Operational Reactor Safety
22.091 /22.903
Professor Andrew C. Kadak Professor of the Practice
Lecture 6 Reactor Energy Removal
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 1
Topics to Be Covered
• Power Distributions
• Peaking Factors
• Fuel-Pin Heat Transfer
• Nuclear Limits in Design
• Peak Centerline Temperature
• Peak Clad Temperature
• Departure From Nucleate Boiling
• Control Rod Impacts
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 2
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BWR Core Lattice
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“ B W R / 6: General Des c r iption of a BW R,” GE, 1980.
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PWR Fuel Assembly
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274 Nuclear Reactor S ysiems
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TOP NO ZZLE
CONTROL R00
BULGE J0IdT
Rod cv Guida Tube
FIGURE 1 0-6
Pr e ssuriz e d - wa tcr reactor ›’esscl. ( Courtesy of 1Vestin¿l›ouse Elcctric Corporation. )
Typical Four-Loop Reactor Core
Assemblies)
Cros s Sectio n (19 3 Fue l
Parameter s
Total heat output ~3250-3411 MWT
Heat gener ated in fuel 97.4%
Nominal s ystem pressure 2250 psia
Total coolant flow rate ~138.4 x 10 6 lb/hr Coolant Temper ature
Nominal inlet Average rise in vessel Outlet from vessel
557.5 ˚ F
61.0 ˚F
618.5 ˚ F
Equivalent core diameter 11.06 ft Core length, betwee n fuel ends 12.0 ft Fuel weight, uranium (first core) 86,270 kg Number of fu el assem blies 193
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Masche, G., Syst ems S u mmary: W PWR NPP, 1971
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Power Density
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 14
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Energy Removal
• Heat Balance in a reactor
– P ower Equation function of neutron flux
• Impact of Power Distribution on ability to remove heat and maintain temperature limits
– Material and Fuel limitations
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 15
Diffusion Theory Flux
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 16
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Flux Shapes
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 17
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Power Peaking Factors
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 18
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Power Distributions
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 19
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Fuel Pin Cross Section
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 21
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Heat Removal Governing Processes
• Fuel Pin Power Production
– Conductive heat transfer
– F ourier Law of Heat Conduction
– P oisson’s Equation
• Clad Heat Transfer
– P oisson’s Equation but no heat source
• Clad to Coolant
– N ewton’s law of cooling
– C onvective Heat Transfer
• Gap to Clad
– C onvective
– Conductive heat tran sfer coefficient – hgap
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 22
Nuclear Limits
• Hot spot factor –
– P eak power in pin
– P revent Fuel Melting
• Hot Channel Factor
– A ssure heat removal from pin
– Minimum Departure from Nucleate Boiling Ratio
• Design Considerations
– Limits on Power
– M aterials
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 23
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 24
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Axial Peaking
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 25
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Control Rod Insertion
Rod “bite”
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 27
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Homework Assignment
Homework: Problems 7.2,5,6,8
Department of Nuclear Science & Engineering
Prof. Andrew C. Kadak, 2008 Page 28
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22.091 Nuclear Reactor Safety
Spring 200 8
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