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Bubble compression and condensation in single component co-current downflow Chang, Ian I. 1986

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C  2  BUBBLE COMPRESSION AND CONDENSATION IN SINGLE COMPONENT CO-CURRENT DOWNFLOW  by  IAN I CHANG B.A.Sc, The University of B r i t i s h Columbia, 19  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in THE FACULTY OF GRADUATE STUDIES Department of Mechanical Engineering  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA October, 1986  © IAN I CHANG, 1986  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I  further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may  be granted by the head o f  department o r by h i s o r her r e p r e s e n t a t i v e s .  my  It i s  understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be allowed without my  permission.  Department o f  Mechanical Engineering  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date  October 15, 1986  written  ABSTRACT  In an i n v e s t i g a t i o n of the process termed hydraulic vapour compression (HVC), a photographic study of bubble compression and condensation rates i n s i n g l e component co-current downflow has been performed. Supplemental to the photographic study, measurements of the deliverable mass flowrates of the HVC process were also carried out. The downward flow of a gas and l i q u i d mixture, as occurs i n the HVC process, r e s u l t s i n the compression of the gas phase because of the increasing hydraulic pressure.  Bubble compression heating provides the  d r i v i n g temperature difference f o r both heat and mass transfer to occur. The minimization of the transfer processes i s desirable to ensure a high compression e f f i c i e n c y . Experiments were carried out using near saturated Freon-11 i n a 2.54 cm I.D., 1.7  m long glass downcomer.  t r a v e l along the downcomer.  Bubbles were filmed during  H i s t o r i e s of the decrease i n i n d i v i d u a l  bubble size were determined from silhouette traces obtained from sequenced single frames selected from the exposed films.  Bubble volumes  and surface areas were inferred by numerically revolving d i g i t i z e d images of the traces about t h e i r p r i n c i p a l centroidal axes.  The  inferred volumes and surface areas provided the basis upon which heat and mass transfer rates were calculated.  Delivered vapour mass  flowrates were measured by hot f i l m anemometry. Results showed that mass condensation rates increased along the length of the downcomer.  Local external Nusselt numbers used to charac-  t e r i z e the transfer processes at the bubble wall, ranged from 0.1 to 16. The deliverable mass flowrates achieved by the HVC process were found to be comparable to those produced by the w e l l known process of hydraulic a i r compression. - ii -  TABLE OF CONTENTS Page ABSTRACT  i i  TABLE OF CONTENTS  i i i  LIST OF TABLES  v  LIST OF FIGURES  vi  NOMENCLATURE  x  ACKNOWLEDGEMENT  xiv  CHAPTER I - INTRODUCTION  1  1.1  H y d r a u l i c Vapor Compression (HVC)  1  1.2  L i t e r a t u r e Review  5  1.2.1  H y d r a u l i c A i r Compression (HAC)  5  1.2.2  Bubble Dynamics and Heat T r a n s f e r  7  1.2.2.1  Experimental  7  1.2.2.2  Theoretical  11  1.3  Scope of the Present I n v e s t i g a t i o n  12  CHAPTER I I - EXPERIMENTAL APPARATUS  13  2.1  General Concept  13  2.2  Working F l u i d  16  2.3  P i p i n g , Tubing, Hose, and F i t t i n g s  16  2.4  Vacuum Chamber, S e p a r a t i o n Tank, Overflow V e s s e l , Accumulator Tank  16  2.5  C i r c u l a t i o n and Vacuum Pumps  17  2.6  Downcomer I n l e t O r i f i c e and C a v i t a t i o n Rod  17  2.7  Downcomer T e s t S e c t i o n  18  2.8  Instrumentation  18  2.9  2.8.1  Temperature Measurement  2.8.2  P r e s s u r e Measurement  19  2.8.3  Depth Measurement  19  2.8.4  L i q u i d F l o w r a t e Measurement  19  2.8.5  Data A c q u i s i t i o n System  20  2.8.6  Hot F i l m Anemometry  20  P h o t o g r a p h i c Equipment  25  I n i t i a l Equipment T e s t i n g  - iii  18  22  CHAPTER I I I - EXPERIMENTAL PROCEDURE 3.1  •••  25  -  TABLE OF CONTENTS  (Continued) Page.  3.2  Routine Apparatus  S t a r t - u p and Shut-down  27  3.3  Bubble Photographic S t u d i e s  29  3.4  Vapour Exhaust V e l o c i t y Measurements  30  CHAPTER IV - DATA ANALYSIS 4.1  31  Film Analysis 4.1.1  31  D e t e r m i n a t i o n o f t h e Instantaneous  Bubble  S u r f a c e Area and Volume  31  4.1.2  D e t e r m i n a t i o n o f Bubble T r a c e I n t e r v a l  33  4.1.3  D e t e r m i n a t i o n o f Bubble T o t a l T r a c k i n g Time and V e l o c i t y  34  4.2  C a l c u l a t i o n o f t h e Bubble E x t e r n a l N u s s e l t Number  34  4.3  C a l c u l a t i o n of the Bubble P e c l e t Number  38  4.4  C a l c u l a t i o n o f the Vapour Mass F l o w r a t e  39  CHAPTER V - RESULTS AND DISCUSSION  41  5.1  Q u a l i f y i n g Remarks  41  5.2  Experimental E r r o r  41  5.3  Rate o f Decrease  42  5.4  Bubble  5.5  Heat T r a n s f e r Rate  49  5.6  Vapour Mass F l o w r a t e  51  o f Bubble S i z e  Condensation Rate  47  CHAPTER VI - CONCLUSIONS AND RECOMMENDATIONS 6.1 6.2 6.3  Condensation and Heat T r a n s f e r Rate T e c h n i c a l F e a s i b i l i t y o f H y d r a u l i c Vapour Compression F u r t h e r Work 6.3.1  53 .  53 54 55  M o d i f i c a t i o n s t o t h e Apparatus and Instrumentation  55  6.3.2  Suggestions Concerning the F i l m A n a l y s i s  55  6.3.3  F u r t h e r Areas o f Study  56  BIBLIOGRAPHY  58  APPENDIX A - HOT FILM ANEMOMETRY DETAILS AND CALIBRATION PROCEDURE  61  APPENDIX B - DETERMINATION OF THE HEAT TRANSFER BETWEEN THE VAPOUR AND LIQUID PHASES  64  APPENDIX C - ERROR ANALYSIS  67  - iv -  LIST OF TABLES Page  1  Experimental Data for the Bubble Photography Tests ....  130  2  Experimental Data f o r the Vapour Mass Flowrate Tests ..  131  3  Data from the Linear Least Squares F i t s of the Variat i o n of the Bubble Surface Area and Volume with Time ..  132  4  Calculated Data f o r the Bubble Photograph Tests  133  A.l  Hot Film Anemometry Details  134  C.l  Experimental Errors  135  - v -  LIST OF FIGURES Page 1.1  Schematic of the Hydraulic Compression Process  70  1.2  Schematic of the Single Compression Stage Open Cycle Heat Pump  71  Schematic of the Hypothetical Radial Temperature P r o f i l e of a Vapour Bubble During Compression  72  2.1  Photograph of the Experimental Apparatus  73  2.2  Photograph of the Instrumentation  74  2.3  Schematic of the Experimental Apparatus  75  2.4  Photograph of a Supercavitation Jet Formed at  1.3  the Test Section Entrance  76  2.5  Details of the Vacuum Chamber  77  2.6  Details of the Separation Tank  78  2.7  Details of the Test Section Inlet O r i f i c e  79  2.8  Flowchart of the Data Acquisition Program  80  2.9  Photograph of the Hot Film Probe Position i n the Vapour Exhaust Tube Schematic of the Bubble Photography Equipment Arrangement  81 82  P a r t i a l Film Sequence of a Vapour Bubble During Hydraulic Compression  83  Schematic of the Numerical Procedure for Estimating Bubble Surface Area and Volume  87  Variation of the Surface Area and Volume with Time: Bubble 311  88  Variation of the Surface Area and Volume with Time: Bubble 613  89  Variation of the Surface Area and Volume with Time: Bubble 621  90  Variation of the Surface Area and Volume with Time: Bubble 622  91  2.10 4.1 4.2 4.3 4.4 4.5 4.6  - vi -  LIST OF FIGURES  (Continued) Page  4.7 4.8 4.9 4.10  4.11 4.12 4.13 4.14 4.15 4.16  5.1 5.2 5.3 5.4 5.5  Variation of the Surface Area and Volume with Time: Bubble 624  92  Variation of the Surface Area and Volume with Time: Bubble 721  93  Variation of the Surface Area and Volume with Time: Bubble 722  94  Variation of the Surface Area and Volume with Time: Bubble 731  95  Variation of the Surface Area and Volume with Time: Bubble 811  96  Variation of the Surface Area and Volume with Time: Bubble 812  97  Variation of the Surface Area and Volume with Time: Bubble 813  98  Variation of the Surface Area and Volume with Time: Bubble 821  99  Variation of the Surface Area and Volume with Time: Bubble 822 .  100  Variation of the Surface Area and Volume with Time: Bubble 823  101  Variation of the Volume with Normalized A l l Bubbles  102  Position:  Variation of the Surface Area with Normalized A l l Bubbles  103  Variation of the Equivalent Diameter with Normalized Position: A l l Bubbles  104  Variation of the Nominal Relative Velocity with Normalized Position: A l l Bubbles  105  Variation of the Bubble Volume with Normalized Position: T = 11 °C  106  Variation of the Bubble Volume with Normalized Position: T = 12 °C  107  £  5.6  Position:  0  - vii-  LIST OF FIGURES (Continued) Page 5.7  Variation of the Bubble Volume with Normalized Position: T^ = 13 °C  108  5.8  Variation of the Bubble Surface Area with Normalized Position: T^ = 11 °C  109  5.9  Variation of the Bubble Surface Area with Normalized Position: T = 12 °C  110  Variation of the Bubble Surface Area with Normalized Position: T = 13 °C  Ill  £  5.10  £  5.11  Variation of the Bubble Spherical Equivalent Diameter with Normalized Position: T • 11 °C  112  Variation of the Bubble Spherical Equivalent Diameter with Normalized Position: T = 12 °C  113  Variation of the Bubble Spherical Equivalent Diameter with Normalized P o s i t i o n : T = 13 °C  114  Variation of the Bubble Condensation Mass Loss with Normalized Position: A l l Bubbles  115  5.15  Variation of the Bubble Condensation Mass Loss with Normalized Position: T^ = 11 °C  116  5.16  Variation of the Bubble Condensation Mass Loss with Normalized P o s i t i o n : T = 12 °C  117  Variation of the Bubble Condensation Mass Loss with Normalized Position: T = 13 °C  118  Variation of the Local External Nusselt Number with Normalized Position: A l l Bubbles  119  5.19  Variation of the Dimensionless Driving Temperature Difference with Normalized Position: A l l Bubbles  120  5.20  Variation of the Local External Nusselt Number with Normalized P o s i t i o n : T% = 11 °C  121  Variation of the Local External Nusselt Number with Normalized Position: T^ - 12 °C  122  Variation of the Local External Nusselt Number with Normalized Position: T = 13 °C  123  Variation of the Local External Nusselt Number with the Nominal Relative Peclet Number  124  £  5.12  £  5.13  £  5.14  £  5.17  £  5.18  5.21 5.22  £  5.23  - viii -  LIST OF FIGURES (Continued) Page 5.24  Variation of the Position Averaged Nusselt Number with the Position Averaged Peclet Number  125  Variation of the Vapour Mass Flowrate with the Liquid Mass Flowrate  126  Variation of the Inlet Liquid Temperature with the Outlet Vapour Temperature  127  A. l  Hot Film Probe Calibration Curve  128  B. l  Schematic of the Bubble Compression Process  129  5.25  5.26  - ix -  NOMENCLATURE  A  c a l i b r a t i o n constant i n King's law  A  bubble surface area [m ] 2  b  A  vapour exhaust tube cross section area [m ] 2  ex  B  c a l i b r a t i o n constant i n King's law  c  l i q u i d s p e c i f i c heat capacity [J/kg °C]  P D  g e  bubble spherical equivalent diameter based on the r a t i o of volume to surface area [m]  D sev  bubble spherical equivalent diameter based solely on volume [ml  e  vapour s p e c i f i c i n t e r n a l energy corresponding to the l o c a l pressure [J/kg]  e  l i q u i d s p e c i f i c i n t e r n a l energy corresponding to the l o c a l pressure [J/kg]  E  i n t e r n a l energy i n the f i r s t law of thermodynamics [J]  E  b  hot f i l m anemometer bridge voltage [V] mass f r a c t i o n of vapour derived from the law of p a r t i a l pressures  g  g r a v i t a t i o n a l constant [m/s ] 2  h  vapour s p e c i f i c enthalpy corresponding to the l o c a l pressure 8  h  [J/kg] l i q u i d s p e c i f i c enthalpy corresponding to the l o c a l pressure  1  [J/kg]  h  l i q u i d depth i n the separation tank [m]  k  a i r thermal conductivity [W/m°C]  k^  l i q u i d thermal conductivity evaluated at the f i l m [W/m°C]  k  vapour thermal conductivity [W/m°C]  g  temperature  k m  vapour/air mixture thermal conductivity [W/m°C]  L  latent heat of condensation corresponding to the l o c a l pressure [J/kg]  - x -  hot f i l m probe heated length [m] m  instantaneous mass condensed [kg]  m  retained vapour mass [kg]  m  retained l i q u i d mass [kg]  n  exponent i n King's law  N  number of 1 cm distance increments along the tracking length f o r a given bubble  Nu  bubble o v e r a l l l o c a l external Nusselt number  c  Nu  P  hot f i l m probe Nusselt number  Pj  c a l i b r a t i o n wind tunnel dynamic pressure [Pa]  p  pressure at the downcomer e x i t [Pa]  g x  p  pressure i n the separation tank [Pa]  P  v c  pressure i n the vacuum chamber [Pa]  Pr  l i q u i d Prandtl number  q^  t o t a l heat transported from the vapour i n t o the l i q u i d [W]  Q  heat transferred i n the f i r s t law of thermodynamics [J]  Q  downcomer i n l e t l i q u i d flowrate [i/s]  R  3  hot f i l m anemometer bridge s e r i e s resistance [ohms] hot f i l m probe cold resistance [ohms]  R  Q  hot f i l m probe operating resistance [ohms]  Rp  hot f i l m probe resistance [ohms]  Re  bubble Reynolds number  Re P t  hot f i l m probe Reynolds number elapsed time referenced to the s t a r t of the tracking length f o r a given bubble [s]  T e  hot f i l m probe c a l i b r a t i o n ambient temperature [°C]  TV  hot f i l m probe ambient temperature [°C]  T  f i l m temperature [°C]  f  - xi -  T  vapour temperature i n the separation tank [ C] c  g  downcomer i n l e t l i q u i d temperature [°C] T T  hot f i l m probe operating temperature [°C] P s  u  a  u  ex  u  g i  U  u u  saturation temperature corresponding to the l o c a l pressure [°C] c a l i b r a t i o n wind tunnel a i r v e l o c i t y l i q u i d v e l o c i t y at the downcomer exit bubble nominal absolute v e l o c i t y Inlet l i q u i d v e l o c i t y  r  \  [m/s]  [m/s]  [m/s]  vapour/air mixture average v e l o c i t y m  [m/s]  bubble nominal r e l a t i v e v e l o c i t y  [m/s]  [m/s]  bubble o v e r a l l l o c a l external heat  transfer c o e f f i c i e n t  volumetric bubble o v e r a l l l o c a l external heat transfer [W/m °C]  [W/m  2  coefficient  3  g  vapour s p e c i f i c volume corresponding to the l o c a l pressure [m /kg]  I  l i q u i d s p e c i f i c volume corresponding to the l o c a l pressure [m /kg]  V  V  3  3  \  bubble volume  W  work done i n the f i r s t law of thermbdynamicE> [J]  f  W  hot  [m ] 3  f i l m probe heated width [m]  x  denotes any thermodynamic property of the vapour/air mixture  m z  position along downcomer length [m]  Greek  vapour density [kg/m ] 3  P g P  £  l i q u i d density [kg/m ] 3  vapour/air mixture density [kg/m ] 3  m  p  - xii -  °C]  y  vapour dynamic v i s c o s i t y [kg/m.s]  y  liquid  P  m  dynamic v i s c o s i t y [kg/m.s]  vapour/air mixture dynamic v i s c o s i t y [kg/m.s]  Subscripts  1  i n i t i a l incremental position  2  f i n a l incremental position  i  i n i t i a l value at start of the tracking length  f  f i n a l value at the end of the tracking length  . Superscripts  -  overbar denotes position averaged  - xiii -  values  ACKNOWLEDGEMENT  The author wishes to express his sincerest gratitude to Dr. E.G. Hauptmann f o r h i s considerable insight and constant encouragement throughout the course of this investigation.  The technical and admini-  s t r a t i v e s t a f f of the mechanical engineering department are to be acknowledged for their conscientiuous assistance.  The author would also  l i k e to thank h i s fellow graduate students for t h e i r invaluable discussions and advice. Special thanks are reserved f o r my parents f o r t h e i r motivating support and unbounded  understanding.  F i n a n c i a l support f o r t h i s study by the Natural Sciences and Engineering Research Council of Canada i s g r a t e f u l l y acknowledged.  - xiv -  1. CHAPTER I INTRODUCTION  1.1  Hydraulic Vapour Compression (HVC) The downward flow of a gas and l i q u i d mixture w i l l r e s u l t i n the  compression of the gas phase because of the increasing hydraulic pressure.  Figure 1.1 shows a schematic of the compression process  achieved i n a large diameter pipe or "downcomer".  Following the  entrainment of the gas into the l i q u i d , the gas phase t y p i c a l l y assumes bubble form and the bubbles are gradually reduced i n size by hydraulic compression as they are carried d ownward by the l i q u i d flow.  This  p r i n c i p l e has been u t i l i z e d i n the well known process of hydraulic a i r compression (HAC), where water i s commonly used as the compression fluid.  A similar process termed hydraulic vapour compression might  employ a single component flow such as water and water vapour.  The  processes of HVC and HAC d i f f e r because compression heating results i n the p a r t i a l condensation of the vapour i n HVC, whereas, the a i r i n HAC does not condense.  The primary motivation for this investigation i s  derived from the current lack of knowledge concerning vapour condensation rates i n the HVC process. A proposed application of the HVC process i s i n a novel open cycle heat pump which w i l l use sea water as the working f l u i d .  The primary  benefit of such a heat pump i s the p o s s i b i l i t y of using the oceans of the world as a source of low grade heat (Ryan [1]). A schematic of a single compression stage open cycle heat pump i s shown i n Figure 1.2. Sea water i s pumped Into a chamber located at the apex of a siphon loop. The vacuum maintained i n the chamber causes p a r t i a l f l a s h i n g of the  2.  