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Presentation for my 2010 senior core design project at The Pennsylvania State University with Westinghouse.
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This presentation will cover the following topics:This presentation will cover the following topics:
1. Introduction
2 di G i2. Loading Pattern Generation
3. Safety Calculations
4. Operational Calculations
5 Thermal‐Hydraulics5. Thermal Hydraulics
6. Conclusions
Section 01
Terminal Objectivej• Become familiar with codes and methods used to generate core loading patterns and perform reload d i l idesign analysis
Enabling ObjectivesEnabling Objectives• Develop an acceptable reload core loading pattern• Perform safety and operational calculations on thePerform safety and operational calculations on the designed LP along with thermal‐hydraulics analysis
• Provide an oral presentation and a written report
ANC: Advanced Nodal Code• Multidimensional nodal code (3D, 2D, 1D)• Licensed by the NRC in 1988 for PWR analysis• Calculates
– Core reactivityA bl d b– Assembly power and burnups
– Rodwise power and burnups– Reactivity coefficientsy– Core depletion– Control rod and fission product worths
APA‐H code set used due to hexagonal geometryAPA H code set used due to hexagonal geometryand consists of:• ALPHA‐H• ALPHA‐H• PHOENIX‐HANC H• ANC‐H
These codes are the same in function as squaregeometry codes but modified to use hexagonalgeometry.
Differences from square geometry versions:Differences from square geometry versions:
• Both the assembly and the core are modeled in 1/6 and full core geometryin 1/6 and full core geometry
• ANC‐H uses only one node per assembly as d f d bl i ANCcompared to four nodes per assembly in ANC
Inputs and outputs are virtually the same
VVER‐1000
• PWR Design – 3000 MWtg t
• Four‐Loop System
• Hexagonal Fuel Assemblies• Hexagonal Fuel Assemblies
http://www.nukeworker.com/pictures/displayimage‐28‐37.html
http://www.elemash.ru/en/production/Products/NFCP/VVER1000/
• Inlet core temperature varies from 533.5 °F to et co e te pe atu e a es o 533.5 to553.1 °F from 0% to 100% power
• Full Power Axial Offset (AO) band is ± 5%• Control rods vary from 0 to 175 steps withdrawn• Rod Insertion Limits (RILs) are a function of core ( )power
• Westinghouse ZrB2 integral fuel burnable absorbers (IFBA) are used. Possible configurations are 0, 18, 24, 30, 36, and 48 rods per assembly.
Section 02
• Cycle LengthCycle Length
• FΔH Peaking Factor
d C ffi i ( C)• Moderator Temperature Coefficient (MTC)
• Feed Inventory
Parameter Limit
Cycle Length ≥ 308 EFPD (11329 MWd/MTU)Cycle Length ≥ 308 EFPD (11329 MWd/MTU)
ARO Peaking Factor (FΔH) ≤ 1.532
HZP MTC ≤ 0.00 pcm/°FHZP MTC ≤ 0.00 pcm/ F
Feed Inventory ≤ 42 Feeds
Customer plans to shut down cycle 4 at a cycleCustomer plans to shut down cycle 4 at a cycle
length of 308 EFPD. This value is used to
l l h OC bcalculate the EOC burnup:
The EOC of the core is identified as when the boron concentration is equal
to 10 ppm. The E‐SUM output edit from cyc4_depl.0949.out confirms that
the designed loading pattern meets the limit of 308 EFPD which occurs at the
11329 MWd/MTU burnup step11329 MWd/MTU burnup step.
FΔH is literally defined as the normalized rise in enthalpy in aΔH y py
given subchannel. Since ANC‐H is a nodal based code based on
the fuel assemblies and not the subchannels, ANC uses
integrated rod power as the value for FΔH.
A portion of the input from
03_anch_B1C4_depl.job is shown
to the right. This input was also g p
used to determine cycle length.
The maximum FΔH at each burnup step is included in the
E‐SUM output edit. The limit of 1.532 must not be
exceeded at any burnup step and is monitored at HFP ARO
conditions.
1.540
1.520
1.530
1.500
1.510
F ∆H
1.480
1.490
Actual
Limit
1.460
1.470
0 2000 4000 6000 8000 10000 12000
Burnup [MWD/MTU]Burnup [MWD/MTU]
The FΔH of each assembly for a particularThe FΔH of each assembly for a particular
burnup step is shown in the C‐FDH output edit.
