i c a l  the  rod  to  studied,  c a n be e x p l a i n e d b y t h e f a c t  recovery  reaching  a  numbers  was  of drag  result  flow closer  Another  Reynolds  increasing  shifting 38).  Number  drag  could  35  Fig.40  shows t h e  sizes  and  in  range  the  position in  Reynolds 1.2  of  the  r e g i m e A and  show  numbers.  < L/D  <  the  for larger  The  It  value  the  for  critical  spacing  first but  spacing  2.4.  critical  some s c a t t e r  spacing  critical  was  was  spacing  between  and  a  for  rod always  that  the  B.  i s toward  rod diameters  is  assumed  i n regime  trend  different  last  the value  The  results  larger  critical  larger  Reynolds  numbers. The drag  Reynolds  (Fig.37  to  number had  39).  the  maximum v a l u e  investigated  experiment,  6.5x10",  expected lower.  that  Reynolds  On  be  could  4.8  in  uniform  flow)  i n the  critical  range.  be  studied here.  Effect  Of  trend  of  number  the  of  were v e r y  for  No  many  ( t h e maximum  value  than  the  of  the  by  limits  of  the  Reynolds  numbers  i t  is  drag  coefficient  reference will  be  than  will  drag  lower  Therefore  change  minimum  practical  higher  fixed  the  lower  will  the  f o r the  in trend  even  coefficient  because  the  be  drag  the  flow  reduction  range of  Reynolds  is anticipated  at  however.  Yaw  effect  results  designed  hand,  consequently  Reynolds  The the  minimum  for  on  be  higher  other  numbers high  here  the  (cylinder may  number  was  For  the  strong effect  Unfortunately,  applications  instrumentation).  a  s m a l l yaw  the  drag  i n a c c u r a t e because  that purpose. drag  on  w i t h yaw  From  was  the  looked  model  the  results  s e e m s t o be  similar  at  was  gathered, to  that  but not the of  36  the  flat  plate.  4.9  F l u c t u a t i n g Side The  fluctuating  circular  cylinder  changing  with  Reynolds the  verified  value  I I .  by  i t s frequency  number.  shedding and  However  S=(fD)/U ,  i s  1  and  the  generally  result  The  results  i n the range of  Other  a l s o shown.  by  (Fig.10),  well  the  by K e e f e  turbulence  Gerrard  (20)  that  oscillating  side  force  in this  was  agrees  RMS  in  with  i s remarkably  of the  described i n two  second  seem  i s  to agree, I t has  sets by left (19)  probably  been  of Reynolds sensitive  in  distortion  (18) and G e r r a r d  levels. range  value  a r e shown  the  None o f t h e r e s u l t s  of d i f f e r e n t  This  accepted.  ( F i g 41(b))  curves  frequency,  are presented  i s c o r r e c t e d f o r frequency  function  on a  intensity  constant.  results  This  C l ' , given  p o i n t s : one  transfer  because  to vortex  f o r c e , was m e a s u r e d b y t h e m e t h o d  uncorrected. are  has  S = 0.195.  intensity  Chapter  the  number  giving  fluctuating  f o r c e due  i n v e s t i g a t e d the non-dimensional  o f S = 0.20  The  data  alone  experimentally  Fig.41(a),  of  side  Reynolds  numbers  Strouhal  the  Force  shown  numbers t h e  to  turbulence  level.  4.10  Side The  sure  Force  On  Model With  fluctuating  that  no p r o b l e m  shows t h e f l u c t u a t i n g rod  d/D  side  = 0.17  was side  Front  force  Rod  was  created  investigated  by t h e f r o n t  f o r c e on t h e  at different  spacings.  rod.  cylinder Similar  to  make Fig.42  with  the  results for  37  d/D  = 0.33  and  d/D  respectively. accurate  The  considered For =  (10  Re  the  small  The  observed,  rod  force  the side  The (Re  Regime  Front two  value same Re  of  44  not as  method  should  to  of  not  be  Regime  force varies =  6.5x10")  f o r c e near  Any In  i s difficult time  too small  Hz).  as r e s u l t s  to  This  a t t h e same  curves  there  to  characteristics  a r e two A  (Figs.42  and  to spacings  flow B  described  where  B corresponds  regimes  the side  to  spacings  0.17  and  = 3.3x10".  at  rapidly.  data  was  result  involved(~20  regimes  A corresponds  sets of  Cl'  and  a r e some common  In a l l cases,  points  of  have  the  the c r i t i c a l  always  (the reference  reduction.  