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The feasibility of using supercritical carbon dioxide as a coolant for the CANDU reactor Tom, Samsun Kwok-Sun 1978-12-31

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THE FEASIBILITY  OF USING SUPERCRITICAL CARBON DIOXIDE  AS A COOLANT FOR THE CANDU REACTOR  by  Samsun  Kwok Sun/TOM  B.A.Sc., The University of B r i t i s h Columbia, 1975  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in  THE FACULTY OF GRADUATE STUDIES Department o f Mechanical Engineering  We accept this thesis as conforming to the. required standard  THE UNIVERSITY OF BRITISH COLUMBIA January, 1978 Samsum Kwok Sun TOM; 1978  In  presenting  this  thesis  an a d v a n c e d  degree  the  shall  I for  Library  f u r t h e r agree scholarly  by  his  of  this  written  at  the U n i v e r s i t y  make  that  it  purposes  for  freely  permission may  representatives. thesis  in p a r t i a l  financial  is  gain  Engineering  The  of  Columbia  Date 1 January 1978  by  shall  Mechanical British  Columbia,  British for  the  that  not  requirements I  agree  r e f e r e n c e and copying  t h e Head o f  understood  Department o f University  of  for extensive  permission.  2075 Wesbrook Place Vancouver, Canada V6T 1W5  of  available  be g r a n t e d  It  fulfilment  of  this  be a l l o w e d  or  that  study. thesis  my D e p a r t m e n t  copying  for  or  publication  without  my  ABSTRACT  This study indicates the technical f e a s i b i l i t y of using superc r i t i c a l carbon dioxide as a coolant for a CANDU-type reactor. cept of s u p e r c r i t i c a l cooling loop i s proposed i n t h i s study.  A new conThe reactor  i s cooled by a single phase coolant, which i s pumped at a high density l i q u i d - l i k e state.  The s u p e r c r i t i c a l - f l u i d - c o o l e d reactor has the advan-  tage of avoiding dryout as i n gas-cooled reactors, and the advantage of low coolant-circulation power as for liquid-cooled reactors.  As a result of eliminating dryout, the maximum operating temperature of the f u e l sheath can be increased to 1021°F (550°C) for existing Canadian f u e l bundles.  Accordingly, the coolant temperature i n the case  study of this work was calculated to be 855°F.  This high temperature  coolant can produce steam at a temperature and pressure comparable to that of conventional f o s s i l - f u e l plants.  However, since the exit coolant tem-  perature from the steam generator may be as low as 280°F, a portion of the s u p e r c r i t i c a l carbon dioxide coolant i s used to produce low-pressure steam.  A new dual-reheat  cycle i s proposed to reduce the high degree of  i r r e v e r s i b i l i t y i n the steam generation process.  In the new dual-reheat  cycle, the coolant heats the low and high pressure feeds i n a p a r a l l e l manner instead of a l t e r n a t i v e heating as i n dual-pressure cycles.  The  ideal overall plant e f f i c i e n c y of the new proposed dual-reheat cycle i s 33.02%, which i s comparable to that of the Pickering generating station.  - i i-  TABLE OF CONTENTS Page ABSTRACT  ..  i i  TABLE OF CONTENTS  i i i  LIST OF TABLE  v  LIST OF FIGURES  vi  NOMENCLATURE  ix  ACKNOWLEDGEMENTS  xii  1. INTRODUCTION  1  2. CRITERIA FOR SELECTING ALTERNATE COOLANTS (FOR CANDU-TYPE REACTORS)  5  2.1 General .  5  2.2 Overall Cost and Performance Criteria  6  2.3 Nuclear Properties 2.4 Chemical Properties  7 9  3. HEAT TRANSFER TO A LIQUID COOLANT AND MAXIMUM FUEL SHEATH OPERATING TEMPERATURE  11  3.1 Dryout in Coolant Channels  11  3.2 Maximum Operating Sheath Temperature  13  4. PROPOSED SUPERCRITICAL C 0 COOLING LOOP FOR CANDU REACTORS 2  16  4.1 Use of the Supercritical Cycle in Reactor Power Generation .... 16 4.2  Supercritical CO2 Cooling Loop  18  5. HEAT TRANSFER TO SUPERCRITICAL «> COOLANT  21  2  5.1 Heat Transfer to Supercritical Fluids i n Pipes 5.1.1  I  Peculiarities of Heat Transfer to Supercritical Fluids ..1 - iii -  21 21  Page 5.1.2 5.2  Previous Studies of Heat Transfer to Supercritical Fluids  . 26  Engineering Calculation of Heat Transfer to Supercritical Fluids  31  5.2.1  Choice of Correlations  31  5.2.2  Examination of Chosen Correlation  34  5.3  Heat Transfer to Single Phase Fluids in Fuel Bundles  39  5.4  Heat Transfer to Supercritical CC^ in Fuel Bundle  42  5.4.1  Specifications and Assumptions  42  5.4.2  Fuel Bundle Geometry and Subchannel Analysis  46  5.4.3  Predicted Heat Transfer to Supercritical Carbon Dioxide in 32-element Fuel Bundles  50  6. POSSIBLE STEAM CYCLES  54  6.1  General  54  6.2  Steam Cycle for the Supercritical Carbon Dioxide Cooled CANDU Reactor Plant  56  7. RESULTS AND DISCUSSION  59  7.1  Typical Heat Transfer in Bundles  59  7.2  Typical Steam Cycles  61  8. SUMMARY AND CONCLUSIONS  63  REFERENCES APPENDIX I.  117 Computing Procedure  124  APPENDIX II. Typical Calculation of Ideal Overall Efficiency  - iv -  137  LIST OF TABLE Page  TABLE 1  8  - v -  LIST OF FIGURES Page FIGURE FIGURE FIGURE  1. 2.  Thermo-hydraulic Features of PHW CANDU Reactor Power Plant  66  Typical Property Variations i n N e a r - c r i t i c a l Carbon Dioxide  67  3. Process Path of S u p e r c r i t i c a l Cooling Loop on P-V Diagram  68  FIGURE  4.  PHW CANDU Reactor Arrangement  69  FIGURE  5.  Fuel Bundle  70  FIGURE  6.  Thermal Hydraulic Regions i n a B o i l i n g Channel  71  FIGURE  7.  B o i l i n g Regions  72  FIGURE  8.  FIGURE  9.  Subchannel Temperature Rises i n a 28-element Bundle Versus Reactor Channel Length (from [12]) , High Sheath Temperature Operation vs. Time for Various Zirconium Alloy Fuel Elements (from [13])  73 74  FIGURE 10. Proposed S u p e r c r i t i c a l C0 Cooling Loop  75  FIGURE 11. Heat Transfer Regions: I - Liquids, I I - S u b c r i t i c a l Gases, I I I - Two-Phase, IV - Above-Critical F l u i d s , V - N e a r - C r i t i c a l Fluids (from [18])  76  FIGURE 12. L i s t of Equations  77  FIGURE 13. Routine f o r Calculating Wall Temperature  79  FIGURE 14. Computer Program Flow Chart for Calculating Heat Transfer to S u p e r c r i t i c a l Flow i n Heated Pipes  80  FIGURE 15. Prediction of Heat Transfer to S u p e r c r i t i c a l Flow, Experimental Results from [61]  81  FIGURE 16. Prediction of Heat Transfer to S u p e r c r i t i c a l Flow, Experimental Results from [49]  82  FIGURE 12. Prediction of Heat Transfer to S u p e r c r i t i c a l Flow, Experimental Results from [55]  83  FIGURE 18. Prediction of Heat Transfer to S u p e r c r i t i c a l Flow, Experimental Results from [42]  84  FIGURE 19. Equivalent Annulus Models f o r Rod-Bundles  85  2  - vi-  Page FIGURE 20.  Lumped Parameter Model for Rod-Bundles (from [71])  86  FIGURE 21.  Thermal Entrance Following a Grid Type Spacer (from [73])  87  Comparison of Heat Transfer Data i n a Uniformly Heated Seven-Rod Bundle (Pr = 0.7) with Wire-Wrap Spacers (from [74])  88  Comparison of F r i c t i o n Factors f o r Seven-Rod Bundle with Wire-Wrap Spacers (1/d = 12, 24, 36, °°) i n a Scalloped Liner (p/d = 1.237) (from [74])  89  Temperature P r o f i l e s i n Coolant Channel with Difference Fuel Bundle Orientation  90  FIGURE 22.  FIGURE 23.  FIGURE 24. FIGURE 25.  Effect of Ratio of Pitch to Rod Diameter on Nusselt Number and F r i c t i o n Factor (from [78])  .  91  FIGURE 26.  Cross Section of Fuel and Coolant Tube (from [12])  92  FIGURE 27.  Channel f o r B o i l i n g Reactor (from [79])  93  FIGURE 28.  Tube-in-Shell Fuel Element (from [79])  93  FIGURE 29.  Maximum Operating Temperature Versus Inlet Coolant Temperature  94  FIGURE 30.  Pressure Drop Versus Inlet Coolant Temperature  95  FIGURE 31.  Selection of Minimum Equivalent Hydraulic Diameter  96  FIGURE 32.  Cross Section of 32-Element Fuel Bundle  97  FIGURE 33.  Radial Neutron Flux D i s t r i b u t i o n i n Fuel Bundle  98  FIGURE 34.  Subchannel Coolant Temperature Rise i n 32-Element Fuel Bundles Versus Reactor Channel Length Subchannel Sheath Temperature Rise i n 32-Element Fuel  99  FIGURE 35.  Bundles Versus Reactor Channel Length  100  FIGURE 36.  Pressure Drop Along Reactor Channel Length  101  FIGURE 37.  Single Pressure Steam Generation  102  FIGURE 38.  Dual-Pressure 600.0/70.3 (psia) Steam Generation  103  FIGURE 39.  Turbine C i r c u i t Heat Balance of Single Pressure Cycle  104  FIGURE 40.  Turbine C i r c u i t Heat Balance of Dual-Pressure 600/70.3 (psia) Cycle  105  - vii -  Page FIGURE 41. Dual-Pressure 1200.0/70.3 (psia) Steam Generation  106  FIGURE 42. Turbine C i r c u i t Heat Balance of Dual-Pressure 1200.0/70.3 (psia) Cycle  107  FIGURE 43. Dual-Reheat 1200.0/70.3 (psia) Steam Generation FIGURE 44. Turbine C i r c u i t Heat Balance Of Dual-Reheat 1200/70.3 (psia) Cycle FIGURE 45. Results of Heat Transfer to S u p e r c r i t i c a l CO Coolant i n 32-Element Fuel Bundles FIGURE 46.  108  109 110  Overall Performance of S u p e r c r i t i c a l Carbon Dioxide Coolant  I l l  FIGURE 47. Overall Dimensions of 32-Element Fuel Bundle  112  FIGURE 48. Summary of Steam Conditions of Thermal Cycles  113  FIGURE 49.  114  Overall Performance of Thermal Cycles  FIGURE 50. Turbo-Generator Heat Balance (from [12])  115  FIGURE 51. Expansion Line of CANDU Reactor Turbine Stages (from [82])  116  - viii -  NOMENCLATURE A  experimental constant  b  experimental constant  Cp  s p e c i f i c heat at constant pressure  Cp  integrated s p e c i f i c heat, equation (13)  CWP  unheated wetted perimeter  c  experimental constant  D  equivalent hydraulic diameter, equation (25)  d  diameter  eff  efficiency  F  integrated f l u i d property  F(T)  f l u i d property as a function of temperature  f  normalized neutron flux  f(x/d)  correction factor, equation (24)  Gr  Grashof number  h  enthalpy  K  thermal conductivity  k  constant, 0.51504  M  mass flow rate  m  experimental constant  Nu  Nusselt number  n  experimental constant .  P  pressure  Pc Pr  '  c r i t i c a l pressure Prandtl number •  Dimensional quantities are evaluated i n both S.I. and B r i t i s h units. - ix -  Pr  integrated Prandtl number, equation (15)  p  pitch distance  Q  heat flux  q  l i n e a r heat rate  Re  Reynolds number  T  temperature  T  integrated temperature, equation (21b)  Tc  c r i t i c a l temperature  T(x)  temperature as a function of distance  TWP  t o t a l wetted perimeter  u  velocity  W  work  x  distance from channel i n l e t  y  distance  Z  dimensionless parameter, equation (5)  Subscripts b  bulk  in  inlet  m  pseudo-critical temperature  min  minimum  0  constant property  out  outlet  w  wall or sheath  z  dimensionless parameter  1  location 1  2  location 2  - x -  Greek Symbols T  shear stress  y  viscosity  p  density  £  m  momentum eddy d i f f u s i v i t y thermal eddy d i f f u s i v i t y  £  f r i c t i o n factor  H  length  pu  average product of pu  o-  p  integrated density  A  d i f f e r e n t i a l change  £  summation  (j>  constant, 0.25744  C r i t i c a l Values_of_Carbon_Dioxide pc  c r i t i c a l pressure, 73.82 bars or 1071.3 psia  Tc  c r i t i c a l temperature, 31.04°C or 87.9°F  - xi -  ACKNOWLEDGEMENTS  I would l i k e to express my sincere thanks and appreciation to my supervisor, Dr. E.G. Hauptmann f o r h i s help and guidance throughout the project.  Additional thanks are due to Dr. P.G. H i l l for invaluable comments  on phases of the research.  I would also l i k e to express my deep gratitude to my parents f o r encouraging me throughout the academic years.  This work was sponsored by the National Research Council of Canada.  - xii-  1  1.  INTRODUCTION  It has become evident that the world's limited o i l and gas resources w i l l have to be supplemented by nuclear energy for e l e c t r i c a l power generation.  Nuclear power plants have already operated  successfully  for many years, and most public u t i l i t i e s are counting heavily on nuclear power to meet the bulk of e l e c t r i c a l demands i n the next century.  Power reactors can be c l a s s i f i e d according to types of coolant, moderator, and f u e l .  The most popular types are the pressurized water and  b o i l i n g water reactors, which use enriched uranium as f u e l and ordinary water as both coolant and moderator.  Of special interest to Canada i s the  CANDU (CANadian JJeuterium Uranium) system, which uses natural uranium as fuel and heavy water (deuterium oxide) as coolant and moderator.  Figure 1  shows the main thermo-hydraulic features of a PHW (Pressurized Heavy Water cooled) CANDU reactor power plant.  The CANDU system i s a successful design i n terms of fuel economy and safety.  Nevertheless, i t s t i l l has several weaknesses.  One of these  i s that the pressurized heavy water coolant cannot be raised to a temperature high enough to generate steam at a pressure and temperature comparable to that of conventional f o s s i l - f u e l stations.  As a r e s u l t , the p r a c t i c a l  overall plant e f f i c i e n c y of the CANDU system i s r e l a t i v e l y low (29.7%). Atomic Energy of Canada Limited (AECL) i s pursuing many routes toward increasing the e f f i c i e n c y of the existing CANDU system.  One such route i s  looking for alternate coolants to heavy w a t e r ^ .  In the development of the CANDU system, a prototype reactor using ordinary water instead of heavy water has been operating at G e n t i l l y ,  2  Quebec since 1971 ' . Li  1  operating since 1966,  A research reactor at Whiteshell, Manitoba has been and i s cooled by terphenyl, an organic l i q u i d that  b o i l s at a temperature above 700°F at atmospheric pressure  . However,  in both b o i l i n g and pressurized water reactors, operation at higher power levels may result i n blanketing of the heat transfer surface with a layer of vapor.  Such blanketing of the surface by vapor may result i n "dryout"  of the coolant with the p o s s i b i l i t y of f u e l sheath f a i l u r e .  Thus, to avoid  accidental rupture of the fuel sheath, i t s maximum temperature must be only s l i g h t l y higher than the saturation temperature of the coolant used.  Because  the temperatures of both coolant and fuel sheath are constrained, the o v e r a l l plant e f f i c i e n c y i s limited.  To obviate dryout and obtain higher coolant temperatures, the reactor can be cooled by gaseous coolants.  Because gaseous coolants do not  change phase throughout the operating temperature range, dryout due to phase change of coolant cannot occur.  The fuel sheath can operate at i t s maximum  temperature (based on metallurgical considerations), which i s usually much higher than the saturation temperature of most coolants.  Compared with  l i q u i d coolants, however, gaseous coolants are characterized by low s p e c i f i c heat at constant pressure, low heat transfer c o e f f i c i e n t s , and low s p e c i f i c volume.  For this reason, gas cooled reactors have large flow passages through  the reactor, and require higher pumping power for coolant c i r c u l a t i o n  [3] .  To retain the^advantages and overcome the disadvantages of gaseous coolants, reactors may be cooled with " s u p e r c r i t i c a l " coolants.  These are  f l u i d s compressed above their c r i t i c a l pressure, and as a result always exist as a single phase.  For a given pressure of a s u p e r c r i t i c a l f l u i d , there i s  a temperature at which the maximum s p e c i f i c heat occurs, known as the pseudo-  3  c r i t i c a l or transposed c r i t i c a l temperature.  The thermophysical properties  of s u p e r c r i t i c a l f l u i d s change d r a s t i c a l l y across the pseudo-critical temperature.  Figure 2 shows the thermal conductivity, v i s c o s i t y , and  of s u p e r c r i t i c a l CO^  at 1100 psia.  density  Above the p s e u d o - c r i t i c a l temperature,  the properties of a s u p e r c r i t i c a l f l u i d are somewhat l i k e a normal gas. The thermal conductivity or dynamic v i s c o s i t y i s not greatly affected by changes i n temperature, and the density i s low. i s termed "vapor-like".  In this region, the f l u i d  Below the p s e u d o - c r i t i c a l temperature, the f l u i d i s  termed " l i q u i d - l i k e " , since i t has properties very much l i k e a l i q u i d .  The  thermal conductivity and dynamic v i s c o s i t y decrease with increasing temperature as i n ordinary l i q u i d s , and the density i s high.  Therefore, a super-  c r i t i c a l cooling loop which has i t s process path as shown i n Figure 3 can be arranged so that the l i q u i d i s pumped while i n a l i q u i d - l i k e state, thereby greatly reducing pumping power.  The purpose of the present work i s to investigate not only the p o s s i b i l i t y of using s u p e r c r i t i c a l carbon dioxide (CO^)  as a coolant, but  also the a p p l i c a t i o n of a s u p e r c r i t i c a l cooling loop to the CANDU system. The major part of this work involves an a n a l y t i c a l study of heat transport in the coolant channels and the thermodynamics of the CANDU reactor power station when s u p e r c r i t i c a l CO^  i s used as a coolant.  Carbon dioxide  was  selected because of i t s a v a i l a b i l i t y at low cost, i t s inertness i n contact with f u e l and reactor materials, and i t s s t a b i l i t y at r e l a t i v e high temperature.  In addition, i t s low c r i t i c a l pressure makes application of a super-  c r i t i c a l cooling loop p a r t i c u l a r l y suitable to the CANDU reactor.  In this  investigation, the basic design of the CANDU reactor was  assumed to be  unchanged when s u p e r c r i t i c a l CO2 was  However, the  used as a coolant.  operating temperature of the fuel sheath was  taken to be the maximum  4  allowable temperature (1021°F or 550°C).  In the i n i t i a l part of t h i s study, standard single and dual reactor steam cycles were analysed when using s u p e r c r i t i c a l CO2 as a coolant. The results indicated the o v e r a l l plant e f f i c i e n c i e s would be lower than the current CANDU i d e a l plant e f f i c i e n c y of 33.94%. reheat reactor steam cycle i s proposed. C0  2  As a r e s u l t , a new dual-  In this new cycle, s u p e r c r i t i c a l  generates high pressure steam at 1200 psia, 815°F and low pressure steam  at 70.3 psia, 567°F simultaneously for high and low pressure turbines respectively.  The expanded steam from the high pressure turbines i s mixed with low  pressure feed water to be evaporated through the low pressure turbines.  i n the steam generator before  expansion  This new steam cycle has a comparable  i d e a l o v e r a l l plant e f f i c i e n c y of ,33.02%.  This indicates the p o s s i b i l i t y  of increasing of the o v e r a l l plant e f f i c i e n c y of CANDU reactor power s t a tions, i f the performance of s u p e r c r i t i c a l CO^ coolant was optimized i n this preliminary study.  This study also points out other possible advantages of using s u p e r c r i t i c a l CO^ as a coolant for the CANDU system:  1. lower coolant c a p i t a l and upkeep costs; 2. compatibility with uranium carbide fuel having high uranium content and high thermal conductivity; 3. increased safety due to elimination of possible dryout.  5  2.  2.1  CRITERIA FOR SELECTING ALTERNATE COOLANTS (FOR CANDU-TYPE REACTORS)  General  Choosing the coolant i s a major consideration i n the design of nuclear  reactors.  I t strongly a f f e c t s the performance of reactors, and  eventually the cost of power generation.  In selecting a good coolant f o r  power reactors, several c r i t e r i a must be considered:  1. o v e r a l l cost and performance: a) low c a p i t a l and upkeep costs, b) a v a i l a b i l i t y ; 2. nuclear properties of coolant: a) low neutron absorption cross-section, b) good r a d i a t i o n - s t a b i l i t y , c) low induced-radioactivity; 3. chemical properties of coolant: a) stable at high temperature, b) compatible with f u e l and reactor materials; 4. heat transport and f l u i d properties of coolant: a) low pumping power, b) high density, c) high heat capacity, d) high heat conductivity, e) high saturation temperature ( l i q u i d coolant). Past studies have not i d e n t i f i e d a coolant which can adequately  6  meet a l l the above c r i t e r i a .  S u p e r c r i t i c a l CO^ i s no exception.  For  example, at high temperature i t has poor heat transfer c h a r a c t e r i s t i c s . However, when used i n a s u p e r c r i t i c a l cooling loop, the designer can s t i l l achieve good o v e r a l l heat exchange by increasing the flow rate. The resulting high pressure losses do not r e s u l t i n excessive pumping power since the coolant i s pumped i n a l i q u i d - l i k e state.  The economics of using s u p e r c r i t i c a l CO^ as a coolant for the CANDU system w i l l be discussed i n t h i s chapter.  Nuclear and chemical  properties of the coolant are also discussed, while heat transport c r i t e r i a are l e f t to a l a t e r  2.2  chapter.  Overall Cost and Performance C r i t e r i a  One of the major direct costs of a CANDU reactor power generation station i s the c a p i t a l and upkeep costs of the coolant.  For example, the  t o t a l cost of b u i l d i n g a 2 x 600 MWe CANDU-PHW (for Pressurized Heavy Water cooled) reactor power generation plant was about 300 m i l l i o n dollars i n [41 1972  . The heavy water cost alone was 65 m i l l i o n d o l l a r s , with 37.4%  of the heavy water used as coolant.  The coolant upkeep cost of the Pickering [2]  station was as high as 35% of the fueling cost  . Because of the r e l a t i v e l y  low cost of CO2, the cost of power generation would be s i g n i f i c a n t l y reduced i f CO^ were used as a substitute for heavy water i n CANDU reactors. The capital.and upkeep costs of a coolant depend on the i n i t i a l inventory and rate of leakage of the coolant.  The evaluation of the costs  of using s u p e r c r i t i c a l C 0 as a coolant for the CANDU system and the compari2  son with heavy water can only be made after a detailed study for a p a r t i c u l a r design of power generating plant, which was beyond the scope of this  i  7  study.  