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Core Thermal Limits PPT

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Operator Generic Fundamentals
Thermodynamics – Core Thermal Limits
© Copyright 2014
Operator Generic Fundamentals
2
Core Thermal Limits Introduction
• This module covers reactor core thermal limits related to
Pressurized Water Reactor plants
– Thermal limit purposes
– Factors affecting these limits
• Core thermal limits are important for ensuring public health and
safety during:
– Steady-state power conditions
– Normal operational transients
– During accident conditions such as loss of coolant accidents
(LOCA)
© Copyright 2014
INTRO
Operator Generic Fundamentals
3
Terminal Learning Objectives
At the completion of this training session, the trainee will demonstrate
mastery of this topic by passing a written exam with a grade of ≥ 80
percent on the following Terminal Learning Objective (TLO):
• TLO 1 Describe the reason for reactor core thermal limits and
factors affecting them.
© Copyright 2014
INTRO
Operator Generic Fundamentals
4
Reactor Core Thermal Limits
TLO 1 – Describe the reason for reactor core thermal limits and factors
affecting them.
• The design and operation of a nuclear power plant helps ensure that
public health and safety is maintained
– Requires maintaining reactor fuel integrity
• Requires operating the reactor within established thermal power and
peaking limits
– Some limits are controlled by the reactor operator
– Some are only affected by reactor fuel and material design
• Surveillances ensure reactor thermal parameters are in compliance,
with corrective action response when required
© Copyright 2014
TLO 1
Operator Generic Fundamentals
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Enabling Learning Objectives for TLO 1
1. Describe the following peaking factors as they relate to local and
average reactor power:
a. Axial peaking factor (APF)
b. Local peaking factor (LPF)
c.
Radial peaking factor (RPF)
d. Total peaking factor (TPF)
2. Describe the reason thermal limits are necessary and the function
of the core protection calculator.
3. Describe the factors that affect peaking and hot channel factors.
© Copyright 2014
TLO 1
Operator Generic Fundamentals
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Peaking Factors
ELO 1.1 - Describe the following peaking factors as they relate to local
and average reactor power: a. Axial peaking factor (APF), b. Local
peaking factor (LPF), c. Radial peaking factor (RPF), d. Total peaking
factor (TPF)
To ensure operation within design limitations, various hot channel and
peaking factor limits apply during reactor operation.
• Ensure even small localized areas of core power does not exceed
design limits.
• If exceeded, could cause fuel damage during either
– Steady-state operation or transient conditions
– Even exceed design criteria for accident condition
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ELO 1.1
Operator Generic Fundamentals
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Peaking Factors
• The consequences of exceeding any of these prescribed limits could
result in
β€’ Fuel damage
β€’ Clad damage resulting in fission product gases released to the
reactor coolant system in an accident condition.
β€’ Potential releases to public
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ELO 1.1
Operator Generic Fundamentals
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Axial Peaking Factor
• Axial peaking factor (APF) is
the ratio of:
– Average heat flux for a
specific elevation (1,2, 3,
or 4) to the average heat
flux over the entire core
• Axial peaking factor is
normally defined in plant
Technical Specifications as
the normalized average axial
power at elevation “z”
Figure: Simplified Core Map
© Copyright 2014
ELO 1.1
Operator Generic Fundamentals
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Axial Peaking Factor
A
The information received from the incore map
would look as follows:
The APF is the ratio of average power density
for one elevation to average power density for
the entire core.
The average power density is determined by
adding all individual power density and dividing
by number of locations measured.
B
C
D
1
2.0
3.0
2.0
1.0
2
3.0
4.0
3.0
5.0
3
5.0
8.0
6.0
7.0
4
3.0
2.0
2.0
3.0
Figure: Simplified Core Map
π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘π‘œπ‘€π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 =
𝐴1 + 𝐡1 + 𝐢1 + 𝐷1 + 𝐴2 + 𝐡2 + 𝐢2 + 𝐷2 + 𝐴3 + 𝐡3 + 𝐢3 + 𝐷3 + 𝐴4 + 𝐡4 + 𝐢4 + 𝐷4
16
π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘π‘œπ‘€π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 =
2+3+2+1+3+4+3+5+5+8+6+7+3+2+2+3
16
π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘π‘œπ‘€π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 = 3.68
© Copyright 2014
ELO 1.1
Operator Generic Fundamentals
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Axial Peaking Factor
A
Referring to the sample core, the
power density at elevation “1” is:
2+3+2+1
=2
4
1
2.0
3.0
2.0
1.0
Now APF (Axial peaking factor) can be calculated
for our simple core for each core elevation.
B
C
D
1
2.0
3.0
2.0
1.0
2
3.0
4.0
3.0
5.0
3
5.0
8.0
6.0
7.0
4
3.0
2.0
2.0
3.0
APFx = Average power density at Elevation x
Average power density
2
3.0
4.0
3.0
5.0
3+4+3+5
= 3.75
4
3
5.0
8.0
6.0
7.0
5+8+6+7
= 6.5
4
4
3.0
2.0
© Copyright 2014
2.0
3.0
3+2+2+3
= 2.5
4
ELO 1.1
𝐴𝑃𝐹1 = 2.00/3.68 = 0.543
𝐴𝑃𝐹2 = 3.75/3.68 = 1.019
𝐴𝑃𝐹3 = 6.50/3.68 = 1.766
𝐴𝑃𝐹4 = 2.50/3.68 = 0.679
Slide 10
Operator Generic Fundamentals
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Axial Peaking Factor
• Rod motion and xenon oscillations have strong effects to the average
linear power density vertically (Z) in the core
– Makes this factor under the control of the operator.