the  a sampling  smaller  same  than  B,  in where  in  Fig.42  shape The  with  side  the  and 25% f o r  regime A gave a s i d e the  at the  alone);  = 6.5x10"  a  minimum  the reference  i s C l ' f o r the c y l i n d e r  spacing  regime  interest  spacing.  m a x i m u m r e d u c t i o n o f C l ' i s 6 7 % f o r Re Re  were  the  of the s i x remaining  constant.  R o d d/D  = 3.3x10"  minimum s i d e  and  diameters.  corresponding  i s almost  4.10.1  of  scatter  frequency  but there  them.  previously.  Cl'  (d/D = 0.17)  i s probably  low  behaviors  a l l of  Figs.43  values  i s t h e r e f o r e d i s c a r d e d as w e l l  f o r the other  where  of  because  these  rod  reason  44) a r e d i f f e r e n t to  values  shows c o n s i d e r a b l e  sec.) f o r the  The  in  definitive.  1.0x10"  result  shown  results  Therefore  as  interpret.  are  measured  as the other  measurement.  Re  = 0.50  force  force varied  38  rapidly, than  t h e maximum s i d e  number  shows  the  f o r t h e r o d d/D  Reynolds  4.10.2 F r o n t Fig.46 number  shows Re  each  spectral  of  high  rod  Strouhal increases  spacing  on  not  a well  was  tested  at  fluctuation  spectral  Re  to ( C l ' ) . 2  Strouhal defined  The  = 3.3x10",  showed  two  the  frequency  of Fig.46.  density  assumed  an e s t i m a t e  that  The  curve  the  being  height  of  of the c o n t r i b u t i o n  contributions  to  (Cl')  2  of in  in Fig.46.  frequencies  were  f r e q u e n c i e s of both the low f r e q u e n c y  assumed  bodies,  the  and the f r o n t  to  be t h e v o r t e x  circular  cylinder  rod producing  the  frequency. values  distortion considering  For  on  6.5x10".  i t was  p e a k was  a r e shown two  The  to  =  the 2  frequency  producing  of  t o t h e S t r o u h a l numbers  to (Cl') ,  frequency  shedding  rod spacing  t h e S t r o u h a l number  There  the  under  proportional  of  0.33  configuration  area  The  =  f o r Re  density  percentage  = 0.17;  = 3.3x10".  peaks corresponding total  effect  the effect  frequency  For  that  larger  number. R o d d/D  for  dominant  each  not s i g n i f i c a n t l y  the reference. Fig.45  with  f o r c e was  Cl'. Re  because  The  Cl'  using  the  were  result  dominant  was  for  function  i n Fig.43  frequency  (Fig.10)  of each of t h e two  i s presented i t  corrected  transfer  the c o n t r i b u t i o n  = 6.5x10" no  of  f o r Re  frequencies =  3.3x10".  not p o s s i b l e t o c o r r e c t the  frequencies  were  and  noticeable;  data these  39  results  are plotted  The  as  trends  significantly. corrected. presence  of  two  Nevertheless,  4.10.3 F r o n t Fig.47  than  R o d d/D shows  =  noticed  a g a i n , but t h i s  dominant  corrected Re  of  curve  not  being  of the d i f f e r e n c e  i s the  is  in  one  relatively  case. low,  not  0.50 of  rod  Two  time  Cl'  f o r frequency  significantly  one  differ  spacing  dominant  the intensity  was at  dominant Re  on  Strouhal  frequencies  were  due  high  to  the  as  shown  by  = 6.5x10"  there  was  the no  noticeable.  values  = 6.5x10".  flat.  the reference.  Again  frequency  The  force  rod)  values.  to  was  (Fig.43)  frequencies  = 3.3x10".  (front  response  curves  cause  the effect  at  percentage  due  side  number  frequency  be  dominant  higher  Re  two  possible  the  significantly  the  T h i s may  Another of  i f the frequency  Again,  (Fig.44)  distortion the  at  but  Re not  = 3.3x10" the  were  values  t r e n d s o f t h e two c u r v e s  f o r t h e same r e a s o n s  as mentioned  in  at  differ section  4.10.2. The 50%  maximum  more t h a n  the  higher.  A  frequency  i s also  low  synchronisation frequency  C l ' , obtained here  of the  reference Cl'  is  in  use  the shedding  structure.  