OPTIMIZATION OF WESTINGHOUSE’S AP1000 CORE DESIGN

THE PENNSYLVANIA STATE UNIVERSITY

SCHREYER HONORS COLLEGE

DEPARTMENT OF MECHANICAL AND NUCLEAR ENGINEERING

OPTIMIZATION OF WESTINGHOUSE’S AP1000 CORE DESIGN

IAN DAVIS

Spring 2011

A thesis

submitted in partial fulfillment

of the requirements

for a baccalaureate degree

in Nuclear Engineering

with honors in Nuclear Engineering.

Reviewed and approved* by the following:

Dr. Maria Avramova

Assistant Professor of Nuclear Engineering

Thesis Supervisor

Dr. Arthur Motta

Chair of Nuclear Engineering

Honors Adviser

*Signatures are on file in the Schreyer Honors College.

i

Abstract The goal of this project was to optimize the core design of Westinghouse’s AP1000 core design.

This was done using Westinghouse’s Advanced Nodal Expansion Code (ANC). Cycle lengths of 12, 18,

and 24 months, and power levels of 3400, 4000, 5000, and 6000 MWt were chosen for the study. Also,

a maximum peaking factor of 1.6 was set for the study. Different combinations of cycle length and

power level were analyzed until an acceptable fuel loading pattern was determined, or the possibility of

attaining one was ruled out. Successful loading patterns were developed for all three cycle lengths at

the 3400 MWt power level, for the 12 and 18 month cycle length requirement for the 4000 and 5000

MWt power levels, and only for the 12 month cycle for the 6000 MWt power level. Constraints on fuel

enrichment prevented the loading patterns from being developed any further.

ii

Table of Contents

1 Introduction .......................................................................................................................................... 1

1.1 Background for Nuclear Core Design .......................................................................................... 1

1.2 Research Objectives .................................................................................................................... 1

1.3 Description of Computer Code .................................................................................................... 2

1.4 Reactor Core Description ............................................................................................................. 2

1.5 Limits and Requirements ............................................................................................................. 7

2 Methodology ......................................................................................................................................... 8

3 Results and Discussion .......................................................................................................................... 9

3.1 LP’s for the 12 month cycle (280-320 EFPD) ............................................................................. 10



4 Conclusions ........................................................................................................................................ .54

5 References .......................................................................................................................................... 55

Nomenclature List……………………...…………………………………………………………………….....……………………………….56

Appendix ..................................................................................................................................................... 57

1

1 Introduction

The efficiency of nuclear fuel loading patterns (LP’s) plays a significant role in cycle length and power

distribution for Pressurized Water Reactors (PWR’s). Determining a reactor’s refueling outages depends

on the cycle length. Furthermore, designers use the power distribution to make the LP’s as safe and

efficient as possible. For instance, Westinghouse’s AP1000 reactor generally operates for an eighteen

month cycle at 3400 MWt. Since the AP1000 is a brand new reactor, its cycle length and power level are

standard. However, there is limited or no estimates of other possible cycle lengths and power levels the

AP1000 could run at. As a result, this project planned to optimize the core design by finding LP’s for

various cycle lengths and power levels.

1.1 Background for Nuclear Core Design

Similar to this project, Penn State’s senior design course for nuclear engineering allows students to

generate realistic LP’s based on a set of guidelines. Within these guidelines, the students are given an

energy requirement and a licensing requirement. The energy requirement determines the cycle length

that the LP needs to meet, and the licensing requirement includes several economic and safety

parameters. Some of these parameters are as follows: maximum average fuel enrichment, maximum

moderator temperature coefficient (MTC), and maximum enthalpy rise hot channel peaking factor (F∆H).

Also, the students are provided with a variety of fuel assemblies from which to choose. Students using

the AP1000 core for their project can use six different enrichments of fuel: 0.740, 1.655, 2.800, 3.200,

3.779, and 4.330 w/o. Some of the fuel assemblies contain burnable absorbers, which can help to

decrease the peaking factor. The AP1000 core project is unique because students are analyzing a first

cycle. In other words, the students are using all fresh feed fuels and no burnt fuel assemblies. Once all

requirements are achieved, a final report is written and the course is complete. The course uses the

same design and objectives every year; nothing has been changed yet to analyze different core designs.

1.2 Research Objectives

The primary objective of this project was to optimize the core design for the Westinghouse AP1000

nuclear reactor. Optimization was carried out through the generation of loading patterns designed for

specific cycle lengths and power levels. These cycle lengths include: 12, 18, and 24 months. These

power levels include: 3400, 4000, 5000, and 6000 MWt. Learning the Westinghouse Advanced Nodal

Expansion code (ANC) and understanding the core design process were parallel objectives, which aided

in the AP1000’s optimization. The end goal was to provide Westinghouse with a report on loading

pattern options for the AP1000.

2

1.3 Description of Computer Code

Nuclear reactor core designers require computer codes to design and simulate the burn up of nuclear

reactors. The particular code used for this project comes from the APA system, which is actually a

combination of three computer codes put into an acronym: ALPHA, PHOENIX-P, and Advanced Nodal

Code (ANC).

The first code, ALPHA, is an automation code for ANC model generation. Essentially, ALPHA prepares

and executes PHOENIX-P calculations for both feed and burned assemblies. It also creates ANC input

from the PHOENIX-P databanks. Some of the data that ALPHA extracts from the PHOENIX-P databanks

include macroscopic cross-sections, micros for fission products, water, boron, and actinides,

discontinuity factors, and pin factor file generation.

