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Cavitation and entrainment in a downcomer entrance Ryan, James Arthur 1983

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CAVITATION AND ENTRAINMENT IN A DOWNCOMER ENTRANCE by JAMES ARTHUR RYAN B . A . S c , U n i v e r s i t y Of B r i t i s h Columbia, 1978  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  Engineering  We accept 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 A p r i l 1983  ©  James Arthur Ryan, 1983  In p r e s e n t i n g  t h i s t h e s i s in p a r t i a l f u l f i l m e n t  of  the  requirements f o r an advanced degree at the U n i v e r s i t y  of  B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t freely  available  for  agree that permission  reference for  extensive  t h e s i s f o r s c h o l a r l y purposes may of  my  and  study.  I further  copying  be granted by  Department or by h i s or her  of  the Head  representatives.  i s understood that copying or p u b l i c a t i o n of t h i s for  f i n a n c i a l gain  written  shall  not  be  Mechanical E n g i n e e r i n g  The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5  Date:  allowed  permission.  Department of  A p r i l 20,  1983  this  It  thesis  without  my  ii  Abstract Two-phase  instabilities  have  been  downcomer entrance i n an experimental n e a r - s a t u r a t e d Freon-11 been  characterized  s u b c o o l i n g at the l i q u i d two  interface  primary  instability  were  entrainment  regimes  that  and  the  in  the  i n the p o o l .  and  cavitation. this  study  The be  c o r r e l a t e d with the p r e v i o u s l y documented occurrence  of  i n c i p i e n t drawdown.  in  involved  can  air-water  observed  parameters  flowrate  mechanisms  entrainment  drains  The regimes have  dimensionless  d e s c r i b i n g the pool depth, downcomer  The  rig  from a v e s s e l . using  observed at a  Drawdown was  observed at  higher p o o l depths than expected ( f o r a given when  vapour  Cavitation, formation  bubbles the and  were  mechanism growth,  has  present  at  the entrance.  responsible been  flowrate)  for  found  to  bubble be  s u s c e p t i b l e to the presence of n u c l e a t i o n s i t e s the  and  to  amount of s u b c o o l i n g at the pool i n t e r f a c e . Severe  the  very  local  velocity  instability  may  occur at a f l o w r a t e where  v e l o c i t y at the entrance i s equal to the of  a  particular  vapour  bubble.  Due  rise to the  g e n e r a t i o n of vapour  through entrainment and  cavitation,  bubbles conglomerate  a t the entrance,  with  the  Some  segregation  having  no  mechanism  occurs, with small  for  bubbles  escape.  discharging  vapour  downwards  and  l a r g e bubbles r i s i n g Downcomer  upwards.  entrance  independent p a r a m e t e r . in  the  similar.  re-entrant  and  geometry  was  varied  as  an  In g e n e r a l , the observed regimes sharp-edged  geometries  were  The flow regimes i n the rounded geometry were  unique due to the e f f e c t of  the  streamlined  r e d u c i n g c a v i t a t i o n at the e n t r a n c e .  curvature  iv  Table of  Contents  Abstract L i s t of F i g u r e s Acknowledgements Nomenclature  i i vi vii viii  Chapter I INTRODUCTION 1.1 P r e l i m i n a r y Remarks 1.2 Review Of The Terminology 1.2.1 Dimensionless Parameters 1.2.2 D e s c r i p t i v e Terms 1.3 Review Of P r e v i o u s Work 1.3.1 I n s t a b i l i t i e s In Two-Phase Systems 1.3.2 C a v i t a t i o n 1.3.3 I n c i p i e n t Drawdown 1.3.4 M i s c e l l a n e o u s S t u d i e s 1.4 Scope Of The Present I n v e s t i g a t i o n  1 1 2 2 5 9 9 10 10 12 13  Chapter II EXPERIMENTAL APPARATUS 2.1 General Concept 2.2 Working F l u i d 2.3 Pipe, Tubing, Hose, And F i t t i n g s 2.4 Vacuum Chamber And V e s s e l s 2.5 Pumps 2.6 Instrumentation 2.6.1 Temperature Measurement 2.6.2 Pressure Measurement 2.6.3 Depth Measurement 2.6.4 Flowrate Measurement 2.6.5 Data A c q u i s i t i o n System 2.6.6 Photographic S t u d i e s 2.7 Assembly And I n i t i a l T e s t i n g  14 14 15 17 18 20 20 20 21 21 22 23 24 25  Chapter III PROCEDURE 27 3.1 Routine Experimental P r e p a r a t i o n 27 3.2 C a l i b r a t i o n 30 3.3 Measurements With F i x e d Pool Depth 31 3.4 Measurement Of Downcomer Flowrate F l u c t u a t i o n s ....32 Chapter IV EXPERIMENTAL RESULTS 4.1 Flow Mapping 4.1.1 I n c i p i e n t Drawdown 4.1.2 Onset Of C a v i t a t i o n Bubbles (OCB) 4.1.3 Requirements For A V i o l e n t I n s t a b i l i t y 4.2 C r i t i c a l Pool Depth (CPD)  34 34 35 36 38 39  V  4.3 Video C a s s e t t e 4.4 Downcomer Flowrate F l u c t u a t i o n  '  40 41  Chapter V DISCUSSION OF RESULTS 43 5.1 Q u a l i f y i n g Remarks 43 5.2 Experimental E r r o r 46 5.3 I n c i p i e n t Drawdown 47 5.4 Onset Of C a v i t a t i o n Bubbles (OCB) 50 5.5 Requirements For A V i o l e n t I n s t a b i l i t y 53 5.6 The Up-Down T r a n s i t i o n 54 5.7 C r i t i c a l Pool Depth (CPD) 55 5.8 Bubble Rise V e l o c i t y In The F u l l y Developed Region 57 5.9 Expected Behaviour At High Values Of Subcooling ...58 5.10 Downcomer Flowrate F l u c t u a t i o n 58 Chapter VI CONCLUSIONS 6.1 General 6.2 I n c i p i e n t Drawdown 6.3 Onset Of C a v i t a t i o n Bubbles (OCB) 6.4 Requirements For A V i o l e n t I n s t a b i l i t y 6.5 C r i t i c a l Pool Depth (CPD) And The Up-Down Transition 6.6 Sample T h e o r e t i c a l Curves 6.7 Downcomer Flowrate F l u c t u a t i o n Chapter VII RECOMMENDATIONS 7.1 I n d u s t r i a l Design 7.2 F u r t h e r Work 7.2.1 M o d i f i c a t i o n s To The Apparatus And Instrumentation 7.2.2 F u r t h e r Areas Of Study  60 60 61 62 63 63 64 64 65 65 66 66 68  BIBLIOGRAPHY  100  APPENDIX A - DIMENSIONAL ANALYSIS  102  APPENDIX B - SAMPLE CALCULATIONS AND ERROR ANALYSIS  105  APPENDIX C - INDEX TO VIDEO CASSETTE  108  vi  List  of F i g u r e s  1. I n d u s t r i a l Example Of The I n s t a b i l i t y (Steam and Condensate) 70 2. I n c i p i e n t Drawdown With L i q u i d L e v e l At Downcomer Entrance (Air-Water) 71 3. I n c i p i e n t Drawdown With L i q u i d Level Below Downcomer Entrance (Air-Water [9]) 72 4. Experimental Schematic 73 5. P i c t u r e s Of Apparatus And Instrumentation 74 6. D e t a i l s Of Vacuum Chamber 75 7. Downcomer Entrance Geometries 76 8. Constant Temperature Anemometer Schematic 77 9. Data A c q u i s i t i o n System Schematic 78 10. The E f f e c t Of Subcooling On I n c i p i e n t Drawdown For The Re-entrant Geometry 79 11. I n c i p i e n t Drawdown For Rounded And Sharp-edged Geometries 80 12. The E f f e c t Of S u b c o o l i n g On The Onset Of C a v i t a t i o n Bubbles (OCB) For The Re-entrant Geometry 81 13. The E f f e c t Of S u b c o o l i n g On The Onset Of C a v i t a t i o n Bubbles (OCB) For The Sharp-edged Geometry 82 14. V i o l e n t Region For The Re-entrant, Rounded And Sharpedged Geometries ' 83 15. C r i t i c a l Pool Depth (CPD) For The Re-entrant Geometry 84 16. C r i t i c a l Pool Depth (CPD) For The Rounded Geometry. ..85 17. The E f f e c t Of S u b c o o l i n g On CPD For The Sharp-edged Geometry 86 18. P i c t u r e s Of I n c i p i e n t Drawdown, Spouting And OCB In The Re-entrant Geometry ..87 19. Froude Number F l u c t u a t i o n And Frequency A n a l y s i s For The Re-entrant Geometry 88 20. Froude Number F l u c t u a t i o n And Frequency A n a l y s i s For The Rounded Geometry 89 21. Froude Number F l u c t u a t i o n And Frequency A n a l y s i s For The Sharp-edged Geometry 90 22. Froude Number F l u c t u a t i o n In The Re-entrant Geometry During B r i d g i n g 91 23. M i s c e l l a n e o u s P i c t u r e s Of The Re-entrant Geometry. ...92 24. S t r e a m l i n e P a t t e r n In L i q u i d - O n l y Flow 93 25. T h e o r e t i c a l OCB Curves 94 26. V i o l e n t Spouting In The Re-entrant Geometry 95 27. Expected Behaviour At D i f f e r e n t Values Of Subcooling 96 28. I d e a l i z e d CPD For The Re-entrant Geometry At SC = 9. .97 29. I d e a l i z e d CPD For The Rounded Geometry At SC = 9 98 30. I d e a l i z e d CPD For The Sharp-edged Geometry At SC = 9 99  vi i  Acknowledgement  The to  author wishes to express h i s s i n c e r e  Professor  and guidance  E.G. Hauptmann, f o r h i s i n v a l u a b l e advice throughout  Thanks are mechanical  due  a l l phases of the i n v e s t i g a t i o n .  to  engineering  the  technical  staff  of  the  department f o r t h e i r a s s i s t a n c e  in the c o n s t r u c t i o n of the experimental  apparatus.  S p e c i a l thanks t o my f e l l o w graduate their  gratitude  students  for  h e l p f u l advice and suggestions, t o Chien Wei Jang  f o r h i s h e l p performing  the experiments,  and t o my w i f e ,  J a n i n , who helped p r o o f - r e a d the t h e s i s and constant  source  my graduate  was  a  of moral support and m o t i v a t i o n during  work.  F i n a n c i a l support Sciences  who  and  f o r t h i s r e s e a r c h by the  Natural  E n g i n e e r i n g Research C o u n c i l of Canada i s  g r a t e f u l l y acknowledged.  vi i i  Nomenclature  B  calibrated y-intercept  D  downcomer i n s i d e diameter  Fr  Froude number V(gD)' V  AFr*  (m)  (dimensionless  Froude number peak-to-peak  Froude  p. 30)  flowrate)  2  expressed  H  (see Ch. I l l ,  as a percentage  fluctuation of the mean  number  chamber pool depth above the top of the entrance  (m)  H/D  dimensionless pool depth  K  l i n e a r c a l i b r a t i o n constant (see Ch. I l l ,  p. 30)  N  number of data p o i n t s  Pch  chamber pressure (Pa)  PV  chamber p r e s s u r e s i g n a l v o l t a g e  Psat  saturation  Q  siphon loop f l o w r a t e  QV  siphon loop f l o w r a t e s i g n a l v o l t a g e  SC  dimensionless  SCAVG  average value of s u b c o o l i n g  SD  standard  Tch  chamber temperature (°C)  TV  chamber temperature s i g n a l  pressure a t temperature Tch (Pa) (litres/s)  s u b c o o l i n g (Pch - Psat)/pgD  deviation  voltage  ix  V  average l i q u i d phase v e l o c i t y  i n the  tube (m/s) Vn  v a l v e number "n" as shown on F i g u r e 4  g  gravitational acceleration  p  l i q u i d density  (kg/m ) 3  Abbreviations  rd  rounded entrance  re  r e - e n t r a n t entrance  shp  sharp-edged entrance  CPD  c r i t i c a l pool depth  ID  i n c i p i e n t drawdown  OCB  onset of c a v i t a t i o n  bubbles  (m/s ) 2  1  I. 1.1  INTRODUCTION  P r e l i m i n a r y Remarks Much  effort  has  been  devoted  i n the l a s t  years to the study of two-phase flow regimes relationship previous  their  to heat and mass t r a n s f e r phenomena.  work  development process  and  forty  has of  industry  been  an  integral  sophisticated technologies,  part  power where  Such  of  the  generation two-phase  and flows  occur f r e q u e n t l y . The  present  study  is  concerned  vapour flow of a one-component temperature  and  pressure.  v e s s e l through  an . entrance  "downcomer".  An  in F i g u r e 1.  The  fluid, The  with the near  liquid  into  a  liquid-  saturation  d r a i n s from a  vertical  tube  or  example of t h i s type of flow i s shown liquid  i s draining  from  the  chamber  i n t o a region of i n c r e a s i n g h y d r o s t a t i c p r e s s u r e , but i n the d i r e c t i o n of d e c r e a s i n g p i e z o m e t r i c p r e s s u r e . common  examples of t h i s type of n e a r - s a t u r a t e d flow are  i n package b o i l e r evaporators When  i n s t a l l a t i o n s and  i n s e v e r a l types  vapour  loss  phase  much  greater)  c o n v e n t i o n a l single-phase The  of  used i n i n d u s t r y . i s present, the r e s u l t i n g tube  f l o w r a t e t u r n s out to be much l e s s (and head  Other  than  that  the  frictional  p r e d i c t e d i n the  analysis.  e x i s t e n c e of t h i s type of i n s t a b i l i t y has  been  2  hinted  at  s e v e r a l times i n the l i t e r a t u r e ,  by Simpson [ 1 ] , but visualized  or  seems  involved,  instability.  pipe  in  near-saturated been  from  0.31  as  to  certain  the  been  design  effect  liquids. attempted (for  downcomer)  without  to 1.0 i n v e r t i c a l  the  of  the avoid  two-phase  t h i s g u i d e l i n e has been used  industry.  instability  regimes  not  Simpson made a  postulate  to minimize  However,  r e s u l t s have been obtained,  have  has  studied.  suggesting  In the past  engineers  it  In essence he s t a t e d that one should  numbers  flow.  that  misleading  g u i d e l i n e s be followed  Froude  seems  systematically  vague, and i t mechanisms  it  f o r example  very  particularly  inconsistent  in  flows  Often t r i a l and e r r o r in  efforts  example  to  by  with  solutions  control  air-injection  the  into  the  any b a s i c understanding of the flow  involved.  1.2 Review Of The Terminology 1.2.1  Dimensionless Parameters In  characterizing  two-phase  flow  regimes,  dimensionless  parameters are sometimes used to d e s c r i b e  the  one  flow  conditions.  of  Then,  fluid using  under the  s i m i l a r i t y , t h i s d e s c r i p t i o n can  a  particular  principle be  applied  of  set  of  dynamic to  other  3  f l u i d s and In  other  liquid  Froude  number  sets of  flow with a l i q u i d - v a p o u r (abbreviated  d i m e n s i o n l e s s group. as  the  conditions.  In pipe  square root of the  f o r c e s , given  Fr) flow  is  i n t e r f a c e , the a  significant  i t is usually  r a t i o of i n e r t i a l  defined  to buoyancy  by  F r ( l i q u i d ) = V(gD)" ^ ( p/( p - p v ) )  1 / 2  Here V i s the average l i q u i d v e l o c i t y i n the tube, D the p  tube diameter, g i s g r a v i t a t i o n a l a c c e l e r a t i o n , and  pv  densities.  are  the  Since  respective  liquid  at low p r e s s u r e s ,  and  the vapour  is and  vapour density  i s n e g l i g i b l e when compared to that of the l i q u i d ,  this  term s i m p l i f i e s to  Fr = V(gD)" / 1  It  is  2  = "dimensionless  assumed  flowrate"  that when the p r i n c i p l e of dynamic  s i m i l a r i t y of Froude numbers i s a p p l i e d to other and  sets  of c o n d i t i o n s , other  as those i n v o l v e d with s u r f a c e  f o r c e s on the tension  are s m a l l r e l a t i v e t o i n e r t i a l and The  pool depth H,  from the v a p o u r - l i q u i d  and  fluids  fluid  such  viscosity,  buoyancy f o r c e s .  d e f i n e d as the v e r t i c a l i n t e r f a c e i n the chamber  distance to  the  4  top  of  the  parameter.  downcomer  entrance,  i s another  I t i s a measure of the suppression of vapour  formation a t the downcomer entrance due pressure  effects.  H  can  be  d i v i d i n g by the tube diameter  H/D  dimensionless  to hydrostatic  non-dimensionalized  depth"  parameter  d e s c r i b e s the magnitude of l i q u i d  the chamber.  by  D, to give  = "dimensionless pool  The t h i r d project  important  used  in  this  subcooling i n  The s u b c o o l i n g number, d e f i n e d here as  SC = (Pch - Psat)/pgD = " d i m e n s i o n l e s s . s u b c o o l i n g "  i s the d i f f e r e n c e between the chamber p r e s s u r e saturation (at  pressure  Psat  the chamber temperature  dividing  by  pgD.  dimensionalizing  The  and  i n the chamber  T c h ) , non-dimensionalized by suitability  of  non-  by pgD w i l l have to be examined i n the  f u t u r e with experimental tube  of the l i q u i d  Pch  studies  using  several  other  diameters. APPENDIX  used t o j u s t i f y  A  contains  a brief  dimensional  the use of these d i m e n s i o n l e s s  analysis groups.  