2.3  Nuclear Properties  If s u p e r c r i t i c a l CO^ nuclear properties.  i s used as a coolant, i t must have good  Since these properties are usually functions of tem-  perature but not pressure, properties to gaseous CC^.  s u p e r c r i t i c a l CC^ has similar imicroscopic  nuclear  Experience with B r i t i s h and French designed  reactors has shown that gaseous CO^  i s a good coolant i n Jterms of nuclear  properties.  The most important requirement of a coolant from a nuclear of view i s that i t has low neutron absorption.  The rate of neutron absorp-  tion i s a function of the macroscopic absorption  cross-section, which i s  proportional to the product of the density and the microscopic cross-section of the coolant molecules. operating conditions of 570°F and. 1450  psia, the macroscopic _5  2 3 cm /cm .  because of the low density of s u p e r c r i t i c a l CO^, —6  absorption  Under present CANDU reactor  cross-section of heavy water i s 2.7095 x 10  section i s only 5.9543 x 10  point  absorption  ' On the other hand,  i t s macroscopic cross-  2 3 cm /cm which i s much smaller than heavy water.  The low macroscopic absorption  cross-section usually means good  radiation s t a b i l i t y and low induced-radioactivity, because the coolant  has  l i t t l e chance to be broken down or capture nuclear p a r t i c l e s and become radioactive.  Moreover, most of the possible neutron capture i n CO2 results  in further stable nuclides.  Therefore,  CO^  i s stable i n a radioactive  environment.  It would be u n r e a l i s t i c to consider coolant-grade C0  2  as a pure  8  substance.  A t y p i c a l coolant analysis might be 10 p.p.m. H^O, 3 p.p.m. Ar,  10 p.p.m. H^, 17 p.p.m. 0^, and 94 p.p.m. N 2 ^ .  The reactions which are  important  i n considering induced r a d i o a c t i v i t y of impurities are l i s t e d i n  Table 1.  Because of the shorter h a l f - l i v e s , the  and 0 ^ nuclides decay  41 quickly.  The Ar  which has an intermediate h a l f - l i f e gives a low residual  a c t i v i t y i n the cooling c i r c u i t , but the a c t i v i t y l e v e l taken i n coolant, leakage from the c i r c u i t as whole i s too small to constitute a hazard.  REACTION Ar (n, )Ar 4 0  4 1  Y  0 (n,Y)0 1 8  0  CROSS-SECTION (barns)  HALF-LIFE  0.53  110 min.  2.2 x 10"  1 9  (n,p)N  29.0 sec.  4  16.0 x 10"  6  7.5 sec.  0 (n,a)C  1 4  0.4  5500 y r s .  C (n,y)C  1 4  0.1  5500 y r s .  1.76  5500 y r s .  1 7  1 3  N  (n,p)C  TABLE 1.  14 From a health physics point of view C  i s an important long-lived c o n s t i -  tuent of the coolant when i t i s released to atmosphere by leakage 14 or during blowdown.  The C  i s expected  from three main sources which are  also l i s t e d i n the Table 1. Although a proper estimate of radiation l e v e l or i n t e n s i t y from 14 C i s beyond the scope of the present study, i t i s clear that because i t s 14 long h a l f - l i f e , any amount of C production i n the coolant w i l l require  9  careful measures to prevent i t s escape.  This i s p a r a l l e l to the require-  3  ment of c o n t r o l l i n g t r i t i u m (T ) discharge while using heavy water as a coolant.  2.4  Chemical Properties  The thermal s t a b i l i t y of s u p e r c r i t i c a l CO^ i s quite s a t i s f a c t o r y up to the temperature envisaged for most reactor operations.  Carbon  dioxide tends to dissociate into CO and 0^ as the temperature i s increased, but even at 1000°K the equilibrium concentration of CO at a pressure as low as 1 0 atmospheres would be only 3 p.p.m. according to the data of Wagman et a l .  t 6 ]  .  Mor eover, CO  i s r e l a t i v e l y stable when i r r a d i a t e d so that the  concentration of r a d i o l y s l s be low.  products i n s u p e r c r i t i c a l CO^ coolant should  This observation i s confirmed by Bridge and N a r i n ^ .  In the  presence of impurities (e.g., NO^) that can react with small equilibrium rg  concentrations of r a d i o l y s i s  products, CO2 i s progressively broken down  1 .  In B r i t i s h and French reactors, which use graphite as a moderator, a further reaction takes place between graphite and the chemically reactive species produced by the i r r a d i a t i o n breakdown of CO^, r e s u l t i n g i n a problem of a t t r i t i o n of graphite.  However, d i s s o c i a t i o n of CO^ i s not a serious  problem i n CANDU reactors which use heavy water instead of graphite as a moderator. When a reactor coolant i s selected, the choice of reactor fuel is restricted.  Today, uranium dioxide (UO^) i s used i n CANDU reactors  because of i t s compatibility with heavy water and l i g h t water.  Uranium  dioxide i s an excellent fuel with a high melting point and high uranium content, but very low thermal conductivity.  Uranium metal and uranium  i I  !  10  carbide are also good fuels.  They have high melting points, high uranium  content and high thermal conductivity, but react vigorously with heavy or l i g h t water.  For this reason, AECL has been looking for alternate coolants [91  which are compatible with uranium carbide f u e l developed by AECL Using s u p e r c r i t i c a l CO2 as a coolant w i l l allow use of uranium metal and uranium carbide as f u e l s .  Although CO^ reacts with uranium metal  and uranium carbide, the rate of reaction i s very slow.  Measurements of the  rate of change of weight of sintered uranium monocarbide specimens i n dry C0  2  over the temperature range of 500°-830°C (931-1525°F) were made by  A t i l l et a l . ^ ^ .  The weight increased only by 120-170 mg/Kg/hr which  was about 100 times as fast as the rate of change of weight of uranium metal under the same condition.  The low rate of reaction between CO^ and  either uranium metal or uranium carbide allows enough time for defective fuel to be recovered before i t becomes a serious problem.  Wyatt  has  pointed out that when high i n t e g r i t y cans are used, i t should be possible to use uranium metal and uranium carbide fuels with C0„ coolant.  11  3.  HEAT TRANSFER TO A LIQUID COOLANT AND MAXIMUM FUEL SHEATH OPERATING TEMPERATURE  3.1  Dryout In Coolant Channels  AECL has pioneered in-reactor heat transfer t e s t i n g with experimental and power reactors, and has gained a large amount of operating experience with effects of coolant flow on f u e l sheath behavior. shows a PHW  Figure 4  CANDU reactor arrangement, and Figure 5 shows the d e t a i l s of  the f u e l bundle.  The coolant flows into the coolant channels and travels  within subchannels between f u e l rods.  The phenomenon of "dryout" has been  detected i n coolant channels, r e s u l t i n g i n sudden and s i g n i f i c a n t increase in fuel sheath temperature.  Figure 6 shows v a r i a t i o n i n sheath or wall tem-  perature i n a coolant channel, along with a notation of the types of flow regions believed to be present.  Forced convection b o i l i n g i n channels i s an extremely phenomenon, but the main idea can be more e a s i l y understood  complex  by considering  heat transfer from a small heating element submerged i n a large stationary pool of l i q u i d (pool b o i l i n g ) .  Figure 7 shows the conventional representa-  tion of the heat flux q versus the temperature difference AT between the heating, surface and l i q u i d coolant bulk temperature.  This curve can only  be obtained i f the temperature of the heating surface i s c a r e f u l l y controlled.  In the region preceeding point "a" on the curve, the heating sur-  face temperature i s nearly at or only a few degrees above the l i q u i d temperature. mation.  Thus, there i s i n s u f f i c i e n t l i q u i d superheat  and no bubble f o r -  Heat transfer i n this region i s therefore by l i q u i d natural con-  vection only.  As the heating surface temperature i s increased, the heat  12  flux increases and the region "a-b" i s reached.  A small number of nuclea-  tion centers become active, and a few bubbles are formed. soon collapse as they move away from the surface.  These bubbles  As AT i s further increased  between "b-c", the number of nucleation centers, and consequently the number of bubbles, increases rapidly with AT. The bubbles cause considerable agitation and turbulence of the liquid i n the boundary layer and consequently a greater increase of the heat flux with AT. Region "b-c" i s called the "nucleate boiling region".  Point "c" i s called the point of "cleparture  from the nucleate boiling" (DNB), and the corresponding heat flux is called the " c r i t i c a l heat flux".  The value of c r i t i c a l heat flux or the temperature  of DNB depends on local coolant conditions. When region "c-d" i s reached, the bubbles become so numerous that they begin to coalesce on the heating surface.  In this case, a portion of the heating surface gets blanketed  with vapor which acts as a heat insulator. This region i s called "mixed nucleate-film boiling".  In the region "d-e", a continuous blanket of vapor  forms over the entire heating surface, and the heat transfer coefficient reaches i t s lowest value.  This region i s called "stable film boiling".  In the region "e-f", called "film and radiation region", the temperature of the heating surface is so high that thermal radiation from the surface comes into play.  The curve in Figure 7 could not be obtained i f the temperature of the heating surface was not closely controlled. In most practical cases, such as heat transfer in reactors, the heat flux i s controlled. Referring to Figure 6, a sequence of events similar to that of pool boiling can now be imagined.  The liquid enters as a single phase; the vapor bubbles start  to form; small bubbles collapse together to form slugs, and a liquid annulus  13  forms.  F i n a l l y , the l o c a l heat flux becomes c r i t i c a l to the l o c a l coolant  condition, corresponding to the point "c" of the curve i n Figure 7. A further increase i n heat flux or increase i n vapor quality results i n a sudden l o c a l temperature jump which corresponds to the jump from "c" to "c"  1  into the film-radiation region.  The heating surface temperature at  "c"  1  may be high enough to exceed the safe operating l i m i t .  The complete  loss of coolant along with a sudden jump of temperature of the heating surface i s c a l l e d "dryout".  Dryout can occur not only i n a b o i l i n g channel where phase change takes place, but also at a point i n a compressed l i q u i d coolant channel because of increase i n l o c a l heat flux or l o c a l coolant starvation.  Dryout  i s very dangerous i n reactor operation, since l o c a l temperature increases may soften the fuel elements.  They may bend toward the coolant tube and  cause poor heat transfer due to l o c a l coolant starvation, which further elevates the temperature.  3.2  This may f i n a l l y r e s u l t i n fuel sheath f a i l u r e .  Maximum Operating Sheath Temperature  Since dryout i s a c r i t i c a l design parameter, a l l coolant channel conditions must be controlled so that a s i g n i f i c a n t margin of safety i s available to prevent dryout from occurring during normal operation.  In  other words, the operating temperature of the fuel sheath must be kept below the c r i t i c a l heat f l u x temperature, which i s approximately equal to the  temperature of the reactor coolant.  [121 . .. . Figure 8  shows the calculated subchannel temperatures i n a  28-element f u e l bundle design with a given heat flux shape along the channel and given maximum l i n e a r rates for i n d i v i d u a l subchannels. The  14  heat flux shape and the maximum l i n e a r heat rates are based on data during steady state operation of a CANDU 500 reactor at the Pickering station . An inter-subchannel mixing rate was assumed i n c a l c u l a t i n g the temperatures i n Figure 8.  The c a l c u l a t i o n agrees w e l l with the measurement, and shows  that the maximum l o c a l external sheath temperature exceeds the coolant saturation temperature by only about 5°F.  Nucleate b o i l i n g would a c t u a l l y  begin on the sheath surface at a temperature about 10°F above the coolant saturation temperature.  The maximum operating sheath temperature i n a CANDU reactor i s usually kept much below the maximum withstanding (metallurgical) temperature of the fuel sheath.  Zircaloy clad  fuel elements ( l i k e those used  in CANDU reactors) can actually operate at an elevated temperature for a certain period without f a i l u r e .  Operating l i f e i s assumed inversely  proportional to the magnitude of the temperature.  Some data from various  [13] tests are summarized i n Figure 9 defect versus temperature.  which i s a semilog plot of time-to-  I t shows that z i r c a l o y clad fuel elements can  operate at a temperature below approximately 550°C without defect for a r e l a t i v e l y long period. If s u p e r c r i t i c a l CO^ were used as a coolant for a CANDU reactor, dryout could not happen since s u p e r c r i t i c a l CO^ would remain i n a single phase throughout the operating temperature range.  Therefore, fuel sheath  temperature jump would no longer be a cause of worry under normal operating conditions.  The saturation temperature of the coolant i s no longer a b a r r i e r  to the upper l i m i t of the maximum fuel sheath temperature, and the operating  _ Pickering station i s the f i r s t commercial CANDU-PHW reactor power generating station, owned and operated by Ontario Hydro.  15  fuel sheath temperature can be as high as 550°C (1021°F).  This implies  that the maximum coolant temperature, and thus the e f f i c i e n c y of reactor power generation, can be higher than the corresponding l i q u i d coolant.  16  4.  4.1  PROPOSED SUPERCRITICAL C0 COOLING LOOP FOR CANDU REACTORS 2  Use of the S u p e r c r i t i c a l Cycle i n Reactor Power Generation  Supercritical in many applications.  f l u i d s have gained much attention as coolant media Currently, s u p e r c r i t i c a l hydrogen i s used as the  f u e l and coolant i n combustion chambers of large rocket engines.  Super-  c r i t i c a l water i s used as a working f l u i d i n f o s s i l - f u e l power generating stations,  and n e a r - c r i t i c a l helium i s used as a coolant i n super-conducting  applications.  Many other applications are being proposed and investigated.  Among them i s an e n t i r e l y s u p e r c r i t i c a l turbine power cycle, with a nuclear reactor as a direct heat source (the e n t i r e l y s u p e r c r i t i c a l turbine power cycle w i l l be referred  to as the s u p e r c r i t i c a l cycle i n this work).  Although the s u p e r c r i t i c a l cycle with a reactor as a direct heat source has not been previously investigated, both the s u p e r c r i t i c a l cycle and  the s u p e r c r i t i c a l f l u i d cooled reactor have been separately studied.  The  performance of s u p e r c r i t i c a l cycles has been analysed by many  w o r k e r s ^ " * " ' , who pointed out the high e f f i c i e n c y of the cycle. 4 ,  a case study of a s u p e r c r i t i c a l CO^ power c y c l e ^ ^ ^ ,  In  the power plant has  an overall e f f i c i e n c y as high as 48%. There are many advantages to the cycle:  low volume-to-power r a t i o , no blade erosion i n turbines, no cavita-  tion i n pumps  and single stage turbine and pump operation.  The SCOTT-R  reactor s y s t e m ^ ^ , which i s cooled by using s u p e r c r i t i c a l l i g h t water, i s currently under investigation.  Reactors cooled by using s u p e r c r i t i c a l  f l u i d s have the advantage of avoiding the limitations heat transfer core.  imposed by b o i l i n g  and also the advantage of high enthalpy r i s e through the  As expected, direct application  of the coolant as the working f l u i d  17  of a s u p e r c r i t i c a l cycle has the combined advantages as discussed above.  The high operating pressure i s the basic engineering problem when a s u p e r c r i t i c a l f l u i d i s used not only as the working f l u i d of the cycle, but also as the coolant of a reactor.  The high operating pressure requires  thicker s t r u c t u r a l parts of the system.  The increase of reactor material  results i n an increase of neutron absorption, and hence, the decrease of the reactor neutron economy which d i r e c t l y determines power generation.  the fueling cost i n nuclear  Therefore, the high e f f i c i e n c y of the s u p e r c r i t i c a l cycle  with a reactor as a d i r e c t heat source can be overshadowed by high fueling costs.  The maximum operating pressure of the s u p e r c r i t i c a l cycle depends on the c r i t i c a l pressure of the f l u i d used.  For example, according to an analysis  [14] of the s u p e r c r i t i c a l CG^ cycle sure to pump i n l e t  , the r a t i o of required turbine i n l e t  pres-  pressure i s equal to two for optimum performance, and pump  i n l e t pressure should be maintained above the c r i t i c a l value.  I f that i s also  true for the s u p e r c r i t i c a l water cycle ( c r i t i c a l pressure of 3206 psia), the turbine i n l e t  pressure must be approximately equal to 6500 psia.  This pres-  sure i s too high to be p r a c t i c a l i n engineering designs. To solve the problem of high pressure operation, alternative f l u i d s having a low c r i t i c a l pressure must be sought as substitutes for water. However, when the f l u i d i s used not only as a working f l u i d but also as a coolant, the choice of the f l u i d i s r e s t r i c t e d not only by the requirement of low c r i t i c a l pressure but also by coolant c h a r a c t e r i s t i c s .  Carbon dioxide  has a low c r i t i c a l pressure (Pc = 1071.3 psia) and seems to meet almost a l l other necessary requirements.  S u p e r c r i t i c a l CO 2 may make use of a super-  c r i t i c a l cycle with a reactor as a direct heat source possible i n the  18  future.  4.2  S u p e r c r i t i c a l CO  Cooling Loop  While the direct cycle described i n the previous section appears attractive for future use, several major hardware development programs are required before a power plant using the cycle could be b u i l t .  For example,  power turbines which could operate with CO^ would have to be developed and built.  In addition, the present CANDU reactors would have to be modified.  In order to be able to use present CANDU reactor technology and conventional steam turbine power generating equipment, an intermediate step of using a s u p e r c r i t i c a l cooling loop i s proposed i n t h i s work.  A schematic diagram of the proposed loop i s shown i n Figure 10, along with i t s process path on a temperature-entropy  diagram.  The loop  contains the following steps: (a)-(b).  l i q u i d - l i k e s u p e r c r i t i c a l CO  i s pumped from low  pressure to high pressure; (b)-(c).  high pressure C0 gains heat i n the recuperator from 2  low pressure CO  leaving the steam generator;  (c)-(d).  s u p e r c r i t i c a l CO  i s heated i n the reactor;  (d)-(e).  hot s u p e r c r i t i c a l CO  generates steam i n the steam  generator; (e)-(f).  low pressure CO  from the steam generator gives up  heat i n the recuperator;  19  (f)-(a).  s u p e r c r i t i c a l CO^ i s further cooled to become a high density l i q u i d - l i k e f l u i d .  Recuperation i s used i n the loop to maintain high entry temperature of the coolant into the reactor.  High entry temperature results i n generation of  higher pressure and temperature steam.  The temperature of the coolant  entering the reactor, i . e . , the temperature of the coolant leaving the steam generator, a f f e c t s the o v e r a l l e f f i c i e n c y of power generation as w i l l be discussed i n a l a t e r chapter.  S u p e r c r i t i c a l CO^ from the recuperator i s  further cooled below the p s e u d o - c r i t i c a l temperature i n order to reduce pumping power.  Although gas-cooled reactors also have no l i m i t a t i o n s imposed by b o i l i n g heat transfer, the basic design concept of a s u p e r c r i t i c a l CO^ cooled CANDU reactor i s e n t i r e l y d i f f e r e n t , due to the d r a s t i c changes of thermophysical properties of s u p e r c r i t i c a l CO^ across the p s e u d o - c r i t i c a l temperature.  In the gas-cooled reactor, because the gaseous coolant i s  circulated i n a low density state, the flow areas are large and the speed of the coolant i s low i n order to have minimum pressure drop and low pumping power.  To cope with the problem of poor heat transfer to the slow  moving coolant, f u e l elements normally have f i n s added to their outer surfaces.  Hence, the flow area i s further increased to deal with the problem  of high pressure drop introduced by the f i n s .  Therefore, gaseous coolants  are not suitable for use i n the CANDU reactor since:  1. large diameter coolant tubes would be required;  2. large amounts of coolant are required i n the reactor, increasing the c a p i t a l and upkeep costs;  20  3. poor heat transport c h a r a c t e r i s t i c s of gaseous coolants may  l i m i t the coolant temperature.  Because the pumping power would be low using s u p e r c r i t i c a l  (X^,  the designer can afford higher pressure drops from high speed coolant flow in smaller cross-sectional area channels i n order to create high heat transfer rates.  For this reason, the s u p e r c r i t i c a l CO^-cooled reactor does not  have the previously discussed problems of gas-cooled reactors, despite the poor thermophysical S u p e r c r i t i c a l CO^  c h a r a c t e r i s t i c s of s u p e r c r i t i c a l CO^  at high temperature.  cooling appears very p r a c t i c a l for the CANDU reactor,  which uses bundle-cluster or tube-in-shell fuel elements i n small diameter coolant  tubes.  21  5.  HEAT TRANSFER TO SUPERCRITICAL C0  2  COOLANT  Heat transfer to s u p e r c r i t i c a l f l u i d s i n f u e l bundles has not been studied as far as the author i s aware.  