<%BANNER%>

Oscillatory Behavior in Boiling Water Reactors

Permanent Link: http://ufdc.ufl.edu/UFE0003800/00001

Material Information

Title: Oscillatory Behavior in Boiling Water Reactors
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0003800:00001

Permanent Link: http://ufdc.ufl.edu/UFE0003800/00001

Material Information

Title: Oscillatory Behavior in Boiling Water Reactors
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0003800:00001


This item has the following downloads:


Full Text

PAGE 1

OSCILLATORY BEHAVIOR IN BOILING WATER REACTORS By THOMAS KEITH BENTLEY A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2004

PAGE 2

Copyright 2004 by Thomas Keith Bentley

PAGE 3

To my Family for their love and support.

PAGE 4

iv ACKNOWLEDGMENTS I would like to acknowledge everyone who assisted me in the development and completion of this thesis. I would like to thank my committee members (Drs. Samim Anghaie, Edward Dugan, and Sherif Sherif) fo r their supreme guidanc e and direction to make this analysis a quality thesis. Their contributions have helped me to achieve my fullest potential. I would al so like to thank Charlie Heck and everyone at Global Nuclear Fuel in Wilmington, N.C., for giving me the in spiration and support to make this thesis a reality, and also allowing me the use of th eir computer codes and resources. Without everyone’s help and encouragement, the comp letion of this thesis would have been impossible.

PAGE 5

v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES..........................................................................................................viiii LIST OF FIGURES...........................................................................................................ix KEY TO EQUATION SYMBOLS.................................................................................xiv ABSTRACT.....................................................................................................................xv i CHAPTER 1 INTRODUCTION........................................................................................................1 Boiling Water Reactor Description..............................................................................2 Boiling Water Reactor Evolution..........................................................................2 Boiling Water Reactor Core Flow.........................................................................3 Flow pattern....................................................................................................4 Channel flow characteristics..........................................................................6 Thermal-Hydraulic Instability......................................................................................7 Flow Oscillation Types..........................................................................................8 Buoyancy-wave oscillations...........................................................................8 Density-wave oscillations..............................................................................8 Flow oscillations due to compressibility........................................................9 Flow oscillations coupled with thermal hysteresis.........................................9 Boundary Condition Interaction..........................................................................10 Boiling Water Reactor Instability Analysis................................................................10 Boiling Water Reactor System Safety Concern..................................................11 Mechanical effects........................................................................................11 Thermal effects.............................................................................................12 Transients that Exhibit HighPower, Low-Flow Scenarios.................................14 Start-up transient..........................................................................................15 Loss-of-flow transient..................................................................................16 Purpose of Analysis....................................................................................................17 2 PROBLEM DESCRIPTION......................................................................................19 Project Model..............................................................................................................19

PAGE 6

vi General KKL Description....................................................................................19 Regional Instability Tests Conducted at KKL.....................................................20 Analysis Tools............................................................................................................21 Computer Program PANAC................................................................................21 Computer Program CRNC..................................................................................22 Computer Program HyCA...................................................................................22 Computer Program TRACG................................................................................22 Model Nodalization....................................................................................................25 Establishment of Computational Points......................................................................26 Critical Eigenvalue Calibration...........................................................................28 Rod-Line Generation...........................................................................................29 Channel Grouping...............................................................................................30 Assumptions...............................................................................................................31 Steady-State Initialization...........................................................................................31 Transient Analysis......................................................................................................32 Unstable Steady-State Operating Conditions......................................................33 Stable Steady-State Operating Conditions..........................................................34 3 STEADY-STATE RESULTS AND DISCUSSION..................................................35 Results from PANAC.................................................................................................35 Initial MCPR.......................................................................................................35 Initial Axial Core Power Distributions................................................................35 Results from CRNC....................................................................................................36 Results from HyCA....................................................................................................38 Results from TRACG.................................................................................................38 4 OSCILLATORY BEHAVIOR RE SULTS AND DISCUSSION..............................41 Global Behavior..........................................................................................................41 Local Power Behavior................................................................................................46 Local Thermal-Hydraulic Behavior............................................................................51 5 OSCILLATORY CHARACTERISTIC RESULTS and DISCUSSION....................57 Measurement Process.................................................................................................57 Rates of Growth/Decay...............................................................................................59 Frequency Results.......................................................................................................62 Comparison to KKL Frequency Test Results.............................................................65 Fuel Safety-Limit Concerns........................................................................................65 6 SUMMARY, CONCLUSIONS AND FUTURE WORK..........................................67 APPENDIX A CHANNEL GROUPING MAPS................................................................................70

PAGE 7

vii B FUEL CHANNEL SPECIFICATIONS.....................................................................74 LIST OF REFERENCES...................................................................................................75 BIOGRAPHICAL SKETCH.............................................................................................77

PAGE 8

viii LIST OF TABLES Table page 2-1 Steady-state operating conditio ns of the KKL instability tests................................20 2-2 Steady-state operating conditio ns of the computational points................................33 2-3 Flow perturbations applied to each computational point for a given RL.................34 5-1 Estimated elapsed time for the unstabl e computational points to experience a loss of thermal margin.........................................................................................................66 6-1 Rates of growth for the two computational points requi ring a 1% out-of-phase flow perturbation to de velop oscillations.........................................................................67 B-1 Fuel channel material compositions.........................................................................74 B-2 Fuel channel dimensions..........................................................................................74

PAGE 9

ix LIST OF FIGURES Figure page 1-1 Cut-out of a typical BWR vessel................................................................................4 1-2 Cross-section of a BWR showing the flow direction of the liquid water...................5 1-3 Cross-section of a jet pump........................................................................................6 1-4 Generic 8 by 8 fuel channel viewed from the top.....................................................12 1-5 Generic 8 by 8 fuel channel viewed from the side...................................................13 1-6 Generic boiling curve...............................................................................................15 2-1 Power-flow map for KKL showing the regions with higher probability of experiencing an instability event an d the test points as green boxes.......................20 2-2 Three-dimensional nodaliz ation of the vessel component.......................................26 2-3 One-dimensional nodalization of the fuel channel component................................27 2-4 Iterative process between the nuclear and thermal-hydraulic solutions...................29 2-5 Power-flow map showing the computa tional points relative to the KKL test points and regions one and two from the KKL power-flow map.......................................30 3-1 Initial MCPR as a f unction of initial core flow........................................................36 3-2 Steady-state axial core power distributions for RL3................................................37 3-3 Radial power map generated by CRNC for RL3 (half-core symmetry)...................37 3-4 Hybrid power map generated by CRNC for RL3 (half-core symmetry)..................38 3-5 Channel grouping map generated by HyCA for RL3...............................................39 3-6 Total core mass flow steady-state convergence for the computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3 (core power = 1286 MWth)...............................................................................................39

PAGE 10

x 3-7 Dome pressure steady-state converg ence for the computational point of 25.2% of rated initial core fl ow and 42.7% of rated initial core power on RL3 (core power = 1286 MWth).............................................................................................................40 3-8 Core inlet temperature steady-stat e convergence for the computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3 (core power = 1286 MWth)...............................................................................................40 4-1 Computational points showing the inherently unstable operating conditions...........41 4-2 Total core mass flow transient resu lts for the inherently unstable computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3...........................................................................................................................4 2 4-3 Total core power transi ent results for the inherently unstable computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3......42 4-4 Dome pressure transient results of the dome pressure for th e inherently unstable computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power on RL3...................................................................................................43 4-5 Core inlet temperature transient resu lts for the inherently unstable computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3...........................................................................................................................4 3 4-6 Total core reactivity transient resu lts for the inherently unstable computational point of 25.2% of rated inti al core flow and 42.7% of rated initial core power on RL3...........................................................................................................................4 4 4-7 Total core mass flow transient results for the inherently stable computational point of 24.4% of rated ini tial core flow and 33.5% of rate d initial core power on RL1 following the instantaneous flow perturbation.........................................................44 4-8 Total core power transi ent results for the inherently stable computational point of 24.4% of rated initial core flow and 33.5% of rated initial core power on RL1 following the instantaneous flow perturbation.........................................................45 4-9 Dome pressure transient results for the inherently stable computational point of 24.4% of rated initial core flow and 33.5% of rated initial core power on RL1 following the instantaneous flow perturbation.........................................................45 4-10 Core inlet temperature transient resu lts of the core inlet temperature for the inherently stable computational point of 24.4% of rated initial core flow and 33.5% of rated initial core power on RL1 followi ng the instantaneous flow perturbation.46 4-11 Channel grouping map for RL3 with its associated first harmonic flux solution (2-D projection)................................................................................................................47

PAGE 11

xi 4-12 First minute of the tran sient event: Power response for the most responsive fuel channels of computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power.............................................................................................48 4-13 First to third minute of th e transient event: Power response for the most responsive fuel channels of computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power........................................................................................48 4-14 First minute of the tran sient event: Symmetric fuel channel power responses of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................49 4-15 Limit cycle of the transient event: Symmetric fuel channel power responses of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................50 4-16 Limit cycle of the transient event: Symmetric fuel channel power responses and total core power response ( bold line) of computationa l point of 25.2% of rated initial core flow and 42.7% of rated initial core power............................................50 4-17 First minute of the tr ansient event: Pressure distribution for channel 27 of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................51 4-18 Limit cycle of the transient event: Pressure distributi on for channel 27 of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................52 4-19 Limit cycle of the transient event: Outlet mass flow rate for channel 27 of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................52 4-20 First minute of the transient event: Av erage fluid density distribution for channel 27 of computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power......................................................................................................53 4-21 Limit cycle of the transient event: Av erage fluid density distribution for channel 27 of computational point of 25.2% of rated in itial core flow and 42.7% of rated initial core power................................................................................................................54 4-22 First minute of the tran sient event: Void fraction distribution for channel 27 of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................54 4-23 Limit cycle of the transient event: Void fraction distribution for channel 27 of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................55

PAGE 12

xii 4-24 First minute of the tran sient event: Axial power di stribution for channel 27 of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................55 4-25 Limit cycle of the transient event: Axial power distributi on for channel 27 of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................56 4-26 Limit cycle of the transient event: Total channel power for channel 27 of computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power................................................................................................................56 5-1 Limiting case for the measurement ra nge in a time domain before any significant responses in the core operat ing parameters. Most responsive fuel channel and total core power responses of computational poi nt 30.0% of rated initi al core flow and 69.4% of rated initial core power.............................................................................58 5-2 Limiting case for the measurement ra nge of avoiding flatte ning regions inside measurement region. Most responsive fuel channel and total core power responses of computational point 24.8% of rated init ial core flow and 37.8% of rated initial core power................................................................................................................58 5-3 Example of measurement range applied to an inherently stable computational point. Most responsive fuel channel and total core power responses of computational point 24.4% of rated initia l core flow and 33.5% of rated initial core power..........59 5-4 Symmetric fuel channel power respons es of computational point of 35.0% of rated initial core flow and 66.1% of rated init ial core power within the measurement range.........................................................................................................................6 0 5-5 Rates of growth/decay as functions of initial core fl ow of most responsive channel power oscillations.....................................................................................................61 5-6 Rates of growth/decay as functions of initial core pow er of most responsive channel power oscillations.....................................................................................................61 5-7 Power-flow map showing the thres hold between stable and unstable operating conditions for this particular model.........................................................................62 5-8 Frequency response as a function of initial core flow of the most responsive channel power oscillations.......................................................................................63 5-9 Frequency response as a function of initial core power of the most responsive channel power oscillations.......................................................................................64 5-10 Time delay between the proceeding channe l flow oscillation peaks to the associated channel power oscillation peaks...............................................................................64

PAGE 13

xiii 5-11 Comparison of the KKL test point fre quency results and the computational test point results..............................................................................................................65 A-1 Channel-grouping map for RL1 generated by HyCA..............................................70 A-2 Channel-grouping map for RL2 generated by HyCA..............................................71 A-3 Channel-grouping map for RL3 generated by HyCA..............................................71 A-4 Channel-grouping map for RL4 generated by HyCA..............................................72 A-5 Channel-grouping map for RL5 generated by HyCA..............................................72 A-6 Channel-grouping map for RL6 generated by HyCA..............................................73 A-7 Channel-grouping map for RL7 generated by HyCA..............................................73

PAGE 14

xiv KEY TO EQUATION SYMBOLS a = all noncondensible gases b = boron c = concentration e = internal energy f = saturated liquid g = gravity h = internal enthalpy i = interface j = neutron energy group l = liquid phase n = delayed neutron precursor group q = heat transfer rate s = saturated steam t = time u = average neutron speed v = velocity w = wall C = delayed neutron precursor concentration D = diffusion coefficient J = total number of neutron energy groups

PAGE 15

xv N = total number of delaye d neutron precursor groups P = pressure = void fraction jn = delayed neutron precursor group with average neutron energy in group j = density = neutron flux = shear tensor = gas phase = average number of neutrons from fission = decay constant = fraction of delayed neutrons emitted from fission f = macroscopic fission cross-section s = macroscopic scattering cross-section t = total macroscopic cross-section = interfacial mass transfer rate = fraction of neutrons emitted from fission

PAGE 16

xvi Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering OSCILLATORY BEHAVIOR IN BOILING WATER REACTORS By Thomas Keith Bentley May 2004 Chair: Samim Anghaie Major Department: Nuclear and Radiological Engineering Boiling Water Reactor (BWR) instability has been an operational concern since initial BWR designs. Preliminary tests conducted at Argonne National Laboratories (ANL) concluded that BWR operation was uns table for low operating pressures but was not a problem for the high pressures experi enced during normal operation of commercial BWRs. However, oscillations in the opera ting parameters have been observed in a number of cases during BWR operation. Th e primary conditions that were found to contribute to oscillatory beha vior for these cases were lo w-flow, high-power scenarios. This analysis characterized the oscillatory response of the reactor for changes in core power and flow. This analysis fo cused primarily on the power response and characteristics during an instability event. The power response was characterized by the rate of growth or decay of its oscillations to determine its degree of stability, and it was also characterized by the frequency of its os cillations. Loss of thermal margin when the critical power of a fuel channel is exceeded is the primary safety concern when

PAGE 17

xvii oscillations exist in a BWR. The potentia l of exceeding fuel safety limits was also considered for this analysis. The main results of this analysis were th e degree of stability and frequency for each computational point. The operating parameters became more stable with a decrease in core power or an increase in core flow. The frequencies of the power oscillations increased linearly with increasing flow and we re independent of the initial core power. In all of the cases, fuel safety limits we re not exceeded assuming a properly working reactor protection system. The main purpose of this analysis was to gain a better understanding of the phenomena that contribute to BWR instability.