MTC – change in core reactivity due to a change inMTC change in core reactivity due to a change in
moderator temperature (fuel temperature is held
constant) and is checked at HZP for all burnup stepsconstant) and is checked at HZP for all burnup steps.
A portion of the input from 03_anch_B1C4_depl.job is:
The E‐SEQ output edit displays the MTC valuesThe E SEQ output edit displays the MTC values
for each burnup step.
The calculation from ANC is verified for the most limiting case (150 MWd/MTU burnup step).limiting case (150 MWd/MTU burnup step).
17000
1100
1300
1500
‐4
‐2
pm]
700
900
1100
‐10
‐8
‐6
n Co
ncen
tration [pp
MTC
[pcm
/°F]
100
300
500
‐14
‐12
10
Boron
MTC
MTC Limit
Boron Concentration
‐100‐16
0 2000 4000 6000 8000 10000 12000
Burnup [MWD/MTU]
Boron Concentration
Design Criteria Target Actual
Cycle Length 308 EFPD 308.8 EFPD
Maximum FΔH 1.532 1.514
Maximum MTC 0.00 pcm/°F ‐1.056 pcm/°F
Feed Inventory 42 42
Section 03
Safety Calculations were performed using theSafety Calculations were performed using the
Westinghouse Reactor Safety Analysis Checklist
( S C) hi h(RSAC) which covers:
• Rodded FΔH• Shutdown Margin
• Rod Ejection AccidentRod Ejection Accident
Since most reactors are permitted to operateSince most reactors are permitted to operate
at full power with some control rods inserted
i h l b h k d i hin the core, FΔH must also be checked with
allowable control rods inserted. For this
particular scenario, the calculation was
performed with the lead control bank at its RILperformed with the lead control bank at its RIL.
Input from roddedFDH.jobp j
Xenon was skewed for conservatism
The rodded FΔH is displayed in the E‐SUM outputThe rodded FΔH is displayed in the E SUM output
edit from roddedFDH.0960.out.
C‐FDH output edit from roddedFDH.0960.out
Burnup [MWd/MTU] Δ Axial Offset (%) Rodded FΔH
150 5.61 1.499150 5.61 1.499
500 5.30 1.496
1000 5.19 1.507
2000 5.16 1.518
3000 5.32 1.514
4000 5.39 1.510
5000 5.49 1.508
6000 5.66 1.504
7000 4.79 1.500
8000 5.86 1.494
9000 6.04 1.485
10000 6.22 1.477
11000 6.43 1.470
11329 6 49 1 46711329 6.49 1.467
11360 6.50 1.467
1.540
1.520
1.530
1.500
1.510
Fdh
1.480
1.490
Fdh
Rodded Fdh
1.460
1.470
0 2000 4000 6000 8000 10000 12000
Burnup [MWD/MTU]
Rodded Fdh
Fdh Limit
Burnup [MWD/MTU]
Shows that in any circumstances the operatorwill be able to safely shut down the core.
Technically defined as the amount by which the core would would be subcritical (%Δρ) at hot shutdown conditions followinga reactor trip, assuming the highest worth control rod is stuck out.
Six cases in ANC:K1 B C t B f I t t (BOC EOC)• K1 – Base Case at Burnup of Interest (BOC or EOC)
• K2 – Rods are Inserted to RILs• K3 – Over‐Power/ Over‐Temperature, Skew Power to Top of Core
(worst conditions for trip)( p)• K4 – Trip to Zero Power• K5 – Full Core at All Rods In (ARI) • K6 – Worst Stuck Rod Out
Calculation performed at both BOC and EOCCalculation performed at both BOC and EOC
l f h illTotal Power Defect‐ amount the core will increase in reactivity due to the trip to HZP
Available SDM =Calculated SDM – Rod Worth Uncertainty – Voids
E‐SUM output edit from sdownemBOC.0979.out
E‐SUM output edit from sdownemEOC.1004.out
Requirement BOC Worth (pcm) EOC Worth (pcm)
Control Banks
Power Defect 1943.7 3152.6
Void Effects 50 50
(1) Total Control Bank Requirement 1993 7 3202 6(1) Total Control Bank Requirement 1993.7 3202.6
Control Rod Worth (HZP)
All rods inserted less most reactive rod stuck out
6867 7677.3
(2) Less 10% 6180.3 6909.6
Shutdown Margin
Calculated Margin (2) – (1) 4186.6 3707
Required Shutdown Margin 1300 1300
Purpose: Simulate the unlikely event of a single p y gcontrol rod being ejected from the core due to failure in the control rod pressure housing. Total peaking factor F and %Δρmust be below limitpeaking factor, FQ, and %Δρmust be below limit for each condition.