Maximum Axial Peaking Factor in the core is calculated based on
the core elevation with the highest average kW/ft.
𝐴π‘₯π‘–π‘Žπ‘™ π‘ƒπ‘’π‘Žπ‘˜π‘–π‘›π‘” πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ 𝐹𝑍𝑁 =
© Copyright 2014
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’
π‘˜π‘Š
π‘˜π‘Š
𝑖𝑛 β„Žπ‘œπ‘Ÿπ‘–π‘§π‘œπ‘›π‘‘π‘Žπ‘™ π‘π‘™π‘Žπ‘›π‘’ π‘€π‘–π‘‘β„Ž π‘šπ‘Žπ‘₯π‘–π‘šπ‘’π‘š
𝑓𝑑
𝑓𝑑
π‘˜π‘Š
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’
𝑖𝑛 π‘‘β„Žπ‘’ π‘π‘œπ‘Ÿπ‘’
𝑓𝑑
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Axial Peaking Factor
When control rods are inserted into the core, axial peaking factor increases
• Control rods initially suppress the neutron flux in the upper portion of the core
– Driving the region of peak flux lower in the core
• If reactor power is maintained constant
– Peak power density increases to compensate for the reduced power
densities high in the core
• If power is increased with no rod motion
– Axial peaking factor will increase due to the primary coolant temperature
increase through the core
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Operator Generic Fundamentals
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Radial Peaking Factor
Radial Peaking Factor (RPF) is the ratio of the hottest part of the core to
the average power on that horizontal slice
– Ratio of the peak heat flux at one core elevation to the average
heat flux for that same core elevation:
𝑅𝑃𝐹 =
© Copyright 2014
π‘ƒπ‘’π‘Žπ‘˜ π‘π‘œπ‘€π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘Žπ‘‘ π‘‘β„Žπ‘’ π‘’π‘™π‘’π‘Žπ‘‘π‘–π‘œπ‘›
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘π‘œπ‘€π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘Žπ‘‘ π‘‘β„Žπ‘’ π‘’π‘™π‘’π‘£π‘Žπ‘‘π‘–π‘œπ‘›
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Radial Peaking Factor
• Strong function of core design
• Under normal conditions, operators have little control of this peaking
factor.
• Has technical specification limit checked periodically to ensure nuclear
heat flux hot channel factor is within prescribed limits.
Referring to the sample core below, the average at elevation “1” was
previously calculated to be 2.0. The peak power density at elevation “1” is
3.0. (Note this is in assembly B).
A
𝑅𝑃𝐹1 = 3.0/2.0 = 1.5
B
C
D
1
2.0
3.0
2.0
1.0
2
3.0
4.0
3.0
5.0
3
5.0
8.0
6.0
7.0
4
3.0
2.0
2.0
3.0
and therefore,
𝑅𝑃𝐹2 = 5.0/3.75 = 1.33
𝑅𝑃𝐹3 = 8.0/6.5 = 1.23
𝑅𝑃𝐹4 = 3.0/2.5 = 1.2
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ELO 1.1
Operator Generic Fundamentals
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Local Peaking Factor
• Ratio of maximum power at a hot spot to average core power.
• Defines the hottest part of a hot nuclear fuel rod.
• Assurance that power in a localized area of a fuel rod does not cause
melting.
• Does not relate to a specific core height (Z) but a hot spot to average
core power.
π‘€π‘Žπ‘₯π‘–π‘šπ‘’π‘š π‘ƒπ‘œπ‘€π‘’π‘Ÿ π‘Žπ‘‘ π‘Ž π»π‘œπ‘‘ π‘†π‘π‘œπ‘‘
πΏπ‘œπ‘π‘Žπ‘™ π‘ƒπ‘’π‘Žπ‘˜π‘–π‘›π‘” πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ =
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ πΆπ‘œπ‘Ÿπ‘’ π‘ƒπ‘œπ‘€π‘’π‘Ÿ
© Copyright 2014
ELO 1.1
Operator Generic Fundamentals
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Heat Flux Hot Channel Factor and Total
Peaking Factor
• Relates to the maximum local power in the core to the average power
in the core.
• Max heat flux hot channel factor (HCF) to:
– Ensure ability of the ECCS to cool the core following a LOCA
– Prevent exceeding specific fuel temperature limits (fuel
melting/clad damage).
• Limits set by plant’s operating license.
• Heat Flux HCF or Total Peaking Factor, 𝐹𝑄 𝑇 – also shown as 𝐹𝑄 𝑧
variable for different heights.
𝐹𝑄 𝑇 =
© Copyright 2014
π‘€π‘Žπ‘₯π‘–π‘šπ‘’π‘š π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘Žπ‘›π‘¦π‘€β„Žπ‘’π‘Ÿπ‘’ 𝑖𝑛 π‘‘β„Žπ‘’ π‘π‘œπ‘Ÿπ‘’
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 𝑖𝑛 π‘‘β„Žπ‘’ π‘π‘œπ‘Ÿπ‘’
ELO 1.1
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Heat Flux Hot Channel Factor and Total
Peaking Factor
• Sometimes referred to as the ratio of the maximum pellet power
generation to the average pellet power generation.
• Varies with
– Fuel loading patterns
– Enrichment
– Control rod bank insertion
– Fuel burn-up, and
– Changes in axial power distribution.
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Operator Generic Fundamentals
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Heat Flux Hot Channel Factor and Total
Peaking Factor
In theory, a known value of 𝐹𝑄 𝑇 can determine maximum local power.
With an average linear fuel rod thermal power of 5.44 kW/ft. and an 𝐹𝑄 𝑇
known value of 2.32, then the maximum local linear power density
anywhere in the core would equal = 2.32 x 5.44 = 12.6 kW/ft.