The second code in the acronym, PHOENIX-P, is based off the original PHOENIX code developed by

R. Stamm’ler. Essentially, PHOENIX-P performs 2D transport lattice calculations to model fuel pins and

fuel assemblies. From these calculations PHOENIX-P generates a massive databank of information,

which includes: spectrum and depletion calculations, cross sections libraries, pin power reconstruction,

isotopic composition of fuel as a function of depletion, fuel temperatures, and burn up chains.

The final computer code in the acronym, ANC, is a multidimensional nodal code. It was licensed by the

NRC in 1988 for PWR core analysis. ANC takes input files from ALPHA and calculates core reactivity,

assembly power and burn ups, rodwise powers and burn ups, reactivity coefficients, core depletion,

control rod worths, and fission product worths.

Since this project deals solely with loading pattern generation, the PHOENIX-P and ALPHA codes have

already been run, and the databanks are already compiled. Furthermore, the fuel patterns were applied

to the ANC code and the burn up simulation was run. The fuel identifiers were generated from the

PHOENIX-P databanks and presented using the ALPHA code.

1.4 Reactor Core Description

The AP1000 is the first Generation III+ nuclear reactor being built in the world. Currently, there are four

AP1000’s under construction in China, and six under contract in the United States. The AP1000 carries

the typical design of a PWR reactor with some major upgrades. The AP1000 will be the first reactor to

use passive safety systems, increasing the stability of the reactor significantly. For example, the new

reactor does not rely on AC power, has no safety related-pumps, and has no safety-related ventilation

system. Also, the AP1000’s modular construction abilities have surpassed all efficiency expectations.

Furthermore, the AP1000 uses 50% fewer safety-grade valve, 35% fewer pumps, 80% less safety-grade

piping, 45% less building volume, and 70% less cable than typical PWR’s.

3

More information about the AP1000 reactor is shown below:

Westinghouse 2 Loop (hot) / 4 Loop (cold) design

Standard Rated thermal power (RTP) is 3400 MWt

Standard target length for Cycle 1 is 467 effective full power days (EFPD)

Control rods vary from 0 to 264 steps withdrawn

Rod insertion limits are a function of both core power and position of the A/O bank

The fuel that I was permitted to use contained the same design and enrichments as the senior design

course. Burnable absorbers were present in some of the higher enriched fuels. The burnable absorbers

include ZrB2 integral fuel burnable absorbers (IFBA) and WABA discrete burnable absorbers (BA) in the

core design. The fuel/BA combinations can be seen in Table 1.1:

Table 1.1: Available Fuel and BA combinations

Region Enrichment IFBA WABA

A 0.740 0 0

B 1.655 0 0

C 2.800 0 0

D 3.200 0 0

E 3.799 88 12

F 4.330 80, 148 0, 4

4

The fuel pin designs can be seen in Figure 1-1. The WABA designs can be seen in Figure 1-2. The radial

IFBA and WABA patterns are shown in Figure 1-3 and Figure 1-4 respectively. Table 1.2 provides a

description of the Integral fuel burnable absorbers and the discrete burnable absorber rods.

Figure 1-1: AP1000 fuel pin designs

Figure 1-2: WABA design

5

Table 1.2: Reactor Core Description for Burnable Absorbers. [1]

IFBA WABA

Material Boride Coating Borosilicate Glass

B10 Content [mg/cm] 0.772 6.24

Absorber Length [in] 152 145

Figure 1-3: Radial IFBA patterns

6

Figure 1-4: Radial WABA patterns

As noted earlier, the control rod insertions can vary from 0 to 264 steps withdrawn. The control rods

were not inserted during this project at all, however, because the goal was to analyze the core at full

power, during the whole cycle. Nevertheless, the control locations were spread out evenly across the

core, and we were not permitted to place fuel that contained WABA in any assembly where a control

rod was located. The control rod locations can be seen in Figure 1-5:

7

Figure 1-5: Control rod locations

1.5 Limits and Requirements

Set parameters enable the simulation of realistic cycle burn up. For instance, the maximum enthalpy

rise hot channel peaking factor (F∆H) must not be greater than 1.60. This limit prevents the power

distribution from varying too much, which could result in the melting of fuel rods inside the core. The

F∆H is essentially a safety parameter for the reactor core. Also, as previously mentioned, there are cycle

length requirements similar to cycle lengths of currently operating reactors. A full cycle is complete

once the Boron concentration inside the core reduces to a critical amount of 10 ppm.

8

2 Methodology

First, the selection of the loading pattern and the data analysis are explained. Then, some of the more

complex methods behind the core design are discussed.

All of the fuel assembly shuffling and designing is done in Microsoft Excel. To make things easier to

visualize, a mock up of a loading pattern in Excel was created and then the fuel assemblies were color

coded. Once, loading pattern has been made, it is inputted into the ANC computer code. The FUEL PAT

is saved and then run through a Secure Shell Client (SSC). The computer simulation takes anywhere

from one to two minutes to complete. Upon completion of the simulation, the output file is opened for

analysis. A search key was used to locate the E-SUM data. In the E-SUM section, the Burn-Up steps,

Boron concentration, and maximum assembly peaking factors can be seen. If Boron concentration and

peaking factor restrictions are not met, then further analysis is carried out at specific Burn-Up step. If

the Boron concentration does not last long enough for the cycle requirement, then higher enriched fuel

is most likely needed in specific parts of the core. If the peaking factor is too high, then fuel assembly

shuffling must be done to even out the power distribution over the core. To figure out where to shuffle

assemblies, first the areas which have large peaking factors were investigated. Once a problem area

was declared, the C-POW (average power distribution) was used to determine where to move fuel

assemblies. An effective method for this step is to replace assemblies that have relatively low power

outputs with assemblies of a higher enrichment. As a result, the power output for that particular

assembly will rise, hopefully lowering the peaking factors across the core. This process is iterated many

times until acceptable conditions are met.