inflowing l i q u i d r e s u l t i n g i n the formation of a vapour cavity above the liquid.  The draining of the l i q u i d into a large downcomer located  beneath the chamber induces vapour into the downflow thus i n i t i a t i n g the HVC process.  Separation of the l i q u i d and compressed vapour follows at  the bottom of the downcomer with the heated vapour being delivered to a condenser.  The heat recovered by the condenser can be used for space  heating of commercial and/or r e s i d e n t i a l buildings.  The temperature-  entropy diagram for the HVC process i s also shown i n Figure 1.2.  Sub-  cooled l i q u i d at position 0 i s flashed to saturated vapour at position 1.  The vapour i s compressed from position 1 to 2.  isentropic compression.  Point 2s denotes  The superheated vapour i s condensed from  position 2 to 3. The f e a s i b i l i t y of the heat pump i s dependent on the e f f i c i e n t compression of large quantities of the extremely low density water vapour generated by the flashing of the sea water.  Preliminary c a l c u l a -  tions have shown that the HVC process may be capable of providing a sufficiently  high vapour flowrate ( i n excess of 8 m /s) 3  necessary to  achieve the economies of scale required for p r a c t i c a l application. Judging from the f a c t that hydraulic a i r compressors are capable of generating a i r flowrates i n excess of 18 m /s 3  (Langborne [2]), s i m i l a r l y  sized hydraulic vapour compressors can be expected to produce comparable vapour flowrates. The HVC process can produce any pressure given a s u f f i c i e n t downcomer length.  The amount of compression i s necessarily less than the  hydrostatic pressure difference across the height of the downcomer completely f i l l e d with the compression l i q u i d .  This i s a result of the  reduction i n the mean density of the downflow caused by the presence of the vapour.  The lowered density dictates that the downcomer height must  be greater than the l i q u i d hydrostatic height i n order to achieve a  3. compression r a t i o equal to that as defined by the l i q u i d hydrostatic height. Condensation, or o v e r a l l heat transfer plays an important l i m i t i n g role i n HVC.  If the compression occurs extremely slowly, or i f the heat  transfer rate i s s u f f i c i e n t l y the  large, the vapour i s simply returned to  l i q u i d state as the evaporation or flashing stage of the process i s  reversed.  If the compression occurs very quickly, or i f the heat  transfer rates from the vapour to l i q u i d are low, the vapour e s s e n t i a l l y undergoes adiabatic compression before being delivered to the separation vessel at the bottom of the downcomer.  The heat flux from the bubble  wall thus plays the dominant r o l e i n determining the amount of compressed vapour which the HVC can d e l i v e r . During vapour compression, the driving temperature difference f o r condensation forms between the vapour and l i q u i d phases because the l i q u i d temperature remains e s s e n t i a l l y constant.  This temperature  gradient varies from the center of each bubble out to the surrounding l i q u i d and increases i n magnitude along the length of the downcomer. Condensation occurs when the vapour i s cooled s u f f i c i e n t l y  below the  saturation temperature corresponding to the l o c a l system pressure. For a vapour bubble suspended i n a l i q u i d which i s s l i g h t l y below the saturation temperature, condensation w i l l occur at the bubble wall.  A  hypothetical temperature p r o f i l e i s shown i n Figure 1.3 extending from the  center of a vapour bubble out to the surrounding l i q u i d .  The  temperature at the bubble center w i l l l i k e l y be a maximum and w i l l be s l i g h t l y above saturation because of compression heating and imperfect heat transfer. bubble w a l l .  The temperature w i l l decrease from the center to the In a high purity single component system, the wall  4.  temperature i s very near the saturation temperature corresponding to the l i q u i d pressure (Isenberg, Moalem, and Sideman [3]). The temperature decreases from the wall to the bulk l i q u i d temperature.  The vapour  temperature i s extremely d i f f i c u l t to accurately measure.  It i s f o r  t h i s reason that the heat transfer from bubbles i s usually calculated based on the temperature difference between the bubble wall and bulk l i q u i d temperatures. The HVC process occurs i n a two-phase bubbly flow regime within the downcomer.  The flow pattern i s characterized by a suspension of  discrete bubbles i n a continuous l i q u i d .  Within t h i s regime, void  f r a c t i o n (vapour cross-section area fraction) can range from less than 1% to approximately 30% f o r pure l i q u i d s .  The existence of contaminants  or the addition of chemical foaming agents can allow bubbly flow to persist v i r t u a l l y up to 100% void.  The absolute and r e l a t i v e directions  of vapour and l i q u i d flow also influence the void f r a c t i o n .  Only  v e r t i c a l co-current downflow i s considered here. The governing forces acting within the bubble flow regime include surface tension, v i s c o s i t y , i n e r t i a , and buoyancy (Wallis [4]). The complex interactions of these forces dictate the v e l o c i t y and pressure f i e l d s of the flow around i n d i v i d u a l bubbles.  In v e r t i c a l co-current  downflow, a s l i p or r e l a t i v e v e l o c i t y tends to develop between i n d i v i d u a l bubbles and the surrounding l i q u i d .  Individual bubble size  and shape determine the balance of buoyancy to viscous and form drag. This force balance i n turn determines the magnitude of the s l i p velocity.  The effect of the s l i p v e l o c i t y i s to cause convection heat  transfer o f f the bubble surface.  Bubble trajectory as w e l l as o s c i l l a -  tion also influence convection o f f the bubble surface.  5.  1.2  L i t e r a t u r e Review L i t e r a t u r e s p e c i f i c a l l y dealing with the process of HVC i s not yet  available.  There i s , however, information of interest i n work related  to the subject.  The l i t e r a t u r e reviewed includes previous work i n HAC,  bubble dynamics, and heat transfer from bubbles.  1.2.1  Hydraulic A i r Compression (HAC) The concept of HVC was evolved d i r e c t l y from the process of HAC.  Accordingly, the importance of gaining a basic understanding cannot be overemphasized.  of HAC  Langborne [2] has managed to trace the  history of HAC back to an I t a l i a n invention c a l l e d the "trompe" b u i l t i n 1588.  The operating p r i n c i p l e of the HAC i s i d e n t i c a l to that of the  trompe; induced a i r entrained i n a downward flow of water i s compressed by the increasing l o c a l hydraulic pressure.  In the f i r s t decade of the  20th century, 13 large HAC plants had been i n s t a l l e d i n Canada, Germany, United States, Sweden and Peru.  Published operating compression  e f f i c i e n c i e s ranged from 55 to 83% with deliverd a i r flowrates ranging from 0.13 to 18.87 m /s at pressures up to 806.7 kPa. 3  Rice [5] conducted experimental  and numerical work i n an attempt to  predict HAC performance f o r varying r a t i o s of air-to-water mass flowrates.  A i r was blown rather than induced into a laboratory scale HAC  downcomer i n order to accomplish  this.  I t was found that f o r a fixed  net applied head, there was a maximum a i r to water mass flowrate r a t i o for which operation was possible.  A HAC f r e e l y inducing a i r rather than  having a t h r o t t l e d source of a i r w i l l operate at the maximum a i r - t o water mass flowrate r a t i o .  Compression e f f i c i e n c y was found to increase  l i n e a r l y with the mass flowrate r a t i o .  The maximum compression  6.  e f f i c i e n c y was  thus achieved at the maximum possible mass flowrate r a t i o  for a given fixed, net, applied head. Rice and Chen published three papers [6-8] concerned with the effects of a i r s o l u b i l i t y on compression e f f i c i e n c y during HAC.  They  found that the amount of a i r d i s s o l v i n g i n the water during compression was d i f f u s i o n rate c o n t r o l l e d . The slowness of the d i f f u s i o n process e f f e c t i v e l y prevented the achievement of the equilibrium amount of dissolved a i r during the downflow period. downcomer geometries,  Accordingly, for i d e n t i c a l  they found that higher mass flowrate compression  processes were much less affected by a i r mass losses through d i s s o l u tion.  For any given t o t a l mass flowrate, however, i t was  concluded that  compression e f f i c i e n c y degradation due to a i r s o l u b i l i t y effects  was  severe. Vapour condensation during HVC  can be considered to be a s i m i l a r  process to a i r dissolution during HAC.  Both events result i n f i n i t e  rate mass transfer to the l i q u i d medium.  As forced convection mass  Is s i g n i f i c a n t l y greater In magnitude than d i f f u s i v e mass transfer i t can be expected that vapour condensation w i l l degrade the vapour production of HVC at least as much as a i r dissolution degrades the a i r production of  HAC.  Berghmans and Ahrens [9], constructed a numerical model to predict HAC  performance c h a r a c t e r i s t i c s as a function of water flowrate and  system geometrical parameters. void of 0.3  Their model assumed a downcomer entrance  for a l l calculations.  system e f f i c i e n c y was sectional area.  Of p a r t i c u l a r interest was  that  found to be a weak function of downcomer cross-  Once a r e l a t i v e l y high flowrate was achieved, system  e f f i c i e n c y ceased to increase.  7.  Summarizing,  the important HAC parameters appear to include the  available head, the a i r induction scheme, and the t o t a l flowrate.  These  parameters are l i k e l y to be important i n the HVC process as well as the two processes are very s i m i l a r .  1.2.2  Bubble Dynamics and Heat Transfer A comprehensive c r i t i c a l review of the previous work on the f l u i d  dynamics, heat trasnfer, and mass transfer of single bubbles, drops and p a r t i c l e s has been compiled by C l i f t , Grace and Weber [10]. The book has an extremely broad emphasis and i s useful as a general reference on single bubble behaviour.  Of s p e c i f i c i n t e r e s t i s previous work  concerned with the dynamics and heat transfer of single vapour bubbles during collapse i n one component systems.  Research on nucleate b o i l i n g  has produced a great deal of empirical data on this subject.  The bulk  of the data obtained, however, does not adequately characterize bubble collapse i n HVC because of the extreme pressure and temperature environments under which bubble collapses occurred.  A few works conducted  under moderate pressure and temperature environments are discussed. Research into desalination has also contributed bubble collapse data though under more comparable conditions to the HVC environment.  Both  bubble collapse i n miscible and immiscible l i q u i d s have been studied. Only bubble collapse i n miscible l i q u i d s are applicable.  A number of  experimental and t h e o r e t i c a l studies are discussed.  1.2.2.1 Experimental With few exceptions, previous experiments conducted were photographic studies of vapour bubble collapses i n i t i a t e d by the application  8.  of step pressure increases. varied.  The methods of step pressure application  A l l methods however, were motivated towards the establishment  of an e a s i l y controllable subcooled environment.  Due to the suddenness  of the applied pressure r i s e s , collapse times were extremely short, ranging from milliseconds to hundreds of milliseconds.  The pressure  difference between I n i t i a l and f i n a l system presures were presented i n corresponding degrees of subcooling, defined as the difference between the vapour saturation temperature (at the f i n a l system pressure) and the bulk l i q u i d temperature f a r from the bubble. One of the pioneering experimental studies was performed by Levenspiel [11]. Liquid side heat transfer c o e f f i c i e n t s were estimated on the order of 50 kW/m °C from steam bubbles collapsing i n water. 2  Bubble shapes were observed to be highly i r r e g u l a r during collapse but bubbles did approach a spherical shape near the end of collapse.  On  average, bubble volumes decreased 100 f o l d during collapse periods approximately 100 ms long.  Mean bubble diameters ranged from 3 to 9 mm.  F i n a l system pressure was atmospheric with subcoolings ranging from 0.6 to 11 °C. Bankoff and Mason [12] estimated the turbulent heat transfer from steam bubbles collapsing i n a water j e t . Bubble Nusselt numbers were correlated with bubble Peclet and Strouhal numbers.  The extremely high  rates of collapse necessitated that Peclet numbers be based on bubble wall v e l o c i t i e s since these were of the same order of magnitude as the liquid jet velocities.  The bubble Strouhal numbers were defined as the  r a t i o of bubble wall v e l o c i t i e s to l i q u i d j e t v e l o c i t i e s . attempt to account for observed bubble shape pulsations.  This was an Nusselt  numbers ranging from 398 to 1485, are considered to be large owing to  9.  the highly turbulent conditions. The flow f i e l d surrounding each bubble i n the HVC  process i s much less turbulent than that generated i n Bankoff  and Mason's study. Florschuetz and Chao [13] studied the mechanics of vapour bubble collapse under free f a l l conditions i n order to maintain bubble sphericity.  It was shown that the collapse mode could be controlled by  l i q u i d i n e r t i a or heat transfer or both, depending on system conditions. During heat transfer controlled collapse, i t was noted that vapour pressure i s nearly equal to system pressure due to the r e l a t i v e l y slow rate of collapse as compared to l i q u i d i n e r t i a controlled collapse.  The  possible effects of bubble translation on collapse rates were acknowledged but not studied.  Wittke and Chao [14,15] l a t e r found that bubble  translation s i g n i f i c a n t l y increased collapse rates for heat transfer controlled collapse.  Further experimental work by Hewitt and Parker  [16], Board and Klimpton  [17], and Delmas and Angelino [18] supported  t h e i r findings. The previous experimental works reviewed so f a r have been performed at or s l i g h t l y below atmospheric pressure.  Brucker and Sparrow [19]  have studied steam bubble condensation i n water at pressures ranging from 10.3  to 62.1 bar with subcoolings ranging from 15 to 100  °C.  Calculated heat transfer c o e f f i c i e n t s were on the order of 10 kW/m °C 2  with Peclet numbers of the freely r i s i n g bubbles ranging from 2000 to 3000.  In general, heat transfer c o e f f i c i e n t s were found to increase  with pressure though there was no clear trend with subcooling.  An  i n t e r e s t i n g observation was made that average Nusselt numbers obtained were within 50% of those for a s o l i d sphere having a diameter equal to the i n i t i a l bubble diameter and a v e l o c i t y equal to that of the bubble.  10.  The presence of noncondensable  gases within vapour bubbles have  been observed by Florschuetz and Chao [13], Wittke and Chao [15], and Brucker and Sparrow [19].  The estimation of the amounts of gas present  have been based on the remaining volumes of bubbles which did not collapse completely.  It i s apparent that the presence of noncondens-  ables retards heat transfer.  A plausible postulate forwarded i s that  gas molecules tend to p i l e up at the interface as bubble collapse proceeds.  This accummulation  i s not necessarily uniform, however, i t  does form a screen against vapour condensation. Moalem, Sideman, O r e l l and Hetsroni [20] have experimentally examined the e f f e c t s of bubble i n t e r a c t i o n on collapse rates i n freely r i s i n g bubble trains i n one and two component systems.  The extent of  bubble i n t e r a c t i o n was controlled by the v a r i a t i o n of bubble generation frequency.  At low generation freuqencies, bubble collapse rates were  observed to decrease i n comparison to the collapse rates of freely ing single bubbles.  ris-  It was postulated that preceding bubbles increased  the temperature of the l i q u i d such that the temperature driving force was reduced for the following bubbles.  At higher generation frequen-  c i e s , following bubbles were observed to enter the wake region of preceding bubbles.  The increased convection counteracted the effects of  the reduced temperature driving force, thus r e s u l t i n g i n collapse rates approaching that of single bubbles. Sekoguchi, Fukui, and Sata [21] s t a t i s t i c a l l y studied the void f r a c t i o n d i s t r i b u t i o n i n v e r t i c a l bubble flow.  For bubbly downward  co-current flow, i t was observed that vapour flow was concentrated near the pipe center.  Bubble paths away from the pipe wall were observed to  be s p i r a l i n pattern.  11. 1.2.2.2  Theoretical  Ruckenstein [22] analyzed the e f f e c t of bubble t r a n s l a t i o n on bubble growth by assuming i t was a quasi-steady process and the l i q u i d flow around the bubble could be modelled by p o t e n t i a l flow.  