© Copyright 2014
ELO 1.1
Operator Generic Fundamentals
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Heat Flux Hot Channel Factor and Total
Peaking Factor
A sub-factor designated as the engineering heat flux HCF (𝐹𝑄 𝐸)
provides an allowance for manufacturing tolerances on fuel rods,
pellets, and cladding.
𝐹𝑄 𝑇 = 𝐹𝑄 𝑁 × πΉπ‘„ 𝐸
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Operator Generic Fundamentals
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Heat Flux Hot Channel Factor and Total
Peaking Factor
πΉπ‘ˆ 𝑁, the nuclear uncertainty factor, is a penalty on the measured
values of the Radial Peaking Factor, πΉπ‘‹π‘Œ 𝑁, and the Axial Peaking
Factor, 𝐹𝑍 𝑁.
Accounts for the fact that the incore mapping system cannot measure
every point in the core
– Entirely possible when operating close to 𝐹𝑄 𝑁 limits that a point
could exceed this value.
𝐹𝑄 𝑁 = πΉπ‘‹π‘Œ 𝑁 × πΉπ‘ 𝑁 × πΉπ‘ˆ 𝑁
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Heat Flux Hot Channel Factor and Total
Peaking Factor
Resulting equation for Total Peaking Factor or Heat Flux Hot Channel
Factor:
𝐹𝑄 𝑇 = πΉπ‘‹π‘Œ 𝑁 × πΉπ‘ 𝑁 × πΉπ‘„ 𝐸 × πΉπ‘ˆ 𝑁
Incore flux mapping system periodically measures the heat flux hot
channel factor when the reactor is at or near steady-state conditions.
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Heat Flux Hot Channel Factor and Total
Peaking Factor
• 𝐹𝑄 𝑧 used to represent 𝐹𝑄 𝑇 in the plant technical specifications,
• Lowers the limit for the Heat Flux Hot Channel Factor as core height
increases.
Figure: 𝐹𝑄 𝑧 Corrections for Core Height
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Operator Generic Fundamentals
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Nuclear Enthalpy Rise Hot Channel
Factor
𝑁
The enthalpy rise hot channel factor πΉβˆ†π»
is the ratio of the integral of
linear power along fuel rod with the highest integrated power to average
integrated fuel rod power.
Measure of highest total power produced by a fuel rod.
Ensures enthalpy rise everywhere in core is low enough to preclude
reaching departure from nucleate boiling (DNB).
𝑁
πΈπ‘›π‘‘β„Žπ‘Žπ‘™π‘π‘¦ 𝑅𝑖𝑠𝑒 π»π‘œπ‘‘ πΆβ„Žπ‘Žπ‘›π‘›π‘’π‘™ πΉβˆ†β„Ž
© Copyright 2014
ELO 1.1
πΌπ‘›π‘‘π‘’π‘”π‘Ÿπ‘Žπ‘‘π‘’π‘‘ π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ
𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘Žπ‘™π‘œπ‘›π‘” π‘Ÿπ‘œπ‘‘ π‘€π‘–π‘‘β„Ž
β„Žπ‘–π‘”β„Žπ‘’π‘ π‘‘ π‘‘π‘œπ‘‘π‘Žπ‘™ π‘π‘œπ‘€π‘’π‘Ÿ
=
πΌπ‘›π‘‘π‘’π‘”π‘Ÿπ‘Žπ‘‘π‘’π‘‘ π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ
𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘œπ‘“ π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘Ÿπ‘œπ‘‘
Operator Generic Fundamentals
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Nuclear Enthalpy Rise Hot Channel
Factor
Fuel loading patterns, enrichments, control rod position, and fuel burnup affect the enthalpy rise hot channel factor.
𝑁
πΈπ‘›π‘‘β„Žπ‘Žπ‘™π‘π‘¦ 𝑅𝑖𝑠𝑒 π»π‘œπ‘‘ πΆβ„Žπ‘Žπ‘›π‘›π‘’π‘™ πΉβˆ†β„Ž
© Copyright 2014
ELO 1.1
πΌπ‘›π‘‘π‘’π‘”π‘Ÿπ‘Žπ‘‘π‘’π‘‘ π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ
𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘Žπ‘™π‘œπ‘›π‘” π‘Ÿπ‘œπ‘‘ π‘€π‘–π‘‘β„Ž
β„Žπ‘–π‘”β„Žπ‘’π‘ π‘‘ π‘‘π‘œπ‘‘π‘Žπ‘™ π‘π‘œπ‘€π‘’π‘Ÿ
=
πΌπ‘›π‘‘π‘’π‘”π‘Ÿπ‘Žπ‘‘π‘’π‘‘ π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ
𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘œπ‘“ π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘Ÿπ‘œπ‘‘
Operator Generic Fundamentals
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Departure from Nucleate Boiling (DNB)
Review
When amount of steam vapor increases in the coolant channel, the fuel
rod cladding is intermittently exposed to steam vapor.
When fuel cladding becomes covered with vapor blanket, heat transfer
changes from forced convection and nucleate boiling to a combination of
conduction and radiation. This condition is called “boiling crisis.”
The point of maximum heat transfer rate sustainable with nucleate boiling
is called the Departure from Nucleate Boiling (DNB). The point at which
DNB occurs is known as the “critical heat flux” (CHF).
Figure: Stages of Nucleate Boiling
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Departure from Nucleate Boiling (DNB)
Review
The consequence of exceeding critical heat flux at any location in reactor
core is, in most cases, cladding failure.
When critical heat flux is exceeded, transition from nucleate boiling to film
boiling occurs rapidly and temperature difference required to transfer heat
from surface of fuel rods to reactor coolant increases substantially.