5  1.2.2  D e s c r i p t i v e Terms Three  downcomers,  terms  used  in  the  with the d e f i n i t i o n s  hydraulic  study  of  i n the context used i n  the present study a r e :  1.  "flow i n s t a b i l i t y " - a spontaneous occurrence rapidly  changing  of  two-phase flow regimes i n a tube,  accompanied by f l u c t u a t i o n s i n the tube f l o w r a t e .  For' a more g e n e r a l instabilities,  the  definition  reader  of  two-phase  flow  i s r e f e r r e d to a review done  on t h i s s u b j e c t by B e r g l e s [ 2 ] .  2.  " c a v i t a t i o n " - v a p o u r - f i l l e d bubble collapse in  a  liquid  caused  by  formation  dynamic  induced) pressure r e d u c t i o n i n an a d i a b a t i c  Knapp [ 3 ]  has  defined  c a v i t a t i o n as the stage of perceptible  as  the  the  cavitation  liquid  pressure  "desinent" c a v i t a t i o n d e s c r i b i n g cavitation  disappears  with  the  term that  (flowflow.  "incipient" is  barely  i s lowered, stage  increasing  and  where  with the  pressure.  T h e o r e t i c a l l y c a v i t a t i o n occurs when the normal s t r e s s e s on an i n f i n i t e s i m a l p a r t i c l e of l i q u i d  are  reduced  to  6  the  vapour  pressure  temperature).  of  The presence  the  liquid  (at the p a r t i c l e  of s u r f a c e  boundary  layers,  particles  (which act as n u c l e a t i o n s i t e s ) ,  requirement liquid.  turbulence,  tension  u n d i s s o l v e d gas and distort  formation and c o l l a p s e  are  phenomena, the time a l i q u i d p a r t i c l e  trapped  i n a low pressure  factor  in  determining  w i l l occur.  the  eddy  will  be  timeremains  an  important  i f and to what extent  cavitation  In the absence of any n u c l e a t i o n s i t e s ,  formation of vapour a f t e r pressure r e d u c t i o n i s due  dust  of zero net normal s t r e s s at a p o i n t i n the  Since bubble  dependent  forces,  to the e x i s t e n c e of a "thermodynamically  the  delayed  metastabl.e"  state.  3.  "incipient  drawdown" - the  point  of  "irrotational"  downflow  incipient  entrainment. Consider  the  s w i r l ) of a l i q u i d or  downcomer.  critical  (without  from a p o o l , through a v e r t i c a l  For  each  pool  depth  f l o w r a t e at which the l i q u i d  there  interface  drain  exists a suddenly  breaks down, and a cone-shaped i n t e r f a c e forms above the entrance.  The  s t r a t i f i e d gas or vapour above the  liquid  s u r f a c e becomes e n t r a i n e d i n the l i q u i d at the v e r t e x of the cone.  7  This drawdown  critical  flowrate,  (abbreviated  ID),  f o r the case of a i r - w a t e r near the tube entrance. depths  above  defined  (H/D  flow  i n t o a l i q u i d l e v e l at or  With water f l o w i n g at very  the entrance  l e s s than 0.25  the maximum water flow phenomenon  (1 or 2 mm),  part  F i g u r e 2. negligible tube  The  is  the  magnitude  r i s e upwards.  g r e a t e r than 0.25)  At  by  a  low  film  i s a maximum f l o w r a t e "circular of  weir"  air  At higher  governed  by  incipient  on  entrainment  is  in  the  pool depths  (H/D  with no net  ( F i g u r e 2b).  Any  Pch)  liquid  attempt  from  or  above  the  at based on the assumption that  from weir flow to i n c i p i e n t  at  curve  w i l l result in  which happens only when the flow  level  the  i n c r e a s e i n the l i q u i d f l o w r a t e .  Figure 2 i s arrived  continuous,  pool  drawdown, shown on  i n c r e a s i n g the chamber pressure  transition  given  curve  bubbles present  the l a r g e s c a l e entrainment of the a i r  the  weir  regime.  to i n c r e a s e the f l o w r a t e above values given by the  interface,  [4])  the maximum f l o w r a t e at a given  upper p a r t of the same curve  (by  pool  circular  or f a l l i n g  i n t h i s regime as any  quickly  depth  of  flowrate i s  where the l i q u i d flows down to  every pool depth, there  by the lower  effects.  is limited  (Figure 2a),  the  low  as suggested by Souders  the l i q u i d l e v e l i n an annular For  incipient  i s i l l u s t r a t e d in F i g u r e 2  s u s c e p t i b l e to s u r f a c e t e n s i o n depths  as  near  drawdown i s is  the tube entrance.  into In  a  this  8  study the phenomena of weir flow and i n c i p i e n t are  described  solely,  by  with the i m p l i c a t i o n that  the term the  drawdown  i n c i p i e n t drawdown,  curve  joining  the  two  phenomena i s continuous. The  transition  from weir flow to i n c i p i e n t drawdown  i s not w e l l d e f i n e d when the l i q u i d l e v e l much  lower  than  the  entrance.  d r a i n i n g from a v e s s e l (under only)  is  shown  observed. wall  of  the  tube  in  an  Eventually  necking occurs at the vena depth  liquid  rises  effects  significantly  following  sequence  is  annular as  the  or  weir  regime  pool  depth  rises,  contracta  ( F i g u r e 3b).  will  bridging,  and  the drawdown curve  the  pool  depth  (Figure 3d).  Despite  persist  in  the  tube  well  region,  flowrates, irrespective  annular  below the pool  Any mechanism f o r i n c r e a s i n g the f l o w r a t e by  i n c r e a s i n g the pressure i n the upper v e s s e l limited  As  The Froude number does not i n c r e a s e  after  from  interface.  be  gravity  As the f l o w r a t e i n t o the  the b r i d g i n g of the annular a i r - f i l l e d flow  of  f u r t h e r , the vapour core b r i d g e s with  (Figure 3 c ) .  diverges  the  example of water  I n i t i a l l y a t h i n f i l m of water runs down the  (Figure 3a).  the  the  i n F i g u r e 3.  upper chamber i s i n c r e a s e d  An  i n the tube i s  by  the  "flooding" of  drawdown will  drawdown  f l o o d i n g , the l i q u i d  curve. occur  At in  will very  again high  the  tube,  ( F i g u r e s 3e and 3 f ) .  During  f i l m b r i d g e s throughout  i t s whole  9  vertical  extent, and the tube flows f u l l  for i t s e n t i r e  length. Both  bridging  approximately  0.5  number approximately  (Froude  number  f o r .Freon-11) 2.0  from  level  independent  is  and f l o o d i n g  0.25.  maintained  at  However, the  tube  Figure  (Froude  if  the  entrance  of f l o w r a t e (by lowering the p r e s s u r e i n the  upper v e s s e l ) , a smooth but d e f i n i t e t r a n s i t i o n bridging  at  [1]) phenomena occur above  a d i m e n s i o n l e s s pool depth of liquid  observed  will  be  observed,  as  shown  without  previously  in  2.  1.3 Review Of P r e v i o u s Work A  literature  concluded  that  c o u l d be found. work on r e l a t e d  1.3.1  search  was  conducted  and  no systematic study of t h i s  it  was  instability  However, v a r i o u s authors have p u b l i s h e d topics.  I n s t a b i l i t i e s In Two-Phase Systems B e r g l e s [2] has p u b l i s h e d a review of p r e v i o u s work  done i n t h i s area. and either  hydrodynamic static  secondary  or  or  T h i s review  included  instabilities dynamic,  compound  nature.  both  thermal  characterized and No  of  a  as  primary,  mention  was  10  made  of  1.3.2  Cavitation Oba  a  any  condition.  micro-orifice, The  effect  instability.  of  under  prescribed  orifice  diameter  c a v i t a t i o n number, given  (Pch  was  entrance  [5] s t u d i e d c a v i t a t i o n i n water flowing  horizontal  desinent  cavitation-induced  through nuclei on  the  by  - Psat)/(pV /2) 2  investigated. Lienhard  varying  the  r a t i o and  the  r a t i o of o r i f i c e - d i a m e t e r - t o - n u c l e a t i o n - s i t e - s p a c i n g  in  magnitude  a  [6]  did  a  similar  study  of the o r i f i c e - t o - p i p e - d i a m e t e r  horizontal  submerged o r i f i c e .  at desinence was  The  c a v i t a t i o n number  c o r r e l a t e d to the product of these  two  ratios.  1.3.3  I n c i p i e n t Drawdown Souders [4]  drawdown  as  fractionation  it  experimentally related  column.  The  to  studied  rotational  downcomer was  three d i s t i n c t c o n d i t i o n s of f l u i d head. operating  as a c i r c u l a r weir at low  incipient  flow  in  a  modelled under These  were;  depths, o p e r a t i n g  as  11  a  free  running  orifice  o p e r a t i n g as an o r i f i c e Davidian development  [7] of  the  experimental  non-circulatory  phenomenon i s e s s e n t i a l l y with  intermediate  depths, and  running f u l l at high depths.  did a  at  incipient  work  on  waterspout. drawdown  of  other  This  reversed,  l i q u i d e n t r a i n e d upwards by the flow of a gas  i n t o a tube, rather than gas e n t r a i n e d downward flow  the  a liquid.  by  the  The r e s u l t s seem to agree w e l l with  published  air-water  incipient  drawdown  irrotational  incipient  experiments. Harleman [8]  analyzed  drawdown using p o t e n t i a l flow, m o d e l l i n g the entrance as a point sink.  An experimental study was then  u s i n g two v e r t i c a l l y  stratified  critical  entrainment p o i n t .  rounded  entrance  diameter  tube.  Kalinske  geometries  performed  l i q u i d s , t e s t i n g f o r the  Re-entrant, sharp-edged and were t e s t e d f o r a 2.54 cm  [9] used r e - e n t r a n t and sharp-edged  pipes  of v a r i o u s diameters and l e n g t h s i n a study of i n c i p i e n t drawdown. closed  While  vessel  draining  with  a  an a i r - w a t e r mixture from a  metered  air inlet,  the  air  entrainment r a t e a t i n c i p i e n t drawdown was measured. Simpson [ 1 ] , i n c i p i e n t drawdown. dependence  of  reviewed  previous  work  done  A l s o reviewed was work done on  on the  bubble r i s e v e l o c i t y on Froude number i n  v e r t i c a l pipe flow.  Bubble  rise  velocity  is  usually  12  defined  in  a stagnant pool of l i q u i d and  mainly of l i q u i d and  shape, and  In  a  local  s u r f a c e t e n s i o n , v i s c o s i t y , bubble  the diameter  downflowing  of the  liquid,  constraining  a bubble  l i q u i d v e l o c i t y at the bubble  calculated  rise  velocity.  numbers ranging from 0.31 prevent  pressure  size  tube.  w i l l r i s e where the is  less  than  the  Simpson s t a t e d that Froude  to 1.0  pulsation  should be and  avoided  vibration)  vertical  pipe flow where entrainment  might be  possible.  1.3.4  is a function  of  air  (to  in a l l  or  vapour  Miscellaneous Studies It  seems that the flow f i e l d  i n an o r i f i c e has  not  been s o l v e d n u m e r i c a l l y (at high Reynolds numbers) u s i n g the  Navier-Stokes  dimensional  equations.  hydrodynamic  However,  flow  theory,  been obtained f o r both r e - e n t r a n t orifices  and  Vallentine  [10]).  layer of  effects,  the l o c a l  sharp-edged These  velocity  siphons.  [11],  s o l u t i o n s have  (Borda's  orifices  solutions  two-  mouthpiece)  (for  neglect  example boundary  but g i v e an order of magnitude estimate  equation) throughout Kelly  using  (and  pressure  from  Bernoulli's  a downcomer entrance.  studied  extensively  the o p e r a t i o n of  In p a r t i c u l a r , the e f f e c t of d i s s o l v e d a i r and  gases i n the siphon flow  of  water  was  investigated.  13  Several  postulates  frequency v i b r a t i o n s Bharathan [12] several  were  (noise) o f t e n found and  W a l l i s [13]  experimental  c o u n t e r c u r r e n t annular with  made as to the source of high  studies flow.  i n siphons. have  into  the  Bharathan  conducted subject  was  of  concerned  f l o o d i n g and i n t e r f a c i a l shear s t r e s s phenomena i n  air-water  flow,  condensation  while  Wallis  studied  e f f e c t s i n steam-subcooled  additional  water flow.  1.4 Scope Of The Present I n v e s t i g a t i o n After  conducting  decided t o conduct the  flow  draining  this  literature  a systematic  instability  that  search, i t was  experimental  fluids  A c c o r d i n g l y , an experimental  from  and  flow  Flow  mapping of any regimes by the  measurement of the d i m e n s i o n l e s s and  a  r i g was  designed and c o n s t r u c t e d to model t h i s occurrence. visualization,  of  was presumed t o e x i s t when  (without s w i r l ) n e a r - s a t u r a t e d  chamber or v e s s e l .  study  flowrate,  pool  depth  s u b c o o l i n g c o n s t i t u t e d the scope of the experimental  work.  The  measurement  of  subcooling  measurement of the chamber pressure and  entailed  temperature.  The r e s u l t s of the i n v e s t i g a t i o n h o p e f u l l y applied  by  engineers  in  attempts  the  to  c o n t r o l the occurrence of the i n s t a b i l i t y .  can  be  p r e d i c t and/or  14  II.  EXPERIMENTAL  APPARATUS  2.1 General Concept The apparatus  d e p i c t e d on the flowsheet  was used t o i n v e s t i g a t e the flow regimes. the  experimental  F i g u r e 5.  P i c t u r e s of  r i g and i n s t r u m e n t a t i o n are shown i n  Two loops  circulation  in Figure 4  are  shown  on  the  loop and a siphon loop.  flowsheet;  In the c i r c u l a t i o n  loop, the l i q u i d was e x t r a c t e d from the lower v e s s e l a  circulation  pump  and passed  through a c o - a x i a l  exchanger i n t o the overflow v e s s e l . was  maintained  in this  vessel  A by  p a s s i n g back i n t o the lower v e s s e l .  a  constant  an  by heat  level  overflow  line  In the siphon loop,  the f l u i d was e x t r a c t e d from the overflow v e s s e l up i n t o the vacuum chamber (Figure 6) where i t d r a i n e d an  attached  entrance  downcomer t e s t s e c t i o n . overflow  weir  geometry  ( F i g u r e 7)  The downcomer emptied  i n the lower v e s s e l .  was evacuated Compared using t h i s  from a vacuum  into  the  into  an  Both the i n l e t and  d i s c h a r g e of the siphon were kept submerged. loop was primed  through  accumulator  The siphon  tank,  which  p e r i o d i c a l l y by a vacuum pump. to  alternative  system t o  methods,  advantages  of  achieve n e a r - s a t u r a t e d c o n d i t i o n s  in the vacuum chamber were:  15  (a) - r e g u l a t i o n of the l i q u i d loop  by  flowrate  simply  (the  controlling  through  controlling  temperature i n the  the  heat  the pressure  the  siphon  cooling  exchanger.  Then  i n the apex of the  vacuum chamber), the l i q u i d  water by  siphon  properties  could  be a d j u s t e d to achieve n e a r - s a t u r a t i o n . (b) - s a t u r a t e d  vapour c o n d i t i o n s c o u l d be maintained  the vacuum chamber d e s p i t e the presence condensibles infiltrated  (ie.  air  leaks)  of any  that  may  the system, by c o n t i n u o u s l y  a s m a l l amount of vapour from  the  in non-  have  evacuating  vacuum  chamber  and generating a d d i t i o n a l s a t u r a t e d vapour. (c) - pressure  control  independent of any a siphon  in  the  vacuum  f l u c t u a t i o n s due  was  to pumping,  as  (with a nominal d r i v i n g head of 60 cm)  was  used to provide the flow through  2.2  chamber  the t e s t s e c t i o n .  Working F l u i d As water was  first  r e a d i l y a v a i l a b l e and non-toxic  considered  operating  the  temperature)  for  siphon would  the loop have  e l e v a t i o n of approximately vessel  working with  water  required 10 m  fluid.  a  (between  (at  i t was  However, ambient  difference the  in  overflow  and vacuum chamber) f o r the siphon apex pressure  16  to  reach  Running decreased  the  saturation  at  higher  this  insulation  vapour  water  height,  pressure  of  temperatures  but  heating  water.  would  have  elements  and  would have added to the o v e r a l l  complexity.  