1. NucE 431W Core Design Presentation
Bayshore Unit 1 Reload Core Design
Group 13
Michael Bertino
Michael Stachnik
Submitted to:
Dr. K Ivanov
Dr. M. Avramova
Mentor: Chris Wagener

2. Table of Contents Introduction Loading Pattern Development
Safety Analysis
Operational Data
Thermal Hydraulics Analysis
Conclusion

3. INTRODUCTION Student Objectives:
To be able to use the codes and methods used by Westinghouse to generate a core loading pattern for a cycle 13 Bayshore Unit 1 reactor and perform reload design analysis.
Perform an analysis for operational conditions and safety requirements for our core loading pattern.
Perform a thermo-hydraulic analysis on our core loading pattern for both steady state and transient conditions.

4. What is ANC? ANC (Advanced Nodal Code) Multidimensional nodal code.
Licensed by NRC for PWR analysis
Calculates:
Core reactivity
Assembly power
Rodwise Power
Reactivity coefficients
Core depletion
Control rod and fission product worths

5. Reactor Core Design CE 2-PWR Loop Core Thermal Power=2700 MWt
4 Control Rods
217 assemblies
5 guide tubes

6. Plant Description
Inlet core temperature is programmed to vary from 532 °𝐹 to 549 °𝐹 from 0 % to 100 % power.
Control rods move from 0 to 137 steps withdrawn.
Rod insertion limits are a function of power.
Full power upper limit of the axial shape index (ASI) is -8 %.

7. Loading Pattern Development

8. Loading Pattern Development
There are four criteria that must be evaluated to development an initial loading pattern (LP)
Energy(cycle length)
FΔ𝐻 peaking factor, ARO
HZP, MTC (all power levels)
Fuel Inventory

9. Loading Pattern Parameters

10. Gadolinia Burnable Absorber
68 feed assemblies
36 assemblies at w/o U235
20 assemblies at w/o U235
12 assemblies at w/o U235
Mixed with UO2, displaces fuel from the core.
Complex depletion chain.
No placement restrictions.
Optimized to reduced peaking within the assembly

11. Summary of ANC Runs to Final LP

12. Final Core Loading Pattern

13. Energy, Cycle Length Requirement
EFPD is defined as the total amount of energy produced from BOC to EOC.
Boron Concentration must be reduced to 10 ppm at HZP conditions
The final burnup step is used to calculate the EFPD of the LP:
𝐸𝐹𝑃𝐷=𝐵𝑈∗ 𝑀𝑇𝑈 𝑃 0 
𝐸𝐹𝑃𝐷=14700 𝑀𝑊𝐷 𝑀𝑇𝑈 ∗ 𝑀𝑇𝑈 2700 𝑀 𝑊 𝑡 =
𝐸𝐹𝑃𝐷=469.51

14. Energy, Cycle Length Requirement
The final burnup step SL213_BE15 concentration target to around 10 ppm for an EFPD of but the boron concentration of the input was 16 ppm with an EFPD of This limit is confirmed at the final burnup step as it should be.

15. Energy, Cycle Length Requirement

16. FΔH Limit Confirmation
FΔH is the normalized enthalpy rise in a given subchannel as the water flows from the bottom of the core to the top of the core.
Represents a localized power with in the core (local power > average power)
The peaking factor (FΔH) is defined in ANC by:
FΔH= 𝑝𝑒𝑎𝑘 𝑖𝑛𝑒𝑔𝑟𝑎𝑡𝑒𝑑 𝑓𝑢𝑒𝑙 𝑟𝑜𝑑 𝑝𝑜𝑤𝑒𝑟 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑡𝑒𝑑 𝑓𝑢𝑒𝑙 𝑟𝑜𝑑 𝑝𝑜𝑤𝑒𝑟

17. FΔH Limit Confirmation

18. FΔH Limit Confirmation
Below is the C-FDH for the 150 BU, the hottest step.

19. FΔH Limit Confirmation
The figure below is the 12th step showing a peak in FΔH due to the boron burning up.

20. MTC Limit Confirmation
The moderator temperature coefficient is defined as the reactivity change per one degree change in the fuel temperature. In a PWR, the moderator is water in the liquid form and the basic units of MTC are pcm/degree temperature.
The MTC of water is negative at most conditions due to as temperature increases→water density decreases→moderation decreases→less reactivity
The more boron that is dissolved in the moderator, the more positive the MTC will be. Water has a naturally negative temperature coefficient while boron has a naturally positive one.