Figure: Transition from Nucleate to Film Boiling
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Departure from Nucleate Boiling (DNB)
Review
Since the temperature of the
reactor coolant is fixed, the
surface temperature of the fuel
rod increases rapidly. If the
temperature increase causes
the fuel rod cladding to
exceed its melting point, a
failure, or burnout, will occur.
If burnout is to be avoided, a
reactor must be operated in a
manner to prevent exceeding
critical heat flux at any point in
the core.
Figure: Radial Fuel Temperature Profile
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Departure from Nucleate Boiling
Figure: Boiling Heat Transfer Regions Curve
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Peaking Factors Example
A PWR core consists of 50,000 fuel rods; each fuel rod has an active
length of 12 feet. The core is producing 3,000 MW of thermal energy.
If the nuclear heat flux hot channel factor, 𝐹𝑄 𝑧 , (total core peaking
factor) is 1.8, what is the maximum local linear power density being
produced in the core?
Solution:
50,000 times 12 feet = 600,000 feet of active fuel rods
(3,000 MW x 1,000 kW/MW)/600,000 ft. = 5 kW/ft.
5 kW/ft. x 1.8 = 9 kW /ft.
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Peaking Factors
Knowledge Check – NRC Bank
A reactor is operating at steady-state conditions in the power range with the
following average temperatures in a core plane:
Tcoolant
= 550°F
Tfuel centerline = 1,680°F
Assume that the fuel rod heat transfer coefficients and reactor coolant
temperatures are equal throughout the core plane. If the maximum total
peaking factor in the core plane is 2.1, what is the maximum fuel centerline
temperature in the core plane?
A. 2,923°F
B. 3,528°F
C. 4,078°F
D. 4,683°F
Answer is: A
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Purpose of Core Thermal Limits
ELO 1.2 - Describe the reason thermal limits are necessary and the
function of the core protection calculator.
• For minimal risk to public health and safety, protecting the reactor
core, and particularly fuel rod integrity is imperative.
• For confidence of maintaining fuel integrity, core operating and core
thermal limits are established.
• Operation within these limits ensures the plant remains within safety
margins that minimize the chance of core (fuel) failure.
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Purpose of Core Thermal Limits
• Core thermal limits, calculated from the plant safety analysis, are
required to ensure fuel cladding integrity during steady-state,
transient and accident conditions.
• Cladding failure is of prime concern due to its role as the first fission
product barrier to the public.
Thermal limit criteria ensures there is “at least a 95-percent probability
at a 95-percent confidence level” that departure from nucleate boiling
(DNB) does not occur on limiting (hottest) fuel rods during normal
operation and operational transients, including any transient conditions
arising from faults of moderate frequency.
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Factors Involved with Reactor Thermal
Limits
• PWR fuel (UO2) melting point – 5,200°F
• Core limits set at 4,700°F – to allow for age and uncertainties
• Some fuel pellets may reach 4,000°F during normal operation
• If peak central (fuel) temperatures (PCTs) are limited, then cladding
temperatures are limited during most analyzed transients and
abnormal conditions.
• 1,800°F is the threshold of zirconium water reactions (clad)
• 2,200°F is the limit set for LOCAs (ECCS criteria)
– Point of acceleration of the zirconium water reaction
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Factors Involved with Reactor Thermal
Limits
• Departure from Nuclear Boiling Ratio (DNBR)
– Measure of the probability that DNB is occurring
– Ratio of critical heat flux (CHF) to actual heat flux, where CHF is
the value of heat flux at which DNB occurs
• Typical limit is greater than or equal to 1.3 during steady-state
conditions
– Limits provide a 95 percent probability at a 95 percent confidence
level that the hottest fuel rod does not reach DNB
• Fuel cladding design, material, and thickness affects the heat
transfer rate from fuel pellet to coolant, and the capability to
withstand internal pressure from fission product gases
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Factors Involved with Reactor Thermal
Limits
• A typical PWR reactor core is limited
– To an average linear power density of 5.44 kW/ft.
– Localized areas may have a higher peak power with limits of 12.62
kW/ft.
– Peak power density during transient operation - 18 kW/ft.
• Limits consider:
– Limits conservative enough to maintain fuel and cladding
temperatures for assurance of fuel integrity.
– Fuel cladding integrity ensured by actual heat flux is always less than
critical heat flux and DNB does not occur.
– Fuel enrichment affects the safety analysis - greater the enrichment
the more limiting the thermal limits due to a higher power density.
– Materials used in manufacturing the fuel and the design are
considered.
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Operator Generic Fundamentals
36
Factors Involved with Reactor Thermal
Limits
• Ability of the ECCS to cool the core following a LOCA combined with the
need to prevent exceeding fuel temperature limits (fuel melting / clad
damage) dictates the maximum heat flux hot channel factor (HCF) or
Total Peaking Factor
• During LOCA conditions, HCF limits and ECCS capability together limit
fuel damage to criteria set in plant licensing requirements and Nuclear
Regulatory Commission regulations: (called ECCS acceptance criteria)
– Maximum fuel clad temperature is 2,200°F.
– 17% maximum clad oxidation
– Maximum hydrogen generation (1 percent of total clad cylinder
metal)
– Maintaining a coolable core geometry
– Able to support long term cooling
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Operator Generic Fundamentals
37
Nuclear Enthalpy Rise Hot Channel
Factor
• RCS coolant flow rates because of their effect on heat removal.
• RCS pressure to maintain subcooling for DNB considerations.
• Fuel pellet design and size affect power density and fuel temperature
margins.
– Smaller pellet has higher core thermal limits due to less power
production.