the  useful  of p r a c t i c a l of  but  i n r e g i m e A, frequency practice  since  frequency  i t  but can  with the  i s about is a  also high  prevent natural  40  4.10.4 G e n e r a l The  side  Re  and  with  superposition It  Remarks force rod  a l l cases,  practical matching If  of  purposes  primarily  dominant  side  and  may  decrease  the device  undertaken present in  reduction to find  results,  regime A would  force  device,  increased  is  from  or the  suitable  the side  for  force  from  is  used  rod)  i t should  not  increase  i s properly  chosen  i t somewhat.  device,  i t seems  on t h e  force.  i n frequency  (front  i f the spacing  i s t o be u s e d  the  frequencies.  side was  the  of the s t r u c t u r e .  reduction  fluctuating  force  frequency  i t prevents  frequency  the  If  increase  i n v e s t i g a t e d here  as a drag  i n fact  frequency  An  because  the natural  varying  conclusions  r o d on t h e f l u c t u a t i n g  the  trends  at different  t o draw g e n e r a l  the shedding  the device  different  happening  of the c y l i n d e r alone.  suppression  side  show  T h e y a l s o a r e , i n some c a s e s ,  difficult  of the front  In that  size.  of r e s u l t s  i s therefore  effect  results  further  optimum that  be t h e most  p r i m a r i l y as a  fluctuating  i n v e s t i g a t i o n should  configuration.  the small efficient.  r o d d/D  be  From  the  = 0.17  used  41  V. 5.1  CONCLUSIONS  Conclusions The  objective  of  this  effect  of p l a c i n g a small  fluid  force  flat  p r o j e c t was t o i n v e s t i g a t e t h e  rod i n f r o n t of a b l u f f  reduction.  Two  p l a t e and a c i r c u l a r  bluff  cylinder.  bodies The  body  were  for  studied: a  conclusions  drawn  are: (1)  -  different always from  Experiments sizes  that  of  number  and  reduction  on at a  diameter  and  occurred  around  spacings  body  studied.  of  the  occurred  58%  smaller  spacing -  effect  A  were  spacing  a  = 0.33 a t  A  while  critical.  was  observed,  i n flow on  The minimum  Regime  regime  the  drag  always  observed  r e g i m e B was  Typical values  rod  for  observed of  the  = 2.  was o b s e r v e d  pressure  drag  cylinder  depending  f o r large rod spacings.  of the rod consisted f i r s t ,  stagnation  a  of Reynolds  r o d d/D  The s w i t c h  number.  w e r e a r o u n d L/D  Regime  reduction  at  circular  regimes  spacing,  critical  than  = 0.33  for  numbers  plate,  independent  found  flow  spacing.  than  d/D  were  spacing.  the Reynolds this  rod  with  6.5x10".  two  rod  drag  For the flat  For the  was  "critical"  larger  spacings  (3)  results  - In a l l cases,  depending  critical  for  body  Reynolds  a significant  body.  L/D = 1.73 a n d Re =  (2)  The  the  i n t h e range  spacing  for  the single  o f 3 6 % was f o u n d  L/D = 1.81  of b l u f f  of f r o n t r o d and d i f f e r e n t  s h o w e d , a t some s p a c i n g ,  reduction  drag  on t h e t w o t y p e s  by s l o w i n g  i n reducing down  the  rear  (on average) t h e  42  fluid  r e a c h i n g i t and  permitted, base rod  i n the case  pressure spacing  for  the  in this  significant  flow  mainly  - For  regime  between where  increased (5) smaller  was  -  (7) Reynolds in  base  with  In the  reduce  of  decreasing  drag,  the  drag  better  especially  reduction  was  critical,  observed;  the  created a closed was  essentially For  a  strong  region  different interaction  in  constant.  the The  smaller spacings  gap  switch  the  drag  case  of of  the the  of  front  rod  same r o d  in a  the  constant  flat  for  plate,  itself  was  uniform the  always  flow.  base  pressure  and  positions  a l l rod s i z e s  B).  In the  - An  case  optimum  (circular  required (9)  the  to  effect  a  of  the c i r c u l a r the  overall  cylinder,  drag  due  increasing  t o an  increase  pressure.  Re  yaw  was  number r e d u c e d  (8)  A  the drag  A and  overall  where  sharply.  drag  essentially  (regime  was  cylinder,  which  again.  The  than  (6)  bodies  drop  back -  The  turbulence  to turbulence.  B)  pressure  made t h e d r a g  circular  cylinder due  in creating  smaller spacings than  two  the  the  regime  (regime  the  of  recovery.  