The basis  of these two assumptions was that the bubble wall v e l o c i t y was  small i n  comparison to the bubble v e l o c i t y and that the thermal boundary layer was small i n comparison to the bubble radius.  Isenberg et a l . [3],  Moalem and Sideman [23], and Dimic [24], adhering to the assumptions forwarded by Ruckenstein, obtained simple a n a l y t i c a l solutions for bubble collapse times with and without the presence of noncondensables. Wittke and Chao [15], and Prisnyakov [25] began with a more general approach but were unable to s i g n i f i c a n t l y improve predictions of collapse times over that of the simpler solutions.  Collapse times were  presented i n dimensionless form parameterized by Peclet number, Jacob number, and i n i t i a l bubble radius.  The collapse times predicted by  these models does not adequately describe the bubble collapse rates i n the HVC process. In addition to t h e i r experimental work, Moalem, Sideman, O r e l l , and Hetsroni [20,26] have t h e o r e t i c a l l y modelled the condensation of vapour bubble t r a i n s i n stagnant l i q u i d .  Their r e s u l t s show that bubble  collapse times increased with increased bubble frequency and increased number of bubbles per unit flow cross-sectional area.  Sideman and  Moalem [27] proceeded one step further and studied the condensation of vapour bubble t r a i n s under counter and co-current flow.  Their findings  were as expected, condensation rates were lower i n co-current flow i n comparison to counter-current flow.  In both cases, increased bubble  density decreased the condensation rate.  At low s u p e r f i c i a l vapour  v e l o c i t i e s ranging from 0.0063 to 0.065 m/s,  the calculated volumetric  heat transfer c o e f f i c i e n t s ranged from 12 to 232 kW/m °C. 3  12.  1.3  Scope of the Present Investigation The review of previous work i n the areas of HAC,  and single bubble  dynamics and associated heat transfer has been performed  to provide  s u f f i c i e n t background information for the present investigation  The  constant pressure environments f o r bubble collapse under which a l l previous work has been conducted may not adequately model the bubble condensation or collapse environment i n the HVC  process.  Bubbles i n a  hydraulic vapour compressor are subjected to an increasing hydraulic pressure during collapse as they t r a v e l along the downcomer. consequence, the rate of collapse may  As a  s i g n i f i c a n t l y deviate from the  rates measured i n previous studies. The lack of experimental data of collapse rates under a pressure gradient, as required for the design of a hydraulic vapour compressor, thus motivated a preliminary experimental study of the phenomenon. The primary objective of t h i s study was to obtain estimates of the vapour condensation rates present during the compression  process.  Appropriate generalizations of these estimates can provide the designer with quantitative information concerning the possible vapour mass losses through the HVC process f o r given sets of operating conditions. To this end, vapour condensation rates were estimated from photographic h i s t o r i e s of bubble size decrease i n an experimental apparatus modelling a hydraulic vapour compressor.  To quantify the heat transferred through  condensation, bubble Nusselt numbers were correlated with the operating parameters described by the Peclet number and the dimensionless downcomer length.  Vapour mass flowrates were also measured to determine  a range of possible compressor outputs.  13. CHAPTER I I EXPERIMENTAL  2.1  APPARATUS  G e n e r a l Concept The e s s e n t i a l purpose o f t h e e x p e r i m e n t a l apparatus used i n t h i s  i n v e s t i g a t i o n was t o a l l o w f o r the p h o t o g r a p h i c c o n d e n s a t i o n d u r i n g t r a v e l a l o n g t h e downcomer. built  p r e v i o u s l y f o r another  experiment.  study of vapour  bubble  The apparatus used  M o d i f i c a t i o n s were made where  n e c e s s a r y , however, t h e b a s i c c i r c u l a t i o n l o o p was kept i n t a c t . d e s c r i p t i o n o f the apparatus  was  A  f o l l o w s with d e t a i l e d i n f o r m a t i o n b e i n g  r e f e r e n c e d t o Ryan [ 2 8 ] . Photographs o f t h e apparatus F i g u r e s 2.1 and 2.2.  A schematic  and i n s t r u m e n t a t i o n a r e p r e s e n t e d i n of the flow c i r c u i t and a s s o c i a t e d  i n s t r u m e n t a t i o n i s shown i n F i g u r e 2.3. of  The f l o w c i r c u i t was  comprised  two s e p a r a t e flow paths, a main c i r c u l a t i o n loop and a siphon l o o p .  The f l o w i n t h e main c i r c u l a t i o n l o o p was e n t i r e l y l i q u i d . pumped  from  The flow was  the s e p a r a t i o n tank, c o n t i n u e d through a c o a x i a l  heat exchanger, and d i s c h a r g e d i n t o t h e o v e r f l o w v e s s e l . c i r c u l a t i o n loop had two primary  f u n c t i o n s ; the f i r s t  counterflow  The main  was t o m a i n t a i n a  c o n s t a n t l e v e l i n t h e o v e r f l o w v e s s e l , t h e second was t o p r o v i d e a degree o f c o n t r o l over the l i q u i d  temperature.  B u i l d i n g supply water  was used as t h e c o o l i n g medium i n t h e heat exchanger. The upward l e g of the s i p h o n loop drew an e n t i r e l y l i q u i d from t h e o v e r f l o w v e s s e l . partially filled  The f l o w proceeded  the vacuum chamber.  i n e f f e c t the t e s t s e c t i o n .  through  flow  a flowmeter  The downward l e g o f the s i p h o n was  The e n t r a n c e o f t h e t e s t s e c t i o n was  l o c a t e d i n s i d e the vacuum chamber.  and  Two-phase flow, formed i n the  14. entrance of the test section, was drained Into the separation tank. Bubbles In the two-phase flow were photographically tracked along the test section. The placement of the vacuum chamber and downcomer test section i n the siphon loop was chosen based on several factors.  The primary  concern was of course to accurately model the actual HVC process.  Other  factors were: (a)  Relatively easy attainment and maintenance of near saturation conditions i n the vacuum chamber.  This was achieved by the place-  ment of the vacuum chamber at the apex of the siphon loop, the point of lowest pressure i n the system. (b)  E f f i c i e n t removal of noncondensable a i r i n the vacuum chamber. This was achieved by the continual evacuation of small amounts of vapour from the top of the vacuum chamber which resulted i n the generation of additional vapour. p o s s i b i l i t y of a i r entrainment  This process minimized the  i n t o the flow entering the downcomer  test section. (c)  Elimination of pressure pulses due to pumping since the vacuum f o r the siphon was pulled through a large accumulator being pulled d i r e c t l y by the vacuum pump.  tank instead of  This allowed smooth  steady flow of l i q u i d through the siphon up-leg and into the downcomer. The inducement of vapour into the flow at the top of the downcomer test section proved to be a d i f f i c u l t problem.  Ideally, single bubbles  were to be introduced into the flow i n order to minimize the effects of bubble i n t e r a c t i o n .  Many unsuccessful attempts were made using a  15. variety of induction tube geometries.  Eventually vapour generation and  entrainment was achieved v i a the breakup of supercavitation jets formed at the base of a square ended, s o l i d , c y l i n d r i c a l rod placed at the downcomer entrance.  Figure 2.4 contains a photograph of a t y p i c a l  supercavitation j e t at the entrance of the test section. Supercavitation jets are a type of 'fixed' cavity as described by Knapp, Daily, and Hammitt [29].  The formation of the supercaviation  jets was due to the s t a t i c pressure drop created by the rapid acceleration of saturated l i q u i d flowing by the end of the rod.  The shapes of  the jets varied depending on l i q u i d flowrate and degree of subcooling. For high subcoolings and high flowrates, the jets produced were small and b u l l e t shaped, usually 1 to 1.5 rod diameters i n diameter and 1 to 3 rod diameters i n length.  Lower subcoolings and lower flowrates produced  jets that were umbrella shaped, 2 to 3 rod diameters i n diameter and 3 to 5 rod diameters i n length.  The breakup of these jets occurred at  their bases where bubbles were observed to be torn o f f from the jets by the turbulent l i q u i d flow.  An obvious and important advantage of this  method of bubble generation was the v i r t u a l certainty that a i r bubbles would not be present i n the downflow.  The disadvantage l i e s i n the  c o n t r o l l a b i l i t y of the number and size of vapour bubbles generated. Every attempt was made to keep the c a v i t a t i o n jets as small as possible to l i m i t the number of bubbles generated. only be controlled to a minor extent.  The sizes of bubbles could  In general, larger and fewer  bubbles were generated at lower subcoolings and flowrates.  16. 2.2  Working F l u i d The reasons f o r the use of Freon-11 In the present investigation  are given i n [28, p.15].  The most important reason for using Freon-11  was that i t had a low b o i l i n g point, 23.8°C at atmospheric  pressure.  Mayinger [30] has noted that i n general, Freon i s a suitable modelling f l u i d f o r scaling steam-water mixtures.  This observation was based on a  l i t e r a t u r e survey and his own scaling experiments. b o i l i n g point of 23.8 temperatures  °C at atmospheric pressure.  Freon-11 has a Typical working  ranged from 10 to 15 °C at pressures ranging from 75 to 104  kPa.  2.3  Piping, Tubing, Hose, and F i t t i n g s The sizes and materials of the piping, tubing, hose, and f i t t i n g s  are given i n [28, p.17].  A number of PVC valves and associated f i t t i n g s  were replaced with i d e n t i c a l components due to breakage apparently caused by Freon embrittlement.  Freon embrittlement  caused minute cracks  to appear In the PVC material.  A l l o-ring seals were replaced as a pre-  cautionary measure.  2.4  Vacuum Chamber, Separation Tank, Overflow Vessel, and Vacuum Accummulator Tank The vacuum chamber configuration (Figure 2.5) was s l i g h t l y modified  from the description presented i n [28, p.18].  A new Nalgene b e l l jar  replaced the old cracked j a r along with a new o-ring s e a l . floor was removed as was  the chamber i n l e t wire basket.  The f a l s e  The support  stand f o r the c a v i t a t i o n rod was screwed and bolted into the aluminum floor for s t a b i l i t y . The separation tank (Figure 2.6) was constructed out of a 15.24 high section of 50.8  cm  cm I.D. PVC pipe sealed at either end by aluminum  17. plates.  Three tube sections were welded i n t o the top plate connecting  to the c i r c u l a t i o n pump intake, the overflow vessel outlet, and the downcomer outlet.  A 1.27 cm I.D. , 20.4 cm long section of tube screwed  into the top plate was used as a vapour exhaust.  A regulating valve was  attached to the end of the exhaust to meter the vapour outflow.  An  additional toggle operated shut-off valve was i n s t a l l e d as an emergency pressure release.  The overflow vessel and vacuum accumulator  tank were  not modified.  2.5  C i r c u l a t i o n and Vacuum Pumps Pump d e t a i l s are given i n [28, p.20].  The c i r c u l a t i o n pump  impeller was overhauled before the start of experimentation, however, the pump continued to sieze occasionally. Prolonged use of the c i r c u l a tion pump often resulted i n the motor overheating. a x i a l flow fan was i n s t a l l e d to cool the pump motor.  A 30 cm diameter The vacuum pump  ran without problems.  2.6  Downcomer Inlet O r i f i c e and Cavitation Rod A sketch of the downcomer entrance o r i f i c e used i s shown i n Figure  2.7.  The purpose of the venturi-type design was to smoothly accelerate  the flow into the downcomer to a t t a i n v e l o c i t i e s high enough to generate cavitation jets at the base of the inserted rod. A number of rod sizes and base geometries were tested. apparent  that rod size rather than rod base geometry influenced the  formation of the caviation j e t s . 6.35  I t became  A square-ended rod with a diameter of  mm was eventually chosen as i t provided small and f a i r l y stable  cavitation jets.  18. 2.7  Downcomer Test Section In order to minimize the d i s t o r t i o n of photographing a t r a v e l l i n g  bubble, the downcomer test section would i d e a l l y be square i n crosssection. available.  Square-section glass tubing i n the desired length was not The alternative solution was to use a conventional round-  section glass with a constructed aluminum-glass composite square-section tube sleeved over top.  The inner round-section tube (actual test  section) was 2.54 cm I.D.  During the photographic tracking of vapour  bubbles, the outer square-section tube was f i l l e d with Freon.  Since the  inner round-section tube contained Freon as well, based on Snell's law of r e f r a c t i o n , the d i s t o r t i o n caused by the curvature of the inner tube was e f f e c t i v e l y  2.8  minimized.  Instrumentation The instrumentation used i n t h i s i n v e s t i g a t i o n recorded the steady  state values of the parameters of i n t e r e s t .  Small fluctuations were  either averaged over time or median values were taken.  2.8.1  Temperature Measurement The l i q u i d temperature  i n the vacuum chamber and the separation  tank were obtained with two Omega type PR-11 platinum resistance thermometer probes (RTD) coupled with an Omega model 199P2 d i g i t a l indicator through an Omega 6 position selector switch.  The d i g i t a l indicator  produced analog output signals to 0.1 °C resolution f o r the data acquis i t i o n system.  Vapour temperature  In the separation tank was measured  with a copper-constantan Y8103 type K bead thermocouple probe connected to a Fluke d i g i t a l multimeter model 8024A.  Temperature was displayed  19. d i r e c t l y to a resolution of 1 °C. Vapour temperatures ranged from 11 to 15 °C.  A l l probes were calibrated at 0 °C and 100 °C.  Fluctuations  were averaged over time. 2.8.2  Pressure Measurement Stagnation pressures were measured i n both the vacuum chamber and  the separation tank.  Simple U-tube water manometers were used to  measure pressures r e l a t i v e to atmospheric since only steady state pressure readings were required.  Maximum and minimum values were  averaged when fluctuations occurred. Ambient pressures were measured with a Mercury manometer.  The vacuum chamber pressure ranged from  approximately 75 to 81 kPa.  Typical separation tank pressures ranged  from atmospheric to 104 kPa.  2.8.3  Depth Measurement Liquid depth measurements were manually recorded f o r both the  vacuum chamber and separation tank using a graduated s t e e l ruler f o r reference. occurred. to 166 mm.  2.8.4  Maximum and minimum values were averaged when fluctuations Operating l i q u i d depth i n the vacuum chamber ranged from 123 Liquid depth i n the separation tank rnaged from 49 to 88 mm.  Liquid FLowrate Measurement Liquid volumetric flowrate i n the siphon loop was determined with a  paddlewheel type measurement device described i n [28, p.22].  No attempt  was made to measure the flowrate i n the downcomer test section as the presence of bubbles i n the flow would have made measurements highly unstable regardless of the measurement technique.  Alternatively, the  flowrate i n the downcomer test section was i n f e r r e d as follows.  Assum-  20.  ing that only small amounts of vapour were evacuated from the vacuum chamber, by holding the l i q u i d l e v e l constant i n the vacuum chamber, the volumetric flowrate passing through the downcomer can be considered to be equal to the volumetric flowrate measured by the paddlewheel device i n the siphone up-leg.  The t o t a l mass flowrate through the downcomer  test section was obtained by multiplying the volumetric flowrate by the l i q u i d density corresponding to the vacuum chamber l i q u i d  temperature.  Fluctuations i n the paddlewheel device output were averaged over time. T y p i c a l flowrates ranged from 0.36  2.8.5  to 0.57  lis.  Data A c q u i s i t i o n System A Neff model 620 data a c q u i s i t i o n system was employed to sample the  analog signals generated by the two RTD rate measurement device.  probes and the paddlewheel flow-  The program written f o r data a c q u i s i t i o n  allowed direct user input of a l l manually measured parameters as well as ambient pressure and temperature,  and current apparatus geometry.  flowchart of the program i s presented i n Figure 2.8. be unreliable, often breaking down completely.  A  The Neff proved to  The data f o r run 8 was  taken e n t i r e l y without the aid of the data a c q u i s i t i o n system.  2.8.6  Hot Film Anemometry A Thermosystem Inc. (TSI) model 1235W hot f i l m wedge probe was  used  to measure the v e l o c i t i e s of the vapour/air mixture existing i n the separation tank.  The v e l o c i t i e s obtained were used to measure the  vapour mass produced i n the test section. powered through a TSI model 1010A  The hot f i l m wedge probe was  constant temperature  anemometer.  The  anemometer output voltage was viewed and stored on a Nicolet model 3091  21. d i g i t a l oscilloscope.  The stored output was then transmitted onto  floppy disc v i a an IBM PC.  