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Operator Generic Fundamentals
38
Nuclear Enthalpy Rise Hot Channel
Factor
• Limits necessary in addition to the Heat Flux HCF to protect the core
against reaching DNB.
– Because DNB is power density (kW/ft.) and local enthalpy
dependent for given plant pressures and flows.
• The fuel rod adding the maximum amount of BTUs to the coolant as
flow proceeds up the core is the fuel rod where DNB is most likely to
occur at some height (Z).
– May very well not be, the same fuel rod that has the peak kW/ft.
– Point where DNB most likely first occurs will not be in the same
horizontal plane as the point of maximum kW/ft.
• Limiting DNB will occur at a higher core elevation.
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Operator Generic Fundamentals
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Nuclear Enthalpy Rise Hot Channel
Factor
𝑁
• If the πΉβˆ†β„Ž
is maintained within limits, the minimum DNBR along the
hottest rod will be maintained greater than acceptable levels.
© Copyright 2014
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Operator Generic Fundamentals
40
Core Protection Calculator
Performs the following functions:
• Monitor reactor plant operating parameters
• Calculate the margins to thermal limits
• Trip reactor if either of them is being approached or exceeded
– Linear Heat Rate (LHR) greater than 21 kilowatts/foot (kW/ft.)
– Departure from Nucleate Boiling Ratio (DNBR) less than 1.26
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41
Core Protection Calculator
• Fuel rod linear heat transfer rate of 21 kW/ft. maintains the operating
temperature below fuel centerline melting temperature.
• DNBR greater than 1.26 provides a 95 percent probability with 95
percent confidence that DNB will not occur.
• Cladding/fuel melt to extreme temperature increase
– Possibly resulting in a breach of the first fission product boundary,
and
– Release of fission products into reactor coolant.
© Copyright 2014
ELO 1.2
Operator Generic Fundamentals
42
Core Protection Calculator
Consists of four computers to rapidly calculate:
– DNBR in limiting coolant channels and
– Peak linear heat rates (LHR) in the most limiting fuel rod
and take corrective action.
• CPC measures reactor power, radial, and axial power shapes to
produce three-dimensional power flux shape
• Core modeled as twenty horizontal planes or nodes.
• Radial power shape calculated as a smooth average power flux shape
modified by monitored control rod positions.
– Comparing the calculated flux shape to thermal limits avoids
localized thermal limit violations due to control rod mispositioning.
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Operator Generic Fundamentals
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Core Protection Calculator
• A peak/average ratio for each plane is calculated
– Flow rate used in DNBR calculations based on RCP speed,
reactor coolant temperatures, and coolant specific volume.
• Multiplying axial and radial flux profiles obtains a 3-D flux profile.
• Points of maximum LHR or minimum DNBR determined from node
point scans.
– Comparing obtained values to limits generates reactor trip signals
as required.
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Operator Generic Fundamentals
44
Purpose of Core Thermal Limits
Knowledge Check
The basis for the maximum power density (kW/ft.) power limit is to...
A. provide assurance of fuel integrity.
B. prevent xenon oscillations.
C. allow for fuel pellet manufacturing tolerances.
D. prevent nucleate boiling.
Answer is: A
© Copyright 2014
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Operator Generic Fundamentals
45
Reactor Operation Effects on Peaking
Factors
ELO 1.3 - Describe the factors that affect peaking and hot channel factors
• Reactor design and operation influence all of the peaking factors;
radial, axial, local, total peaking, and enthalpy rise hot channel
factors.
• Fuel design and enrichment, materials, and power densities
considered during reactor design greatly influence the peaking
factors and thermal margins.
© Copyright 2014
ELO 1.3
Operator Generic Fundamentals
46
Reactor Operation Effects on Peaking
Factors
• During reactor operation, core power distribution and DNBR margins
affected by:
– Core power
– Flux distribution
– Fission product poisons
– Control rod position
– RCS temperatures and pressures
• Higher peaking factors and lower DNBR margins mean lower safety
margins
– Careful monitoring and surveillance of thermal limits important to
ensure public health and safety.
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Operator Generic Fundamentals
47
Reactor Operation Effects on Peaking
Factors
• During normal reactor operations, axial peaking factors are within
control of the reactor operator.
• Control rod motion, reactor power level, and xenon oscillations affect
the axial flux profile of the core.
– Affecting average linear power density vertically (Z) in the core.
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Operator Generic Fundamentals
48
Reactor Operation Effects on Peaking
Factors
• Normally, the maximum flux is toward the center portion of the core;
however, the effects mentioned can cause an up or down flux shift.
– Causes increased axial peaking factors.
Figure: Axial Flux Profile
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Operator Generic Fundamentals
49
Reactor Operation Effects on Peaking
Factors
• Certain abnormal reactor operations can cause changes to the axial
and radial flux profiles.
• A single dropped rod can affect the axial peaking factor, shifting the
flux vertically, but
– Has larger effect on the radial peaking factor
– Especially for a dropped rod away from the center of the core
causing one quadrant of the core to produce less power.
• Recall that the axial and radial peaking factors make up the total
peaking factor:
𝐹𝑄 𝑇 = πΉπ‘‹π‘Œ 𝑁 × πΉπ‘ 𝑁 × πΉπ‘„ 𝐸 × πΉπ‘ˆ 𝑁
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Operator Generic Fundamentals
50
Reactor Operation Effects on Peaking
Factors
• Since 𝐹𝑄 𝑧 is 𝐹𝑄 𝑇 adjusted for
height, limits on 𝐹𝑄 𝑧 could be
reached in the event the flux
profile shifts upward.
• DNBR is lower near the top of
the core because of higher
coolant temperatures and
slightly lower pressures.
β€’ Higher power toward the
top of the core lowers
DNBR further.