However, the separate cases of heat  transfer to s u p e r c r i t i c a l f l u i d s i n heated  pipes and to single phase f l u i d s  in fuel bundles are currently under investigation.  This chapter w i l l d i s -  cuss the previous investigations of these cases i n d i v i d u a l l y .  Finally,  based on these separate studies, heat transfer to s u p e r c r i t i c a l CO^ i n f u e l bundles i s analysed.  5.1  5.1.1  Heat Transfer to S u p e r c r i t i c a l Fluids i n Pipes  P££ ii£Ei i?f?_ .f_5£2*: l £ § B 5 l E _ ^ 2 _ § y P £ E £ i t i £ £ i _ l ! i y i ^ u  t  e  0  r  This section discusses the p e c u l i a r i t i e s of heat transfer to s u p e r c r i t i c a l f l u i d s which must be taken into account i n actual design of heat exchanger equipment.  These p e c u l i a r i t i e s strongly a f f e c t the per-  formance of a s u p e r c r i t i c a l cooling loop.  Heat transfer problems are c l a s s i f i e d according to the f l u i d T181 states as shown i n Figure 11  .  The f i v e regions are the l i q u i d , gas,  two-phase, a b o v e - c r i t i c a l , and n e a r - c r i t i c a l regions.  Regions I and II  refer to single phase l i q u i d and gas i n which heat transfer rates can be predicted by the usual forced convection equations.  The f l u i d i n region  III i s a.two-phase f l u i d and heat transfer occurs by b o i l i n g .  Region IV  i s the a b o v e - c r i t i c a l region where the mechanism for heat transfer i s not well understood.  Region V i s the n e a r - c r i t i c a l region where special heat  transfer phenomena s t i l l require a great deal of study. It i s very d i f f i c u l t to precisely define the boundaries of the  22  regions, especially the boundaries which separate the n e a r - c r i t i c a l region from i t s adjacent regions.  There are two important reasons for t h i s :  the  t r a n s i t i o n i s not abrupt and sharp, and the extent of the influence of the c r i t i c a l region on heat transfer i s a function of the process or path by which the f l u i d approaches the c r i t i c a l point.  For example, a hysteresis  [19] loop i n density near the c r i t i c a l point heating and then cooling along an isobar.  could be obtained by f i r s t The s u p e r c r i t i c a l CO^  cooling  loop investigated i n this study uses a f l u i d which passes through the above-critical and n e a r - c r i t i c a l regions. Interest i n the study of heat transfer to s u p e r c r i t i c a l f l u i d s was i n i t i a t e d by the work of Schmidt  i n the early 1930's.  He pointed  out that because the s p e c i f i c heat at constant pressure and the compressib i l i t y both grow very large at the c r i t i c a l point, the heat transfer c o e f f i c i e n t , which i s : a function of the Prandtl and Grashof numbers (Pr, Gr),  should be very large.  For s u p e r c r i t i c a l ammonia, Schmidt  later  found an apparent thermal conductivity (the thermal conductivity required of a s o l i d bar of the same dimension as the test chamber to transfer the experimentally observed amount of heat for a given temperature gradient) as large as 4000 times that of pure copper over a narrow temperature range.  However, u n t i l the mid-1950's, very few investigations into super-  c r i t i c a l heat transfer were reported.  Because of the increase of applica-  tions of heat transfer to s u p e r c r i t i c a l f l u i d s , investigations i n this region have been greatly increased i n recent years. workers  Although some  ["22 23 2A 231 ' ' ' reported that the heat transfer c o e f f i c i e n t  was  T 26 27 28 291 enhanced as proposed previously by Schmidt, many other workers  '  reported that heat transfer i n the n e a r - c r i t i c a l region actually  approached  a minimum value.  '  '  23  In h i s survey, Petukov^^"' c l a s s i f i e d the heat transfer to superc r i t i c a l f l u i d s into three regimes:  normal, reduced, and improved.  In  the normal heat transfer regime, there i s s i g n i f i c a n t v a r i a t i o n i n physical properties of the s u p e r c r i t i c a l f l u i d across the flow, but the dependence of Nusselt number (Nu) on Reynolds number (Re) and Pr i s approximately the same as i n the case of heat transfer to constant property flows. Therefore, relationships which govern the normal heat transfer can usually be derived. In the reduced heat transfer regime, the heat transfer c o e f f i c i e n t and wall temperature do not s a t i s f y the same relationships which govern normal heat transfer i n the s u p e r c r i t i c a l region.  The heat transfer c o e f f i -  cient depends not only on Re and Pr but also on the heat f l u x , and i s less than the value calculated from the normal heat transfer relationships. The reduced heat transfer condition usually occurs when the mean f l u i d temperature i s less than the pseudo-critical temperature at a p a r t i c u l a r combination of bulk v e l o c i t y and heat flux, and the wall temperature i s usually, but not necessarily, much greater than the pseudo-critical temperature.  The improved heat transfer regime occurs only at a high heat flux with the bulk temperature less than the pseudo-critical and the wall temperature s l i g h t l y greater than the pseudo-critical temperature.  The heat transfer  rate increases with increasing bulk density and v e l o c i t y , but decreases with increasing bulk temperature.  As i n the reduced heat transfer regime,  the heat transfer c o e f f i c i e n t depends on Re, Pr, and also the heat flux. [371 Hsu  explained the increases and decreases of heat transfer  rates by comparison with the b o i l i n g mechanisms of a l i q u i d , discussed i n Chapter 3.  He pointed out that when the temperature difference i s small,  24  the mechanism can be l i n k e d to n u c l e a t e b o i l i n g , a regime of v e r y good heat t r a n s f e r , thus the maximum-  When the temperature  difference i s large,  mechanism can be compared to f i l m b o i l i n g , a regime of poor heat  the  transfer,  [31 32 331 thus the minimum.  Many other workers  '  e x p l a n a t i o n of a pseudo-two-phase f l u i d . fluid  '  s t r o n g l y supported  this  However, when a s u p e r c r i t i c a l  i s i n e q u i l i b r i u m , i t must e x i s t as a s i n g l e phase, which opposes  [34]  such a pseudo-two-phase f l u i d h y p o t h e s i s . Hauptmann showed t h a t " b o i l i n g " does not e x i s t d u r i n g heat t r a n s f e r to s u p e r c r i t i c a l f l u i d s , concluded  and  t h a t a l l of the unusual r e s u l t s c o u l d be e x p l a i n e d i n s i n g l e phase [35]  terms.  Kafengauz  of  t r a n s f e r at s u p e r c r i t i c a l pressure.  heat  observed  e x p l a i n e d the p h y s i c a l n a t u r e of the unusual  i n some experiments  developed which was  suggested  b o i l i n g c o u l d be  because f l u c t u a t i o n s i n p r e s s u r e caused  p r e s s u r e to f a l l below the c r i t i c a l . was  He  results  bulk  In h i s work, a t h e o r e t i c a l approach  v e r i f i e d by e x p e r i m e n t a l d a t a w i t h  diisopropyl  cyclohexane. D i s r e g a r d i n g the p o s s i b l e e x i s t e n c e of b o i l i n g , d e s c r i b e d r e d u c t i o n and improvements i n heat f l u i d s with a rather clear picture. heat of  t r a n s f e r to  Petukhov^^ supercritical  The onset of the regime w i t h  reduced  t r a n s f e r i s a p p a r e n t l y a s s o c i a t e d w i t h a change i n the hydrodynamics  the f l o w and,  i n p a r t i c u l a r , w i t h t u r b u l e n t t r a n s f e r p r o c e s s e s due  the g r e a t v a r i a t i o n i n t h e r m o p h y s i c a l p r o p e r t i e s of the medium over  to  the  F361 c r o s s s e c t i o n of the flow.  For example, Wood  p r o f i l e s during s u p e r c r i t i c a l f l u i d  found M-shape v e l o c i t y  flow i n p i p e s .  T h i s was  very  different  from the U-shape v e l o c i t y p r o f i l e s of constant p r o p e r t y f l u i d  i n pipes.  Free c o n v e c t i o n due  a l s o have a  to the l a r g e d e n s i t y g r a d i e n t p r e s e n t may  s i g n i f i c a n t e f f e c t on the n a t u r e of the flow. the f a c t t h a t reduced  T h i s p o i n t i s confirmed  heat t r a n s f e r o c c u r s o n l y i n a heated  tube  with  by  25  ascending flow but not descending flow. t r a n s f e r i s observed.  In the l a t t e r case, normal  T h i s i s p r o b a b l y because  heat  of the more i n t e n s e m i x i n g  due to opposing d i r e c t i o n s of f o r c e d and f r e e c o n v e c t i o n near the w a l l .  P e t u k h o v ^ " ^ e x p l a i n e d t h a t improvement i n heat t r a n s f e r at h i g h heat f l u x i s a l s o a p p a r e n t l y due to the v e r y pronounced  changes i n  t h e r m o p h y s i c a l p r o p e r t i e s o f the medium (mainly d e n s i t y and s p e c i f i c h e a t at  c o n s t a n t p r e s s u r e ) over the c r o s s s e c t i o n of the f l o w .  The d e n s i t y o f  the medium a t the w a l l i s s e v e r a l times l e s s and the s p e c i f i c heat i s s e v e r a l times more than i n the c o r e o f the flow.  F l u i d which reaches the  hot w a l l from the c o r e , owing t o t u r b u l e n t t r a n s p o r t , has a r e l a t i v e l y h i g h thermal c o n d u c t i v i t y and low s p e c i f i c heat.  I f there are large  i n temperature between the f l u i d next to the w a l l and the f l u i d from the c o r e , the f l u i d e x p l o s i v e manner. fluid  differences arriving  p i c k s up heat v e r y r a p i d l y and expands i n an  T h i s p r o c e s s must r e s u l t i n more i n t e n s e m i x i n g of the  i n the l a y e r next to the w a l l , and hence, i n improved  heat  transfer.  These s p e c i a l f e a t u r e s o f v a r i a b l e p r o p e r t y t u r b u l e n t heat t r a n s f e r a r e not taken i n t o account i n e x i s t i n g t h e o r i e s , and t h e r e f o r e , p r e s e n t t h e o r i e s cannot  s a t i s f a c t o r i l y d e s c r i b e the improved  heat t r a n s f e r  regime.  Although d r y o u t due t o b o i l i n g would n o t be a l i m i t a t i o n i n t h e d e s i g n o f a s u p e r c r i t i c a l c o o l i n g l o o p , o t h e r l i m i t a t i o n s due  to the  p e c u l i a r i t i e s o f heat t r a n s f e r to s u p e r c r i t i c a l f l u i d s must be taken i n t o account. of  The reduced heat t r a n s f e r regime c o u l d occur i n the r e c u p e r a t o r  the .proposed s u p e r c r i t i c a l c o o l i n g l o o p , where the c o o l a n t i s a t a  temperature regime  near the c r i t i c a l v a l u e .  However, the reduced heat  transfer  can be avoided by c a r e f u l d e s i g n o f the heat t r a n s f e r s u r f a c e and  the f l u i d v e l o c i t y , e t c . , f o r a g i v e n  heat f l u x d i s t r i b u t i o n .  On  the  26  other hand, a compact and e f f i c i e n t recuperator can be designed based on knowledge of the improved heat transfer c h a r a c t e r i s t i c s of s u p e r c r i t i c a l fluids.  5.1.2  Previous_Studies of_Heat Transfer  to S u p e r c r i t i c a l Fluids  Heat transfer mechanisms i n s u p e r c r i t i c a l f l u i d s are not yet well understood.  However, many investigations are currently underway i n the  n e a r - c r i t i c a l region where most of the heat transfer p e c u l i a r i t i e s take place.  Heat transfer i n the a b o v e - c r i t i c a l region, where v a r i a t i o n s i n  thermophysical properties of the f l u i d across the flow a f f e c t heat transfer to a lesser extent, i s usually thought of as a special case of the nearc r i t i c a l region.  Therefore, the mechanisms of heat transfer i n the near-  c r i t i c a l region may also apply to the a b o v e - c r i t i c a l region.  Theoretical analyses of heat transfer i n the s u p e r c r i t i c a l region with allowance for the temperature dependence of thermophysical properties of the f l u i d were f i r s t made by Deissler  f381  T391 and Goldmann . In these  investigations, f l u i d s were assumed to be incompressible, the e f f e c t of body forces were n e g l i g i b l e , the d i s s i p a t i o n of k i n e t i c energy and f l u c t u a tion of the thermophysical properties were ignored, and the pressure was assumed to be constant over the cross section of the flow.  In some l a t e r  [40 41] investigations  '  , the e f f e c t of f l u i d i n e r t i a and buoyant forces were  also taken into account. . Theoretical analyses which are based on the continuity, energy, and Navier-Stokes equations usually employ the Prandtl mixing length concept.  The basic idea i s to simplify the shear stress term of the Navier-  Stokes equation and the heat conduction term of the energy equation.  Then  27  the shear stress and heat f l u x can be expressed i n the simpler  forms  *? 1^ '  T = ( y + p£  (1)  q = - (K + p p e ) | ^ C  h  .  (2)  Most types of eddy d i f f u s i v i t i e s can be broken into two (1) continuous, and  (2) multiple-part.  categories:  In each category, the  turbulent  momentum transport can be further considered as a function of l o c a l thermophysical properties.  Numerical solutions are usually presented as a part of t h e o r e t i c a l analyses.  However, c o r r e l a t i o n of predictions and experiments are success-  f u l only for the p a r t i c u l a r experiments used to provide the modified eddy diffussivities.  For this reason, t h e o r e t i c a l methods are not widely used  for designing heat transfer equipment using s u p e r c r i t i c a l f l u i d s .  Experimental studies have been a major part of the research heat transfer to s u p e r c r i t i c a l f l u i d s .  The experimental works can  c l a s s i f i e d as either free or forced convection.  on  be  Since free convection i s  minimal i n the s u p e r c r i t i c a l cooling loop of t h i s study, i t i s not  discussed  further.  Forced convection experiments can be further divided into major categories:  two  experiments which attempt to explain the mechanism of  heat transfer to s u p e r c r i t i c a l f l u i d s , and conventional heated pipe experiments which are used to determine dimensionless correlations.  The  second  category i s d i r e c t l y related to the application of a s u p e r c r i t i c a l CO^ cooling loop and i s the only one discussed  here.  28  Many heated tube experiments have been carried out i n England, Japan, U.S.A., and U.S.S.R.  A l l of these experiments were very similar  in design and used mainly water and CC^ as experimental f l u i d s .  Hydrogen,  * oxygen, and Freon  have also been studied by some authors.  The results of  most of these e f f o r t s f a l l into the range of the n e a r - c r i t i c a l region, where heat transfer d i f f e r s most from normal heat transfer as governed by single phase f l u i d correlations. The e a r l i e s t form of c o r r e l a t i o n was i n the form of the Dittusn iBoelter equation [42,43,44]:  Nu = A ( R e ) ( P r ) b  z  ,  C  w  (3)  where A, b, and c are experimental constants.  The Reynolds number Re  is z  evaluated at the reference temperature T^ for a given pressure, which i s expressed i n the form: T  = T z  + Z(T -T, ) b  w  .  (4)  b  The parameter Z i s a function of the dimensionless temperature: Z = (T -T )/(T -T ) m  b  w  ,  (5)  b  and Pr^ i s the Prandtl number evaluated at the wall temperature.  The sub-  s c r i p t s represent the conditions of f l u i d bulk, w a l l , and p s e u d o c r i t i c a l , respectively. Another early correlation was proposed by Miropolski and [451 Shitsman Freon:  .  I t has a form s i m i l a r to the Dittus-Boelter equation:  dichlorofluqr methane (12).  29  Nu = 0.023(ReJ°'  Pr .  8  b  where Pr . mm  (6)  mm  i s the minimum Prandtl number defined as: /•Pr * b  ; Pr, < Pr b w  L  Pr .  =<  (7)  mm  *Pr  ;  Pr < Pr w b  w  This simple modification, however, produces some remarkable  results.  It  correlates some experimental data at the n e a r - c r i t i c a l region with great [54] accuracy Correlation factors were l a t e r introduced for-bulk temperature^^'' and thermophysical property variations  '"^.  The correlations  can be expressed as:  Nu = Nu (T. /T ) o b w  Nu = N u ( y / y ) Q  w  b  a  (K/K/  ,  n  (8)  (p /p ) w  c  b  (C /Cp ) P  where a, b, c, d, and n are experimental constants. NU  q  d  b  ,  (9)  The Nusselt number  i s evaluated from constant property f l u i d flow correlations:  Nu  = 0.023(Re, ) ° ' ( P r J 8  o  b  ,  0 , 4  (10)  b  , [51] or by :  (5/8.0) Re P r b  Nu  °  =  Tjo  12.7[? / 8 . 0 ] o  ± / Z  b  2/1 [(Pr, T * - 1.0] + 1.07 1  b  '  30  £  = [1.82 Log ( R e J - 1.64] o b  2  ,  .  0  (12)  The term Cp i n equation (9) i s c a l l e d the integrated s p e c i f i c heat, defined as: Cp" =' (h -h, )/(T -T ) w b w b  .  .... (13)  The integrated s p e c i f i c heat has been proven by experiments to be [23] an e f f i c i e n t term f o r correlating data.  Therefore, Swenson et a l .  generalized their experimental data f o r heat transfer by: n , tT) N0.923 ,-—.0.63 , , .0.231 Nu = 0.00459 (Re ) (Pr ) (p /p, ) w w w b n n  c n  ,  (14)  where Pr i s called the integrated Prandtl number and defined as: w Pr  = Cp (u /K ) w  (15)  WW  The concept of using not only integrated s p e c i f i c heat but a l l physical properties on an integrated average basis was suggested by [52] Hiroharu et a l .  for s u p e r c r i t i c a l f l u i d s .  They suggested the normal  correlations for heat transfer to single phase f l u i d s be used as c o r r e l a tions for s u p e r c r i t i c a l f l u i d s .  However, the Nusselt number i s evaluated  at integrated property values which would be expressed as: T F = _ w  T b  i „ •* b  F  (  T  )  d T  •  ( 1 6 )  T  As with theoretical analyses, most of the experimentally determined correlations must be modified to f i t the data of p a r t i c u l a r experiments.  31  However, these correlations usually predict heat transfer with  greater  accuracy than the t h e o r e t i c a l analyses, e s p e c i a l l y i n the experimental data  range from which the correlations have been derived.  Some c o r r e l a -  tions cover a rather wide range of experimental data, and have s u f f i c i e n t accuracy for engineering designs.  Therefore, i t i s possible to study  some applications of heat transfer to s u p e r c r i t i c a l f l u i d s simply by chosing an appropriate  5.2  correlation.  Engineering Calculation of Heat Transfer to S u p e r c r i t i c a l Fluids  5.2.1  Choice_of_Correlations The c o r r e l a t i o n chosen for the s u p e r c r i t i c a l CG^  this work must be: operating  (1) accurate i n correlating heat transfer i n the  range of the proposed s u p e r c r i t i c a l cooling loop, and  to use i n computing programs. tion are  cooling loop of  (2) easy  In t h i s section, several types of c o r r e l a -  discussed.  Although reference  temperature correlations were the e a r l i e s t  ones developed, there are drawbacks i n their use.  F i r s t , they f a i l to pre-  dict heat transfer c o e f f i c i e n t s accurately i n the temperature range near the pseudo-critical temperature; a small difference of the reference value T  z  temperature  can cause a large v a r i a t i o n i n the predicted heat transfer c o e f f i -  cient because of the extremely sharp property variations near the pseudoc r i t i c a l temperature.  Second, t h i s type of c o r r e l a t i o n i s very inconvenient  when heat flux i s s p e c i f i e d and the wall temperature i s to be In contrast to the reference  calculated.  temperature correlations, the minimum  Prandtl number correlations produce accurate results i n the n e a r - c r i t i c a l  32  region.  Although these types of c o r r e l a t i o n were derived from s u p e r c r i t i c a l  water heat transfer data, they successfully correlated oxygen data of Powell  and CO^ data of Bringer and Smith  .  predict heat transfer to s u p e r c r i t i c a l hydrogen.  However, they f a i l e d to More important i s the  fact that these correlations can account for the maximum heat transfer reported by Powell'" ^, as well as Dickson and Welch^ ''. 2  4  Therefore, the  minimum Prandtl number correlations should be considered for use i n c a l culating heat transfer to s u p e r c r i t i c a l CO . The correction factor types of c o r r e l a t i o n are also popular, although the temperature correction factor i s not very accurate. example, the c o r r e l a t i o n  For  [471  Nu = Nu  (T /T ) " o w b  0 , 2 7  ,  (17)  adequately predicts heat transfer to s u p e r c r i t i c a l f l u i d s at high temperature but breaks down when the heat flux i s increased. This i s mainly due to the fact that the dependence of f l u i d properties on temperature i s d i f f e r e n t i n d i f f e r e n t temperature ranges.  Therefore, correction factors  must be used on f l u i d properties which strongly affect the f l u i d dynamics and heat transfer of the flow.  The f i r s t correlation with property factors [22]  was introduced by Petukhov et a l .  Nu = Nu  (u. /U ) O  D  W  0  ,  1  1  :  (K, /K ) " ° ' D  W  33  (Cp/Cp ) ' 0  35  K  (18)  D  The key feature of this correlation i s the use of the integrated s p e c i f i c heat Cp.  This c o r r e l a t i o n covers a rather wide range of experimental data  for water and CO^.  However, i t f a i l s to predict heat transfer rates  correctly at very high heat flux, possibly because at high temperature  drops (high heat flux) the density difference becomes important.  The s i g -  nificance of the density correction factor was pointed out by Kutateladze and Leontev'" '', and also by Swenson et a l . ^ " ^ . 48  A c o r r e l a t i o n modified by a density r a t i o correction factor was [491 f i r s t introduced by Kranshchekov  and Protopopov  , based on CO^ data.  