21. MTC Limit Confirmation
The MTC is checked at HZP conditions for the core, RELPOW=0 /
The MTC should also have no xenon, DEPLETE= HDALL, NAXE /

22. MTC Limit Confirmation
The calculation to solve for the MTC of the first case to see if the limit was below 0.50 pcm°F
𝑀𝑇𝐶 𝑝𝑐𝑚 °𝐹 = ln ∗1𝐸 −527 °𝐹 =0.379 𝑝𝑐𝑚 °𝐹

23. Loading Pattern Limit Confirmation
Margins
Target Values
Actual Values
Energy
468.2 EFPD
EFPD
ARO peaking factor(Fdh)
1.635
1.627
HZP, MTC (all power levels)
.50 pcm/F
.37 pcm/F
Fuel inventory
68 Feeds
Boron Concentration(ppm)
10 ppm
16 ppm

24. Safety Analysis

25. Westinghouse RSAC Process
Reload Safety Analysis Checklist.
Transient analyst does calculations to determine damage to the core and environment in case of accident.
Core Designer must confirm that reload design does not violate assumed values.
Always go to the extreme, worst case scenario
Safety calculations done in conservative manner.(most limiting condition)

26. Safety Analysis Westinghouse RSAC Process: Rodded FΔH
Rod Ejection Accident
Shutdown Margin

27. Rodded FΔH
Rodded FΔH must be met when the leading control rod bank is in to is insertion limit (RIL).
The RIL is the deepest possible insertion for any rod bank. This is done to make sure there is enough rod worth left to shut down the core in case of accident or emergency.

28. Rodded FΔH Input file for rodded FΔH: Xenon must be reconstructed
Xenon must be skewed to save time

29. Rodded FΔH

30. Rodded FΔH
Below is the Rodded FΔH output from E-SUM:

31. Rod Ejection Accident
A mechanical failure where a control rod is ejected from the core
Causes large power increase, fuel and clad temperature increase and increase in DNB
The limits found are the ejected rod worth Δρ(E), and the ejected rod hot channel factor FQ(E)

32. Rod Ejection Accident
There are two limits evaluated at two conditions.
BOC, HFP, ARO, equilibrium xenon
EOC, HFP, ARO, no xenon
BOC, HZP, ARO, equilibrium xenon
EOC, HZP, ARO, non xenon

33. Rod Ejection Accident, HFP
The most limiting rod ejection is at the EOC
The most limiting FQ is at BOC
Sample input deck from BOC RELPOW=1.00

34. Rod Ejection Accident, HFP
The output E-SRW for HFP BOC

35. Rod Ejection Accident, HFP
The output E-SRW for HFP EOC

36. Rod Ejection Accident, HFP
𝐻𝐹 𝑃 𝐵𝑂𝐶 = 16𝑝𝑐𝑚 1000 ±0.10∗ 16𝑝𝑐𝑚 1000 =0.016% %= % →𝐿𝑖𝑚𝑖𝑡 𝑀𝑎𝑋 𝐸𝑗𝑒𝑐𝑡𝑒𝑑 𝑅𝑜𝑑 𝑊𝑜𝑟𝑡ℎ=0.25% 𝑀𝑎𝑥 𝐹 𝑄 = ∗2.090=2.3617→Max Allowable FQ=5.25 𝐻𝐹 𝑃 𝐸𝑂𝐶 = 18.9𝑝𝑐𝑚 1000 ±0.10∗ 18.9𝑝𝑐𝑚 1000 =0.0189% %= % 𝑀𝑎𝑥 𝐹 𝑄 = ∗1.990=2.2487→Max Allowable FQ=5.25