There are a number of techniques that accompany the basic methodology for core design. For example,

industry desires a low leakage design for economic and safety reasons. A low leakage design involves

placing the lower enriched assemblies on the periphery of the loading pattern. As a result, fewer

neutrons are leaked to the pressure vessel’s cladding and shielding; higher enriched fuel assemblies

would leak larger amounts of neutrons to the pressure vessel, wasting these precious particles and

damaging the pressure vessel. Placing lower enriched assemblies on the periphery often result in

peaking factor issues. To counteract this problem, a “ring of fire” technique can be used. The ring of fire

design involves placing the highest enriched assemblies on the inside of the lower enriched assemblies,

which reside on the periphery. In doing so, the highly enriched fuel creates a high flux of neutrons close

to the periphery, without causing large amounts of leakage. Another design method, called the

checkerboard, is used to help even the power distribution over the core. As the name suggests, the fuel

is arranged in a checkerboard fashion across the core.

As the process continues and we get closer to a sufficient loading pattern, fine tuning techniques are

used. For instance, if the cycle length is short by only a couple hundred burn-up steps, then only slight

variations in the average enrichment of the core should be made. A large change in the enrichment may

significantly increase the cycle length; however, it may also result in a rise in the peaking factor. Fine

tuning for peaking factor issues involves two different approaches. If the problem exists in the first 6000

burn-up steps, then the problem can usually be resolved using fuel that contains some burnable

absorbers. The burnable absorbers can preserve cycle length, while suppressing the assembly’s power

to lower the peaking factor. However, burnable absorbers only last until about burn-up step 6000, so

9

peaking factor problems after this step require some shuffling. It is important to note that this type of

shuffling should only be done with fuel assemblies of similar enrichment. If the difference in enrichment

is too great, then the power distribution will be thrown off too much and the peaking factor may

actually increase.

All of these design techniques are extremely important for creating a loading pattern to meet specific requirements.

3 Results and Discussion

Using the methods learned for generating loading patters, eight successful LP’s were found for various

cycle lengths and power levels. For a 12 month cycle (280-320 EFPD), loading patterns were created for

all four power levels: 3400, 4000, 5000, and 6000 MWt. For the 18 month cycle (480-520 EFPD), loading

patterns were created for the first three power levels. However, the 24 month cycle could only be

reached at a rated power level of 3400 MWt. The restrictions on the enrichments of the fuel limited

how far the loading patterns could be pushed. Even with an entire core of the highest enriched fuel

assemblies, 18 months at 6000 Mwt and 24 months at the higher power levels could not be reached.

The following sub-sections show all eight loading patterns that were generated. Also, peaking factor

curves, Boron letdown curves, beginning of cycle data, and end of cycle data is provided for further

analysis of the LP designs. Table 3-1 shows the available fuel inventory, which was color-coded so that

the pattern could be visualized better.

Table 3.1: Fuel and BA Inventory

Region Enrichment IFBA WABA

A1__000 0.74 0 0

B1__000 1.655 0 0

C1__000 2.8 0 0

D1__000 3.2 0 0

E112088 3.779 88 12

F1__148 4.33 148 0

F104080 4.33 80 4

F104148 4.33 148 4

All of the output data from ANC is given in relation to burn up steps, which have the unit megawatt days

per metric ton of Uranium (MWd/MTU). Since the results are desired in the form of effective full power

days (EFPD), a conversion must be made. Equation (1) gives the conversion for cycle length units from

burn up to effective full power days:

(1)

10

where

BU = Burn Up

P0 = Power Level

Note: There are 84.718 MTU inside the AP1000 core, as stated ANC input file.

3.1 LP’s for the 12 month cycle (280-320 EFPD)

Figure 3-1 shows the loading pattern created for a 12 month cycle (280-320 EFPD) running at a rated

power level of 3400 MWt. This loading pattern was generated for lowest cycle length and power level

requirements. Therefore, this LP has the lowest average enrichment: 2.19 w/o. A low-leakage design

was easily preserved with this loading pattern. Even though the relatively higher enriched C1__000 fuel

sits on the periphery of the core, its fuel enrichment is on the lower half of all the available enrichments.

Figure 3-2 shows the peaking factor curve as a function of burn up steps. As expected, the peaking

factor begins to rise as the steps near 6000 MWd/MTU, and continue to increase after step 6000. This

increase occurs because burnable absorbers wear off around a burn up of 6000 MWd/MTU, resulting in

an increase of power in those assemblies.