This c o r r e l a t i o n was l a t e r developed for c a l c u l a t i o n of heat transfer to s u p e r c r i t i c a l CO^ at a normalized pressure (P/Pc) = 1.02 - 5.25^"^ as: Nu = NU  where:  q  (Cp/Cp )  n  b  b  m  ,  .... (19)  ,  n = n, = 0.22 + 0.18 (T /T ) I w m at 1.0 < T /T < 2.5 - w m -  and,  w  m = 0.35 - 0.5(P/Pc), and n = 0.4 at T /T < 1.0 or I /T > 1.2 w m b m -  and,  (P /P )  ,  n = n. + (5n - 2) (1 - T./T ) I I D m n  at 1.0 < T./T < 1.2 - b m -  .  The c o r r e l a t i o n was l a t e r tested by Kransnoshchekov  et a l . ^ " ^ with data  from heat transfer to s u p e r c r i t i c a l CO^ at temperature differences up to 805°C.  Experimental data agreed with this c o r r e l a t i o n within an accuracy T561  of + 15%.  Petukhov et a l .  also tested this c o r r e l a t i o n with t h e i r  experimental data, and gained s a t i s f a c t o r y agreement.  This c o r r e l a t i o n  was further used to calculate l o c a l heat transfer rates to s u p e r c r i t i c a l CO2 i n annular channels with i n t e r n a l heating by Glushcheznko  and Gandzyuk^ T581  and i n a rectangular channel heated from one side by Protopopov Despite the fact that the c o r r e l a t i o n (19) was derived from heat transfer data for a c i r c u l a r heated tube, i n both the previous cases the calculated  34  wall temperatures agreed well within the experimental data range of T,b > T m and T,b < T m .  Heat transfer rates were most unpredictable r  T,b = T m with heat transfer c o e f f i c i e n t s about 30-50% too  at  low.  An integrated Prandtl number c o r r e l a t i o n has been developed for f59l studying heat transfer to s u p e r c r i t i c a l water coolant i n reactors However, t h i s type of c o r r e l a t i o n was  based on s u p e r c r i t i c a l water data  and gave poor results when used to predict heat transfer to s u p e r c r i t i c a l [52] Hiroharu et a l .  confirmed experimentally the accuracy of  the types of correlation using a l l properties as integrated  properties.  However, a l l t h e i r experiments were carried out with low temperature differences (low heat f l u x ) , and the correlations have not been tested by other authors.  This suggests that these types of correlations have no  guarantee of accuracy for predicting heat transfer rates at high temperature differences. The above discussion shows that the minimum Prandtl number and integrated s p e c i f i c heat types of correlations are preferable for c a l c u l a tion of heat transfer for the s u p e r c r i t i c a l CO^ cooling loop of t h i s work. The c o r r e l a t i o n given i n equation (19) was  f i n a l l y chosen instead of the  minimum Prandtl number c o r r e l a t i o n because not only does i t meet a l l requirements pointed out at the beginning of t h i s section, but because i t has been widely tested with experimental heat transfer data for s u p e r c r i t i cal  5.2.2  co' . 2  Examination of Chosen Correlation  When the correlation given by equation (19) was  f i r s t developed,  35  i t was based on the data range: 0.6 < T /T -wm0.09  < 2.6; 2 x 10  < P /P w  b  < 1.0; 0.02  and H/d > 15.0.  1.01 < P/Pc < 1.33; 0.6 < T,/T < 1.2; — - b m < Re < 8 x 10 ; 0.85 < Pr,_ < 55.0; b - b -  4  5  < Cp/Cp < 4.0; 2.3 x 10  4  <  < 2.6 x 10  6  W/cm ; 2  This c o r r e l a t i o n predicted heat transfer c o e f f i c i e n t s i n  a heated c i r c u l a r pipe within the accuracy of + 15.0%.  Later, this corre-  l a t i o n was further developed to cover data up to P/Pc =5.25.  It was par-  t i c u l a r l y i n t e r e s t i n g that this c o r r e l a t i o n predicted the pronounced peak of wall temperatures i n experiments within the suggested accuracy up to the data range of Re, = (0.6 - 1.2) x 10 b In equation (19), NU  q  6  and T /T < 3.6. w m -  i s calculated from equation (11).  This  formula was developed by Petukhov and Kirillov'"^''"'' from a t h e o r e t i c a l analysis of f u l l y developed heat transfer to a single phase, constant property flow i n a c i r c u l a r , heated pipe.  This formula predicts heat  transfer c o e f f i c i e n t s for constant property f l u i d s within the accuracy of + 10.0% for the range: -  0.5 < Pr^ < 2000.0 and 1.0 x 10 b -  4  < Re < 5.0 x 10 . b 6  v  It must be noted that i n contrast to the conventionally used formula with constant exponents for Re^ and P^,  this formula more accurately corresponds  to the dependence of heat transfer on Re^ and Pr^.  This i s p a r t i c u l a r l y  apparent i n the case of Re, > 1.0 x 10^ and Pr. > 10.0. b -  ta-  i n the regions more remote from the c r i t i c a l state, the properties of a s u p e r c r i t i c a l f l u i d become approximately constant over a r e l a t i v e l y wide range of temperature and the c o r r e l a t i o n i n equation (19) reduces to [22] equation (11).  Petukhov et a l .  showed that the formula i n equation (11)  also agrees with experimental data i n the near c r i t i c a l region under the condition of small v a r i a t i o n of properties over the cross section; i . e . , at small temperature drops.  Thus, the correlation i s a very general  36  expression for heat transfer i n the n e a r - c r i t i c a l region as well as i n regions remote from the c r i t i c a l state.  In order to calculate the temperature  d i s t r i b u t i o n along a  heated channel, the pressure d i s t r i b u t i o n of the s u p e r c r i t i c a l f l u i d along the channel must be known since the thermophysical properties which determine heat transfer are a function of both temperature  and pressure.  Many  works are devoted to the investigation of heat transfer at s u p e r c r i t i c a l pressure.  However, studies of flow and pressure drop are scant.  Tarsova and Leontez  developed one of the f i r s t engineering  correlations for the c a l c u l a t i o n of f r i c t i o n c o e f f i c i e n t s .  Later,  r 621 Kuraeva and Protopopov  further developed this c o r r e l a t i o n by including  the effects of possible free convection.  The improved c o r r e l a t i o n was based  [49]  on the data of Kranoshchekov et a l .  . This c o r r e l a t i o n can be put into  the following form:  € = Ks = to (UA>°' w D 2  0  E = E 2.15 (Gr/Ref) s b  *  22  f  o  Gr/Re b <— 5 x 1 0  r  2  1  for  _ 4  -4 2 -1 5 x 10 * < Gr/Ref < 3 x 10 b— 1  , (20)  where E  Q  i s calculated from equation (12).  The v i s c o s i t y u  b  i s evaluated  at the temperature T^ which corresponds to the average pressure and i n t e grated density:  Ail n P  =  -1- f ML  J  I "  1  dx p(x)  I  ••• (  2  1  a  )  37  and the v i s c o s i t y u i s evaluated at the temperature w temperature of the tube:  T  A JI  w " M  T  .w-  ( x )  T  •  d x  which i s the wall w  • • • < 1W 2  The pressure drop i s then calculated from the formula:  .2  A  p  =  , l £ u L _ M  +  (  p  u  2pd  )  2  ^ _ _  (  p  out  P  in  Thus, when the equation (22) i s applied outside the n e a r - c r i t i c a l region and the physical properties of the flow do not change d r a s t i c a l l y , the equation can reduce to the form:  Q  - -  AP = £ (pu) A£/2pd 2  .  (23)  Based on the c o r r e l a t i o n i n equation (19) f o r heat transfer,  the formula i n equation (22) for pressure drop, the energy equation, and the continuity equation, a computer program was designed to calculate the wall temperatures, bulk f l u i d temperatures, and pressure drop along a heated pipe with a given heat flux as a function of distance from the entrance.  The basic assumptions i n the program are:  (1) the pipe i s h y d r a u l i -  c a l l y smooth; (2) the heat transfer c o e f f i c i e n t i s a function of l o c a l conditions only; (3) the flow i s turbulent and f u l l y developed; and (4) pressure i s constant at a cross section.  An additional factor f(x/d) allows for the  38  increase i n heat transfer i n the i n i t i a l portion of the p i p e ^ ;  f(x/d) = 0.95 + 0.95(x/d)"  .  0,8  (24)  A l l required equations f o r the c a l c u l a t i o n are l i s t e d i n Figure 12. The flow chart for the program i s shown i n Figures 13 and 14, and d e t a i l s of the procedure are given i n Appendix I.  The program was f i r s t tested against the experimental data of Jackson and Evans-Lutterodt  . As shown i n Figure 15, the program  accurately predicts the wall and bulk temperatures the case i n which buoyancy forces do not e x i s t .  along the heated pipe f o r  Both the bulk and wall tem-  peratures along the pipe are below the pseudo-critical  temperature.  This program was also used to predict heat transfer to superc r i t i c a l flow i n pipes under other conditions as shown i n Figures 16, 17, and 18.  Figure 16 compares predicted values with the experiments of [49]  Kranoshchekov et a l .  .  In this case, both the bulk and wall  along the pipe are above the pseudo-critical temperature. between the calculated wall and bulk temperature of the experimental values. et a l . ^ " ^  pseudo-critical temperature.  The difference  p r o f i l e s i s within + 10%  Figure 17 shows data from Kranoshchekov  i n which the bulk temperatures  pseudo-critical temperature  temperatures  along the pipe are less than the  and the wall temperatures  are greater than the  The computed r e s u l t s correspond  well with the experimental data.  amazingly  The heat flux and wall temperatures i n  Figure- 17 are beyond the range of l i m i t s f i r s t suggested f o r the c o r r e l a [42] tion.  Figure 18 shows the special case of Schnurr  , i n which the f l u i d  bulk temperature spans the pseudo-critical temperature.  However, the calcu-  lated results s t i l l match well with the experimental data.  39  In general,  the program predicts heat transfer rates within  expected accuracy of the c o r r e l a t i o n .  Accuracy increases  the  i n regions further  away from the c r i t i c a l state, but calculated temperatures are higher than the actual at an intermediate distance from the c r i t i c a l state. l a t t e r condition, the c o r r e l a t i o n factor i n equation (19) may than a unity.  In conclusion,  Under the  s t i l l be less  the program based on the c o r r e l a t i o n i n  equation (19) and the conservation  equations i s suitable for analyses of  the s u p e r c r i t i c a l CO^ cooling loop i n t h i s study.  5.3  Heat Transfer to Single Phase Fluids i n Fuel Bundles Heat transfer i n fuel bundles (see Figure 4) can be  as either single or two-phase.  classified  The work i n each class i s further divided  into theoretical and experimental studies.  In t h i s section, only previous  studies on the prediction of heat transfer to single phase f l u i d s i n bundles are discussed.  The single phase f l u i d s of concern are compressed l i q u i d s  and s u b c r i t i c a l gases.  The  t h e o r e t i c a l works mainly involve prediction of performance  characteristics of clustered rod bundles under conditions of f u l l y developed heat transfer to a x i a l l y uniform heat flux, together with the related hydrodynamic problems for longitudinal flows.  The coolant  can be i n laminar,  turbulent, or slug flow.  There are three methods for analysing heat transfer i n bundles currently i n use: The  fundamental, equivalent  annulus, and lumped parameter.  fundamental method "for' t h e o r e t i c a l prediction of heat transfer to  single phase f l u i d s i n bundles i s based on solution of the momentum and energy equations.  This approach has gained c e r t a i n success for laminar  40  flow, where a n a l y t i c a l solutions have been found for the v e l o c i t y f i e l d s of:  (a) i n f i n i t e rod clusters, (b) semi-infinite rod c l u s t e r s , and  (c) some special geometry f i n i t e rod c l u s t e r s .  Based on the known v e l o c i t y  f i e l d s , heat transfer rates can be determined for laminar longitudinal flow i n an i n f i n i t e rod c l u s t e r .  In the case of turbulent flows, heat transfer  has also been successfully analysed for i n f i n i t e rod c l u s t e r s . three approaches i n these analyses:  (1) both v e l o c i t y and  There are  temperature  f i e l d s are computed by i t e r a t i v e procedures; (2) the v e l o c i t y f i e l d i s f i r s t determined graphically and used i n the d i f f e r e n t i a l form of the energy balance, which i s numerically integrated by f i n i t e difference procedures; (3) both the d i f f e r e n t i a l forms of the momentum and energy balance are integrated numerically by f i n i t e difference procedures to obtain the v e l o c i t y and temperature f i e l d s .  Despite the f a i r l y accurate predictions made for simple  geometries, the fundamental method i s not so easy to apply to more complex flow geometries.  In the equivalent annulus method, the complicated rod c l u s t e r i s divided into many annuli.  An equivalent model can be used to describe the  T671 entire array of rods i n the bundle as shown i n Figure 19a  .  The bundle  i s approximately divided into annuli, with some being heated from both sides and others from one side only. i s then applied to each region.  The basic solution for the concentric annulus This method i s mainly used by designers to  adjust rod spacing to obtain the desired flow s p l i t between regions, and has been found to be quite s a t i s f a c t o r y for r e l a t i v e l y widely spaced bundles. Another equivalent annulus model considers i n d i v i d u a l rods i n  T681 p a r a l l e l rod arrays.  As seen i n Figure 10b  , the hexagonal flow passage  defined by zero shear planes around a rod may be approximated by a c i r c u l a r  41  tube of equivalent area.  This flow passage  (bounded by the rod and the  zero shear planes) i s assumed to be equivalent to the region between the center tube and the zero shear plane of an annulus.  The advantage of the equivalent annulus model i s that heat transfer rates can be e a s i l y calculated by applying available solutions for the concentric c i r c u l a r tube annulus.  The.principal l i m i t a t i o n , of course, i s  how w e l l the equivalent annulus represents the actual flow.  The  experimen-  t a l data shows that the equivalent annulus method i s only roughly c o r r e c t ' .  The analogy tends to underestimate the Nusselt number at  high Reynolds number, and breaks down completely at close rod spacing ( i . e . , Pitch/Rod Diameter ^ 1.1) because the c i r c u l a r shear plane i s no  longer a  good approximation to the actual zero shear planes.  In the lumped parameter type of analysis, the flow i n the array i s divided into many subchannels as shown i n Figure 2 0 ^ ^ .  The c h a r a c t e r i s t i c  dimension of each subchannel i s expressed as the equivalent hydraulic diameter:  n h  = 4 x Cross-sectional Area Wetted Perimeter  '  . . ^ 2 5 )  The a x i a l pressure gradient i n each subchannel i s then determined on the basis of the equivalent hydraulic diameter and a f r i c t i o n factor which i s calculated from a given correlation.  The flow i s balanced for a l l sub-  channels i n the array by equating the pressure drops.  The f l u i d bulk tem-  perature i n each subchannel i s calculated from the known heat flux d i s t r i bution and inter-subchannel mixing rates.  Based on the equivalent hydraulic  diameter, subchannel flow rate and l o c a l f l u i d bulk temperature, the l o c a l heat transfer c o e f f i c i e n t and wall temperature can be calculated from a  42  given correlation.  The lumped-parameter  method can deal with large and complicated  geometry rod arrays incorporating non-uniform heating from rod to rod as well as i n the a x i a l d i r e c t i o n , and e a s i l y accommodates f l u i d property changes. approach.  Many computer programs have been developed based on t h i s The work of O l d a k e r ±  s  t y p i c a l example of computer pro-  a  grams developed by AECL to study the performance of Canadian f u e l bundles. However, the lumped-parameter  method requires judgement i n defining sub-  channels and determining f r i c t i o n and heat transfer correlations.  The  application of t h i s method must be incorporated with experiments, since experiments are needed to determine mixing rates between subchannels.  Besides mixing rate experiments, many other experiments have been carried out i n order to predict heat transfer i n bundles and supplement the a n a l y t i c a l works, especially i n the early state of the development of nuclear power reactor designs. Experiments have been conducted not only...on the effects of rod cluster geometry on heat transfer but also the effects of rod spacers, bearing pads, and end-plates of f u e l bundles. Today, the accumulated and combined knowledge from the a n a l y t i c a l and experimental works i s adequate for predicting the performance of fuel i n preliminary designs.  However, the actual performance of a new f u e l bundle  design must s t i l l be checked by experiments.  5.4  Heat Transfer to S u p e r c r i t i c a l C0  5.4.1  9  i n Fuel Bundle  Specifications_and Assumptions  Heat transfer to s u p e r c r i t i c a l carbon dioxide i n f u e l bundles has  r  not been studied before.  43  However, reasonable estimates can be based on the  separate studies of heat transfer to s u p e r c r i t i c a l carbon dioxide i n heated pipes and heat transfer to single phase f l u i d s i n bundles.  This section  w i l l discuss the approach and the assumptions of the analysis of heat transfer to s u p e r c r i t i c a l carbon dioxide i n CANDU-type f u e l bundles.  Because of the complicated geometry of CANDU f u e l bundles, the fundamental method discussed i n the previous section i s not useful.  Because  of the small r a t i o of pitch to rod diameter for CANDU f u e l bundles, the equivalent annulus method i s also not suitable.  Therefore, the lumped-  parameter method was the only method used for analysis of heat transfer to s u p e r c r i t i c a l carbon dioxide i n bundles. in order to put the method into use.  Certain assumptions were made  Because there i s no available experi-  mental data for s u p e r c r i t i c a l carbon dioxide mixing rates between subchannels of fuel bundles, the f i r s t assumption was that of zero mixing between subchannels.  The mixing can be caused by turbulent interchange, [72]  diversion cross-flow, flow scattering, and flow sweeping  . Turbulent  interchange results from eddy d i f f u s i o n between subchannels and can be characterized by the eddy d i f f u s i v i t y of momentum.  Diversion cross-flow  i s the direct flow caused by r a d i a l pressure gradients between adjacent subchannels.  These gradients may be induced by gross differences between  the subchannel heat flux d i s t r i b u t i o n s , and the differences i n subchannel equivalent hydraulic diameters.  Flow scattering refers to the non-  d i r e c t i o n a l mixing e f f e c t s associated with spacers, bearing pads, and endplates.  Flow sweeping i s the direct cross-flow effect Associated with  mechanisms designed to create mixing between subchannels.  These mechanisms  are mainly wire wrap spacers, h e l i c a l f i n s , contoured grids, and mixing vanes, but they are not used i n present CANDU f u e l bundles.  Therefore,  44  i f s u p e r c r i t i c a l carbon dioxide were used as a coolant for the CANDU reactor, mixing due to flow sweeping does not e x i s t , but strong mixing due to the effects of the other three causes can be expected. 1  Mixing can balance the enthalpies and average the f l u i d bulk temperatures of subchannels.  I f there i s no mixing, the bulk temperature  of the coolant i n the p a r t i c u l a r subchannel which has the maximum l i n e a r heat rate can be over-predicted.  Also, because the l o c a l wall temperature  depends on the l o c a l f l u i d bulk temperature for a given flux, the wall temperature i s then over-predicted.  Evidently, the zero mixing assumption i s  not only untrue but also a very serious assumption.  I t w i l l cause under-  estimation of the performance of a fuel bundle i n an analysis when maximum withstanding temperature of the fuel bundle i s used as the upper l i m i t for design.  The second assumption i s that the rod bundle i s smooth.  There-  fore, turbulence created by spacers, bearing pads, and end-plates i s not taken into account i n this analysis.  The structural arrangements  i n fuel  bundles create not only mixing between subchannels, but also high eddy d i f f u s i v i t y of momentum and heat i n each subchannel. i s closely related to heat transfer.  The eddy d i f f u s i v i t y  As the degree of d i f f u s i v i t y increases, [731  the heat transfer c o e f f i c i e n t increases.  Hoffman et a l .  found that  spacers improve the l o c a l heat transfer by tripping the boundary  layer.  This results i n s t a r t i n g a new thermal entry length as shown i n Figure 21. Other mechanisms also can improve the general heat transfer throughout the r 731 entire bundle as well as l o c a l heat transfer.  For example, Figure 22  shows that the Nusselt numbers i n a fuel bundle with wire wrap spacers are greater than Nusselt numbers calculated from the c o r r e l a t i o n for single  45  phase f l u i d s flowing i n c i r c u l a r smooth tubes.  Hence, the second assump-  tion w i l l over-predict the wall temperature p r o f i l e s i n subchannels. In other words, the "smooth bundle" assumption w i l l under-estimate the performance of fuel bundles i n term of maximum withstanding operating temperature.  The smooth bundle assumption may also under-predict pressure drop through the bundle.  The increase of turbulence created by the fuel bundle  structure increases the skin f r i c t i o n along the f u e l bundle.  In addition,  the direct drag due to the structure can cause further pressure drop. [741 On the other hand, Figure 23  shows that the f r i c t i o n factor  i n a closely packed bundle (pitch to rod diameter, p/d = 1.141) may actually be less than that of a smooth c i r c u l a r tube. due to the e f f e c t of close-packing.  