circular  (4)  secondly,  Re.  - Yaw  found  tandem  5°  was  size  cylinder  f o r lower  of  (10)  rod  c a n c e l s 50%  only);  t o be of  was  determined a  larger  important  the  flat  but  rod diameter  f o r drag  plate  i t changed  drag  was  reduction.  reduction in  configuration. - The  fluctuating  side  force  (circular  cylinder  43  only)  was  front as  rod  d/D  than  not and  =  a  significantly  was  0.17  reduced  seemed  larger  rod  was  side  force  frequency  and,  for  itself  (high  (position  and  determined  in this  (1) force  on  =  increased  the  became  size  of  the  front  reduction  a  force The  rod  upstream  by  the  rod  on  the  important  for  such  side  produced very  the  (regime A).  placing  frequency  of  rod  Cl'  The  spacings by  use  small  0.50.  optimum c o n f i g u r a t i o n  least  side not  force  rod)  was  precisely  the  fluctuating  work.  Further  Work  - A more e x t e n s i v e the  d/D larger  frequency)  The  A r e a s Of  at  A  the  more e f f e c t i v e f o r  as  was  rods,  cylinder.  5.2  be  better  by  i n most c a s e s .  such  reduction  large  to  increased  circular  study  of  side  c y l i n d e r would p r e c i s e l y determine  optimum c o n f i g u r a t i o n  for a  fluctuating side  the  force  reduction  force  reduction  device. (2) device  Many  are  studied carry  -  at  (3)  -  different (4)  Similar  - The be  (5)  Further  model w i t h  two  fluid  numbers would at  than  the  therefore higher  be  maximum useful  Re,  if  to the  permits.  experiments bluff  e f f e c t of  should  It  this  experiments  apparatus  shapes of  -  Reynolds  (7.0x10").  similar  experimental  flow  higher  here out  a p p l i c a t i o n s of  body,  should such as  turbulent  be a  flow  c a r r i e d out  square instead  on  cylinder. of  smooth  tested.  rods,  work one  could at  the  include front  testing a  and  the  bluff  second  at  body the  44  back. a  A preliminary  r o d a t t h e back  front the  rod) drag  did  study  of t h i s  not change when  the  at the c r i t i c a l  with  rod only.  be  practical  a  applications.  two  spacing  If this  bidirectional  that  adding  model  (with  substantially the overall  symmetrically  would  showed  ( i n t h e wake) o f t h e p r e s e n t  reduction  the front  model  rods  was a b o u t  device  device  were  and  i s  drag;  located  t h e same a s  successful,  would  find  i t many  45  BIBLIOGRAPHY 1.  E v e r y , M . J . , K i n g , R., W e a v e r , D.S., " V o r t e x - E x c i t e d V i b r a t i o n s of C y l i n d e r s and Cables and T h e i r S u p p r e s s i o n " , Ocean Engng, V o l . 9 , No.2, pp.135-157, 1982.  2.  M o r e l , T., B o h n , M., " F l o w O v e r Two C i r c u l a r D i s k s i n Tandem", J . F l u i d s E n g n g , V o l . 1 0 2 , M a r c h 1980.  3.  R o s h k o , A. a n d K o e n i g , K., " I n t e r a c t i o n E f f e c t s o n t h e D r a g o f B l u f f B o d i e s i n Tandem", P r o c e e d i n g s o f t h e Symposium on A e r o d y n a m i c D r a g M e c h a n i s m s , Ed.G. S o v r a n , T. M o r e l a n d W.T. Mason, J r . , Plenum P r e s s , New Y o r k , 1 9 7 8 .  4.  I g a r a s h i , T . , " C h a r a c t e r i s t i c s o f a F l o w A r o u n d Two C i r c u l a r C y l i n d e r s of D i f f e r e n t Diameters Arranged i n Tandem", B u l l . J . S . M . E . , V o l . 2 5 , No.201, M a r c h 1982.  5.  Z d r a v k o v i c h , M.M. a n d P r i d d e n , D.L., " I n t e r f e r e n c e B e t w e e n Two C i r c u l a r C y l i n d e r s ; S e r i e s o f U n e x p e c t e d D i s c o n t i n u i t i e s " , J . I n d . A e r o . , 2(1977) 255-270  6.  H i w a d a , M., T a g u s h i , T., M a b u s h i , I . , K u m a n a , M., " F l u i d F l o w a n d H e a t T r a n s f e r A r o u n d Two C i r c u l a r C y l i n d e r s of D i f f e r e n t Diameters i n Cross Flow", B u l l . J . S . M . E . , V o l . 2 2 , No.167 ( 1 9 7 9 ) , p . 7 1 5 .  7.  S t a n s b y , P.K., " T h e E f f e c t o f E n d P l a t e s o n t h e B a s e Pressure C o e f f i c i e n t of a C i r c u l a r C y l i n d e r " , Aero.J., J a n u a r y 1974, pp.36-37  8.  