This presentation covers loading pattern generation, safety calculations, operational calculations, and thermal hydraulics analysis for a nuclear reactor reload design. The objectives are to develop an acceptable core loading pattern, perform safety and operational calculations on the design including thermal hydraulics, and provide reports. Calculation methods include the ANC advanced nodal code and Westinghouse safety analysis checklist. Key parameters like cycle length, power peaking factors, reactivity coefficients, and control rod worth are analyzed.

2. This presentation will cover the following topics:
This presentation will cover the following topics:
1. Introduction
2.
2 Loading Pattern Generation
di G i
3. Safety Calculations
4. Operational Calculations
5. Thermal Hydraulics
5 Thermal‐Hydraulics
6. Conclusions

4. Section 01

5. Terminal Objective
j
• Become familiar with codes and methods used to
generate core loading patterns and perform reload
design analysis
d i l i
Enabling Objectives
Enabling Objectives
• Develop an acceptable reload core loading pattern
• Perform safety and operational calculations on the
Perform safety and operational calculations on the
designed LP along with thermal‐hydraulics analysis
• Provide an oral presentation and a written report

6. ANC: Advanced Nodal Code
• Multidimensional nodal code (3D, 2D, 1D)
• Licensed by the NRC in 1988 for PWR analysis
• Calculates
– Core reactivity
– Assembly power and burnups
A bl db
– Rodwise power and burnups
– Reactivity coefficients
y
– Core depletion
– Control rod and fission product worths

7. APA H code set used due to hexagonal geometry
APA‐H code set used due to hexagonal geometry
and consists of:
• ALPHA‐H
• PHOENIX‐H
• ANC H
ANC‐H
These codes are the same in function as square
geometry codes but modified to use hexagonal
geometry.

8. Differences from square geometry versions:
Differences from square geometry versions:
• Both the assembly and the core are modeled
in 1/6 and full core geometry
in 1/6 and full core geometry
• ANC‐H uses only one node per assembly as
compared to four nodes per assembly in ANC
d f d bl i ANC
Inputs and outputs are virtually the same

9. VVER‐1000
• PWR Design – 3000 MWt
g
• 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/

10. • Inlet core temperature varies from 533.5 °F to
et co e te pe atu e a es o 533.5 to
553.1 °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.

14. Section 02

15. • Cycle Length
Cycle Length
• FΔH Peaking Factor
• Moderator Temperature Coefficient (MTC)
d C ffi i ( C)
• Feed Inventory

16. Parameter Limit
Cycle Length
Cycle Length ≥ 308 EFPD (11329
≥ 308 EFPD (11329 MWd/MTU)
ARO Peaking Factor (FΔH) ≤ 1.532
HZP MTC
HZP MTC ≤ 0.00 pcm/ F
≤ 0.00 pcm/°F
Feed Inventory ≤ 42 Feeds

18. Customer plans to shut down cycle 4 at a cycle
Customer plans to shut down cycle 4 at a cycle
length of 308 EFPD. This value is used to
calculate the EOC burnup:
l l h OC b

19. 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 step.
11329 MWd/MTU burnup step

20. FΔH is literally defined as the normalized rise in enthalpy in a
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.

21. 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.

22. 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.

23. 1.540
1.530
1.520
1.510
F∆H
1.500
1.490
1.480
Actual
Limit
1.470
1.460
0 2000 4000 6000 8000 10000 12000
Burnup [MWD/MTU]
Burnup [MWD/MTU]

24. The F of each assembly for a particular
The FΔH of each assembly for a particular
burnup step is shown in the C‐FDH output edit.

25. MTC change in core reactivity due to a change in
MTC – change in core reactivity due to a change in
moderator temperature (fuel temperature is held
constant) and is checked at HZP for all burnup steps.
constant) and is checked at HZP for all burnup steps
A portion of the input from 03_anch_B1C4_depl.job is:

26. The E SEQ output edit displays the MTC values
The E‐SEQ output edit displays the MTC values
for each burnup step.

27. The calculation from ANC is verified for the most
limiting case (150 MWd/MTU burnup step).
limiting case (150 MWd/MTU burnup step).