The most s e r i o u s problem would have been the e f f e c t s dissolved Air  may  a i r i n the water, as r e v e a l e d by K e l l y [11].  have come out of s o l u t i o n near the apex  siphon,  of  lowering  the  average  preventing  s a t u r a t i o n from o c c u r r i n g  height.  This  phenomenon  would  fluid at have  required  apex  to be c o n s i d e r a b l y l a r g e r than 10 m.  chosen as the  common  working  and apex  siphon,  a  density given  f o r water, measured on the  1  the  a  heights  Freon-11 ,  of  rising  leg  r e f r i g e r a n t , was  fluid.  It  has  the  of  the  eventually following  characteristics:  (a) - a poor solvent of both a i r and water (b) - low and  toxicity usage  (c) - low 23.8  boiling  normal c o n d i t i o n s of handling  (group 5a - Underwriter's  Classification and Vapours  under  Laboratories  of Comparative L i f e Hazard of Gases  [14]) point  at  atmospheric  pressure  of  °C  ' F r e o n - l l , CCL F ( t r i c h l o r o f l u o r o m e t h a n e ) trademark of the Du Pont c o r p o r a t i o n 3  i s a registered  1  (d) - r e l a t i v e l y  low  7  -  cost  (the  l e a s t expensive of the  Freons) (e) - low v i s c o s i t y and s u r f a c e t e n s i o n ( f ) - e x c e l l e n t thermal and chemical s t a b i l i t y (g) - inflammable, non-conductive and n o n - c o r r o s i v e (h) - w e l l documented thermodynamic p r o p e r t i e s There were some disadvantages to u s i n g Freon-11 the  working  fluid.  It  was  still  purchase compared to water, and properties material.  necessitated For example,  the elastomer  neoprene  very expensive to  i t s peculiar  careful  choice  the  plastic  both  react  as  of  chemical apparatus  polyethylene unfavourably  and with  Freon-11.  I t was very important to keep  the.  clean  as  Freon-11  f o r grease and  oils.  The presence of these  has a great a f f i n i t y substances  in  apparatus  sufficient  q u a n t i t i e s would have s i g n i f i c a n t l y a f f e c t e d the Freon's saturation  2.3  properties.  P i p e , Tubing, Hose, And 1.3  Fittings  and 2.5 cm PVC pipe and f i t t i n g s were used f o r  the Freon c i r c u i t  because  and easy to assemble.  PVC  they  were  readily  available  b a l l v a l v e s with t e f l o n seats  were used f o r t h r o t t l i n g and s h u t o f f  purposes.  18  The  tubing i n i t i a l l y  s e c t i o n was tubing. to  3.2  It  cm  was  Freon-11  I.D.  chosen f o r the downcomer t e s t by  chosen  under  a  slight  fitted  long  polycarbonate  as  a  vacuum,  replacement.  over  exposed  severe  crazing  G l a s s tubing of 2.54  f a s t e n e d to the tube where seal  m  found that when the t u b i n g was  (micro-cracking) o c c u r r e d . was  1.8  the  the tube.  Brass vacuum  cm  collars chamber  The  To allow v i s u a l i z a t i o n of leg  of  a simple c o - a x i a l s h e l l  and  a l s o f a b r i c a t e d out of g l a s s tube.  heat exchanger was  tube type made  from  2.5  1.3  pipe  (tube),  cm  were O-ring  vapour formation, the top p o r t i o n of the r i s i n g the siphon was  copper  cm  copper with  pipe  (shell)  b u i l d i n g supply water was  and  brass Swagelok heat  exchanger f i t t i n g s s e a l i n g the ends of t h e , s h e l l .  2.4  I.D.  Cold  used as the c o o l i n g medium.  Vacuum Chamber And V e s s e l s The  vacuum  chamber  polycarbonate b e l l p l a t e , with an present risen  was  a 17 l i t r e  to  the  to  Nalgene  j a r ( F i g u r e 6) p l a c e d over a mounting  O-ring  providing  the  seal.  i n the chamber d u r i n g the experiments  vapour i s denser inlet  used  top than  of  Any  air  would have  the vacuum chamber, s i n c e Freon air.  the vacuum pump was  Therefore  the  extraction  l o c a t e d at the top of the  chamber, where i t would keep the l i q u i d - v a p o u r i n t e r f a c e  19  c l e a r of non-condensibles. A f a l s e f l o o r made plates  from  two  perforated  aluminum  (with a f i n e brass screen sandwiched between) was  l o c a t e d around spaced  the t e s t s e c t i o n entrance.  vertical  this false remove  straightening  floor.  large  The  scale  vanes  arrangement  turbulence  prevent the b u i l d u p of s w i r l .  Three e q u a l l y  were a t t a c h e d to was  from  intended  to  the pool and to  The incoming  j e t of Freon  was d i s s i p a t e d d i r e c t l y a t the chamber i n l e t by  a  wire  basket f i l l e d with brass wool. Some bell  crazing  problems  j a r s , but these were minimized  mounting  inherent  propagate  encountered  with the  by t a k i n g c a r e  when  the j a r s so as not t o form any small c r a c k s i n  the w a l l s of the j a r . their  were  When present, these c r a c k s  stress  concentrations)  upon f u r t h e r exposure  would  (with rapidly  to the Freon.  An aluminum c o n t a i n e r with 2.5 cm threaded  nipples  a t t a c h e d was used f o r the overflow v e s s e l , while a spare bell  j a r was used f o r the lower v e s s e l .  Loose  lids  were  to  placed  evaporation  over  these  vessels  minimize  losses.  A 51 cm diameter  by 152 cm high m i l d s t e e l p r e s s u r e  v e s s e l was used f o r the vacuum accumulator equipped  fitting  tank.  I t was  with an analog p r e s s u r e gauge f o r l o c a l vacuum  indication.  20  2.5  Pumps An E a s t e r n Model MD-80 magnetic d r i v e pump was used  to c i r c u l a t e the Freon. a  polypropylene  was  T h i s was a s e a l - l e s s pump  c a s i n g and i m p e l l o r .  with  Maximum c a p a c i t y  r a t e d at 1.0 l i t r e s / s with a s h u t - o f f head of 10 m.  The pump was d r i v e n by a 249 W at 3450 rpm motor. A Bendix Model AAF vacuum  pump  was  used  direct-  coupled to a 373 W at 1800 rpm motor.  2.6  Instrumentation The  i n s t r u m e n t a t i o n measured the chamber p r e s s u r e ,  temperature, through of  and  pool  depth,  the  amplitude  (see F i g u r e 4 ) .  Temperature Measurement Temperature was measured with an Omega  general (RTD)  flowrate  the siphon loop, and the peak-to-peak  downcomer f l o w r a t e f l u c t u a t i o n s  2.6.1  average  purpose coupled  indicator. (± 0.1°C  platinum with  The  resolution)  acquisition  system.  PR-11  r e s i s t a n c e thermometer probe  an, Omega  indicator  Type  Model  199p2  digital  had an analog output o p t i o n  for interfacing  with  the  data  21  2.6.2 Pressure Measurement Chamber Bourns Model pressure  pressure 441  was  initially  measured  bellows/potentiometer  transducer,  with  a  type  range of 0-101  transducer had a s t a t i c e r r o r band of 1.2% including  the  effects  of  r e s o l u t i o n and r e p e a t a b i l i t y .  that  instrument  this  measure the  small  characterize  the  kPa.  The  scale,  friction,  I t was  found  was not s u f f i c i e n t l y a c c u r a t e to  pressure  differences  subcooling.  was then connected  absolute  full  linearity,  hysteresis,  with a  necessary  to  A simple water manometer  t o the system.  I t was  found  to  be  a c c u r a t e f o r s t e a d y - s t a t e measurements but clumsy to use if  the chamber pressure f l u c t u a t e d .  then used  only  for  transient  operating  characteristics  of  The transducer  measurements the  system  when were  was the  being  studied.  2.6.3 Depth Measurement Pool depth (± 1.0 mm)  in  against  the a  vacuum  stainless  mounted on the f a l s e f l o o r .  chamber  was  measured  s t e e l graduated  scale  22  2.6.4  Flowrate Measurement Average flowrate i n the siphon  with  a  Signet  MK  sensor was  mounted i n a 1.3  with 30 pipe diameters the sensor. analog  The  sensor was  conditioner  a c q u i s i t i o n system. was  cavitation cm diameter  effects. PVC  fitting  for  coupled with a Signet MK indication interfacing  and  a  with  309  MK  314-6  the  data  T h i s method of f l o w r a t e measurement  chosen because c a v i t a t i o n occurs when n e a r - s a t u r a t e d  liquid was  measured  l e n g t h of s t r a i g h t p i p e preceding  "flometer" for l o c a l  signal  was  315 paddlewheel " f l o s e n s o r " , with an  open paddle design that minimized The  loop  flows through an o r i f i c e p l a t e or a v e n t u r i .  found  that  this  accurate r e s u l t s velocity  in  instrument  gave  r e p e a t a b l e and  (± 0.003 l i t r e s / s ) p r o v i d i n g the  the  sensor was  It  kept above 30 cm/s  fluid (Froude  number of 0.17). F l u c t u a t i o n s i n downcomer with  a  ThermoSystem  Inc.  Model  were  measured  1010-A  constant  temperature  anemometer coupled with a DISA  linearizer  and  analyzer.  A  TSI  a  Nicolet  The a n a l y z e r  d i g i t a l plotter  1  flowrate  used  f o r hardcopy  Model  1230  F a s t F o u r i e r Transform  Model  Model  660A  FFT  a  Tektronix  1  55D10  spectrum  Model  4662  output.  hot f i l m sensor was  used as the  23  anemometer  probe.  constructed  This  from  a  quartz  platinum f i l m band at because  of  rigidity.  conical  the  shaped  rod  cone  i t s ruggedness,  with  sensor  was  a quartz-coated  t i p , and spatial  was  chosen  resolution  and  The probe was p l a c e d at the d i s c h a r g e of  the  downcomer, i n the f u l l y developed region of the flow. The  TSI  anemometer  unit  circuit  Wheatstone bridge arrangement  with  variable  resistance  leg  and  a  decade  v a r i a b l e l e g (Figure 8 ) .  c o n s i s t e d of a  the  probe as  as  one  the other  The bridge had a feedback loop  which s u p p l i e d s u f f i c i e n t power to r a i s e  or  lower  the  probe r e s i s t a n c e so that the bridge was kept i n balance. V a r y i n g the decade r e s i s t a n c e v a r i e d the probe o p e r a t i n g resistance,  and t h e r e f o r e the probe temperature.  the heat  transfer  linearly  with  rate  the  l i n e a r i z e r was used  from  liquid to  the  probe  velocity  create  a  varied  Since non-  at the probe, the  linear  relationship  between f l o w r a t e and output v o l t a g e .  2.6.5 Data A c q u i s i t i o n The average  signals  from  flowrate  interfaced  with  acquisition minicomputer.  System the  pressure,  measurement the  system  devices  department's  and  temperature and  processed  were  then  Neff Model 620 data by  a  PDP-11/34  24  Provision  was  shown i n F i g u r e 9. pool  depth,  made  f o r the two types of sampling  The f i r s t  prompting  type  was  at  five  seconds  at  a  sampling  pool,  temperature  and  flowrate  r a t e of 10 Hz.  second type was while lowering or r a i s i n g the  constant  f o r the pool depth and manometer  reading and then sampling the temperature, for  a  the  The  depth  of  sampling the p r e s s u r e (from the t r a n s d u c e r ) , and f l o w r a t e f o r 50 seconds  at  a  sampling  r a t e of 1 Hz.  2.6.6 Photographic' S t u d i e s Film  footage was shot of the regimes u s i n g a Bolex  16 mm c i n e camera (at 24 frames per second). was  used  specific purposes.  for  initial  analysis  frames of i n t e r e s t developed A  HaRco  Mini-Max  of  cassette  the regimes, with for presentation  the  preparation  d e s c r i b i n g the regimes.  Still  some regimes were taken with a standard 35 mm  u s i n g 400 ASA b l a c k and white  film  Model CTC-3000 black and  white video camera was used f o r video  of  This  film.  of  a  pictures camera  25  2.7  Assembly The  And I n i t i a l  components  assembled  Testing of  the c i r c u l a t i o n  and the loop f i l l e d with t a p water.  loop  were  The  heat  exchanger  response was t e s t e d with the c i r c u l a t i o n pump  running.  Leaks  subsequently A  in  the  system  were  amount  of  Freon  was then t e s t e d i n the  c i r c u l a t i o n loop t o observe whether would  Some problems reduced  seriously  occurred  for a  seize,  v a p o u r - l o c k i n g and  impair  when  pump performance.  the Freon  flowrate  ambient.  Occasionally  the pump  but i t was r e p a i r e d simply by d i s m a n t l i n g  the l i q u i d end of the pump and p r y i n g l o o s e the impellor  assembly  s u r f a c e s were  was  l e n g t h y p e r i o d of time, when the l i q u i d  temperature was near would  and  repaired.  small  cavitation  noted  then  from  the c a s i n g .  sanded  smooth"  The  and  plastic roughened  the pump r e -  assembled. Subsequently  the  siphon  loop  t e s t e d with both water and Freon.  was  After  assembled and running  water  in the apparatus, i t was found that i t was i m p o s s i b l e t o completely  drain  the system.  leave small amounts of water then  could  then  find  Condensation alone would  i n the p i p i n g .  i t s way  to  This  water  the v a p o u r - l i q u i d  i n t e r f a c e i n the vacuum chamber (Freon-11 and water immiscible)  where  i t s entrainment would g r o s s l y  are  affect  26  any  observed It  flow  was  accumulator  found tank  control  than  vacuum  chamber.  The  conditioning the  as  at a  this  buffer  stage  program elements  apparatus  was  was  the  then  ready  vacuum  and  in  the  the  vacuum  collection  the  the  an  vacuum  pump t o  Finally  placed for  using  much b e t t e r  installed  written. were  that  provided  direct-coupling  instrumentation  acquisition  and  regimes.  the  data flow  chamber, of  data.  27  III.  PROCEDURE  3.1 Routine Experimental P r e p a r a t i o n After  s e v e r a l t e s t runs using water as the working  f l u i d , a r o u t i n e procedure was developed  f o r p l a c i n g the  Freon i n t o the system while minimizing the water to  and other contaminants.  presence  The procedure,  of  referring  F i g u r e 4, was t o :  (1) - d r a i n the p i p i n g . (2) - d i s c o n n e c t the unions c o u p l i n g the  piping  to the  v e s s e l s , and empty a l l v e s s e l s . (3) - remove  any r e s i d u a l s o l i d s from the v e s s e l s , ( i e .  rust and c h i p s  of  plastic)  and  wipe  clean a l l  s u r f a c e s of any grease and d i r t with rags soaked i n Freon. (4) - disconnect the heat exchanger water  from  any  low  spots  and blow out r e s i d u a l that  d i d not  drain  completely. (5) - reconnect the p i p i n g . (6) - pour the Freon through a c l o t h f i l t e r plastic causes  f u n n e l , i n t o the overflow v e s s e l . the  circulation pump.  placed  liquid loop  to  flow  down  in a Gravity  through  the  t o the lower v e s s e l , priming the  28  (7) - t u r n on the heat (Figure 4). initial  exchanger  by  opening  valve  V5  T h i s a l l o w s the Freon t o p i c k up some  s u b c o o l i n g , which minimizes  evaporation  in  the v e s s e l s and prevents c a v i t a t i o n and vapour-lock d u r i n g pump s t a r t u p . (8) - c i r c u l a t e  the Freon u n t i l  i t a c h i e v e s i t s maximum  possible subcooling. (9) - shut the c i r c u l a t i o n pump down v i s i b l e water and contaminants v e s s e l , where they have now  It  was  contaminants and  were  found  most  present  o f f any  i n the lower  accumulated.  solid  were a t t r a c t e d t o t h i s t h i n f i l m of  water,  removed.  of  I t soon became e v i d e n t that  complete removal of the water was not pump  skim  the v i s i b l e  easily  that  and  suction  tended  required  as the  not t o e n t r a i n and c i r c u l a t e  these  i m p u r i t i e s when the amounts present were very s m a l l . I t was during  necessary  to  externally  prime  water runs using the priming connection a t v a l v e  V3.  A i r - l o c k s prevented  the  overflow v e s s e l down t o the lower v e s s e l .  