PAGE 18

1 CHAPTER 1 INTRODUCTION In this era of greater ecological emph asis, dwindling fossil fuel supply, and increased electric power demand, it becomes n ecessary to use to the fullest extent possible all technological adva nces available to us. Nu clear fuel—replacing coal, oil, and gas—provides the most economi cal, the most reliable, and the most stabilized power source of the era. [1:1.1] ‘Stabilized power’ in this sense ironically does not refer to the potential risk of coupled nuclear-thermal-hydrau lic instability occurrences that can exist in operating nuclear power plants. The operation of nuclear power plants is closer today to allowable fuel safety limits than ever before, crea ting new engineering problems to be solved. Presently, 104 nuclear power reactors are operating in the United States of America (US) comprised of both Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs). Lamarsh [2] gives a good genera l description of the many features distinguishing the two types of reactors. A primary difference between PWRs and BWRs is the existence of bulk boili ng inside the core of a BWR. A PWR is maintained at sufficiently high pressures (on the order of 15 MPa) to prevent bulk boiling inside the core for normal operating temperatures. The operating pressures for a BWR (on the order of 7 MPa) are approximately half as in a PWR. Both PWRs and BWRs use water as their coolant. The existence of bulk boiling in a BWR is a huge benefit for heat removal from the core, but it also adds co mplication because of the presence of twophase flow. Two-phase flow in BWRs has raised concern that unstable conditions can result from uneven and random formati on and movement of the steam bubbles.

PAGE 19

2 Boiling Water Reactor Description The BWR is characterized by the presence of bulk boiling inside the core. All of the BWRs operating in the US were de signed and developed by General Electric Company (GE). Five major designs of GE BWRs operate in the US today. Lahey and Moody [3] give a good historical evolution of BWRs, and a brief summary is given below. Boiling Water Reactor Evolution The BWR/1 design was introduced in 1955. The BWR/1 plants we re essentially a series of prototypes that incl uded both dual-cycle and direct -cycle plants. Dual-cycle plants as opposed to direct-cycle plants incorporated a steam ge nerator. All BWR/1 plants were built to different specifications for each site. There are no longer any BWR/1 plants operating in the US today. The BWR/2 design was introduced in 1963. The BWR/2 design and all subsequent designs took advantage of the direct-c ycle design simplicity and a common design approach. This design featured an internal steam separation system and introduced 7 by 7 lattice fuel assemblies. All of the core fl ow was driven by five external recirculation loops. The recirculation pumps were capable of variable speed for core-load following. The BWR/3 design was introduced in 1965. The main design change from the BWR/2 design was the addition of internal jet pumps to assi st in recirculation flow. Adding internal jet pumps redu ced the total number of reci rculation loops. The pipes were also smaller in diameter, since only about 1/3 of the total core flow was needed as the driving force flow when operating at rated core flow. The BWR/4 design was introduced in 1966. This design was similar to the BWR/3 design, except the power density of the core was increased approximately 20%.

PAGE 20

3 The BWR/5 design was introduced in 1969. Th e differences with this design were the Emergency Core Cooling System (ECCS) and the recirculation system. The ECCS and the recirculation system were redesigne d to improve reactor safeguards. Flow control in the core was changed from va riable-speed recirculation pumps to a combination of flow-control valves a nd constant-speed recirculation pumps. The BWR/6 design was introduced in 1972. The most significant change was the introduction of 8 by 8 fuel assemblies. There were also modifications in the containment design, the ECCS, and the control blade drives. Further advances in BWR designs by GE include the Advanced Boiling Water Reactor (ABWR) currently opera ting in Japan. Key reactor features of the ABWR are fine motion control rod drives and internal recirculati on pumps. Adding internal recirculation pumps dramatically decreases the amount of external piping, improving safety design and lowering manufacturing costs. Improvements to fuel assembly designs include 9 by 9 and 10 by 10 fuel assemblies. This analysis focused on the BWR/6 design w ith 8 by 8 fuel assemblies. Hereafter, all references to BWRs and fuel assemblie s correspond to the BWR/6 (Figure 1-1) and 8 by 8 fuel assembly designs by GE. Boiling Water Reactor Core Flow The flow of water in a BWR is unique to the BWR system and design. Accurate modeling of the core flow is a challenge and is needed to predict and assess the effects of inter-related reactor parameters during normal and accident scenarios. Two aspects of the core flow are the flow pattern (direction) and the flow characteristics present in the fuel channels.

PAGE 21

4 Figure 1-1 Cut-out of a typical BWR vessel—adapted a nd modified from the TRACG Qualification Report [4] Flow pattern Lamarsh [2] gives a good description of th e core flow (Figure 1-2). Beginning at the lower plenum, the slightly subcooled c oolant flows upward through the core within and around the fuel channels. Heat transfer to the coolant incr eases the coolant’s temperature and changes its phase from liqui d to vapor. A significant fraction of the coolant has been vaporized by the time it reaches the top of the core entering the upper plenum region. The volume fraction of the c oolant occupied by steam is defined as the void fraction. The two-phase mixture enters the steam separators and dryers, removing the liquid water. The dry steam then exits the reactor via the main steam line to the steam turbine.

PAGE 22

5 Figure 1-2 Cross-section of a BWR show ing the flow direction of the liquid water— adapted and modified from Lamarsh [2] Liquid water separated from the steam separators and dryers passes downward along an annular region external to the core. This annular region is between the core shroud and the reactor vessel and is known as the downcomer. Feedwater from the condenser also enters the downcomer region via the main feedwater line. The recirculation system provides the driv ing force for the total core flow. The recirculation system consists of two loops external to the reactor vessel. Each recirculation loop contains a constant-speed pump with a low-speed and high-speed setting. These pumps withdraw water from near the bottom of the downcomer and pump the water to a higher pressure. The water th en exits through a pipe manifold to a number

PAGE 23

6 of jet pumps. The jet pumps are located at the bottom of the downcomer region. Water from the recirculation flow emerges at th e nozzle of the jet pumps at high speed and pressure. The recirculation flow entrains surrounding water in the downcomer due to viscous effects. The jet pumps have no mov eable parts and convert pressure head into velocity head, and then velocity head into pressure head through th e use of a converging and diverging component, respectively (Figur e 1-3). The recirculation and entrained water then emerge from the bottom of the jet pumps into the lower plenum of the reactor vessel. Figure 1-3 Cross-se ction of a jet pump Channel flow characteristics The core is designed to have two-phase flow within the fuel channels. The coolant is heated as it traverses through the fuel cha nnel to saturation temper ature. Small bubbles

PAGE 24

7 begin to form on the surface of the fuel rods at nucleation sites. The adjacent flow of liquid water practically strips the bubbles from the surface because of an increase in total surface adhesion as the bubble grows in size. Initially, the bubbles collapse in the bulk fluid prior to the boiling boundary. The bo iling boundary is the instantaneous location where the bulk fluid temperature reaches saturation. Above the boiling boundary, the flow enters into two-phase flow regime. The bubbles then increase in size and do not collapse, increasing the void fraction of the coolant. The void distribution depends on the syst em pressure, channel geometry, flow rates, power level, power di stribution, and amount of init ial subcooling. Todreas and Kazimi [5] described the two-phase flow regimes for a BWR. The two-phase flow regimes present in a fuel channel are bubbl y, churn, and annular regimes. The bubbly regime is characterized by dispersed vapor bubbles in a continuous liquid phase. The churn regime is essentially the transiti onal regime characterized by large bubbles separated by liquid slugs (sever al small bubbles may also be di spersed within the liquid). The annular regime is charac terized by a continuous core of vapor surrounded by a liquid film annulus present on the surface of the fuel rods. This liquid film along the surface of the fuel rods is essential to provide adequate cooling of the fuel rods. Thermal-Hydraulic Instability Instability of BWRs has been an operati onal concern since their development. Instability describes an event where there is an oscillatory characterization of the core parameters. Inherently, boiling two-phase flow in BWRs is thermodynamically unstable. Oscillatory behavior can exist under th e proper conditions. Thermal-hydraulic oscillations are caused by dynamic interactio ns among the flow parameters (flow rate, density, pressure, enthalpy, and their distributions).

PAGE 25

8 Flow Oscillation Types Flow oscillations are characterized by th eir regularity in shape, frequency, and amplitude. Four categories classify flow oscillations: 1. Flow oscillations due to buoyancy effect are caused by the interaction between fluctuations in the hydrostat ic head and the flow rate. 2. Flow oscillations due to fluctuating density waves cau se periodic reductions of flow followed by a resurgence of flow. 3. Flow oscillations due to compressibility are caused by the interaction of a large compressible volume and inertia. 4. Flow oscillations coupled with therma l hysteresis occur when the transition between heat transfer modes occurs in response to fluctuations in the flow. It is likely that multiple types of flow osci llations exist during an instability event. Buoyancy-wave oscillations Flow oscillations due to buoyancy waves usually occur in a natural circulating system. A natural circulation loop imposes a constant pressure drop from the liquid height in the downcomer. The buoyancy force is connected to void distributions in the core. The void distributions are functions of local heat rates and fluid velocities. The oscillatory behavior of the flow over and undershoots a stable operating point. Density-wave oscillations Lahey and Moody [3], Hsu a nd Graham [6], and Bour [7] found that density-wave oscillations are the most co mmonly encountered instability. Density waves are the type of oscillations most often found in boiling two-phase flow with initial subcooling. Density-wave oscillations are due to the feedback and interaction between the various types of pressure drop components. They are caused specifically by the lag introduced through the density head term becau se of the finite speed of density-wave

PAGE 26

9 propagation. Density-wave propagation, qua litatively described by Lahey and Moody [3], is limited and governed primarily by the mass flow rate. Density-wave oscillations begi n in a heated fuel channe l with random fluctuations inherent in boiling two-phase flow. Inlet flow fluctuations create enthalpy perturbations in the single-phase region. The boiling boundary begins to oscillate from the enthalpy perturbations. Changes in flow and the boili ng boundary combine to create an oscillatory single-phase pressure drop. At the boili ng boundary, the enthalpy perturbations are converted to void fraction perturbations. The combined effects of changes in flow, void fraction, and boiling boundary create an oscillatory two-phase pressure drop. The singlephase pressure drop plus the two-phase pre ssure drop can either dampen or amplify oscillatory behavior. Flow oscillations due to compressibility The two-phase mixture in the upper portion of the fuel channel can also act as a compressible volume. The liquid phase compre sses the two-phase section because of the induced lag originating from the boiling boundary. This oscillatory behavior is forced by the growth of vapor slugs that slow down the inlet water velocity. This type of oscillation is particularly noticeable when a fuel channel operates with a low exit quality. Flow oscillations coupled with thermal hysteresis Unstable flow is also influenced by transiti ons in the flow patter n. This instability occurs when flow conditions are close to the transition point be tween churn flow and annular flow. A momentary increase in bubbl e formation during churn flow may change the flow pattern from churn flow to annular flow. Increase in bubble formation may arise from a temporary reduction in flow, a reduction in pressure, or an increase in power. The transition to annular flow, with its characteristically lower pressure loss, will produce an

PAGE 27

10 excess of driving pressure force and increase the mass flow rate. The flow quality is reduced as more liquid is pushed-up the fu el channel, and the amount of steam may become insufficient to maintain annular flow The flow pattern then reverts to churn flow. This cycle may repeat itself in a peri odic fashion. This os cillatory behavior is partly a result of the delay incurred in the acceleration and decelera tion of the flow rate. Boundary Condition Interaction The dynamic flow behavior within a syst em is governed by the relevant physical laws and interaction of the boundary conditi ons. There are four sets of boundary conditions, also known as operating paramete rs because their values determine the operating conditions sufficient fo r steady-state computations: 1. The pressure imposed at the dome of the re actor or at the turbine header (pressure boundary condition). 2. The pressure drop between the inlet and outlet of the fuel channel is the same for all parallel paths because of a bypass outlet (hydrodynamic boundary condition). 3. The inlet temperature of the coolant is determined by the recirculation ratio, the power level, and the amount and temperat ure of the feedwater (inlet thermal boundary condition). 4. The heating power is determined by the nuc lear characteristics of the fuel (wall thermal boundary condition). The inter-relational dependen ce of the boundary conditions and the system properties may either dampen or amplify oscillatory behavior. Boiling Water Reactor Instability Analysis During early development of BWR tec hnology, there was considerable concern over nuclear-thermal-hydraulic coupled instab ility. The coupled relationship between the nuclear and thermal-hydraulic processes is directly affected by the random boiling process and the void-reactiv ity feedback mechanism. Argonne National Laboratory