Conversion of 280 EFPD to burn up steps for 3400 MWt:

Conversion of 320 EFPD to burn up steps for 3400 MWt:

11

Figure 3-1: LP for a 12 month cycle at 3400 MWt

Figure 3-2: Peaking Factor for the LP shown in Figure 3-1 over a 12 month cycle

12

Figure 3-3: Boron letdown curve for the LP shown in Figure 3-1 over a 12 month cycle

Figure 3-4: BOC axial power distribution for the LP shown in Figure 3-1 over a 12 month cycle

13

Figure 3-5: EOC axial power distribution for the LP shown in Figure 3-1 over a 12 month cycle

Beginning of Cycle:

C-POW AVERAGE ASSEMBLY POWER

1 2 3 4 5 6 7 8

1 0.957 0.909 0.506 0.992 1.131 1.413 1.134 1.047

2 0.909 0.917 0.921 0.963 1.073 1.157 1.268 0.799

3 0.506 0.921 0.912 1.026 0.554 1.150 1.196

4 0.992 0.963 1.026 0.488 1.169 1.378 0.861

5 1.131 1.073 0.554 1.169 1.274 0.629

6 1.413 1.157 1.150 1.378 0.629

7 1.134 1.268 1.196 0.861

8 1.047 0.799

14

E-AX RADIAL AVERAGED VALUES BY AXIAL INTERVAL

End of Cycle:


1 2 3 4 5 6 7 8

1 0.951 0.952 0.799 0.997 1.039 1.400 1.003 0.805

2 0.952 0.966 1.008 1.039 1.044 1.041 1.208 0.656

3 0.799 1.008 1.088 1.460 0.902 0.989 0.890

4 0.997 1.039 1.460 0.975 1.415 1.074 0.626

5 1.039 1.044 0.902 1.415 1.138 0.573

6 1.400 1.041 0.989 1.074 0.573

7 1.003 1.208 0.890 0.626

8 0.805 0.656

15

E-X RADIAL AVERAGED VALUES BY AXIAL INTERVAL

C-BU AVERAGE ASSEMBLY BURNUP

1 2 3 4 5 6 7 8

1 12429 12263 9118 13076 13994 18428 13330 10943

2 12263 12461 12923 13352 13756 13916 15621 8672

3 9118 12923 13656 17401 10097 13219 12298

4 13076 13352 17402 10419 17260 14728 8597

5 13994 13756 10097 17260 15071 7350

6 18428 13916 13219 14728 7350

7 13330 15621 12298 8597

8 10943 8672

16

Figure 3-4 shows the loading pattern created for a 12 month cycle at 4000 MWt. Compared to

Figure 3-1, this LP is slightly more enriched to meet the higher power requirement. The average

enrichment of this loading patter is 2.37 w/o. Also, since this cycle requires more burn up steps than

Figure 3-1’s loading pattern, the gradual decrease of the peaking factor can be seen towards the end of

the cycle. This gradual decrease occurs because, overall, the assemblies are being burned more than

the assemblies in Figure 3-1. Reference Figure 3-5 to see the peaking factor curve.

Conversion from EFPD to burn up steps for 4000 MWt:


17



18



19

Beginning of Cycle:


1 2 3 4 5 6 7 8

1 1.037 1.264 1.046 1.046 1.035 1.262 1.339 0.906

2 1.264 1.047 1.065 1.044 1.047 0.990 1.033 0.643

3 1.046 1.065 1.052 1.276 1.046 0.965 0.611

4 1.046 1.044 1.276 1.071 1.293 1.181 0.600

5 1.035 1.047 1.046 1.293 1.245 0.544

6 1.262 0.990 0.965 1.181 0.544

7 1.339 1.033 0.611 0.600

8 0.906 0.643


20

End of Cycle:


1 2 3 4 5 6 7 8

1 1.116 1.400 1.009 0.980 1.012 1.384 1.198 0.807

2 1.400 1.051 1.017 1.012 1.016 1.019 1.176 0.641

3 1.009 1.017 1.055 1.407 1.046 0.947 0.676

4 0.980 1.012 1.407 1.118 1.360 1.016 0.569

5 1.012 1.016 1.046 1.360 1.080 0.538

6 1.384 1.019 0.947 1.016 0.538

7 1.198 1.176 0.676 0.569

8 0.807 0.641


21


1 2 3 4 5 6 7 8

1 15327 19039 13946 13433 13505 17668 15937 10450

2 19039 14524 14099 13793 13623 13142 14326 7934

3 13946 14099 14413 18716 13978 12358 8206

4 13433 13793 18716 15005 17997 13865 7258

5 13505 13623 13978 17997 14932 6903

6 17668 13142 12358 13865 6903

7 15937 14326 8206 7258

8 10450 7934

Again, as expected, the LP shown in Figure 3-7 has a higher average enrichment than in the previous LP.

The average enrichment of this loading pattern is 2.72 w/o. It is important to note that the C1__000 fuel

was either kept or replaced only with lower enriched fuel. This was done to keep the low-leakage

criteria intact. Also, note that the “checkerboard” technique is starting to arise in the loading pattern

choices.


22



23



24


Beginning of Cycle:


1 2 3 4 5 6 7 8

1 0.826 1.045 0.870 1.127 0.947 1.171 1.208 0.793

2 1.045 0.853 1.115 0.969 1.043 0.946 1.041 0.571

3 0.870 1.115 0.958 1.312 1.496 1.184 0.577

4 1.127 0.969 1.312 1.107 1.354 1.170 0.577

5 0.947 1.043 1.496 1.354 1.217 0.519

6 1.171 0.946 1.184 1.170 0.519

7 1.208 1.041 0.577 0.577

8 0.793 0.571

25


End of Cycle:


1 2 3 4 5 6 7 8

1 1.038 1.327 1.031 1.285 0.979 1.278 1.093 0.732

2 1.327 1.036 1.319 1.006 0.983 0.980 1.172 0.592

3 1.031 1.319 1.030 1.303 1.156 1.200 0.673

4 1.285 1.006 1.303 1.018 1.236 0.951 0.548

5 0.979 0.983 1.156 1.236 0.957 0.491

6 1.278 0.980 1.200 0.951 0.491

7 1.093 1.172 0.673 0.548

8 0.732 0.592

26



1 2 3 4 5 6 7 8

1 17882 22963 17534 21538 15937 20195 17766 11369

2 22963 17782 22666 17060 16427 15476 17937 8812

3 17534 22666 17665 22644 20775 19183 9803

4 21538 17060 22644 17544 21047 16016 8398

5 15937 16427 20775 21047 16478 7609

6 20195 15476 19183 16016 7609

7 17766 17937 9803 8398

8 11369 8812

27

To reach the cycle length for the highest power level requirement, 6000 MWt, there was a significant

shift in the loading pattern for Figure 3-10, compared to Figure 3-7. Almost all of the B1__000 fuel

inside the core was replaced with C1__000. Interestingly enough though, some of the B1__000 fuel was

able to be placed on the periphery of the core, while still maintaining an even distribution of power.



28



29



30

Beginning of Cycle:


1 2 3 4 5 6 7 8

1 0.766 1.036 0.864 1.260 1.419 1.334 1.255 0.714

2 1.036 1.160 1.194 1.349 1.313 1.333 1.195 0.550

3 0.864 1.194 1.342 1.271 1.245 1.007 0.707

4 1.260 1.349 1.271 1.223 0.965 0.722 0.254

5 1.419 1.313 1.245 0.965 0.714 0.263

6 1.334 1.333 1.007 0.722 0.263

7 1.255 1.195 0.707 0.254

8 0.714 0.550


31

End of Cycle:


1 2 3 4 5 6 7 8

1 0.954 1.225 0.956 1.239 1.138 1.227 0.996 0.659

2 1.225 1.112 1.233 1.130 1.256 1.106 0.965 0.537

3 0.956 1.233 1.131 1.259 1.143 1.172 0.770

4 1.239 1.131 1.259 1.147 1.213 0.931 0.424

5 1.138 1.256 1.143 1.213 0.951 0.476

6 1.227 1.106 1.172 0.931 0.476

7 0.996 0.965 0.770 0.424

8 0.659 0.537


32


1 2 3 4 5 6 7 8

1 19529 25734 19985 26716 24862 24708 19279 11350

2 25734 24453 26659 25131 26339 22537 18504 9061

3 19985 26659 25363 26779 23588 21452 13359

4 26716 25131 26779 23862 22446 16100 6338

5 24862 26339 23588 22446 16564 7193

6 24708 22537 21452 16100 7193

7 19279 18503 13359 6338

8 11350 9061


Figure 3-12 shows the loading pattern created to run for an 18 months cycle at base power of 3400

MWt. The average enrichment of this design is 3.04 w/o. There was a significant increase in the average

enrichment of the LP from the 12 month to the 18 month cycle. A low-leakage design and checkerboard

technique was used to create this LP.


33

Figure 3-21: LP for an 18 month cycle at 3400 MWt

Figure 3-22: Peaking Factor for the LP shown in Figure 3-21 over an 18 month cycle

34

Figure 3-23: Boron letdown curve for the LP shown in Figure 3-21 over an 18 month cycle

Figure 3-24: BOC axial power distribution for the LP shown in Figure 3-21 over an 18 month cycle

35

Figure 3-25: EOC axial power distribution for the LP shown in Figure 3-21 over an 18 month cycle

Beginning of Cycle:


1 2 3 4 5 6 7 8

1 1.013 1.312 1.305 1.079 0.877 1.273 1.335 0.786

2 1.312 1.361 1.167 0.842 1.158 1.368 1.307 0.632

3 1.305 1.167 0.849 1.108 1.223 1.185 0.846

4 1.079 0.842 1.108 1.196 1.018 0.606 0.451

5 0.877 1.158 1.223 1.018 0.852 0.474

6 1.273 1.368 1.185 0.606 0.474

7 1.335 1.307 0.846 0.451

8 0.786 0.632

36


End of Cycle:


1 2 3 4 5 6 7 8

1 0.952 1.200 1.102 1.235 0.989 1.229 1.181 0.682

2 1.200 1.092 1.222 0.986 1.246 1.097 0.981 0.552

3 1.102 1.222 0.982 1.249 1.126 1.219 0.774

4 1.235 0.986 1.249 1.132 1.203 0.803 0.546

5 0.989 1.246 1.126 1.203 0.953 0.613

6 1.229 1.097 1.219 0.803 0.613

7 1.181 0.981 0.774 0.546

8 0.682 0.552

37



1 2 3 4 5 6 7 8

1 21676 28236 25816 26346 20194 26161 25003 13339

2 28236 26150 27193 20369 26366 24129 20974 10626

3 25816 27193 20524 26500 24397 25141 15293

4 26346 20369 26500 24523 23899 14426 9626

5 20194 26366 24397 23899 18396 10818

6 26161 24129 25141 14426 10818

7 25003 20974 15293 9626

8 13339 10626

38

Figure 3-16 shows the loading pattern generated to meet the 18 month cycle length requirement at a

power level of 4000 MWt. The average enrichment of this LP is 3.30 w/o. Similar to previous loading

patterns, this LP utilizes the low-leakage design and checkerboard technique.