As a f i n a l step, the contents of the floppy  discs were transferred to the VAX 11/750 f o r processing. For a l l measurements, the hot f i l m probe was positioned In the center of the vapour exhaust tube as shown i n Figure 2.9.  To ensure  that the vapour flow was f u l l y developed before measurement, the probe was inserted at the end of the exhaust tube which was over 40 tube diameters i n length.  The choice of using a hot f i l m wedge probe over  that of a hot wire probe was based on a v a i l a b i l i t y and ease of use. Only steady flow measurements were desired, therefore the frequency response c a p a b i l i t y of a hot wire was not required. The hot f i l m probe c a l i b r a t i o n was carried out i n a wind tunnel f o r a i r speeds ranging from 1.14 to 14.9 m/s.  The s e n s i t i v i t y of the  alcohol manometer used limited the minimum measureable a i r v e l o c i t y i n the wind tunnel.  The probe operating temperature was set at 64.1 °C  corresponding to an overheat r a t i o of 1.15.  The maximum probe operating  temperature, as recommended by the manufacturer, was 66.7 °C. Since the actual measurements were to be performed i n a d i f f e r e n t medium (vapour/air mixture) than that of the c a l i b r a t i o n medium  (air),  It was necessary to use dynamic s i m i l a r i t y to obtain the corrected v e l o c i t i e s i n the measurement medium.  To t h i s end, probe c a l i b r a t i o n  Nusselt numbers were determined as a function of the c a l i b r a t i o n Reynolds numbers.  Further, since the temperature differences between  the measurement and c a l i b r a t i o n mediums were s i g n i f i c a n t i n comparison to the probe operating temperature, measurement bridge voltages were scaled using temperature correction factors based on the difference betwen the c a l i b r a t i o n and measurement f l u i d temperatures.  The scaled  22. measurement voltages were used to calculate the vapour/air mixture Nusselt numbers based on f l u i d conductivities estimated from the r a t i o s of the p a r t i a l pressures of the vapour to a i r .  From the c a l i b r a t i o n  curve of a i r Nusselt versus a i r Reynolds numbers, the measurement Reynolds numbers were obtained.  The exhaust v e l o c i t i e s of the vapour/  a i r mixture were then determined from the Reynolds numbers based on f l u i d kinematic v i s c o c i t i e s also estimated from the r a t i o s of vapour/air p a r t i a l pressures.  Details of the probe geometry, the anemometer used,  and the c a l i b r a t i o n procedure are contained i n Appendix A.  2.9  Photographic Equipment The high speed photographic tracking of vapour bubbles  accomplished using the arrangement sketched i n Figure 2.10.  was The camera  was manually pivoted on the tripod i n order to track i n d i v i d u a l bubbles t r a v e l l i n g down the test section.  The maximum t i l t or included angle of  t r a v e l necessary to view the entire legnth of the downcomer was degrees.  27.2  The maximum size d i s t o r t i o n occurred at 13.6 degrees above or  below the horizontal and can be estimated from the cosine of the angle. At 13.6 degrees this i s approximately 2.8%.  In view of the possible  magnitudes of other inherent experimental errors, t h i s error i s acceptable. The camera used was a Red Lake Hycam rotating-prism type 16 high-speed motion-picture camera.  mm  The framing speed of the camera was  c a l i b r a t e d against the d r i v i n g AC voltage.  It was operated at a  constant voltage setting to maintain a steady framing speed, however, i t was observed that f i l m speed through the camera varied considerably and a steady framing speed was not achieved a f t e r the i n i t i a l acceleration.  23. This resulted i n minor exposure v a r i a t i o n s within a s i n g l e r o l l of f i l m , but the variations were consistent from f i l m to f i l m . used ranged from 600 to 1400 voltage of 50 VAC. which was  The framing  rates  frames per second at a nominal applied  The camera was  equipped with a Neon timing l i g h t  driven at frequencies of 100 and 1000 Hz by a Red Lake model  TLG-3 M i l l i m i t e timing l i g h t generator.  The marks produced by the  timing l i g h t were used to estimate the instantaneous i n d i v i d u a l bubbles.  Frequency c a l i b r a t i o n of the timing l i g h t  showed l e s s than a 0.5%  deviation at both 100 and 1000  The lens used was a Tamron 200-500 mm photography was  v e l o c i t y of  performed at 500 mm F/6.9  of approximately 3 cm.  Extreme care was  F/6.9  generator  Hz.  ultra-telezoom.  All  r e s u l t i n g i n a depth of f i e l d exercised when focussing but  the inherent play i n the tripod pivoting mechanism often shifted the focus of the lens and consequently a number of exposed films were discarded due to poor focus. The pin-pointing of i n d i v i d u a l bubbles necessitated the use of a Spectra-Physics  model 155 optic l a s e r .  This was  because through-the-  lens v i s u a l tracking was made impossible by f i l m blockage of the camera eyepiece, a c h a r a c t e r i s t i c of rotating-prism type cameras.  The laser  was mounted on the same tripod platform as the camera and thus moved i n synchronization with the camera allowing f a i r l y precise location of the f i e l d of view of the lens. To obtain the highest d e t a i l i n g of bubble shape and size, a backl i g h t i n g technique was used to silhouette the bubbles tracked.  Two  1000  W quartz-Bromine studio lamps were placed behind the downcomer test section facing the camera.  The l i g h t was  dispersed through sheets of  vellum placed over the glass of the r e f r a c t i o n tube.  In consideration  24. of the extreme heat put o f f by the two l i g h t s , they were only switched on during actual filming; these periods extended no longer than two minutes. 100 foot r o l l s of Kodak 4-X negative black and white f i l m were used.  Under the described l i g h t i n g conditions, the e f f e c t i v e ASA of the  f i l m was 400.  The f i l m i s commonly used f o r i n d u s t r i a l photography and  has good depth of f i e l d q u a l i t i e s at low levels of illumination.  25. CHAPTER I I I EXPERIMENTAL PROCEDURE  3.1  I n i t i a l Equipment Testing The i n i t i a l testing of equipment involved two stages.  The f i r s t  stage was simply to f i l l the c i r c u l a t i o n loop, the siphon loop, and the heat exchanger with water i n order to check f o r leaks. were stopped and the c i r c u i t s r e f i l l e d .  A l l leaks found  During water batching, the  paddlewheel flow measuring device, the two water manometers, the two temperature  probes, and the data a c q u i s i t i o n system were v e r i f i e d f o r  proper operation. for  As the basic c i r c u i t of the apparatus had been unused  over two years, the water was allowed to freely c i r c u l a t e for a  number of hours i n attempt to f l u s h out any residual debris i n the pipes. The second stage of i n i t i a l t e s t i n g involved the introduction of Freon to the c i r c u l a t i o n and siphon loops.  Before the addition of the  Freon, both loops were dismantled and blown free of any water with compressed a i r . The c i r c u l a t i o n pump was disassembled, dried and checked for  roughness on the impeller body.  The apparatus was reassembled and  Freon was tested f i r s t i n the c i r c u l a t i o n loop and then i n the siphon loop.  I t was observed that considerably more vacuum had to be generated  i n the vacuum chamber with the Freon i n comparison to the water. The Freon was apparently vapourizing i n the chamber thus a higher vacuum was necessary to establish the flow i n the siphon loop.  The c i r c u l a t i o n  pump was found to cavitate badly i f either the Freon l e v e l i n the separation tank was too low or the Freon temperature was too close to saturation.  P a r t i c u l a r care had to be taken to maintain a high l i q u i d  26. l e v e l (> 15 cm) i n the tank when the Freon temperature was over 16 °C. During the i n i t i a l Freon testing, i t was discovered that a large amount of Freon would gradually be l o s t through evaporation over a few hours. Additional Freon was Invariably required to maintain a constant l e v e l i n the separation tank. Following the i n i t i a l Freon t e s t s , a number of days were spent i n f a m i l i a r i z a t i o n with the system reactions to pressure, temperature and flowrate changes.  Maximum and minimum attainable values f o r each para-  meter were noted.  Various bubble generation schemes were attempted  u n t i l success came with the supercavitation j e t s . The i n i t i a l testing of the photographic equipment involved equipment arrangement and operation to obtain the correct exposure s e t t i n g . The camera t i l t i n g mechanism on the tripod consisted of a manually cranked worm gear driving a curved rack gear.  The mechanism was care-  f u l l y shimmed and well greased for smooth operation but the inherent backlash i n the gearing could not be removed.  The camera was positioned  l e v e l with the horizontal center of the test section at a distance of 3.5 m. of  Care was taken to ensure the lens was perpendicular to the face  the r e f r a c t i o n tube.  camera.  The optic laser was then mounted beside the  Viewed through the camera lens, the l a s e r beam was aligned with  the horizontal cross-hair of the lens.  V e r t i c a l alignment was set such  that the v e r t i c a l cross-hair was l y i n g on the test section centerline and the laser beam was pin-pointed on the right frame edge of the r e f r a c t i o n tube.  This was to ensure that the l a s e r did not r e f l e c t into  the downcomer. The focussing of the camera involved both lens and camera eyepiece focussing.  The camera eyepiece was focussed by s l i d i n g the eyepiece  27. along i t s sleeve, focussing on a l i n e scratched on a frame of a dummy r o l l of f i l m loaded i n the camera. ing  the lens to be focussed.  The f i l m was then taken out, allow-  Obtaining a correct exposure setting  proved to be a task complicated by the combination of an unreliable l i g h t meter and the speed v a r i a t i o n i n camera framing rate.  Once the  correct exposure setting was found, a l l films were shot at that setting.  3.2  Routine Apparatus Start-Up and Shut-Down Routine apparatus start-up and shut-down procedures were adhered to  i n order to maintain proper equipment function and cleaniness. Prior to any actual experimental runs, a l l instrumentation was switched on and allowed to warm up.  The separation tank, overflow vessel and vacuum  chamber were cleaned and wiped down with rags soaked i n Freon to remove contaminants. c o l l e c t e d dust.  Compressed a i r was blown through the piping to remove Preparation of the vacuum chamber involved the  centering of the cavitation rod i n the downcomer o r i f i c e and the f i l l i n g of the r e f r a c t i o n tube with Freon since the f i l l e r hole was located i n the f l o o r of the vacuum chamber.  The chamber was subsequently closed by  gently forcing the Nalgene b e l l j a r over the o-ring seal around the base of  the chamber.  The vacuum pump was started, evacuating the accumulator  tank i n preparation f o r the priming of the siphon loop.  The water f o r  the heat exchanger was turned on. Freon was manually poured into the overflow vessel through a p l a s t i c funnel to f i l l the c i r c u l a t i o n loop.  Once the separation tank  was h a l f - f i l l e d , the c i r c u l a t i o n pump was switched on.  This was to give  the c i r c u l a t i o n pump a s u f f i c i e n t starting i n l e t head.  Further addition  of Freon was continued u n t i l the separation tank was two-thirds f i l l e d .  28. The vacuum chamber was then evacuated through the accumulator tank, to prime the siphon loop.  I t was extremely important that the evacuation  of the vacuum chamber was carried out gradually or otherwise v i o l e n t l y unstable flow would result at the entrance to the downcomer. The f i n a l step i n the experimental preparation was to e s t a b l i s h a cavitation j e t . The following procedure was necessary: 1)  Apply enough vacuum so that the l i q u i d l e v e l i n the vacuum chamber was at least 15 cm above the downcomer o r i f i c e .  2)  Quickly close the vacuum regulation valve and allow the l i q u i d l e v e l to drop.  3)  This action i n i t i a t e d the cavitation j e t .  Slowly adjust the vacuum regulation valve to obtain a stable l i q u i d flowrate.  The s t a b i l i t y of the cavitation j e t was dependent on the  s t a b i l i t y of the flow. Following an experimental run a s t r i c t shut-down procedure was practiced.  The pressure i n the vacuum chamber was gradually Increased,  allowing Freon to drain from the siphon loop.  The c i r c u l a t i o n pump was  kept running to prevent the Freon i n the overflow vessel from e n t i r e l y draining into the separation tank, which would cause an overflow.  Freon  was drained slowly from the separation tank through q u a l i t a t i v e medium porosity f i l t e r paper.  This appeared to remove most of the contaminants  the Freon would pick up during the experiment.  The f i l t e r i n g process  would often take over two hours and to minimize evaporation, the Freon was kept as cold as possible by continued c i r c u l a t i o n of the remaining Freon through the heat exchanger.  The overflow vessel and c i r c u l a t i o n  pump had to be disassembled to be completely drained. always stored separately from new Freon.  Used Freon was  New Freon was e a s i l y  29. distinguishable from used Freon as exposure to a i r would cause the Freon to become progressively more yellow i n colour.  The l a s t step was to  disassemble the vacuum chamber to r e l i e v e the stress on the Nalgene b e l l jar.  3.3  Bubble Photographic Studies The two parameters that were independently varied during the bubble  photographic studies were the l i q u i d flow rate into the vacuum chamber (0.36 to 0.51 i/s), and the l i q u i d temperature  i n the vacuum chamber  (10.9 to 13.3 °C). Both the l i q u i d flowrate and temperature were limited by the building supply water temperature and the available vacuum.  After the i n i t i a l preparation described previously, the experi-  mental procedure was as follows: 1)  The heat exchanger cooling water flowrate was adjusted u n t i l the desired Freon temperature  2)  was achieved.  The vacuum chamber pressure was adjusted to give the desired flowrate and to s t a b i l i z e the cavitation j e t .  3)  The pressures and l i q u i d l e v e l s i n both the vacuum chamber and separation tank were recorded along with the vapour temperature i n the separation tank.  4)  The data a c q u i s i t i o n system was enabled, recording the l i q u i d flowrate, the vacuum chamber l i q u i d temperature, tank l i q u i d  5)  temperature.  The l i g h t i n g was switched on along with the timing l i g h t generator and l a s e r .  6)  and the separation  The camera was then switched on.  30. After the completion of step 2), the apparatus was allowed to run f o r a minimum of 10 minutes to achieve conditions approaching steady state. Steps 3) through 5) were usually completed i n less than two minutes. During runs at higher flowrates, large fluctuations i n l i q u i d l e v e l and pressure were observed i n the separation tank. the  This was attributable to  high turbulence l e v e l i n the tank caused by the rapid entrance of  l i q u i d and vapour Into the tank. For  a single r o l l of f i l m , the maximum possible number of filming  passes along the length of the test section was limited by the v e l o c i t y of  the i n d i v i d u a l bubbles tracked.  At the framing rate used, the 100  f t . r o l l would l a s t approximately 6 s.  Allowing for the time to r e -  pivot the camera back to the top of the test section, two filming passes could be completed i f the tracking v e l o c i t y was greater than 1 m/s. This was achieved only at the highest l i q u i d flowrate of 0.51 l/s. The tracking strategy involved the selection of the smallest bubble that could e a s i l y be tracked.  Each of these bubbles would be filmed u n t i l  they were v i s u a l l y lost among other bubbles.  When this occurred,  another bubble would immediately be selected and filmed f o r the remaining test section length.  3.A  Vapour Exhaust Velocity Measurements The vapour exhaust v e l o c i t y measurements were conducted using the  same procedure as the bubble photographic study. was substituted f o r the photography procedure.  Hot f i l m anemometry  The l i q u i d flowrates  were varied from 0.42 to 0.57 £/s while l i q u i d temperatures were varied from 9.4 to 14.8 °C. For each vapour v e l o c i t y measurement, the probe was switched on for a minimum of 5 minutes before the actual measurement.  The measurement period extended f o r 4 s at an oscilloscope  sweep rate of 1 sample/ms.  31. CHAPTER IV DATA ANALYSIS  4.1  Film Analysis The analyses of the films taken i n the bubble photographic study  were performed on a sequenced  individual frame basis.  Each f i l m was  projected onto a wall and viewed repeatedly to select bubbles that were continuously tracked for minimum of 20 cm along the test section. Figure 4.1 contains part of a t y p i c a l tracking sequence. obtained from these sequences  The quantities  included bubble instantaneous projected  area, instantaneous v e l o c i t y , and t o t a l tracking time.  