PAGE 28

11 (ANL) conducted an extensive se ries of experiments in the early 1950s to indicate that instability behavior was not a problem at higher operating pr essures typical of modern BWRs. Chiang et al. [8] observed that power oscillations primarily result from fueltemperature, void-fraction, moderator-temper ature, and moderator-density feedback during induced flow oscillations in a BWR opera ting near natural circulation. They have further generalized that oscillations are mo re probable and sensitive in relatively highpower, low-flow scenarios. Boiling Water Reactor System Safety Concern The importance of analyzing BWR instabilit y is to determine how it affects fuel safety limits. Prolonged instability events may contribute to forced mechanical vibration of reactor components or system control proble ms, and they can also lead to fuel cladding dry-out causing fuel damage. The primary safety concern with current operational nuclear power plants is fuel failure. Mechanical effects Boiling water reactors contain an arrangeme nt of parallel fuel channels with common inlet and outlet plenums. Each fuel channel also contains an outlet near the bottom of the fuel channel for bypass flow. The common pressures at the bypass, inlet, and outlet regulate the proper flow required for each fuel channel. However, the hydrodynamic properties within each fuel cha nnel are exclusive beca use of a channel box surrounding the fuel assembly (Figures 1-4 and 1-5). Multiple fuel channels in a BWR can lead to coupled oscillations. The probability of fuel channels oscillating in -phase diminishes with increas ing number of fuel channels. The oscillations can result in a 180 out-ofphase pressure fluctuation under special circumstances from geometrical arrange ment, operating conditions, and boundary

PAGE 29

12 conditions. Pressure fluctuati ons immediately affect inlet flow rate and can become selfsustained. In situations where oscillations grow, flow and pressure amplitudes increase with time and may cause flow reversal leading to mechanical failure of the system. Figure 1-4 Generic 8 by 8 fu el channel viewed from the top Thermal effects The cladding integrity is the primary safety concern to prevent the release of radioactivity. The fuel pellets are loca ted inside the clad ding along with highly radioactive fission products. Fuel failure refers to the releas e of the fission products into the coolant. It is imperative to assure adequate cooling to preserve the cladding integrity. This criterion is satisfied when the fuel rod surface remains wet at all times. There are three main types of boiling pro cesses: nucleate boiling, transition boiling, and film boiling. Boiling water reactors are designed to operate in the nucleate boiling regime, where heat transfer to the coolant is extremely efficient. The fuel cladding

PAGE 30

13 temperature maintains a fairly constant va lue during nucleate boiling. Transition boiling is manifested by unstable fuel cladding temp eratures from vapor formation and rewetting on the clad surface. With increased bundle power, the cladding surface may experience film boiling resulting in a large increase in surface temperature. Figure 1-5 Generic 8 by 8 fuel channel viewed from the side—adapted and modified from the TRACG Qualification Report [4] The transfer of heat from the fuel rod to the reactor coolan t depends on the heat transfer mode, flow characteristics, and ther mal properties of the clad and coolant. Incropera and DeWitt [9] discussed the relatio nships between the heat transfer mode,

PAGE 31

14 surface temperature, and heat flux (Figure 16). Flow characteristics in the nucleate boiling regime offer considerable fluid mixing near the surface, substantially increasing the heat transfer coefficient. The nucleate boiling regime continues to a maximum heat flux. The maximum heat flux is known as the cr itical heat flux. The critical heat flux separates the nucleate boiling regime and the transition boiling regime, or unstable film boiling regime. During transiti on boiling, bubble formation is so rapid that a vapor film begins to form on the surface, and conditions may oscillate between film and nucleate boiling. The lengthened presence of the vapor film decreases the heat transfer coefficient to a minimum heat flux. The minimum heat flux occurs because th e fuel rod surface is completely covered by a vapor blanket. The dom inant heat transfer mode at this point is conduction through the vapor. The minimum h eat flux separates the transition boiling regime and the stable film boiling regime. Radi ation heat transfer through the vapor film becomes more significant, increasing the heat flux. If film boiling persists, then the fuel rod will experience dry-out. Dry-out causes th e fuel rod to overheat leading to fuel damage. A consequence of an instability event is elevated clad temperatures. Clad temperatures in transition and film bo iling can cause weakening and accelerated corrosion of the clad. Design margin has been established, and must be maintained, to prevent any fuel channel operati on close to its critical power. Transients that Exhibit HighPower, Low-Flow Scenarios Instability occurrences are not observed during normal operati ons at rated core power and flow. The potential for instability occurrences arises predominantly for reduced core flow and elevated core power scenarios. A BWR experiences reduced flow operations during start-up and af ter a loss-of-flow transient.

PAGE 32

15 Surface Temperature (Arbitrary Scale)Heat Flux (Arbitrary Scale) Critical Heat Flux Leidenfrost Point Nucleate Boiling RegimeTransition Boiling RegimeFilm Boiling Regime Figure 1-6 Generic boiling curve Start-up transient During start-up of the reactor from cold conditions, the core ha s the potential to experience oscillatory behavior For actual start-ups, small oscillations exist when control blades are withdrawn but normally converge to equilibrium conditions. The start-up process from cold conditions requires the following major steps: 5. The start-up of the recircul ation pumps at minimum speed with the flow control valves set at their minimum setting, corre sponding to approximately 25% of rated core flow. 6. The control blades are manually withdr awn to achieve criticality. Following criticality, further withdrawal of the cont rol blades is simultaneous to opening the flow control valves to their maximum position. 7. Once approximately 30% of rated core power is achieved, the flow control valves are set to their minimum position, and the recirculation pumps are transferred to their rated speed.

PAGE 33

16 8. After the recirculation pumps are transferred to their rated speed, the power level is increased to approximately 40% primar ily by opening the flow control valves. 9. After the power level reaches approximately 40%, the control blades are normally withdrawn to increase the power level to approximately 75%. 10. Above approximately 75% of rated power, the power level is increased to rated power normally by opening the flow control valves further. The coolant temperature is increased from nuc lear heat-up before the recirculation pumps are started to initiate core flow. The control blades are withdrawn according to a predetermined schedule to achie ve criticality. Throughout the start-up process, the main feedwater flow is also adjusted to maintain a constant liquid level in the reactor vessel. A BWR experiences high-power conditions du ring the start-up process to provide sufficient pressure drop across the core. As the core heats up, twophase flow increases the two-phase pressure loss in the core. Sufficient pressu re loss in the reactor is necessary to supply adequate pressure head to prevent recircul ation pump cavitation. Loss-of-flow transient A loss-of-flow transient occurs when one or both recirculation pumps trip during normal operations. The core can experience a relatively high power level for low core flow. For some BWRs, the reactor does not necessarily trip even if both recirculation pumps trip. However, the reactor must main tain a proper liquid level. The liquid level must not become too low to keep the core fu lly covered, and it must not become too high to prevent liquid water from entering the main steam lines. During a loss-of-flow transient, the power level also decreases mainly from an increase in void production—negative void-co efficient feedback. The power level follows a particular rod-line to attain a new equilibrium point If the power level is not reduced further, the reactor has a high er probability of becoming unstable.

PAGE 34

17 In this day and age, nuclear power plants are operated at the maximum power level possible to meet energy demands and produ ce revenue. The main question for plant operators is whether furthe r action is needed to redu ce the power level further by inserting control blades. If the plant operators determine to reduce the power level further, then the next ques tion is the amount of reducing the power level to maintain operational confidence at the maximum power level possible. Currently, BWRs use a conservative estimate of the boundary between st able and unstable oper ations relative to their power-flow map. Purpose of Analysis The boundary between stable and unstable oper ations is defined as the threshold or onset of oscillations. The main problem with oscillations is predicting the threshold. In realistic scenarios, the threshold is not well defined because of random fluctuations in the system. Instability of BWRs is analyzed to accurately predict the threshold between stable and unstable operating conditions. Al so, computer models are being qualified to accurately predict the frequency and amplitude of flow oscillations. The importance of analyzing BWR instability is to increase operational margin during loss-of-flow transients and start-up procedures. Assuring sufficient thermal margin between anticipated transient heat fluxes and the critical heat flux is a majo r design factor. It is importa nt to assess any exceedance of thermal mechanical limitations, namely the Cr itical Power Ratio (CPR), in the event of an instability occurrence. The scope of this analysis included ch aracterizing power os cillations during an instability event. This analysis also fo cused on the effects of power oscillations on

PAGE 35

18 thermal-limit margins and general oscillatory be havior during an instability event. The main objectives of this analysis were as follows: Analyze the general behavior during an instability event. Determine the rates of growth or decay of the power oscillations as functions of initial core power and flow. Determine the frequencies of the power osci llations as functions of initial core power and flow. Determine if a fuel channel exceeds its cr itical power during an instability event.

PAGE 36

19 CHAPTER 2 PROBLEM DESCRIPTION Boiling water reactor instability is depe ndent on system geometry and is casespecific; however, an analysis on a specifi c model can be informative, and general conclusions can be applied to additional models. Also, an efficient and proven methodology developed in this analysis can be applied toward future analyses. There were two options to use as the model, LaSa lle and Leibstabt (KKL) nuclear power plants, because they each had actual data to compare with the results of this analysis. LaSalle experienced core-wide oscillati ons meaning all the fuel channe ls oscillated in-phase, and KKL experienced regional oscillations where th e fuel channels in one half of the core oscillated 180 out-of-phase with the fuel channels in the other half of the core. Project Model This analysis extended from the regional in stability tests conducted at KKL nuclear power plant in Europe. This model was chosen because of the availability and accessibility of the original input decks of the computer model. The original input decks included the necessary parameters, such as fuel characteristics, exposure point, core features, and other pertinent informati on, needed by the computer model. General KKL Description Nuclear power plant KKL [10] is a BWR/6 reactor design by GE. The instability tests were conducted during it s first cycle of operation at a cycle exposure of 2.05 GWD/STU. At the time the tests were conduc ted, the core was loaded with 8 by 8 fuel

PAGE 37

20 assemblies supplied by GE. Also, the total number of fuel channels was 648, the rated core power was 3012 MWth, and the rated core flow was 11151 kg/s. Regional Instability Tests Conducted at KKL The KKL instability tests were conducted to measure the unstable behavior at highpower, low-flow scenarios (Table 2-1 and Figure 2-1). There was minimal plant data available; however, the key data were the osci llatory frequencies. All four tests resulted in an oscillatory frequency of 0.45 Hz [4]. Table 2-1 Steady-state operating c onditions of the KKL instability tests Test Core flow—kg/s Core powe r—MWth Dome pressure— Feedwater point (% of rated) (% of rated) MPa temperature—K A 3211 (28.8) 1392 (46.2) 6.698 434 B 3211 (28.8) 1599 (53.1) 6.736 448 C 3434 (30.8) 1528 (50.7) 6.698 434 D 3434 (30.8) 1686 (60.0) 6.736 448 0 20 40 60 80 100 120 0102030405060708090100110 Total Core Flow (% of rated)Total Core Power (% of rated) Scram Rod Block A MEOD Boundary BC D FCV Cavitation Jet Pump Cavitation Minimum Flow Control Line for Transfer to Rated Pump Speed Scram Rod Block A : Natural Circulation Line B: Min. FCV Setting & Low Pump Speed C: Min. FCV Setting & High Pump Speed D: Max. FCV Setting & Low Pump Speed Region 1: Operation not Allowed Region 2: OPRMs Armed Figure 2-1 Power-flow map for KKL showi ng the regions with higher probability of experiencing an instability event and the test points as green boxes

PAGE 38

21 Analysis Tools The entire analysis was performed using computational code packages developed by GE for BWR application. The comput ational codes were PANAC11A (PANAC), CRNC-06A (CRNC), HyCA01B (H yCA), and TRACG04A,P (TRA CG). It was assumed that these computational codes were a pplicable and valid for this analysis. Computer Program PANAC The computer program PANAC [11] is a static, three-di mensional coupled nuclearthermal-hydraulic computer code simulating a BW R core. It is primarily a core diffusion neutron code with incorporated thermal-hydrau lic models. It was used for detailed threedimensional, steady-state design and opera tional calculations of BWR neutron flux, power distributions, and thermal performance. The nuclear model is based on a coarse mesh nodal, 1-1/2 group static diffusion theory. The fast energy group is used to solve the diffusion equations. The resonance flux is related to the fast energy flux to account for the resonance energy nuclear effects. The thermal flux is asymptotically repres ented using a slowing down source from the epithermal region. The nuclear parameters used by PANAC we re originally obtained from a twodimensional lattice physics computer code. For each computational point, PANAC was used for the following: Characterize the steady-state operating parameters. Generate the nodal steady-stat e power shape in the core. Solve the fundamental and first harmonic modes of the neutron diffusion equation. Generate the reactivity feedback coefficien ts of the core for the specific exposure point.