Evaluated at Four Conditions:1. BOC HFP2. EOC HFP3. BOC HZP4. EOC HZP
Input sample from rodejectionHFP.job
Only control bank 10 is ejected from core at HFP.jSince rod ejection is a fast transient, all ,feedback effects are frozen under an adiabatic assumption.
The E SUM output edit fromThe E‐SUM output edit from
rodejectionHFP.0963.out contains the total
peaking factor and eigenvalues.
The rod ejection worth is calculated for eachThe rod ejection worth is calculated for each
case using the equation:
Case Eigenvalue dk/k %Δρ %Δρ (10% uncertainty)
FQFQ (13%
uncertainty)
Rod Ejection at HFP
BOC Full Core 1.000000 ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
BOC Bank 10 1.000128 0.000128 0.012799 0.014079 1.949 2.20237
EOC Full Core 0 999200 ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐EOC Full Core 0.999200 ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
EOC Bank 10 0.999377 0.000177 0.017713 0.019484 1.811 2.04643
Approach is virtually same as
for HFP with the exception beingfor HFP with the exception being
the number of control rods ejected.
Now four locations are ejectedNow four locations are ejected
individually.
Case Eigenvalue dk/k %Δρ%Δρ (10% uncertainty) FQ
FQ (13% uncertainty)
BOC Rod Ejection at HZP
Full Core 1.000001 ‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
Bank 10 1.001415 0.001413 0.141300 0.158256 2.929 3.60267
Bank 9 1.002729 0.002724 0.272428 0.305120 4.922 6.05406
Bank 9 (center)
1.002328 0.002324 0.232429 0.260321 3.137 3.85851
Bank 8 1.000479 0.000478 0.047789 0.053523 2.750 3.38250
Case Eigenvalue dk/k %Δρ%Δρ (10% uncertainty) FQ
FQ (13% uncertainty)
EOC Rod Ejection at HZP
Full Core 1.037299 ‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
Bank 10 1.039348 0.001973 0.197337 0.221018 3.923 4.82529
Bank 9 1.040963 0.003526 0.352603 0.394915 6.408 7.88184
Bank 9 (center)
1.039740 0.002350 0.235046 0.263252 3.909 4.80807
Bank 8 1.038825 0.001470 0.147005 0.164645 5.159 6.34557
Rod Ejection Overview
Case (Bank)Calculated
%Δρ%Δρ Limit
CalculatedFQ
FQ Limit
BOC HFP 0.014079 0.200 2.20237 5.8
j
BOC HFP 0.014079 0.200 2.20237 5.8
EOC HFP 0.019484 0.200 2.04643 6.5
BOC HZP (10) 0.158256 0.860 3.60267 13.0
(BOC HZP (9 0.305120 0.860 6.05406 13.0
BOC HZP (9c) 0.260321 0.860 3.85851 13.0
BOC HZP (8) 0.053523 0.860 3.38250 13.0
EOC HZP (10) 0.001018 0.900 4.82529 21.0
EOC HZP (9) 0.394915 0.900 7.88184 21.0
EOC HZP (9c) 0 263252 0 900 4 80807 21 0EOC HZP (9c) 0.263252 0.900 4.80807 21.0
EOC HZP (8) 0.164645 0.900 6.34557 21.0
Section 04
Several Calculations must be performed beforeSeveral Calculations must be performed before
the reactor can go back online after an outage:
OC d h• BOC HZP Rodworths
• Xenon Reactivity after Startup and Trip
• Differential Boron Worth
• Isothermal Temperature CoefficientIsothermal Temperature Coefficient
• BOC HZP Critical Boron Concentration
Rodworths of control banks are determinedRodworths of control banks are determined
using the boron dilution method.