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Operator Generic Fundamentals
51
Reactor Operation Effects on Peaking
Factors
• During plant operations, to ensure DNBR maintained within its limits
the following are maintained within operational bands:
– Coolant temperatures
– Primary pressures
– Reactor power level & axial flux profiles
– Core flow rates
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Operator Generic Fundamentals
52
Reactor Operation Effects on Peaking
Factors
• Lowering primary coolant subcooling places the coolant closer to
saturation conditions.
– At normal full power, primary coolant is approximately 30ο‚°F
subcooled with subcooled nucleate boiling occurring.
– If plant conditions reduced subcooling by increased temperatures
or decreased pressures, saturated boiling could occur in upper
regions of core.
• This increases the potential for onset of DNB due to saturated
nucleate boiling in upper regions of the core.
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Operator Generic Fundamentals
53
Reactor Operation Effects on Peaking
Factors
• Additionally, with higher primary pressures, a decreased heat transfer
rate exists because of a reduction in nucleate boiling.
• To maintain the same heat transfer rate (at higher pressures) a larger
βˆ†T is necessary between the coolant and fuel rod surface
temperatures.
Figure: Fluid Heat Transfer Regions
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Operator Generic Fundamentals
54
Reactor Operation Effects on Peaking
Factors
• This means that for a constant power level, fuel temperatures will
increase if primary pressure is increased.
• Similarly, DNB would occur at smaller T values at lower pressures,
because nucleate boiling occurs sooner at lower pressures with
identical power levels.
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Operator Generic Fundamentals
55
Reactor Operation Effects on Peaking
Factors
• A reduction in flow rate, at any power level, increases the temperature
of coolant (T increases, causing Thot to increase).
– This also brings the coolant closer to saturation conditions.
• Maintaining adequate flow rates is essential to maintaining a minimum
acceptable DNBR.
• The lower the flow, the less capacity to remove heat.
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Operator Generic Fundamentals
56
Reactor Operation Effects on Peaking
Factors
• High local power densities produce higher heat flux and higher
coolant and cladding temperatures.
• As a result, heat transfer conditions more closely approach CHF
conditions with a reduction in DNBR.
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Operator Generic Fundamentals
57
Critical Heat Flux (CHF)
• Heat flux associated with DNB
• Heat flux that causes DNB to occur for given pressure and
temperature conditions.
• With increasing differential temperature heat flux reaches a turning
point within the nucleate boiling region.
– A rapid increase in differential temperature between the heat
transfer surface and the liquid
– Indicates the heat transfer surface loosing cooling, heating, and
potentially causing damage, in this case the nuclear fuel.
© Copyright 2014
Information Slide
Operator Generic Fundamentals
58
Critical Heat Flux (CHF)
• Limits boiling heat transfer use.
• Causes physical burnout of the heated surface materials due to:
– Sudden inefficient heat transfer rate through a vapor film
displacing the liquid adjacent to the heat transfer surface.
• When CHF occurs a large increase in the heat transfer surface
temperatures occurs.
© Copyright 2014
Information Slide
Operator Generic Fundamentals
59
Most Limiting Channel
• Two basic types of fuel assemblies found in PWR cores are unrodded
assemblies and thimble assemblies.
• Unrodded assemblies consists of a cross-sectional area bordered by
four individual fuel rods.
• Thimble cell contains a cross-sectional area bordered by three fuel
rods and one thimble guide tube.
– The thimble guide tube has wider diameter than typical fuel rod.
– This design reduces flow significantly from the unrodded
assembly.
– Large surface of thimble guide tube has a greater resistance to
flow from the large frictional surface.
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Operator Generic Fundamentals
60
Most Limiting Channel
Figure: Unrodded (Normal) Fuel Assembly and Thimble Fuel Assembly
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Operator Generic Fundamentals
61
Most Limiting Channel
• With three instead of four fuel rods, the thimble assembly power
production is less.
• However, the moderator in thimble cell is relatively cooler than the
average coolant temperature across the core.
– Causes a peak in thermal neutron flux in the thimble rodlet
vicinity.
• Because of the thermal neutron flux peak, power density in each of
three fuel rods is greater than average power density.
• Lower coolant flow and higher power density causes a higher than
normal enthalpy rise in thimble assembly channel.
– Leads to thimble assembly channels more likely to encounter
DNB.
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Operator Generic Fundamentals
62
Most Limiting Channel
• Several factors can contribute to a fuel channel becoming DNB or hot
channel limiting
– Clad thickness
– Enrichment
– Manufacturing tolerances in rod diameter
– Fuel pellet dimensions
– Crud buildup, and
– Non-uniform flow distribution.
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Operator Generic Fundamentals
63
Most Limiting Channel
• Over core life, the fuel itself changes its thermal performance.
– Fuel pellet densification
– Swelling
– Clad deformation (clad creep), or
– Buildup of fission product gases
• These can affect the heat transfer to coolant characteristics.
– These affect fuel temperatures and cladding temperatures
causing a reduction in safety margins.
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Operator Generic Fundamentals
64
Most Limiting Channel
• Generally, to ensure an adequate safety margin, the worst possible
combinations of manufacturing tolerances, highest linear power
density, and lower than nominal flows factor into thermal design limits.
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Operator Generic Fundamentals
65
Sample Problem
A reactor is operating at steady-state 80 percent power with all control
rods fully withdrawn and in manual control. Compared to a 50 percent
insertion of one control rod, a 50 percent insertion of a group (or bank) of
control rods will cause a __________ increase in the maximum axial
peaking factor and a __________ increase in the maximum radial
peaking factor. (Assume reactor power remains constant.)