37. Rod Ejection Accident, HZP
The rod ejection for HZP is the same thing except RELPOW=0 /

38. Rod Ejection Accident, HZP
The output E-SRW for HZP BOC

39. Rod Ejection Accident, HZP
The output E-SRW for HZP EOC

40. Rod Ejection Accident, HZP
𝐻𝑍 𝑃 𝐵𝑂𝐶 = 12.4𝑝𝑐𝑚 1000 ±0.12∗ 12.4𝑝𝑐𝑚 1000 =0.0124% %= % →𝐿𝑖𝑚𝑖𝑡 𝑀𝑎𝑋 𝐸𝑗𝑒𝑐𝑡𝑒𝑑 𝑅𝑜𝑑 𝑊𝑜𝑟𝑡ℎ=0.60% 𝑀𝑎𝑥 𝐹 𝑄 = =2.6347→Max Allowable FQ=15.0 𝐻𝑍 𝑃 𝐸𝑂𝐶 = 13.1𝑝𝑐𝑚 1000 ±0.12∗ 13.1𝑝𝑐𝑚 1000 =0.0131% %= % 𝑀𝑎𝑥 𝐹 𝑄 = =2.69→Max Allowable FQ=26.25

41. Rod Ejection Accident

42. Shutdown Margin
The amount of reactivity in the core at subcritical following a trip.
Shows that the operators will be able to safely shut down the core.
There are components that affect the SM in ANC:
Doppler Defect-fuel pellet temperature increases with power and so does resonance absorption due to Doppler. Doppler decrease reactivity
Voids-Local boiling in the moderator can also cause small voids to form. Voids decrease reactivity but collapsing gives a small increase.
Axial Flux redistribution-enthalpy in the core rises causing a flux tilt towards the bottom of the core. When its goes from HFP to HZP(power defect) there is no rise in enthalpy causing the flux to shift to the top of the core which increases reactivity.

43. Shutdown Margin
4. Power Defect- amount of total reactivity associated with a change in power. It is larger at EOC because the MTC is more negative due to less boron. So reactivity increases. 5. Rod insertion allowance- cannot assume a full worth of control rod banks. The core may have only partially inserted rods at trip. The reactivity depends on how much rod worth there is. 6. Variable Moderator Temperature- The moderator temperature is greater at HFP so when it trips to HZP causes the temperature to decrease causing a spike in reactivity.

44. Shutdown Margin Use six cases for ANC input:
K1- Base Case at Burnup of Interest (BOC or EOC)
EOC, boron should be set to 0 ppm
BOC, boron should be constant
K2-Rods at Insertion Limits
Lead bank is inserted which means less rod worth out of the core
Less negative reactivity upon trip
K3-Over-power/Over Temperature, Skew Power to Top of Core
Increase core power from 100%to 105%
Higher power means that the initial temperature will be higher and it will increase power defect
Xenon is skewed so that the AO shifts to most positive side(xenon to the bottom of the core, shifts power to the top
Increases the worth of partially inserted rods and the power defect

45. Shutdown Margin K4-Trip to Zero Power K5-Full Core-All Rods In
Holds the Xenon, boron and D bank and it goes from HFP to HZP
K5-Full Core-All Rods In
All rods inserted in full core
K6-Worst Stuck Rod Out
Removes the worst stuck rod

46. Shutdown Margin
To calculate the shutdown margin we took the worst stuck rod case at BOC and EOC
𝑆𝐷 𝑀 𝐵𝑂𝐶𝑐𝑎𝑙𝑐 = 0.9∗ln 𝑘 4 𝑘 6 ∗100000= ln ∗100000= 𝑝𝑐𝑚
𝑅𝑜𝑑 𝑊𝑜𝑟𝑡ℎ 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦= ln 𝑘 4 𝑘 3 ∗ = ln ∗1𝐸5= 𝑝𝑐𝑚
𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑆𝐷𝑀=𝑆𝐷 𝑀 𝑐𝑎𝑙𝑐 −𝑅𝑜𝑑 𝑊𝑜𝑟𝑡ℎ 𝑈𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦−𝑣𝑜𝑖𝑑 𝑒𝑓𝑓𝑒𝑐𝑡=
− −50= 𝑝𝑐𝑚 1000 =5.466% →𝐿𝑖𝑚𝑖𝑡 𝑆𝐷𝑀=3.6%
This meets the limit for the shutdown margin by 1.866%Δ𝑝.