as  mentioned  externally  the g r a v i t y  previously  prime  due t o i t s lower The  the pump  i t was  flow of water  not  However,  required  the pump when running Freon,  from  to  probably  surface tension.  vacuum chamber and t e s t  section  were  aligned  29  and  l e v e l l e d and the video equipment and l i g h t i n g given  f i n a l preparation. "signed  on"  and  The  data  acquisition  the computer  program  system  was  prepared f o r  execution. The vacuum accumulator  tank was then evacuated with  the vacuum pump t o approximately loop  was  then  primed  to  50  kPa.  the d e s i r e d  The  pool depth by  c l o s i n g v a l v e V8 and opening needle v a l v e V7. amount  of  vapour  was  generated and l o s t  vacuum pump) d u r i n g t h i s i n i t i a l chamber of  period  siphon  A  large  (through the  as  the  vacuum  and t e s t s e c t i o n were c o o l e d t o the temperature  the Freon.  Subsequently a small amount  of  gas was  b l e d c o n t i n u o u s l y from the vacuum chamber t o account f o r the air  removal  of any non-condensibles  initially  present,  l e a k s , and any s t e a d y - s t a t e vapour g e n e r a t i o n . Great care had t o be taken t o ensure that both ends  of  the siphon remained  level.  If  either  submerged below the l i q u i d  end  became  uncovered due t o a low  l e v e l i n e i t h e r the overflow or lower v e s s e l s , Freon  charge  Freon  an  air-  would shoot up i n t o the vacuum chamber as  i t became p r e s s u r i z e d . The  cooling  throttling within building  water  flowrate  was  adjusted  by  v a l v e V5 t o c o n t r o l the amount of s u b c o o l i n g  the vacuum supply  chamber.  water  The  temperature  minimum Freon temperatures  variation  of  cold  with season allowed  of 11°C i n winter months, but  30  only  13°C  in  temperature Higher  summer  months.  observed  temperatures  which caused  in  caused  The  maximum  Freon  the vacuum chamber was 16°C. excessive  vapour  generation,  stoppage of the siphon flow at the apex due  to the absence of l i q u i d .  3.2 C a l i b r a t i o n The  data  experiment  acquisition  measured  temperature  chamber  Tch, and  relationship by  the  device existed  data  used  pressure  for this  Pch,  chamber  siphon loop f l o w r a t e Q, with the  chamber pool depth H measured Assuming  system  manually.  linearity,  the  following  between the measured v o l t a g e s read  acquisition  system  and  the  variables  measured:  Pch(Pa)  = K1xPV + B1  Tch(°C)  = K2xTV + B2  Q ( l i t r e s / s ) = K3xQV.+ B3  where  PV,  TV,  and QV were the v o l t a g e s i g n a l s  the data a c q u i s i t i o n 0-1.0  volt  system ( a f t e r a t t e n u a t i o n i n t o  D.C. range)  and  Pch,  calculated  values ( i n r e a l u n i t s )  file  the  by  read by  computer.  K1,  Tch, and Q were the  output  K2,  the  and  to  the  data  K3  were  the  31  c a l i b r a t e d p r o p o r t i o n a l i t y constants and B1, were  the  calibrated y-intercepts.  a c q u i s i t i o n system with s e v e r a l Tch,  and  Q,  3.3  known 'values TV,  linear regression  s o l v e f o r the s i x c a l i b r a t i o n  and  B3  By running the data  the measured values of PV,  entered i n t o a "best f i t "  B2,  of  Pch,  and QV were program  to  constants.  Measurements With F i x e d Pool Depth For  the  purposes  of  flow  mapping, a reading of  chamber p r e s s u r e , temperature,  pool  flowrate  was  (or  measurement  Froude at  measurements  number)  constant the  pool  pressure  depth  and  required depth.  was  account  the  used.  This  transducer  day-to-day  calculated variation  for For  each these  signal  n e g l e c t e d and the manometer-indicated value pressure  siphon  of  was  chamber  value took in  into  atmospheric  pressure. The  Freon  l e v e l was  where a c h a r a c t e r i s t i c adjusting  the  chamber  r a i s e d to a d e s i r e d pool depth  flow  occurring  by  p r e s s u r e using v a l v e V7 and  the  Froude number u s i n g v a l v e V4. lower  regime  Valve V6  the pool depth i f an overshoot  c o o l i n g water flow  was  then  was  was  opened  had o c c u r r e d .  adjusted  amount  of  reached  the d e s i r e d l e v e l of s u b c o o l i n g .  until  a  vapour g e n e r a t i o n had occurred and the The  to The  small Freon  p o o l depth  32  and the manometer computer.  reading were  After  waiting  then  temperature of  was  instructed  the computer. the  computer  particular  to  and siphon f l o w r a t e .  the temperature  into  the  approximately 30 seconds f o r  any t r a n s i e n t s t o d i e out, the data (Figure 9)  entered  acquisition record  Time  system  the  chamber  averaged  values  and f l o w r a t e were then c a l c u l a t e d by  A d e s c r i p t i v e code was then entered which  described  into  qualitatively  the  regimes observed d u r i n g the measurement.  presence was noted of entrainment, c a v i t a t i o n ,  The  incipient  drawdown, upward or downward d i s c h a r g e of vapour and any special  characteristics  of  the  observed  regimes.  Comments as to the q u a l i t y of the p a r t i c u l a r measurement were  also  recorded.  A video r e c o r d i n g of each  regime  was made d u r i n g t h i s p e r i o d .  3.4 Measurement Of Downcomer Flowrate F l u c t u a t i o n s The overflow weir i n the lower v e s s e l  was  removed  for these measurements and a hot f i l m probe was  inserted  i n t o the d i s c h a r g e of the t e s t s e c t i o n . spectrum  The l i n e a r i z e r ,  a n a l y z e r , and anemometer u n i t were then turned  on and warmed up f o r at l e a s t two  hours  prior  to  the  t a k i n g of d a t a . The it  Freon  was c i r c u l a t e d through the system  reached a temperature  of  approximately  13°C.  until The  33  "cold"  resistance  of  the  hot  film  probe  was  then  measured and the o p e r a t i n g r e s i s t a n c e set at a value 0.2  ohms  higher.  The  probe  was  compensated, t h e r e f o r e care had to be the  not  of  temperature  taken  to  ensure  temperature of the Freon d i d not vary f a r from  13°C  when measurements were taken. The probe and l i n e a r i z e r were c a l i b r a t e d with Freon flowing through the c i r c u l a t i o n phase  regime,  flowrate. "zero", output  with  the  "gain",  voltage  proportional  from  to  liquid  f l o s e n s o r p r o v i d i n g the known  The l i n e a r i z e r was the  loop i n a s t a b l e  and  c a l i b r a t e d by s e t t i n g  the  the  "exponent"  linearizer  flowrate  in  the  so that the  was  linearly  the downcomer, with z e r o  f l o w r a t e g i v i n g zero v o l t a g e . The f l o w r a t e , p o o l depth and s u b c o o l i n g adjusted  in  the  f l u c t u a t i o n was  were  downcomer u n t i l the l a r g e s t r e a l observed  on  the  analyzer.  then time  Hardcopy  output of the flowrate i n the time domain (Froude number vs.  time)  and i n the frequency domain (RMS  frequency) was produced. produced and  after  performing  frequencies.  The frequency domain p l o t  was  ensemble averaging 16 time domain p l o t s a The  spectral RMS  analysis  power was  root of the ensemble average magnitudes.  power v s .  of  for  dominant  formed from the square the  squared  spectral  34  IV. 4.1  EXPERIMENTAL RESULTS  Flow Mapping Typical  measurements  of  regimes  obtained  at  constant pool depth are shown i n F i g u r e s 10 to 14. flow  regimes  are  grouped  according  r e s p o n s i b l e f o r the presence with  Figure  The  of vapour i n the  pool  subcooling  present  SC  entrance, "violent"  regimes are mapped on diagrams  dimensionless  described  to the mechanism  14 showing the l o c u s of the most  regime observed.  The  depth  vs.  during  statistically  Froude the  of  number.  The  measurements  is  on the diagrams by s t a t i n g  the  number of data p o i n t s N, the range of s u b c o o l i n g of points  ( i f a p p l i c a b l e ) , the average  value of s u b c o o l i n g  SCAVG and the standard d e v i a t i o n of the v a l u e s inset  is  included  on  regime being mapped. range than  of  values  The  SD.  An  diagrams to i l l u s t r a t e results  presented  n e a r - s a t u r a t e d Freon-11  the  cover (SC  a  less  45). Re-entrant,  been t e s t e d . extensively when the Also,  for  the  the  the  The  rounded, and  r e - e n t r a n t entrance  because  regimes  sharp-edged entrances have  it  was  involved  re-entrant  was  investigated  the f i r s t geometry t e s t e d , were  shape  completely  unknown.  allowed unobstructed  flow  v i s u a l i z a t i o n a t the vena c o n t r a c t a . F i g u r e s 10  to 17  show  a  reference  curve  from  35  experimental The  incipient  drawdown data of K a l i n s k e [ 9 ] .  p o i n t s c i t e d were from h i s experiment with  flow  in a  4.4  entrance.  cm  diameter  T h i s curve  tube  with  below  the  sharp-edged  i s an i d e a l i z a t i o n of the drawdown  phenomenon as i t a p p l i e s to a i r - w a t e r level  a  air-water  tube  entrance,  flow  into a l i q u i d  but at Froude numbers  below the b r i d g i n g f l o w r a t e of water.  4.1.1 I n c i p i e n t Figure drawdown  10  Drawdown shows  the  occurrence  incipient  i n t o the r e - e n t r a n t geometry, f o r both low and  high ranges of penetrated  subcooling.  into  a  The  region  variation  i n the r e s u l t s  air-water  experiments).  of  scatter,  drawdown  containing  accumulated at the entrance,  amount  of  which  caused  points  particularly  often  vapour that had  (compared to data The  cone  significant from  previous  exhibit  at  low  a large  values  of  subcooling. Figure the  11 shows s i m i l a r  rounded  i n c i p i e n t drawdown data f o r  and sharp-edged entrances.  No d i s t i n c t i o n  i s made between high and low v a l u e s of s u b c o o l i n g . diagram at  shows  a d e f i n i t e trend i n that drawdown  lower pool depths f o r a given  geometry  than  in  compared t o F i g u r e  the  The occurs  f l o w r a t e i n the rounded  sharp-edged  geometry.  When  10, i t seems t h a t r e - e n t r a n t drawdown  36  occurs  at  higher  edged drawdown. entrances entrant  pool  depths than rounded and sharp-  The s c a t t e r f o r rounded and sharp-edged  i s also s i g n i f i c a n t l y case.  Drawdown  for  l e s s than  for  the r e -  the sharp-edged geometry  f o l l o w s very c l o s e l y the sharp-edged a i r - w a t e r  data  of  Kalinske [ 9 ] . Figure  18a  shows  a  picture  geometry d u r i n g i n c i p i e n t drawdown subcooling)  with  of  the  re-entrant  (at  low  values  bubbles present a t the entrance.  drawdown cone i s w e l l d e f i n e d d e s p i t e bridged annular  the  of The  presence  of  flow downstream from the entrance.  4.1.2 Onset Of C a v i t a t i o n Bubbles (OCB) In  the flow of a n e a r - s a t u r a t e d l i q u i d  above the drawdown curve vapour), depth  there  where  vena of  is a limiting  incipient  infinitesimally contracta  ( i n the  initial  cavitation  will  of  occur.  An  small vapour bubble w i l l n u c l e a t e at the of the tube entrance.  At a given value  i s dependent on both  the Froude number and the d i m e n s i o n l e s s pool defining  absence  f l o w r a t e a t a given pool  subcooling, i n c i p i e n t c a v i t a t i o n  curve  i n a region  this  depth.  A  r e l a t i o n s h i p can be d e r i v e d a f t e r  making a few s i m p l i f y i n g assumptions (APPENDIX A ) . Once the f i r s t eventually  forming  bubble has formed i t grows i n a  ring-shaped  cavity  of  size, bubbles  37  (similar  i n shape to a " s t r i n g of beads") that surrounds  the p e r i p h e r y sequence  of  is  the  defined  tube.  The  initial  nucleation  here  as the "Onset of C a v i t a t i o n  Bubbles" ( a b b r e v i a t e d OCB).  Successive p i c t u r e s of t h i s  regime i n the r e - e n t r a n t  entrance  (taken  from  16  mm  f i l m ) are shown i n F i g u r e s I8d, 18e and I 8 f . On  Figure  12,  experimental  OCB  p o i n t s have been  p l o t t e d f o r the r e - e n t r a n t geometry, with low subcooling expected,  as  with  scatter  distinguishing  f l o w r a t e s f o r a given  low s u b c o o l i n g .  parameter.  pool  depth  than  i n the p o i n t s . sharp-edged  entrance,  the parameters of high and low s u b c o o l i n g .  p o i n t s with h i g h s u b c o o l i n g tend t o be right  As  There i s a l a r g e amount of  F i g u r e 13 shows OCB f o r the with  high  n u c l e a t i o n p o i n t s with h i g h s u b c o o l i n g tend t o  occur a t higher those  the  and  (at  higher  Again,  further  to  f l o w r a t e s ) on the diagram than  the those  with low s u b c o o l i n g . No evidence  of pure c a v i t a t i o n  only regime was found flowrates  possible  oscillating  vapour  in  the  bubbles  geometry  present  study.  were  at  occurred.  C a v i t a t i o n was observed  bubbles.  entrance  rounded  persisted  the  the  i n the  (OCB) from a l i q u i d -  observed  at  However, and  often  long a f t e r entrainment a t the  the  periphery  had of  38  4.1.3  Requirements For A V i o l e n t I n s t a b i l i t y At the same c h a r a c t e r i s t i c area on the flow map a l l  three was  entrances  showed  a regime where the  s u b j e c t i v e l y judged to be  formation,  "violent".  oscillation,  and  accompanied by the r i s i n g and at the pool i n t e r f a c e . boundary)  is  numbers 0.25 than  shown  to 0.65  Rapid  collapse  bubble  occurred,  spouting of l a r g e  T h i s g e n e r a l region on  instability  Figure  14  as  at dimensionless  bubbles  (but not  between  pool  the  Froude  depths  less  0.8. In  the  rounded  entrance  a  large  bullet-shaped  bubble would move every  few  a  position  at  and a p o s i t i o n s e v e r a l  diameters  the  tube  entrance  seconds between  downstream during t h i s " v i o l e n t " regime. form  at  the  bubble's  Vapour  p e r i p h e r y or wake.  upper p o s i t i o n vapour would be e j e c t e d from in  the  form  of  violently  upwards  chamber.  Spouting  geometries was  smaller against  bubbles the  which  roof  When at the the  bubble  would  of  the  with the r e - e n t r a n t and  much l e s s severe and  would  spout vacuum  sharp-edged  the bubbles i n v o l v e d  were s m a l l e r . F i g u r e 18b interacting  shows a p i c t u r e of t h i s  with  a  geometry, and F i g u r e  drawdown 18c  cone  in  violent  regime  the r e - e n t r a n t  shows a p i c t u r e from above  r e - e n t r a n t geometry during  spouting.  the  39  Vapour  phase  existed  everywhere  on  the diagram  where f l o w r a t e s were higher and pool depths at  a  previous  OCB  the s e v e r i t y of  any  function  occurrence.  The  instability  of the p a r t i c u l a r  lower  than  regime present  was  found  to  and  be  l o c a t i o n on the flow map  a and  the value of s u b c o o l i n g at that p o i n t .  4.2  C r i t i c a l Pool Depth Despite OCB  (CPD)  having not yet occurred  (due  to  s u b c o o l i n g ) , a regime with o s c i l l a t i n g bubbles observed  at  the  p a s s i n g through this  v a r i o u s entrances.  the  vena  instability.  However  (keeping the f l o w r a t e where  these  contracta by  of vapour. defined CPD).  The  here CPD  to 17.  dependent.  triggered  depth  was  would r i s e  reached into  event  the free  occurred  is  as the " C r i t i c a l Pool Depth" ( a b b r e v i a t e d  i s shown  a  usually  bubbles  l e a v i n g the entrance  p o i n t at which t h i s  Therefore  such, but  a  bubbles  chamber or e x i t down the tube,  Entrained  often  r a i s i n g the pool depth  constant)  "semi-trapped"  was  high  for CPD  region The  CPD  each  entrance  on  Figures  15  does not d e f i n e a flow regime as  on  the  region  flow is  map  that  the tube entrance.  