This phenomenon i s apparently  The decrease of f r i c t i o n factor i n a  closely packed bundle (such as a CANDU fuel bundle) may counter balance the increase of f r i c t i o n factor due to the e f f e c t of end plates and other parts of the fuel bundle structure.  Therefore, as a f i r s t approximation, the  f r i c t i o n factor used i n this work was calculated from a correlation for s u p e r c r i t i c a l carbon dioxide flowing i n a smooth tube. The l a s t assumption i n applying the lumped-parameter method i s that subchannels are continuous throughout the reactor core.  In other  words, i t was assumed that the r e l a t i v e orientation of bundles i n the reactor core does not affect heat transfer or hydrodynamics of coolant flow i n subchannels.  Fortunately, experiments^"''^•1  confirm that although  there may be d i s c o n t i n u i t i e s i n subchannels between fuel bundles, the r e l a t i v e orientation of fuel bundles has l i t t l e effect on average heat transfer.  Figure 2 4 ^ ^ shows calculated results of wall temperature  46  discontinuities due to change i n orientation of f u e l bundles, and the general shape of the wall temperature p r o f i l e when the subchannel i s assumed to be continuous.  Similar to the analysis of heat transfer to single phase f l u i d s in c i r c u l a r pipes, heat transfer c o e f f i c i e n t s for s u p e r c r i t i c a l carbon dioxide flow i n f u e l bundles are assumed to depend only on the l o c a l conditions.  Also, the coolant flow i n subchannels i s assumed to be f u l l y  developed (but with a factor f(x/d) as i n equation (23) allowing for increase i n heat transfer i n the i n i t i a l portion of the subchannel). In addition, the effect of the r a t i o p/d can be taken into account for heat  * transfer by using Figure 25 . From the above discussion, despite the many assumptions, an analysis of heat transfer to s u p e r c r i t i c a l carbon dioxide i n the CANDUtype f u e l bundles can be made.  Moreover, the result of this analysis  should be on the conservative side, that i s the maximum calculated sheath temperatures should be larger than actual expected values.  5.4.2  Fuel Bundle_Geometry and Subchannel Analysis  As discussed previously, f u e l bundle design must be based on balance of subchannel enthalpies for optimum performance.  This enthalpy  balance can minimize temperature differences between subchannels, and reduce the a x i a l increase of bulk temperature i n a p a r t i c u l a r subchannel which has the maximum heat rate.  Figure 25: Kay summarized the effect of the r a t i o p/d on Nusselt number for f u l l y developed, turbulent flow p a r a l l e l to a bank of smooth c i r c u l a r rods.  47  Enthalpy balance can be controlled  by creating mixing with  s p e c i a l l y designed mechanisms such as wire-wrap spacers. Mixing also can be created by properly arranging the geometry of the fuel bundles. [12] Figure 26  shows the geometry of an existing f u e l bundle used i n the  CANDU 500 reactor at Pickering.  Because of the d i f f e r e n t  cross-sectional  areas of subchannels, subchannel flow rates and v e l o c i t i e s are d i f f e r e n t . This can result i n cross-sectional pressure gradients, hence, subchannel mixing.  Figure 8 shows the subchannel temperature p r o f i l e s for a given  a x i a l and r a d i a l heat flux d i s t r i b u t i o n .  Because of the enthalpy balance  due to mixing, the temperature differences between flows are very small. However, this same bundle cannot achieve s u f f i c i e n t enthalpy balance when s u p e r c r i t i c a l carbon dioxide i s used as a coolant.  Because of  the low density of s u p e r c r i t i c a l carbon dioxide at high temperature and resulting high flow speed, the resistance i n subchannel 4 does not allow adequate flow for a given heat output.  Therefore, despite the mixing  between subchannels, the enthalpy, bulk temperature, and hence the wall temperature i n this subchannel w i l l increase rapidly.  The wall  tempera-  ture may eventually exceed the l i m i t i n g value. A similar problem has been encountered i n the development of the CANDU b o i l i n g reactor, fog reactor, and once-through reactor, i n which low [79] density l i g h t water i s used as a coolant  .  In order to solve the problem  of rapid a x i a l increase of temperature due to enthalpy unbalance, f i l l e r s (or blockers, see Figure 27) are introduced to block subchannel passages which have too large a flow area.  Tube-in-shell fuel elements (see  Figure 28) have also been suggested.  The geometries of these f u e l elements  allow coolant d i s t r i b u t i o n according to subchannel heat rate, and  resulting  48  good enthalpy balance and small temperature differences between subchannels. In order to find a suitable f u e l bundle geometry for the proposed s u p e r c r i t i c a l carbon dioxide cooled CANDU reactor, the subchannel dimensions must be determined.  I f necessary, f i l l e r s have to be introduced into the  fuel bundle to a s s i s t subchannel flow balance. are  The subchannel dimensions  governed by heat transfer rates and a relationship must be found  between the coolant flow rate and the maximum subchannel wall temperature with a given operating condition.  Figure 29 i s a plot of subchannel maximum wall temperatures versus i n l e t coolant temperatures for a given a x i a l heat flux d i s t r i b u t i o n and a given outlet coolant temperature.  The heat flux d i s t r i b u t i o n i s the  average a x i a l value for the CANDU reactor at Pickering.  Each curve  represents the relationship between the maximum wall temperature and the i n l e t coolant temperature for a constant equivalent hydraulic diameter. The i n l e t temperature can be interpreted as the coolant flow rate which can be expressed as:  (Axial Heat Flux Distribution) dl M = 0  where:  h(T  out  (26)  ) - h(T. ) in  £ i s the length of the subchannel^ h(T  ) i s the outlet coolant enthalpy, which i s a function of the outlet coolant temperature, T  out'  h(T. ) i s the i n l e t coolant enthalpy, which i s a function of the i n l e t coolant temperature, T.  in  49  When the a x i a l heat flux d i s t r i b u t i o n and the outlet temperature i s fixed, the  flow rate i s approximately proportional to the i n l e t coolant  tempera-  ture.  . The outlet temperature was f i r s t chosen to be 775°K.  However,  when the equivalent diameter i s larger than 1.4 Do (7.4 cm), the maximum wall temperature exceeds the safety l i m i t of 550°C which has been d i s cussed previously. was chosen. the  Therefore, a lower coolant outlet! temperature of 750°K I  A similar plot i s also used to show the relationship between  i n l e t temperature, i . e . the flow rate, and pressure drop as shown i n  Figure 30. Figures 29 and 30 show that for a given equivalent hydraulic diameter of a subchannel, the t o t a l pressure drop increases, and the maximum wall temperature decreases with increase of the i n l e t coolant temperature; i . e . , the flow rate or v e l o c i t y i n a subchannel.  For a very  small equivalent diameter subchannel, the f i n a l pressure drops below the c r i t i c a l pressure.  Therefore, the coolant cannot be maintained i n a super-  c r i t i c a l state throughout the cooling loop.  For a large equivalent  hydraulic diameter subchannel, the pressure drops less quickly, which allows higher i n l e t coolant temperature; i . e . , higher flow rates.  The  high coolant flow rate w i l l produce high heat transfer rates and guarantees a maximum wall temperature below the safety l i m i t .  High i n l e t coolant  temperature i s also very desirable for steam generation as w i l l be d i s cussed i n a l a t e r chapter.  However, use of large subchannel equivalent  hydraulic diameters w i l l require large diameters for fuel bundles and coolant channels.  Coolant channels which have large diameters and fixed  wall thickness cannot withstand higher pressures, and f a i l to meet the  50  c r i t e r i a of compactness for reactor design.  Today, only small diameter  coolant channels are used i n the CANDU reactor.  Because t h i s work i s only a preliminary study, without any attempt being made to optimize the coolant performance i n bundles i n terms of power station e f f i c i e n c y , an equivalent subchannel hydraulic diameter of 0.75 cm = 1.44 Do and a coolant i n l e t temperature of 400°K were chosen for this study.  These values were chosen on the basis of maximum wall  temperatures and reasonable pressure drop.  flow rates and therefore, r e l a t i v e l y low  As a r e s u l t , the fuel bundles can be operated  safely, and  the carbon dioxide coolant can be kept i n a s u p e r c r i t i c a l state throughout the cooling loop.  For given i n l e t and outlet coolant temperatures, and a s p e c i f i e d heat flux d i s t r i b u t i o n , the relationship between the equivalent hydraulic diameter and maximum wall temperature, and also the f i n a l pressure for a given i n l e t pressure can be studied.  Figure 31 shows that for a constant  flow rate, the equivalent hydraulic diameter increases with maximum wall temperature and f i n a l pressure.  The upper l i m i t of equivalent hydraulic  diameter occurs when 1.02 cm = 2.3 Do and the maximum wall temperature reaches the safety l i m i t of 550°C. bundles i s approximately  0.75 cm = 1.44 Do, since the f i n a l pressure drops  d r a s t i c a l l y from this point. was  5.4.3  The lower l i m i t to achieve compact fuel  An equivalent hydraulic diameter of 0.75 cm  chosen to make the design as safe and compact as possible.  5££dicted_Heat_Transfer_to_Supe Fuel Bundles An equivalent subchannel hydraulic diameter of 0 . 7 5 cm was chosen  51  coolant.  However, specifying the equivalent hydraulic diameter does not  uniquely determine the exact geometry of subchannels since equivalent hydraulic diameter depends on flow area and wetted perimeter i n a subchannel.  F i n a l design selections must also take into account o v e r a l l  compactness of the bundle.  When the subchannel equivalent hydraulic diameter i s chosen to be 0.75 cm and with 1.52 cm diameter f u e l rods (the same as those at Pickering), the most compact subchannel geometry i s the square array.  Figure 32 shows  the geometry of a 32-element f u e l bundle with a square array of f u e l rods, along with pertinent dimensions.  The o v e r a l l diameter of this  32-element  fuel bundle i s approximately equal to the existing f u e l bundle used i n CANDU reactors (Pickering type).  This ensures that the basic design of  the CANDU reactor would remain the same i f s u p e r c r i t i c a l carbon dioxide were used as a coolant.  This type of f u e l bundle i s not the best when  considering the coolant enthalpy balance.  In the CANDU reactor, the heat  flux d i s t r i b u t i o n within a fuel bundle increases away from the center of the bundle.  Therefore, the proposed fuel bundle f a i l s to d i s t r i b u t e  coolant flow according to the r a d i a l heat flux d i s t r i b u t i o n .  However,  blockers can be used to reduce the large flow area subchannels which are near the coolant tube wall.  Heat transfer performance of this 32-element  fuel bundle was  analysed i n a t y p i c a l case when using s u p e r c r i t i c a l carbon dioxide as a coolant for the CANDU reactor.  The heat flux d i s t r i b u t i o n was based on [12]  data obtained during steady operation of the Pickering station  .  The  a x i a l heat flux d i s t r i b u t i o n i s : Q(x) = q(n) • s i n (kx + (j))  ,  (27)  52  where:  Q(x) i s the a x i a l heat flux d i s t r i b u t i o n for a subchannel as a function of distance from the i n l e t , i n KW/M, q(n) i s the maximum l i n e a r heat rate of a subchannel n, i n KW/M, x i s the distance from the i n l e t of a subchannel, i n M, k i s a constant, 0.51504, <j) i s a constant, 0.25744.  The maximum l i n e a r heat rate q(n) i s based on the r a d i a l neutron flux d i s ro o i  t r i b u t i o n i n the Pickering 28-element bundle shown i n Figure 33  . The  formula f o r the calculation i s : , q  where:  (  v n  )  =  f F . 9 6 "  TWP - CWP , 4. 775 ' 3  5  c Q , 8  , ....(28) O O N  >  f i s the normalized neutron flux at the r a d i a l distance of the center of the subchannel, TWP i s the t o t a l wetted perimeter i n cm, CWP i s the cold (unheated) wetted perimeter i n cm.  Based on the assumptions and lumped parameter method discussed previously, heat transfer to s u p e r c r i t i c a l carbon dioxide i n the proposed 32-element bundle was studied i n d e t a i l .  The computer program used was  similar to that already described for c i r c u l a r tubes, with the exception that subchannel flow rates were balanced to produce equal subchannel pressure drops.  Typical results are shown i n Figures 34 to 36. The  coolant temperature p r o f i l e s i n i n d i v i d u a l subchannels are shown i n Figure 34. Wall temperature p r o f i l e s are shown i n Figure' 35. Pressure drop along the coolant tube i s shown i n Figure 36. When the i n l e t  tempera-  ture of s u p e r c r i t i c a l coolant was 400°K (260°F), the f i n a l bulk temperature at the outlet of the coolant channel was found to be 730.7°K (855.6°F).  53  These results w i l l be summarized and discussed i n Chapter 7.  54  6.  6.1  POSSIBLE STEAM CYCLES  General  The ultimate goal of this study i s to study ways to improve the o v e r a l l e f f i c i e n c y of the CANDU reactor.  Accordingly, i t i s important to  investigate potential steam cycles i n association with the CANDU reactor when s u p e r c r i t i c a l carbon dioxide i s used as a coolant.  The coolant temperature i s one of the most s i g n i f i c a n t parameters i n steam generation.  The higher the coolant temperature,  the  higher w i l l be the thermal e f f i c i e n c y of the cycle, and hence, the lower w i l l be the fueling cost.  Coolant temperatures  f i x the steam temperature  and the associated saturation pressure as shown i n Figure 37.  Line "e-g"  i n Figure 37 represents the state points of the CO^ as i t cools down i n the steam generator from "e" to "g".  This i s approximately a straight l i n e  since dH = M • Cp ••: dT for high temperature s u p e r c r i t i c a l carbon dioxide and the s p e c i f i c heat at constant pressure varies only s l i g h t l y with temperature.  The l i n e "a-b-c-d" represents constant pressure heating of  the water-steam system.  Because of the second law of thermodynamics and  i t s l i m i t a t i o n on d i r e c t i o n of heat flow, the saturation temperature of the water must be lower than the temperature of the CO^,  approximately  at the point where the coolant l i n e intercepts the saturation curve on the enthalpy versus temperature diagram.  Therefore, the cycle pressure i s also  fixed .according to the saturation temperature.  Iii other words, although  only the entry temperature of the coolant into the steam generator determines the maximum temperature of the steam, both the entry and exit temperatures determine the steam pressure.  Because the maximum temperature  55  as well as the pressure of the steam cycle determine the e f f i c i e n c y of the reactor power plant, high coolant entry and exit temperatures The problem of low coolant exit temperature i n nuclear reactor power generation.  are desirable.  i s often encountered  In order to solve the problem of low [80]  steam pressure due to the low coolant exit temperature, Wooten et a l . suggested a dual-pressure steam cycle.  Figure 38 shows the paths of the  different processes with dual-pressure steam generation.  I t i s necessarily  drawn on a d i f f e r e n t basis from that of Figure 37 which has enthalpy of water as an abscissa, and instead, the abscissa of Figure 38 i s the d i s tance along the steam generator from the entrance to the e x i t . In the dual-pressure steam generation cycle, feedwater i s separated into two branches where i t i s pumped by two feedwater pumps to two d i f f e r e n t pressures.  The temperatures  steam generator are equal i n both branches.  of the feedwater entering the As shown i n Figure 38, the  low pressure feedwater i s further heated i n the economizer from "a" to "b", evaporated at a p a r t i c u l a r constant pressure and temperature  from  "b" to "c", superheated i n the superheating section from "c" to "d", and then fed to a low pressure turbine stage. The high pressure water i s heated i n a second economizer from "a"' to " b , i n which i t i s subjected to the same downstream coolant as , M  the low pressure feedwater economizer.  I t i s further heated i n a t h i r d  economizer from "b" to " c " , evaporated from " c " to "d"', then super1  1  1  heated from "d"' to "e" by the incoming coolant. 1  the high pressure turbine i n l e t .  F i n a l l y , i t i s fed to  In this process of dual-pressure steam  generation, the coolant heats the high and low pressure steam a l t e r n a t i v e l y .  56  The dual-reheat steam generation cycle was also discussed by  T781  Wooten et a l .  .  Dual-reheat steam generation i s similar to dual-  pressure steam generation, except that the expanded high pressure steam from the high pressure turbine i s joined with the low pressure feedwater and superheated  together before expansion through the low pressure turbine  stage.  The dual-pressure steam cycle can result i n higher thermal e f f i c i e n c i e s than the single-pressure steam cycle.  Of course, the more  complicated dual-pressure steam cycle c i r c u i t increases the c a p i t a l cost of the plant.  The dual-reheat cycle has the additional advantage of lower  moisture content at turbine exhaust and higher work output per unit mass of working f l u i d .  However, the advantages of the dual-pressure steam sys-  tem are reduced when the coolant exit temperature increases and approaches the temperature of coolant entering the steam generator.  6.2  Steam Cycle for the S u p e r c r i t i c a l Carbon Dioxide Cooled CANDU Reactor Plant  This section discusses the possible steam cycles with s u p e r c r i t i c a l carbon dioxide coolant conditions based on the previous calculated results of heat transfer i n the 32-element bundle.  The previously calculated outlet  temperature of the s u p e r c r i t i c a l carbon dioxide coolant i s 855.6°F (730.7°K), and the i n l e t temperature was  chosen to be 260°F (400°K).  For.some heat loss  the coolant entry temperature into the steam generator was chosen to be 845°F.  The coolant temperature leaving the steam generator was chosen to  be 280°F, which assures heat exchange i n the recuperator.  57  In analyzing steam cycle performance, only pressure drop across the reactor and turbine stages was taken into account.  The pressure losses  in piping, recuperator, and steam generator were not considered.  The  l a t t e r pressure losses depend on s t r u c t u r a l d e t a i l s , but with good engineering design, these pressure drops can be kept small.  For example,  the pressure drop for gaseous carbon dioxide flowing through the steam r g-j^ i  generator at the Hinkley Point gas-cooled power plant i s only 1.6 The single-pressure steam cycle was analyzed f i r s t .  psia  From the  temperature versus enthalpy diagram i n Figure 37, when the entry and exit temperatures  are 845°F and 280°F respectively, the generated steam has a  pressure of 130 psia and a maximum temperature of 815°F.  Based on the  turbine c i r c u i t , shown i n Figure 39, the ideal o v e r a l l plant e f f i c i e n c y i s only 26.73%.  The low e f f i c i e n c y i s mainly due to the low steam pressure,  which i n turn i s due to the low exit  temperature.  The dual-pressure cycle was also studied as a potential energyconversion cycle.  Figure 38 shows the s u p e r c r i t i c a l carbon dioxide coolant  and steam paths i n the steam generator for the case of high to low pressure r a t i o of 600/70.3 (psia).  Figure 40 shows the corresponding turbine c i r c u i t .  This cycle gives an i d e a l o v e r a l l plant e f f i c i e n c y of 29,42%; higher than the single-pressure cycle.  To study the effect of high to low pressure r a t i o on the e f f i ciency of the cycle, the case of the dual-pressure cycle of 1200/70.3 (psia) was also analyzed.  Figures 41 and 42 show steam generation and enthalpy  balance for the turbine c i r c u i t respectively.  The ideal o v e r a l l plant  e f f i c i e n c y for t h i s case i s 29.87%, which i s about the same as the previous dual-pressure cycle.  In the dual-pressure cycle, the r a t i o of flow rates  58  of high pressure to low pressure steam decreases when the pressure r a t i o increases.  Therefore, the ideal o v e r a l l e f f i c i e n c y of the dual-pressure  cycle remains approximately constant under given coolant conditions. To study the further possible improvement of e f f i c i e n c y with given coolant conditions, a new dual-reheat steam cycle having a pressure ratio of 1200/70.3 (psia) i s proposed. tion loop.  Figure 43 shows the steam genera-  Figure 44 shows the heat balance for the turbine c i r c u i t .  In  this cycle, the expanded high pressure steam i s joined with low pressure feedwater and evaporated pressure steam.  together i n the steam generator to become the low  In t h i s case, the high and low pressure feeds are heated  in a p a r a l l e l fashion instead of a l t e r n a t i v e l y as i n the dual-pressure (non-reheat) cases.  This reheating method i s somewhat d i f f e r e n t from the [80]  method suggested by Wooten et a l .  .  Because of p a r a l l e l heating, the  large temperature difference between the coolant and the feeds i s eliminated. This decreases the i r r e v e r s i b i l i t y of the steam generation process.  There-  fore, the ideal o v e r a l l plant e f f i c i e n c y of the new dual-reheat cycle i s increased for a given coolant condition.  