PAGE 39

22 Computer Program CRNC The computer program CRNC [12] is a postp rocessor code used to convert neutron kinetics, thermal-hydraulics, and reactor st ate information from PANAC to a form suitable for input into other computer programs. It collapsed the three-dimensional nodal neutron flux distributions (fundamental and first harmonic modes) calculated by PANAC to generate a radial power map and a hybr id power map. The radial power map is essentially the assembly power peaking ma p, and the hybrid power map is the radial power map multiplied by the scaled harmonic flux. Computer Program HyCA The computer program HyCA is a preprocessor code to TRACG. It is a detailed channel assignment code that processed th e radial power map and the hybrid power map to generate a channel grouping map. The fuel channels were assi gned to similar groups to analyze multiple modes of instability behavi or simultaneously. The fuel channels were assigned to similar groups based on the rela tive importance between the radial power map and the hybrid power map. The resultan t channel grouping map was then used for modeling purposes in TRACG. Computer Program TRACG The computer program TRACG [13] origin ated due to continued efforts by GE after collaboration with Idaho National E ngineering Laboratory in developing a BWR version of TRAC. TRAC was originally developed for PWR analyses by Los Alamos National Laboratory. The computer program TRACG is a ‘bes t estimate’ coupled nuclear-thermalhydraulic computer program. It solves a c oupled set of field equations describing the thermal-hydraulic behavior of the fluid in the system, the flow of energy, and the

PAGE 40

23 generation of nuclear power in the core [14]. It consists of a multi-dimensional two-fluid model for the reactor thermalhydraulics with an incorporated three-dimensional neutron kinetics model for the reactor core. The ne utron kinetics model simulates the feedback processes (moderator density and temperature, fuel temperature, void fraction, and core flow) affecting the core power. The two-fluid thermal-hydraulic model solv es the conservation equations of mass, momentum, and energy for the gas and liquid phases. The basic two-phase two-fluid thermal-hydraulic model, similar to the coll aborative BWR version of TRAC, consists of volume and time averaged conservation e quations of mass, momentum, and energy. The fundamental conservation of mass equation governs that the time rate of change of the mass of a material is zero The computer program TRACG incorporates detailed accounts for the conser vation of mass in the system with four different equations representing the gas phase of water (Equati on 2-1), the liquid phase of water (Equation 22), total noncondensible gases in the system (Equation 2-3), and dissolved boron in the fluid—should it be present (Equation 2-4). vi v v vt (2-1) li l l lt 1 1 (2-2) v a at (2-3) l b bc c t (2-4) The fundamental conservation of momentum equation governs that the time rate of change of the linear momentum of a material region is equal to the sum of the forces on

PAGE 41

24 the region. The computer program TRACG inco rporates detailed accounts for the conservation of momentum in the system w ith two different equations representing the gas phase of water (Equation 2-5), and th e liquid phase of water (Equation 2-6). v v v v v v v v vM g P t (2-5) where: vi vi vi vi vP M l l l l l lP t 1 1 1 l l lM g 1 1 (2-6) where: li li li li lP M 1 1 The fundamental conservation of energy equation governs that the time rate of change of energy within a materi al region is equal to the rate that energy is received by heat and work transfers. The computer program TRACG incorporates detailed accounts for the conservation of energy in the system with two different equations representing the gas phase of water (Equation 2-7), and th e liquid phase of water (Equation 2-8). 2 22 2 v v v v v v ve t P e t s s iv wv vh q q P (2-7) 2 1 2 12 2 l l l l l l le t P e t f s il wl lh q q P 1 (2-8) An extensive set of basic models, consisting of constitutive correlations for shear, mass, and heat transfer at the gas-liquid in terface and surfaces, pr ovide closure to the

PAGE 42

25 conservation equations of mass, momentum, an d energy. The constitutive correlations depend on flow and boiling regime. A basi c flow regime map (bubbly flow regime, annular flow regime, and tran sitional flow regime—between the bubbly and annular flow regimes) is used in TRACG. Instability analysis performed by TRACG is enhanced by input specifications and incorporated models. A refined fuel-cha nnel nodalization detect s density-waves and decreases numerical dissipa tion of density-wave propagati on. The neutron diffusion kinetics model, similar to the model us ed in PANAC, includes six delayed neutron precursor groups (Equation 2-9). J j j j j s j j t j j j gD t u11 N n jn n n J j j j f jC1 11 (2-9) where: j j f J j n n n nC t C 1 Model Nodalization The TRACG thermal-hydraulic model contai ns a set of basic components (fuel channel, heat exchanger, jet pump, pipe, re circulation pump, steam separator and dryer, tee, valve, and vessel component s) constructed together to perform system simulations. The thermal-hydraulic model is a multi-dimens ional representation of the reactor vessel and a one-dimensional representation for all other reactor components. The vessel nodalization is composed of 15 ax ial levels and four radial rings with no subdivision in the azimuthal direction (Fi gure 2-2). The fuel channel nodalization consists of more refined spatial nodes in the lower portion of the heated section to

PAGE 43

26 accurately predict the boiling boundary and allow more sensitivity to density-wave fluctuations (Figure 2-3). The 16 lower nodes of the heated section are 3.81 cm apart, and the 21 upper nodes of the heated section are 15.24 cm apart. Figure 2-2 Three-dimensional nod alization of the vessel component Establishment of Computational Points The available input decks were initially c onstructed to model test point B in Table 2-1; therefore, it was used as the standard point for the analysis. The standard point encompassed the nuclear parameters for the given core, bundle type and exposure point of the fuel. All computational points were derived from this standard point.

PAGE 44

27 Figure 2-3 One-dimensional nodali zation of the fuel channel component Bypass Heated Section Inlet 1 28 25 22 19 2 37 34 31 40

PAGE 45

28 The variables necessary to develop additional computational points from the standard point were the critical eigenvalue, total core flow, total core power, total core bypass flow, and control blade positions. For all of the co mputational points, three variables were prescribed while the other tw o variables were determined by iterating the nuclear and thermalhydraulic solutions. Critical Eigenvalue Calibration The first step was to determine a critical eigenvalue for the standard point. In theory, the critical eigenvalue is exactly 1.0 corresponding to no change in neutron population from one point in time to another point in time. However, in practice, the critical eigenvalue from a computer program is rarely 1.0 for a reactor at steady-state. Moreover, the calculated critical eigenvalue for different operati ng conditions will not necessarily be the same—even for the same exposure point. Total core flow, total core power, and cont rol blade positions were prescribed for the standard point; therefore, the critical eigenvalue and core bypass flow were iterated to find a solution. Using a guess for the core bypass flow, the case was executed in PANAC to determine the critical eige nvalue, along with the associat ed nodal power distribution. The nodal power distribution is the parameter directly used in TRACG as opposed to the critical eigenvalue. The nuclear data a nd nodal power distribution from PANAC were inputted into TRACG to obtain an implicit st eady-state solution. The resultant core bypass flow from TRACG was then used as a second guess for input into PANAC to generate a new nodal power distribution (Figure 2-4). This process was iterated a couple times before the core bypass flow from TR ACG and the critical eigenvalue from PANAC converged to constant solutions. The cr itical eigenvalue converged to 1.00413.

PAGE 46

29 All computational points were calibrated to this critical eigenvalue to differ no more than 1E-5. It was assumed that the cr itical eigenvalue did not directly affect any development of an instability event. Calib ration to a critical eigenvalue established a consistent and repeatable method fo r additional computational points. Original Standard Wrap-Up File & Variable Operating Parameters PANAC harmonic flux iterative loop once CRNC per new new RL radial & wrap-up bypass hybrid file flow power maps rate HyCA channel groups TRACG steady-state converged steady-state solution TRACG transient Analysis Results Figure 2-4 Iterative process between the nuclear and therma l-hydraulic solutions Rod-Line Generation For a given blade pattern, multiple co mputational points were generated by prescribing the core flow and iterating the co re power and core bypass flow. The critical

PAGE 47

30 core flow and core power exhibits a linear relationship, and the line traced is known as a rod-line (RL). The computational points we re defined at 5% core flow increments. Additional RLs were generated by changing control blade positions to encompass and expand beyond the exclusion regions of the power-flow map (Figure 2-5). The control-blade positions were adjusted uniform ly to preserve their relative displacements to each other. Using a prescribed 30% of rated core flow, the control blades were adjusted to achieve approximately 5% core power increments. Seven RLs were generated containing about 10 computational points. 0 20 40 60 80 100 120 202530354045505560657075 Initial Core Flow (% of rated)Initial Core Power (% of rated) RL1 RL2 RL3 RL4 RL5 RL6 RL7 KKL Test Points Region 1 Region 2 Figure 2-5 Power-flow map showing the comp utational points relative to the KKL test points and regions one and two from the KKL power-flow map Channel Grouping The fuel channels, with similar characteristics, were grouped together before executing TRACG to conserve computational time and resources. The main

PAGE 48

31 characteristics considered were orifice type (periphery channels) and relative channel powers. A simplified channel grouping map, based on the radial power map, was used for the iterative process involved with estab lishing the computational points. However, the transient analysis included the hybrid power map to accurately model various harmonic modes of instability behavior. Oscillations in a BWR follow the predominant neutron flux mode. It was important to assign the channels appropria tely to not influence any oscillatory development or behavior. Therefore, an optimized, comprehensive channel-grouping scheme was developed to accurately and confid ently predict the onset and characteristics of an instability event. Each RL had an associated channel grouping map generated by HyCA. Assumptions The primary steady-state operating conditions included the total core power, total core flow, feedwater temperature, and exit pr essure. The independent variables were the total core power and total core flow, si nce there was no change in the feedwater temperature and exit pressure. The calibra ted critical eigenvalue and control-blade movement were assumed to not affect a ny oscillatory development or behavior. Steady-State Initialization After establishing the com putational points (Table 2-2), TRACG was executed in the steady-state mode. The steady-state mode in TRACG simulates a transient solution while maintaining a constant power level and shape to allow the thermal-hydraulic solution to attain equilibrium. The convergence criterion was 1E-4 with a maximum time step of 0.05 s. The convergence criterion is applied to convergence parameters of temperature, pressure, and

PAGE 49

32 void fraction between the predictor and subse quent iterative steps for each spatial node. After using an implicit numerical scheme to accelerate convergence, an explicit numerical scheme was used in the last minute of the time domain to use in the transient mode of TRACG. The time domain was sufficient to allow the thermal-hydraulic solution to attain equilibrium. Transient Analysis In theory, steady-state c onditions indicate the system properties are not time dependent. In practice, however the system properties experi ence small fluctuations and perturbations constantly. This analysis fo cused on inherent qualities of the operating conditions to become unstable; therefore, there were no initiating transients. The transient mode of TRACG activated the nuclear feedback mechanisms to simulate actual core operating conditions. Oscillatory behavi or and characteristic s were analyzed as functions of initial core power and initial core flow only. The convergence criterion was 1E-4 with a maximum time step based on the material courant limit—typically no more than 0.025 s. An explicit numerical scheme was used for the transient solution. The mate rial courant limit is based on the size of the spatial node and the fluid velocities. The time step must be less than the material courant limit for the explicit numerical scheme to be numerically stable. Also, the time step must be as close as possible to the material c ourant limit to decrease numerical dissipation of density-wave propagation. Ande rsen et al. [15] discussed numerical dissipation of a propagating density wave. For these reasons, the time step for the transient solution was variable within the time domain. The time do main was sufficient to demonstrate a fullydeveloped behavior or pattern of the operating parameters.

PAGE 50

33 Table 2-2 Steady-stat e operating conditions of the computational points Core flow—kg/s Core power—MWth Core flow—kg/s Core power—MWth (% of rated) (% of rated) (% of rated) (% of rated) 2721 (24.4) 1008 (33.5) 5576 (50.0) 1888 (62.7) 2765 (24.8) 1139 (37.8) 5576 (50.0) 2071 (68.8) 2810 (25.2) 1286 (42.7) 5576 (50.0) 2248 (74.6) 2832 (25.4) 1436 (47.7) 5576 (50.0) 2409 (80.0) 2844 (25.5) 1585 (52.6) 5576 (50.0) 2564 (85.1) 3211 (28.8) 1599 (53.1) 5576 (50.0) 2725 (90.5) 3345 (30.0) 1187 (39.4) 6133 (55.0) 1769 (58.7) 3345 (30.0) 1340 (44.5) 6133 (55.0) 1984 (65.9) 3345 (30.0) 1490 (49.5) 6133 (55.0) 2178 (72.3) 3345 (30.0) 1639 (54.4) 6133 (55.0) 2354 (78.2) 3345 (30.0) 1791 (59.5) 6133 (55.0) 2525 (83.8) 3345 (30.0) 1943 (64.5) 6133 (55.0) 2685 (89.1) 3345 (30.0) 2090 (69.4) 6133 (55.0) 2845 (94.5) 3903 (35.0) 1345 (44.6) 6691 (60.0) 1848 (61.4) 3903 (35.0) 1511 (50.2) 6691 (60.0) 2072 (68.8) 3903 (35.0) 1674 (55.6) 6691 (60.0) 2268 (75.3) 3903 (35.0) 1833 (60.8) 6691 (60.0) 2451 (81.4) 3903 (35.0) 1991 (66.1) 6691 (60.0) 2622 (87.1) 3903 (35.0) 2140 (71.0) 6691 (60.0) 2786 (92.5) 3903 (35.0) 2292 (76.1) 6691 (60.0) 2949 (97.9) 4460 (40.0) 1473 (48.9) 7248 (65.0) 1923 (63.9) 4460 (40.0) 1657 (55.0) 7248 (65.0) 2159 (71.7) 4460 (40.0) 1830 (60.7) 7248 (65.0) 2356 (78.2) 4460 (40.0) 1995 (66.2) 7248 (65.0) 2546 (84.5) 4460 (40.0) 2149 (71.4) 7248 (65.0) 2723 (90.4) 4460 (40.0) 2298 (76.3) 7248 (65.0) 3056 (101.4) 4460 (40.0) 2456 (81.6) 7360 (66.0) 2909 (96.6) 5018 (45.0) 1585 (52.6) 7806 (70.0) 1996 (66.3) 5018 (45.0) 1780 (59.1) 7806 (70.0) 2234 (74.2) 5018 (45.0) 1959 (65.0) 7806 (70.0) 2447 (81.2) 5018 (45.0) 2127 (70.6) 7806 (70.0) 2635 (87.5) 5018 (45.0) 2287 (75.9) 7806 (70.0) 2819 (93.6) 5018 (45.0) 2438 (80.9) 7806 (70.0) 2980 (98.9) 5018 (45.0) 2600 (86.3) 7806 (70.0) 3153 (104.7) 5576 (50.0) 1682 (55.8) Note: Dome pressure = 6.736 MP a, feedwater temperature = 448 K Unstable Steady-State Operating Conditions The nuclear feedback in a BWR is strongl y influenced by two-phase flow; likewise, the thermal-hydraulic parameters are strongly influenced by the heat generation. This