A. smaller; smaller
B. smaller; larger
C. larger; smaller
D. larger; larger
Answer is: C
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Operator Generic Fundamentals
66
Reactor Operation Effects on Peaking
Factors
Knowledge Check – NRC Bank
Consider a new fuel rod operating at a constant power level for several
weeks. During this period, fuel pellet densification in the fuel rod
causes the heat transfer rate from the fuel pellets to the cladding to
__________; this change causes the average fuel temperature in the
fuel rod to __________.
A. decrease; increase
B. decrease; decrease
C. increase; increase
D. increase; decrease
Answer is: A
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Operator Generic Fundamentals
67
TLO 1 Summary
1. Peaking Factors
• Axial Peaking Factor - Rod motion and xenon oscillations have
strong effects to the average linear power density vertically (Z) in
the core.
π‘˜π‘Š
𝑖𝑛 β„Žπ‘œπ‘Ÿπ‘–π‘§π‘œπ‘›π‘‘π‘Žπ‘™
𝑓𝑑
π‘˜π‘Š
π‘π‘™π‘Žπ‘›π‘’ π‘€π‘–π‘‘β„Ž π‘šπ‘Žπ‘₯π‘–π‘šπ‘’π‘š
𝑓𝑑
=
π‘˜π‘Š
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’
𝑖𝑛 π‘‘β„Žπ‘’ π‘π‘œπ‘Ÿπ‘’
𝑓𝑑
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’
𝐴π‘₯π‘–π‘Žπ‘™ π‘ƒπ‘’π‘Žπ‘˜π‘–π‘›π‘” πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ 𝐹𝑍𝑁
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Operator Generic Fundamentals
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TLO 1 Summary
• Local Peaking Factor - This is the ratio of maximum power at a hot
spot to average core power.
• The local peaking factor defines the hottest part of a hot nuclear
fuel rod.
π‘€π‘Žπ‘₯π‘–π‘šπ‘’π‘š π‘ƒπ‘œπ‘€π‘’π‘Ÿ π‘Žπ‘‘ π‘Ž π»π‘œπ‘‘ π‘†π‘π‘œπ‘‘
πΏπ‘œπ‘π‘Žπ‘™ π‘ƒπ‘’π‘Žπ‘˜π‘–π‘›π‘” πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ =
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ πΆπ‘œπ‘Ÿπ‘’ π‘ƒπ‘œπ‘€π‘’π‘Ÿ
© Copyright 2014
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TLO 1 Summary
• Radial Peaking Factor - This factor is a strong function of core
design and under normal conditions, operators have little control of
this peaking factor.
– This ratio has a specific limit periodically verified for compliance
with technical specifications.
– Ensures that the nuclear heat flux hot channel factor is within
prescribed limits.
– Measured using the incore system flux mapping system provides a rough approximation of core power distribution status.
π‘…π‘Žπ‘‘π‘–π‘Žπ‘™ π‘ƒπ‘’π‘Žπ‘˜π‘–π‘›π‘” πΉπ‘Žπ‘π‘‘π‘œπ‘Ÿ 𝐹π‘₯𝑦
π‘˜π‘Š
π‘˜π‘Š
π‘€π‘Žπ‘₯π‘–π‘šπ‘’π‘š
𝑖𝑛 β„Žπ‘œπ‘Ÿπ‘–π‘§π‘œπ‘›π‘‘π‘Žπ‘™ π‘π‘™π‘Žπ‘›π‘’ π‘π‘œπ‘›π‘‘π‘Žπ‘–π‘›π‘–π‘›π‘” π‘‘β„Žπ‘’ π‘šπ‘Žπ‘₯π‘–π‘šπ‘’π‘š
𝑖𝑛 π‘‘β„Žπ‘’ π‘π‘œπ‘Ÿπ‘’
𝑓𝑑
𝑓𝑑
=
π‘˜π‘Š
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’
𝑖𝑛 π‘‘β„Žπ‘Žπ‘‘ π‘ π‘Žπ‘šπ‘’ π‘π‘™π‘Žπ‘›π‘’
𝑓𝑑
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Operator Generic Fundamentals
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TLO 1 Summary
• Heat Flux Hot Channel Factor (FQ(z)) - relates to the maximum
local power in the core to the average power in the core.
• 𝐹𝑄 𝑇 is adjusted to core height due to lower DNBR at higher temps
and lower pressures – uses term 𝐹𝑄 𝑧 .
• Affected by fuel design, core loading patterns, control rod position,
fuel burn-up, AFD.
• 𝐹𝑄 𝑇 is derived from the axial and radial peaking factors, with
corrections for uncertainty and engineering factors.
π‘€π‘Žπ‘₯π‘–π‘šπ‘’π‘š π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘Žπ‘›π‘¦π‘€β„Žπ‘’π‘Ÿπ‘’ 𝑖𝑛 π‘‘β„Žπ‘’ π‘π‘œπ‘Ÿπ‘’
𝐹𝑄 𝑇 =
π΄π‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ 𝑑𝑒𝑛𝑠𝑖𝑑𝑦 𝑖𝑛 π‘‘β„Žπ‘’ π‘π‘œπ‘Ÿπ‘’
© Copyright 2014
TLO 1
Operator Generic Fundamentals
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TLO 1 Summary
𝑁
• The nuclear enthalpy rise hot channel factor πΉβˆ†π»
maximum total power produced in a fuel rod.