Descriptions of  the methods used to obtain these quantities follow.  4.1.1  Determination of the Instantaneous Bubble Surface Area and Volume The inference of a three-dimensional shape from a two-dimensional  projection can be accomplished by revolving the projection about an axis of symmetry.  The inference of surface areas and volumes from the  projected areas of the bubbles filmed, however, was complicated by the absence of a continuous axis of symmetry.  A numerically implemented  method of revolving sections of a projected area about their respective axes of symmetry was used to i n f e r both an approximate surface area and volume for i n d i v i d u a l bubbles. For an i n d i v i d u a l frame taken from a selected sequence, the projected area of a bubble of interest was traced onto graph paper.  As the  magnification factor was r e l a t i v e l y high (17.5), i t was often d i f f i c u l t to distinguish the exact outline of the bubble silhouette.  The author  was forced to rely on personal judgement i n an attempt to accurately  32. trace the actual outline. error could conceivably  For a poorly focussed silhouette, judgement  be as high as 10%.  obtained, the outline was ferred to the VAX  Once a bubble trace  d i g i t i z e d and the numerical coordinates  11/750.  was trans-  The number of d i g i t i z e d points for a given  bubble trace varied from 40 to 120 depending on the number of severity of i n f l e c t i o n s contained  i n the trace.  Before the surface area and volume f o r a given bubble trace calculated, the p r i n c i p l e centroidal axis of the projected area determined from the d i g i t i z e d coordinates.  A coordinate  of a l l data points to the p r i n c i p l e centroidal axis was The purpose of the coordinate  transformation  was  was was  transformation then performed.  to provide a  reference  axis that best approximated the probable axis of rotation of the bubble. The new  reference axis was  nearest  to the o r i g i n a l v e r t i c a l axis.  Following  taken to be the p r i n c i p l e centroidal axis  the transformation,  the trace was  divided into a top  and  bottom half with each respective half being curve f i t t e d with either a second, t h i r d , or fourth degree polynomial. f i t used was  The degree of polynomial  dependent on the number of i n f l e c t i o n points present i n  that half of the trace.  Each half was  further divided into a minimum of  50 trapezoidal sections and a minimum of 1 spherical cap section as shown i n Figure 4.2.  The top half was  considered  first.  For each of  the trapezoidal sections, an axis of revolution p a r a l l e l to the v e r t i c a l p r i n c i p l e centroidal axis was the section.  defined such that i t bisected the base of  The cross-section areas generated by revolution about  these axes would have the highest l i k e l i h o o d of matching the actual bubble cross-section i n the same plane of revolution.  This would mini-  mize the error introduced by the method of volume generation  through  33. revolution of the projected area.  The t y p i c a l volume of revolution  generated can best be described as a frustum of a skewed cone.  Both the  volume and side surface area of each frustum was calculated through double numerical integration because of the unusual shape involved.  The  volume and upper surface area of the spherical cap sections were also calculated.  The bottom half of the trace was analyzed i d e n t i c a l l y .  The  t o t a l volume and surface area f o r the given bubble trace were obtained by the summation of the values calculated for each section.  4.1.2  Determination of the Bubble Trace Interval The rate of decrease of bubble size provided the basis f o r estimat-  ing  the heat transfer from the vapour to the surrounding l i q u i d .  To  quantify t h i s rate, bubble traces were i n i t i a l l y taken every ten frames for each selected sequence.  Plots of calculated bubble surface area and  volume as a function of time are shown i n Figures 4.3 to 4.16.  Each  data point represents either the surface area or volume obtained from a single trace. ing  The time i n t e r v a l between points was determined by d i v i d -  the t o t a l tracking time by the number of frames from which bubble  traces were taken.  The high degree of f l u c t u a t i o n i n the data was a  consequence of either non-symmetry or bubble shape o s c i l l a t i o n . number of the plots i n Figures 4.3 to 4.16 oscillations.  A  show f a i r l y regular shape  Ideally, bubble traces should be taken at a frequency  equal to a dominant shape o s c i l l a t i o n frequency.  The bubble would then  present approximately the same "face" or projection of i t s e l f to the viewer each time a trace would be taken.  This would minimize the degree  of fluctuation i n the bubble surface area and volume data when plotted versus time.  In pursuit of t h i s , Fourier frequency analyses of f i r s t  34. order trend removed bubble volume data were done.  These analyses, how-  ever, did not produce any consistently dominant regular shape o s c i l l a t i o n frequencies.  The influence of l o c a l flow conditions dictated by  the average flowrate and the presence of other bubbles caused enough scatter of bubble shape o s c i l l a t i o n frequencies that accurate predictions for each bubble was not possible.  No attempt was made to take  bubble traces at a smaller frame i n t e r v a l .  4.1.3  Determination  of Bubble T o t a l Tracking Time and V e l o c i t y  The t o t a l tracking time f o r each bubble was obtained by counting the number of timing marks between the i n i t i a l and f i n a l frames of the sequence of i n t e r e s t .  Bubble positions were obtained using the 1 cm  increment reference scale drawn on the r e f r a c t i o n tube. average v e l o c i t y was  The bubble  calculated by d i v i d i n g the t o t a l tracked distance  by the t o t a l tracking time.  Bubble "instantaneous" velocity was  esti-  mated from the elapsed time taken to t r a v e l v e r t i c a l l y down 1 cm along the test section.  This i s i n contrast to the actual velocity which  would l i k e l y be higher since bubbles often t r a v e l l e d downward i n a s p i r a l fashion.  4.2  Calculation of the Bubble External Nusselt Number The c a l c u l a t i o n of the f l u i d properties necessary f o r the estima-  tion of bubble external Nusselt number required a number of assumptions to be made due to the lack of experimental data. 1)  The assumptions were:  The s t a t i c pressure at the c a v i t a t i o n j e t was equal to the saturat i o n pressure corresponding the vacuum chamber.  to the l i q u i d temperature measured i n  The true pressure at the cavitation jet was  35. probably lower than the saturation pressure but the difference would not be substantial. 2)  The pressure at the exit of the downcomer was calculated from a Bernoulli analysis  P  3)  ex  = p - p, g h - K *st I st ex &  (0.5 p„ u ) £ ex' 2  (4.1)  The pressure gradient from the point of bubble formation to the downcomer exit was l i n e a r .  This assumption i s f a i r l y accurate  since the flowrates were low enough such that f r i c t i o n a l losses were n e g l i g i b l e i n comparison to the hydrostatic pressure r i s e . 4)  The bubble wall temperature was equal to the saturation temperature corresponding to the l o c a l pressure.  This was previously discussed  i n Section 1.1.  The Nusselt number was used to characterize the heat transfer between the vapour and l i q u i d phases.  The heat transferred through  condensation was estimated from the f i r s t law of thermodynamics.  The  complete derivation of the equations approximating the heat transferred i s contained i n Appendix B.  The main r e s u l t , which i s v a l i d at any  position along the downcomer length, was given by  dQ dt  ^< g2- gl) bl P  p  V  gl^2 " V  +  p  +  g2( b2- bl^ 2 V  ^l  ( h  V  *2  '\ l  L  ) ] / ( t 2  " ^  (4.2)  36. The mass condensed and can be rewritten as  m  c  " gl bl p  " g2 (p  )V  +  p  g2< b2 V  "bl> V  (4  -  3)  The second and third terms i n Equation (4.2) are much smaller than the f i r s t term and can be neglected.  The heat transferred from the bubble  can now be approximated by  §  =m L /(t c  2  2  -  t l  )  (4.4)  The t o t a l heat transferred into the l i q u i d can be described by  <* - V b i s " V  •  (T  ( 4  -  5 )  Equating Equations (4.4) and (4.5) gives  m L /(t c  2  2  -  t l  )  = U A (T A  b l  - Tz)  s  .  Equation (4.8) was solved for the l i q u i d side overall  (4.6)  heat transfer  coefficient  U =m L /[(t -t )A £  In dimensionless form, U number  c  2  2  1  b l  (T -T )] s  £  .  (4.7)  can be redefined as a bubble external Nusselt  37. Nu = U„D /k,. I se f  (4.8)  The c h a r a c t e r i s t i c length used i n the Nusselt number was a spherical equivalent diameter defined as  D  =6 V/A, . b b  se  This followed normal practice i n l i t e r a t u r e .  (4.9)  It may have been more  appropriate, however, to use a c h a r a c t e r i s t i c length based on a e l l i p s o i d rather than a sphere since the t y p i c a l bubble shape was ellipsoidal.  This would have added unnecessary complexity  to the  Nusselt number d e f i n i t i o n since e l l i p s o i d s have a minimum of two c h a r a c t e r i s t i c lengths. The l o c a l or instantaneous  external Nusselt number was calculated  for each bubble at one centimeter  increments along their respective  tracked lengths along the test section.  The p o s i t i o n averaged external  Nusselt number was calculated using  N TJu = (1/N) I Nu , j-l where N i s the number of one centimeter  (4.10)  increments along the tracking  distance. An a l t e r n a t i v e volumetric o v e r a l l heat transfer c o e f f i c i e n t was calculated for comparison purposes as Sideman and Moalem [27] have presented  t h e i r r e s u l t s using a volume based o v e r a l l heat transfer  coefficient.  The d e f i n i t i o n of the volumetric o v e r a l l heat transfer  c o e f f i c i e n t was  38. U = ;  m c  L /[(t 2  2  t l  )V  b l  (T -T )] s  (4.11)  £  Typical volumetric heat transfer c o e f f i c i e n t s have been calculated and are c i t e d i n the discussion.  4.3  Calculation of the Bubble Peclet Number The bubble Peclet number was the dimensionless parameter used to  characterize the bubble r e l a t i v e v e l o c i t y .  The bubble Peclet Number can  be written as the product of the bubble Reynolds number and the l i q u i d Prandtl number.  The bubble Reynolds number was defined based on the  bubble r e l a t i v e v e l o c i t y  u  = u T  The bubble v e l o c i t y u  - u  i  .  (4.12)  g  was determined from a linear least squares g  approximation to the bubble "instantaneous" v e l o c i t y measured across 1 cm i n t e r v a l s along the downcomer (Section 4.1.3).  The bubble Reynolds  number was defined as  Re - p u D /u . % r se %  (4.13)  The l i q u i d Prandtl number was defined as  Pr = U c /k Jl  p  f  .  The bubble l o c a l Peclet number was determined by  (4.14)  39. Pe = Re Pr  (4.15)  The bubble position averaged Peclet number was calculated i n the same fashion as the bubble p o s i t i o n averged Nusselt number  Pe = (1/N)  4.4  N I  Pe .  (4.16)  Calculation of the Vapour Mass Flowrate The c a l c u l a t i o n of the vapour mass flowrate was complicated by the  presence of a i r i n the separation tank.  This was made apparent when the  separation tank "vapour" temperature measurement was found to be lower than the saturation temperature corresponding to the s t a t i c pressure measured.  This indicated that a s i g n i f i c a n t amount of a i r was present  i n the tank.  To estimate the mass r a t i o of Freon vapour to a i r ,  Dalton's law of p a r t i a l pressures was used.  Assuming that the vapour  and a i r were ideal gases and well mixed, the r a t i o of the p a r t i a l pressure of the vapour to the measured s t a t i c pressure was taken to be equal to the mass r a t i o of vapour to the entire vapour/air mixture.  The  mass f r a c t i o n was calculated as F g  = P /P . s st  (4.17)  The mass f r a c t i o n was required to calculate the properties of the vapour/air mixture using the law of mixtures written as  x =Fx + (1 - F )x m g g g a  (4.18)  40. The mixture properties were used i n the c a l c u l a t i o n of the Nusselt and Reynolds numbers, which i n turn, were used to determine the exhaust v e l o c i t y of the mixture.  Since exhaust v e l o c i t y was measured at the  center of the exhaust tube, i t was necessary to i n f e r an average veloc i t y from the measurement.  An i t e r a t i v e c a l c u l a t i o n was used to deter-  mine the exhaust tube Reynolds number which was found to be less than 2000 i n a l l cases.  The mixture average v e l o c i t y was then taken to be u  m  - 0.5 u  m  (4.19)  The mass flowrate of the vapour/air mixture was obtained from the mixture average v e l o c i t y m  = (p)u A mm ex  m  (4.20)  The vapour mass flowrate was f i n a l l y given by  m  g  (4.21)  CHAPTER V RESULTS AND DISCUSSION  5.1  Qualifying Remarks As with a l l investigations of a preliminary nature, some simpli-  f i c a t i o n s of the processes and events involved are necessary to gain a s u f f i c i e n t overview of the subject matter i n a limited time and budget frame.  The intent i s usually to gain a basic understanding of the prob-  lems involved and to seek general trends to at least p a r t i a l l y quantify the parameters of i n t e r e s t .  The present study was conducted  i n this  s p i r i t and consequently detailed information concerning the l o c a l v e l o c i t y , pressure, and temperature f i e l d s adjacent to each bubble were not obtained. temperatures  Rather, estimates of the gross v e l o c i t i e s , pressures and across the downcomer length were used to calculate quanti-  t i e s such as the condensation rates, and the Nusselt and Peclet numbers.  5.2  Experimental Error The three types of experimental errors present i n t h i s study  included instrumentation errors, time lapse errors, and judgement errors.  Instrumentation errors were determined by the accuracy and  precision of the individual measurement devices. the measurements taken are given i n Appendix C.  Estimated errors f o r Included are the  assumption of l i n e a r i t y made during the c a l i b r a t i o n procedure for both the temperature probes and flowrate measurement device. Time lapse errors resulted from the short delays i n taking measurements of the time varying parameters.  Included were l i q u i d depth and  pressure measurements i n both the vacuum chamber and separation tank.  The delays were caused by the manually performed reading of each manometer and depth scale prior to the filming of the bubbles i n the test section.  The magnitude of the time lapse error was dependent on the  operating conditions.  Under higher l i q u i d flowrates and temperatures,  the l i q u i d depth and pressure i n both the vacuum chamber and separation tank varied more rapidly.  This type of error, although d i f f i c u l t to  quantify, i s believed to be small since the f i l m i n g intervals were extremely short i n duration, usually less than a minute i n length. Judgement errors were the r e s u l t of unavoidable reading errors during fluctuations i n l i q u i d depth, pressure, and temperature.  They  were reduced by averaging the maximum and minimum values of the parameter during fluctuation. operating conditions.  This type of error was also dependent on the  Larger fluctuations were observed at higher  l i q u i d flowrates and temperatures. are  5.3  The magnitude of judgement errors  thought to be considerably less than that of the time delay errors.  Rate of Decrease of Bubble Size As determined by f i l m analyses and data reduction procedures  previously described, the v a r i a t i o n of bubble volume and surface area for each of the bubbles tracked i s presented as functions of time i n Figures 4.3 to 4.16.  The three d i g i t designation for each bubble i s  used to r e l a t e each bubble to the experimental conditions during i t s filming.  By example, bubble 613 refers to experiment No. 6, f i l m  number 1, and f i l m sequence number 3.  roll  The experimental conditions f o r  each run are l i s t e d i n Tables 1 and 2. To enable the c a l c u l a t i o n of bubble mass loss and heat transfer c o e f f i c i e n t s , the rates of decrease of bubble volume and surface area  43. were required. Figures 4.3  It was necessary to curve f i t the data contained i n  to 4.16.  The high degree of fluctuation In the data a  discussed previously i n Section 4.1.2, however, presented ties.  some d i f f i c u l -  Attempts at using the correlations for bubble collapse rates i n  the l i t e r a t u r e reviewed were unsuccessful since the time scales were up to three orders of magnitude lower than observed In this i n v e s t i g a t i o n . It was  decided a l i n e a r l e a s t squares f i t of the data would be adequate  i n giving a preliminary unbiased estimate of the rate of decrease of bubble s i z e .  The slopes and intercepts of the least squares f i t s f o r  each bubble are contained In Table  4.  For ease of comparison and to provide further physical i n s i g h t i n t o the rates of decrease of bubble size, the least squares f i t s of bubble volume and surface area have been replotted i n dimensionless functions of bubble position along the downcomer.  