PAGE 51

34 coupled system increases the probability of an instability event and has the tendency to amplify the magnitude of the oscillations. Sm all fluctuations and pe rturbations inherent in the boiling process have a greater probability of triggering an instability event for highpower, low-flow scenarios because of an imbalance between the average single-phase and two-phase pressure drops. The computa tional points were initially executed with no perturbations to determine if the operati ng conditions were inherently unstable. Stable Steady-State Operating Conditions For the inherently stable operating conditions, an instan taneous flow perturbation (step change) was instigated at the beginning of a second exec ution of the transient mode from the steady-state initialization. The flow perturbation was not held constant to allow the system properties to once again attain equilib rium conditions. The main purpose of inducing oscillations was to extract the osci llatory characteristic s—rate of decay and frequency. A regional flow perturbation was i nduced because the unstable operating conditions exhibited out-of-phase oscillations. The flow pe rturbation was applied to the fuel channels’ inlet flows. The inlet flows were perturbed by a specific percentage of their initial flows (Table 2-3). The inlet flows of the fuel ch annels on one side of the first harmonic boundary line were increased, while th e inlet flows of the fuel channels on the other side were decreased to initiate out-ofphase oscillations. This method maintained a constant total core flow. Table 2-3 Flow perturba tions applied to each comput ational point for a given RL RL1 RL2 RL3 RL 4 RL5 RL6 RL7 95% 90% 85% 80% 75% 70% 65%

PAGE 52

35 CHAPTER 3 STEADY-STATE RESULTS AND DISCUSSION The steady-state initialization is highli ghted using primarily one computational point representative of all other computat ional points. Unless otherwise noted, the computational point highlighted is 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3. Results from PANAC The initial Minimum Critical Power Ra tio (MCPR) values and axial power distributions were the rele vant parameters describi ng the steady-state operating conditions. The MCPR values indicate the initial thermal margin of the core, and the axial power distributions i ndicate the initial average boiling boundary of the core. Initial MCPR During an instability event, MCPR is the mo st relevant fuel safety limit, because it indicates the amount of thermal margin befo re departure from nucleate boiling. The MCPR is defined as the minimum ratio in th e core between a fuel assembly’s critical power and its operating power. Current technical specifications for a BWR/6 dictate that MCPR must be at least 1.07 for two recirc ulation loop operation. All of the MCPR values were above 1.2 indicating sufficient thermal margin for steady-state operations (Figure 3-1). Initial Axial Core Power Distributions The initial axial core power distributions generated by PANAC for the steady-state mode of TRACG were not constant for all of the computational point s (Figure 3-2). As

PAGE 53

36 the core flow is increased, the axial power distribution becomes less bottom peaked and displays a flatter profile. This trend is primarily due to the greater increase in the percentage of rated core flow than the incr ease in the percentage of rated core power. This behavior, of the core flow and power, results in raising the height of the boiling boundary. The raised height of the boiling boun dary increases moderation in the top half of the fuel channel increasing its relative power. 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 202530354045505560657075 Initial Core Flow (% of rated)Initial MCPR RL1 RL2 RL3 RL4 RL5 RL6 RL7 Figure 3-1 Initial MCPR as a function of initial core flow Results from CRNC Each RL had a corresponding radial pow er map and a hybrid power map. The radial power map (Figure 3-3) and hybrid power map (Figure 3-4) were half-core symmetric. 33.5% of rated initial core p owe r 66.3% of rated initial core p owe r 104.7% of rated initial core p owe r 69.4% of rated initial core p owe r

PAGE 54

37 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 00.20.40.60.811.21.41.61.82 Relative Axial Core PowerNormalized Fuel Channel Height 25.2% rated core flow 30.0% rated core flow 35.0% rated core flow 40.0% rated core flow 45.0% rated core flow 50.0% rated core flow 55.0% rated core flow 60.0% rated core flow 65.0% rated core flow 70.0% rated core flow Figure 3-2 Steady-state axial core power distributions for RL3 Figure 3-3 Radial power map generate d by CRNC for RL3 (half-core symmetry) 0.250.30.33 0.280.380.690.760.8 0.350.680.830.9311.03 0.290.40.490.921.021.111.161.19 0.350.690.840.971.071.161.21.251.27 0.370.750.91.011.11.191.211.221.191.26 0.360.760.931.061.071.141.191.240.930.991.21 0.290.710.921.081.171.161.141.311.210.941.21 0.410.851.051.181.271.221.321.271.331.181.251.25 0.340.480.981.131.261.231.281.211.331.231.251.171.25 0.280.670.91.021.151.221.280.930.991.181.250.880.931.18 0.380.831.011.11.191.321.210.990.921.251.160.930.881.18 0.250.690.931.111.211.31.281.341.191.251.221.31.161.231.23 0.30.760.991.141.231.251.361.261.251.171.291.221.241.181.25 0.330.791.011.141.091.111.271.230.880.881.181.20.960.971.21 0.330.791.011.141.091.111.271.230.880.881.181.20.960.971.21 0.30.760.991.141.231.251.361.261.251.171.291.221.241.181.25 0.250.690.931.111.211.31.281.341.191.251.221.31.161.231.23 0.380.831.011.11.191.321.210.990.921.251.160.930.881.18 0.280.670.91.021.151.221.280.930.991.181.250.880.931.18 0.340.480.981.131.261.231.281.211.331.231.251.171.25 0.410.851.051.181.271.221.321.271.331.181.251.25 0.290.710.921.081.171.161.141.311.210.941.21 0.360.760.931.061.071.141.191.240.930.991.21 0.370.750.91.011.11.191.211.221.191.26 0.350.690.840.971.071.161.21.251.27 0.290.40.490.921.021.111.161.19 0.350.680.830.9311.03 0.280.380.690.760.8 0.250.30.33

PAGE 55

38 Figure 3-4 Hybrid power map generate d by CRNC for RL3 (half-core symmetry) Results from HyCA The radial power map and hybrid power ma p were used to generate a channel grouping map (Figure 3-5). Channel 28 is the fuel channel with th e highest magnitude from the radial power map. Channel 27 is the fuel channel with the highest negative magnitude, and channel 29 is the fuel channe l with the highest positive magnitude from the hybrid power map. The bold central lin e indicates the first harmonic flux boundary line. The connected lines show the ring st ructure designated in TRACG for the threedimensional vessel component nodalization. Results from TRACG The steady-state mode converged the ther mal-hydraulic soluti on to equilibrium while maintaining a constant core power leve l and shape (Figure 36 through Figure 3-8). After steady-state initialization, the transien t analysis was performed to determine the oscillatory behavior and ch aracteristics of model. -0.11-0.18-0.22 -0.13-0.31-0.81-1.08-1.21 -0.19-0.72-1.24-1.71-2.06-2.24 -0.11-0.26-0.51-1.44-2.02-2.51-2.85-3.03 -0.16-0.58-0.99-1.5-2.07-2.57-2.91-3.2-3.39 -0.16-0.63-1.08-1.49-1.94-2.45-2.7-2.76-2.81-3.16 -0.13-0.57-1.04-1.45-1.59-1.94-2.37-2.51-1.64-1.81-2.63 -0.07-0.42-0.89-1.37-1.7-1.76-1.89-2.48-2.25-1.6-1.53-2.37 -0.14-0.6-1.08-1.52-1.84-1.89-2.2-2.27-2.4-2.02-2.15-2.31 -0.06-0.2-0.69-1.11-1.5-1.61-1.73-1.75-2.09-1.95-1.88-1.78-2.02 -0.03-0.18-0.41-0.65-0.95-1.23-1.35-0.88-1-1.44-1.53-0.91-0.98-1.47 -0.05-0.25-0.45-0.62-0.82-1.08-1.01-0.71-0.69-1.17-1.1-0.72-0.68-1.13 -0.01-0.11-0.25-0.42-0.57-0.73-0.81-0.88-0.74-0.81-0.88-0.94-0.78-0.82-0.9 -0.01-0.09-0.19-0.3-0.4-0.47-0.56-0.54-0.54-0.52-0.6-0.58-0.57-0.54-0.59 -0.01-0.05-0.09-0.13-0.14-0.16-0.2-0.2-0.13-0.13-0.2-0.2-0.15-0.14-0.19 0.0020.0120.0290.0520.0690.090.1220.130.0960.1040.1590.1690.1320.1380.192 0.0090.060.1360.2240.3120.3810.4710.4660.4750.4690.5580.5430.5460.530.588 0.0090.0820.2020.3470.4890.6380.7230.7950.6850.7590.8330.9040.7550.8140.901 0.0450.210.3910.5510.7420.9950.9410.6730.6631.1281.0630.7080.6751.124 0.0250.1620.3710.60.8851.1531.2760.8460.9661.4011.4980.90.9711.47 0.0550.1820.651.0461.4241.5421.6741.6962.0361.9181.8581.7712.014 0.1290.5691.0341.4551.7741.8362.1482.2212.3581.9942.1362.303 0.0650.4020.8521.3161.6421.7161.8532.442.2221.5871.5232.364 0.1260.551.0071.4071.5571.8992.3292.4781.6281.8042.621 0.1560.6111.0531.4611.9072.4182.6742.7342.7973.151 0.1570.5710.9711.4752.0472.5482.8873.1833.379 0.1040.2560.4991.422.0052.4932.8333.019 0.1890.7171.2311.7022.0542.231 0.130.3040.8051.0711.206 0.1110.180.216

PAGE 56

39 Figure 3-5 Channel grouping ma p generated by HyCA for RL3 2750 2800 2850 2900 2950 3000 3050 3100 3150 3200 3250 0100200300400500600 ConvergenceTime (s)Total Core Flow (kg/s) Figure 3-6 Total core ma ss flow steady-state convergence for the computational point of 25.2% of rated initial core flow and 42.7% of ra ted initial core power on RL3 (core power = 1286 MWth) 535353535353 53534947464647495353 535045434141414143455053 53535345424038373738404245535353 5350484441403837 27 363738404245485053 5350474442353938383737383939354245475053 53504745444235344343393943443435424445475053 535048454343423235444435354444353242434345485053 534947443334323332423434343442323332343345474953 5353484633343335323434433434433434323533343346485353 53504847463533484845344848454548483445484833344647485053 53494747463235484833464849464649484634484835324646474953 535048463532333152515151525151515152515151513133323546485053 535048463434313351525151515251515251515152513328343446485053 534947464746333452525251525251515252515252523433464746474953 23191716171634222222212222212122222122222243161716171923 2320181644132122212121222121222121212221314416182023 2320181652312121212122212121212221212122132516182023 23191716162518184161819161619181631818521617171923 23201817164318181541818151518184151818351617182023 232318163435244134413442534316182323 2319171534232124444122324314171923 232018151313122514145514145212131315182023 23201715141254141399131345121415172023 232017151259987788951214172023 232018151210876 29 78101114182023 2323231512108778101215232323 232015131111111113152023 23231917161617192323 232323232323 Control Blades 25.0% INSERTED29.2% INSERTED45.8% INSERTED70.8% INSERTED 70.8% INSERTED75.0% INSERTED83.3% INSERTED87.5% INSERTED

PAGE 57

40 6.7357E+06 6.7358E+06 6.7359E+06 6.7360E+06 6.7361E+06 6.7362E+06 6.7363E+06 6.7364E+06 6.7365E+06 0100200300400500600 Convergence Time (s)Dome Pressure (Pa) Figure 3-7 Dome pressure steady-state convergence for the computational point of 25.2% of rated initial core flow and 42.7% of rated init ial core power on RL3 (core power = 1286 MWth) 529 530 531 532 533 534 535 536 537 538 0100200300400500600 Convergence Time (s)Core Inlet Temperatures (K) Figure 3-8 Core inlet te mperature steady-state convergen ce for the computational point of 25.2% of rated initial core flow and 42.7% of ra ted initial core power on RL3 (core power = 1286 MWth)

PAGE 58

41 CHAPTER 4 OSCILLATORY BEHAVIOR RESULTS AND DISCUSSION The oscillatory behavior results are high lighted using primarily one computational point that is representative of all other computational point s. Unless otherwise noted, the computational point highlighted is 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3. Only 14 of th e 69 computational point s were inherently unstable (Figure 4-1). 0 20 40 60 80 100 120 202530354045505560657075 Initial Core Flow (% of rated)Initial Core Power (% of rated) RL1 RL2 RL3 RL4 RL5 RL6 RL7 Unstable Computational Points Region 1 Region 2 Figure 4-1 Computational poi nts showing the inherently unstable operating conditions Global Behavior The total core power showed the most si gnificant oscillatory be havior (Figure 4-2 through Figure 4-5). The main reason for the large response in core power was due to the large reactivity changes, mainly from the void-reactivity feedback (Figure 4-6). As expected, the inherently stable computationa l points converged to equilibrium after the instantaneous flow perturbation (Figure 4-7 through Figure 4-10).