Figure 3-26: LP for an 18 month cycle at 4000 MWt

39

Figure 3-27: Peaking Factor for the LP shown in Figure 3-26 over an 18 month cycle

Figure 3-28: Boron letdown curve for the LP shown in Figure 3-26 over an 18 month cycle

40

Figure 3-29: BOC axial power distribution for the LP shown in Figure 3-26 over an 18 month cycle

Figure 3-30: EOC axial power distribution for the LP shown in Figure 3-26 over an 18 month cycle

41

Beginning of Cycle:


1 2 3 4 5 6 7 8

1 1.452 1.390 1.450 1.373 1.410 1.075 0.902 0.459

2 1.390 1.444 1.372 1.481 1.225 1.109 0.892 0.378

3 1.450 1.372 1.372 1.228 1.149 1.008 0.677

4 1.373 1.481 1.228 1.133 0.926 0.803 0.392

5 1.410 1.225 1.149 0.926 0.742 0.428

6 1.075 1.109 1.008 0.803 0.428

7 0.902 0.892 0.677 0.392

8 0.459 0.378


42

End of Cycle:


1 2 3 4 5 6 7 8

1 1.028 1.141 1.042 1.173 1.120 1.207 1.172 0.687

2 1.141 1.034 1.157 1.102 1.200 1.076 0.980 0.555

3 1.042 1.157 1.059 1.192 1.088 1.200 0.807

4 1.173 1.102 1.192 1.087 1.174 0.961 0.558

5 1.120 1.200 1.088 1.174 0.939 0.616

6 1.207 1.076 1.200 0.961 0.616

7 1.172 0.980 0.807 0.558

8 0.687 0.555


43


1 2 3 4 5 6 7 8

1 26822 29003 27066 29403 27793 26936 24323 12656

2 29003 26900 29170 28116 28451 24538 20600 10158

3 27066 29170 26834 28466 25383 26048 16348

4 29403 28116 28467 25266 24868 19815 10445

5 27793 28451 25383 24868 19075 11588

6 26936 24537 26048 19815 11588

7 24323 20600 16348 10445

8 12656 10158

Figure 3-19 shows the loading pattern created for the 18 month cycle, running at a power level of

5000MWt. The average enrichment of this LP is 3.89 w/o. In this particular loading pattern, a low-

leakage design was not able to be used. Based on the fixed enrichment of the fuel, it was not possible to

meet the cycle length requirement at this power level, without placing a highly enriched fuel on the

periphery. Therefore, the D1__000 type fuel was placed on the outside of the core to extend the cycle

length and even out the power distribution over the core.


44



45



46


Beginning of Cycle:


1 2 3 4 5 6 7 8

1 1.328 1.109 1.145 1.026 1.140 1.036 1.053 0.681

2 1.109 1.176 1.034 1.135 1.052 1.180 1.068 0.549

3 1.145 1.034 1.134 1.040 1.181 1.223 0.869

4 1.026 1.135 1.040 1.158 1.124 0.967 0.555

5 1.140 1.052 1.181 1.124 1.049 0.630

6 1.036 1.180 1.223 0.967 0.630

7 1.053 1.068 0.869 0.555

8 0.681 0.550

47


End of Cycle:


1 2 3 4 5 6 7 8

1 0.958 1.064 1.129 1.108 1.182 1.150 1.119 0.673

2 1.064 1.116 1.091 1.156 1.136 1.178 1.039 0.552

3 1.129 1.091 1.148 1.122 1.179 1.121 0.753

4 1.108 1.156 1.122 1.173 1.143 1.015 0.546

5 1.182 1.136 1.179 1.143 0.889 0.599

6 1.150 1.178 1.121 1.015 0.599

7 1.119 1.039 0.753 0.546

8 0.673 0.552

48



1 2 3 4 5 6 7 8

1 31630 33856 36592 34237 35848 31610 28445 15205

2 33856 36362 34308 36457 33414 33278 26391 12313

3 36592 34308 36532 33827 34877 30930 18790

4 34237 36457 33827 34997 31919 25766 12594

5 35848 33414 34877 31919 23382 14222

6 31610 33278 30930 25766 14223

7 28445 26391 18790 12594

8 15205 12313

49


Figure 3-22 shows the loading pattern created to run a 3400MWt for a 24 month cycle. This average

enrichment of this LP is 3.69 w/o. Although the required cycle length for the LP shown in Figure-22 was

longer than the previous LP, the LP shown in Figure 3-22 was able to maintain a low-leakage design. The

low-leakage design was maintained because the LP shown in Figure 3-22 ran at a much lower power

level than the previous loading pattern. Also, the LP shown in Figure 3-22 utilizes the ring-of-fire

technique to flatten the power distribution over the core.



50



51



52

Beginning of Cycle:


1 2 3 4 5 6 7 8

1 1.278 1.168 1.131 0.950 1.025 0.911 0.895 0.487

2 1.168 1.281 1.038 1.074 0.980 1.087 0.925 0.410

3 1.131 1.038 1.124 1.049 1.235 1.255 0.830

4 0.950 1.074 1.049 1.295 1.422 1.163 0.549

5 1.025 0.980 1.235 1.422 1.253 0.688

6 0.911 1.087 1.255 1.163 0.688

7 0.895 0.925 0.830 0.549

8 0.487 0.410


53

End of Cycle:


1 2 3 4 5 6 7 8

1 0.950 1.093 1.176 1.159 1.237 1.190 1.142 0.649

2 1.093 1.017 1.131 1.209 1.181 1.216 0.939 0.525

3 1.176 1.131 1.193 1.159 1.208 1.136 0.758

4 1.159 1.209 1.159 1.197 1.139 0.879 0.507

5 1.237 1.181 1.208 1.139 0.883 0.553

6 1.190 1.216 1.136 0.879 0.553

7 1.142 0.939 0.758 0.507

8 0.649 0.525


54


1 2 3 4 5 6 7 8

1 28857 32462 36046 34283 35904 30955 26828 13113

2 32462 31276 33845 36572 33405 32642 22461 10556

3 36046 33845 36446 33973 34881 30285 17887

4 34283 36572 33973 35299 31944 22361 11179

5 35904 33405 34881 31944 23034 12808

6 30955 32642 30285 22361 12808

7 26828 22460 17887 11179

8 13113 10556

4 Conclusions

One of the most important conlcusions to take away from this project is that the AP1000 has flexibility

in regards to its cycle length and power level. Based on the given fuel inventroy, eight working loading

patterns were able to be generated for different circumstances. At base power level of 3400MWt, all

three cycle lengths were abel to be achieved: 12, 18, and24 months. At a power level of 4000MWt,

cycle lengths of 12 months and 18 months were achieved. Next, at a power level of 5000MWt, cycle

lengths of 12 months and 18 months were achieved. However, for the highest power level of 6000MWt,

only the 12 month cycle was able to be achieved. Some of the objectives were not achieved and this

was a result of not being able to increase the fuel enrichment. Making changes to the fuel inventroy

required access to the ALPHA and PHOENIX codes, which was not available. Therefore, combinations of

higher power levels with longer cycle lengths were not met. Suggestions for future work would be to

increase the enrichment of the available fuel, and attempt to push the AP1000 to more extreme cycle

lengths and power levels.

Based on the scope of this project, not all of the core design parameters were studied. Specifically, this

project took into account the peaking factor, power distribution, k-infinity, and boron concentration.

Furthermore, the peaking factor was kept a more flexible limit of 1.60. This particular limit was chosen

so that more non-conventional loading patterns could be investigated. Also, due to the time constraint

of the project, a more in-depth study was not possible. Another suggestion for future work would be to

take the loading patterns created in this project and run computer simulations to check more of the

safety and operational parameters, such as the rod insertion limits and the moderated temperature

coefficient. Also, further studies could investigate the second cycle for the AP1000. Since this project

focused on the first cycle, fuel assemblies could only burn for a maximum value equal to the cycle length

of the core.

55

5 References

1. Nuclear Regulatory Commission. AP1000 Design Control Document, Table 4.3-1. (2007)

2. Avramova, Maria N. and Ivanov, Kostadin N. Nuclear Reactor Core Design Synthesis.

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University. [Lecture

Notes] Spring 2010.

3. Westinghouse. Core Design Training Course. (Spring 2010)

56

Nomenclature List

AC = Alternating Current

ANC = Advanced Nodal Code

APA = ALPHA, PHOENIX-P, and Advanced Nodal Code

BA = Burnable Absorber

BU = Burn-Up

C-POW = Average Power Distribution

E-SUM = End of Cycle Summary of Data

EFPD = Effective Full Power Days

FΔH = Maximum enthalpy hot rise channel peaking factor

IFBA = Integral fuel burnable absorbers

LP = Loading Pattern

MTC = Moderated Temperature Coefficient

MTU = Metric tons of Uranium

MWd = Mega-Watt days

MWt = Mega-Watt thermal

ppm = parts per million

PWR = Pressurized Water Reactor

RDFMG = Reactor Dynamics and Fuel Management Group

SSC = Secure Shell Client w/o = weight percent

WABA = WABA discrete burnable absorbers

57

Appendix

Example of ANC input:

#-----------------------------------------------------

# REMOVE PREVIOUS DATABANKS IF THEY EXIST

# ----------------------------------------------------

rm -f $J/ap1000_adv_cy1_anc_rev1.db

#

# ----------------------------------------------------

# LINK UP THE PIN, PINMAP AND ANC INPUT FILES

# ----------------------------------------------------

#

ln -s $J/adv_cy1.pin pin

#

# remove for psu course ln -s $J/adv_cy1.pinmap pinmap

#

ln -s $J/adv_cy1_anc.inp hfp_cross_sections

#

#

# ----------------------------------------------------

# LINK UP THE BLACK ROD INPUT FILES

# ----------------------------------------------------

#

ln -s $J/boc_black_constants boc_black_rcca

#

ln -s $J/moc_black_constants moc_black_rcca

#

ln -s $J/eoc_black_constants eoc_black_rcca

#

# ----------------------------------------------------

# LINK UP THE GRAY ROD INPUT FILES

# ----------------------------------------------------

#

ln -s $J/boc_gray_constants_rev1 boc_gray_rcca

#

ln -s $J/moc_gray_constants_rev1 moc_gray_rcca

#

ln -s $J/eoc_gray_constants_rev1 eoc_gray_rcca

58

#

# ---------------------------------------------------

# CREATE CYCLE N ANC MODEL DATABANK

# ---------------------------------------------------

#

bankin -u 1 -p $J/ap1000_adv_cy1_anc_rev1.db

#

# ---------------------------------------------------

# EXECUTE ANC

# ---------------------------------------------------

anc.876

# ---------------------------------------------------

# BANKOUT AFTER JOB COMPLETION

# ---------------------------------------------------

bankout -elp

#

/EOF

TITLE = Advanced Cycle 1 AP1000

/

/----------------------------------------------------------------------------

----

/ CROSS-SECTION INPUT

/----------------------------------------------------------------------------

----

/

#INCLUDE "hfp_cross_sections"