form as  The bubble position  has been normalized  with respect to the t o t a l length of the downcomer.  Figures 5.1 and 5.2  contain the v a r i a t i o n of bubble volume and  area along the downcomer f o r a l l the bubbles tracked.  surface  It i s emphasized  that the discussion at this point concerns only the rates of bubble s i z e decrease. Section  Discussion of the amount of vapour condensed follows i n  5.4.  Figure 5.3  contains the v a r i a t i o n of dimensionless  equivalent diameter with normalized equivalent diameter was  downcomer p o s i t i o n .  bubble spherical The spherical  calculated to provide a c h a r a c t e r i s t i c length to  determine the bubble Nusselt and Peclet numbers.  I t , however, may  also  be viewed to be a representative function of the r e l a t i o n s h i p between the bubble volume and surface area.  A low volume to surface area r a t i o  indicates a large departure from s p h e r i c i t y since i t i s well known that  44. with spherical shapes, volume per unit surface area Is  maximized.  As  an estimate of the sphericity of each bubble, a volume based aspect r a t i o was calculated by d i v i d i n g the i n i t i a l spherical equivalent diameters (D  ) , as based on the r a t i o of volume to surface area, by a  alternative form of a spherical equivalent diameter (D  )., based  solely on the i n i t i a l volume as defined by  D  sev  =  (6 V / T T )  1 / 3  b  (5.1)  The aspect ratios for each bubble are l i s t e d i n Table 3. To estimate the flow f i e l d around each bubble, a nominal r e l a t i v e or  s l i p velocity was calculated from the bubble instantaneous v e l o c i t y .  Due to the method with which the bubble instantaneous v e l o c i t i e s were obtained (Section i n the data.  4.1.3),  a s i g n i f i c a n t amount of scatter was generated  Following the treatment of the bubble volume and surface  area, i t was decided a linear least squares f i t of the instantaneous v e l o c i t y data would be adequate.  The nominal r e l a t i v e v e l o c i t y was  obtained by subtracting the instantaneous v e l o c i t y from the downcomer inlet liquid velocity.  The i n l e t l i q u i d v e l o c i t y was used as a r e f e r -  ence since the l o c a l v e l o c i t y f i e l d about each bubble was not known. The values were non-dimensionalized with the i n l e t l i q u i d v e l o c i t y and plotted as a function of the bubble normalized position along the downcomer.  The nominal r e l a t i v e v e l o c i t i e s f o r a l l the bubbles tracked are  shown i n Figure 5.4. increase or decrease. of  It i s apparent that the r e l a t i v e v e l o c i t i e s may This i s due i n part to the influence of the wake  larger bubbles which create turbulent eddies, which i n turn, may  accelerate, deccelerate, or change the trajectory of s i m i l a r l y sized or  45. smaller bubbles.  Bubble shape o s c i l l a t i o n s may also increase or  decrease the drag c o e f f i c i e n t thus changing the bubble v e l o c i t y . supplement the p l o t of the instantaneous r e l a t i v e v e l o c i t i e s were calculated.  To  r e l a t i v e v e l o c i t i e s , average  These were based on the average  bubble v e l o c i t i e s as determined from the procedure outlined i n Section 4.1.3.  The average r e l a t i v e v e l o c i t i e s are l i s t e d i n Table 4.  In Figures 5.1 to 5.3, i t i s i n t e r e s t i n g to note some parallelism of the curves even though the tracking intervals were widely d i s t r i b u t e d along the length of the downcomer.  This was not unexpected since the  rate of increase of hydraulic pressure does not vary with position along the downcomer.  The non-dimensionalization of the volume and surface  area with respect to the i n i t i a l values shows the apparent i n s e n s i t i v i t y of the collapse rates to I n i t i a l bubble s i z e .  This observation,  however, should be tempered with regard to the fact that the majority of the bubbles were f a i r l y similar i n s i z e . Each of the four plots (Figures 5.1 to 5.4) has been subdivided and the curves grouped according to the experimental parameter of downcomer i n l e t l i q u i d temperature.  Figures 5.5 to 5.7, Figures 5.8 to 5.10, and  Figures 5.11 to 5.13 repeat Figures 5.1 to 5.3, respectively at i n l e t l i q u i d temperatures of 11, 12, and 13 °C.  The clearest example of the  parallelism between the curves are shown i n Figures 5.7, 5.10, and 5.13. The experimental  conditions for each of these bubbles were i d e n t i c a l and  a l l of these bubbles were s i m i l a r l y sized.  Bubble 822 had an unusually  low rate of surface area decrease which appears to have been moderated by the rate of volume decrease when the spherical equivalent diameter was calculated.  The low collapse rate of bubble 822 may be p a r t i a l l y  a t t r i b u t a b l e to i t s near s p h e r i c i t y .  Having an aspect r a t i o of 0.917,  46. bubble 822 had a proportionally lower surface area available f o r heat and mass transfer i n comparison to the other bubbles i n this group.  Any  convective e f f e c t s which would a i d the heat and mass transfer of the other bubbles i n the group appear to be n e g l i g i b l e since bubble 822 had one of the higher average s l i p v e l o c i t i e s of a l l the bubbles i n the group. In Figures 5.5, 5.8 and 5.11 l e s s parallelism i s shown between the curves.  Bubbles 311, 621, and 622 have similar rates of size decrease  i n comparison to the bubbles grouped at the i n l e t l i q u i d temperature of 13 °C. Bubbles 613 and 624, however, have lower rates of size decrease. The possible reasons behind t h i s are not c l e a r .  The two bubbles have  the lowest aspect ratios i n the group suggesting that perhaps the s l i p v e l o c i t i e s of the other bubbles were high enough to e f f e c t a higher heat and mass transfer thus compensating f o r their r e l a t i v e l y smaller surface areas.  The r e l a t i v e magnitudes of the s l i p v e l o c i t i e s indicate  otherwise. Referring to Figures 5.6, 5.9 and 5.12, bubbles 721 and 731 show size decrease rates comparable to the majority of the other bubbles. Bubble 722, however, has the lowest rate of surface area decrease among a l l the bubbles.  Aside, with regard to bubble 722 i n Figure 5.12,  because of the extremely low rate of surface area decrease i n proportion to the rate of decrease of volume, i t s spherical equivalent diameter drops o f f at a higher rate than f o r bubble 721.  Bubble 721 i s by f a r  the largest bubble tracked whereas bubble 722 i s one of the smallest bubbles tracked.  Bubble 731 i s of s i m i l a r size to bubble 722.  This  emphasizes the near sphericity of small bubbles i n comparison to large bubbles when the aspect r a t i o s of these bubbles are examined.  Continuing, bubble 722, though being one of the smallest bubbles tracked, had the highest nominal average s l i p v e l o c i t y .  Both i t s near  s p h e r i c i t y and high s l i p v e l o c i t y contradict i t s low collapse rate. More detailed information concerning surrounding  the pressure and flow f i e l d s  the bubble i s required to provide possible reasons f o r the  discrepancies. Comparisons to previous bubble collapse studies are d i f f i c u l t  to  j u s t i f y as the conditions under which collapses proceed i n this study occur under a varying pressure environment instead of a step pressure application as discussed previously.  It i s s u f f i c i e n t to state that  bubble collapse rates are s i g n i f i c a n t l y slower under a varying pressure environment.  The impulse experienced  by bubbles i n collapses i n i t i a t e d  by a step pressure a p p l i c a t i o n appears to lead to more rapid collapses.  5.4  Bubble Condensation Rate Estimates of the condensation  rate f o r each bubble was determined  in conjunction with the Nusselt number calculation as described previously i n Section 4.2.  It was necessary  to extrapolate the least  squares f i t s of the decrease of bubble volume with position back to the downcomer entrance to obtain approximate i n i t i a l volumes f o r each bubble.  This assumes i d e n t i c a l collapse rates outside the tracking  length.  This may not be j u s t i f i a b l e , but the extrapolated portions of  the condensation  rates for each bubble do give a probable collapse rate  based on a v a i l a b l e data.  Beginning with the i n i t i a l mass calculated  from the extrapolated i n i t i a l volume, the mass loss across 1 cm Increments was calculated and subtracted from the retained mass to obtain the condensation  rate f o r i n d i v i d u a l bubbles.  48. Figure 5.14  shews the dimensionless condensation curves f o r a l l the  bubbles tracked as functions of normalized position along the downcomer. The extrapolated parts of each curve l i e outside the portion bounded by two dots.  The downward concavity of the curves i s a result of the  l i n e a r approximation of the decrease of bubble volume. of decrease of bubble volume was  Since the rate  taken to be constant, the mass  condensed per centimeter increment of downcomer length becomes progressi v e l y larger as vapour density increases with hydraulic pressure. Subtraction of the calculated mass condensed from the retained vapour mass yields a nonlinear reduction i n vapour mass.  The extrapolated  condensation curves indicate that two bubbles would survive the length of the downcomer.  Bubbles 622 and 624 would retain approximately 6% and  32% of t h e i r o r i g i n a l masses respectively.  The remainder of the bubbles  tracked however, would collapse at various points along the downcomer. Complete collapses of bubbles were not however, v i s u a l l y confirmed during experimentation.  The l i n e a r approximation of the rate of  decrease of bubble volume coupled with the hydraulic pressure induced increase of vapour density may have resulted i n the overestimation of the condensation rates.  The condensation rates presented are conserva-  tive i n the sense that they may be viewed as upper bound rates. 5.15  to 5.17  curves.  repeat Figure 5.14  Figures  to a i d i n distinguishing between the  As previously, the curves are grouped according to the i n l e t  l i q u i d temperature.  It i s apparent that the curves r e f l e c t the v a r i a -  tion i n slopes of the least squares f i t s of the volume data i n each of the three p l o t s .  49. 5.5  Heat Transfer Rate To quantify the heat l o s t through condensation, bubble external  o v e r a l l heat transfer  c o e f f i c i e n t s were calculated.  The values of the  heat transfer c o e f f i c i e n t s based on bubble surface area ranged from 6 to 775 W/m  2  °C.  These were considerably lower than those obtained by  Levenspiel [11] (50 kW/m °C), and Brucker and Sparrow [19] (10 kW/m 2  °C).  2  A more favourable comparison with existing data was obtained when  the volumetric heat transfer c o e f f i c i e n t s were considered. The volumetric heat transfer  c o e f f i c i e n t s estimated i n this study ranged  from 24 to 957 kW/m °C. These values agreed well with those of Sideman 3  and Moalem [26] (12 to 232 kW/m °C) obtained for a pentane co-current 3  flow system.  Sideman and Moalem did not give a general range of sizes  of their bubbles.  The discrepancy between the data obtained for the  surface area based heat transfer c o e f f i c i e n t s may be p a r t i a l l y a t t r i b u t able to the extremely large surface area to volume ratios of the e l l i p s o i d a l bubbles i n t h i s study. To broaden the a p p l i c a b i l i t y of the heat transfer c o e f f i c i e n t s to other f l u i d s and operating conditions, the results were non- dimensiona l i z e d i n Nusselt number form.  The c a l c u l a t i o n procedure f o r Nusselt  number i s contained i n Section 4.2.  Only the surface area based heat  transfer c o e f f i c i e n t s were non-dimensionalized to adhere to normal practice  pursued i n the l i t e r a t u r e .  Figure 5.18 shows the l o c a l external Nusselt number f o r each bubble tracked plotted versus their repsective normalized positions downcomer.  along the  The general trend i s one of rapid decrease near the down-  corner entrance with gradual s t a b i l i z a t i o n towards the exit of the downcomer.  The high Nusselt numbers near the downcomer entrance are a  50. d i r e c t r e s u l t of the extremely low d r i v i n g temperature difference near the  s i t e of bubble formation.  This i s necessarily the case since the  vapour mass condensed i s calculated based on a constant rate of decrease of bubble volume.  The steep i n c l i n a t i o n of the driving temperature  difference near the downcomer entrance i s i l l u s t r a t e d i n dimensionless form i n Figure 5.19 for a l l the bubbles tracked.  The highest l o c a l  Nusselt number obtained was 16.05, the lowest was 0.10. Figures 5.20 to 5.22 repeat Figure 5.18 i n the previous fashion. An i n t e r e s t i n g event occurs as shown i n Figure 5.20.  Bubbles 311, 621,  and 622 collapse neatly onto a single composite curve forming i n effect a track of a composite bubble taken over 80% of the downcomer length. The Nusselt number v a r i a t i o n of bubble 613 appears to p a r a l l e l the composite curve. To investigate the e f f e c t s of r e l a t i v e v e l o c i t y on the heat transferred from vapour to l i q u i d , l o c a l Nusselt numbers were plotted as functions of l o c a l Peclet numbers.  The l o c a l Peclet numbers were  calculated as described i n Section 4.3.  Figure 5.23 shows the r e l a t i o n -  ship between the l o c a l Nusselt and Peclet numbers f o r a l l the bubbles tracked.  In general as expected, higher Nusselt numbers corresponded to  higher Peclet numbers. trend. the  Bubbles 311 and 813, however, contradict t h i s  Bubble 311 has an extremely low s l i p velocity i n comparison to  other bubbles.  At t h i s magnitude, the increase i n condensation  caused by convection due to the s l i p v e l o c i t y may well be n e g l i g i b l e . The s l i g h t decrease of Nusselt number with Peclet number f o r bubble 813 i s well within the error brought about by the coarseness of the l i n e a r l e a s t squares f i t s of the bubble v e l o c i t y and size decrease raw data.  The p o s i t i o n averaged values of the Nusselt and Peclet numbers were calculated and plotted i n Figure 5.24 for individual bubbles.  In  general, the Nusselt number appears to be a weak function of the Peclet number.  The convective effects over this r e l a t i v e v e l o c i t y range did  not s i g n i f i c a n t l y a f f e c t the heat transfer.  As a reference, the r e l a -  tionship between Nusselt and Peclet number f o r a f l u i d sphere i n potential flow i s also plotted.  The Nusselt numbers obtained i n t h i s  investigation are considerably lower than those predicted by the potential flow model.  This i s understandable i n view of the assumption  of perfect heat transfer used i n the potential flow model. averaged Nusselt number ranged from 0.10 to 6.68. Peclet numbers ranged from 5516 to 22699.  The p o s i t i o n  The p o s i t i o n averaged  The considerable scatter i s  primarily a result of the turbulence encountered by each bubble.  The  wide variations i n the s l i p v e l o c i t y are reflected In the Peclet number. An estimate of the possible uncertainty i n the Nusselt number i s given i n Appendix C.  Within the l i m i t s of the assumptions made i n the  analysis, the uncertainty i n the bubble l o c a l external Nusselt number i s approximately  5.6  37%.  Vapour Mass Flowrate The primary reason f o r the measurement of vapour mass flowrate was  to obtain q u a l i t a t i v e data on the relationships between HVC operating parameters and the vapour mass flowrate. independently  The HVC parameters that were  varied included i n l e t l i q u i d flowrate and temperature.  The i n l e t l i q u i d flowrate was a d i r e c t function of the applied pressure r a t i o across the length of the downcomer.  Figure 5.25 contains plots of  vapour mass flowrate versus l i q u i d mass flowrate.  Each curve  represents  52. quantities obtained at varying vapour temperatures as measured i n the separation tank.  The increase i n o v e r a l l magnitude of vapour mass flow-  rate with vapour temperature can be d i r e c t l y attributed to the larger cavitation jets formed at higher i n l e t l i q u i d temperatures.  The larger  c a v i t a t i o n j e t s introduced correspondingly larger amounts of vapour i n t o the flow.  The relationship between the l i q u i d and vapour temperatures  i s shown i n Figure 5.26.  Referring to an i n d i v i d u a l curve i n Figure  5.25, the vapour mass flowrate can be seen to increase with l i q u i d mass flowrate. tures.  The increase i s more pronounced at higher vapour  tempera-  This could be attributed to a non-linearity In flashing  rate at  the downcomer i n l e t as the i n l e t l i q u i d temperature approaches saturation. In comparison to HAC, i t appears that at least on a laboratory scale, HVC produces a s l i g h t l y lower output f o r a given l i q u i d flowrate. Rice [5] achieved a maximum air/water mass flowrate r a t i o of 1.91E-4 (at a mass flowrate of a i r of 4.02E-5 kg/s) i n a 1.905 cm diameter downcomer.  