PAGE 59

42 0.99 0.995 1 1.005 1.01 0306090120150180210240270300 Time (s)Relative to Initial Value Figure 4-2 Total core mass flow tran sient results for the inherently unstable computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 0306090120150180210240270300 Time (s)Relative to Initial Value Figure 4-3 Total core power transient results for the inherently unstable computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3

PAGE 60

43 0.9999 0.99992 0.99994 0.99996 0.99998 1 1.00002 1.00004 1.00006 1.00008 1.0001 0306090120150180210240270300 Time (s)Relative to Initial Value Figure 4-4 Dome pressure transient resu lts of the dome pressure for the inherently unstable computational point of 25.2% of rated init ial core flow and 42.7% of rated initial core power on RL3 0.9992 0.9993 0.9994 0.9995 0.9996 0.9997 0.9998 0.9999 1 1.0001 0306090120150180210240270300 Time (s)Relative to Initial Value Figure 4-5 Core inlet temperature transient results for the inherently unstable computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power on RL3

PAGE 61

44 -0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006 0306090120150180210240270300 Time (s)Core Total Reactivity Figure 4-6 Total core reactivity tran sient results for the inherently unstable computational point of 25.2% of rated intial core flow and 42.7% of rated initial core power on RL3 0.99 0.995 1 1.005 1.01 020406080100120 Time (s)Relative to Initial Value Figure 4-7 Total core mass fl ow transient results for the inherently stable computational point of 24.4% of rated initial core flow and 33.5% of rated initial core power on RL1 following the instan taneous flow perturbation

PAGE 62

45 0.97 0.98 0.99 1 1.01 1.02 1.03 020406080100120 Time (s)Relative to Initial Value Figure 4-8 Total core power transient results for the inherently stable computational point of 24.4% of rated initial core flow and 33.5% of rated initial core power on RL1 following the instan taneous flow perturbation 0.9999 0.99992 0.99994 0.99996 0.99998 1 1.00002 1.00004 1.00006 1.00008 1.0001 020406080100120 Time (s)Relative to Initial Value Figure 4-9 Dome pressure tr ansient results for the inherently stable computational point of 24.4% of rated initial core flow and 33.5% of ra ted initial core power on RL1 following the instantaneous flow perturbation

PAGE 63

46 0.999 0.9992 0.9994 0.9996 0.9998 1 1.0002 1.0004 1.0006 1.0008 1.001 020406080100120 Time (s)Relative to Initial Value Figure 4-10 Core inlet temperature transient re sults of the core inlet temperature for the inherently stable computational point of 24.4% of rated ini tial core flow and 33.5% of rated initial core power on RL1 following the instantaneous flow perturbation Local Power Behavior The unique feature of the model was the out-of-phase oscillations. Channels 27 and 29 correspond to the extremes in the firs t harmonic flux solution (Figure 4-11). The channels’ power responses ini tially oscillated in-phase unt il the first harmonic neutron flux became the dominant mode in the core (Figure 4-12). The oscillations obtained a limit cycle after an elapsed time of approxi mately two minutes (Figure 4-13). The oscillatory behavior analysis focused on the limit cycle because the parameters are translationally invariant with respect to time.

PAGE 64

47 535353535353 53534947464647495353 535045434141414143455053 53535345424038373738404245535353 5350484441403837 27 363738404245485053 5350474442353938383737383939354245475053 53504745444235344343393943443435424445475053 535048454343423235444435354444353242434345485053 534947443334323332423434343442323332343345474953 5353484633343335323434433434433434323533343346485353 53504847463533484845344848454548483445484833344647485053 53494747463235484833464849464649484634484835324646474953 535048463532333152515151525151515152515151513133323546485053 535048463434313351525151515251515251515152513328343446485053 534947464746333452525251525251515252515252523433464746474953 23191716171634222222212222212122222122222243161716171923 2320181644132122212121222121222121212221314416182023 2320181652312121212122212121212221212122132516182023 23191716162518184161819161619181631818521617171923 23201817164318181541818151518184151818351617182023 232318163435244134413442534316182323 2319171534232124444122324314171923 232018151313122514145514145212131315182023 23201715141254141399131345121415172023 232017151259987788951214172023 232018151210876 29 78101114182023 2323231512108778101215232323 232015131111111113152023 23231917161617192323 232323232323 Control Blades 25.0% INSERTED29.2% INSERTED45.8% INSERTED70.8% INSERTED 70.8% INSERTED75.0% INSERTED83.3% INSERTED87.5% INSERTED Figure 4-11 Channel grouping map for RL3 w ith its associated first harmonic flux solution (2-D projection) A A B B

PAGE 65

48 0.7 0.8 0.9 1 1.1 1.2 1.3 0102030405060 Time (s)Relative to Initial Values Channel 27 Channel 29 Figure 4-12 First minute of the transient even t: Power response for the most responsive fuel channels of computational point of 25.2% of rated ini tial core flow and 42.7% of rated initial core power 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 6090120150180 Time (s)Relative to Initial Values Channel 27 Channel 29 Figure 4-13 First to third mi nute of the transient event: Power response for the most responsive fuel channels of computati onal point of 25.2% of rated initial core flow and 42.7% of rated initial core power

PAGE 66

49 When the power responses of channels 23, 21, 51, and 53 were included (Figure 414 and Figure 4-15), the results indicated an os cillatory behavior shown by the arrows on the first harmonic neutron flux solution in Figu re 4-11. Channels 27 and 29 are referred to as the most responsive fuel channels because they exhibited the largest oscillatory amplitudes. All of the fuel channels’ power responses oscillated with equal frequency. The oscillatory peaks displayed a greater magnitude than the oscillatory troughs illustrating an undertone presence of the le ss dominant fundamental neutron flux mode. As a result, the total core power oscillated wi th half the period, since it is the cumulative effect of the channel power osci llations (Figure 4-16). These results show that oscillatory behavior during an instability event is dictated by the predominant neutron flux mode in the core. Because the neutron flux behavior is affected by the total core power and flow, the rates of growth/decay of the channel power oscillations were expected to also depend on the total core power and flow. 0.7 0.8 0.9 1 1.1 1.2 1.3 0102030405060 Time (s)Relative to Initial Values Channel 21 Channel 51 Channel 29 Channel 27 Channel 23 Channel 53 Figure 4-14 First minute of the transient even t: Symmetric fuel channel power responses of computational point of 25.2% of ra ted initial core flow and 42.7% of rated initial core power

PAGE 67

50 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 150160170180 Time (s)Relative to Initial Values Channel 21 Channel 51 Channel 29 Channel 27 Channel 23 Channel 53 Figure 4-15 Limit cycle of the transient even t: Symmetric fuel channel power responses of computational point of 25.2% of ra ted initial core flow and 42.7% of rated initial core power 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 150160170180 Time (s)Relative to Initial Values Channel 21 Channel 51 Channel 29 Channel 27 Channel 23 Channel 53 Total Core Power Figure 4-16 Limit cycle of the transient even t: Symmetric fuel channel power responses and total core power respons e (bold line) of computat ional point of 25.2% of rated initial core fl ow and 42.7% of rate d initial core power

PAGE 68

51 Local Thermal-Hydraulic Behavior The fuel channels in a BWR are therm odynamically independent; therefore, the most responsive fuel channel was used to analyze its thermal-hydraulic characteristics and distributions. The most responsive fuel channel (channel 27) displayed the greatest variation and change in the thermal-hydraulic parameters. The pressure distribution (Figure 4-17 and Figure 4-18) in the fuel channel is the driving influence for mass flow to the fuel ch annel (Figure 4-19). Pr essure variations in the lower portion of the fuel channel are almost instanta neously observed in the upper portion of the fuel channel. This trait is b ecause pressure waves travel with a magnitude on the order of the sonic velocity. 1.002 1.003 1.004 1.005 1.006 1.007 1.008 0102030405060 Time (s)Normalized to Initial Dome Pressure 6.5% of fuel channel height 10.5% of fuel channel height 14.5% of fuel channel height 26% of fuel channel height 42% of fuel channel height 58% of fuel channel height 74% of fuel channel height 90% of fuel channel height Figure 4-17 First minute of the transient even t: Pressure distribution for channel 27 of computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power

PAGE 69

52 1.002 1.003 1.004 1.005 1.006 1.007 1.008 150160170180 Time (s)Normalized to Initial Dome Pressure 6.5% of fuel channel height 10.5% of fuel channel height 14.5% of fuel channel height 26% of fuel channel height 42% of fuel channel height 58% of fuel channel height 74% of fuel channel height 90% of fuel channel height Figure 4-18 Limit cycle of the transient even t: Pressure distribution for channel 27 of computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 150160170180 Time (s)Normalized to Initial Value Figure 4-19 Limit cycle of the transient even t: Outlet mass flow rate for channel 27 of computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power

PAGE 70

53 Flow oscillations in the fuel channel a ffect the average fluid density (Figure 4-20 and Figure 4-21). Average fluid density vari ations in the lower portion of the fuel channel are not immediately obser ved in the upper portion of the fuel channel. This trait is because density waves travel with a magn itude on the order of the mass flow rate. Void fraction is the counterpart of the av erage fluid density (F igure 4-22 and Figure 4-23). The importance of the void fraction distri bution in the fuel channel is its effect on nuclear feedback. The strong dependence of nuclear feedback from the void distribution in the fuel channel governs the behavior of the axial power distribution in the fuel channel (Figure 4-24 and Figure 4-25). This be havior translates to a total fuel channel power response with the same period (Figure 4-26). These results suggested that the frequencies of the channel power oscillations only depend on the initial core flow and not the initial core power. 0 0.2 0.4 0.6 0.8 1 1.2 0102030405060 Time (s)Normalized to Initial Lower Plenum Density 6.5% of fuel channel height 10.5% of fuel channel height 14.5% of fuel channel height 26% of fuel channel height 42% of fuel channel height 58% of fuel channel height 74% of fuel channel height 90% of fuel channel height Figure 4-20 First minute of the transient ev ent: Average fluid density distribution for channel 27 of computational point of 25. 2% of rated initial core flow and 42.7% of rated initial core power

PAGE 71

54 0 0.2 0.4 0.6 0.8 1 1.2 150160170180 Time (s)Normalized to Initial Lower Plenum Density 6.5% of fuel channel height 10.5% of fuel channel height 14.5% of fuel channel height 26% of fuel channel height 42% of fuel channel height 58% of fuel channel height 74% of fuel channel height 90% of fuel channel height Figure 4-21 Limit cycle of the transient ev ent: Average fluid density distribution for channel 27 of computational point of 25. 2% of rated initial core flow and 42.7% of rated initial core power 0 0.2 0.4 0.6 0.8 1 1.2 0102030405060 Time (s)Void Fraction 6.5% channel height 10.5% channel height 14.5% channel height 26% channel height 42% channel height 58% channel height 74% channel height 90% channel height Figure 4-22 First minute of the transient even t: Void fraction dist ribution for channel 27 of computational point of 25.2% of ra ted initial core flow and 42.7% of rated initial core power

PAGE 72

55 0 0.2 0.4 0.6 0.8 1 1.2 150160170180 Time (s)Void Fraction 6.5% channel height 10.5% channel height 14.5% channel height 26% channel height 42% channel height 58% channel height 74% channel height 90% channel height Figure 4-23 Limit cycle of the transient even t: Void fraction dist ribution for channel 27 of computational point of 25.2% of ra ted initial core flow and 42.7% of rated initial core power 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0102030405060 Time (s)Relative Axial Power 6.5% of fuel channel height 10.5% of fuel channel height 14.5% of fuel channel height 26% of fuel channel height 42% of fuel channel height 58% of fuel channel height 74% of fuel channel height 90% of fuel channel height Figure 4-24 First minute of the transient ev ent: Axial power dist ribution for channel 27 of computational point of 25.2% of ra ted initial core flow and 42.7% of rated initial core power

PAGE 73

56 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 150160170180 Time (s)Relative Axial Power 6.5% of fuel channel height 10.5% of fuel channel height 14.5% of fuel channel height 26% of fuel channel height 42% of fuel channel height 58% of fuel channel height 74% of fuel channel height 90% of fuel channel height Figure 4-25 Limit cycle of the transient ev ent: Axial power dist ribution for channel 27 of computational point of 25.2% of ra ted initial core flow and 42.7% of rated initial core power 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 150155160165170175180 Time (s)Relative to Initial Value Figure 4-26 Limit cycle of the transient ev ent: Total channel pow er for channel 27 of computational point of 25.2% of rated initial core flow and 42.7% of rated initial core power

PAGE 74

57 CHAPTER 5 OSCILLATORY CHARACTERISTIC RESULTS AND DISCUSSION This analysis focused on the power respons e in the core beca use of its direct measurability by the neutron monitoring system and its effect on thermal-limit margin. The power response was described by its oscillat ory rate of growth or decay, frequency, and any fuel safety-limit concerns. The pow er response of the most responsive fuel channel for each computational point is spec ifically analyzed, because it is the most limiting with respect to fuel safety-limit concerns. Measurement Process A constant measurement range was used for consistency for each computational point. The range was determined using the following criteria: Measure in a time domain before any signi ficant responses in the core operating parameters—namely the total core power. Avoid any flattening regions of the channel power oscillations. The oscillatory behavior between the ch annel powers and the total core power differed because of the out-ofphase oscillatory nature. The rate of growth of the total core power was initially damped until well in to the instability event (Figure 5-1). The flattening regions of the channel power oscill ations, as a limit cycle (Figure 5-2) or equilibrium (Figure 5-3) is a pproached, can have a significa nt effect on measuring rates of growth/decay. For a specific computational point, the same range and, consequently, the same data points were used to determine the oscillatory rate of growth/decay and frequency. A constant range between 103% and 117% of the initia l channel power was