and  low values of s u b c o o l i n g  path  a r e g i o n that must be  avoided to ensure that no vapour phase w i l l at  is  be  present  Sometimes at h i g h Froude numbers (Fr greater than  0.06  and  40  SC  less  than 20) OCB would occur  than CPD.  at higher  pool depths  P h y s i c a l l y t h i s meant any unattached  would s t i l l  bubbles  e x i t the tube a t CPD, but a s m a l l and s t a b l e  c a v i t a t i o n bubble (OCB) would reappear at the entrance. Figures rounded  15  entrances  subcooling. entrance up"  and 16  A  at  show CPD f o r the r e - e n t r a n t and relatively  "resonant"  constant  values  peak e x i s t s f o r the rounded  (Figure 16) at the t r a n s i t i o n between  and  "bubble-down"  flowrates  However  in  Figure  entrant geometry reached a p l a t e a u flowrate  mentioned 15, at  and d i d not decrease r a p i d l y .  the  violent  "bubble-up"  Figure  i n the sharp-edged entrance,  high  of  subcooling.  the  CPD f o r the r e -  this situation ranges  "bubble-  (at approximately  same f l o w r a t e s as f o r the p r e v i o u s l y instability).  of  Subcooling  17 shows  f o r low has  and  little  apparent e f f e c t on the s i z e of the r e g i o n .  4.3 Video  Cassette  A video c a s s e t t e was recorded in the three entrances. and  a  brief  showing these  See APPENDIX C f o r an index  description  of  to  the regimes, and nominal  values of the Froude number, pool depth (where a p p l i c a b l e ) .  regimes  and  subcooling  41  4.4 Downcomer Flowrate A  Fluctuation  r e a l time p l o t of downcomer f l o w r a t e  (peak-to-peak) i s shown i n F i g u r e  19a.  fluctuation  T h i s measurement  was taken during the " v i o l e n t " regime f o r the r e - e n t r a n t geometry. of  the  The magnitude of f l u c t u a t i o n mean  Froude  number)  is  (as a percentage  approximately  10%.  Figure  19b shows a s p e c t r a l a n a l y s i s of the same regime.  Taken  over  a  64  second  sampling p e r i o d , i t shows no  dominant s p e c t r a l frequency  other  than 60 Hz n o i s e .  F i g u r e s 20a and 21a show r e a l time rounded  and  regime.  F l u c t u a t i o n s of approximately  shown  sharp-edged  here.  F i g u r e s 20b  a n a l y s i s f o r these no  entrances  dominant  plots  d u r i n g the v i o l e n t  and 21b  27% and  15% are  show  spectral  a  two r e s p e c t i v e entrances,  frequencies  other  f o r the  than  60  and  again  Hz noise are  evident. F i g u r e 22a shows s t e a d y - s t a t e of  80%  for  the r e - e n t r a n t entrance.  was of a p e r i o d i c change drawdown  regime  F i g u r e s 22b  flowrate  and  between  a  T h i s measurement bridged  and a bridged annular 22c).  The  low  fluctuation  incipient  flow regime (see  frequency  component  (0.4 Hz) i s the r a t e a t which the regimes are changing. The  type  of  b r i d g i n g observed v a r i e d from t h a t with a  l i q u i d core and vapour annulus, to that core  and  a  l i q u i d annulus.  with  a  vapour  The presence of the l a r g e  42  vapour space in the regime disqualifies it from analysis  in this project,  but it does illustrate how  large hydraulic fluctuations (without phase can occur in downcomer flow.  further  transition)  43  V. 5.1  DISCUSSION OF RESULTS  Q u a l i f y i n g Remarks A  clear  experimental quantative  statement  of  the  limitations  method used must be made before a or  qualitative  regimes can be undertaken. for  the  m a t e r i a l of any  o b s e r v a t i o n s of a new  or  is  the  detailed  d e s c r i p t i o n of the This  of  observed  particularly  true  i n v e s t i g a t i o n where s u b j e c t i v e pioneering  nature  are  being  made. The  experimental  represents certain  an  data  attempt  observed  to  flow  presented locate  regimes  the  on  e x i s t e n c e of the regimes in the areas boundaries  in  a  t h i s report  boundaries flow  map.  adjacent  of The  to  the  has been v e r i f i e d v i s u a l l y to a much g r e a t e r  degree of c e r t a i n t y than number of data p o i n t s  statistically  i n d i c a t e d by  the  taken.  The q u a n t i t a t i v e measurement of instantaneous  fluid  p r o p e r t i e s during an unstable phenomenon, such as a  two-  phase  very  instability  difficult  in  near-saturated  to do a c c u r a t e l y .  q u i c k l y due  The  is  regimes can change very  to small p e r t u r b a t i o n s i n f l o w r a t e and  depth, a l l o w i n g n o n - e q u i l i b r i u m These  fluid,  regimes  would  regimes to be  pool  observed.  not have been seen i f the changes  were made s y s t e m a t i c a l l y and  slowly.  A c e r t a i n amount of s w i r l was  always evident  i n the  44  chamber  pool.  generated any  in  grow  vortex,  finite  the  s w i r l not  would  A  f l u i d at the  removed by the with  or  time  core  of  of  vorticity  a l a r g e and  Depending  on  regimes  the  the w h i r l p o o l c o u l d penetrate  well  there.  s t r a i g h t e n i n g c r o s s was this  developed  at  variation  placed  swirl. the  elements  size,  occurring  eliminate  and  unpredictable  its  down i n t o the downcomer entrance where i t any  was  i n l e t to the chamber  flow c o n d i t i o n i n g  into  whirlpool.  rotational  amount  i n regimes (see  affect  E a r l y i n the p r o j e c t a over the tube entrance to  However cross  would  the  walls  Figure  boundary  caused  23a)  as  layers  significant compared  to  those observed i n flow without the s t r a i g h t e n i n g c r o s s . Therefore,  it  was  decided  to use  s t r a i g h t e n i n g vanes  l o c a t e d r a d i a l l y away from the tube entrance to minimize (but  not  regimes  eliminate) where  the  s i g n i f i c a n t were The an  swirl.  Measurements  whirlpool  effect  a  parameter  container  l a r g e or  that  was  of  unused,  Freon  batch  "clean"  were  made  Freon.  of the experimental work the Freon had  "dirtier",  with  a  slight  observed.  Contaminants  yellow  that  act  t i n g e not as  was  watched c l o s e l y . up  Thus,  contaminants c o n t i n u a l l y accumulated i n the system, by the end  of  neglected.  Losses of Freon from the o p e r a t i n g from  seemed  e f f e c t of t r a c e contaminants i n the  uncontrolled  taken  and  become  originally  surface-active  45  agents  are  thought  to  inhibit  however there seemed to be no the  degree  of  bubble  coalescence,  systematic  variation  of  s a t u r a t i o n observed (at a given chamber  p r e s s u r e and temperature) over the time p e r i o d . The presence  of  a  large  bridged  vapour  cavity  trapped a t the entrance r e q u i r e d an e x t r a parameter size The  of the c a v i t y ) to c h a r a c t e r i z e f u l l y f l o w r a t e became dependent  (the  the regimes.  on the shape and  size  of  the vapour r e g i o n , and independent of chamber p r e s s u r e . This  cavity  u s u a l l y formed at h i g h f l o w r a t e s , when the  chamber p r e s s u r e became h i g h enough to liquid  level  (defined  at  zero  force  flowrate  as  a  normal  ring-shaped  bubbles (OCB), but a f t e r a short became  attached  to  the  of  growth  ( F i g u r e 23b).  w a l l , forming a l a r g e bubble i n the Measurements  were  the  The  detached  center of the tube.  until  it  down  the  tube  cavity  c a v i t y grew a x i a l l y from  the  wall  This  set of c a v i t a t i o n  period  tube  tube  at the same  chamber p r e s s u r e ) below the tube entrance. nucleated  the  vapour  neglected  when  the vapour c a v i t y became l a r g e enough that a decrease i n chamber  pressure  did  not  cause  an  increase in pool  depth. When the vapour c a v i t y o c c u p i e d tube,  violent  the  core  up-venting of l a r g e bubbles was  of  the  observed  ( F i g u r e 23c) over a wide range of f l o w r a t e s . A s t a t i o n a r y vapour c a v i t y was  not observed i n  the  46  rounded  entrance  but  was  entrant and sharp-edged  seen  frequently  i n the r e -  geometries.  5.2 Experimental E r r o r It  i s important  i n the measurement of these  to have a good estimate of the  type  experimental  The t h r e e types of e r r o r  error  involved.  and  regimes  size  of  the  i n v o l v e d i n t h i s work were i n s t r u m e n t a t i o n e r r o r s ,  time  lapse e r r o r s , and judgement e r r o r s . Instrumentation the  accuracy  transducers  process. using  of and  assumptions  errors  were those which d e s c r i b e d  measurement  measuring  of l i n e a r i t y  of  the  devices.  made  particular  Included were the  during  the  calibration  These e r r o r s were r e l a t i v e l y easy t o determine both  estimated  the  during  APPENDIX B uncertainty  an  manufacturers' the  estimate  analysis  figures  calibration of  this  equations  Fr ± 0.01, SC ± 1.17, and H/D  and  errors  procedure.  type of e r r o r quoted  in  In (using  [15]) i s ;  ± 0.04.  Time lapse e r r o r s r e s u l t e d from a d e l a y i n t a k i n g a measurement  of a f l u i d p r o p e r t y .  when a p o o l  depth  manually,  just  and before  recorded the chamber Although  hard  to  manometer the  data  temperature quantify,  this  T h i s u s u a l l y happened reading  were  acquisition and  Froude  type  of  taken system  number. error  was  47  thought to be q u i t e s m a l l . I n c o n s i s t e n c i e s i n judgement were attempting to  to d i s t i n g u i s h the t r a n s i t i o n  another.  quantify  at  experimenter  who  also  on  recorder pressure  times  was  from one regime  probably  made the o b s e r v a t i o n s the  and a d j u s t e d  lighting,  large.  The  and judgements,  activated  the  video  the f l o w r a t e , pool depth, chamber  and temperature.  Performance  while c o n t r o l l i n g an extremely unstable a  when  T h i s t h i r d type of e r r o r was a l s o hard to  and  turned  inevitable  of  these  tasks  flow regime made  compromising of the q u a l i t y of s u b j e c t i v e measurement  inevitable.  5.3 I n c i p i e n t Drawdown . P i n p o i n t i n g the l o c a t i o n was  a  very  important  of  objective  drawdown  entrainment  s i n c e entrainment of  s a t u r a t e d vapours was one of the mechanisms  responsible  f o r t r i g g e r i n g the i n s t a b i l i t y . Incipient where  drawdown  the  has been i d e a l i z e d as a regime  liquid-vapour  instantaneously  from  a  planar  cone as the downcomer f l o w r a t e i s (for  a  existed  given over  consistently  interface  changes  surface into a pointed increased.  Actually  pool depth) a drawdown cone of some type a  small  determine  range the exact  of  flowrates.  To  l o c a t i o n of the f i r s t  48  entrainment example  requires  those  warranted  sophisticated  than  (for  used by Harleman [8]) which d i d not seem  for this project.  The measurement of with  procedures  incipient  drawdown  in  fluids  low values of s u b c o o l i n g was much more complicated i n the standard case of a i r - w a t e r flow  (with  high  values of water s u b c o o l i n g ) .  Because of the presence of  vapour  the  in  the  downcomer,  flow  "saw"  e f f e c t i v e pool depth* than a c t u a l l y e x i s t e d . rise  to i n c i p i e n t drawdown (entrainment)  pool depths than otherwise The the  lower  This  gave  a t much higher  expected.  e f f e c t of s u b c o o l i n g on i n c i p i e n t drawdown  re-entrant  F i g u r e 10. depths  a  geometry  can  be  interpreted  When i n c i p i e n t drawdown occurs, higher  (at a  given  flowrate)  can be expected  for from pool  a t low  values of s u b c o o l i n g . The (Figure pool  drawdown  curve  11) was much lower depth)  c o n f l i c t s with  than  f o r the  data  entrance  (higher f l o w r a t e s f o r a given  f o r the  the  rounded  other  presented  geometries. by  This  Harleman,  who  r e p o r t e d no s i g n i f i c a n t d i f f e r e n c e between the curve f o r rounded  and  sharp-edged geometries.  However, Harleman  used a much sharper p a r a b o l i c entrance c u r v a t u r e . a rounded entrance given  w i l l carry a larger  flowrate  pool depth) than a sharp-edged entrance,  probable  the same tendency should occur  Since (at a  i t seems  f o r drawdown.  49  The  drawdown cone was much "wider" i n  entrance cone  the  rounded  than i n the other geometries s i n c e the drawdown  tended  to  follow  the  entrance  curvature.  This  again c o n f l i c t s with the f i n d i n g s of Harleman who s t a t e d the cones were g e o m e t r i c a l l y s i m i l a r Kalinske entrance  [9]  reported  that  has a lower drawdown curve  entrance.  This  data presented presence any  has  does in  not  Figures  i n a l l entrances. the  re-entrant  than the sharp-edged  seem to be confirmed 10  and  11,  by the  although  of vapour phase ( i n n e a r - s a t u r a t e d  the  flow) makes  d i r e c t comparison of l i t t l e use. A sketch of the s t r e a m l i n e s  entrances  ( l i q u i d - o n l y flow) i s shown i n F i g u r e 24.  particular present  i n the three r e s p e c t i v e  s i g n i f i c a n c e are the l a r g e s e p a r a t i o n  a t the vena c o n t r a c t a  for  the  Of  eddies  re-entrant  and  sharp-edged geometies but not f o r the rounded geometry. The  lack of eddies  i n the rounded entrance  bubbles d i d not become attached  a t the vena c o n t r a c t a .  There was a much g r e a t e r tendency become  trapped  in air-water viscosity  (at a l l entrances)  flow.  and  e x p l a i n s why  f o r bubbles  i n Freon-11  flow  T h i s was due p a r t i a l l y to the  surface  tension  of  the  c a v i t a t i o n e f f e c t s at the vena c o n t r a c t a .  Freon  to than  lower and to  50  5.4  Onset Of C a v i t a t i o n Bubbles Cavitation  vertical  (OCB)  i s the mechanism that d i s t i n g u i s h e s  downflow of n e a r - s a t u r a t e d l i q u i d  l i q u i d at higher values of s u b c o o l i n g . the  introduction,  the  from that of  As mentioned  local  T h i s occurrence  velocity  gradient  head  at  this  point.  The  flow methods or by s o l v i n g the  Navier-Stokes  numerically  geometry.  approximations field  may  each entrance  made necessary  make  the  final  to  solve  for  r e s u l t of l i t t l e  by  of an OCB  the  flow  practical present.  general  shape  number (at a given value of s u b c o o l i n g  chamber p r e s s u r e ) . of  entrainment  in  experimental  Theoretical  subcooling  are  i n F i g u r e 25a and  in F i g u r e 25b. changes  equations  curve on a diagram of dimensionless pool depth  Froude  values  potential  making the same s i m p l i f y i n g assumptions as  s t a t e d i n APPENDIX A one can p r e d i c t the  vs.  velocity  The amount of  s i g n i f i c a n c e when small amounts of vapour are However,  vena  depends on the value of the  at the entrance c o u l d be obtained by  for  in  s t a t i c pressure g r a d i e n t i n the  downflowing l i q u i d can have a minimum value at the contracta.  the  curves  shown  for  different  f o r the case  the case with  without  entrainment  Note the p r e d i c t e d s e n s i t i v i t y of OCB  subcooling  that  and  to  are small compared to the  e r r o r (SC ± 1.17).  There were s e v e r a l f a c t o r s that  caused  deviations  51  from  these  theoretical  the pressure the  At the vena c o n t r a c t a  was higher at the tube c e n t e r l i n e . than  tube w a l l .  -  curves.  This gradient channelled  the v e r t i c a l d i r e c t i o n and e x p l a i n e d  at  the f l u i d  why  OCB  into  occurred  c l o s e to the tube w a l l (Figure I 8 d ) . As expected, OCB was very of  nucleation  sites.  s e n s i t i v e to the presence  Small  u n d i s s o l v e d vapour or gas  bubbles ( p r e v i o u s l y e n t r a i n e d by the flow or  in a  w h i r l p o o l ) caused OCB w h i l e t r a v e l l i n g  contracta. explains curve  The s e n s i t i v i t y of OCB t o the  pinpoint t r u e at  effects.  (at  nucleation  sites  entrances.  I t was found that OCB was very  flowrate  i n t o the vena  l a r g e amount of s c a t t e r near the drawdown  observed f o r a l l three  equilibrium  drawdown  I t was d i f f i c u l t  constant  the high  pool  location values  sensitive  depth)  of  of  OCB.  to  non-  to i n c r e a s e the  slowly  enough  to  T h i s was p a r t i c u l a r l y  subcooling  where  velocities  became very l a r g e a t the vena c o n t r a c t a . The  first  bubble q u i c k l y grew i n s i z e a f t e r  generated at the vena c o n t r a c t a .  A rapid  i t was  conglomeration  of other bubbles q u i c k l y formed and converged around the i n s i d e of the tube, without pool  depth  or  any  flowrate.  significant In  a  few  change seconds  e q u i l i b r i u m c o n d i t i o n s changed from a l i q u i d - o n l y to  one where a ring-shaped  periphery  of the tube.  in the  regime  vapour c a v i t y surrounded  the  The vapour region grew l a r g e r as  52  the  flowrate increased.  detached  E v e n t u a l l y some of the  from the r i n g and moved e i t h e r up or  bubbles  down  the  did  not  tube. After  an  OCB  occurrence  n e c e s s a r i l y c o l l a p s e at the initially  formed.  d e s i n e n t and  the  same  Hysteresis  incipient  bubbles  flowrate of  this  cavitation  has  where  they  type, between been  reported  p r e v i o u s l y , f o r example Knapp [ 3 ] . It lower  would  seem  the l i q u i d  more  severe  points  slightly  the  sharp-  flows over the p r o t r u d i n g tube) causes a contracta.  This  trend  lacks  s i g n i f i c a n c e c o n s i d e r i n g the number of data  taken.  The  OCB.  should occur at  The more pronounced change i n d i r e c t i o n  vena  statistical  false  OCB  f l o w r a t e s f o r the r e - e n t r a n t than f o r  edged geometry. (as  that  r e - e n t r a n t geometry protruded  floor  and  There was  well  above  allowed unobstructed v i s u a l i z a t i o n of  a s i g n i f i c a n t amount of o b s t r u c t i o n when  l o o k i n g h o r i z o n t a l l y at the rounded  entrance.  from a viewpoint w e l l above the f a l s e f l o o r the entrance  could  observed  at  cavitation  be  the was  seen,  and  flowrates not  no  tested.  surprising  c u r v a t u r e of the entrance.  The  from above.  However complete  evidence of OCB The  was  absence  of  c o n s i d e r i n g the smooth sharp-edged  the most d i f f i c u l t to work with although OCB be seen e a s i l y  the  entrance could  was  still  53  5.5 Requirements For A V i o l e n t All  three  several  entrances  small  bubbles  Instability  displayed  (from  a  regime  previous  entrainment or  c a v i t a t i o n ) o s c i l l a t e d up and down at the tube T h i s regime o c c u r r e d i n the up-down of  where  entrance.  transitional  f l o w r a t e s f o r bubbles at the entrance.  range  Some bubbles  would r i s e out of the entrance, to be r e p l a c e d by vapour generated at the p e r i p h e r y of bubbles a l r e a d y Vertical  segregation  according  to  bubbles.  Small  the  of  size,  bubbles  bubbles shape  would  and  present. take  location  place of  tended to be s p h e r i c a l and had  small r i s e v e l o c i t i e s while l a r g e bubbles tended bullet-shaped  and  l o c a t i o n of  the  discern  there  wall.  as  had  large  cavitation was  rise  to  velocities.  varied  and  was  be The  hard  to  no f i x e d c a v i t y a t t a c h e d to the  The regime looked s i m i l a r to n u c l e a t e b o i l i n g but  without  the temperature  g r a d i e n t i n the tube.  T h i s o s c i l l a t i o n was between  observed  at  0.25 and 0.50 at pool depths  drawdown curve.  Froude  caused  an  R a i s i n g the pool depth u s u a l l y  increase  periodically  resulted but  also  i n the s i z e of the bubbles and the  s e v e r i t y of the regime.  bubbles.  numbers  s l i g h t l y above the  in a lowering of the frequency of o s c i l l a t i o n ,  seen  the  Often a drawdown cone c o u l d  interacting  The drawdown cone would  with  the  appear  as  be  oscillating a  rising  54  bubble h i t the pool When  at  its  i n t e r f a c e , and  greatest  then would  severity  this  primary component observed i n the judged to be  5.6  The  regimes  was  the  subjectively  "violent".  transitional  expelled  upwards  (bubble-down) transition.  is  depth.  between  (bubble-up)  or  defined  here  (to higher  This  trend  hemispherical  area  increases,  velocities  flowrate  T h i s t r a n s i t i o n has  the r i g h t  depth  regime  Up-Down T r a n s i t i o n  The  to  disappear.  in  be  made which  the  expelled as  in  This  to  move  i n c r e a s i n g pool  explained  results  pool.  "up-down"  been observed  available  being  downwards  the  f l o w r a t e s ) with  can  bubbles  by  the  larger  to the flow as lower  the  downward  i n turn allows upward  buoyancy f o r c e s on the bubbles to predominate at  higher  flowrates. Negligible observed at while  bubble  flowrates  at higher  interface  below  the  down  the tube  up-down  was  transition,  f l o w r a t e s p e n e t r a t i o n depended upon the  p a r t i c u l a r entrance The  penetration  regime.  v e l o c i t y of the spouting tended  to be g r e a t e r  bubble  at  the  pool  f o r l a r g e r pool depths,  as the bubble had more time to a c c e l e r a t e upwards to i t s terminal  velocity.  55  5.7 C r i t i c a l Pool Depth (CPD) CPD was s i g n i f i c a n t as i t emphasizes the importance of  the up-down t r a n s i t i o n on the presence  the  tube.  In a constant  l e v e l process  f l o w r a t e ) vapour phase i n i t i a l l y eliminate  vapour completely  of  vapour  in  (with i n c r e a s i n g  forms at  OCB,  but  the process must f i r s t  to  pass  o u t s i d e the OCB and CPD r e g i o n s . At high values of s u b c o o l i n g vapour  bubbles  exist.  In the l i m i t  bubbles  should r e a d i l y c o l l a p s e .  to  presence  the  self-vent  a  tendency  f o r the  t o c o l l a p s e and/or s h r i n k i n s i z e  of  should  (at very h i g h v a l u e s of subcooling) Those that do not (due  non-condensibles)  should  as i n the case of a i r - w a t e r flow.  Yet at low  v a l u e s of s u b c o o l i n g excess  vapour  generated.  should cause a shrinkage of  the  CPD  These tendencies region  large of  actually  at h i g h values of s u b c o o l i n g .  not shown by the data relatively  would  readily  i n F i g u r e 17, perhaps due  be  This i s to the  small range of s u b c o o l i n g examined, or to the  amount of non-condensibles  present at h i g h values  subcooling. In the r e - e n t r a n t entrance with i t s pronounced vena  contracta directly  (Figure 24a), above  the  entrance  maximum l i q u i d v e l o c i t y . the  only  bubbles will  on  streamlines  be a f f e c t e d by the  Therefore a t a given  tendency i s smaller f o r bubbles  flowrate  i n the g e n e r a l area  56  above the entrance to  be  plateau  the  observed  on  e x p l a i n e d by t h i s effect  explains  occur  at  (Figure  CPD  the  curve The  up-down  flowrates  mentioned  particularly  near the CPD  in  in  the  significant  up-down  in  tube.  The  Figure  15 i s  opposite  of  transition  the  this  seems to  rounded  previous  entrance  chapter  f o r the rounded  transition.  As  CPD  entrance  curve, a l a r g e b u l l e t - s h a p e d bubble  bubbles.  is near  the p o o l depth i s r a i s e d  diameter n e a r l y that of the tube) smaller  the  16).  As  the  down  phenomenon. why  lower  swept  formed  from  The bubble would o s c i l l a t e  (with a merging  (every few  seconds) between two p o s i t i o n s ;  one  downstream  and one at the entrance  from  the  entrance  ( F i g u r e s 26a and 26b). the  bubble  pressure). roof  of  was  diameters  Severe s p o u t i n g took p l a c e  at the upper p o s i t i o n  when  (low h y d r o s t a t i c  L i q u i d d r o p l e t s were thrown up  against  was  bubble.  A  smaller  amount  of  a l s o evolved i n the lower p o s i t i o n but most  bubbles c o a l e s c e d or were swept through the tube. regime  the  the chamber by r i s i n g bubbles generated i n and  e j e c t e d from the l a r g e vapour  several  continued  indefinitely  long  wake  the  bubble.  [16] observed a s i m i l a r regime  gas-liquid  phenomenon,  described  as  or  was  the  co-current  periphery  as vapour  generated from Taitel  lower  as  flow.  This  an  oscillatory  This  entry  of  i n upward region  motion  of  57  " T a y l o r " bubbles, was c l a s s i f i e d as "churn"  flow.  5.8 Bubble Rise V e l o c i t y In The F u l l y Developed Simpson [1]  has  r e p o r t e d that f o r bubbles  the s i z e of the tube diameter, the f u l l y developed approximately  number  0.31.  but  very  large in  bubbles  A  large  amount  a  remaining  large  Freon)  bubble  in  i t was the  merging and s e p a r a t i o n of l a r g e r bubbles,  The  tube.  bubbles  impossible  to  The constant with  smaller  and the momentum interchange d u r i n g c o l l i s i o n ,  probably had a s i g n i f i c a n t involved.  stationary.  f l o w r a t e s c o u l d be e x p l a i n e d by the f a c t  ( i n near-saturated  isolate  and  air-water  segregation o c c u r r e d at t h i s Froude number with only  difference that  of  Large bubbles were f r e q u e n t l y trapped  i n the tube around Froude number 0.46.  the  at  i t d i d not c o r r e l a t e w e l l with the observed  flow of Freon-11.  of  occur  During the p r o j e c t  t h i s phenomenon was v e r i f i e d f o r the case flow,  roughly  the up-down t r a n s i t i o n i n  region of the tube should  Froude  Region  effect  on the buoyancy f o r c e s  The d i f f e r e n c e i n v i s c o s i t y  between  water should have been i n s i g n i f i c a n t  was t u r b u l e n t (Reynolds  numbers  57,000 as the Froude number ranged  varied  Freon-11  s i n c e the flow from  9500  from 0.2 t o 1.2).  to  58  5.9  Expected When  Behaviour the  At High Values Of  instability  is  Subcooling  plotted  on  three  dimensional axes of d i m e n s i o n l e s s pool depth vs.  Froude  number  three-  vs.  dimensional  dimensionless volume  subcooling,  (bounded  by  OCB  a  and  drawdown s u r f a c e s ) s i m i l a r to F i g u r e 27 i s exist.  vapour phase can r e a d i l y accumulate OCB  surface  i d e a l i z e d as independent  Downcomer Flowrate Interpretation  account the  to  f o r the low  experimental  curve, where the  at  the  entrance.  moves t o higher Froude numbers as the  subcooling i s increased.  5.10  expected  Only at low v a l u e s of s u b c o o l i n g i s the up-down  t r a n s i t i o n under the s u r f a c e of the OCB  The  incipient  of  Incipient  drawdown  has  been  signals  must  of s u b c o o l i n g .  Fluctuation the  anemometer  frequency  oscillation  procedures.  produced  T h e r e f o r e , the r e a l  by time  p l o t s were u s u a l l y q u i t e i n d i c a t i v e of the t r u e v e l o c i t y f l u c t u a t i o n , but the frequency a n a l y s i s 64  seconds)  frequency  have  picked  up  some  of  over  these  low  amount  of  components.  With the vapour  may  (performed  exception  of  F i g u r e 20  the  that . p e n e t r a t e d down the tube was  these measurements.  negligible in  In F i g u r e 20 vapour bubbles  passing  59  by the  anemometer  liquid  velocity  was  large.  probe  caused  fluctuations  at the probe, e s p e c i a l l y  These  randomly  at  low  frequency  analysis.  fluctuations  each  generally  occurred  f r e q u e n c i e s and were n e g l e c t e d i n the  entrance.  The  measurement  magnitude of f l u c t u a t i o n  found t o be l e s s than 27% of the mean Froude each  case,  thus  suggesting  that  the  entrance i n s t a b i l i t y on the l i q u i d small. free  number  effect  phase  turbulence present  same Reynolds previous  number.  chapter,  this  in  was  have  been  i n any pipe flow at the  However does  was  of the  flowrate  A large amount of t h i s f l u c t u a t i o n may stream  the  i f the bubble  A " v i o l e n t " regime was p i c k e d f o r t h i s for  in  as  mentioned  not  mean that  in  the  hydraulic  i n s t a b i l i t i e s due to p e r i o d i c a l l y changing regimes c o u l d not cause f l u c t u a t i o n of up t o and g r e a t e r than  80%  of  the mean f l o w r a t e . Inferences  cannot  be  drawn  as  magnitude  of the regime i n s t a b i l i t i e s  without  further  measurements,  but  to in  the r e l a t i v e each  the  geometry  preliminary  f i n d i n g s suggest the rounded entrance as the most to f l o w r a t e  fluctuation.  prone  60  VI. 6.1  CONCLUSIONS  General Two-phase  instabilities  have  been  downcomer entrance i n an experimental near-saturated  rig  Freon-11 from a v e s s e l .  have been r e s t r i c t e d to those without and without a l a r g e b r i d g e d vapour the  observed at a that  drains  Regimes s t u d i e d noticeable  space.  swirl  In t h i s study  regimes have been c h a r a c t e r i z e d f o r the f i r s t  using  dimensionless  parameters  depth,  downcomer  flowrate  liquid  interface  in  the  describing  and  the  pool.  the  pool  s u b c o o l i n g at the  Downcomer  geometry has been v a r i e d as an independent video  time,  entrance  parameter.  r e c o r d i n g has been made of the regimes  A  for future  reference. The  two  primary  mechanisms  instability  were  entrainment  entrainment  regimes  observed  correlated air-water higher  and in  in  the  cavitation.  The  this  study  can  be  with the p r e v i o u s l y documented occurrence of i n c i p i e n t drawdown.  pool  flowrate) entrance. bubble  involved  depths  when  than  vapour  Cavitation,  Drawdown was  was  bubbles the  expected were  mechanism  observed (at  present  to  given at  the  responsible for  formation and growth, has been found to  susceptible  a  at  be  very  the presence of n u c l e a t i o n s i t e s and to  the amount of s u b c o o l i n g at the pool  interface.  61  The local  up-down  velocity  transition, at  the r i s e v e l o c i t y been  found  flowrates  where the  a p o i n t i n the entrance  i s equal t o  of a  at  particular  t o be a very  vapour  important  physical  When coupled  with  the g e n e r a t i o n  entrainment  and  cavitation,  a  of  a t the entrance,  vapour  through  near  severe.  this  Bubbles  with the vapour having no  mechanism f o r escape from the r e g i o n . occurs,  has  phenomenon.  flowrate  t r a n s i t i o n makes the i n s t a b i l i t y very conglomerate  bubble,  Some  segregation  with small bubbles e x p e l l e d downwards and l a r g e  bubbles e x p e l l e d upwards.  and  In g e n e r a l , the observed  regimes i n the  sharp-edged  were  geometries  similar.  