The i d e a l o v e r a l l plant e f f i c i e n c y  of the dual-reheat cycle of this case was calculated to be 33.02%. The results of cycle performance are summarized and discussed i n the next chapter.  Comparisons are also made with the performance of the  existing Pickering station.  59  7.  7.1  RESULTS AND DISCUSSION  Typical Heat Transfer i n Bundles  The f l u i d dynamic and heat transfer conditions of s u p e r c r i t i c a l carbon dioxide i n the subchannels of the 32-element  f u e l bundles are  summarized i n Figure 45. This figure shows that the highest subchannel maximum wall temperature occurs i n subchannel 6, which has the highest enthalpy among a l l the subchannels.  The lowest subchannel maximum wall  temperature i s only 409.0°C, which i s 137.0°C lower than the highest subchannel maximum wall temperature.  The great difference between the sub-  channel wall temperatures and between the subchannel coolant temperatures shows that the assumption of zero mixing between subchannels has a major effect on subchannel enthalpy balance. temperature of the 32-element  Therefore, the maximum operating  f u e l bundles, i . e . the highest subchannel  maximum wall temperature, i s over predicted.  The o v e r a l l performance of s u p e r c r i t i c a l carbon dioxide coolant i n the 32-element  f u e l bundles i s summarized i n Figure 46. For the purpose  of comparison, the t y p i c a l o v e r a l l performance of heavy water coolant i n the 28-eiement  f u e l bundles for Pickering Station i s also l i s t e d .  Because of  the high heat extraction per unit mass f o r s u p e r c r i t i c a l carbon dioxide coolant, the t o t a l mass flow rate i s much lower than for heavy water coolant at a given channel power.  Since there i s no dryout when using  s u p e r c r i t i c a l carbon dioxide as a coolant, the allowable operating temperature of the f u e l bundle i s much higher.  As a r e s u l t , the coolant temperature  i s much higher than the existing case of heavy water coolant.  However, the  pressure drop i n the case of s u p e r c r i t i c a l carbon dioxide coolant may be  60  underestimated  as pointed out i n the previous discussion.  The d e t a i l sizes of the proposed 32-element fuel bundle and the existing 28-element Pickering f u e l bundle are shown i n Figure 47 f o r comparison.  The o v e r a l l dimensions of these two f u e l bundles are approximately the  same; this s a t i s f i e s the design r e s t r a i n t that the basic structure and reactor physics of the CANDU reactor remain the same.  The 32-element fuel  bundle has a s l i g h t l y larger radius but contains more f u e l , thereby reducing the required number of f u e l channels for a given reactor power.  Thus, the  larger radius and thicker coolant tubes may not increase the t o t a l weight of structural material i n the reactor core.  To balance the excess flow i n the outer subchannels, blockers are used in.the 32-element fuel bundle.  flow r e s t r i c t i n g  This r e s u l t s i n an increase  i n reactor structural material and hence a possible decrease of neutron economy, which determines  the fueling cost.  However, t h i s can be minimized  by selecting blockers which are f a i r l y transparent to neutrons  although  impermeable to coolant flow (possibly high temperature p l a s t i c or ceramics). Optimum design of f u e l bundle geometry would allow for subchannel balance.  In other words, the subchannel  enthalpy  flow areas should allow f o r sub-  channel flow rates proportional to the subchannel  l i n e a r heat rates. I f  blockers are not used i n the 32-element fuel bundle and subchannel enthalpies are balanced, the average flow area of each subchannel would be larger than proposed here.  This allows higher flow rate of the coolant, and hence, higher  i n l e t coolant temperature into the reactor; i . e . , higher exit temperature from the steam generator.  Therefore, the plant e f f i c i e n c y can be increased.  61  7.2  Typical Steam Cycles  The steam conditions for the thermal cycles which were analysed previously are summarized i n Figure 48.  For purposes of comparison, the [121  corresponding  steam conditions of the Pickering generating s t a t i o n  also l i s t e d .  The performance of these thermal cycles i s summarized i n  the table of Figure 49.  are  The ideal o v e r a l l plant e f f i c i e n c y of the Pickering  generating station i s 33.94%, which i s based on the turbo-generation heat  [121 balance as shown i n Figure 50  , and the actual plant e f f i c i e n c y i s only  29.1%. One of the conditions which strongly effects the ideal r e s u l t s and i s not usually noted, i s the turbine e f f i c i e n c i e s assumed i n the c a l c u l a t i o n . The e f f i c i e n c y of the low pressure turbines i n both cases of the dualpressure cycle i s assumed to be 88.5%.  This i s based on the existing  e f f i c i e n c y of the low pressure turbines of the Pickering Station.  For the  low pressure turbine of the dual-reheat cycle and the high pressure turbines of a l l cycles using s u p e r c r i t i c a l carbon dioxide, turbine e f f i c i e n c i e s are assumed to be 90%.  This i s j u s t i f i e d on the basis of higher inlet-steam  pressures and temperatures and lower outlet moisture content. The steam condition when using s u p e r c r i t i c a l carbon dioxide as a coolant i s very much different from the steam condition of the Pickering generating station because of the d i f f e r e n t coolant conditions. the steam condition also depends on the method of generation.  However, Therefore,  despite similar coolant conditions i n the three cases of the single pressure, dual-pressure, and dual-reheat cycles, the e f f i c i e n c i e s are different.  The calculated ideal o v e r a l l plant e f f i c i e n c y of the  dual-reheat  62  cycle i s 33.02% which i s competitive with the calculated ideal o v e r a l l plant e f f i c i e n c y of the Pickering generating station.  This shows that the use of  s u p e r c r i t i c a l carbon dioxide coolant may improve the existing thermal e f f i c i e n c y of CANDU reactor power plants when the performance of superc r i t i c a l carbon dioxide coolant i s optimized further from the design of this study.  Another p o s i t i v e r e s u l t of t h i s study shows the advantage of the concept of pumping i n the s u p e r c r i t i c a l cooling loop; the pumping power required by the s u p e r c r i t i c a l carbon dioxide i s small.  Despite  that s u p e r c r i t i c a l carbon dioxide i s assumed to be pumped at a temperature of 90°F, which i s s l i g h t l y lower than the p s e u d o - c r i t i c a l temperature of 99.5°F at 1240 p s i a , the i d e a l pump work i s only s l i g h t l y larger than for heavy water coolant of the Pickering Station.  The annual average tempera-  ture of lake or r i v e r water i n Southern Canada i s approximately  48°F.  Therefore, the estimate of pumping power for the s u p e r c r i t i c a l carbon dioxide coolant i s very conservative.  63  8.  SUMMARY AND  CONCLUSIONS  This study indicates the technical f e a s i b i l i t y of using superc r i t i c a l carbon dioxide as a coolant for a CANDU-type reactor.  The reactor  i s cooled by a single phase coolant, which i s pumped at a high density l i q u i d - l i k e state.  The s u p e r c r i t i c a l - f l u i d - c o o l e d reactor may  have the  combined advantage of avoiding dryout as i n gas-cooled reactors, and the advantage of low coolant c i r c u l a t i o n power as for liquid-cooled reactors.  As a result of eliminating dryout, the maximum operating temperature of the fuel sheath can be increased to 550°C (1021°F) for existing Canadian fuel bundles. work was  The coolant temperature i n the case study of this  calculated to be 855°F.  This high temperature coolant can pro-  duce steam at a temperature and pressure comparable to that of conventional f o s s i l - f u e l plants.  However, since the exit coolant temperature  from the steam generator may be as low as 280°F, a portion of the superc r i t i c a l carbon dioxide coolant i s used to produce low pressure steam.  In the cases of single pressure and dual-pressure cycles, the steam generation process i r r e v e r s i b i l i t y i s high, and as a r e s u l t , the useful energy extracted from the s u p e r c r i t i c a l coolant i s low.  The  ideal  o v e r a l l plant e f f i c i e n c i e s of the single pressure, dual-pressure 600/70.3 (psia), and dual-pressure 1200/70.3 (psia) cycles are 26.73%, 29.42%, and 29.87% respectively, compared to 33.94% for the Pickering generating station.  A new  dual-reheat  cycle i s proposed to reduce the high degree of  64  i r r e v e r s i b i l i t y i n the steam generation process.  In the new dual-reheat  cycle, the coolant heats the low and high pressure feeds i n a p a r a l l e l manner instead of alternative heating as i n dual-pressure cycles.  The  ideal o v e r a l l plant e f f i c i e n c y of the new proposed dual-reheat cycle i s 33.02%, which i s comparable to that of the Pickering generating s t a t i o n .  The present r e s u l t i s conservative since the performance of s u p e r c r i t i c a l carbon dioxide has been underestimated tions of:  because of the assump-  (1) no mixing between subchannels, and (2) smooth and continuous  subchannels.  Mixing can improve heat transfer c o e f f i c i e n t s and also  minimize the coolant and wall temperature r i s e i n the p a r t i c u l a r having the maximum l i n e a r heat rate. temperature,  subchannel  For a given maximum f u e l bundle sheath  the no-mixing assumption underpredicts the i n l e t and outlet  temperature of the reactor ( i . e . , the exit and entry temperature of the steam generator respectively).  The smooth and continuous subchannel  assump-  tion also contributes to the underprediction of the performance of superc r i t i c a l carbon dioxide by underestimating the heat transfer c o e f f i c i e n t and overestimating the difference between wall and bulk  temperatures.  Therefore, the calculated ideal o v e r a l l plant e f f i c i e n c y of the dualreheat cycle i s a conservative estimate.  The performance of s u p e r c r i t i c a l carbon dioxide has not been optimized i n this work. subchannel  I f f u e l bundle geometry was designed to achieve  enthalpy balance without using blockers, the net flow area i n a  given diameter coolant channel could be larger.  A larger net flow area  allows higher flow rates, i . e . higher reactor i n l e t coolant without higher pressure drops.  temperatures  The optimization of f u e l bundle geometry  should be included i n future research.  65  While the technical f e a s i b i l i t y of using s u p e r c r i t i c a l carbon dioxide as a reactor coolant has been demonstrated i n the present work, a great number of other factors must be considered i n the design of an actual power station.  L o g i s t i c s of coolants supply and storage, safety,  supporting hardware designs  and o v e r a l l cost must be considered.  The  complexity of financing a modern e l e c t r i c a l generating s t a t i o n would demand serious study i n i t s own r i g h t .  It was not possible to consider a l l of  these features i n a preliminary study l i k e the present.  I t might be noted,  however, that because of the great cost involved i n heavy water production, the use of carbon dioxide may  also o f f e r an economic advantage.  a great deal of research on this matter i s required.  Evidently,  4. Turbine shaft turns the generator rotor to generate electricity. TURBINE , Steam pressure turns the turbine.  fo  c  Power lines take the electric power to communities.  W o,  Hb o  , 'Heavy water' coolant transfersW o o the heat from the fuel to the boiler where ordinary water is turned into steam.  1. Heat is produced by fissioning uranium fuel in the reactor.  Figure  1. Thermo-Hydraulic  CONDENSER 7. Water is pumped back into the boiler.  6. Lake or river water cools the used steam to condense it into water.  F e a t u r e s o f PHW CANDU Reactor Power  Plant  TEMPERATURE,  igure 2.  °F  T y p i c a l P r o p e r t y V a r i a t i o n s i n N e a r - C r i t i c a l Carbon D i o x i d e  68  VOLUME F i g u r e 3. P r o c e s s P a t h of S u p e r c r i t i c a l  C o o l i n g Loop on P-V  Diagram  1, Thsfue! pellet becci radioactive in the reactor. __ PELLET  FUEL BUNDLE  3. The fuel bundle is immersed in coolant flowing through a zirconium tube. The coolant is continuously monitored to detect radioactivity  Figure 4.  PHW CANDU Reactor Arrangement  4, The tubes are fixed reactor vessel of stainless steel.  QUALITY  TEMPERATURE  \ Dry Out  —^.  Wall Temperature  Steam Quality'"'  Low Flux  \ —0/  Temperature  Figure 6.  wt % Steam  Steam Heated Wall\^  FLOW REGIMES Single Phase Liquid Deficient  Annular •1  1 t  $.  Slug Bubble Single Phase  Water  Thermal Hydraulic Regions i n a Boiling Channel  1000  Figure 7.  Boiling Regions  Figure  8.  SUBCHANNEL  (FROM [ 1 2 ] )  TEMPERATURE  RISES  10 12 DISTANCE FROM INLET |*T|  IN  A  28 E L E M E N T  BUNDLE  VERSUS  REACTOR  CHANNEL  LENGTH  <4.J7J00-4  ms  74  1 10,000-,  Figure 9.  High Sheath Temperature Operation vs Time for Various Zirconium Alloy Fuel Elements (from [13])  75  ENTROPY  Figure 10.  Proposed S u p e r c r i t i c a l C0„ Cooling Loop  76  Figure 11.  Heat Transfer Regions: I - Liquids, II - S u b c r i t i c a l Gases, III - Two-Phase, IV - Above-Critical F l u i d s , V - N e a r - C r i t i c a l Fluids (from  [18])  77  'Ah M, u  " , =-  -1  -  '2  AP-4  1. Continuity M = Constant. 2. Energy Conservation Equation: h  = h  + Mh  ±  2  E  = [1.82 log (Re, ) - 1.64]" . 2  O  D  4. Heat_Transfer_Correlation for_Constant_Property_Flow: , Nu  a/8) o  °  Re. Pr b b  ——-  =  x  12.7  JTW O  •  7yj\  - 1) + 1.07 D  5. Pressure Drop Equation for Supercritical_Flow:  AP-C^t^ W  (i-i) ,  2Pd E = E  s  = E (y /U, ) ° ' o w b  E = E 2.15 (Gr/Re, s b p,.y  b  W  2 2  2  H  l  for  Gr/Re  for  5 x 10  evaluated at P = P^ +  2  b  < 5 x 10 < Gr/Re  _ 4  AP, T = ( T  b l  ,  _ 4  2  b  + T )/2 b2  U evaluated at P = P. + \ AP, T = (T . + T „)/2 w 1 2 wl w2  < 3 x 10 ,  .  (FIGURE 12 continued on the following page.)  - 1  ,  78  6.  Heat_Transfer_Correlation_f2£_§upercritical_Flow: Nu = NU  q  n = 0.4 n = n  1  (P /P )°' w  at  b  3  (C?/Cp )  T./T < 1 b m -  = 0.22 + 0.18  n  b  or T./T > 1.2 b m -  (T /T ) wm  n = n, + (511, - 2) (1 - T./T ) 1 1 bm  Figure 12.  , ,  at 1 < T /T < 2.5 -wmat  ,  1 < T./T < 1.2 - b m -  L i s t of Equations  .  CALCUALTE Nu FROM o CONSTANT PROPERTY CORRELATION  BASED  ON BULK PROPERTIES  CALCULATE N.u "FROM  CALCULATE LOCAL WALL TEMPERATURE FOR  CONSTANT  T '  FIND PROPERTIES  j  SUPERCRITICAL FLOW  AT  I  CORRELATION  w  WALL TEMPERATURE T '  PROPERTY FLOW  w  ITERATION  T ' = T ' + AT w w  CALCULATE HEAT FLUX  IF |Q - Q'|/Q > 0.001  Q' = f(Nu, T , T ', Aj)  IF |Q - 0'|/0 < 0.001  b  w  1 1  OUTPUT T = T ' w w  Figure 13. Routine for Calculating Wall Temperature  WALL  BASED  AND BULK  PROPERTIES  INPUT INFORMATION: T> ,  FIND WALL TEMPERATURE AT  WP, A , G, Q, P  POINT 1, [SEE FIGURE 13]  h  1  r  T. bl  FIND  BULK AND WALL  PROPERTIES AT POINT 1  CALCULATE PRESSURE DROP AP' FROM CONSTANT PROPERTY FLOW CORRELATION  FIND AVERAGE BULK AND WALL TEMPERATURES, AND PRESSURE OF POINT 1 AND 2  AP' 2  CALCULATE PRESSURE DROP  = AP  = P  P *  - AP'  h * = h ' 2  2'  Figure 14.  AP  FROM  FIND OTHER PROPERTIES BASED  SUPERCRITICAL P™*"  FLOW CORRELATION  2  = P  I  T = T bl b2  AVERAGE BULK AND WALL  TEMPERATURE, AND PRESSURE  IF |AP - AP'| > 0.01  1  IF |AP - AP'| < oToi  j  Computer Program Flow Chart for Calculating to S u p e r c r i t i c a l Flow i n Heated Pipes  ON  OUTPUT P,  Heat Transfer  )  FLOW RATE = 0.159 Kg/Sec WALL HEAT FLUX =1.01 W/cm  2  PIPE DIAMETER = 18.97 mm PRESSURE = 1100 Psia TEMPERS!  DOWNFLOW, EXPERIMENT UPFLOW, EXPERIMENT PREDICTION  10  20  30  40  50  60  70  80  90  100  DISTANCE ALONG TEST SECTION FROM START OF HEATING, DIAS. Figure 15.  P r e d i c t i o n of Heat Transfer to S u p e r c r i t i c a l Flow, Experimental Results from [60]  110  120  130  DISTANCE ALONG TEST SECTION FROM START OF HEATING, DIAS. Figure 16. Prediction of Heat Transfer to S u p e r c r i t i c a l Flow, Experimental Results from [49]  CO  100  75  E3  H  50  H  25  10  20  DISTANCE ALONG TEST SECTION FROM START OF HEATING,  30 DIAS.  Figure 17. Prediction of Heat Transfer to S u p e r c r i t i c a l Flow, Experimental Results from [55]  CO  DISTANCE ALONG TEST SECTION FROM START OF HEATING, In Figure 18. Prediction of Heat Transfer to S u p e r c r i t i c a l Flow, Experimental Results from [42]  (b) Single Rod Equivalent Figure 19.  Annulus [68]  Equivalent Annulus Models for Rod-Bundles  86  Wire wrap i s used to increase mixing between subchannels which are divided at the minimum spacings between fuel-rods. The. subchannels are c l a s s i f i e d and designated with numbers, according to their geometry and mixing condition.  Figure 20.  Lumped Parameter Model for Rod Bundles (from [71])  300  o TUBE NO. 4 • TUBE NO. 7 SPACER  2 00O O  o • o  ° o  88 100  0  «i 0  10  20  0  °oo  0  n  I —.8S8888S8WS  30  40  50  AXIAL POSITION, L/d  Figure 21.  Thermal Entrance Following a Grid Type Spacer (from [73])  oo  • Ill  1  I  I  I I I  11  1  1  'r  REYNOLDS NUMBER Figure 22.  Comparison of Heat Transfer Data i n a Uniformly Heated Seven-Rod Bundle (Pr = 0.7) with Wire-Wrap Spacers ( f m [74]) r0  0.03  |  \  Figure 23.  F " " f ^ ^ » ^ « ~ — ^ • ^ ^ ^ ^ ^ • ^ — ^ ^ ^ ^  Comparison of F r i c t i o n Factors for Seven-Rod Bundle with Wire-Wrap Spacers (1/d = 12, 24 36, oo) i n a Scalloped Liner (p/d = 1.237) (from [74]) oo  90  1500  400  0  3.0  6.0  9.0  12.0  DISTANCE FROM CORE INLET, In. Figure 24. Temperature P r o f i l e s i n Coolant Channel with Different Fuel Bundle Orientation(from [77])  15.0  0.5;  1.0  1.1  1.2 . s/r  1.4  1.6 1.8 2.0  0  Nu  NUSSELT NUMBER OF ROD BUNDLES  Nu  NUSSELT NUMBER OF.CIRCULAR TUBES  f  FRICTION FACTOR OF ROD BUNDLES  cir  f  cir  ;  FRICTION FACTOR OF CIRCULAR TUBES  Figure 25. E f f e c t of Ratio of Pitch to Rod Diameter Nusselt Number and F r i c t i o n Factor (from [78])  92  28  ELEMENT  BUNDLE  FULL S C A L E CROSS SECTION OF FUEL A N D COOLANT TUBE  F i g u r e 26.  CROSS  SECTION  (FROM [12])  OF  FUEL  AND  C O O L A N T TUBE  4  <. o.  RCV.'l.  3750  3  .966  93  CALANDRIA TUBE  OXIDE FUEL ROD SHEATH: ZIRCALOY-2  AIR GAP FILLER(OR BLOCKER) PRESSURE TUBE  Figure 27.  MINIMUM SPACING: 0.02 In  Channel f o r B o i l i n g Reactor  (from [79])  AIR GAP CALANDRIA TUBE  PRESSURE TUBE  U0  2  FUEL  ZIRCALOY SHEATH  COOLANT FLOW  Figure 28. Tube-in-Shell Fuel Element  (from [79])  D  h  =  P ° , T _ = 775 °  K  MAXIMUM WITHSTANDING TEMPERATURE OF FUEL SHEATH 550  w  P  OS  ± n  = 100.0 .Bar  REACTOR CORE LENGTH = 594 cm SUBCHANNEL POWER = 92.3 KW HEAT FLUX DISTRIBUTION: sin(kx + <f>)  S3 .J  w  WHERE k = 0.51504  500  i = 0.02574 x = DISTANCE Do = 1 UNIT OF EQUIVALENT HYDRAULIC DIAMETER = 0.521 cm  450 320,  340  360  380  420  400  INLET TEMPERATURE OF COOLANT,  440  K  Figure 29. Maximum Operating Temperature Versus Inlet Coolant Temperature  Figure 30.  Pressure Drop Versus Inlet Coolant Temperature  vo  i  0.5  0.6  I  r  0.7  0.8  1  0.9  1  1.0  r  1.1  EQUIVALENT HYDRAULIC DIAMETER, cm Figure 31.  Selection of Minimum Equivalent Hydraulic Diameter  1.2  (I.D. 4.457 in.)  FULL SCALE CROSS SECTION OF FUEL BUNDLE AND COOLANT TUBE  Figure 32. Cross Section of 32-Element Fuel Bundle  98  1.9 o H  1.8  EXPERIMENTAL DATA FROM REFERENCE [83] -j  oi  AECL REPORT 2772  w  1.7  (AUG. 1967)  fe o Pi  fe-  1.6 1.5 1.4 1.3  1.2 1.1 1.0 I  0.9 1  2  3  4  RADIAL DISTANCE FROM BUNDLE CENTERLINE, cm  Figure 33. Radial Neutron Flux D i s t r i b u t i o n i n Fuel Bundle  0  1.0  2.0  3.0  4.0  5.0  6.0  DISTANCE FROM INLET, Meters AO  vo Figure 34.  Subchannel Coolant Temperature Rise i n 32-Element Fuel Bundles Versus Reactor Channel Length  600  0  1.0  2.0  3.0  4.0  5.0  6.0  DISTANCE FROM INLET, Meters Figure 35.  Subchannel Sheath Temperature Rise i n 32-Element Fuel Bundles Versus Reactor Channel Length  o o  80  I  I  0  1.0  _L_ 2.0  I  I  I  3.0  4.0  5.0  _ J 6.0  DISTANCE FROM INLET, Meters  Figure 36.  Pressure Drop Along Reactor Channel Length  i—  1  o  1000  REPRESENTATIVE POSITION IN STEAM GENERATOR Figure 38.  Dual-Pressure 600.0/70.3 (psia) Steam Generation  104  FROM REACTOR SUPERCRITICAL C0 3.4905X10 Lbm/Hr 845 °F 272.7 Btu/Lbm  2  7  HEAT EXCHANGER  200.0 Btu/Lbm  Figure 39. Turbine C i r c u i t Heat Balance of Single Pressure Cycle  105  FROM REACTOR SUPERCRITICAL CO 3.4905X10 Lbm/Hr 845 °F 272.7 Btu/Lbm 7  TO RECUPERATOR SUPERCRITICAL C0 280 °F 11 £..05 i'f.. /T h,~.  2  LEGEND: g p h x s w  -  FLOW RATE, Lbm/Hr PRESSURE, Psia ENTHALPY, Btu/Lbm STEAM QUALITY, % STEAM WATER  REPRESENTATIVE POSITION IN STEAM GENERATOR  Figure 41.  Dual-^Pressure 1200.0/70.3 (psia) Steam Generation  107  FROM REACTOR SUPERCRITICAL CO, 3.4905X10 g 845 °F, 272.7 h 7  1  POINT A , 2.4547X10° g 1200 p, 815 °F 1389.03 h  LEGEND: g p h x s w  -  FLOW RATE, Lbm/Hr PRESSURE, Psia ENTHALPY, Btu/Lbm QUALITY OF STEAM STEAM VJATER  POINT D 96680 gw 225833 gs 3.8 p 120.56 hw 1087.06 hs Figure 42.  Turbine C i r c u i t Heat Balance of Dual-Pressure 1200.0/70.3 (psia) Cycle  REPRESENTATIVE POSITION IN STEAM GENERATOR  Figure 43.  Dual-Reheat 1200.0/70.3 (psia) Steam Generation  o 00  109  FROM REACTOR SUPERCRITICAL CO, 3.4905X10 g 845 °F 272.7 h  LEGEND:  7  g - FLOW, Lbm/Hr h - ENTHALPY, Btu/Lbm  1200 Psia 815 °F 1389.03 h  70.3 Psia 567.19 °F 1315.4 h  116.05 h  Figure 44.  