L e e , B . E . , " T h e S u s c e p t i b i l i t y o f T e s t s o n TwoDimensional B l u f f Bodies t o I n c i d e n t Flow V a r i a t i o n " , J . I n d . A e r o . , 2 ( 1 9 7 7 ) 133-148  9.  S t a t h o p o u l o s , T., " T e c h n i q u e o f P n e u m a t i c a l l y A v e r a g i n g P r e s s u r e s " , R e s e a r c h R e p o r t BLWT-2-1975, F a c u l t y of E n g i n e e r i n g Science, U n i v e r s i t y of Western O n t a r i o , London, Canada.  10.  M a s k e l l , E . C . , "A T h e o r y o f B l o c k a g e E f f e c t s o n B l u f f B o d i e s and S t a l l e d Wings i n a C l o s e d Wind T u n n e l " , Aero.Res.Coun. R&M 3 4 0 0 , 1 9 6 5  11.  F a g e , A. a n d J o h a n s e n , F.C.,."On t h e F l o w o f A i r B e h i n d an I n c l i n e d F l a t P l a t e o f I n f i n i t e Span", P r o c . R o y . S o c . L o n d . , A 116, 170, 1927.  12.  P a r k i n s o n , G.V., J a n d a l i , T., "A Wake S o u r c e M o d e l f o r B l u f f Body P o t e n t i a l F l o w " , J . F l u i d Mech. (1970), V o l . 4 0 , pp.577-594.  46  13.  E n g i n e e r i n g S c i e n c e D a t a I t e m Number 7 1 0 1 6 , J u l y 1973, F i g u r e 19, E n g i n e e r i n g S c i e n c e D a t a U n i t s L i m i t e d , London.  14.  T o w n s e n d , A.A., 1956, The S t r u c t u r e o f T u r b u l e n t Flow, Cambridge U n i v e r s i t y P r e s s , London.  15.  A c h e n b a c h , E., " F l o w P a s t R o u g h C y l i n d e r s a t H i g h J . F l u i d M e c h . , V o l . 4 6 , No.2 (1971-3), p.321.  16.  E n g i n e e r i n g Science Data E n g i n e e r i n g Science Data  17.  W e s t , G.S. a n d A p e l t , C . J . , "The E f f e c t o f T u n n e l B l o c k a g e a n d A s p e c t R a t i o on t h e M e a n F l o w P a s t a C i r c u l a r C y l i n d e r w i t h R e y n o l d s N u m b e r s b e t w e e n 10" and 1 0 " , J . F l u i d Mech ( 1 9 8 2 ) , V o l . 1 1 4 , pp.361-377  Shear Re",  I t e m Number 7 0 0 1 3 , F i g u r e L t d , London, 1970.  12,  5  18.  K e e f e , R.T., 1 9 6 1 , "An I n v e s t i g a t i o n o f t h e F l u c t u a t i n g F o r c e s A c t i n g on a S t a t i o n a r y C i r c u l a r C y l i n d e r i n a S u b s o n i c S t r e a m and t h e A s s o c i a t e d Sound F i e l d " , Univ. Toronto Inst. Aerophys. Rep. No.76.  19.  G e r r a r d , J.H., 1 9 6 1 , "An E x p e r i m e n t a l I n v e s t i g a t i o n o f the O s c i l l a t i n g L i f t and Drag of a C i r c u l a r C y l i n d e r S h e d d i n g T u r b u l e n t V o r t i c e s " , J . F l u i d Mech., 11, 244.  20.  G e r r a r d , J.H., 1 9 6 5 , "A D i s t u r b a n c e S e n s i t i v e Reynolds Number Range o f t h e F l o w P a s t a C i r c u l a r C y l i n d e r " , J . F l u i d Mech., V o l . 2 2 , p.187.  L/D  d/D  7.00  0.17  .721  2.32  0.17  1.98  Cp(centre)  L/d  1 /D  .151  41.2  .436  .548  .260  13.6  .251  0.17  .516  .280  11.6  .232  1.81  0.17  .540  .290  10.6  .221  7.17  0.33  .621  .212  21.7  .615  3.15  0.33  .467  .317  9.5  .408  2.78  0.33  .431  .343  8.4  .383  2.44  0.33  .401  .367  7.4  .359  2.13  0.33  .384  .380  6.5  .335  Table  U  I - C a l c u l a t e d wake v e l o c i t y d e f i c i t ( U ) n  0  /  U  l  and c h a r a c t e r i s t i c wake  0  width(l ) n  Figure  2  -  Smoke  tunnel  Turning  vanes  Figure  3 - O u t l i n e of the U.B.C. tunnel  a e r o n a u t i c a l wind  50  Wind  vs y  y y s s s s .?