Input sample from rodworth.job
E‐SUM edit from rodworth.0981.outE SUM edit from rodworth.0981.out
Control Banks Inserted CBC [ppm] Bank No. Bank Worth [ppm]
Control Bank Worth Overview
ARO 1872 ‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐
10 1796 10 76
10 + 9 1656 9 14010 + 9 1656 9 140
10 + 9 + 8 1563 8 93
10 + 9 + 8 + 7 1480 7 83
Reactivity worth of xenon is calculated in ANC‐HReactivity worth of xenon is calculated in ANC H
for the following cases:
S• Startup– BOC, MOC, EOC at 50% and 100% power
• Trip– BOC, MOC, EOC at 50% and 100% power
• Core is collapsed to 2‐D for calculation
• Xenon reactivity found over 100 hour periodp
• No change in burnup after startupafter startup
E‐SUM output edit from su_boc_fp.0983.out
500
0
500
0
1500
‐1000
‐500
ty [p
cm]
BOC Full Power
BOC Half Power
1500
‐1000
‐500
y [pcm
]
MOC Full Power
MOC Half Power
2500
‐2000
‐1500
Reactivit
2500
‐2000
‐1500
Reactivit
‐3000
‐2500
0 20 40 60 80 100 120
Time [hr]
‐3000
‐2500
0 20 40 60 80 100 120
Time [hr]Time [hr] Time [hr]
Reactivity after Startup
0
‐1000
‐500
pcm]
EOC Full Power
EOC Half Power
‐2000
‐1500
Reactivity [
‐3000
‐2500
0 20 40 60 80 100 1200 20 40 60 80 100 120
Time [hr]
Reactivity after Startup
‐500
0
‐500
0
‐2000
‐1500
‐1000
y [pcm
]
‐2000
‐1500
‐1000
y [pcm
]
‐3500
‐3000
‐2500
Reactivit
BOC Full Power
BOC Half Power‐3500
‐3000
‐2500
Reactivit
MOC Full Power
MOC Half Power
‐4500
‐4000
0 20 40 60 80 100 120
Time [hr]
BOC Half Power
‐4500
‐4000
0 20 40 60 80 100 120
Time [hr]Time [hr] Time [hr]
Reactivity after Trip
‐500
0
‐2000
‐1500
‐1000
pcm]
‐3500
‐3000
‐2500
Reactivity [p
EOC Full Power
EOC Half Power
‐5000
‐4500
‐4000
0 20 40 60 80 100 1200 20 40 60 80 100 120
Time [hr]
Reactivity after Trip
Necessary to understand theNecessary to understand the
reactivity effect of boron in the
d i di icore under various conditions.
Obtained by varying the boron
concentration by ± 25 ppm
throughout cyclethroughout cycle.
Input sample from dbw_HFP.job
E‐SUM output edit from dbw_HFP.0998.out
E‐SUM edit from dbw_hzp.0999.out
‐6.5
‐7
m/ppm
]
‐8
‐7.5
eren
tial W
orth [p
cm
HZP
‐8.5
Diffe HZP
HFP
‐9
0 2000 4000 6000 8000 10000 12000
Burnup [MWd/MTU]
The isothermal temperature coefficient (ITC) isThe isothermal temperature coefficient (ITC) is
used to confirm the validity of the MTC
prediction.
ITC = MTC + DTC
Most limiting case occurs at BOC HZP where
the boron concentration is highestthe boron concentration is highest.
Input Sample from itc.job
E‐SUM edit from itc.0997.out
The value for ITC is not calculated in ANC‐HThe value for ITC is not calculated in ANC H,
so it must be hand calculated:
Confirmation of the BOC critical boronConfirmation of the BOC critical boron
concentration at HZP is one of the final steps
i d b frequired before startup can occur.
E‐SUM output edit from hzp_cbc.1000.out
Section 05
Objective: perform realistic and conservativeObjective: perform realistic and conservative calculations to determine the departure from nuclear boiling (DNBR) at full power and thenuclear boiling (DNBR) at full power and the power level at which a boiling crisis occurs.