Turbine C i r c u i t Heat Balance of Dual-Reheat 1200/70.3 (psia) Cycle  -  UNHEATED WET. PER. cm  HEAT POWER RATE Q, KW/M , KW  MAX. FLOW FINAL TEMP. . RATE ENTHALPY °C , Kg/Sec . KJ/Kg  4.775  35.8  143.0  409.0  0.4651  545.8  298.3  0.8947  4.775  37.8  151.0  426.0  0.4638  563.7  316.2  4  0.8947  4.775  44.5  177.8  505.0  0.4238  650.5  403.0  4  4  0.8947  4.775  39.7  158.6  457.0  0.4394  598.2  350.7  5  12  0.6571  3.777  31.4  125.6  532.0  0.3018  651.7  404.2  6  8  0.8947  4.775  48.2  192.7  546.0  0.4178  695.3  411.8  7  4  1.3872  8.921  60.8  242.9  538.0  0.5839  651.7  404.2  FLOW AREA cm ^  TOTAL WET. PER. cm  SUBCHANNEL  NO. OF SUBCHANNELS  1  1  0.8947  2  4  3  1.116 3.773  ASSUMED.HEAT INPUT DISTRIBUTION: q =Q-sin(kx WHERE  k = 0.51504  4)  TOTAL COOLANT CHANNEL POWER: 6113 MW TOTAL COOLANT CHANNEL MASS FLOW RATE: 15.091 Kg/Sec  A = 0.02547 x = DISTANCE INLET CONDITION:  ENTHALPY CHANGE KJ/Kg  OUTLET CONDITION:  PRESSURE = 100 Bar = 1450 Psia  PRESSURE = 85.5 Bar = 1240 Psia  TEMPERATURE = 126.85 °C = 260 °F  TEMPERATURE = 457.8 °C = 855.6 °F  ENTHALPY = 247.5 KJ/Kg = 110.26 Btu/Lbm  ENTHALPY =640.9 KJ/Kg = 275.60 Btu/Lbm  Figure 45. Results of Heat Transfer to S u p e r c r i t i c a l CO  Coolant i n 32-Element Fuel Bundles  Ill  "* CHARACTERISTICS  COOLANT — —  1 HEAVY WATER  CARBON DIOXIDE  1 1443  1450  OUTLET PRESSURE (Psia)  1254  1240  PRESSURE DROP (Psia)  189  210  MAXIMUM SHEATH TEMPERATURE (°C)  304  550  COOLANT INLET TEMPERATURE (°C)  249  127  COOLANT OUTLET TEMPERATURE (°C)  293  458  4.070  4.458  J  FUEL ELEMENT DIA. (In.)  0.598  0.598  §  NO. OF FUEL ELEMENTS IN A BUNDLE  28  32  1  INLET PRESSURE (Psia)  COOLANT TUBE INNER DIA. (In.)  j  |j  MAXIMUM CHANNEL POWER(MW)  |j 5.125  6.113  |  MAXIMUM CHANNEL MASS FLOW RATE  |j  15.1 Kg/Sec  1  POSSIBILITY OF DRYOUT  |[ YES  NO  |  COOLANT COST  |] HIGH  LOW  j  | FUEL USED  22.2 Kg/Sec  | °2 U  U 0  2  U  C  Figure 46. Overall Performance of S u p e r c r i t i c a l Carbon Dioxide  i Coolant  112  I  PICKERING  NEW DESIGN  COOLANT  HEAVY WATER  SUPERCRITICAL C 0 |  CORE LENGTH  19 F t . 6:In.  19 F t . 6 In.  MAXIMUM CHANNEL POWER  5.125  6.113 MW  NO. OF FUEL RODS  28  32  0. D. OF SHEATH  0.598 In.  0.598 In.  0. D. OF FUEL BUNDLE  4.03 In.  4.358 In.  INTER-ELEMENT SPACING (MIN.)  0.05 In  0.496 In.  COOLANT TUBE X-SECTIONAL AREA  13.010. Sq. In.  15.605 Sq. In.  BLOCKER X-SECTIONAL AREA  NIL  1.622 Sq. In.  FUEL BUNDLE X-SECTIONAL AREA  7.864 Sq. In.  8.988 Sq. In.  COOLANT FLOW AREA  5.146 Sq. In.  4.995 Sq. In.  COOLANT TUBE I. D.  MW  1 4.070 In.  2  1 4.457 In.  Figure 47. Overall Dimensions of 32-Element Fuel Bundle  I  B  j  PICKERING  SINGLE PRES. CYCLE  DUAL PRESSURE CYCLE 600/70  DUAL PRESSURE CYCLE 1200/70  DUAL-REHEAT CYCLE 1200/70  TURBINE EFFICIENCY  H.P. 72.6% L.P. 88.5%  90,0%  H.P. 90.0% L.P. 88.5%  H.P. 90.0% L.P. 88.5%  H.P. 90.0% L.P. 90.0%  STEAM PRESSURE, Psia  H.P. 585 L.P. 70.3  130  H.P. 600 L.P. 70.3  H.P. 1200 L.P. 70.3  H.P. 1200 LIP. 70.3  MAXIMUM STEAM TEMPERATURE, °F  H.P. 483;5 L.P. 435.0  815.0  H.P. 815.0 L.P. 435.0  H.P. 815.0 L.P. 435.0  H.P. 815.0 L.P. 567.2  PRESSURE RATIO, H.P./L.P.  8.321  8.535  17.07  17.07  H.P. 3036500 L.P. 4246800  H.P. 2454700 L.P. 4452600  H.P. 2946300 L.P. 4045800  0.7150  0.5513  0.7282  H.P. Super. L.P. 9%  H.P. 3.9% L.P. 9%  H.P. 3:9% L.P. 9%  STEAM FLOW RATE I Lbm/Hr  H.P. 5969862 L.P. 5550833  400600  STEAM FLOW RATE RATIO, H.P./L.P  1.075  EXHAUST STEAM WETNESS  Hi P.  EXHAUST STEAM PRESSURE, Psia  H.P. 70.3 Psia 1.5 In Hg L.P. 1.5 In Hg  H.P. 75.0 Psia H.P. 75.0 Psia H.P. 75.0 Psia L.P. 1.5 In Hg L.P. 1.5 In Hg L.P. 1.5 In Hg  TURBINE CYCLE EFFICIENCY  34.60%  30.3%  11% L.P. 1Q%  5.4%  27.6%  30.7%  Figure 48. Summary of Steam Conditions of Thermal Cycles  33.8%  PICKERING  SINGLE PRES. CYCLE  DUAL PRESSURE ' DUAL PRESSURE CYCLE 600/70.3 CYCLE 1200/70  DUAL-REHEAT CYCLE 1200/70  5.67 x 1 0  5.67 x 10  5.67 x 10  HEAT TRANSFERRED TO SECONDARY CIRCUIT, Btu/Hr  5.67 x 10  SHAFT WORK OUTPUT, Btu/Hr  1.9760 x 10  9  1.5640 x 10  9  1.7212 x 1 0  9  1.7504 x 10  9  1.9263 x 10  9  COOLANT FLOW RATE, Lbm/Hr  6.1300 x 1 0  7  3.4905 x 1 0  7  3.4905 x 1 0  7  3.4905 x 1 0  7  3.4905 x 1 0  7  PRIMARY PUMP WORK, Btu/ Hr  3.9365 x 1 0  7  4.3170 x 1 0  7  4.3170 x 1 0  7  4.3170 x 10  7  4.3170 x 1 0  7  FEED WATER FLOW RATE, Lbm/Hr  H.P. 5,969,362 DRAIN 489,525  4,006,600  SECONDARY PUMP .WORK, Btu/Hr  1.2229 x 1 0  7  2.0030 x 10  NET WORK OUTPUT, Btu/Hr  1.9224 x 10  9  1.5147 x 10  IDEAL OVERALL EFFICIENCY  33.94%  Figure 49.  9  26.73%  9  5.67 x 10  9  9  9  H.P. 3,036,500 L.P. 1,210,300  H.P. 2,454,700 L.P. 1,997,900  H.P. 2,946,300 L.P. 1,099,500  6  6.7061 x 10  6  1.0443 x 1 0  7  1.0714 x 1 0  7  9  1.6672 x 10  9  1.6927 x 10  9  1.8724 x 1 0  9  29.42%  Overall Performance of Thermal Cycles  29.87%  33.02%  189525  |T0 CONDENSER  lh/hr  MECHANICAL LOSSES 13X7 KW  O Ib/hr BUILDING HCATING  ELECTRICAL LOSSES 8162 KW NET  GENERATOR OUTPUT 543320 KW  '  I  I  1  ^  LJ  II  MAIN STM. CHESTS  nln n  LEGEND g . Flow in Ib/hr a - Pressure in PSIA f - Temperature in degrees F h . Enthalpy b l u / l b x - Q u a l i t y of steam i n percent Ib/hr • Flow o l steam lb/, rw. Flow of water s • Enthalpy of steam . btu/lb  AtOH  /"  —WlfATERr  I  .,.04  J—I  BOILER LIVE STEAM REHEATER DRAINS 48952S l»/hr 468.37 h  [WATER EXTRACTION BE.LT  »  ; L  »'  •*-*-*•  - i - - C — — * • — r — • 11 y  *i.  1  \\  * *.—*.  , \««.-*\> .' . u.  *•  4—4i  <  »• »  —*  A' j•*  A * •«•— ' ! | J  ff  160637 I b / h r  NO. 4 DE AERATOR HEATER  S 9 8 9 B 6 2 Ib/hr 312.05h 339.98 F  38 0 PSIA 2M.IT F 319.42 HIT.2« 91503 3IS036 124.45  h h* Ib/S^-W Ib/hr PSIA  272.90 h 1175.78 h i J 6 5 4 8 6 Ik/hrtfi IM>IZ3 IWhr ' 66.79 PSIA  i J ^  1275.13 h [30576 r Ji033*!b/>»/  NO. 4 HEATER  NO. 5 HEAT5S  2 0 8 0 Ib/h, 1201.8 h  120.56 h '087.06 h. 96680 Ib/hrW 2 Z 5 8 3 9 16/hr 3.8 PSIA  NO.3 HEATE*  Figure 50.  T  NO. 2 H'ATSS  U  R  3  70. o r h 102.10 V 676613  NO. 1 M?ATE1!  0 G  E  N  E  R  A  T  O  R H  E  A  T B  A  U  N  C  c (FRO  116  .0  1.1  1.2  1.3  Figure 51.;  1.A  1.5  1.6  ENTROPY, Btu/Lbm  Expansion Line of CANDU reactor Turbine Stages (from [ 8 2 ] )  117  REFERENCES 1. Mooradian, A.J.; "Nuclear Research and Development i n Canada", Nuclear Engineering International, Survey of Canada, Pg. 13, June 1974. 2. Mclntyre, H.C.; "Natural-Uranium Heavy-Water Reactors", S c i e n t i f i c American, Vol. 233, No. 4, Pg. 17, 1975. 3. El-Wakil, M.M.; Toronto, 1971.  NUCLEAR ENERGY CONVERSION, Intext Educational Publishers,  4. Bate, D.L.S.; "Cost", AECL Nuclear Power Symposium, Lecture 16,  1971.  5. Eltham, B.E. and Bowen, J.H.; "Plant Survey", Chapter 3, THE DESIGN OF GAS-COOLED GRAPHITE-MODERATED REACTORS, Edited by Poulter, D.R. , Oxford University Press, Toronto, 1963. 6. 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Petukhov, B.S., Kransnosehzkov, E.A., and Protopopov, V.S.; "An Investigation of Heat Transfer to Fluids Flowing i n Pipes Under C r i t i c a l Conditions", International Development i n Heat Transfer, International Heat Transfer Conference, Colorado, U.S.A., Paper 67, 1961. 23. Swenson, H.S., Cariver, J.R., and Kakarala, CR. ; "Heat Transfer to S u p e r c r i t i c a l Water i n Smooth Bore Tubes", J . Heat Transfer, Vol. 87, No. 4, Pg. 447, 1965. 24. Goldman, K.; "Heat Transfer to S u p e r c r i t i c a l Water at 5000 PSI Flowing at High Mass Flow Rate Through Round Tubes", International Development i n Heat Transfer, International Heat Transfer Conference, Colorado, U.S.A., Paper 66, 1961. 25. Koppel, L.B. and Smith, J.M. ; "Turbulent Heat Transfer i n C r i t i c a l Region", International Developments i n Heat Transfer, International Heat Transfer Conference, Colorado, U.S.A., Paper 69, 1961. 26. Powell, W.B.; "Heat Transfer to Fluids i n the Region of C r i t i c a l Temperature", Jet Propulsion, Vol. 27, No. 7, Pg. 776, 1957. 27. Shitman, M.E.; "Impairment of the Heat Transmission at S u p e r c r i t i c a l Pressures", High Temperature, V o l . 1, No. 2, Pg. 237, 1963. 28. Yamagata, K., Nishikawa, K., Hasegawa, S., and F u j i i , T.; "Forced Convective Heat Transfer i n the C r i t i c a l Region", Japan Society of Mechanical Engineers, Semi-international Symposium, September, 1967.  119  29. M i l l e r , W.S., Steader, J.D., and Trebes, P.M.; "Forced-convection Heat Transfer to Liquid Hydrogen at S u p e r c r i t i c a l Pressures", Bult. Inst. Intern. Froid, Annexe, No. 2, Pg. 173, 1965. 30. Petukhov, B.S.; "Heat Transfer i n a Single-phase Medium Under Superc r i t i c a l Conditions", Translated from T e p l o f i z i k a Vysokikh Temperature, Vol. 9, No. 4, Pg. 732, 1968. 31. Abadzic, Z. and Goldstein, R.J.; "Film B o i l i n g and Free Convection Heat Transfer to Carbon Dioxide Near the C r i t i c a l State", Int. J . Heat Transfer, V o l . 13, Pg. 1163, 1970. 32. Tanaka, H., Nistwaki, N., Hrata, M., and Tsuge, A.; "Forced Convection Heat Transfer to F l u i d Near C r i t i c a l Point Flowing i n C i r c u l a r Tube", Int. J . Heat Mass Transfer, V o l . 14, Pg. 739, 1971. 33. Knapp, K.K. and Sabersky, R.H.; "Free Convection Heat Transfer to Carbon Dioxide Near the C r i t i c a l Point", Int. J . Heat Mass Transfer, Vol. 9, No. 1, Pg. 41, 1966. 34. Hauptmann, E.G.; "An Experimental Investigation of Forced Convective Heat Transfer to a F l u i d i n the Region of i t s C r i t i c a l Point", Ph.D. Thesis, C a l i f o r n i a I n s t i t u t e of Technology, 1966. 35. Kafengaus, N.L.; "On Physical Nature of Heat Transfer at S u p e r c r i t i c a l Pressure with Pseudo-boiling", Heat Transfer - Soviet Research, V o l . 1, No. 1, Pg. 88, 1969. 36. Wood, R.D. and Smith, J.M.; "Heat Transfer i n the C r i t i c a l Region: Experimental Investigation of Radial Temperature and Velocity P r o f i l e s " , Am. Inst. Engrs. J . , Vol. 10, No. .2, Pg. 10, 1964. 37. Hsu, Y.Y.; "Discussion of an Investigation of Heat Transfer of Fluids Flowing i n Pipes Under S u p e r c r i t i c a l Conditions", ASME, International Development i n Heat Transfer, Pg. 1-180, 1963. 38. Deissler, R.G.; "Heat Transfer and F l u i d F r i c t i o n for F u l l y Developed Water with Variable F l u i d Properties", ASME Trans., J . Heat Transfer, Vol. 76, No. 1, Pg. 73, 1954. 39. Goldmann, K.; "Heat Transfer to S u p e r c r i t i c a l Water and Other Fluids with Temperature-Dependent Properties", Chem. Eng. Progr. Symp., Series 3, V o l . 50, No. 11, 1954. 40. Malhotra, A. and Hauptmann, E.G.; "Heat Transfer to a S u p e r c r i t i c a l F l u i d During Turbulent, V e r t i c a l Flow i n a C i r c u l a r Duct", International Center for Heat and Mass Transfer, Beograd, Yugoslavia, 1976. 41. Jackson, J.D. and Feloster, J . ; "Enhancement of Turbulent Heat Transfer Due to Buoyancy for Downward Flow of water i n V e r t i c a l Tubes", International Center for Heat and Mass Transfer, Deograd, Yugoslavia, 1976.  120  42. Schnurr, N.M.; "Heat Transfer to Carbon Dioxide i n the Immediate V i c i n i t y of the C r i t i c a l Point", ASME Transactions, J . Heat Transfer, Vol. 9, Pg. 16, 1969. 43. Bringer, R.P. and Smith, J.M. ; "Heat Transfer i n the C r i t i c a l Region", AICHE J . , Vol. 3, No. 1, Pg. 41, 1957. 44. Sastry, V.S. and Schnurr, N.M.; "An A n a l y t i c a l Investigation of Forced Convection Heat Transfer to Fluids Near the Thermodynamic C r i t i c a l Point", ASME Transactions, J . Heat Transfer, Vol. 97, No. 5, Pg. 226, 1975. 45. Miropolski, L. and Shitsman, M.E.; "Heat Transfer to Water and Steam at Variable S p e c i f i c Heat i n N e a r - C r i t i c a l Region", Soviet Phy.-Tech. Phys., V o l . 2, No. 10, Pg. 2196, 1957. 46. Colburn, A.P.; "A Method of Correlating Forced Convection Heat Transfer Data", AICHE Journal, V o l . 29, Pg. 174, 1933. 47. Boure, P.J., P u l l i n g , D.J., G i l l , L.E., and Denton, W.H.; "Forced Convection Heat Transfer to Turbulent CO2 i n the S u p e r c r i t i c a l Region", Int. J . Heat Mass. Transfer, V o l . 13, Pg. 1339, 1968. 48. Kutateladze, S.S. and Leontiev, A.I.; TURBULENT BOUNDARY LAYER IN COMPRESSIBLE GASES, Arnold, London, 1964. 49. Kranoshchekov, E.A. and Protopopov, V.S.; "Experimental Study of Heat Exchange i n Carbon: Dioxide i n the S u p e r c r i t i c a l Range at High Temperature Drops", High Temperature, USSR, V o l . 4, Pg. 375, 1965. 50. Kranoshchekov, E.A. and Protopov, V.S.; "A Generalized Relationship for Calculation of Heat Transfer to Carbon Dioxide at S u p e r c r i t i c a l Pressure", High Temperature, U.S.S.R., V o l . 9, Pg. 125, 1971. 51. Petukhov, B.S. and K i r i l l o v , V.V.; "On the Question of Heat Transfer to a Turbulent Flow of Fluids i n Pipes", Teploenergetika, No. 4, Pg. 63, 1958. 52. Hiroharu, K., N i i c h i , H., and Masaru, H.; "Studies on the Heat Transfer of F l u i d at a S u p e r c r i t i c a l Pressure", B u l l e t i n of JSME, Pg. 654, 1967. 53. Shiralkar, B.S. and G r i f f i t h , P.; "Deterioration i n Heat Transfer to Fluids at S u p e r c r i t i c a l Pressure and High Heat Fluxes", ASME Transactions, J. Heat Transfer, V o l . 91, No. 2, Pg. 27, 1969. 54. Dickinson, N.L. and Welch, O.P.; "Heat Transfer to S u p e r c r i t i c a l Water", ASME Transactions,;J. Heat Transfer, V o l . 80, No. 4, Pg. 746, 1958. 55. Kranoshchekov, E.A., Protopopov, V.S., Parhovhik, I.A., and S i l i n , V.A.; "Some Results of an Experimental Investigation of Heat Transfer to Carbon Dioxide at S u p e r c r i t i c a l Pressure and Temperature Heads up to 850°C", High Temperature, USSR, Vol. 19, No. 5, Pg. 992, 1971.  121  56. Petukhov, B.S., Grigorev, V.S., and Polyakov, A.F.; "Experimental Investigation of Heat Transfer i n Single-Phase N e a r - C r i t i c a l Region with Heat Input Varying Along the Length of the Pipe", Toploenergetika, Vol. 20, No. 3, Pg. 71, 1973. 57. Glushchenko, L.F. and Gandzyuk, O.F.; "Temperature Conditions at the Wall of an Annular Channel with Internal Heating at S u p e r c r i t i c a l Pressure", High Temperature, USSR, V o l . 10, No. 4, Pg. 734, 1972. 58. Protopopov, V.S. and Igamberdyev, A.T.; "Results of an Experimental Investigation of Local Heat Transfer at S u p e r c r i t i c a l Pressure i n a Rectangular Channel Heated From One Side", High Temperature, USSR, Vol. 10, No. 6, Pg. 116, 1972. 59. Kellogg, H.B. and Brown, G.B.; "Seventh Quarterly Progress Report for 1000 MWE S u p e r c r i t i c a l Pressure Nuclear Reactor Plant Study", WCAP-2525, October, 1963. 60. Jackson, J.D. and Evans-Lutterodt, K.; "Impairment of Turbulent Forced Convection Heat Transfer to S u p e r c r i t i c a l Pressure CO2 Caused by Buoyancy Forces", Research Report N.E. 2, University of Manchester, Department of Nuclear Engineering i n the Faculty of Science, March, 1968. 61. Tarasova, N.V. and Leontz, V.A.I.; "Hydraulic Resistance During Flow of Water i n Heated Pipes at S u p e r c r i t i c a l Pressure", High Temperature, USSR, Vol. 6, No. 4, Pg. 721, 1968. 62. Kuraeva, I.V. and Protopopov, V.S.; "Mean F r i c t i o n Coefficient for Turbulent Flow of Liquid at a S u p e r c r i t i c a l Pressure i n Horizontal Circular Tubes", High Temperature, USSR, Vol. 12, No. 1, Pg. 194, 1974. 63. Sastry, V.; "Thermophysical Properties of CO2 i n the Near C r i t i c a l Region". 64. Vargaftirk, N.B.; TABLES ON THE THERMOPHYSICAL PROPERTIES OF LIQUIDS AND GASES, Second Edition, Hemisphere Publishing Corporation, Washington, London, 1974. 65. Altunin, V.V. and Sakhabetdinov, M.A.; "The V i s c o s i t y of Liquid and Gaseous Carbon Dioxide at Temperatures of 220 - 1300°K and Pressure up to 1200 Bar", Thermal Engineering, Vol. 19, No. 8, Pg. 124, 1972. 66. Altunin, V.V. and Sakhabetdinov, M.A.; "The Thermal Conductivity of Liquid and Gaseous Carbon Dioxide i n the 220 - 1300°K Temperature Range at Pressure up to 1200 Bar", Thermal Engineering, V o l . 20, No. 5, Pg. 121, 1973. 67. Brown, G., Packman, G. and Greenough, G.B.; "Fuel Elements", J . B r i t . Nucl. Energy Society, V o l . 2, No. 2, Pg. 186, 1963. 68. Sutherland, W.A.; "Experimental Heat Transfer i n Rod Bundles", Heat Transfer i n Rod Bundles, ASME, New York, 1968.  122  69. Maresca, M.W. and Dwyer, D.E.; "Heat Transfer to Mercury Flowing i n Line Through a Bundle of Circular Rods", ASME Trans., J . Heat Transfer, Vol. 86, No. 3, Pg. 180, 1964. 70. Friedland, A.J., Dwyer, D.E., and B o n i l l a , C.F.; "Heat Transfer to Mercury i n P a r a l l e l Flow Through Bundles of C i r c u l a r Rods", International Development i n Heat Transfer, International Heat Transfer Conference, Colorado, USA, Paper 62, 1961. 71. Oldaker, I.E.; "Sheath Temperature, a G-20 Computer Program for Fuel Bundles", AECL-2269, May, 1965. 72. Rogers, J.T. and Todreas, H.E.; "Coolant Interchannel Mixing i n Reactor Fuel Rod Bundles Single Phase Coolants", Heat Transfer i n Rod Bundles, ASME, New York, 1968. 73. Hoffman, H.W., Wentland, J.L., and Stelzman, W.J.; "Heat Transfer with A x i a l Flow i n Rod Clusters", Int. Development i n Heat Transfer, International Heat Transfer Conference, Colorado, USA, Paper 65, 1961. 74. Hoffman, H.J., M i l l e r , C.W., Sozei, G.L., and Sutherland, W.A.; "Heat Transfer i n Seven Rod Clusters - Influence of Linear and Spacer Geometry on Sheath Fuel Performance", GEAP-5289, General E l e c t r i c Co., San Jose, C a l i f o r n i a , October, 1966. 75. Midvioy, W.I.; "An Investigation Into the CHP Performance of Horizontal and V e r t i c a l 37-Element Assemblies Cooled by Freon", Proceedings of the 6th Western Canada Heat Transfer Conference, May, 1976. 76. Kidd, G.J., J r . , Stelzman, W.J., and Hoffman, H.W.; "The Temperature Structure and Heat Transfer Characteristics of an E l e c t r i c a l l y Heated Model of Seven Rod Cluster Fuel Element", Heat Transfer i n Rod Bundles, ASME, New York, 1968. 77. Samuels, G.; "Design and Analysis of the Experimental Gas-Cooled Reactor Fuel Assemblies", Nuclear Science and Engineering, V o l . 14, Pg. 37, 1962. 78. Kays, W.M.;  CONVECTIVE AND MASS TRANSFER, McGraw-Hill, New York, 1966.  79. Pon, G.A.; "Light Water-Cooled Heavy-Water-Moderated Natural-Uranium Power Reactor", The Ninth AECL Symposium on Atomic Power, Toronto, Ontario, AECL-1807, 1963. 80. Wooten, W.R.A., Taylor, A.J., and Worley, N.E.; "Steam Cycles for Gas-Cooled Reactors", Proc. Second United Nations, International Conf. on Peaceful Uses of Atomic Energy, Geneva, V o l . 7, Paper P/273UK, 1958. 81. Fraas, A.P. and Ozisik, M.N.; Sons, Inc., New York, 1965. 82. Renshaw, R.H.; 6, 1971.  HEAT EXCHANGER DESIGN, John Wiley and  "Heat Transport", AECL Nuclear Power Symposium, Lecture  123  83. Serdual, K.J. and Green, R.E.; " L a t t i c e Measurements with 28-Elements Natural UO2 Fuel Assemblies, Part I I : Relative Total Neutron Densities and Hyperfine A c t i v a t i o n Distributions i n a L a t t i c e C e l l " , AECL-2772 Chalk River, Ontario, August 1967.  124  APPENDIX I.  Computing Procedure  The basic approach of the computer program for heat transfer to s u p e r c r i t i c a l carbon dioxide i s i t e r a t i o n .  Figure 13 shows the routine  for calculating a l o c a l wall temperature when a l o c a l f l u i d bulk temperature, pressure, heat flux, flow rate, and geometry are given. c r i t i c a l flow i s f i r s t assumed to have constant properties.  The super-  The l o c a l heat  transfer c o e f f i c i e n t and wall temperature are calculated from a c o r r e l a t i o n for constant property flow, i . e . equation (11).  Then, an assumed new value  of the wall temperature i s increased or decreased from the calculated value in an i t e r a t i v e manner, and the corresponding heat transfer c o e f f i c i e n t i s , therefore, calculated from the correlation for s u p e r c r i t i c a l flow; i . e . equation (19).  This i t e r a t i o n continues u n t i l the heat flux (evaluated from  the given l o c a l conditions, assumed wall temperature, and corresponding heat transfer c o e f f i c i e n t ) i s equal to the given heat flux.  The f i n a l value  of the assumed wall temperature i s the r e s u l t .  Thermophysical properties of carbon dioxide near the c r i t i c a l T 631 point i n the calculation are taken from Sastry  .  Thermal properties of  carbon dioxide i n the above c r i t i c a l region are taken from the data of V a r g a f t i k ^ " ' , and physical properties are calculated from the formulas * M. • [65,66] of Altunin et a l . 4  Figure 14 shows the routine for calculating pressure drop from one increment to the next along a heated pipe.  An assumed pressure drop i s  f i r s t calculated from the correlation of constant property flow; i . e . equation (23).  Then, the assumed pressure of the second increment i s  calculated from P  0  = P  1  - dP.  The f l u i d bulk enthalpy i s calculated from  125  the given enthalpy and input heat rate of the f i r s t increment, i . e . h,  9  - h, + dh. n  Based on the assumed pressure and calculated enthalpy,  other f l u i d properties and also the wall temperature of the second increment can be evaluated.  Assuming l i n e a r temperature and pressure variations  between increments, a new pressure drop i s calculated from the c o r r e l a t i o n for s u p e r c r i t i c a l flow, i . e . equation (22).  Based on the new pressure  drop and known enthalpy, the properties and wall temperature of the second increment are evaluated again for the c a l c u l a t i o n of another new pressure drop.  These steps are repeated u n t i l the calculated pressure drop i s con-  verged.  The procedure based on the above routines i s carried out from one increment to another u n t i l the f l u i d bulk temperatures, wall temperatures, and pressure drop along the entire pipe are calculated. program i s l i s t e d i n this  Appendix.  The computer  126  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 2* 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  C **  10 81  82  11 20 21 91  92  66 30 31 83  26 24 36  77  62 61 63 40  MAIN PROGRAM * * REAL P ( 3 0 ) . TM( 30) T(30, 100), MD(30,100), H ( 3 0 , 1 0 0 ) , CP(30,100) REAL V K 3 0 . 1 0 0 I , M 3 0 . 1 0 0 ) REAL L ( I O O O ) , T P ( 1 0 0 0 ) , T P ( I O O O ) , PP(IOOO) REAL MOP, MOW, MORX, MDWX, MOB A, MOWA REAL K B , KW, KBX, KWX, KRA, KWA, MFR INTEGER INC 1=0 1=1+1 RFA0<8,81) P ( I ) , TM(I) FORMAT(F10.5, F9.2) I F ( T M ( T I . E O . 0 . 0 ) GO TO 20 DO 11 J-lt 100 REftD(8,82) T ( I , J > , M D ( I , J I , H ( I , J ) , CP(I,J) FORMAT(F 1 0 . 2 , F 1 4 . 3 , F 1 3 . 2 , F 1 2 . 2 ) IF(TfI,J) . E O . 0 . 