47. Shutdown Margin

48. Shutdown Margin BOC WORTHS (pcm) EOC WORTHS (pcm) POWER DEFECTS 1483.7
BOC WORTHS (pcm)
EOC WORTHS (pcm)
POWER DEFECTS
1483.7
Void Effects 50
Total Control Bank Requirement(1)
1533.7
SDMCALC
Less 10% (2)
Available SDM (2)-(1)
Required SDM
3600

49. Operational Data

50. Operational Data
Calculations that must be performed to make sure the core is running at normal conditions
Rod Worth
Xenon Worth
Differential Boron Worth
Isothermal Temperature Coefficient
Critical Boron Concentration

51. Rod Worth Measured at BOC, HZP
The rodworth is found using the boron dilution method:
Core at BOC, HZP, ARI, subcritical (high CB)
Withdraw rods (ARO)
Dilute CB to ARO critical boron, CBARO
Insert lead control bank (Bank D)
Insert Remaining Control Banks, One at a Time, in Normal Sequence

52. Rod Worth
As more rod worth is inserted, the fraction of rated thermal power decreases.
The lead bank in our
case is bank5

53. Rod Worth

54. Rod Worth Configuration CB (ppm) Inserted Worth (ppm) ARO 1605 ----- D
1479
126
D+C
1436 43
D+C+B
1336
100
D+C+B+A
1247 89
D+C+B+A+BANK1
1197 50
D+C+B+A+BANK1+BANK6
884
313
D+C+B+A+BANK1+BANK6+BANK7
503
381

55. Xenon Worth
Reactivity due to the absorption on neutrons Xe-135 in the core.
A fission product with a high absorber worth produced from the decay of I-135
𝑑𝐼 𝑑𝑡 = 𝛾 𝐼 Σ 𝑓 Φ 2 − 𝜆 𝐼 𝐼
𝑑𝑋𝑒 𝑑𝑡 = 𝜆 𝐼 𝐼+ 𝛾 𝑥𝑒 Σ 𝑓 Φ 2 − 𝜆 𝑥𝑒 𝑋𝑒− 𝜎 𝑎 𝑥𝑒 Φ 2 𝑋𝑒
Xe-135 is removed by two effects:
Absorption by thermal neutron flux
Radioactive decay

56. Xenon Worth
Xenon reactivity after startup and trip is what is calculated using ANC
Startup
BOC,MOC,EOC at 50 % and 100 % Power
2. Trip

57. Xenon Worth
Speed up calculations core is collapsed from 3-D to 2-D Deplete the Xenon for over 100 hours

58. Xenon Worth Use the Eigenvalues to calculate the reactivity
𝑆𝑎𝑚𝑝𝑙𝑒 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑅𝑒𝑎𝑐𝑡𝑖𝑣𝑖𝑡𝑦 =100000∗𝐿𝑁 =−31.41𝑝𝑐𝑚

59. Xenon Worth, Startup

60. Xenon Worth, Startup

61. Xenon Worth, After Trip
~9Hours

62. Xenon Worth, After Trip

63. Differential Boron Worth
Change in reactivity due to a unit change in boron concentration.
Calculated at both HZP and HFP varying by ±25 ppm.
Input sample from HZP job file
At HZP, differential boron worths were calculated at a wide range of boron concentrations

64. Differential Boron Worth
DBW = 𝐿𝑁 ∗ = 𝑝𝑐𝑚

65. Differential Boron Worth
Shows the amount of soluble boron throughout the cycle at HFP

66. Differential Boron Worth
HZP DBW for 5 different boron concentrations over the length of the cycle

67. Isothermal Temperature Coefficient
ITC is defined as the change in reactivity of a core with a change in core temperature.
DTC is defined as the reactivity change per one degree change in the fuel temperature. In a PWR, the fuel is UO2 in ceramic form and the basic units of DTC are in pcm/F or pcm/C.
𝐼𝑇𝐶=𝑀𝑇𝐶+𝐷𝑇𝐶
It will follow the behaviors of both the MTC and DTC.
DTC remains constant, ITC will follow the MTC, boron decreases so does ITC.
In ANC the most limiting case is at BOC HZP where the boron is at the highest.