PAGE 75

58 chosen to satisfy the above criteria. The data extracted from the measurement region corresponded to the amplitude peaks of the oscillations. 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 02468101214161820222426283032 Time (s)Relative to Initial Values Most responsive channel power Lower measurement limit Upper measurement limt Total core power Figure 5-1 Limiting case for the measurem ent range in a time domain before any significant responses in the core operati ng parameters. Most responsive fuel channel and total core power responses of computationa l point 30.0% of rated initial core fl ow and 69.4% of rate d initial core power 0.75 0.85 0.95 1.05 1.15 1.25 0306090120150180 Time (s)Relative to Initial Values Most responsive channel power Lower measurement limit Upper measurement limt Total core power Figure 5-2 Limiting case for the measur ement range of avoiding flattening regions inside measurement region. Most re sponsive fuel channel and total core power responses of computational point 24.8% of rated initial core flow and 37.8% of rated initial core power

PAGE 76

59 0.8 0.9 1 1.1 1.2 1.3 0102030405060708090100110120 Time (s)Relative to Initial Values Most Responsive Fuel Channel Lower Measurement Limit Upper Measurement Limit Total Core Power Figure 5-3 Example of measurement ra nge applied to an inherently stable computational point. Most responsive fuel channel and total core power responses of computational point 24.4% of rated initial core flow and 33.5% of rated initial core power Rates of Growth/Decay The rates of growth/decay are similar to the neutron multiplication factor. The rate of growth/decay is a measure of the percent change between two subsequent amplitude peaks. All of the amplitude peaks in the m easurement range were analyzed to obtain an average rate of growth/decay for each computational point. The rate of growth/decay of the most res ponsive fuel channel was representative of all other fuel channels because of the osci llatory behavior discu ssed in the previous chapter (Figure 5-4). Thus, measuring the ra te of growth/decay of the most responsive fuel channel was a valid and legitimate indi cator of the general power response of the fuel channels.

PAGE 77

60 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 200205210215220225230 Time (s)Relative to Initial Values Ch29 Ch27 Ch22 Ch52 Ch23 Ch53 Figure 5-4 Symmetric fuel channel power responses of com putational point of 35.0% of rated initial core flow and 66.1% of rated initia l core power within the measurement range Initially, the rates of growth/decay decr eased linearly, as total core flow is increased, along a particular RL (Figure 5-5) However, they level-off because as the operating conditions became more stable, the amplitudes reduced at a lower rate. The measurement process for the rate of decay was not efficient for very stable operating conditions; fortunately, this was not much of a concern. Before leveling-off, the dependence of the rates of grow th/decay on initial core flow behaved in a linear fashion. For a prescribed core flow, the rates of gr owth/decay also followed a linear trend with increasing initial core power (Figure 5-6). Rates of growth /decay greater than one indicate instability; whereas, rates of grow th/decay less than one indicate stability. The results were linearly interpolated to determine the threshold between stable and unstable operating conditions (Figure 5-7). Th e threshold appears linear on the powerflow map iterating the fact that the rate s of growth/decay of the channel power oscillations are linearly de pendent on the initial core flow and initial core power.

PAGE 78

61 0.94 0.96 0.98 1 1.02 1.04 1.06 20304050607080 Initial Core Flow (% of rated)Rate of Growth/Decay RL1 RL2 RL3 RL4 RL5 RL6 RL7 stability line Figure 5-5 Rates of growth/decay as functi ons of initial core flow of most responsive channel power oscillations 0.94 0.96 0.98 1 1.02 1.04 1.06 30405060708090100 Initial Core Power (% of rated)Rate of Growth/Decay 30% of rated initial core flow 35% of rated initial core flow 40% of rated initial core flow 45% of rated initial core flow 50% of rated initial core flow 55% of rated initial core flow stability line Figure 5-6 Rates of growth/decay as functi ons of initial core power of most responsive channel power oscillations

PAGE 79

62 0 20 40 60 80 100 120 202530354045505560657075 Initial Core Flow (% of rated)Initial Core Power (% of rated) RL1 RL2 RL3 RL4 RL5 RL6 RL7 Unstable Computational Points Instability Threshold Region 1 Region 2 Figure 5-7 Power-flow map showing the threshold between stable and unstable operating conditions for th is particular model Frequency Results The oscillatory frequency is a measur e of the inverse period between tow subsequent amplitude peaks. All of the am plitude peaks in the measurement range were analyzed to obtain an average oscillatory frequency for each computational point. The oscillatory frequency was determined using the same data used to determine the rates of growth/decay for consistency in the calculation method and results. The oscillatory frequency of the most res ponsive fuel channel was representative of all other fuel channels because of the osci llatory behavior discu ssed in the previous chapter (Figure 5-4). Thus, measuring the os cillatory frequency of the most responsive fuel channel was a valid and legitimate indi cator of the general power response of the fuel channels.

PAGE 80

63 The oscillatory frequencies followed a linear trend with increasing initial core flow (Figure 5-8). The oscillator y frequencies along different RLs are very closely packed, indicating they do not depend on th e initial core power. For a prescribed core flow, the oscillatory frequencies showed no significant changes for different initial core power levels (Figure 5-9). The channel power frequencies were equal to the channel flow frequencies with an associated time delay (Figure 5-10). The tim e delay was defined as the time between an initial channel flow amplitude peak to the subsequent channel power amplitude peak. Almost all the time delay results are within a band of 0.1 s illustrating the channel power frequency is strictly governed by flow oscill ations. These results indicate that the position of the average boiling boundary in th e core does not aff ect the oscillatory frequency—only its rate of change. 0.4 0.45 0.5 0.55 0.6 0.65 0.7 20304050607080 Initial Core Flow (% of rated)Channel Power Frequency (Hz) RL1 RL2 RL3 RL4 RL5 RL6 RL7 Figure 5-8 Frequency response as a function of initial core flow of the most responsive channel power oscillations

PAGE 81

64 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 020406080100120 Initial Core Power (% of rated)Oscillatory Frequency (Hz) 30% of rated initial core flow 35% of rated initial core flow 40% of rated initial core flow 45% of rated initial core flow 50% of rated initial core flow 55% of rated initial core flow 60% of rated initial core flow 65% of rated initial core flow 70% of rated initial core flow Figure 5-9 Frequency response as a func tion of initial core power of the most responsive channel power oscillations 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 20304050607080 Total Core Flow (% of rated)Delay Response (s) RL1 RL2 RL3 RL4 RL5 RL6 RL7 Figure 5-10 Time delay between the proceedi ng channel flow oscillation peaks to the associated channel power oscillation peaks

PAGE 82

65 Comparison to KKL Frequency Test Results As mentioned previously in Chapter 2, the four test poi nts from the KKL instability tests resulted in oscillatory fr equencies of 0.45 Hz. Only te st point B from the KKL tests was duplicated in this analysis; however, sinc e the oscillatory fre quencies depended only on initial core flow, the test results were compar ed to the analysis resu lts of similar initial core flow (Figure 5-11). The analysis re sults agreed within 0.11 s of the KKL test results. 0.42 0.43 0.44 0.45 0.46 0.47 0.48 2828.52929.53030.531 Initial Core Flow (% of rated)Power Frequency Response (Hz) Test Point A Test Point B Test Point C Test Point D Experimental Points Experiment Result for Test Point B Figure 5-11 Comparison of the KKL test poin t frequency results and the computational test point results Fuel Safety-Limit Concerns The main fuel safety-limit concern for the safe operation of BWRs is MCPR. During normal operations, MCPR safety-limit is 1.07 when both recirculation pumps are in operation and 1.08 when one recirculation pump is in operation. During transient

PAGE 83

66 events, however, the thermal-limit margin can be temporarily eroded to allow additional operational flexibility. The time when the most responsive fuel channel exceeds its critical power corresponds to an MCPR less than one. Large power oscillations in the most responsive fuel channel and significant power oscillations in the total core power existed before there was a loss of thermal margin (Table 5-1). A loss of thermal margin is not a concern during an inst ability event as long as the reactor protection system is working properly. Table 5-1 Estimated elapsed time for th e unstable computational points to experience a loss of thermal margin Initial Initial El apsed time Corresponding most Corresponding core core for MCPR to responsive channel core power flow power drop below 1.0 power peak amplitude peak amplitude (% of rated) (% of rated) (s) (% of initial) (% of initial) 24.8 37.8 N/A 120* 101* 25.2 42.7 N/A 170* 108* 25.4 47.7 72.1 211 120 25.5 52.6 40.0 233 148 28.8 53.1 130.2 205 114 30.0 54.4 223.0 196 113 30.0 59.5 58.1 186 118 30.0 64.5 37.0 142 111 30.0 69.4 32.6 157 112 35.0 66.1 259.6 183 116 35.0 71.0 58.5 145 105 35.0 76.1 51.0 143 106 40.0 76.3 83.2 143 104 40.0 81.6 72.6 153 107 *Note: Limit cycle power peak amplitudes.

PAGE 84

67 CHAPTER 6 SUMMARY, CONCLUSIONS AND FUTURE WORK The stable computational points in this an alysis sustained at least a 65% out-ofphase flow perturbation; how ever, two of the unstable computational points required a 1% out-of-phase flow perturbation to become unstable (Table 6-1). The rate of growth closest to 1.0 of an inherently unstable computational point was 1.00491 for 30.0% of rated core flow and 54.4% of ra ted initial core power on RL4. Table 6-1 Rates of growth for the two computational point s requiring a 1% out-ofphase flow perturbation to develop oscillations Computational point Rate of growth 24.8% of rated initial core flow and 1.00434 37.8% of rated initial core power on RL2 35.0% of rated initial core flow and 1.00264 66.1% of rated initial core power on RL5 This implies that a BWR is susceptible to small flow perturbations when operating close to the region of instability, or there is an analytical error possibly associated with numerical dissipation in the computational solution. The flow perturbations were induced at 180 out-of-phase conditions to maintain a constant average core flow; therefore, numerical dissipation in the co mputational solution is attributed to the necessary 1% flow perturbation. This would indicate a numer ical dissipation of approximately 0.5%. The results showed that the operating para meters stabilized, and the oscillatory frequencies increased, with increasing core flow. (A higher frequency translates to a

PAGE 85

68 shorter period.) The relationship between a larger amplitude reduction per cycle and a shorter period demonstrates a faster rate of approach to stable conditions. Therefore, increasing the total core flow, when power os cillations are detected, is a good alternative to inserting control blades. However, if in creasing total core flow is infeasible, then inserting control blades would be necessa ry to suppress any power oscillations. If out-of-phase oscillations exist in the core and are undetected then a number of fuel channels will experience a loss of thermal margin causing heat-up of the clad. Additional analyses are necessa ry to determine the probability of unstable operations during start-up or loss-of-flow from a single recirculation pump trip. However, a loss-offlow transient from a two recirculation pu mp trip, according to these results, requires inserting control blades to avoid an instab ility event while the recirculation pumps are brought back online. Also, additional analyses are necessary to determine the effects of lower plenum temperature and system pressu re on the threshold of unstable operations. Instability occurrences can possibly be predicted by having knowledge of the operating parameters: total core flow, total core power, lower plenum temperature, and system pressure. These parameters are believed to have first order effects on the stability of the core. This analysis has shown that decreasing the total core power or increasing the total core flow has a stabilizing eff ect on BWR operations. Hsu and Graham [6] founded that decreasing the lower plenum temp erature has a stabilizing effect on thermalhydraulic instability. Bour [7] founded that increasing the system pressure, increasing the inlet pressure drop, or decreasing the tw o-phase pressure drop by reducing the outlet restrictions have stab ilizing effects on thermal-hydrau lic instabilities. The stabilizing effects of these parameters (reducing the core power, increasing the core flow, increasing

PAGE 86

69 the system pressure, and decreasing the lowe r plenum temperature) are sufficient for thermal-hydraulic instabilities. Each of these stabilizing actions directly result in raising the average core boiling boundary, thereby increasing the liquid pressure drop and decreasing the two-phase pressure drop. A BWR features nuclear feedback interl ocking the operating parameters. Except for reducing the core power by inserting contro l blades, the other three stabilizing actions increase neutron moderation and, thereby, increase core power. This analysis has sufficiently shown that although increasing the total core flow increase s the total core power, it has a stabilizing effect on the operatin g parameters. The main conclusions that can be drawn from the results in this analysis are Decreasing the core power with control bl ades has a stabilizing effect on reactor conditions. Increasing the core flow has a stabilizing e ffect on reactor cond itions, as long as the increase in power from nuclear feedback does not dominate. The power oscillatory frequencies depe nd linearly on the average core flow. The power oscillatory frequencie s do not depend on the core power. Additional work is needed to quantify the dependence of instability behavior and characteristics on the system pressure and lo wer plenum temperature. Attention can be given to determine any dependence on cycle exposure, core loading pattern, fuel assembly lattice types…. Also, stability analysis could be performed on the reactor kinetics equation with temperature and void-re activity feedbacks. Individual instability analyses would need to be conducted for ot her BWRs, since Bour [7] determined that effects of various geometric parameters can not be generalized and are case-specific. Understanding the general effects of the opera ting parameters on stability is a necessary prerequisite to assisting and accelerating the process of analyzing other BWRs.