-\  y y ^y  T u n n e l  Roof  s s s s s s y y y y y r  End plates  Pressure tapl location  Front Rod Circular Cylinder  S.S  /- y  y y y/  y  y y y y y y y y y ^  y y y y y  y y y y y  y  Wind Tunnel Floor -Movable Support  Stand  ////A'///////' I Balance  Figure  4 - Sketch of a t y p i c a l tunnel  model  inside  t h e wind  yy  51  FRONT ROD (2 sizes of end plates depending on spacing)  Figure  5 - End p l a t e s  52  6.35  3.2  r  FRONT RODS  Figure  6 - Cross  s e c t i o n o f models tap location  showing  pressure  53  2.4  I  1  i  1  1  1  1  1  1  1  1  r  12.7 mm  Figure  8 - Sketch  of  manifold  for pneumatic  averaging  54  Frequency  Generator  Vibrator  VoltmeterOscilloscope  52 mm d i a . Channel 1 Cylinder Scanivalve  & Transducer  I |o  Channel  Manifold  9-914 914 mm l o n g  mm l o n g Tygon  tubing  Tyqon tubing  Figure 9 - Apparatus measuring system  f o r c a l i b r a t i o n of the side force against frequency d i s t o r t i o n  F i g u r e 10 - T r a n s f e r f u n c t i o n f o r t h e m e a s u r i n g s y s t e m . ^The s o l i d l i n e was u s e d  side force to correct  data  56  Figure  11  -  Pressure distribution (Re=4.0xlO ) a  on  flat  plate  57  n  1  r.—i  1  1  1  1  1  1  1  1  1  r  i  i  i  r  0.6  t  tx  +  0.4  X  X  • 0.2  0.0  -  •0.2  "  •0.4  -  -0.6  -  CD  +  -0.8  -1.2  -  7.17  -  3.15  —  2.78 X  -1.0  L/D  2.13  -  1.97  11  "  _1  0.0  I  I  I  0.2  I  I  J  0.4  l_  J  I  I  L_  0.6  F i g u r e 12 - P r e s s u r e d i s t r i b u t i o n o n f l a t f r o n t r o d d/D = 0.33 ( R e = 4 . O x 1 0 ) ; F l o w 0  I  1  0.8  I  I  L_  x/D  plate with regime A  1.0  58  1.0 i  1  1  1 — i — i — i  '—i  1  1  — — — 1  1  1  1  1  1  '  1  r  X  X  +  +  0  • X  ID  o  X  x  •  X  X  8  0.4 L/D 0.6  0.8  1.0  l  -  e>  -  +  1.81 1.47  -  1.29  -  X  1.16  -  a  0.84  ' l 2  I  0.0  I  0.2  t  I  I  I  0.4  I  I  I  I  0.6  F i g u r e 13 - P r e s s u r e d i s t r i b u t i o n o n f r o n t r o d d/D = 0.33 ( R e = 4 . 0 x 1 0 " ) ;  I  I  1  J  1  1  L  0.8  1.0 x/D  flat plate with Flow regime'B  59  1.0  I  0.8  -  0.6  -  1  1  1  1  i  1  i  1  1  1  1  1  -  0.2  -  0.0  -  •0.2  '  *  1  1  1  r  I  I  I  L  X  L/D  -  CD  7.00  -  +  2.32  -  1.98 X  J  0.0  1  CD  -  •0.8  1  CD  i 0.4  1  1  I  L  0.2  J  I  I  0.4  1.81  1  1  I  I  1  I  i  0.8  0.6  F i g u r e 14 - P r e s s u r e d i s t r i b u t i o n o n f r o n t r o d d/D = 0.17 (Re=4.0x10*);  flat Flow  x/D  plate with regime A  1.0  60  1. 0 i  0.8  r  0.6  h  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  i  r  o X  +  0.4  CD  6  0.2  8  S  9  cb  8  CD  0.0  L/D 1.64  J  0.0  I  I  I  0.2  I  I  I  +  1.30  «>  1.13  X  0.97  CD  0.83  I  0.4  I  1  1  1  1  L.  I  I  1_  0.8  0.6  F i g u r e 15 - P r e s s u r e d i s t r i b u t i o n o n f r o n t r o d d/D = 0.17 (Re=4.0x10");  J  1.0 x/D  flat Flow  plate with regime B  F i g u r e 16 - P r e s s u r e d i s t r i b u t i o n o n t h e f r o n t r o d d/D = 0.33 a t t w o d i f f e r e n t s p a c i n g s ( R e = 5 . O x 1 0 * ) ; L/D = 3.42 ( r e g i m e A) a n d L/D = 1.42 ( r e g i m e B)  Figure  17  - V e l o c i t y d e f i c i t (U ) versus for flow regime A 0  spacing  (L/d)  -0.6  i  r  i  r  i  1  r  Cp(base) d/D -0.8  +  0.17  CD  0.33  *  —  -  -1.0  CD  -1.2  Plate  4+0+°  ,9  CD  alone  °  -1.4  J  -1.6 0.0  I  I  L  1.0  2.0  I  l  L  3.0  4.0  I 5.0  I  I  I  6.0  I  L  7.0  8.0 L/D  Figure  18  - Base  pressure  f o r regimes A and  B  64  Figure r o d d/D  19 - F l o w v i s u a l i s a t i o n a t Re = 5 X 1 0 for front = 0.21; ( a ) L/D = 1.36 ( r e g i m e A ) ; ( b ) L/D = 0.79 ( r e g i m e B) 3  2.4  i  i  r  1  1  i  r  1  r  CD Plate  2.0  alone  + + 1.6  /  ++  +  +0  CD  + CD  CD  CD  1.2 CD en ui  0.8  CD  Plate  only  +  Overall  L  J  0.4  J  0.0 0.0  1.0  J  L Z.O  I  L  3.0  J 4.0  5.0  I  6.0  I  L  7.0  8.0 L/D  F i g u r e 20 - D r a g c o e f f i c i e n t d/D = 0 . 3 3  of  flat  (Re^.OxlO *) 1  plate with  rod  2.4  i  i  r  i  r  1  1  1  r  CD Plate  2.0  alone  + O 1.6  1.2  0.8  ©  Plate  only  +  Overall  0.4  i  0.0 0 0  i  I  1.0  I 2.0  I  I 3.0  I  1 4.0  J  L 5.0  I  6.0  I  L  7.0  8.0  L/D Figure  21  - Drag c o e f f i c i e n t of f l a t p l a t e w i t h d/D = 0.17 (Re=4.0xl0")  rod  67  Figure  23  - Separated flow past a normal f r o m wake s o u r c e m o d e l  flat  plate  68  F i g u r e 24 - S t r e a m l i n e s o v e r p o t e n t i a l m o d e l c o n d i t i o n f o r s t a t i o n a r y p a i r o f v o r t i c e s ; Cpb  using =1.24  CD Subcritical  . Q-i'ical i Supercritical)  Re  Figure  crit  Transcfitical  Re  25 - T y p i c a l d r a g c o e f f i c i e n t v e r s u s number f r o m A c h e n b a c h  Reynolds  69  F i g u r e 26 - P r e s s u r e d i s t r i b u t i o n a r o u n d c y l i n d e r a t v a r i o u s Reynolds numbers; s o l i d ESDU f o r s u b c r i t i c a l range  a circular l i n e i s from  -1.8  -i  i  i  _  i  60  i  i  i  i  i  t 120  i  i  i  -1.8  i  _i  i  i  i  180  F i g u r e 30 - P r e s s u r e d i s t r i b u t i o n a r o u n d a c y l i n d e r a t Re = 1 . 