68. Isothermal Temperature Coefficient
Input deck and E-Sum for ITC

69. Isothermal Temperature Coefficient
ITC must be calculated by doing it the old fashion way, by hand. MTC and DTC are found by ANC and ITC is found using the equation below: 𝐼𝑇𝐶= ln 𝑘 ­ +5 𝑘 −5 ∗ 10 5 Δ 𝑇 𝑎𝑣𝑔 𝐼𝑇𝐶= ln ∗ −527.0°F 𝐼𝑇𝐶=−.670 𝑝𝑐𝑚/°𝐹

70. Critical Boron Concentration
Critical boron concentration is found at BOC, HZP, ARO, no xenon
It is done to predict cycle length and reactor control.
It has a heavy effect on MTC and Xenon Worth.
Good agreement between the measured value and the value predicted by the design code. Gives accuracy of the design model of the reactor.
NRC says that the difference should not exceed 1 %.

71. Critical Boron Concentration

72. Thermal-Hydraulic Analysis

73. Why Thermal-Hydraulic Analysis is Needed
A thermal-hydraulic analysis is necessary for any core design before the design is implemented.
The goal is to determine the range of operation and the conditions that the reactor can safely operate without resulting in fuel failure over the reactor life considering both steady-state and anticipated transient operation.
With thermal hydraulic analysis, the temperature distribution throughout the core can be determined with a given fission power distribution and coolant inlet condition.

74. Core Design Subchannel Code (CDSC)
CDSC is a three-dimensional thermal hydraulic code that solves for mass flow, quality, void fraction, fluid temperature, and pressure for each subchannel.
CDSC also models assembly-to-assembly mixing as well as subchannel-to-subchannel mixing.
CDSC assumes homogeneous equilibrium two-phase flow (no slip and same temperatures for each phase).
The output provides a 3D enthalpy and flow distribution and data for the evaluation of thermal safety limits.

75. Boundary Conditions Nominal Power
Inlet Mass Flux: kg/ 𝑚 2 /s
System Exit Pressure: 15MPa
Inlet Temperature: 278 𝑜 𝐶
Power Input: w/ 𝑚 2
Spacer Grid Loss Coefficient: 0.8
3D power Distribution

76. Geometry of the Subchannel Analysis
Flow Channel Dimensions
Rod Dimensions
Flow Channel Gap and Distance
Heated and Wetted Parameters

77. Overpower Uncertainties
5% decrease in Inlet Mass Flux: kg/ 𝑚 2 /s
50psia Increase in Exit Pressure: 15.34MPa
7 𝑜 𝐶 Increase in Inlet Temperature: 285 𝑜 𝐶
Power Input Increased until DNBR of 1.3: w/ 𝑚 2
10% Increase in Spacer Grid Loss Coefficient: 0.88
Decrease of Pitch by inches in Hottest Subchannel: 0.5in

78. Nominal and Overpower Cases
Type
Power
Hottest Rod
Hottest Channel
Axial Location (m)
Min DNB Ratio
Nominal
100% 16 22
3.3969
Overpower+unc
151% 28
1.3007

79. Bayshore Reactor Vessel at Nominal Power and Overpower
Water In at 285 C
Water In at 278 C
Water Out at C
Water Out at C

80. Coolant Temperature

81. Fuel Temperature in Nominal and Overpower

82. Cladding Temperature

83. Departure From Nucleate Boiling Ratio

84. Void Fraction

85. Mass Flux

86. Conclusion
Learned how to develop a loading pattern under restrictions.
Made sure our core was safe using the RSAC process.
Calculated operational data to confirm that our core performed properly at all phases of the cycle.
Performed thermal-hydraulics calculations to evaluate the subchannels and rods to nominal and overpower conditions.

87. References
1.Dr. K. Ivanov, Dr. M. Avramova. Nuclear Engineering 431W: Nuclear Reactor Core Design. Department of Mechanical and Nuclear Engineering, The Pennsylvania State University: Spring C. Wagener. Core Design Training Course. Westinghouse Electric Company, presented to Penn State University: Spring 2014

88. QUESTIONS?