28. 0 1700
‐2 1500
1300
‐4
pm]
1100
n Concentration [pp
‐6
MTC [pcm/°F]
900
‐8
700
‐10
10
Boron
500
MTC
‐12
300
MTC Limit
‐14 100
Boron Concentration
Boron Concentration
‐16 ‐100
0 2000 4000 6000 8000 10000 12000
Burnup [MWD/MTU]

29. 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

30. Section 03

31. Safety Calculations were performed using the
Safety Calculations were performed using the
Westinghouse Reactor Safety Analysis Checklist
(RSAC) which covers:
( S C) hi h
• Rodded FΔH
• Shutdown Margin
• Rod Ejection Accident
Rod Ejection Accident

32. Since most reactors are permitted to operate
Since most reactors are permitted to operate
at full power with some control rods inserted
in the core, FΔH must also be checked with
i h l b h k d ih
allowable control rods inserted. For this
particular scenario, the calculation was
performed with the lead control bank at its RIL.
performed with the lead control bank at its RIL

33. Input from roddedFDH.job
p j
Xenon was skewed for conservatism

34. The rodded
The rodded FΔH is displayed in the E‐SUM output
is displayed in the E SUM output
edit from roddedFDH.0960.out.

35. C‐FDH output edit from roddedFDH.0960.out

36. Burnup [MWd/MTU] Δ Axial Offset (%) Rodded FΔH
150 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
6 49 1.467
1 467
11360 6.50 1.467

37. 1.540
1.530
1.520
1.510
Fdh
1.500
1.490
1.480
Fdh
Rodded Fdh
Rodded Fdh
1.470
Fdh Limit
1.460
0 2000 4000 6000 8000 10000 12000
Burnup [MWD/MTU]
Burnup [MWD/MTU]

38. Shows that in any circumstances the operator
will 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 following
a reactor trip, assuming the highest worth control rod is stuck out.
Six cases in ANC:
• K1 B
K1 – Base Case at Burnup of Interest (BOC or EOC)
C tB fI t t (BOC 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

39. Calculation performed at both BOC and EOC
Calculation performed at both BOC and EOC
Total Power Defect‐ amount the core will
l f h ill
increase in reactivity due to the trip to HZP
Available SDM =
Calculated SDM – Rod Worth Uncertainty – Voids

40. E‐SUM output edit from sdownemBOC.0979.out

42. E‐SUM output edit from sdownemEOC.1004.out

44. Requirement BOC Worth (pcm) EOC Worth (pcm)
Control Banks
Power Defect 1943.7 3152.6
Void Effects 50 50
(1) Total Control Bank Requirement
(1) Total Control Bank Requirement 1993.7
1993 7 3202.6
3202 6
Control Rod Worth (HZP)
All rods inserted less most
6867 7677.3
reactive rod stuck out
(2) Less 10% 6180.3 6909.6
Shutdown Margin
Calculated Margin (2) – (1) 4186.6 3707
Required Shutdown Margin 1300 1300

45. Purpose: Simulate the unlikely event of a single
p y g
control rod being ejected from the core due to
failure in the control rod pressure housing. Total
peaking factor, F and %Δρ must be below limit
peaking factor FQ , and %Δρ must be below limit
for each condition.
Evaluated at Four Conditions:
1. BOC HFP
2. EOC HFP
3. BOC HZP
4. EOC HZP

46. Input sample from rodejectionHFP.job
Only control bank 10 is
j
ejected from core at HFP.
Since rod ejection is a
,
fast transient, all
feedback effects are
frozen under an adiabatic
assumption.

47. The E‐SUM output edit from
The E SUM output edit from
rodejectionHFP.0963.out contains the total
peaking factor and eigenvalues.

48. The rod ejection worth is calculated for each
The rod ejection worth is calculated for each
case using the equation:

49. Rod Ejection at HFP
%Δρ (10% FQ (13%
Case Eigenvalue dk/k %Δρ FQ
uncertainty) uncertainty)
BOC Full Core 1.000000 ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
BOC Bank 10 1.000128 0.000128 0.012799 0.014079 1.949 2.20237
EOC Full Core
EOC Full Core 0.999200
0 999200 ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
EOC Bank 10 0.999377 0.000177 0.017713 0.019484 1.811 2.04643

50. Approach is virtually same as
for HFP with the exception being
for HFP with the exception being
the number of control rods ejected.
Now four locations are ejected
Now four locations are ejected
individually.

52. BOC Rod Ejection at HZP
%Δρ (10% FQ (13%
Case Eigenvalue dk/k %Δρ uncertainty) FQ uncertainty)
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
1.002328 0.002324 0.232429 0.260321 3.137 3.85851
(center)
Bank 8 1.000479 0.000478 0.047789 0.053523 2.750 3.38250

53. EOC Rod Ejection at HZP
%Δρ (10% FQ (13%
Case Eigenvalue dk/k %Δρ uncertainty) FQ uncertainty)
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
1.039740 0.002350 0.235046 0.263252 3.909 4.80807
(center)
Bank 8 1.038825 0.001470 0.147005 0.164645 5.159 6.34557

54. Rod Ejection Overview
j
Calculated Calculated
Case (Bank) %Δρ Limit FQ Limit
%Δρ FQ
BOC HFP
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)
EOC HZP (9c) 0.263252
0 263252 0.900
0 900 4.80807
4 80807 21.0
21 0
EOC HZP (8) 0.164645 0.900 6.34557 21.0