𝑁
πΈπ‘›π‘‘β„Žπ‘Žπ‘™π‘π‘¦ 𝑅𝑖𝑠𝑒 π»π‘œπ‘‘ πΆβ„Žπ‘Žπ‘›π‘›π‘’π‘™ πΉβˆ†β„Ž
is measure of
πΌπ‘›π‘‘π‘’π‘”π‘Ÿπ‘Žπ‘‘π‘’π‘‘ π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ
𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘Žπ‘™π‘œπ‘›π‘” π‘Ÿπ‘œπ‘‘ π‘€π‘–π‘‘β„Ž
β„Žπ‘–π‘”β„Žπ‘’π‘ π‘‘ π‘‘π‘œπ‘‘π‘Žπ‘™ π‘π‘œπ‘€π‘’π‘Ÿ
=
πΌπ‘›π‘‘π‘’π‘”π‘Ÿπ‘Žπ‘‘π‘’π‘‘ π‘™π‘–π‘›π‘’π‘Žπ‘Ÿ π‘π‘œπ‘€π‘’π‘Ÿ
𝑑𝑒𝑛𝑠𝑖𝑑𝑦 π‘œπ‘“ π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘Ÿπ‘œπ‘‘
• Necessary in addition to the Heat Flux Hot Channel factor to
protect the core against reaching DNB.
– DNB is power density (kW/ft.) and local enthalpy dependent for
given plant pressures and flows.
𝑁
• If πΉβˆ†β„Ž
is within limits, the minimum DNBR along the hottest rod
will be maintained greater than acceptable levels.
• The fuel rod adding the maximum amount of BTUs to the coolant
as flow proceeds up the core is the fuel rod where DNB is most
likely to occur at some height (Z).
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Operator Generic Fundamentals
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TLO 1 Summary
2. Purpose of Core Thermal Limits
• Reactor fuel integrity ensured by establishing and maintaining
core operating limits, and core thermal limits.
• Core thermal limits, calculated from the plant safety analysis, are
required to ensure fuel cladding integrity during steady-state,
transient, and accident conditions.
β€’ Cladding failure is of prime concern due to its role as the first
fission product barrier to the public.
β€’ Thermal limit criteria ensures there is “at least a 95-percent
probability at a 95-percent confidence level” that departure
from nucleate boiling (DNB) does not occur on limiting (hottest)
fuel rods during normal operation and operational transients,
including any transient conditions arising from faults of
moderate frequency.
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TLO 1 Summary
– Heat flux hot channel factors setpoints for preventing fuel
damage following a loss of coolant accidents.
o HCF setpoints and ECCS capability together limit fuel
damage to criteria set in plant licensing requirements and
Nuclear Regulatory Commission regulations.
o Maximum fuel clad temperature is 2,200°F., etc.
© Copyright 2014
TLO 1
Operator Generic Fundamentals
74
TLO 1 Summary
• Peak cladding temperature is limited to 2,200°F to minimize to
probability of zirc-water reaction.
• PWR fuel (UO2) has a melting point of 5,200°F, core limits are set at
4,700°F to allow for age and uncertainties. Some fuel pellets may
actual reach 4,000°F during normal operation.
• Typical linear power density limits (Westinghouse):
– Steady-state average: 5.44 kW/ft.
– Maximum local power density: 12.62 kW/ft.
– During transient conditions peak: 18 kW/ft.
• Typical linear power density limits (Combustion Engineering):
– Steady-state average: 6.2 kW/ft.
– Maximum local power density: 10.18 kW/ft.
© Copyright 2014
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Operator Generic Fundamentals
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TLO 1 Summary
3. Reactor Operation Effects on Peaking Factors
• Operation within the power density limits ensures fuel integrity
during normal and transient operations.
• Average linear power density is the total thermal power being
produced in the core divided by the active length of all the fuel
rods and is expressed in kW/ft.
• The heat flux necessary to cause DNB for a given set of
parameters (pressure, temperature, flow and power) is the Critical
Heat Flux (CHF).
• Control rod motion, reactor power level and xenon oscillations
affect the axial flux profile of the core – axial peaking.
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TLO 1 Summary
• Radial peaking not affected during normal operations – abnormal
dropped rod would affect.
• During plant operations coolant temperatures, primary pressures,
reactor power level, and core flow rates have operational limits to
ensure DNBR maintained within its criteria.
• Clad thickness, enrichment, manufacturing tolerances in rod
diameter, fuel pellet dimensions, crud buildup, and non-uniform
flow distribution can contribute to a fuel channel becoming DNB
or hot channel limiting.
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TLO 1 Summary
• Over core life the fuel itself changes its thermal performance.
β€’ Fuel pellet densification
β€’ Swelling
β€’ Pellet-cladding interaction (PCI)
β€’ Clad deformation (clad creep), or
β€’ Buildup of fission product gases
• Affect the heat transfer to coolant characteristics – affecting fuel
and cladding temperatures possibly causing a reduction in safety
margins.
• To ensure an adequate safety margins, worst possible
combinations of manufacturing tolerances, highest linear power
density, and lower than nominal flows factor into thermal design
limits.
© Copyright 2014
TLO 1
Operator Generic Fundamentals
Crossword Puzzle
• It’s crossword puzzle time!
© Copyright 2014
Summary
Operator Generic Fundamentals
79
Terminal Learning Objectives
At the completion of this training session, the trainee will demonstrate
mastery of this topic by passing a written exam with a grade of ≥ 80
percent on the following Terminal Learning Objective (TLO):
• TLO 1 Describe the reason for reactor core thermal limits and factors
affecting them.
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Enabling Learning Objectives for TLO 1
1. Describe the following peaking factors as they relate to local and
average reactor power:
a. Axial peaking factor (APF)
b. Local peaking factor (LPF)
c.
Radial peaking factor (RPF)
d. Total peaking factor (TPF)
2. Describe the reason thermal limits are necessary and the function
of the core protection calculator.
3. Describe the factors that affect peaking and hot channel factors.
© Copyright 2014
TLO 1
Operator Generic Fundamentals
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