0 ) GO TO 10 MD( I , J ) = 1 C 0 0 . 0 / M D U , J I CONTINUE 1=9 1=1*1 R E A 0 ( 7 , 9 1 ) P ( I ) , TMt-1) FCRMAT(F9.5, F10.2) I F { T M { I | . E O . 0 . 0 ) GO TO 3 0 DO 66 J = l , 100 '"• RFAD<7,92> T ( I , J ) , M O ( I , J ) , H ( I , J » , C P U . J I , V I ( I , J ) , K(I,JI F0RMAT(F10.2, F14.3, F13.2, F12.2, E16.4, E15.4) I F ( T ( I , J » . E O . 0 . 0 ) GO TQ 21 MD(I,JJ=100C.0/MD(I,J) CONTINUE READ<5,31> D, MFR, 0 , PG, T B , BTU FORMAT(F10.6, 5F10.1) R F A D ( 5 , 8 3 ) INC, CONT FORMA T{I 1 0 , F 1 0 . I ) IF(CC.NT . E O . 0 . 0 ) GO TO 24 WRITF<6,26) PORMAT (*.-' , ' T H I S CALCULATION IS AT CONSTANT P R E S S U R E ' ) I F ( 3 T U .'EO. 0 . 0 ) GO TO 77 WRITE(6,36I FORM A T ( * - • ' G I V E N DIAMETER, MASS FLOW R A T E , HEAT F L U X , PRESSURE•, I • , 9 U L K - T E M P P R A T U R E , * * * * * B R I T I S H UNITS * * * * * •) W R I T E ( 6 ' » 1 7 ) D, MFR, 0 , PG, T B , BTU 0=0*0.0254 MFR=MFR*0.45359 0=0*0.003154 PG=PG*1.01325/14.7 TB=(TB+460.0)*5.0/9.0 MFR=MFR/3600.0 I F { ( O G . G E . 7 5 . 0 ) . A N D . (PG . L E . 1 0 0 . 0 ) ) GO TO 61 W P ! T F ( 6 , 6 2 1 PG F ORM AT ( • - • , F 1 0 . 2 . ' INPUT PG IS OUT OF DATA R A N G E ' ) GC TO 13 IF ( ( TP . G E . 2 7 3 . 1 5 1 . A N D . (TB . L E . 1 5 0 0 . 0 ) ) GO TO 40 W R I T E ( 6 , 6 3 ) TB FORMAT{• - ' , F 1 0 . 2 , ' TNPUT TB IS OUT OF DATA R A N G E ' ) GO TO 13 N=10 I F ( ( T B .C,T. 4 0 0 . 0 ) . O R . (PG . G T . 8 2 . 7 0 ) ) N= 1 CALL P R O P ( P G , T B , T M , P , T , H , M O , V I , C P , K , T M C , H B , M C B , V I B . C P B , K B , N ) f  127  59  I F ( N . N E . 1 ) GO  60  CALL  VISCJPG,  CALL  COND(PG,  61 62  51  63  32  64  T  B,  FORMAT('l',  "GIVEN  OIAMFTER,  F O R M A T t•  MFR,  HI=HB  68  DL=  69  A=3.1415926*0*0/4.0  70  AL=3.1415926*D*DL TL=FLOAT(INC)*OL  72  VM=MFR/A  73  G=9.81  74  9S=l.O  75  M=l  76  CALL  HEAT  FLUX,  PRESSURE•,  INCREMENTS')  PG, T B , HB, INC  118)  HFATID,  D L , M,  Q,  AH)  CALL FTNO(D,MFR,AH,PG,HB,TM,P,H,T,MD,VI,CP,K,TW,FAIL,DS,M) IF( F A IL .NE . 0 . 0 ) GO TO 4 5 N=10  78 79 80 81  IFUTW  82  CALL  83  I F ( N . N E . 1 ) GO  84  CALL  85  CALL 33  .GT. 4C0.0)  .OR.  IPG ,GT. 82.7))N=l  PROP(PG,TW,TM,P,T,H,MO,VI TO  ,CP,K,TMW,HW,MOW,VIW,CPW,KW,N)  33  VISC(PG,TW,VDW,VIW) CONO(PG,TW,MDW,KW)  TPNTINUE L(M)=(FLOATIM)-0.5>*DL*l000.0  87 88  TF(M)=TB  89  TP(M)=TM  90  PP(M)=PG  91  I F ( M . G E . INC,) G O  92  M=M+1  93  HBX=HB+AHB  94  IFUHPX  95  W R I T E ( 6 , 1 9 ) HBX 19  97  TO  .GE. -95.0>  FORMAT(•—',  F10.2,  98  . AMD. •  (HBX . L E . 1 6 0 0 . 0 ) ) HBX  I S C U T OF  GC TO 45 18  99  CONTINUE CALL  HEATI 0,  100  AHBX=AHX/MFR  101  IFICONT  102  PX=PG  103  O L , M,  . E O . 0 . 0 ) GO  0, A H X ) TO 27  PF=PG  104 105  RATE, OF  AHB=AH/MFR  77  98  FLOW NO.  0  71  96  MASS  ENTHALPY,  0,  ', 6E17.4,  67  86  KB I  •, B U L K - T E M P F R A T U R E , W R I T E ( 6 , 1 7 ) D,  17  MDB,  WRITE(6,32) 1  65 66  T O ,51  T B , MOB, V I B )  GO 27  106  TO  15  RF=VM*D/VTB F=1.0/(I1.82*AL0G10(RE)-1.64?**21  107  IFIRE  108  .GT. 1CCOO0.O)  F=0.01796894  EV=E*((VIW/VIR)**0.22)  109  P0=FV*{VM**2)*DL*2.0/(*MDB*D)  110  PD=PD*0.00001  111  PX=PG-PO  112 113 114  TEST=0.0 NM=0 NN-NM+l  44  115  IFINM  116  WRITE(6,55) M  . L E .2 5 ) GO  TO  54  OATA  GO  TO  RANGE')  18  128  117 118 119 120 121 12? 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174  55 54  16 15  46  F O R M A T P - ' , * * * * * * * * ITERATION OF PRESSURE DROP DOES NOT COVERGE * * * * * * GO TO 45 CONTINUE I F ( ( P X . G E . 7 5 . 0 ) . A N D . ( P X . L E . 1 0 0 . 0 ) ) GO TO 15 WPITE(6,16I PX FORMAT(•- * t F l 0 . 2 • PX IS OUT OF DATA R A N G E ' ) GO TO 45 N=10 I F U H B X . G T . 2 8 5 . 0 ) .OR. (PX .GT . 8 2 . 7 ) ) N=l C A L L PROP<"X,HBX ,T M , P, H,T , MD , V I , CP , K , TMC i T BX , MC BX, V IBX ,C PB X, KBX, N ) I F J N . N E . 1) GO TO 46 C A L L V I S C ( P X , T S X , MCBX, V I B X ) C A L L C 0 N 0 ( P X , T B X , MDBX. KBX) C A L L F IND ( 0 , MFR , AH X , PX ,HBX , T M , P, H, T , MD , VI , CP ,K ,TWX , F AI I, DS ,M) T F ( F A IL . N E . 0 . 0 ) GO TO 45 TFJCONT . N E . C O ) GC TO 88 N=10 I F U T W X . G T . 4 0 0 . 0 1 . O R . ( X . G T . 8 2 . 7 0 ) 1 N=l CALL P R O P ( P X , T W X , T M , P , T , H , M D , V l , C P , K , T M C t H W X , M D W X , V I W X . C P W X , K W X , N ) I F ( N . N E . 1) GO TO 49 C A L L V I S C ( P X , TUX» MQWX, VIWX) CALL C.OND(PX, TWX, MDWX, KWX) TPA=(TB+TBX ) / 2 . 0 TWA=(TW+-TWX)/2.0 PA=(PG+PX)/2.0 N=10 IF({TBA . G T . 4 0 0 . 0 ) .OR. (PA . G T . 8 2 . 7 0 ) ) N=l C A L L PROP(PA , T P A , T M , P , T , H , M D , V I , C P , K , T M C , H B A , M O B A , V I B A , C P B A , K B A , N ) I F ( N . N E . 1) GO TO 65 CALL V T S C C P A , T 3 A , MDBA, V I B A ) CALL CCND(.P.A, TB A, MCPA, KBA) CONTINUE N=10 I F U T W A . G T . 4 0 0 . 0 ) .OR. (PA . GT . 8 2 . 7 0 ) ) N= 1 CALL P R O P ( P A , T W A , T M , P , T , H , M D , V t , C P , K , T M C , H W A , M O W A , V I W A , C P W A , K W A , N ) I F ( N . N E . 1) GO TO 67 C A L L V I S C ( P A , TWA, MCWA, V TWA) CALL CONDI ".'A, TWA, MDWA, KWA) REA=VM*D/VIB PAR=(1.0—MDWA/MDBA ) * G * C * ( M D B A * * 2 ) / ( V M * * 2 ) IF(PAR . G T . C . 0 0 0 5 ) GO TO 72 FACTOR=l .0 GO TO 75 IF((PAP . G T . 0 , 0 0 0 5 ) .AND. (PAR . L E . 0 . 3 ) ) GO TO 73 W R I T E ( 6 , 7 4 ) PAR FORMAT!•-• , F 1 0 . 6 , • PAR IS TOC L A R G E ' ) GO TO 45 FACT0P=2.15*(PAR**0.1) EA=1.0/((1.82*AL0G10(REA)-l.64)**2) EF=EA*((VIWA/VIBA)**0.22) EF=FF*FACTOR P D N = ( V M * * 2 ) * ( ( E F * D L / ( 2 . 0 * M D B A * D ) ) + (MCB-MDBX)/(KDB*MDBX )) PDN=PDN*0.00001 PF=PG-PDN CHECK=PX-PF t F T ( T E S T . G F . 0 . 0 ) . A N D . (CHECK . G E . 0 . 0 ) ) GO TO 53 WRITE(6,97) PG,PX,PA,PF.CHECK,TEST FORMAT(• ' , •PGPXPAPF • , 4 F 1 0 . 4 , ' C H E C K , T E S T • , 2 F 1 5 . 6 ) t  p  49  65  67  7? 74 73 75  97  129  175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192  IF(ABS(CHFCK) . L E . 0 . 1 ) GO TO 88 IF(ABS(TEST) . L E . 0 . 1 ) GO TO 88 PX=PG-(TEST+CHECK) TEST=CHEGK GO TO 44 TFST=CHECK OIF=ABS(PX-PF) I F { O I F . L T . C . O O i ) GO TO 88 PX=PF GO TO 44 PG=(PX+PF)/2.0 TB=TBX TW=TWX HB=HBX VIB=VIBX GO TO 33 WRITE(6,22) «=ORMAT(«-«, « * * * R F S U L T * * * J ,  53  88  98 22  193  194 195 196 197 198 199 200 201 202 203 2 04 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 ?30 231 232  233  !F(BTU  93 78  79 39 14 34  ' 35 37  99  45  . EO.  CO)  GO  L(J),  TF(J),  TP<J),  PP(J)')  78  WRTTE<6,93) F G R M A T C ' t ' R E S U L T S APE IN BR TT ISH U N I T S ' ) 00 34 J =l . M I F J R T U . E O . 0 . 0 ) GO TO 79 L(J)=L(J)/25.4 TF(J)=TF(J)*9.0/5.0-460.0 TP(J)=TP(J)*9.0/5.0-460.0 P P U » =PP{ J ) * 1 4 . 7 / 1 . 0 1 3 2 5 GO TO 39 TF ( J ) =T.F ( J ) - 2 7 3 .15 TP(J|=TP{J)-273.15 WPITE(6,14) J , U J ) , T F ( J ) , T P ( J ) , PP(J) F C R M A T ( ' ' , I 10 , F12 .2 , • * * * * * > ' , 2F 10 . 2, ' • * * * * ' , F I 5.2> CONTINUE ENTH=HB-HI WATT=ENTH*MFR WRITE16.35) ENTH F O R M A T ( * - ' , ' E N T H A L P Y CHANGE ( K J / K G ) ' , F 2 0 . 2 ) WRITE('6,37) WATT FORMAT(* - * , "HEAT INPUT RATE ( K J / S E C ) ' , F 2 0 . 2 ) TPd)-TF(J) C A L L S C A L E I L , M, 1 2 . 0 , LMIN, O L , I) C A L L S C A L E C T P , M, 1 0 . 0 , TPMIN, O T P , I) DC 99 1=1, M TF{ I )^.(TF( I ) - T P M I N ) / O T P CONTINUE C A L L A X I S J O . O , 0 . 0 , 6HLENGTH, - 6 , 1 2 . 0 , 0 . 0 , L M I N , D L ) CALL AX!S(0.0,0.0,11HTEMPERATURE,11,10.0,90.0,TPMIN,OTP) C A L L L I M F ( L , T P , M, 1) C A L L L T M E f L , T F , M, 1) C A L L PLOTND GO TC 13 M=M-1 I F I M . G T . 0) GO TO 98 WRITE 1 6 , 2 5 ) FORMAT(• — ' , ' I N P U T CONOITIGN IS OUT OF R A N G E . ' ) WRITE(6,23) FORMA T ( • 1 ' » • •) STOP ;  25 13 23  TO  END  130  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  C **  SUBROUTINF FOP CALCULATING LOCAL WALL TEMPERATURE * * SUBROUTINE F I N D ( D , M F R , A H , P G , H R , T M , P , H , T,MD,VI,CP,K,TW,FAIL,DS,M) REAL P ( 3 0 ) , T M ( 3 0 ) , M D ( 3 0 , 1 0 0 ) , H 1 3 0 . 1 0 0 ) , C P ( 3 0 , 1 0 0 ) REAL T ( 3 C , 1 0 C I , V H 30.100), K(30,100) REAL MFR, MDB, MOW, KB, KW RFAL P F , PR, NUO, NUL L O G I C A L T R Y 1 , T R Y 2 , T R Y 3 , T R Y 4 , T R Y 5 , TRY6 I F ( A H . C E . 0 . 0 ) GO TO 77 WRITE(6,79) 79 FORMAT!•-', ' * * * T H I S SUBROUTINE FOP THE C A L C U L A T I C N OF T H E ' , 1 •• HEATING PROCESS C N L Y * * * * ) GO TO 13 77 FAIL=0.0 DL=D A=3.1415926*0*0/4.0 AL=3.1415926*0*DL I F U P G . L E . 1 0 0 . 0 ) . AND. (PG . G E . 7 5 . 0 ) ) GO TO 74 W R I T E I 6 . 3 4 ) PG 34 FORMAT(•-•, F10.3, • PG IS OUT CF DATA R A N G E . ' ) GO TO 13 74 I F K H R . L E . 1 6 0 0 . 0 ) . A N D . (HB . G E . - 9 5 . 0 ) ) GC TO 75 W R I T E < 6 , 3 6 ) HB 36 FORMATC-', F10.3, • HB IS CUT CF DATA R A N G E * ' ) GO TO 13 75 N=10 I F ( ( H « . G T . 2 8 5 . 0 ) . C R . IPG . G T . 8 2 . 7 0 ) ) N=l CALL P R O P ( i > G , H B , T M , P , H , T , M O , V I ,CP , K , TMB , TB , MPB , V I 5 ,C.PB , K B , N ) IF(N . F O . 10) GO TO 66 CALL V I S C I P G , T B , MCB, V I B ) C A L L C C M n i P G , B , MCB, KB) 66 RF=4.0*MFR/(3.1415926*D*VI8) I F I R E . G T . 50CO0.O)GO TO 63 WRITE(6,51) RE 51 FORMAT!.'-', F10.0, ' RE IS OUT CF OPERATION RANGF' ) GO TO 13 63 PR=CPR*VIB/Ke ' TPYl=.FALSE. TRY 2 = . F A L S E . TRY3=.FALSE. TRY4=.FALSE. TRY5=.FALSE. TRY6=.FALSE. F P = { 1 . 0 / 8 . 0 ) / ( ( 1.8 2 * A L 0 G n < R E ) - l . 6 4 ) * * 2 ) NUO=FF*RF*PR/(12.7*S0RT(FP » * ( P R * * ( 2 . 0 / 3 . 0 ) - l . 0 1 + 1.07) X=OL*(PLOAT(M)-0.5) FACTOP=0.95+0.95*1I0/X»**0.8) COO=FACTO *NUO*KB/D TW=TR+4H/(C0C*AL*DS) 73 IFUTW-TBt .LE. O.C) TW=TB+0.5 I F ( ( T W . L E . 1 5 0 0 . 0 ) . A N D . (TW . G E . 2 7 5 . 0 ) ) GO TO 78 W R I T E ( 6 , 3 8 ) TW 38 FORMAT!'-', FlO.3, • TW IS OUT OF DATA RANGE*) GO TO 13 78 N-10 I F U T W . G T . 4 0 0 . 0 ) . O R . (PG . G T . 8 2 . 7 0 ) ) N=l C A L L P R O P ( P G , T W , T M , P , T , H , M D , V I , C P , K,TMW,HW,MDW,VIW,CPW,KW,N) I F ( N . N E . II GO TO 88 CALL V I S C I P G , TW, MOW, VIW) T  D  131  59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 fll 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116  88  53 61 58 59  56 57  20 41 22 43  81  82 92  83 84  CALL C O N D ( P G , TW, MOW, KW) RTB=TR/TMB RTW=TVi/TMW PN=0.0 I F I R T B . G E . 1.2) GO TO 59 TFJRTW . L F . 1.0) GO TO 59 I F U P R . G E . 0 . 8 5 ) . A N D . (PR . L E . 6 5 . 0 ) ) GO TO 61 W R I T E ( 6 , 5 3 ) PR FORMAT( • » F10.2, • PR IS OUT OF OPERATION R A N G E ' ) GC TO 13 I F ( ( ( P T B . G T . 0 . 0 9 ) . A N D . (RTB . L T . 1 . 2 ) ) .AND. 1 U R T W . G T . 0 . 0 9 ) . A N D . (RTW . L T . 4 . 0 ) ) ) GO TO 59 W R I T E ( 6 , 5 8 ) RTB, RTW FORMAT(• 2F10.1, • RTB OR RTW IS OUT OPERATIONAL RANGE.') GO TO 13 IFI I RT Vi . G T . 1 . 0 ) . A N D . (RTW . L E . 4 . 0 ( 1 PN = 0 . 2 2 + 0 . 18*RTW I F ( ( R T B . G E . 1.0) . A N D . (RTB . L E . 1 . 2 1 ) PN=PN+(5.0*PN-2.0)*(1-RTB) I F ( ( R T B . G E . 1.2) .OR. (RTW - L E . 1 . 0 ) ) PN=0.4 I F ( P N . N E . 0 . 0 ) GO TO 57 W I T E ( 6 , 5 6 ) PN F O R M A T ! ' - ' , ' P N IS NOT S P E C I F I E D ' , F10.4J GO TO 13 CONTINUE CPA=!HW-HB)/(TW-TB) P.CP=CPA/CPB I F U R C P . G E . 0 . 0 2 ) . A N D . ( RCP . L E . 4 . 0 ) ) GO TO 41 W R I T E ( 6 , 2 0 ) RCP FORMAT!•-', F10.2, • RCP IS OUT CF OPERATICN R A N G E ' ) GO TO 13 RMD=MDW/M08 IF(RMD . G T • 0 . 0 0 ) GO TO 43 W R I T F ( 6 , 2 2 ) RMD FORMAT!'-', F10.2, ' RMD IS SMALLER THAN 0 . 0 9 . ' ) GO TO 13 EP=(RMD**0.3)*(RCP**PN) HA=COO*FR*AL+(TW-TBI DF=ABS(HA-AH)/AH I F ( D E . L T . 0 . 0 0 0 0 5 ) GO TO 99 I F ( T R Y 5 . O R . TRY6) GO TO 93 I F I T R Y 3 . O R . T R Y 4 ) GO TO 92 I F ( ( H A - A H ) . G T . 0 . 0 ) GO TO 81 TRY1=.TRUE. I F { T R Y 2 I GO TO 92 TW=TW+10.0 GO TO 82 TRY2=.TRUE. I F ( T R Y ! ) GO TO 92 TW=TW-10.0 I F ! . N O T . TRYI . O R . . N O T . TRY2) GO TO 73 T F ! 1 H A - A H ) . G T . 0 . 0 ) GO TO 83 TRY3=.TRUE. I F I T R Y 4 ) GO TO 93 TW=TW+5.0 GO TO 84 TRY4=.TRUE. I F 1 T R Y 3 ) GO TO 9 3 TW=TW-5.0 I F ! . N O T . . TRY3 . O R . . N O T . TRY4) GO TO 73  117 118 119 120 121 122 123 124 125 126 127 128 129  93  85 86 13 99  I F U H A - A H ) . G T . 0 . 0 ) GO TO 85 TH=TWfl.0 TRY5=.TRUE. GO TO 86 TW=TW-1.0 TRY6=.TRUE. I F ( . N O T . TRY5 . O R . . N O T . TRY6) GO TO 99 FAILM3.0 ER= 1.0 DS=ER RETURN END  '  1  GO  133  1 2 3 4 5 6 7 8 9 10 11 12  C * * SUBROUTINE FOR INTERPOLATING TH FR MO PHYSIC A L PROPERTIES FROM THF TABLE * C * * THE SUBROUTINE S fiI NT USED HERE IS A V A I L A B L E IN THE UBC COMPUTER LIBRARY SUBROUTINF P " O P I P G , H G » T M P , H , T , M D , V I , C P , K , T M C , T C , M D C , V T C . C P C , K C , N ) REAL P ( 3 0 ) , H I 3 0 , 1 0 0 ) , T ( 3 0 , l O O ) , TM(30) RF AL M C ( 3 0 , 1 0 0 ) , V I ( 3 0 , 1 0 0 ) , C P C 3 0 , 1 0 0 1 . K ( 3 0 , 1 0 0 l REAL X ( 6 0 ) , Y ( 6 0 ) , 0 ( 1 3 ) RFAL T I , M O I , V I I , C P I , KI REAL T F , MDF, V I F , C P F , KF REAL T C , MOC, V I C , C P C , K C , TMC p=4 I F ( N . E O . 10) M=2 NN=35 f  13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 20 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58  IF(N . N E . 10) NN=58  33 22  10  20  30  *  81  40  50  99  15  DO 33 !=N, 30 CP=PG-P(I) I F ( O P . E O . 0 . 0 ) TMC = TMI 11 I F ( D P . L T . 0 . 0 ) TMC=( ( P G - P ( I - l ) ) / ( P ( I ) - P ! I - l ) ) ) * ( T M ( I ) - T M ( I - l ) 1 TM(I-l) ! F ( D P . L E . 0 . 0 ) GO TO 22 CONTINUE DO 10 J = l , NN X(JI=H(I,J) Y(J)=T(I,J) CCNTINUE TF= SAI NT(NN , X, Y, H G , M, 0) DO 20 J = l , NN YIJ)=«0(T,J) CONTINUF. MDF= S A I N T ( N N , X, V , HG, M, 0) DO 30 J = l , NN Y(JI=CP(I,J) CONTINUE C P F = S A I N T ( N N , X , Y , HG, M, 0) I F ( O P . N E . 0 . 0 ) GO TO 81 TC=TF MDC=MDF CPC=CPF I F ( N . N E . 1 0 ) GO TO 88 I F ( N . N E . 1 0 ) GO TO 99 DO 40 J = l . NN Y(J)=VI(I,J) CONTINUF V I F = S A I N T ( N N , X, Y , H G , M, 01 DO 50 J = l , NN Y(J)=K(I,J) CONTINUF K F = S A I N T ( N N , X, Y , HG, M, 0) I F I O P . N E . 0 . 0 ) GO TC 99 VIC=VTF KC=KF GO TO 73 00 15 J = l , NN X(J)=H((I-1),J) Y(J)=T((I-l),J) CONTINUE TI = SAI N T ( N N , X, Y , HG, M, 0) DO 25 J = l , NN Y(J) = MD((I-l ),J)  )+  134  59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85  25  CONTINUE MDI = SA I NT ( NN » X , Y H G M, 0» DO 35 J = l , NN Y(JJ=CP((T-ll,J) CONTINUE C P I = S A I N T I M N , X, Y , HG, M, 0) I P ( N . N E . 10) GO TO 66 DO 45 J = l , NN Y(J)=VI((I-l),J) CCNTINUE V I I = S A I N T ( N N , X, Y , H G , M, 0) DO 55 J = l , NN Y(J)=K((I—1),J) CONTINUE K I = S A T N T ( N N , X, Y , H G , M, Q) FACTOR=(PG-PII-l)»/(P(I)-P(I-l)) TC=FACTOR*(TF-TI)+TI MPC, = FACTOR* (VCF-MO II+M0I CPC=F6CT0R*(CPF-CPI)+CPI I F ( N . N F . 10) GO TO 88 VIC=FACTOR*(VIF-VII)+VII KC=FACTOR*(KF-KI)+KI GO TO 73 VIC=0.0 KC=0.0 RETURN END v  35  45  55 66  88 73  t  135  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  C **  SUBROUTINE FOR C A L C U L A T I N G V I S C O S I T Y * * SUBROUTINE V I S C C P G , TG» OG, U» j REAL A ( 5 , 5 I | A<I,1)=0.24856612 A(I,2)=0.004894942 A I 2 t I) =- 0 . 3 733C066 A(2,2)=l.22753488 A<3,1,=0.363854523 A(3,2)=-C.774229021 Al.4,1 ) = - 0 . 0 6 3 9 0 7 0 7 5 5 A(4,21=0.142507049 TC=TG/304.2 DC=DC/468.0 UT=lSORT(TCI>*(1.0E-8>*(2722.46461-1663.46068*(1.O/TCt• 1 466.920556*{1.0/(TC*TC))) X=0.0 DO 71 M = l , 4 DO 71 N = l , 2 X=X+A(M,N)*(DC**MI/(TC**JFLOAT(N-t.III CONTINUE Y=EXP(X) U=Y*UT RETURN END  j  71  1  136  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32  C **  71  SUBROUTINE FOR CALCUALTING THERMAL CONDUCTIVITY * * SUBROUTINE CONDIPG, T G , DGt K) REAL A ( 5 , 5 ) REAL K A(1,1)=1.18763738 A(l,2>=-2.73693975 A(1,31=2.52042816 A(2,l)=-2.30778414 A(2 , 2 » = 4 . 4 1 9 9 4 8 7 2 A(2,3)=-0.0915667463 AC3. 1 ) = 2. 61294395 A(3,2)=-4.0C329344 A(3,3)=-i.35345324 Al.4,1 , = - 1 . 2 8 3 2 5 5 9 A(4,2)=2.13659771 A(4,3)=0.376570783 A(5,11=0.219542368 A(5,2)=-0.402133782 A«5,3)=0.000 TC=TG/304.2 DC=DG/468.0 EXK><1.OE-6J*(57 .2860124-78.14 35192*(1.O/TC)+ I 4 9 . 1 8 7 1 1 8 4 * U . 0 / ( T C * T C ) I —11 . 5 0 9 43 47 *( I . 0 / ( T C * * 3 . 0 ) ) >*SQRT(TC, X=0.0 DC 71 M = l , 5 DO 71 N = l , 3 X=X+A(M,Ni*(CC**M,/(TC**(FLOATtN-l)lJ CONTINUE Y=EXP(X» K=Y*EXK RETURN END  137  APPENDIX I I .  Typical Calculation of Ideal Overall E f f i c i e n c y  1. Ideal Overall E f f i c i e n c y of Duel-reheat Cycle Data required f o r calculation;: Water 1200 psia Temperature, °F 815 567.19 (saturation) 245 140.6  Enthalpy, Btu/£bm 1389.03 571.85 (liquid) 215.00 110.59  Water 70.3 psia Temperature, °F 567.19 302.93 (saturation) 245 140.6  Enthalpy, Btu/£bm 1315.4 272.74 (liquid) 215.00 110.59  Carbon Dioxide 85.5 Bar Enthalpy, Btu/£bm 272.70 203.72 131.18 116.05 110.26  Temperature, °F 845 597.19 333.0 280.0 260.0 a) Steam Generation_(steam  produced by 1.0 &bm carbon dioxide)  A l l carbon dioxide i n temperature  range of 597.19°F to 845°F  i s required f o r producing H.P. steam (see steam generation process path as shown i n Figure 43).  Therefore, the enthalpy balance i s  (1.0)(272.7 - 203.72) = x (1389.03 - 571.85) x = 0.08441  bm H.P. steam  ,  .  If H.P. steam were expanded i s o t r o p i c a l l y from 1200 psia to 75.0 p s i a , the ideal f i n a l state enthalpy i s 1117 Btu/&bm (from Steam Enthalpy  138  Versus Entropy diagram). Therefore, f o r a turbine e f f i c i e n c e of 90.0%, the actual f i n a l state enthalpy i s h  f  = 1389.03 - (0.9)(1389.03 - 1117) = 1144.2 Btu/£bm  .  Enthalpy balance f o r heating H.P. and L.P. steam from 302.93°F to 567.19°? by carbon dioxide i s (203.72 - 131.18) = 0.08441[(571.85 - 272.74) + (1315.4 - 1144.2)] + y(1315.4 - 272.74)  ,  y = 0.0315 £bm L.P. steam. Enthalpy of feed water which i s heated by 280°F to 333°F carbon dioxide i s calculated from (131.18 - 116.05) = 0.08441(272.74 - h ) + 0.03150(272.74 - tu) ±  ,  h. = 142.21 Btu/£bm for feed water, l [12] Heat transferred to coolant loop  1661.30 x 10  6  i s given by  watt = 5.67 x 10  9  Btu/hr  .  Therefore, mass flow rate of s u p e r c r i t i c a l carbon dioxide coolant i s  M  C0  = 5.67 x 10 /(272.7 - 110.26) 9  2  = 3.4905 x 10  H.P. steam flow rate i s  7  Jtbm/Hr.  139  "HP = ° -  0 8 4 4 1  M  co  2  = 2.9463 x 10 £bm/Hr. 6  L.P. steam flow rate i s  \v  = °-  0 3 1 5 0  M  co  2  = 1.0995 x 10 &bm/Hr. 6  Total L.P. steam flow rate which includes reheated steam i s = 2.9463 x 10" + 1.0995 x 10* 4.0458 x 10 &bm/Hr. 6  Recuperation enthalpy balance (see Figure 44) i s (1.0995 x 10 + 2.9643 x 10 )(142.21 - 59.71) = 1^(1105 - 70.0) 6  6  ,  = 322500 JLbm/Hr recuperating steam.  b) Ideal_Overall_Efficiency_^calcu  )  From the flow rates at the i n l e t s and outlets of the tubines, and their corresponding enthalpies, shaft work output can be calculated as  W  SHAFT  =  ^  ( h  '  M  )  INLET " I <  h  *  M  )  OUTLET  = 2.9463 x 10 (1389.03 - 1144.2) 6  + 4.0458 x 10 (1315.4) - 322500(1105) 6  - (4.0458 x 10 - 322500)(1010.0) 6  = 1.9263 x 10 Btu/Hr. 9  For 100% pump e f f i c i e n c y , pump work f o r feed water c i r c u l a t i o n i s  140  W  = AP • M/p  = [(1200 x .144)(2.9463 x 10 ) + (70.3 x 144)(1.0995 x 10 )]/62.4 6  6  = 8.3374 x 10 Ft-Abf/Hr 9  = 1.0714 x 10 Btu/Hr. 7  Therefore, turbine e f f i c i e n c y i s eff = (1.9263 x 10 - 1.0714 x 10 )/5.67 x 10 9  7  9  = 33.80%. For 100% pump e f f i c i e n c y , pump work f o r coolant c i r c u l a t i o n i s W  c  = AP • M/p  = (210 x 144)(3.4905 x 10 )/31.419 7  =3.3595 x 1 0  1 0  Ft-£bf/Hr  = 4.317 x 10 Btu/Hr. 7  Therefore, ideal o v e r a l l e f f i c i e n c y i s  (1.9263 x 10 e  f  f  - 1.0714 x 10  - 4.317 x 10 )  — .  =  5.67 x 10 = 33.02%.  2. Ideal Overall E f f i c i e n c y of Pickering Station The calculation i s based on the turbo-generator heat balance of Figure 50  ri21  T821 , and the expansion l i n e s shown i n Figure 51 . The mass flow  rate at the i n l e t of the H.P. turbine i s 5964622 Jlbm/Hr, and the flow rates at the outlet are 550833, 91503, 318836, 190, and 210 bm/Hr.  141  There i s 3050 &bm/Hr drain l o s s . high wetness of the H.P. steam. t o t a l flow rate (0.05%).  The drain loss i s expected because of However, i t i s a small percentage of the  From the flow rates and t h e i r corresponding  enthalpies, the power output of the H.P. turbine can be calculated and is W = 7(h • M) . HP ^ 'inlet TTT1  W__  L  - Y(h • M) outlet L  = 1201.8(5964622 - 3050)  HIT  - 1083.8(5550833) - 319.42(91503) - 1117.28(318836) - 1201.8(210 + 190) = 7.6269 x 10  8  But/Hr.  Similarly, the power output of the L.P. turbine stage can be calculated. The i n l e t flow rate i s 4819224 £bm/Hr, and the outlet flow rates are (2080 - 210 - 190), 11816, 33860, 96680, 225833, 180707, 173393, and 180637 £bm/Hr.  The main exhaust flow rate i s calculated to be  3914738 Jtbm/Hr based on the "no mass l o s s " assumption.  The enthalpy of  the main exhaust steam i s interpolated from the expansion l i n e at the  \82 1 pressure of 1.5 i n Hg (see Figure 51 and  .  The associated steam wetness  enthalpy i s 10% and 1000 Btu/£bm respectively.  power of the L.P. turbine stage i s equal to LP  = £  W  = 1250.28(4819224)  W  ( h  * inlet " £ M )  ( h  • outlet M )  jLilr  - 1201.80(2080 - 210 - 190) - 1068.37(11816)  Therefore, the output  142  - 100.79(33860) - 120.56(96680) - 1087.06(225833) - 1116.08(180707) - 1163.65(173393) - 1210.71(180637) - 1000.00(3914738) = 1.2133 x 10 Btu/Hr. 9  The t o t a l shaft work i s w  i™  + T , = 1-9760 x 10 . W  9  For 100% pump e f f i c i e n c y , the pump work for feed water c i r c u l a t i o n i s  W  feed  =  £  ( A P  '  M  /  p  )  = (38.0 - 1.5 x 0.491)(144)(4647277)/62.4 + (700 - 38)(144)(5969862)/62.4 = 9.5197 x 10  9  Ft-Jlbf/Hr  = 1.2236 x 10 Btu/Hr. 7  Therefore, the turbine cycle e f f i c i e n c y i s 1.9760 x 10 - 1.2236 x 10 9  eff =  5.67 x 10  7  9  = 34.61%.  The heavy water coolant i s circulated at a rate of 61300000 ilbm/hr, and [12] the pressure drop i s (1443 - 1254) psia  . For 100% pump e f f i c i e n c y ,  the pump work for heavy water coolant c i r c u l a t i o n i s  143  W = AP COOLANT =  • M/o ' M  [(1443 - 1254) x 144] • (61300000) 54.476  = 30625 x 1 0  Ft-Jibm/Hr  1 0  = 3.9365 x 10  Btu/Hr.  7  F i n a l l y , the o v e r a l l e f f i c i e n c y i s eff = (7.629 x 10 -f 1.2133 . x 10 ) - (1.2236 x 10 + 3.9365 x 10 ) 5.67 x 10 8  = 33.94%.  9  7  7  

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