The maximum vapour/liquid mass flowrate r a t i o obtained i n t h i s  study was 1.27E-4 (at a mass flowrate of vapour of 1.01E-4 kg/s) i n a 2.54 cm diameter downcomer. condensation  In consideration of the mass loss through  along the downcomer, the quantity of vapour entrained i n t o  the downcomer may well be s i m i l a r to that achievable i n a hydraulic a i r compressor.  53. CHAPTER VI CONCLUSIONS AND RECOMMENDATIONS  6.1  Condensation and Heat Transfer Rate During HVC, the mass condensation rates have been found to  increase along the length of the downcomer.  The lowest calculated  mass transfer rates occurred near the downcomer entrance with the highest calculated rates occurring at the e x i t .  This finding i s s i g n i -  ficant because i t suggests that vapour mass losses may be minimized by using a m u l t i p l i c i t y of cascading compression stages to achieve a desired delivery pressure. The condensation rates presented i n Figure 5.14 may be viewed as an upper bound f o r estimating the vapour mass losses i n the HVC process. Extrapolation of the inferred condensation rates predict that the majority of the vapour bubbles induced into the downflow would condense e n t i r e l y before a r r i v a l at the e x i t of the test section. v i s u a l l y confirmed during experimentation.  This was not  The linear least squares  method of approximating the rate of change of bubble volume used to calculate the mass transferred may have resulted i n the overestimation of the condensation rates. The l o c a l external Nusselt numbers used to characterize the magnitude of the heat transferred through vapour condensation ranged from 0.1 t o 16.  The highest l o c a l Nusselt numbers were calculated to  occur near the entrance of the downcomer.  This was primarily due to the  existence of extremely low d r i v i n g temperature differences near the downcomer entrance.  As the v a r i a t i o n of the heat transfer rate from the  vapour to the l i q u i d was based on a l i n e a r l e a s t squares approximation  54. of the decrease i n bubble volume, the average values of the l o c a l Nusselt numbers presented may be more indicative of the actual heat transfer rates occurring during the HVC process. "The bubble external Nusselt numbers were found not to be a strong function of bubble Peclet numbers." Within the range of r e l a tive v e l o c i t i e s considered here, the heat transfer o f f the bubble surface d i d not appear to strongly depend on convection.  6.2  Technical F e a s i b i l i t y of Hydraulic Vapour Compression The technical f e a s i b i l i t y of HVC i s dependent on the minimization  of  the vapour condensation rates which result from the compression  process.  The output gas mass flowrate of the laboratory scale hydraulic  vapour compressor studied here compared favourably with a s i m i l a r l y sized hydraulic a i r compressor.  The comparison was based e n t i r e l y on  output gas mass flowrates without regard to the i n l e t or i n i t i a l gas mass flowrates.  The favourable comparison indicated that the conden-  sation rates occurring i n the hydraulic vapour compressor were not s u f f i c i e n t l y severe that the output gas mass flowrate was reduced substantially below that of the hydraulic a i r compressor.  Since only  output gas mass flowrate was considered, the p o s s i b i l i t y exists that the  HVC process i s able to induce or generate a greater i n i t i a l gas mass  flowrate than the HAC process.  Further study i s required to determine  possible output vapour temperatures for d i f f e r e n t compression r a t i o s . The f e a s i b i l i t y of the HVC process w i l l be dependent on the ouptut vapour temperature.  55. 6.3 6.3.1  Further Work Modifications to the Apparatus and  Instrumentation  Listed below are suggestions concerning possible improvements to the existing apparatus and instrumentation. (a)  The Nalgene b e l l jar should be replaced preferably with a glass b e l l j a r to minimize slow leaks which developed due to the crazing of the Nalgene at the jar mouth.  (b)  Multiple pressure taps placed along the length of the test section would allow a more accurate measurement of the pressure r i s e .  (c)  Pressure and displacement transducers ( f o r the measurement of l i q u i d depth i n both the vacuum chamber and separation tank) t i e d into the data a c q u i s i t i o n system should be purchased to obtain more accurate and precise data.  This would also allow the data c o l l e c -  tion during the actual f i l m i n g i n t e r v a l s . (d)  The separation tank should either be insulated or replaced with one which has a much smaller free surface. evaporation which may  This would minimize Freon  result i n the overestimation of the output  vapour mass flowrate. (e)  For the f i l m i n g of bubbles, a synchronized two-camera arrangement should be used. each other.  The cameras should be placed at ninety degrees to  This arrangement would r e s u l t i n an a d d i t i o n a l  dimension upon which to base the calculation of bubble volumes. The r e f r a c t i o n tube w i l l have to be replaced with a square crosssection glass tube to allow the f i l m i n g . 6.3.2  Suggestions Concerning  the Film Analyses  Due to the discrete and nonrepeatable nature of this type of study, a s t a t i s t i c a l approach to the measurement of bubble collapse would be  56. highly desirable i n the interests of accuracy.  Such an approach,  however, would be extremely time intensive and labourious without the proper a n a l y t i c a l equipment.  Machines are available which can d i s t i n -  guish varying shades of darkness of a given area i n a photographic image (Hyzer [31]).  This would provide the experimenter with a means f o r  obtaining an unbiased measurement of the projected area of a bubble image.  More sophisticated machines are able to d i g i t i z e the bubble  image d i r e c t l y allowing extremely fast processing of f i l m data from the frame and bubble s e l e c t i o n stage to the estimation of the bubble volumes.  The speed of processing would certainly allow a s t a t i s t i c a l  approach to be used i n the measurement of bubble collapse.  6.3.3  Further Areas of Study The process of HVC i s very much i n the early stages of development.  The process can be divided into three d i s t i n c t areas of investigation: the downcomer i n l e t vapour generation or induction scheme; the vapour condensation rate i n the downcomer; the downcomer exit vapour/liquid separation scheme. optimization.  Each of these areas requires further study and  This work provides estimates of the vapour condensation  rates as w e l l as the achievable vapour mass output of a laboratory scale compressor.  The discussion of further work i s r e s t r i c t e d to these two  sets of r e s u l t s . Further work on both the vapour condensation rate and the achievable vapour mass output should i n i t i a l l y concern the v e r i f i c a t i o n of the r e s u l t s presented here.  Ideally, such v e r i f i c a t i o n would involve the  use of water as the working f l u i d i n a compressor of a s i g n i f i c a n t l y larger scale.  The use of water i n the v e r i f i c a t i o n w i l l be advantageous  57. since i t i s the intended working f l u i d i n the open cycle heat pump f o r which the HVC process i s slated.  A larger scale experimental unit has  the advantage of a higher volume flowrate c a p a b i l i t y .  Higher volume  flowrates would lessen the measurement error of each operating parameter. Optimization l o g i c a l l y follows v e r i f i c a t i o n .  To minimize the  vapour condensation rate, the two most important dimensionless parameters to consider would be the downcomer length to diameter r a t i o and the void f r a c t i o n .  For a given downcomer length, v a r i a t i o n of the void  f r a c t i o n w i l l d i c t a t e the achievable pressure r a t i o .  The pressure r a t i o  would control the volume flowrate through the downcomer.  The effects of  varying each dimensionless parameter, downcomer length to diameter r a t i o and void f r a c t i o n , should be investigated to maximize the mass of vapour delivered. Optimization l o g i c a l l y follows v e r i f i c a t i o n .  To minimize the  vapour condensation rate, the three most important dimensionless parameters to consider would be the downcomer length to diameter r a t i o , the void f r a c t i o n , and the bubble diameter to downcomer diameter r a t i o .  For  a given downcomer length, v a r i a t i o n of the void f r a c t i o n w i l l d i c t a t e the achievable pressure r a t i o .  The pressure r a t i o would control the  volume flowrate through the downcomer. the compression  To minimize bubble condensation,  process must occur as quickly as possible.  high flowrates are therefore desirable.  Extremely  Bubble size i s an important  parameter since smaller bubbles would maintain bubble sphericity.  The  volume per unit surface area would then be maximized and the a v a i l a b l e heat transfer area would be minimized.  The effects of varying each  dimensionless parameter should be investigated to maximize the mass of vapour delivered.  58. BIBLIOGRAPHY 1.  Ryan, J.A., "Cycle Analysis for a Sea Water Heat Pump," University of B r i t i s h Columbia, Internal Report, 1983.  2.  Langborne, P.L., "Hydraulic A i r Compression, Old Invention - New Energy Source?", CME, Nov. 1979, pp. 76-80.  3.  Isenberg, J . , Moalem, D., Sideman, S., "Direct Contact Heat Transfer with Change of Phase: Bubble Collapse with Translatory Motion i n Single and Two Component Systems," Proceedings of 4th I n t l . Heat Transfer Conf., V o l . V, Paper B2.5, 1970.  4.  Wallis, G.B., One-Dimensional Two-Phase Flow, McGraw-Hill, New York, 1969, pp. 243.  5.  Rice, W., "Performance of Hydraulic Gas Compressors," ASME J . of Fluids Engng., V o l . 98, Dec. 1976, pp. 645-653.  6.  Rice, W. and Chen, Li-Ting, "Effects of Incomplete Separation and of A i r S o l u b i l i t y on the Performance of a Hydraulic A i r Compressor (HAC)," Proceedings, I n t l . Conf. on Hydropower. (Water Power '81), Washington, D.C., June 22-24, 1981.  7.  Chen, Li-Ting and Rice, W., "Some Psychrometric Aspects of a Hydraulic A i r Compressor (HAC)," ASME Journal of Energy Resources, Vol. 104, Sept. 1982, pp. 274-276.  8.  Chen, Li-Ting and Rice, W., "Properties of A i r Leaving a Hydraulic A i r Compressor (HAC)," ASME J . of Energy Resources, V o l . 105, Mar. 1983, pp. 54-57.  9.  Berghmans, J.A. and Ahrens, F.W., "Performance of a Hydraulic A i r Compressor f o r Use i n Compressed A i r Energy Storage Power Systems."  10.  C l i f f , R., Grace, J.R. and Weber, M.E., Bubbles, Drops and P a r t i c l e s , Academic Press, New York, 1978.  11.  Levenspiel, 0., "Collapse of Steam Bubbles In Water," I n d u s t r i a l and Engineering Chemistry, V o l . 51, No. 6, June 1959, pp. 787-790.  12.  Bankoff, S.G. and Mason, J.P., "Heat Transfer from the Surface of a Steam Bubble i n Turbulent Subcooled Liquid Stream," A.I. Ch. E. Journal, Vol. 8, No. 1, Mar. 1962, pp. 30-33.  13.  Florschuetz, L.W. and Chao, B.T., "On the Mechanics of Vapour Bubble Collapse," ASME J . of Heat Transfer, Series C, V o l . 87, No. 2, May 1965, pp. 209-220.  14.  Wittke, D.D., Ph.D. Thesis, University of I l l i n o i s , Urbana, 1966.  59. 15.  Wittke, D.D. and Chao, B.T., "Collapse of Vapour Bubbles With Translatory Motion," ASME J . of Heat Transfer, Series C, V o l . 89, No. 1, February 1969, pp. 157-159.  16.  Hewitt, H.C. and Parker, J.D., "Bubble Growth and Collapse i n Liquid Nitrogen," ASME J . of Heat Transfer, February 1968, pp. 22-25.  17.  Board, S.J. and Klimpton, A.D., "Spherical Vapour Bubble collapse," Chemical Engineering Science, V o l . 29, 1974, pp. 363-371.  18.  Delmas, H. and Angelino, H., 'Contraction de bulles de vapeur nonspheriques," Canadian J . of Chemical Engineering, V o l . 55, Dec. 1977, pp. 644-650.  19.  Brucker, G.G. and Sparrow, E.M., "Direct Contact Condensation of Steam Bubbles i n Water at High Pressure," I n t l . J . Heat Mass Transfer, V o l . 20, 1977, pp. 371-381.  20.  Moalem, D., Sideman, S., O r e l l , A., and Hetsroni, G., "Direct Contact Heat Transfer with Change of Phase: Condensation of a Bubble Train," I n t l . J . Heat Mass Transfer, V o l . 16, 1973, pp. 2305-2319.  21.  Sekoguchi, K., Fukui, H., and Sato, Y., "Flow Characteristics and Heat Transfer i n V e r t i c a l Bubble Flow," Two-Phase Flow Dynamics, Hemisphere Publishing Corp., Washington, 1979, pp. 59-74.  22.  Ruckenstein, E., "On Heat Transfer Between Vapour Bubbles i n Motion and the B o i l i n g Liquid From Which They are Generated," Chemical Engineering Science, No. 10, 1959, pp. 22-30.  23.  Moalem, D. and Sideman, S., "The Effect of Motion on Bubble Collapse," I n t l . J . Heat Mass Transfer, V o l . 16, 1973, pp. 23212329.  24.  Dimic, M., "Collapse of One-Component Vapour Bubble With Translatory Motion," I n t l . J . Heat Mass Transfer, V o l . 20, 1977, pp. 1325-1332.  25.  Prisnyakov, V.F., "Condensation of Vapour Bubbles i n Liquid," I n t l . J. Heat Mass Transfer, V o l . 14, 1971, pp. 353-356.  26.  Moalem, D., Sideman, S., O r e l l , A., Hestroni, G., "Condensation of Bubble Trains: An Approximate Solution," Prog. Heat Mass Transfer, 6, 1972, pp. 155-157.  27.  Sideman, S. and Moalem, P., "Direct Contact Heat Exchangers: Comparison of Counter and Co-Current Condensers," I n t l . J . Multiphase Flow, V o l . 1, 1974, pp. 555-572.  28.  Ryan, J.A., M.A.Sc. Thesis, University of B r i t i s h Columbia, 1983.  60. 29.  Knapp, R.T., Daily, J.W. and Hammitt, F.G., Cavitation, McGrawH i l l , New York, 1970, pp. 1-19.  30.  Mayinger, F., "Scaling and Modelling Laws i n Two-Phase Flow and B o i l i n g Heat Transfer," Two-Phase Flows and Heat Transfer, V o l . 1, Hemisphere Publishing Corp., Washington, 1977, pp. 129-161.  31.  Hyzer, W.G., Engineering and S c i e n t i f i c High Speed Photography, Macmillan, New York, 1962.  32.  Kline, S.J., and McClintock, F.A., "The Description of Uncertainties i n Single Sample Experiments," Mechanical Engineering, Jan., 1953, pp. 3.  61. APPENDIX A HOT FILM ANEMOMETRY  DETAILS AND CALIBRATION PROCEDURE  The geometric and o p e r a t i o n d e t a i l s of the Thermosystem I n c . ( T S I ) model 1235W p a r a b o l i c h o t f i l m wedge probe a r e g i v e n i n T a b l e A . l . probe was c a l i b r a t e d  against a p i t o t  tube i n an open wind t u n n e l .  The The  t u n n e l a i r v e l o c i t y was c a l c u l a t e d from t h e dynamic p r e s s u r e p  u  a  - (2.0 P / P ) ° ' d  •  5  a  (A.l)  The probe Reynolds number based on the f i l m l e n g t h was g i v e n by  Re  = p u L /p • a a f a  (A.2)  £  p  The probe N u s s e l t number based on the f i l m  l e n g t h was determined by  e q u a t i n g t h e heat t r a n s f e r r e d through c o n v e c t i o n and t h e e l e c t r i c a l power d i s s i p a t e d  Nu  p  = [(E2 R ) L ] / [ ( R p  f  p  + R )2 L W  where the a i r thermal c o n d u c t i v i t y k  3  a  f  f  <T  p  - T ^ k J ,  (A.3)  was e v a l u a t e d a t the f i l m  temperature  T. = 0.5 (T + T ) . r p e  The form of the c o o l i n g law used was based on King's law  (A.4)  62. Nu  P  = A + B Re° . P  (A.5)  Figure A . l shows the parabolic hot f i l m wedge probe c a l i b r a t i o n curve. The c a l i b r a t i o n constants obtained were  A = 233.2 , B - 195.7 , n = 0.23  .  The vapour/air mixture v e l o c i t i e s exiting the separation tank were determined by calculating the probe Reynolds number as a function of the probe Nusselt number.  The probe Nusselt number was calculated from  Nu = [ E ( T ' / T ) R L . ] / [ ( R + R )2 L W (T - T')k ] . p e e p r p J r i p em 2  n  J  where the mixture thermal conductivity k  (A.6)  was calculated from the law of m  mixtures by  k = F k + (1 - F )k , m g g g a  (A.7)  with the conductivities of both the a i r and vapour evaluated at the f i l m temperature  T f  The probe Reynolds number Re  = 0.5 (T + T') . p e  (A.8)  determined from Equation (A.5) was used to P calculate the vapour/air mixture v e l o c i t y  63. u = (p Re )/(p L ) . m m p m r  (A.9)  The mixture density p and dynamic v i s c o s i t y p were calculated from the m m law of mixtures  P = E p + (1 - F )p m g g g a  (A.10)  p =F p +(1-F)p . m g g 8 a  (A.11)  m  and  64. APPENDIX B RATE OF HEAT TRANSFER BETWEEN THE VAPOUR AND LIQUID PHASES  The heat transferred away from the bubble may be determined directly  from the f i r s t law of thermodynamics f o r a closed system.  Consider a vapour bubble enclosed by a thin l i q u i d f i l m moving through an increasing hydrostatic pressure f i e l d from position 1 to position 2 as shown i n Figure B . l .  As the bubble moves to position 2, compression  of the vapour creates a temperature driving force f o r heat transfer at the system boundary.  The compression process i n the central portion of  the vapour bubble i s e s s e n t i a l l y isentropic whereas the remainder of the vapour external to the central portion i s compressed  isothermally.  The f i r s t law written i n d i f f e r e n t i a l form i s  dQ = dE - dW .  (B.l)  The change i n i n t e r n a l energy i s  d E  =  (m  g2 g2  ~"glV  + (  g  e  m g 2  z  " gl m  2  +  8 Z  2  ( m  >  £2 £2 e  +  ( m  " £l £l m  6  £2 2  )  " tl  g Z  m  8  z  l  )  '  ( B  *  2 )  The work done at the l i q u i d f i l m interface i s  dW - -p [ ( m v g 2  g 2  - m v ) + (m v g l  g l  £ 2  £ 2  - m ^ ) ]  .  (B.3)  Substituting Equations (B.2) and (B.3) into Equation ( B . l ) , the heat transferred becomes  dQ - ( m  +  g 2  e  g 2  + m  £2 £2  ( m  e  + (m  g 2  +  gz  m  g 2  pv  £2  2  P V  - m  g 2  ) - (m  £2 g  g l  )  Z l  ~  ( m  g l  e  £l £l e  ) - (m  + m  g l  A 2  +  g  m  £l  Z 2  g l  P V  pv  £l  g l  )  (B.4)  }  - in^gz^  ,  or  d Q  =  (m  " "glV  +  g2 g2 h  + (m  For  g 2  gz  2  - m  g l  (  g  ' £l £l m  ^2 £2 h  Z l  h  ) - (m gz £ 2  )  2  - n^gz^.  (B.5)  s m a l l increments i n p o s i t i o n , the p o t e n t i a l energy terms may be  n e g l e c t e d thus t h e heat t r a n s f e r r e d  dQ = ( m  g 2  h  g 2  - m  g l  h  g l  from t h e bubble i s  ) + (m  £ 2  h  £ 2  - m  £ l  h  £ l  )  .  (B  M a n i p u l a t i o n o f E q u a t i o n (B.6) l e a d s t o  dQ =  ( m „ - m , ) h „ - m , ( h „ - h , ) g2 g l g2  g2  gl'  gl'  v  + (m „ - m , )h „ + m , (h - h , ) . £2 £ l £2 £ l £2 £l' y  From c o n t i n u i t y ,  v  n  (B  the mass e q u a l i t y i s  m  £2  "£l m  =  " g2 ( m  " "gl* *  ( B  66. Substituting Equation (B.8) into Equation (B.7), the heat transferred becomes dQ = (m  g2  - m )(h g l  - h ) + m (h  g 2  £ 2  g l  - h ) + m (h  g 2  g l  £ l  £ 2  - h  £ l  ) . (B.9)  The difference i n the vapour mass flowrate between positions 1 and 2 i s the mass condensed.  This was calculated using the l i n e a r least f i t  slope obtained for the measured decrease i n bubble volume as  m  g2  - g l " g2 m  (p  " gl p  ) V  +  P  b l  g2 b2 - bl> (V  V  '  ( B  '  1 0 )  The vapour densities i n Equation (B.10) were taken to be the saturation values corresponding to the l o c a l pressure.  These are approximations to  the actual vapour densities which l i e above saturation.  The d i f f i c u l t y  in determining the actual vapour densities stems from the fact that the compression process l i e s between an i s e n t r o p i c process and an isothermal process.  Since small differences i n vapour densities have been  considered, the error of the approximation i n n e g l i g i b l e i n comparison to the error incurred i n the estimation of the rate of decrease of bubble volume. The difference i n the vapour and l i q u i d enthalpies at p o s i t i o n 2 i s the heat released  through condensation h  - h  g 2  £ 2  - L  2  .  (B.ll)  Substituting Equations (B.10) and ( B . l l ) into Equation (B.9) and dividing by the time increment, the rate of heat transferred may  be  written as  f  " t^ g2- gl> bl P  +  W  p  V  "V  +  +  P  g2< b2- bl» 2 V  »n<\2  V  L  "^iW'W  •  (B  '  12)  67. APPENDIX C ERROR ANALYSIS  The l i s t of estimated errors for pressure, temperature and flowrate measurements are contained i n Table C . l .  Often, fluctuations of the  measurements determined the reading accuracy. An attempt at quantifying the possible error i n the calculated bubble l o c a l external Nusselt number was made through the analysis given [32].  If Y i s the dependent v a r i a b l e and Y = Y(x.,x„,...,x ), then the i ^ n percentage uncertainty of the result i s ±y/Y with  y/Y = ([(e 3Y/3x )/Y]2 1  1  + [(e 3Y/3x )/Y]2 2  2  + ... [(e 3Y/3x )/Y]2)0.5 n n  (C.l)  where e, to e are the uncertainties or probable errors of the variables 1 n x^ to x respectively. n  The l o c a l external Nusselt number i s given by  Nu = [ 6 ( p  g2  -  P g l  )(dV /dt)V ]/[A b  b  b  (T - T )k ] g  £  f  (C.2)  P a r t i a l d i f f e r e n t i a t i o n of the Nusselt number with respect to each of the variables i n Equation (C.2) followed by d i v i s i o n with the Nusselt number yields  [3Nu/3(p  g2  - p ) ] / N u = l/(p gl  g2 " g l ' P  }  (C3)  68. [9Nu/3(dV /dt)]/Nu b  1 / V  = l/(dV /dt),  (C4)  b  (C5)  b'  [9Nu/9A ]/Nu = -:  [9Nu/9(T  (C6)  - T )]/Nu = -1/(T n  S  £  s  - T) ,  (C7)  £  (C8)  Having defined the p a r t i a l derivatives, the related uncertainties are now considered.  The uncertainties of the vapour density and the  saturation temperature are dependent on the uncertainty i n the pressure measurements taken at the vacuum and separation vessels, and the assumption of a linear pressure gradient between the two measurements.  Both  the vapour density and the saturation temperature are obtained from the Freon-11 saturation table given the pressure at any point along the downcomer. estimated  The percentage uncertainty i n the pressure measurements i s  to be 1%.  The uncertainty introduced by the assumption of  l i n e a r i t y between the pressures i n the two vessels i s l i k e l y to be much smaller than the uncertainty i n the actual measurements due to the low flow v e l o c i t i e s and short length of downcomer used.  The determination  of the values of vapour density and the saturation temperature from the Freon-11 saturation table introduces an a d d i t i o n a l error.  This error,  however, i s n e g l i g i b l e because of the limited operational pressure  range  used i n t h i s experiment (75 kPa < pressure < 104 kPa). Both the vapour density and the saturation temperature are approximately l i n e a r l y  69. related to the pressure and thus t h e i r uncertainties may as 1%.  also be taken  The uncertainty i n the measurement of the l i q u i d temperature i s  2% as given by the probe manufacturer. The uncertainty of the f i l m conductivity i s dependent on both the pressure measurements and the l i q u i d temperature measurements.  It i s  s u f f i c i e n t that the uncertainty of the f i l m conductivity be taken to be equal to the uncertainty of the l i q u i d temperature measurement. The largest uncertainty belongs to the measurements of bubble surface area and volume.  Based on a probable bubble trace error of  10%,  the error introduced by assuming a volume of revolution would l i k e l y be s i g n i f i c a n t l y smaller.  The t o t a l error f o r a given estimate of the  bubble surface area or volume i s taken to be 15%.  The  uncertainty  introduced by the l i n e a r l e a s t squares approximation of the v a r i a t i o n of bubble volume with time was  d i f f i c u l t to quantify.  t i o n varied tremendously and was  The standard  often greater than one.  devia-  In view of  t h i s , the standard deviation would not be useful as an estimate of he uncertainty introduced by the curve f i t t i n g .  It i s reasonable  to assume  that the uncertainty i s at least the same magnitude as the bubble surface area and volume uncertainty. When the uncertainties are given i n percentages, Equation (C.l) reduces to the square root of the sum of squares of the uncertainties. Thus the uncertainty of the bubble l o c a l external Nusselt number i s calculated to be approximately  37%.  70.  VAPOUR  LIQUID  oo O  O o  o  O  Fig.  1.1  t  O  o o  INCREASING PRESSURE  9  o DOWNCOMER  Schematic of the Hydraulic Compression Process  72.  R RADIUS  F i g . 1.3  Schematic of the Hypothetical Radial Temperature P r o f i l e of a Vapour Bubble During Compression  Fig. 2.1  Photograph of the Experimental Apparatus  F i g . 2.2  Photograph of the  Instrumentation  VACUUM CHAMBER  CAVITATION ROD SIPHON LOOP  -CXXl  CF—  VACUUM ACCUMULATOR MANOMETER  TEST SECTION (2.54 cm I.D.)  NEFF . D.A.S.  RTD PROBE FLOW SENSOR •I RTD PROBE THERMOCOUPLE  -H  _J  MULTIMETER  HOT FILM PROBE MANOMETER SEPARATION TANK  CONSTANT TEMPERATURE ANEMOMETER OSCILLOSCOPE IBM PC  T  VAX 11/750  CIRCULATION PUMP Fig.  2.3  Schematic of the Experimental Apparatus  VAX 11/750  76.  Fig. 2.4  Photograph of a Supercavitation Jet Formed at the Test Section Entrance  NALGENE BELL JAR CAVITATION ROD  ALUMINUM COLLAR  ALUMINUM MOUNTING PLATE  ALL DIMENSIONS IN CENTIMETERS Fig.  2.5  Details of the Vacuum Chamber  RUBBER O-RINGS DOWNCOMER (TEST SECTION)  78.  ALL DIMENSIONS IN CENTIMETERS Fig.  2.6  D e t a i l s of  the  S e p a r a t i o n Tank  79.  ^2.60 D 3.60 D 5.40 D ALL DIMENSIONS IN CENTIMETERS MATERIAL : ALUMINUM Fig.  2.7  Details of the Test Section Inlet O r i f i c e  80.  Q START ^ PROMPT FOR : CONTROL CHARACTER (CC)  PROMPT FOR : OUTPUT FILE NAME, EXPERIMENTAL RUN NUMBER, APPARATUS GEOMETRIC PARAMETERS, AMBIENT PRESSURE, AMBIENT TEMPERATURE, INITIAL VACUUM CHAMBER PRESSURE, INITIAL SEPARATION TANK PRESSURE  SAMPLE G» 25 HZ FOR 2 SECONDS FOR : LIQUID VOLUMETRIC FLOWRATE, DOWNCOMER INLET LIQUID TEMPERATURE, DOWNCOMER OUTLET LIQUID TEMPERATURE  PROMPT FOR : FINAL VACUUM CHAMBER PRESSURE, FINAL SEPARATION TANK PRESSURE, DELIVERED VAPOUR TEMPERATURE  I  TIME AVERAGE ALL MEASUREMENTS J WRITE TO OUTPUT FILE  —  I  PROMPT FOR : CONTROL CHARACTER (CC)  Fig.  2.8  Flowchart of the Data Acquisition Program  Fig. 2.9  Photograph of the Hot Film Probe Position in the Vapour Exhaust Tube  VACUUM CHAMBER 3.5 m  I I  C  Fig. 2.10  Schematic of the Bubble Photography Equipment  Arrangement  83.  Fig. 4.1  P a r t i a l Film Sequence of a Vapour Bubble During Hydraulic Compression  84.  85.  87.  PRINCIPAL CENTROIDAL AXIS SILHOUETTE TRACE DIGITIZED POINT  SECTION AXIS OF REVOLUTION SPHERICAL CAP SECTION TRAPEZOIDAL SECTION  SPHERICAL CAP SECTION  Fig.  4.2  Schematic of the Numerical Procedure for Estimating Bubble Surface Area and Volume  *88  VOLUME (cubic mm) o  •68  on  o  in  SURFACE AREA (square mm) o  o  o  o  o  o  o  o  V O L U M E (cubic mm)  •06  SURFACE AREA (square  mm)  V O L U M E (cubic mm) O  •T6  Ul  SURFACE AREA (square o  o  mm)  _  W  IH  o  o  o  VOLUME (cubic mm)  SURFACE AREA (square mm)  c  09  -J  o  < o  o  o  CM  3  mp  m  CO e n  o  > -a  i-h  o  CO  o  m a P  o  . tn  i-t »  » 3 a.  o  m  <! O  o cn  ID  o  > o  H s fD  o bo  CO C a* cr  o o  ON  o CO  'Z6  ELAPSED TIME (s)  Fig. 4.8  Variation of the Surface Area and Volume with Time: Bubble 721  VOLUME (cubic mm) O o-4 o  o 00  o  o  <  to l-t  o  o 3  o 3"  o  m °  (0 v> c  It  >  01  O  o o  Hi  n n  o  m o  > i-t  n  o o  »  m  3  a. < o (0  * sr s o  W e a  00  o  1  o  S3  o o  6  *V6  SURFACE AREA (square mm)  ELAPSED TIME (s)  F i g . 4.10  Variation of the Surface Area and Volume with Time: Bubble 731  VOLUME (cubic mm)  '96  SURFACE AREA (square mm)  VOLUME (cubic mm) o  m  o  m  SURFACE AREA (square o  o  o  mm) o  Fig. 4.13  Variation of the Surface Area and Volume with Time: Bubble 813  VOLUME (cubic mm)  '66  SURFACE AREA (square mm)  •ooi  "TOT  Fig. 5.1  Variation of the Volume with Normalized Position: A l l Bubbles  Fig. 5.2  Variation of the Surface Area with Normalized Position: A l l Bubbles  F i g . 5.3  Variation of the Equivalent Diameter with Normalized Position: A l l Bubbles  Fig. 5.4  Variation of the Nominal Relative Velocity with Normalized Position: A l l Bubbles  0.8-  0.6-  0.4-  0.2 0.1  0.2  0.3  NORMALIZED POSITION ALONG DOWNCOMER o -J Fig. 5.6  Variation of the Bubble Volume with Normalized Position: T» = 12 °C  Fig. 5.7  Variation of the Bubble Volume with Normalized Position: T  0  = 13 °C  Fig. 5.8  Variation of the Bubble Surface Area with Normalized Position: T. = 11 "C  0.8  0.6  0.4H  0.2 0.3  NORMALIZED POSITION ALONG DOWNCOMER  F i g . 5.9  Variation of the Bubble Surface Area with Normalized Position:  = 12 °C  Fig. 5.10  Variation of the Bubble Surface Area with Normalized Position: T» = 13 °C  F i g . 5.11  Variation of the Bubble Spherical Equivalent Diameter with Normalized Position: T- = 11 °C  0.0  0.1  0.2  NORMALIZED POSITION ALONG DOWNCOMER  F i g . 5.12  Variation of the Bubble Spherical Equivalent Diameter with Normalized Position: T. = 12 °C  0.3  Fig. 5.14  Variation of the Bubble Condensation Mass Loss with Normalized Position: A l l Bubbles  NORMALIZED POSITION ALONG DOWNCOMER  Fig. 5.15  Variation of the Bubble Condensation Mass Loss with Normalized Position: T = 11 °C £  \\\  \ \\  N  \  \  \  \ \ \  \ \\ \  o.o  0.1  0.2  \  \  \  \  \  \  \ 0.3  0.4  0.5  NORMALIZED POSITION ALONG DOWNCOMER  Fig. 5.16  Variation of the Bubble Condensation Mass Loss with Normalized P o s i t i o n :  0.6  Fig. 5.18  Variation of the Local External Nusselt Number with Normalized Position: A l l Bubbles  Fig. 5.19  Variation of the Dimensionless Driving Temperature Difference with Normalized Position: A l l Bubbles  < o o  0.1-  o.oi-f  1  0  0.2  =  ^ — 0.4  — i 0.6  1  f  0.8  1  NORMALIZED POSITION ALONG DOWNCOMER  Fig. 5.20  Variation of the Local External Nusselt Number with Normalized Position: T = 11 °C £  Fig. 5.21  Variation of the Local External Nusselt Number with Normalized P o s i t i o n : T = 12 °C £  T  T  0.2  0.4  0.6  0.8  NORMALIZED POSITION ALONG DOWNCOMER  Fig. 5.22  Variation of the Local External Nusselt Number with Normalized Position: = 13 °C  LOCAL PECLET NUMBER  Fig. 5.23  Variation of the Local External Nusselt Number with the Nominal Relative Peclet Number  1  I 10000  1  5000  I  I  I  15000  20000  25000  POSTION AVERAGED PECLET NUMBER  <J1 Fig. 5.24  Variation of the Position Averaged Nusselt Number with the Position Averaged Peclet Number  2•  12.0  VAPOUR TEMPERATURE 10.0-  A 11 degrees Celsius O 12 degrees Celsius •  8.0-  13 degrees Celsius  H 14 degrees Celsius 15 degrees Celsius  6.0-  4.0  ^ 0  2.0-  0.0 0.60  0.65  0.70  0.75  0.80  LIQUID MASS FLOWRATE ( kg / s )  i  0.85  0.90  S3  ON  Fig. 5.25  Variation of the Vapour Mass Flowrate with the Liquid Mass Flowrate  Fig. 5.26  Variation of the Inlet Liquid Temperature with the Outlet Vapour Temperature  1150 1100 1050 1000 950 900-fl 850 800 750 700 650  1 0  A  CALIBRATION DATA CALIBRATION CURVE  100  200  300  400  500  600  700  REYNOLDS NUMBER  Fig.  A.l  Hot Film Probe C a l i b r a t i o n Curve  800  900  1000  129.  SYSTEM BOUNDARY  VAPOUR / LIQUID INTERFACE •  VAPOUR  LIQUID  Fig. B . l  Schematic of t h e Bubble Compression P r o c e s s .  130.  Bubble  p vc (kPa)  Pst (kPa)  311  80.50  613  (z)  U/s)  T e (°C)  (cm)  (cm)  107.18  0.36  11.3  12.0  54.0  80.08  107.08  0.36  10.9  11.0  110.0  621  75.57  102.10  0.47  10.9  59.0  89.0  622  75.57  102.10  0.47  10.9  91.0  141.0  624  75.57  102.10  0.47  10.9  100.0  136.0  721  76.66  104.00  0.32  12.0  8.0  41.0  722  76.66  104.00  0.32  12.0  5.0  27.5  811  76.61  104.03  0.50  13.1  54.0  101.0  812  76.61  104.03  0.50  13.1  66.0  101.5  813  76.61  104.03  0.50  13.1  104.0  141.5  821  78.94  105.53  0.42  13.3  31.0  72.5  822  78.94  105.53  0.42  13.3  101.0  135.0  823  78.94  105.53  0.42  13.3  82.0  110.0  r  Table 1.  ±  (z)  f  Experimental Data for the Bubble Photography Tests  131.  T  T  (°C)  g (°C)  0.57  9.5  12.0  101.75  0.54  9.5  11.0  75.83  103.24  0.51  9.4  12.0  4  78.08  105.14  0.43  9.4  12.0  5  77.89  105.29  0.43  9.5  12.0  6  77.69  105.04  0.45  9.4  12.0  7  74.55  101.80  0.54  12.2  14.0  8  74.45  101.60  0.54  12.1  14.0  9  76.38  103.69  0.47  12.0  14.0  10  77.10  104.84  0.45  12.0  14.0  11  74.26  101.50  0.53  11.9  13.0  12  74.45  101.65  0.53  14.3  15.0  13  75.14  102.35  0.51  14.2  15.0  14  77.30  104.39  0.45  14.4  15.0  15  77.65  104.69  0.44  14.6  15.0  16  77.10  104.09  0.46  14.3  15.0  17  75.37  102.77  0.55  9.4  11.0  18  77.13  104.31  0.52  9.2  11.0  19  77.58  105.06  0.49  9.1  12.0  20  78.96  106.30  0.45  9.1  12.0  21  79.54  106.90  0.43  9.1  12.0  22  75.58  102.77  0.54  12.0  13.0  23  76.74  103.91  0.51  12.0  14.0  24  77.82  104.91  0.48  12.0  13.0  25  78.66  105.86  0.45  12.0  14.0  26  79.27  106.31  0.42  12.0  14.0  27  76.82  103.17  0.53  13.8  15.0  28  79.70  104.76  0.47  13.7  15.0  29  77.01  104.16  0.49  13.6  15.0  30  79.01  106.01  0.42  14.0  15.0  31  78.44  105.31  0.45  13.8  15.0  p vc (kPa)  st (kPa)  1  74.65  101.90  2  74.45  3  Run  Table 2.  r  p  \  U/s)  Experimental Data for the Vapour Mass Flowrate Tests  132.  Bubble  dA /dt  b  (mm )  (mm /s)  311  18.50  -  5.34  5.34  -  2.88  613  25.56  -  2.75  7.73  -  1.16  621  17.57  -  6.11  5.04  -  2.26  622  16.05  -  1.12  4.94  -  1.16  624  20.03  -  2.40  5.50  -  0.94  721  53.96  - 29.48  20.03  722  13.11  -  0.15  3.73  -  1.06  731  12.08  -  7.08  3.84  -  4.33  811  24.96  -  7.22  6.92  -  2.65  812  23.48  -  8.96  8.06  -  4.47  813  22.77  -  8.59  6.93  -  3.19  821  31.39  -  7.08  10.09  -  3.59  822  20.15  -  1.79  7.47  -  1.98  823  21.81  -  6.15  7.90  -  3.04  2  Table 3.  dV /dt  b  2  (mm ) 3  (mm /s) 3  - 11.78  Data From the Linear Least Squares F i t s of the Variation of the Bubble Surface Area and Volume with Time  133.  < se>i D  Bubble  u  g (m/s)  311  0.799  0.43  0.33  613  0.740  0.26  0.50  621  0.809  0.40  0.59  622  0.874  0.33  0.66  624  0.752  0.38  0.61  721  0.661  0.27  0.72  722  0.887  0.23  0.84  731  0.982  0.39  0.68  811  0.704  0.29  0.79  812  0.828  0.39  0.66  813  0.772  0.30  0.76  821  0.719  0.28  0.78  822  0.917  0.25  0.80  823  0.880  0.22  0.83  D  Table 4.  u  < sev>i  r (m/s)  Calculated Data for the Bubble Photography Tests  134.  Anemometer model  : TSI 1010A  Bridge s e t t i n g  : high  sensitivity R  Bridge series resistance  3  = 40.0 ohms = 3.1 v o l t s  Bridge standby voltage  TSI 1235W parabolic hot f i l m wedge  Probe model  = 1.016 mm  Probe sensing area length W  Probe sensing area width  f  = 6.47 ohms  Probe resistance at 0 °C (TSI specified) Probe cold resistance (measured)  R  Probe oprating resistance used  R  Probe operating  T  temperature used  Probe overheat r a t i o used  Table A . l .  = 10.16 mm  c o P  = 6.76 ohms =7.44 ohms = 6.41 °C = 1.15  Hot Film Anemometry D e t a i l s  135.  Ambient pressure  +  100 Pa  Downcomer i n l e t l i q u i d temperature  +  0.2 °C  +  1.0 °C  +  500 Pa  +  500 Pa  +  0.005 1/s  +  2 mm  Separation tank vapour temperature  T g  Vacuum chamber pressure  P  Separation tank pressure  P  st  Downcomer i n l e t l i q u i d  Q  *  h  st  flowrate  Separation Tank Liquid depth  vc  Table C . l . Experimental Errors  

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