Analysis performed using the COBRA‐IV PC code
for the hot typical cell and the hot thimble cell
• Applies numerical solutions to determineApplies numerical solutions to determine thermal‐hydraulic parameters using subchannel analysis methodsubchannel analysis method
• Capable of determining flow and enthalpy distribution at various axial and radialdistribution at various axial and radial locations
U h H E ilib i M d l• Uses the Homogeneous Equilibrium Model (HEM)
COBRA‐IV used to calculate:COBRA IV used to calculate:
• fuel, clad, and coolant temperature distributionsdistributions
• flow quality and void fraction distributions
• pressure drop
• inter‐channel crossflow
• Calculated as a function of elevationCalculated as a function of elevation
i l d hi bl ll l l d i h• Typical and thimble cells calculated with nominal and overpower cases directly
dcompared
Mass Flux for Hot Typical Channel
2.95
3
3.05
2.8
2.85
2.9
x (M
lb/hr/ft2 )
2.65
2.7
2.75
Mass Flux
Nominal Case
Overpower Case
2.55
2.6
0 20 40 60 80 100 120 140
Axial Location (in)
Overpower Case
Axial Location (in)
Mass Flux for Hot Thimble Channel
2.8
3
2.4
2.6
x (M
lb/hr/ft2 )
2
2.2
Mass Flux
Nominal Case
Overpower Case
1.6
1.8
0 20 40 60 80 100 120 140 160
Axial Location (in)Axial Location (in)
Plotting coolant and cladding temperaturesPlotting coolant and cladding temperatures
illustrates different regions of the core that may
dundergo:– Forced Convection
– Nucleate Boiling
– Saturated Boiling
750
Hot Typical Cell Nominal Temperatures
Coolant Temperature750
Hot Typical Cell Overpower Temperatures
Coolant Temperature
650
700
erature (F)
Cladding Temperature
650
700
rature (F)
Cladding Temperature
550
600
Tempe
600
Tempe
550
0 50 100 150
Axial Location (in)
550
0 50 100 150
Axial Location (in)
750
Hot Thimble Cell Nominal Temperatures
Coolant Temperature 750
Hot Typical Cell Overpower Temperatures
Coolant Temperature
650
700
erature (F)
Cladding Temperature
650
700
rature (F)
Cladding Temperature
600
Tempe
600
Tempe
550
0 50 100 150
Axial Location (in)
550
0 50 100 150
Axial Location (in)
Since the onset of nucleate boiling can beSince the onset of nucleate boiling can be
problematic for reactor kinetics, quality and
id f i l dvoid fraction are evaluated.
Void Fraction: percentage of volume in a channel occupied by vaporp y p
0.14
0.16
Hot Typical Cell Quality
0.4
0.45
Hot Typical Cell Void Fraction
Nominal Void Fraction
0.08
0.1
0.12
Qua
lity
Nominal Quality
Overpower Quality
0.2
0.25
0.3
0.35
d Fraction
Nominal Void Fraction
Overpower Void Fraction
0.02
0.04
0.06
Q
0.05
0.1
0.15
Voi
0
0 50 100 150
Axial Location (in)
0
0 50 100 150
Axial Location (in)
0.14
0.16
Hot Thimble Cell Quality
0.4
0.45
Hot Thimble Cell Void Fraction
0.08
0.1
0.12
Qua
lity
Nominal Quality
Overpower Quality
0.2
0.25
0.3
0.35
d Fraction
Nominal Void Fraction
Overpower Void Fraction
0.02
0.04
0.06
Q
0.05
0.1
0.15
Voi
0
0 50 100 150
Axial Location (in)
0
0 50 100 150
Axial Location (in)
Departure from Nucleate Boiling Ratio: ratio of the heat flux needed to cause DNB to thethe heat flux needed to cause DNB to the actual heat flux of a fuel rod
Minimum DNBR (MDNBR) limit is 1 17Minimum DNBR (MDNBR) limit is 1.17.
i d d i hPower was increased to determine at what
overpower the limit was reached
Power MDNBR Rod Channel Axial Location (in.) Cell Type
100% 3.37 2 2 107.2 Thimble100% 3.37 2 2 107.2 Thimble
153% 1.174 11 31 135.8 Typical
Typical Cell DNBR
20
25
Nominal Case
15
DNBR
Nominal Case
Overpower Case
Boiling Crisis
5
10
D
0
0 20 40 60 80 100 120 140
Axial Location (in)Axial Location (in)
Thimble Cell DNBR
20
25
Nominal Case
15
DNBR
Nominal Case
Overpower Case
Boiling Crisis
5
10
D
0
0 20 40 60 80 100 120 140
Axial Location (in)Axial Location (in)
Section 06
Terminal ObjectiveTerminal Objective
• Successfully became familiar with codes (ANC and COBRA IV) used to generate core loadingand COBRA‐IV) used to generate core loading patterns and perform reload design analysis
Enabling ObjectivesEnabling Objectives
• Successfully developed an acceptable core reload pattern that met all limitationsreload pattern that met all limitations
• Safety, Operational, and Thermal‐Hydraulic l l i f dcalculations were performed
• Written report completed