Download - Basics of Nuclear Energy
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NUCLEAR PHYSICSANDREACTOR THEORYA one-hour overview
RADIOACTIVITY
Nuclear instability
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TYPES OF RADIATION
NUCLEAR STABILITY CURVE
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BINDING ENERGY
FISSION
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ACTUAL FISSION
FISSION
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FISSION PRODUCT YIELD
FISSION PRODUCTSVARY WITH FUEL TYPE
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CHAIN REACTION
NEUTRONLIFE-CYCLE
Multiplication Factork ≡ neutrons in this generation divided by k ≡ neutrons in this generation divided by
number of neutrons in previous generation
“Four – Factor” Formulak = ε•p•f•ηk∞ = ε•p•f•η
“Six – Factor” Formulakeff = ε•Lf•p•Lt•f•η
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NEUTRON LIFE-CYCLE
keff = ε•Lf•p•Lt•f•η
Term Range Typical
Fast Fission Factor (ε) > 1.0 1.04Fast Non-leakage Probability (Lf) < 1.0 0.86Resonance Escape Probability (p) < 1.0 0.49Thermal Non-leakage Probability (Lt) < 1.0 0.84Thermal Utilization (f) < 1.0 0.90Neutron Production Factor (η) > 1.0 2.65
NEUTRON LIFE-CYCLE
Fission Production of Fast Neutrons (η)
Ni = N0ηN i+1= NiηεLfp Ltf
Fast Fission Factor (ε)
Ni = N0ηεNi = N0ηεLfp Lt
Thermal Utilization
(f)
Keff=Ni+1/Ni
Keff=ηεLfp Ltf
Fast Non-leakage
(Lf )
Ni = N0ηεLfResonance Escape
Probability (p)
Ni = N0ηεLfpLf p
Thermal Non-Leakage
(Lt)
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CORE DESIGN
keff = ε•Lf•p•Lt•f•η
Minimize LeakageLf•p•Lt
Maximize Use and Production
ε•f•ηε•f•η
By varyingGeometryCore Contents
NUCLEAR CROSS SECTIONS(1 BARN = 1 E-24 CM2
R=σNφ
1/v region
Approximate Energy of Thermal Neutrons
Resonance Absorption Peaks
fission production
region
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THERMALIZATION OF NEUTRONS
FUEL DESIGN ANDCORE DESIGN
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CORE GEOMETRY AND MASS FRACTIONS
Fuel Pin Pitch
Water Gap
Fuel Pins
Instrumentation
Control Rodor
Water Channel
MODERATOR TEMPERATURE COEFFICIENT
ter) Negative FeedbackPositive Feedback
R ti itactio
n M
oder
ator
(Wat
Area of Operation
Reactivity
Fra
Temperature
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REACTIVITY
The number of neutrons present in the core after a given number of generations isgiven number of generations is
Nn = No (keff)Reactivity is the fractional change in neutron
population per generation.Reactivity is then:
ρ = (k ff-1)/k ffρ = (keff-1)/keffand
keff= 1/(1-ρ)
POWER CHANGES
Reactor Power = F(prompt neutrons) + F(delayed neutrons)F(delayed neutrons)
(in 235U, β = 0.007)
Typically 6 groups of delayed neutrons are modeledfrom fission product decay processes that emits neutrons (arbitrarily arranged into 6 groups of similar decay rate) – referred to as precursors
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POWER CHANGES
By observation, power changes follow the sum of exponential curves, i.e.exponential curves, i.e.
P(t) = P0ekot + Σβi(0)ekit + other stuff
REACTOR DYNAMICS
Inhour Equation
(where power will be in an hour)
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INHOUR SOLUTIONS(IF ANYONE CARES….)
POWER INCREASE
Steady Exponential Increase
Ln(P
ower
)
Initial Power
Prompt Jump
Time
Proportional to Reactivity ‘added’
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POWER DECREASE
Initial PowerInitial PowerPrompt Drop
Steady Exponential DecreaseLn
(Pow
er)
Proportional to Negative Reactivity
Inserted
Time
POWER GENERATIONAFTER A REACTOR TRIP
300
350
7%
8%
100
150
200
250
300
2%
3%
4%
5%
6%
7%
Pow
er (M
Wt)
Pow
er (%
or R
ated
)
0
50
0%
1%
0.1 1 10 100 1000 10000
Seconds after Reactor Trip
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REACTOR DYNAMICS
What mattersAll power changes follow compound exponential All power changes follow compound exponential curves Power never goes to zeroTime to make power level change depends on whether prompt or delayed neutrons are governingAll power reactor operations are in delayed neutron governed regions
QUESTIONS?