re-entrant The  regimes i n the rounded geometry were unique due effect  of the s t r e a m l i n e d c u r v a t u r e  reducing  flow  t o the  cavitation  at the entrance.  6.2 I n c i p i e n t The show  Drawdown  experimental  considerable scatter  p a r t i c u l a r l y at explained  by  low  subcooling.  for incipient  drawdown  with the r e - e n t r a n t geometry,  values  the i n t e r a c t i o n  and vapour bubbles, low  results  of  subcooling.  This  is  between the drawdown cone  commonly found at  the entrance  at  62  The  i n c i p i e n t drawdown curve f o r the sharp-edged  geometry  behaves  roughly as p r e d i c t e d i n p r e v i o u s a i r -  water work [ 9 ] , while the rounded lower  curve than was expected.  themselves it  had  a  It was d i f f i c u l t given  a  rarely attached  entrance  because  geometries.  value  the  (OCB)  t o d e l i n e a t e a complete of  subcooling, nucleation explain  exhibits  much l e s s severe vena c o n t r a c t a than the r e -  6.3 Onset Of C a v i t a t i o n Bubbles  a  Bubbles  t o the tube i n the rounded  entrant and sharp-edged  at  geometry  subcooling. sites,  and  OCB  curve  The s e n s i t i v i t y t o experimental  l a r g e amount of s c a t t e r .  error  For a given pool  depth, c a v i t a t i o n occurs a t higher f l o w r a t e s with higher v a l u e s of s u b c o o l i n g .  The general shape of an OCB curve  can be p r e d i c t e d from t h e o r e t i c a l c o n s i d e r a t i o n s . C a v i t a t i o n from an (OCB)  was  not  observed  f l o w r a t e s attempted  infinitesimal  nucleation  site  i n the rounded entrance a t the  in this  study.  63  6.4 Requirements For A V i o l e n t I n s t a b i l i t y The the  i n s t a b i l i t y was most severe  up-down t r a n s i t i o n  i n the v i c i n i t y  f o r a l l three entrances.  t h i s regime, a high head l o s s due  to  expected  spouting  in  the  tube.  Severe  vacuum chamber has been observed,  friction  of  During can be  up i n t o the  particularly  i n the  rounded geometry.  6.5 C r i t i c a l Pool Depth (CPD) And The Up-Down T r a n s i t i o n Flow mapping of the p r e v i o u s l y mentioned regimes by itself  cannot  instability. disturbance  predict  fully  the  occurrence  Some regimes can be t r i g g e r e d by or  entrained  bubble.  This  s u b c o o l i n g higher than normally expected clear  of the a  large  may occur a t f o r OCB.  To  the tube of t h i s d i s t u r b a n c e the f l o w r a t e or pool  depth must.be changed so that i t no longer f a l l s region  enclosed  particularly  by  the CPD and OCB c u r v e s .  important  requirement  i n the  This i s a  f o r the  rounded  entrance, where OCB does not e x i s t . The  CPD  curve  i s significant  occurs a t the up-down t r a n s i t i o n . occur a t lower geometry geometries.  than  This  in  that the peak  peak  seems  to  f l o w r a t e s and pool depths f o r the rounded f o r the  sharp-edged  Because of i t s narrow vena  and  re-entrant  c o n t r a c t a , the  64  r e - e n t r a n t geometry e x h i b i t s more of a " p l a t e a u " at high flowrates. The of  CPD region should -  subcooling.  s h r i n k i n s i z e a t high  T h i s shrinkage  small range of s u b c o o l i n g  was not evident  values  over the  tested.  Freon vapour bubbles i n the f u l l y developed of  the  tube  were not trapped  region  at Froude number 0.31 as  expected, but at a higher Froude number of around 0.46.  6.6 Sample T h e o r e t i c a l Curves I d e a l i z e d flow diagrams a r e shown on F i g u r e s 28, 29 and  30  f o r the  re-entrant,  rounded  and  sharp-edged  geometries at a common value of s u b c o o l i n g . At  higher values of s u b c o o l i n g  to the r i g h t  ( t o higher  flowrates)  the OCB curve while  the  CPD  moves and  " v i o l e n t " regions do not move but s h r i n k i n s i z e .  6.7 Downcomer Flowrate  the  Fluctuation  Fluctuations  i n downcomer f l o w r a t e of up t o 27% of  mean  number  "violent" hydraulic  Froude regime.  have  However,  been  observed  much l a r g e r low  i n the frequency  f l u c t u a t i o n s can be expected d u r i n g a p e r i o d i c  change of regimes such as i n t e r m i t t e n t b r i d g i n g .  65  VII. 7.1 I n d u s t r i a l The  described  Design  following  controlling  or  may the  prove  helpful  violent  in  instability  study:  at  transition  guidelines preventing  in this  (a) - operate  RECOMMENDATIONS  flowrates region  0.25 to 0.65)  which  avoid  the  up-down  ( i e . , a v o i d Froude numbers from  using  flowrate  control  (refer  to  F i g u r e s 28, 29 and 30). (b) - r a i s e  the  lowering  value  of  subcooling  i t s temperature or r a i s i n g  thus moving the OCB curve shrinking feasible  the in  CPD  evaporator  pool  depths  (d) - i f p o s s i b l e provide the  pool i n t e r f a c e  "violent"  and  boiler  f l o w r a t e s and regions  (not  installations  requirement).  much  diameter through l e v e l  i t s pressure,  t o a higher  and  where s a t u r a t i o n i s a (c) - use  i n the l i q u i d by  g r e a t e r than the downcomer control.  some means of v i s u a l i z a t i o n or the downcomer entrance.  performance of the downcomer  can  then  be  of The  easily  evaluated and m o d i f i c a t i o n s made i f necessary.  66  7.2 F u r t h e r Work 7.2.1 M o d i f i c a t i o n s To The Apparatus As  i n any  experimental  study  nature, suggestions f o r ways t o and  instrumentation  became  And Instrumentation of  improve  a preliminary the  apparatus  obvious upon completion of  the work. A s m a l l e r c i r c u i t , perhaps using a 1.9 cm test  section,  diameter  and s m a l l e r c i r c u l a t i o n pump and p i p i n g ,  would l e s s e n the v o l u m e t r i c requirements  of Freon  used.  Use of a s h o r t e r t e s t s e c t i o n , perhaps 1.0 m would  lessen  the vacuum  requirements,  s e v e r i t y of c r a z i n g problems This  would  be  d e c r e a s i n g the  i n the vacuum  accomplished  without  s i g n i f i c a n t l y the length-to-diameter  long,  chamber.  compromising  r a t i o of  the  test  section. A  water-cooled  condensor  d i s c h a r g e t o the vacuum pump Freon  vapour  losses.  i t can be achieved  could  to  be p l a c e d a t the  recover  part  of the  T h i s should be attempted  without  a  large  increase  only i f i n the  complexity of the apparatus. Pressure  and  displacement  transducers  purchased  f o r the a c c u r a t e and r e l i a b l e  chamber  pressure  acquisition chamber  and  pool  depth  should be  measurement using  the  system, synchronous with the measurement  temperature  and  siphon  flowrate.  of data of  The f l o a t -  67  operated displacement  transducer would be mounted  the vacuum chamber, l e a v i n g make  qualitative  regimes. very  experimenter  observations  Both of these  expensive  the  due  and  instruments  to  to  free  control  would  to the  probably  be  their stringent specifications  (Pch ± 100 Pa i n 0-101 kPa range and H ± 0.5 mm 0-10  inside  with  a  cm range). Greater  vertical  (say 1.5 m) should be  difference  allowed  in  f o r between  elevation the  lower  v e s s e l and the pump to l e s s e n c a v i t a t i o n problems at the pump  suction.  Similarly  a  "U-shaped"  p l a c e d i n the siphon loop where the overflow  vessel,  the loop.  l o o p c o u l d be  liquid  leaves  the  with the f l o s e n s o r near the bottom of  T h i s would p r o v i d e greater s u b c o o l i n g a t the  f l o s e n s o r , completely  e n s u r i n g no c a v i t a t i o n o c c u r r e d on  the paddlewheel. A  large,  easily  used t o c o n t r o l flow changes  in  flowrate  r e g u l a t e d needle v a l v e should be in  the  are  siphon  loop.  significant,  As  small  i t i s important  that the e f f e c t s of a small change i n v a l v e p o s i t i o n  be  p r e d i c t a b l e , and adjustments e a s i l y made. A  temperature compensated probe should be used f o r  flowrate f l u c t u a t i o n the  effect  indicated  of  measurement,  changes  velocity.  in  liquid  thereby  eliminating  temperature on the  68  7.2.2 F u r t h e r Areas Of Study The  r e s u l t s presented here should be  verified,  preferably  d i f f e r e n t diameter should  be  using  a  of downcomer.  investigated  independently  different Further  fluid  and  topics  that  i f the i n s t a b i l i t i e s are to be  completely understood a r e :  (a) - f u r t h e r measurement of f l o w r a t e f l u c t u a t i o n  ( i n the  v a r i o u s regimes) f o r each entrance (b) - the e f f e c t of a l a r g e u n c o n t r o l l e d w h i r l p o o l on the observed  regimes  (c) - the e f f e c t of a h o r i z o n t a l entrance  leading  to  a  downcomer (d) - minimizing  the  effect  s p e c i a l l y designed  of  and  instability  with  entrances  (e) - the i n t e r a c t i o n and feedback flowrate  the  pressure  between the  downcomer  f l u c t u a t i o n s , and the two-  phase regimes present at the entrance (f) - the e f f e c t of the s i z e , shape and l o c a t i o n large  bridged  observed  vapour  space  parameter  of  the  on  any  regimes  (g) - u s i n g p o t e n t i a l flow techniques velocity fields  for several  [10], s o l v e f o r the  entrance  geometries.  Using t h i s i n f o r m a t i o n , p r e d i c t i o n s can be made f o r the  flowrate  at  incipient  cavitation  and  the  69  flowrates  at  which the  up-down  transition  occurs.  70  VACUUM PUMP  I  -SATURATED  VAPOUR  SATURATED LIQUID AND VAPOUR FROM P R O C E S S SATURATED  LIQUID  ENTRANCE INSTABILITY -DOWNCOMER -CONDENSATE TANK  •**  cH—  -CONDENSATE RETURN TO PROCESS  Figure  1 -  I n d u s t r i a l E x a m p l e Of T h e I n s t a b i l i t y (Steam a n d C o n d e n s a t e ) .  71  H/D  Pch  ft i  REGION WHERE F r DEPENDS ON H/D AND Pch  -LIQUID LEVEL AT F r • O  0-25 INACCESSIBLE REGION Fr  Figure  2-  I n c i p i e n t Drawdown With L i q u i d L e v e l At Downcomer Entrance ( A i r - W a t e r ) .  72  Figure  3 -  I n c i p i e n t Drawdown With L i q u i d L e v e l Downcomer Entrance (Air-Water [ 9 ] ) .  Below  VCR 4 16 mm EQUIPMENT  -VACUUM CHAMBER  PHOTOGRAPHIC  0  KJ38  II11 loo  www  V7  V8  3^  V4 SIPHONLOOP  TEST SECTION H (2-54 cm 0x|83cmLG.)  r I  PRESS. TRANSD TEMP. PROBE  H I h-f  FLOSENSOR HOT FILM PROBER LOWER VESSEL  TO ATM. VACUUM ACCUMULATOR  TO MANOMETER  V6  VACUUM PUMP  I  NEFF D.A.S.  PDP-11 MINI.  CONSTANT TEMPERATURE ANEMOMETER LINE ARI2ER FFT  ANALYZER M CIRCULATION PUMP  CIRCULATION LOOP Figure  PLOTTER  4-  Experimental Schematic.  Figure  75  PLAN  r  ELEVATION  gure  6 -  D e t a i l s Of Vacuum Chamber.  POLYCARBONATE BELL JAR  ALL DIMENSIONS IN cm  13 0 (TYP.)  CTi  -2-54  2-54R  1—1-3  V 2-54  45° (TYP.)  I. D. x 183 LONG GLASS TUBE (TYP.)  7a  SHARP-EDGED  7b  RE-ENTRANT  7C  ROUNDED  MAT'L : ALUMINUM t ALL DIMENSIONS IN cm Figure  7 -  Downcomer Entrance Geometries. 7b - r e - e n t r a n t , 7 c - rounded)  ( 7 a - sharp-edged, r  77  Figure  8  -  Constant Temperature Anemometer Schematic.  78  PROMPT FOR: DATE. Patm. CONTROL CHARACTER ( C O  r SCAN •' - SAMPLE Pch. Tch, Fr g> 1 0 Hz FOR 50 SECONDS  PROMPT FOR: H, Pch (MANOMETER)  I  SCAN:-SAMPLE Tch. Fr g l O H 2 FOR 5 SECONDS  I TIME  AVERAGE  I  CONVERT TO REAL UNITS  I  NOTE  PROMPT FOR DESCRIPTIVE CODE  I  CC * O USED FOR ALL FINAL DATA ACQUISITION  OUTPUT DATA AT TERMINAL £ IN OUTPUT FILE  • Figure  9 -  Data A c q u i s i t i o n  t  System  Schematic.  79  1.6  — • o  air —water low S C high S C  1.2  H/D  0.8  0.4  0 0.4 Froude  Figure  10 -  0.8 Number =  1.2  V/\[QD  The E f f e c t Of Subcooling On I n c i p i e n t Drawdown For The Re-entrant Geometry, ( a i r - w a t e r drawdown data from [ 9 ] , Low SC i s SC £ 9.0, N = 32, SCAVG = 3.9, SD = 2.6, High SC i s SC £ 9.0, N = 8, SCAVG = 16.8, SD = 10.3)  80  1.6  — • 1.2  H / D  Figure  air —water shp  "V"  A  0.8  11 -  I n c i p i e n t Drawdown For Rounded And Sharp-edged Geometries. ( a i r - w a t e r drawdown data from [ 9 ] , Rounded (rd) - N = 30, SCAVG = 12.5, SD = 5.6, Sharp-edged (shp) - N = 24, SCAVG = 21.9, SD = 14.5)  81  3.0  —  a o  air-water low SC high SC  0  1  2.4  H/D  '///////.  m. »  1.6  0.8  0.4 Froude  Figure  12 -  0.8 Number = v / / g D "  The E f f e c t Of S u b c o o l i n g On The O n s e t Of C a v i t a t i o n B u b b l e s (OCB) F o r The R e - e n t r a n t Geometry, ( a i r - w a t e r drawdown d a t a f r o m [ 9 ] , Low SC i s SC <> 9.0, N = 37, SCAVG = 4.8, SD • 2.4, H i g h SC i s SC £ 9.0, N = 13, SCAVG = 18.8, SD = 7.2)  1.2  82  3.0  — ° o  air - water low SC high SC  2.4  H/D  1.6  co • 0.8  0.4 Froude  Figure  13 -  0.8 Number = V / / g D  The E f f e c t Of S u b c o o l i n g On The O n s e t Of C a v i t a t i o n B u b b l e s (OCB) F o r The S h a r p - e d g e d Geometry. ( a i r - w a t e r drawdown d a t a f r o m [ 9 ] , Low SC i s SC £ 9.0, N • 10, SCAVG • 6.2, SD = 2.6, H i g h SC i s SC £ 9.0, N = 4, SCAVG = 12.4, SD - 2.2)  83  1.6  Froude  Figure  14 -  Number = V / / g D  V i o l e n t R e g i o n F o r The R e - e n t r a n t ( r e ) , Rounded ( r d ) And S h a r p - e d g e d ( s h p ) G e o m e t r i e s . (air-water drawdown d a t a f r o m [ 9 ] , r e - N = 5, SCAVG = 13.0, SD = 15.8, r d - N = 3, SCAVG = 15.5, SD = 3.7, s h p - N = 5, SCAVG = 9.3, SD =1.9)  84  —  air-water  o  o  2.4 o  o o  H/D  1.6  o  o  0.8 o o  0  0.4  0.8  Froude Number = V//gD  gure 15 -  C r i t i c a l Pool Depth (CPD) For The Re-entrant Geometry. ( a i r - w a t e r drawdown data from [ 9 ] , N = 9, SCAVG = 21.2, SD = 6.4)  85  1.6  air-water  Figure  16 -  C r i t i c a l Pool Depth (CPD) For The Rounded Geometry. ( a i r - w a t e r drawdown data from [ 9 ] , N = 23, SCAVG = 10.1, SD = 2.1)  86  3.0 — air - water • low SC o high SC o  2.4  a o  H/D  o  o  1.6  o  o D  •  0.8  •  ( • °  DD  D  0.4 Froude Number =  Figure  17 -  o  0.8  1.2  V/\[QD  The E f f e c t Of S u b c o o l i n g On CPD F o r The S h a r p edged Geometry. ( a i r - w a t e r drawdown d a t a f r o m [ 9 ] , Low SC i s SC <, 9.0, N = 9, SCAVG = 6.0, SD = 1.2, H i g h SC i s SC * 9.0, N = 9, SCAVG = 19.0, SD = 7.6)  18a  18b  18d Figure  18 -  18e  18c  18f  P i c t u r e s Of I n c i p i e n t Drawdown, Spouting And OCB In The Re-entrant Geometry. (18a - drawdown cone and c a v i t a t i o n bubble, 18b - drawdown cone d u r i n g v i o l e n t regime, 18c - s p o u t i n g from above, I8d, I8e, and 18f - OCB at 0, 1.8 and 2.5 sees.)  88  WVrV>rVy^  0  4.0  2.0 TIME  6.0  8.0  75  100  (SECONDS)  0.0100  0.0075  tr iii o Q. cn  0.0050  0.0025  25  50 FREQUENCY (Hz)  Figure  19 -  F r o u d e Number F l u c t u a t i o n And F r e q u e n c y A n a l y s i s F o r The R e - e n t r a n t G e o m e t r y . ( A F r * = 10% ( a p p r o x i m a t e l y ) )  89  0  1.0  2.0  3.0  4.0  TIME (SECONDS)  0.0250  1  0.0175 tr. Ixi  £  0.0125  co 5 rr 0.0063  V 50  100  150  200  FREQUENCY (Hz) Figure  20 -  F r o u d e Number F l u c t u a t i o n A n d F r e q u e n c y A n a l y s i s F o r The Rounded Geometry. (AFr* = 27% (approximately), note - small b u b b l e s t r a v e r s i n g by probe)  90  4.8  3.2 o w  1.6  O >  1.0  2.0  3.0  4.0  TIME (SEC)  0.020  0.015 te. UJ  o 0. tn S  0.010  0.005  * 50  100 FREQUENCY  Figure  21 -  150  L 200  (Hz)  Froude Number F l u c t u a t i o n And Frequency A n a l y s i s For The Sharp-edged Geometry. (AFr* = 15% (approximately))  91  '//////A  22b F i g u r e 22 -  777777, 77777} 777777A  22c Froude Number F l u c t u a t i o n In The Re-entrant Geometry During B r i d g i n g . (22a - f l u c t u a t i o n (AFr* = 80% ( a p p r o x i m a t e l y ) ) , 22b - b r i d g i n g with vapour annulus, 22c - b r i d g i n g w i t h vapour core)  23a  Figure  23 -  23b  23c  M i s c e l l a n e o u s P i c t u r e s Of The Re-entrant Geometry. (23a - asymmetric s p o u t i n g o c c u r i n g with s t r a i g h t e n i n g c r o s s , 23b - vapour r e g i o n a t t a c h e d at vena c o n t r a c t a , 23c - spouting o c c u r r i n g from l a r g e b r i d g e d vapour space)  F i g u r e 24 -  Streamline Pattern In L i q u i d - O n l y Flow. (24a - re-entrant geometry, 24b - sharp-edged geometry, 24c - rounded geometry)  25a  25b  FROUDE NUMBER • V//gTT  Figure  25 -  FROUDE NUMBER « V/VgD~  T h e o r e t i c a l OCB Curves. Note s c a l e change. (25a - without entrainment, 25b - with entrainment, d e r i v e d from; H/D = F r / 2 - SC with Pch of 76000 Pa (nominal), g i v i n g H/D = -118.9 + 7.56Tch + F r / 2 ) 2  2  0  o  0  o 0o  o°o  26a  F i g u r e 26 -  26b  V i o l e n t Spouting In The Re-entrant Geometry. (26a - bubble at p o s i t i o n near entrance with evolved vapour spouting upwards, 26b - bubble a t p o s i t i o n below entrance with evolved vapour swept downwards)  0  0.4  0.8  1.2  Froude Number = V/JgD F i g u r e 27 -  Expected Behaviour At D i f f e r e n t V a l u e s Of S u b c o o l i n g . (Three-dimensional volume bounded by OCB and I n c i p i e n t Drawdown s u r f a c e s )  97  3.2  LIQUID PHASE ONLY  C P D .  