55. Section 04

56. Several Calculations must be performed before
Several Calculations must be performed before
the reactor can go back online after an outage:
• BOC HZP Rodworths
OC d h
• Xenon Reactivity after Startup and Trip
• Differential Boron Worth
• Isothermal Temperature Coefficient
Isothermal Temperature Coefficient
• BOC HZP Critical Boron Concentration

57. Rodworths of control banks are determined
of control banks are determined
using the boron dilution method.
Input sample from rodworth.job
E SUM edit from rodworth.0981.out
E‐SUM edit from rodworth.0981.out

58. Control Bank Worth Overview
Control Banks Inserted CBC [ppm] Bank No. Bank Worth [ppm]
ARO 1872 ‐‐‐‐‐‐‐‐‐‐‐‐ ‐‐‐‐‐‐‐‐‐‐‐‐‐
10 1796 10 76
10 + 9
10 + 9 1656 9 140
10 + 9 + 8 1563 8 93
10 + 9 + 8 + 7 1480 7 83

59. Reactivity worth of xenon is calculated in ANC H
Reactivity 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

60. • Core is collapsed to 2‐D
for calculation
• Xenon reactivity found
p
over 100 hour period
• No change in burnup
after startup
after startup

61. E‐SUM output edit from su_boc_fp.0983.out

62. 0 0
500
‐500 ‐500
500
BOC Full Power MOC Full Power
‐1000 ‐1000
ty [pcm]
Reactivity [pcm]
BOC Half Power MOC Half Power
1500
‐1500 ‐1500
1500
Reactivit
‐2000 ‐2000
2500
‐2500 ‐2500
2500
‐3000 ‐3000
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Time [hr]
Time [hr] Time [hr]
Time [hr]
Reactivity after Startup

63. 0
‐500
EOC Full Power
‐1000
EOC Half Power
Reactivity [pcm]
‐1500
‐2000
‐2500
‐3000
0 20 40 60 80 100 120
Time [hr]
Reactivity after Startup

64. 0 0
‐500 ‐500
‐1000 ‐1000
‐1500 ‐1500
Reactivity [pcm]
Reactivity [pcm]
‐2000 ‐2000
‐2500 ‐2500
‐3000 ‐3000
MOC Full Power
BOC Full Power
‐3500 ‐3500
MOC Half Power
BOC Half Power
BOC Half Power
‐4000 ‐4000
‐4500 ‐4500
0 20 40 60 80 100 120 0 20 40 60 80 100 120
Time [hr]
Time [hr] Time [hr]
Time [hr]
Reactivity after Trip

65. 0
‐500
‐1000
‐1500
pcm]
‐2000
Reactivity [p
‐2500
‐3000
EOC Full Power
‐3500
EOC Half Power
‐4000
‐4500
‐5000
0 20 40 60 80 100 120
Time [hr]
Reactivity after Trip

66. Necessary to understand the
Necessary to understand the
reactivity effect of boron in the
core under various conditions.
d i di i
Obtained by varying the boron
concentration by ± 25 ppm
throughout cycle.
throughout cycle
Input sample from dbw_HFP.job

67. E‐SUM output edit from dbw_HFP.0998.out

68. E‐SUM edit from dbw_hzp.0999.out

69. ‐6.5
‐7
m/ppm]
erential Worth [pcm
‐7.5
‐8
HZP
Diffe
HFP
‐8.5
‐9
0 2000 4000 6000 8000 10000 12000
Burnup [MWd/MTU]

70. The isothermal temperature coefficient (ITC) is
The 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 highest.
the boron concentration is highest

71. Input Sample from itc.job
E‐SUM edit from itc.0997.out

72. The value for ITC is not calculated in ANC H,
The value for ITC is not calculated in ANC‐H
so it must be hand calculated:

73. Confirmation of the BOC critical boron
Confirmation of the BOC critical boron
concentration at HZP is one of the final steps
required before startup can occur.
i db f
E‐SUM output edit from hzp_cbc.1000.out

74. Section 05

75. Objective: perform realistic and conservative
Objective: perform realistic and conservative
calculations to determine the departure from
nuclear boiling (DNBR) at full power and the
nuclear 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

76. • Applies numerical solutions to determine
Applies numerical solutions to determine
thermal‐hydraulic parameters using
subchannel analysis method
subchannel analysis method
• Capable of determining flow and enthalpy
distribution at various axial and radial
distribution at various axial and radial
locations
• U
Uses the Homogeneous Equilibrium Model
h H E ilib i M d l
(HEM)