PAGE 87

70 APPENDIX A CHANNEL GROUPING MAPS 535353535353 53535047464647505353 535046434141414243465053 53535345423938373738394245535353 5350494442393837 27 363738394245495053 5350484543403939383737383939414345485053 53504845454341354544404044453541434545485053 535049464444443242454641414645423244444446495053 535048443335323432423535353543323432353345485053 5353494733353444323543443535444335324434343347495353 53505049473533505046455050454550504546505033354749495053 53504948473247505046475050474750504746505046324748485053 535049473532333152515151525251515252515151513133323547495053 535048473534313351525151515251515251515152513333343547485053 535048474848343552525252525252525252525252523534484847485053 23201817181845222222222222222222222222222254181817182023 23201817542832122212121222121222121212221314517182023 2320191752312121212122222121222221212122132517192023 232018181721620201617202017172020171620201721718192023 2320191917532020161520201515202015162020351719202023 2323191734414251314551413521445317192323 2320181535242135555122425314182023 2320191614141421215161111161512214141416192023 232018151513115151410101415511131515182023 23201815131199877899101315182023 23201915129876 29 7891214192023 23232315129877891215232323 232016131211111113162023 23232017161617202323 232323232323 Control Blades 37.5% INSERTED41.7% INSERTED58.3% INSERTED83.3% INSERTED 87.5% INSERTED91.7% INSERTED100% INSERTED100% INSERTED Figure A-1 Channel-grouping map for RL1 generated by HyCA

PAGE 88

71 535353535353 53535047464647505353 535046444241414244465053 53535345424038373738404245535353 5350484542393837 27 363738404245485053 5350484543403939383737383939414345485053 53504845444341404444404044443541434545485053 535049454444433341454541414545423343444446495053 535047453443323432423535353543323432433445485053 5353494734443444324343443535444343324434453447495353 53504948474734504945455049454549504545495034474748495053 53504848473347495047475050474750494747504947324747485053 535049474733343251515151525151515152515151513134334747495053 535048474635313551525151515251515251515152513434354647485053 535048474848344752525252525252525252525252524734484847485053 2320181718184172222222222222222222222222222174181817182023 2320181716528421222121212221212221212122215151617182023 232019171734121212121222121212122212121212431717192023 232018171721719201717192017172020171720191731718182023 232019181717420191515201915151920151519204171718192023 23231917415414213131455141313214414417192323 232018154132421355551224213415172023 2320191614141331215151111151511313141415192023 2320181515131151414101014141011131415182023 23201815131199877899101315182023 232018151210876 29 7891215182023 2323231512108778101215232323 232016141211111214162023 23232017161617202323 232323232323 Control Blades 29.2% INSERTED33.3% INSERTED50.0% INSERTED75.0% INSERTED 79.2% INSERTED83.3% INSERTED87.5% INSERTED95.8% INSERTED Figure A-2 Channel-grouping map for RL2 generated by Hy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ontrol Blades 25.0% INSERTED29.2% INSERTED45.8% INSERTED70.8% INSERTED 70.8% INSERTED75.0% INSERTED83.3% INSERTED87.5% INSERTED Figure A-3 Channel-grouping map for RL3 generated by HyCA

PAGE 89

72 535353535353 53535048474749505353 535047444241414244475053 53535346424039373839414346535353 5350494542403837 27 363738404245495053 5350484542403938383637383939404345485053 53504845444240394342393943444041424445495053 535049464343423241444440404444413242434446495053 535048453442323431423434343442313432433445485053 5353494735443443313534433434433435314434453547495353 53505048474634494845354948454549493446484934474748495053 53504947473247494934474949474749494734494947324747495053 535049484733343152515151525151515152515151513134324748495053 535049474735283551525151515151515151515152513531354747495053 535049474747344652525251525251515252515252523534474717192023 535049471717452222222122222121222221222222164171717192023 232019171751521222121212121212121212122215151717192023 232019181724121212121222121212122212121221431718192023 2320191717217191941719191717191917419191721717192023 2320191817174191816419191515181951518194161718202023 2323191751541415413441345113414517192323 232018154132411244441214212415182023 2320191614131221114141010141411212131316192023 23201915141211101413991213910121415182023 23201815131099876889101215182023 232019151210876 29 78101215192023 2323231613119879101216232323 232017141211111214172023 23232019171718202323 232323232323 Control Blades 16.7% INSERTED20.8% INSERTED37.5% INSERTED62.5% INSERTED 66.7% INSERTED70.8% INSERTED79.2% INSERTED83.3% INSERTED Figure A-4 Channel-grouping map for RL4 generated by HyCA 535353532323 53535050505020202323 535050484848481818202023 53535348484747461617171818232323 5350494847464646355516161718192023 535049474746464646344161616161718182023 535047454545463448473551718416161616172023 5350464443434432464747344171716215141314172023 534743423442313331463333321613112412141723 53534441404133433134334633316341133111011142323 5350454239393345454533484846161818315161539912152023 534642393736404446334648483551818163161410779121723 53504441383636315152525252525222222222222221176811142023 534843403737 27 385152525252525222222222222221867810131823 5348434041403739525252525252522222222222222247101111131823 5348434141403734525252525252522222222222222297101110131823 534843403837283851525252525252222222222222218 29 7710131823 53504441383637315152525252525222222222222221166811142023 534742393737404446334648483551818163161410679121623 5350454239393345464533484846161818315151539912152023 53534441404133433134334633316341133111011142323 534744423442313331463233331613112412131723 5350474443444532464747344171716214131314162023 535047464646463448473551718416151515172023 535048484746464646344161616161717192023 53504948474646353551616161718192023 53535348484747461617171818232323 535050484848181818202023 53535050502020202323 535353232323 Control Blades 16.7% INSERTED33.3% INSERTED58.3% INSERTED 58.3% INSERTED66.7% INSERTED75.0% INSERTED75.0% INSERTED Figure A-5 Channel-grouping map for RL5 generated by HyCA

PAGE 90

73 535353535353 53535050505050505353 535050494848484849505053 53535349474647474747474849232323 535048464544444535354646474818192023 5350464443424335453434463546161718192023 535045424134413346473535474831641717192023 53504542403839313545473434484751431617192023 534743403838313331353232323251314416181923 535344413838323434333235323235241425415172323 5350454238373243433532484835354818251718251314182023 5347433936 27 394344313548483434181852181651412151923 535045413836363151515252525252522222222222221321113162023 5349444138373633515252525252525222222222222231101112152023 5349434141413334525252525252522222222222222243111212141923 5349444242413334525252525252522222222222222243111111131923 53504542414031335252525252522222222222222221367811141923 53504643413233315252525252522222222222222121166811152023 534945423431354648323548484418185114139 28 69131723 5350484443353248473532481855181825131327812152023 535347453435323431343252252329428811142323 53494846343431333135222251318810131723 535049474633343135171844171551981012152023 5350494747344633181755171631141112152023 535049484746165164415513121314162023 5350494818171616551514141516182023 53535319181717171717161719232323 232020191818181819202023 23232020202020202323 232323232323 Control Blades 29.2% INSERTED54.2% INSERTED 54.2% INSERTED58.3% INSERTED70.8% INSERTED70.8% INSERTED Figure A-6 Channel-grouping map for RL6 generated by HyCA 535353532323 53535050505020202323 535049484848181818202023 53535348474747471617171818232323 535049484747464646161616171718192023 535048474646464646355161616161717182023 53504745443545344746355161741651415172023 5350474342343532354647344171652541314172023 5347434235353133313532322251315512141823 53534442414133352734323432242415311512142323 5350454240403343443532474633316172515143101012152023 53474241373740434532354647333171652151357811131723 53504441383637315152525252525222222222222221176811152023 534843413737 28 395152525252525222222222222221967711131923 534843413938373952525252525252222222222222224791011131823 53484341403937345252525252525222222222222222978911131823 534943413737363951525252525252222222222222219 29 7711131823 53504541383637315152525252525222222222222221176811142023 534743413837354345323546473331716521513107711121723 5350454240403344453532474633316172514133101012152023 535344423541333531343234322424153111112142323 5348444235353133313532322251315512131723 5350474443343532354647344171652541213172023 53504745443546344746355161741551415172023 535048474746464646355161616161617182023 535049484747464646161616171718192023 53535348484747461717171718232323 535050484848181818192023 53535050502020202323 535353232323 Control Blades 20.8% INSERTED50.0% INSERTED 50.0% INSERTED54.2% INSERTED62.5% INSERTED66.7% INSERTED Figure A-7 Channel-grouping map for RL7 generated by HyCA

PAGE 91

74 APPENDIX B FUEL CHANNEL SPECIFICATIONS Table B-1 Fuel cha nnel material compositions Element Material Fuel pellet Uranium Dioxide Fuel rod Zircaloy Channel box Zircaloy Table B-2 Fuel channel dimensions Element Dimension Fuel pellet radius 0.52 cm Inner radius of fuel rod 0.53 cm Outer radius of fuel rod 0.61 cm Inner radius of water rod 0.67 cm Outer radius of water rod 0.75 cm Fuel rod pitch to diameter ratio 1.32 Inside channel width 13.2 cm Thickness of channel box wall 0.305 cm

PAGE 92

75 LIST OF REFERENCES 1. “BWR/6 General Description of a Boiling Water Reactor,” 2nd rev., Global Nuclear Fuel—General Electric Company, Wi lmington, North Carolina (1980). 2. J. R. LAMARSH, Introduction to Nuclear Engineering 2nd ed., Addison-Wesley Publishing Company, Inc., Boston, Massachusetts (1983). 3. R. T. LAHEY and F. J. MOODY, The Thermal-Hydraulics of a Boiling Water Reactor American Nuclear Society, Chicago, Illinois (1977). 4. J. G. M. ANDERSEN, Y. K. CHEUNG, C. L. HECK, L. A. KLEBANOV, J. C. SHAUG, and B. S. SHIRALKAR, “TRACG Qualification Licensing Topical Report,” 2nd rev., Global Nuclear Fuel—General Elect ric Company, Wilmington, North Carolina (2000). 5. N. E. TODREAS and M. S. KAZIMI, Nuclear Systems I: Thermal-Hydraulic Fundamentals Taylor & Francis, Bost on, Massachusetts (1993). 6. Y. HSU and R. W. GRAHAM, Transport Processes in Boiling and Two-Phase Systems Hemisphere Publishing Corporation, Washington, D.C. (1976). 7. J. A. BOUR, “Oscillatory Two-Phase Flows,” Two-Phase Flows and Heat Transfer with Application to Nucl ear Reactor Design Problems J. J. GINOUX, Ed. Hemisphere Publishing Corporation, Washington, D.C. (1978). 8. R. T. CHIANG, A. K. CHUNG, C. L. KUNZ, R. E. STACHOWSKI, L. TROSMAN, and R. M. FAWCETT, “Impacts of Fuel Design, Core Design and Reactor Operation on BWR Stability Behavior,” Proc. Topical Meeting on Advances in Nuclear Fuel Management (III) (ANFM 2003) Hilton Head Island, South Ca rolina, October 5-8, 2003, on CD-ROM, American Nuclear Society (2003). 9. F. P. INCROPERA and D. P. DEWITT, Fundamentals of Heat and Mass Transfer 4th ed., John Wiley & Sons, Inc., New York City, New York (1996). 10. “Leibstabt Nuclear Power Plant Safe ty Analysis Report,” Global Nuclear Fuel— General Electric Company, Wilmington, North Carolina (1990). 11. A. P. CHOPELAS, B. R. MOORE, R. STACHOWSKI, L. TROSMAN, and H. ZHANG, “PANAC11A User’s Manual,” 2nd rev., Global Nuclear Fuel—General Electric Company, Wilmington, North Carolina (2003).

PAGE 93

76 12. R. W. SCHRUM, “CRNC-06A User’s Manual,” Global Nuclear Fuel—General Electric Company, Wilmingt on, North Carolina (1998). 13. J. G. M. ANDERSEN, C. L. HECK, and J. C. SHAUG, “TRACG04A,P User’s Manual,” Global Nuclear Fuel—General Electri c Company, Wilmington, North Carolina (2002). 14. J. G. M. ANDERSEN, Y. K. CHEUNG, C. L. HECK, L.A. KLEBANOV, J. C. SHAUG, and B. S. SHIRALKAR, “TRACG Model Description,” 2nd rev., Global Nuclear Fuel—General Electric Compa ny, Wilmington, North Carolina (1999). 15. J. G. M. ANDERSEN, J. C. SHAUG, a nd A. L. WIRTH, “TRACG Time Domain Analysis of Thermal-Hydraulic Stability Sensitivity to Numerical Method and Comparison to Data,” Proc. INEL Stability Symposium Idaho Falls, Idaho, USA, August 10-11, 1989, p. 17-30, Idaho Nationa l Engineering Laboratory (1989).

PAGE 94

77 BIOGRAPHICAL SKETCH Thomas Keith Bentley was born on July 24, 1980. Keith has spent all of his life in Florida. He graduated from South Fork Hi gh School in 1998, and entered the University of Florida to earn a Bachelor of Science degr ee in nuclear engineer ing. He graduated with high honors earning his undergraduate degr ee along with a minor in mathematics in 2002. He then entered graduate school also at the University of Fl orida. He will begin his professional career after obtaining hi s Master of Engineer ing degree in nuclear engineering. Keith has membership in th e Order of the Engineer and the American Nuclear Society.