2.4  OCB VAPOUR , VAPOUR BUBBLES/ BUBBLES • "° ' DOWN •  VAPOUR AND LIQUID P H A S E  0.8 INSTABILITY*  ID  FLOW IMPOSSIBLE IN THIS REGION  0.4 Froude  gure 28 -  0.8  1.2  Number = V/^gD  I d e a l i z e d CPD For The Re-entrant Geometry At SC=9. (the OCB curve i s the l o c a t i o n of c a v i t a t i o n from pure l i q u i d phase, and CPD i s the depth that must be exceeded t o e x p e l any p r e v i o u s l y e n t r a i n e d or generated vapour)  98  3.2  LIQUID  PHASE  ONLY  2.4  H/D  1.6  0.8  FLOW IMPOSSIBLE IN THIS REGION  0 0.4  0.8  1.2  Froude Number = V / / g D  Figure  29 -  I d e a l i z e d CPD F o r The Rounded G e o m e t r y A t SC=9. (CPD i s t h e d e p t h t h a t must be e x c e e d e d t o e x p e l any p r e v i o u s l y e n t r a i n e d generated vapour)  or  99  3.2  LIQUID PHASE ONLY  2.4 C P D  H/D  VAPOUR / VAPOUR BUBBLES • BUBBLES UP / DOWN /  /  1.6  VAPOUR AND LIQUID PHASE  0.8  •  I  /  • VIOLENT » INSTABILITY /  ID  FLOW IMPOSSIBLE IN THIS REGION  0.4 Froude  Figure  30 -  0.8  1.2  Number = V//gD~  I d e a l i z e d CPD F o r T h e S h a r p - e d g e d G e o m e t r y A t SC=9. ( t h e OCB c u r v e i s t h e l o c a t i o n o f c a v i t a t i o n f r o m p u r e l i q u i d p h a s e , a n d CPD i s t h e d e p t h t h a t must be e x c e e d e d t o e x p e l any p r e v i o u s l y e n t r a i n e d o r generated vapour)  100  BIBLIOGRAPHY 1.  Simpson, L. " S i z i n g P i p i n g For Process P l a n t s " , Chemical E n g i n e e r i n g , June, 1968, p. 192 - 214.  2.  B e r g l e s , A.E., C o l l i e r , J.G., Delhaye, J.M., Hewitt, G.F. and Mayinger, F. Two-Phase Flow And Heat T r a n s f e r In The Power And Process I n d u s t r i e s . McGraw-Hill, New York, 1981.  3.  Knapp, D. and Hammit, F.G. C a v i t a t i o n . E n g i n e e r i n g S o c i e t i e s Monographs, McGraw-Hill, Toronto, 1970.  4.  Souders, M., C o r n e i l , H.G., Emert, F.L. and Huntington, R.L. "Performance Of Bubble-Plate Columns", I n d u s t r i a l and E n g i n e e r i n g Chemistry, Vol. 30, 1938, p. 86 - 91 .  5.  Oba, R., Ikohagi, T. and Kim, K.T. " C a v i t a t i o n In An Extremely L i m i t e d Flow Through Very Small O r i f i c e s " , I n t e r n a t i o n a l Symposium on C a v i t a t i o n I n c e p t i o n , ASME Polyphase Flow Committee of F l u i d s E n g i n e e r i n g D i v i s i o n , New York, 1979, p. 147 152.  6.  L i e n h a r d , J.H. and Goss, C D . " I n f l u e n c e s Of S i z e And C o n f i g u r a t i o n On C a v i t a t i o n In Submerged O r i f i c e Flows", ASME Paper 71-FE-39, 1971.  7.  D a v i d i a n , J . and G l o v e r , J.E. "Development Of The N o n - C i r c u l a t o r y Waterspout", Proceedings, ASCE, J o u r n a l of the H y d r a u l i c s D i v i s i o n , V o l . 82, Paper No. 1038-3, August, 1956, p. 1038-3 1038-7.  8.  Harleman D., Morgan R. and Purple R. "Selective Withdrawal From A V e r t i c a l l y S t r a t i f i e d F l u i d " , 8th Congress I n t e r n a t i o n a l A s s o c i a t i o n For H y d r a u l i c Research, August, 1959, p. 10-C-1 - 10-C-16.  9.  K a l i n s k e , A.A. " H y d r a u l i c s Of V e r t i c a l D r a i n And Overflow P i p e s " , B u l l e t i n 26, U n i v e r s i t y of Iowa S t u d i e s , 1939-1940, p. 26 - 40.  10.  V a l l e n t i n e , H. R. A p p l i e d Hydrodynamics. Butterworths, London, 1967.  101  11.  K e l l y , A.G. " H y d r a u l i c Design Of Siphons", Proceeds I n s t i t u t e of Mechanical Engineers, V o l . 180, 1965-1966, p. 981 - 1011.  12.  Bharathan, D. "Air-Water CounterCurrent Annular Flow", E l e c t r i c Power Research I n s t i t u t e , NP-1165, September, 1979.  13.  W a l l i s , G.B., deSieyes, D.C., R o s s e l l i , R.J. and Lacombe, J . "CounterCurrent Annular Flow Regimes For Steam And Subcooled Water In A V e r t i c a l Tube", EPRI NP-1336, January, 1980.  14.  Handbook Of A i r C o n d i t i o n i n g System Design. C a r r i e r A i r C o n d i t i o n i n g Company, McGraw-Hill, Toronto, 1965.  15.  K l i n e , S.J., and M c C l i n t o c k , F.A. "The D e s c r i p t i o n Of U n c e r t a i n t i e s In S i n g l e Sample Experiments", Mechanical E n g i n e e r i n g , January, 1953, p. 3.  16.  T a i t e l , Y., Bornea, D. and Dukler, A.E. "Modelling Flow P a t t e r n s For Steady Upward GasL i q u i d Flow In V e r t i c a l Tubes", AIChE J o u r n a l , Vol. 26, May, 1980, p. 345 - 354.  102  APPENDIX A - DIMENSIONAL ANALYSIS  Two methods of dimensional  a n a l y s i s are used; (A1) a  d e r i v a t i o n from a simple model using B e r n o u l l i ' s equation and (A2) a c l a s s i c a l  Buckingham ir  analysis  AJ_ B e r n o u l l i ' s Equation  Pch  Note: Po and Vo are the pressure and v e l o c i t y at point "o"  Assumptions: (a) - no v e l o c i t y or pressure g r a d i e n t a c r o s s the tube (b) - no temperature g r a d i e n t i n the pool or downcomer (c) - no vapour phase i n t i t i a l l y  present  (d) - no s u r f a c e t e n s i o n e f f e c t s (e) - no flow s e p a r a t i o n or  entrainment  (f) - no f r i c t i o n a l d i s s i p a t i o n  i n the pool  (g) - thermodynamic e q u i l i b r i u m e x i s t s at a l l times (h) - uniform n u c l e a t i o n s i t e  spacing  103  Using B e r n o u l l i ' s equation between the pool  interface  and p o i n t "o" and s u b t r a c t i n g Psat  Po - Psat = Pch - Psat + pgH - pVo /2 2  D i v i d i n g by pgD  (Po - Psat)/pgD = (Pch - Psat)/pgD + H/D - Vo /2gD 2  But  s i n c e Vo /2gD = F r / 2 2  2  (Po - Psat)/pgD = (Pch - Psat)/pgD + H/D - F r / 2 2  From t h i s equation we  observe:  Po - Psat = 0 a t i n c i p i e n t c a v i t a t i o n  (OCB)  (Pch - Psat)/pgD = dimensionless s u b c o o l i n g (SC) H/D = dimensionless pool  depth  Fr = dimensionless f l o w r a t e  T h e r e f o r e , when i n c i p i e n t c a v i t a t i o n occurs at the tube entrance  SC + H/D - F r / 2 2  = 0  104  A2 Buckingham TT  The r e l e v a n t  Analysis  independent v a r i a b l e s a r e :  Pch - P s a t ( T c h ) , p, g, D, H, V, n,  a  These v a r i a b l e s are comprised of the fundamental dimensions [M], [ L ], and [ T ] ,  Using p, g, and D as the  r e c u r r i n g set of v a r i a b l e s , the f o l l o w i n g  five  d i m e n s i o n l e s s groups are o b t a i n e d :  TT1 = (Pch - Psat (Tch) )/pgD, TT2 = H/D,  TT3 = V ( g D ) "  l/2  ,  TT4 = ^ / ( p g ^ D ^ ) , TT5 = a/(pgD ) 3  2  Making the same assumptions as i n (A1) with the v i s c o u s and s u r f a c e t e n s i o n f o r c e s having no e f f e c t on the flow regimes velocity  ( i e . the bubbles are l a r g e and t h e i r  rise  i s determined by the tube diameter) the  f o l l o w i n g three d i m e n s i o n l e s s groups remain:  TT1 = SC = (Pch - Psat (Tch) )/pgD, TT2 = H/D, TT3  = Fr = V(gD) -  1/2  Note that 7r3/7r4 = Reynolds number and ir3/'(^5)^ number  = Weber  1 05  APPENDIX  B - S A M P L E C A L C U L A T I O N S AND  Sample  calculated.  manually  H a n d AZ  a value  o f H/D,  (manometer) were  and Tch and Q were  acquisition  ANALYSIS  Calculations  NOTE: - f o r e a c h m e a s u r e m e n t was  ERROR  recorded  by t h e  F r and recorded data  system  Units: H,  D,  Psat,  AZ  (m)  P c h , Patm  V(m/s),  (Pa)  Q(litres/s)  Constants: p  = p(Freon-11) =  pw  = p(water)  D  = 0 . 0 2 5 4 m,  =  1500  1000  kg/m  kg/m  g = 9.8  3  m/s  2  3  a t 15°C  (from [14])  SC  1 06  Therefore: Fr  = V(gD)-  H/D  = H/0.0254  SC  = (Pch - Psat)/pgD  1/2  = 4Q/( 1 000TT( 0 . 0254) - ( 9 . 8 ) ^ ) = 3.96Q 2  5  With Psat = 2823Tch + 31650 ( l i n e a r i z e d  f o r small ATch  from [14]) Pch  = Patm - pwgAZ (AZ from manometer)  Error  Analysis  As s t a t e d i n [15], i f Y i s the dependent v a r i a b l e and Y = Y(x1,x2...xn), then the u n c e r t a i n t y of the r e s u l t i s Y ± y with  y = [(e19Y/9xl)  2  + (e29Y/9x2)  2  + ...(en9Y/9xn) ]** 2  where e1 t o en are the u n c e r t a i n t i e s or probable e r r o r s of  the v a r i a b l e s x1 to xn r e s p e c t i v e l y .  1 07  The  uncertainty Psat ± 300  Pa  (as Tch  Pch  ± 300  Pa  (as AZ  Q  ± 0.003 l i t r e s / s  H  ± 0.001  D  ± 0.0005 m  Placing using H/D,  estimates (e's)  ± 0.1°C) ± 0.02  partial derivatives SC,  AH/D  = ±  0.04  AFr  = ±  0.01  ASC  = ±  1.17  m and  Patm ± 100  Pa)  m  these u n c e r t a i n t i e s  Fr and  are:  i n t o the above equation  from the equations d e f i n i n g  e r r o r e s t i m a t e s (y's) are obtained  of:  Notes: - f l u c t u a t i o n s i n chamber pressure prevented reading the manometer with greater  than the above  mentioned accuracy - t h i s a n a l y s i s has  n e g l e c t e d both time lapse  judgement e r r o r s which may  be q u i t e  large  and  108  APPENDIX C - INDEX TO VIDEO CASSETTE REGIME NUMBER and PAGE NUMBER (refer to text)  ENTRANCE GEOMETRY, REGIME AND COMMENTS  #1 - p. 6,7,8  RE-ENTRANT NOTE: - a i r - w a t e r t h i s regime only - i n c i p i e n t drawdown i n twocomponent flow - entrainment of a i r bubbles with small s p h e r i c a l bubbles r i s i n g up i n t o the chamber - small v o r t i c e s v i s i b l e periodically - trapped a i r bubbles r i s i n g through the f a l s e f l o o r around the entrance - annular flow (with necking) when the l i q u i d l e v e l i s lowered below the entrance  #2 - p. 36,39  RE-ENTRANT NOTE: - Freon-11 i s shown i n the f o l l o w i n g regimes - OCB from a l i q u i d - o n l y regime - t r i g g e r i n g of c a v i t a t i o n by bubble p a s s i n g through the vena contracta - v i o l e n t spouting of r i s i n g bubbles  #3 - p. 8  RE-ENTRANT NOTE: - annular flow i n a l i q u i d l e v e l w e l l below the downcomer entrance - the lower v i s c o s i t y of Freon-11 w i l l cause a higher f l o w r a t e (and more necking) a t a g i v e n pool depth than i n a i r - w a t e r flow - nominal H/D = 0.20, F r = 0.20 and SC = 11.1  109  REGIME NUMBER and PAGE NUMBER ( r e f e r to text)  ENTRANCE GEOMETRY, REGIME AND COMMENTS  #4 - p.  38,53  RE-ENTRANT NOTE: - a violent instability - f l o w r a t e i n the up-down t r a n s i t i o n , t h e r e f o r e bubbles accumulate i n , but cannot escape from the entrance region - c a v i t a t i o n o c c u r r i n g throughout the entrance region - nominal H/D = 0.28, F r = 0.43 and SC = 7.7  #5 - p.  39,45  RE-ENTRANT NOTE: #5a - bubbles formed i n OCB c l e a r e d by CPD (CPD curve above OCB) - nominal H/D = 1.42, F r = 0.39 and SC = 4.5 #5b - OCB at h i g h Froude number showing a vapour c a v i t y a t t a c h e d t o the tube w a l l with a l l generated bubbles (small) swept down the tube  #6 - p.  38,45  RE-ENTRANT NOTE: - v i o l e n t regime - an annular c a v i t y ( s i m i l a r t o regime #5b forms, and with i n c r e a s i n g f l o w r a t e the vapour moves t o the core of the tube, g i v i n g r i s e to s p o u t i n g a t h i g h Froude number - nominal H/D = 1.02, Fr =0.76 and SC = 9.3  1 10  REGIME NUMBER and PAGE NUMBER (refer to text) #7 - p.  45,38  ENTRANCE GEOMETRY,, REGIME AND COMMENTS  RE-ENTRANT NOTE: - the annular c a v i t y (#5b) w i l l detach as the f l o w r a t e i s decreased i n t o the up-down t r a n s i t i o n area - v i o l e n t spouting then occurs - the l a r g e bubbles ( s l u g s ) tend t o be b u l l e t - s h a p e d - nominal H/D = 0.71, F r = 0.39 and SC = 4.1  #8 - p. 53  RE-ENTRANT NOTE: - small bubbles i n high frequency o s c i l l a t i o n a t verge of c a v i t a t i o n inception - i n t e r a c t i o n and coalescence of bubbles downstream - the i n s t a b i l i t y becomes more v i o l e n t with i n c r e a s i n g f l o w r a t e as the bubbles become l a r g e r - e v e n t u a l l y a vapour c a v i t y a t t a c h e s a t the entrance - nominal H/D = 0.32, F r = 0.25 and SC = 3.7  #9 - p.  RE-ENTRANT NOTE: #9a - OCB with small bubbles swept down the tube - a s t a t i o n a r y c a v i t y forms and grows i n s i z e u n t i l l a r g e bubbles break loose and r i s e (segregation of bubbles due t o shape and s i z e )  53,40  #9b - CPD a t "constant" f l o w r a t e (the pool depth must be changed very slowly i f the flowrate a t the f l o s e n s o r i s t o be equal t o that i n the downcomer) - OCB r e t u r n s a f t e r the bubbles have c l e a r e d (OCB curve above CPD)  111  REGIME NUMBER and PAGE NUMBER (refer to text)  ENTRANCE GEOMETRY, REGIME AND COMMENTS  #10 - p. 8  RE-ENTRANT NOTE: - necking chokes o f f the flow as b r i d g i n g occurs with i n c r e a s i n g flowrate - necking i s enhanced by the presence of a c a v i t a t i o n bubble a t the entrance  #11 - p. 53  RE-ENTRANT NOTE: - h i g h frequency o s c i l l a t i o n of small bubbles a t low pool depths and f l o w r a t e s - i n t e r a c t i o n between o s c i l l a t i n g bubbles and c a v i t a t i o n a t the entrance - nominal H/D = 0.59, F r = 0.29 and SC = 5.8  #12 - p.  ROUNDED NOTE: - v i o l e n t i n s t a b i l i t y with spouting - s i m i l a r t o "churn" flow [16] - l a r g e bubbles remain "mobile" and detached from the w a l l - vapour g e n e r a t i o n a t p e r i p h e r y of bubble - nominal H/D =1.3, F r = 0.34 and SC = 22.3  56,46  1 12  REGIME NUMBER and PAGE NUMBER (refer to text)  ENTRANCE GEOMETRY, REGIME AND COMMENTS  #13 - p. 49  ROUNDED NOTE: - i n c i p i e n t drawdown showing l a r g e drawdown cone that f o l l o w s the c u r v a t u r e of the entrance  #14 - p. 38  ROUNDED NOTE: - a l a r g e s l u g of vapour moves between a p o s i t i o n a t the entrance and a p o s i t i o n downstream - a l l generated vapour i s swept down the tube except when the bubble i s a t the tube entrance - v i o l e n t spouting a g a i n s t the chamber roof - p e n e t r a t i o n of vapour down the tube - nominal H/D = 1.46, Fr = 0.48 and SC = 27.3  #15 - p.  SHARP-EDGED NOTE: #l5a - v i o l e n t regime p a s s i n g through CPD (with "constant" flowrate) - nominal H/D = 0.51, Fr = 0.33 and SC = 11.1  39,45  #15b - c a v i t a t i o n t r i g g e r e d by a r i s i n g bubble - the s i z e and shape of a " l a r g e " bubble becomes an e x t r a parameter necessary t o d e s c r i b e the flow - nominal H/D = 0.91, F r = 0.61 and SC = 24.8 #15c - i n c i p i e n t drawdown - nominal H/D = 0.35, Fr = 0.36 and SC = 25.6  

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