0 x 1 0 " w i t h f r o n t r o d d/D ( a ) r e g i m e A; ( b ) r e g i m e B  i  u 60  circular = 0.33.  _l  I  120  I  I  l_  L_  180  (a) 1.0  1  -I  1  1  1  1  1  1  1  (b) 1  1  1  1  1  1  1  1.0  r  L/D  Cp  0.6  e  1.73  +  2.06  «  2.24  X  2.61  EJ  2.94  1  -i  1  1  1  1  1 1  1  1 1 1  i  1  1  r-  L/D  Cp  0.6  +  X  1.02  -  1.10  -  1.45  -  1.60  -  -0.6  -1.0  -1.4  -1.4  -1.8  I 0  i  i  J  i  i  1—i 60  L.  i  i 120  i  i  i  i  i_ 180  -1 al 0  i  i  i  '  F i g u r e 31 - P r e s s u r e d i s t r i b u t i o n a r o u n d a c y l i n d e r a t Re = 3 . 3 x 1 0 " w i t h f r o n t r o d d/D ( a ) r e g i m e A; ( b ) r e g i m e B  i  i 60  i  i  i  circular = 0.33.  i  i  i 120  i  i—i—i—i— 180  (b)  (a) 1.0  -i  1 1 1  1 1 1 1  1  Cp  1 1  r — i  i  i  1.0  r  0.6  1.91  t  2.06  •  2.40  L/D  Cp  L/D 0  1 1 1 1 1 1 r  -i  0.6  1.02  -  +  1.10  -  »  2.94  X  0  6.74  1.45  -  X  1.60  -  a  1.73  -  •1.4  -1.8  I  60  I  I  I  I  1 1 1 120  i  L  1 1—  180  •1.8  •  F i g u r e 32 - P r e s s u r e d i s t r i b u t i o n a r o u n d a c y l i n d e r a t Re = 6 . 5 x 1 0 " w i t h f r o n t r o d d/D ( a ) r e g i m e A; ( b ) r e g i m e B  I  I  60  I  I  I  circular = 0.33.  I  1—I  120  1 1 1  1  1- 180  (a) ~i  i  1  1  (b)  1  1  1  1  1  1  1.0  r  L/D  i  i  1  1  1 1  1  r  Cp  2.26 +  2.56  ©  2.74  X  6.56  0.6  0.2  -0.2  -0.6  -1.0  -1.4  -I—1  1—I—I  1  I  120  I  I  I  I  I  180  -1.8  I—i—i  - i — i — i  L.  0  F i g u r e 33 - P r e s s u r e d i s t r i b u t i o n a r o u n d a c y l i n d e r a t Re = 1 . 0 x 1 0 " w i t h f r o n t r o d d/D ( a ) r e g i m e A; ( b ) r e g i m e B  60  circular = 0.50.  i_  (b)  (a) 1.0  -i  1  1  1  1  1  1  1  1  1  1  1.0  i i r  1  L/D  Cp  e 0 . 6 A-  -I  1  1  1  1 1  1  2.06  «  2.26  X  2.74  EJ  6.56  1  1  1  C.6  1  1  1  r-  1  L/D  -  o  1.08  -  +  1.23  -  o  1.42  -  X  1.55  -  Cp  1.90  +  1  0.2  -1.4  -1.4  -1.8  I  60  I  I  I  1  J  1—  120  •1.8  I—_J—1_  180  I  l  l  60  F i g u r e 34 - P r e s s u r e d i s t r i b u t i o n a r o u n d a c i r c u l a r c y l i n d e r a t Re = 3 . 3 x 1 0 " w i t h f r o n t r o d d/D = 0 . 5 0 . ( a ) r e g i m e A; ( b ) r e g i m e B  1  I  I  120  1  1  1  1  _L.  180  (b)  (a) 1.0  -i  1  1  1  1 1  1  1  1  1  1  1  1.0  r  L/D  Cp  i  1 1 r  n  1  1  1 1  1  1  1  I  I  1  1  r  I  I  1_  L/D  Cp  1.72 0.6  1  0.6L  e  0.63  +  1.08  +  2.06  o  2.26  o  1.23  X  2.74  X  1.42  B  6.56  El  1.55  0.2  -1.4  -1.8  _J  I  L.  60  '  I  I  I  I  120  I  ,J  I  l_  180  1.81—i L.  60  F i g u r e 35 - Pressure d i s t r i b u t i o n around a c i r c u l a r c y l i n d e r at Re = 6.5x10" with f r o n t rod d/D = 0.50. (a) regime A; (b) regime B  120  180  1  1  1  —r  r  -  t  i  i  i  Cylinder  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  i  alone  1.0  0  0.8 CD  +\  . ' 0  \  O  O  ^  ©  Re  0.6  ° i  'O.O  i  3.3xl0  0  6.5xl0  4  4  ~~~  i  II  i  1.0  +  2.0  3.0  4.0  1  i  5.0  i  i  i  i  6.0  7.0 L/D  Figure  37 - O v e r a l l d r a g c o e f f i c i e n t f o r c y l i n d e r f r o n t r o d d/D = 0 . 3 3  with  i  Figure  38 - O v e r a l l d r a g c o e f f i c i e n t f o r c y l i n d e r f r o n t r o d d/D =0.50  with  0.6  1  1  1  d/D  1  i  1  1  1  1  1  1  1  1  1  Re 0.5  -  ©  6.5xl0  -  +  3.3xl0 l.OxlO  —  0.2  ©—®  <W—«vf  —  -  4  -  4  —  4  —•  CD  O  -  —m\—o  -  0.1  1  .0  1  0 .4  I 0.8  l  l 1.2  1  1  1.6  1  1  2.0  1  1  i L  F i g u r e 40 - C r i t i c a l s p a c i n g r a n g e s f o r d i f f e r e n t r o d and R e y n o l d s numbers ( c i r c u l a r c y l i n d e r )  i 2.8  2.4  / crit. D  sizes  84 0.3  "i  0 . 