77. COBRA IV used to calculate:
COBRA‐IV used to calculate:
• fuel, clad, and coolant temperature
distributions
• flow quality and void fraction distributions
• pressure drop
• inter‐channel crossflow

78. • Calculated as a function of elevation
Calculated as a function of elevation
• Typical and thimble cells calculated with
i l d hi bl ll l l d ih
nominal and overpower cases directly
compared d

79. Mass Flux for Hot Typical Channel
3.05
3
2.95
2.9
x (Mlb/hr/ft2)
2.85
2.8
Mass Flux
2.75
2.7
Nominal Case
2.65
Overpower Case
Overpower Case
2.6
2.55
0 20 40 60 80 100 120 140
Axial Location (in)
Axial Location (in)

80. Mass Flux for Hot Thimble Channel
3
2.8
2.6
x (Mlb/hr/ft2)
2.4
Mass Flux
2.2
2
Nominal Case
Overpower Case
1.8
1.6
0 20 40 60 80 100 120 140 160
Axial Location (in)
Axial Location (in)

81. Plotting coolant and cladding temperatures
Plotting coolant and cladding temperatures
illustrates different regions of the core that may
undergo:
d
– Forced Convection
– Nucleate Boiling
– Saturated Boiling

82. Hot Typical Cell Nominal Hot Typical Cell Overpower
Temperatures Temperatures
750 750
Coolant Temperature Coolant Temperature
Cladding Temperature
Cladding Temperature
700 700
erature (F)
Temperature (F)
650 650
Tempe
600 600
550
550
0 50 100 150
0 50 100 150
Axial Location (in)
Axial Location (in)

83. Hot Thimble Cell Nominal Hot Typical Cell Overpower
Temperatures Temperatures
750
Coolant Temperature 750
Coolant Temperature
Cladding Temperature
Cladding Temperature
700 700
erature (F)
Temperature (F)
650 650
Tempe
600 600
550 550
0 50 100 150 0 50 100 150
Axial Location (in) Axial Location (in)

84. Since the onset of nucleate boiling can be
Since the onset of nucleate boiling can be
problematic for reactor kinetics, quality and
void fraction are evaluated.
id f i l d
Void Fraction: percentage of volume in a
p y p
channel occupied by vapor

85. Hot Typical Cell Quality Hot Typical Cell Void Fraction
0.16 0.45
0.14 0.4
Nominal Void Fraction
Nominal Void Fraction
Nominal Quality 0.35
0.12
Overpower Void Fraction
Overpower Quality 0.3
0.1
Void Fraction
0.25
Quality
0.08
0.2
Q
0.06
0.15
0.04
0.1
0.02 0.05
0 0
0 50 100 150 0 50 100 150
Axial Location (in) Axial Location (in)

86. Hot Thimble Cell Quality Hot Thimble Cell Void Fraction
0.16 0.45
0.14 0.4
0.35
0.12
Nominal Void Fraction
Nominal Quality 0.3
0.1
Void Fraction
Overpower Void Fraction
Overpower Quality 0.25
Quality
0.08
0.2
Q
0.06
0.15
0.04
0.1
0.02 0.05
0 0
0 50 100 150 0 50 100 150
Axial Location (in) Axial Location (in)

87. Departure from Nucleate Boiling Ratio: ratio of
the heat flux needed to cause DNB to the
the heat flux needed to cause DNB to the
actual heat flux of a fuel rod

88. Minimum DNBR (MDNBR) limit is 1.17.
Minimum DNBR (MDNBR) limit is 1 17
Power was increased to determine at what
i d d i h
overpower the limit was reached
Power MDNBR Rod Channel Axial Location (in.) Cell Type
100% 3.37 2 2 107.2 Thimble
153% 1.174 11 31 135.8 Typical

89. Typical Cell DNBR
25
20
Nominal Case
Nominal Case
Overpower Case
Boiling Crisis
15
DNBR
D
10
5
0
0 20 40 60 80 100 120 140
Axial Location (in)
Axial Location (in)

90. Thimble Cell DNBR
25
20
Nominal Case
Nominal Case
Overpower Case
Boiling Crisis
15
DNBR
D
10
5
0
0 20 40 60 80 100 120 140
Axial Location (in)
Axial Location (in)

91. Section 06

92. Terminal Objective
Terminal Objective
• Successfully became familiar with codes (ANC
and COBRA‐IV) used to generate core loading
and COBRA IV) used to generate core loading
patterns and perform reload design analysis

93. Enabling Objectives
Enabling Objectives
• Successfully developed an acceptable core
reload pattern that met all limitations
reload pattern that met all limitations
• Safety, Operational, and Thermal‐Hydraulic
calculations were performed
l l i f d
• Written report completed