2 r-  <3  i  i  ® 0  i  i  i  i  © B C D ©  i  i  O ©  i  ID  i  S  i  ffi  i  B  r  ffl  O.i h  J  0.0 0  I  I  1  I  I  i  i  '  I  I  i  6  1  I  i  i  7  8  Re(xl0" ) 4  (a)  F i g u r e 41 - F l u c t u a t i n g s i d e f o r c e o n a c i r c u l a r c y l i n d e r ; ( a ) S t r o u h a l number v e r s u s R e y n o l d s number; (b) i n t e n s i t y C l v e r s u s R e y n o l d s number 1  85  F i g u r e 42 - F l u c t u a t i n g s i d e f o r c e o n a c i r c u l a r c y l i n d e r w i t h r o d d/D = 0 . 1 7 ; C l ' i s from F i g . 4 1 ( b ) r e f >  86 i  i  r  i  r  i  0.6  r  -  Re  C 1  3.3xl0  ci'  0  0.4  ,^0  +  6.5xl0  'ref. —  0.36  4  -  1.36  4  0  o  +-  0.2  J  L  J  i  L  I  I  6.  7. L/D  0.0.  F i g u r e 43 - F l u c t u a t i n g s i d e f o r c e on a c i r c u l a r c y l i n d e r with rod d/D = 0.33  i  r  1  0.6 OH  Cl 0.4 Cl '  Re 3.3xl0  0.2  0.0' 0.  J  L  1.  J  I 2.  I  11 3.  1  6.5xl0  1  1  4.  1 5.  0.36  4  +  f  1.36  4  1  1 6.  1 L/D  F i g u r e 44 - F l u c t u a t i n g s i d e f o r c e on a c i r c u l a r c y l i n d e r with rod d/D = 0.50  87  0.3  1  1  1  1  I  1  - 4 + 4+4 4 + .  I  I  1'  I  4 o  0.2  4 C5  -  -  Re  0.1 -  +  6.5xl0  -  CD  3.3xi0  0.0  1 0.  1 1.  l  l  1  i  i  i  -  4  -  4  -  i  i  I  6.  7. L/D  F i g u r e 45 - S t r o u h a l number on a c i r c u l a r f r o n t rod d/D = 0.17  0.6  1 • l  I  1  I —1 0  ^  34% cK25%  r — i  1  c y l i n d e r with  1  1  • 1  1  22%  38% ;  /  0.4  / /  -  -  / / / /  o  ® 0  0.2  -  0X 0  -  0.0 0.  1  J  1  J  I  1  i  i  3.  i  i  i  i  i  6.  7. L/D  F i g u r e 46 - S t r o u h a l number on a c i r c u l a r c y l i n d e r ' w i t h f r o n t rod d/D = 0.33 (Re = 3 . 3 x 1 0 " ) ; percentages shown represent percentage of ( C l ) due t o t h a t frequency 1  2  88  i  i  r  "i  1  1  r  0.4  CD  •a 69% o  /  '80%  56% J  79%  CD (D CD  0.2  a  o—o — ©  J  0.0 0.  1  L  J  3.  4.  1  5.  I  I  6.  7. L/D  F i g u r e 47 - S t r o u h a l n u m b e r o n a c i r c u l a r c y l i n d e r w i t h f r o n t r o d d/D = 0.50 ( R e = 3 . 3 x 1 0 " ) ; p e r c e n t a g e s s h o w n represent percentage of ( C l ' ) due t o t h a t f r e q u e n c y 2  89  A P P E N D I X A ~ PRESSURE TAP L O C A T I O N MEASUREMENT Consider distribution:  a circular  cylinder  FOR  submitted  S I D E FORCE  to a  pressure  Now d i v i d e t h e Y a x i s i n t o e i g h t e l e m e n t s a n d c o n s i d e r e a c h . element as being subjected t o a uniform pressure equal t o the a c t u a l pressure a t the c e n t r e of the element.  The u n i f o r m l y d i s t r i b u t e d p o i n t f o r c e F: F We of  pressure  c a n be r e p l a c e d by a  = pAA = p A y / s i n 8  are interested F: Fy  only  i n the side force,  or the Y  component  = F s i n e = pAy  where F y i s t h e s i d e f o r c e on t h e e l e m e n t c o n s i d e r e d . t o t a l s i d e f o r c e o n t h e . c y l i n d e r i s t h e sum o v e r a l l elements: Fy  T  =  Fy  = p Ay 1  If  FY  + x  1  """  + 2  +  f  Y q  + P A y + --2  2  +P Ay 8  g  t h e e l e m e n t s h a v e t h e same l e n g t h , Fy  T  =  ^  + p  =  (  =  (average  P l  +  p ?  + 2  +  -— —  +  then:  P8> y A  + r ^ ) x 8Ay  pressure)  x  (diameter)  The  90  If the elements are of equal length, only the average p r e s s u r e h a s t o be m e a s u r e d t o o b t a i n t h e s i d e f o r c e . For e l e m e n t s o f t h e same l e n g t h , t h i s i s t h e l o c a t i o n o f pressure taps:  Cl'  i s calculated Cl'  =  i n the following  way:  2 x manifold pressure(RMS) x D 0.5PU, x D 2  The f a c t o r 2 i s t h e r e t o i n c l u d e t h e s i d e f o r c e f r o m t h e other side of the c y l i n d e r . By d o i n g t h a t i t i s a s s u m e d t h a t t h e f l u c t u a t i n g s i d e f o r c e i s o u t o f p h a s e b y 180° f r o m one s i d e t o t h e o t h e r . T h i s a s s u m p t i o n was n o t v e r i f i e d h e r e h o w e v e r , b u t , i f a n y t h i n g , C l ' w i l l be overestimated.  

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