/

/TEST

/----------------------------------------------------------------------------

-----

/ CORE GEOMETRY CARDS

/----------------------------------------------------------------------------

-----

FUELPAT( 1, 1)=

B1__000,B1__000,B1__000,B1__000,B1__000,B1__000,B1__000,B1__000/

FUELPAT( 1, 2)=

B1__000,B1__000,B1__000,B1__000,B1__000,B1__000,B1__000,B1__000/

FUELPAT( 1, 3)=

B1__000,B1__000,B1__000,B1__000,B1__000,B1__000,B1__000/

59

FUELPAT( 1, 4)=

B1__000,B1__000,B1__000,B1__000,B1__000,B1__000,B1__000/

FUELPAT( 1, 5)=

B1__000,B1__000,B1__000,B1__000,B1__000,B1__000/

FUELPAT( 1, 6)=

B1__000,B1__000,B1__000,B1__000,B1__000/

FUELPAT( 1, 7)=

B1__000,B1__000,B1__000,B1__000/

FUELPAT( 1, 8)=

B1__000,B1__000/

/----------------------------------------------------------------------------

-----

/ FUEL ASSEMBLY CONFIGURATION INPUT

/----------------------------------------------------------------------------

-----

REGCOMP(1, 1, 1) = B1__000 , 8.0517, B1BLKBM ,

75.4848, B1MIDBM ,

77.4977, B1MIDTP ,

8.0517, B1BLKTP /

REGCOMP(1, 1, 2) = E112088 , 8.0517, EB088BK ,

15.0970, EB08812 ,

53.3426, EB08812 ,

56.3620, ET08812 ,

28.1810, ET08812 ,

8.0517, ET088BK /

REGCOMP(1, 1, 3) = F1__148 , 8.0517, FB148BK ,

75.4848, FB__148 ,

77.4977, FT__148 ,

8.0517, FT148BK /

REGCOMP(1, 1, 4) = D1__000 , 8.0517, D1BLKBM ,

75.4848, D1MIDBM ,

77.4977, D1MIDTP ,

8.0517, D1BLKTP /

REGCOMP(1, 1, 5) = F104080 , 8.0517, FB080BK ,

15.0970, FB080IE ,

46.2973, FB08004 ,

42.2715, FT08004 ,

49.3167, FT080IE ,

8.0517, FT080BK /

REGCOMP(1, 1, 6) = A1__000 , 8.0517, A1BLKBM ,

60

75.4848, A1MIDBM ,

77.4977, A1MIDTP ,

8.0517, A1BLKTP /

REGCOMP(1, 1, 7) = F104148 , 8.0517, FB148BW ,

15.0970, FB148IE ,

46.2973, FB14804 ,

42.2715, FT14804 ,

49.3167, FT148IE ,

8.0517, FT148BW /

REGCOMP(1, 1, 8) = C1__000 , 8.0517, C1BLKBM ,

75.4848, C1MIDBM ,

77.4977, C1MIDTP ,

8.0517, C1BLKTP /

/------------------------------------------------------------------

/ SET OUTPUT

/------------------------------------------------------------------

OUTPUT(1) = 7*1, 2*0, 1, 15*0, 1, **0 /

/------------------------------------------------------------------

/ FIRST CORE NEEDED DATA

/------------------------------------------------------------------

COREGEOM = QUART-CY

/

DZ = -30/ # of axial meshes;

/

ZL =

28.06,2*10.2252,2*5.1126,10.2252,17.8941,10.2252,18*17.8941,7.6689,2*5.1126,2

*10.2252,32.13/

/------------------------------------------------------------------

/ CONTROL ROD SETUP

/------------------------------------------------------------------

/

RODLOC(1,1) = **0/

RODLOC(1,1) = 8, 0, 5, 0, 6, 0, 4, 0 /

RODLOC(1,2) = 0, 9, 0, 11, 0, 10, 0, 0 /

RODLOC(1,3) = 5, 0, 2, 0, 8, 0, 12 /

RODLOC(1,4) = 0, 11, 0, 9, 0, 7, 0 /

RODLOC(1,5) = 6, 0, 8, 0, 3, 0 /

RODLOC(1,6) = 0, 10, 0, 7, 0 /

RODLOC(1,7) = 4, 0, 12, 0 /

RODLOC(1,8) = 0, 0 /

61

/

RZONE = **0.0 / CLEAR DATA - 1 is for black - 2 is for gray

RZONE(2,2) = 264 / BANKID(2) = MA / MSHIM GRAY A

RZONE(3,2) = 264 / BANKID(3) = MB / MSHIM GRAY B

RZONE(4,2) = 264 / BANKID(4) = MC / MSHIM GRAY C

RZONE(5,2) = 264 / BANKID(5) = MB / MSHIM GRAY D

RZONE(6,1) = 264 / BANKID(6) = M1 / MSHIM BLACK 1

RZONE(7,1) = 264 / BANKID(7) = M2 / MSHIM BLACK 2

RZONE(8,1) = 264 / BANKID(8) = AO / AO CONTROL BLACK

RZONE(9,1) = 264 / BANKID(9) = SD1/ SHUTDOWN BLACK 1

RZONE(10,1) = 264 / BANKID(10)= SD2/ SHUTDOWN BLACK 2



/

NRODSTEP = 264 /

RODSTEP = **264 /

RODBOTM = 12.192 / RCCA ROD BOTTOM POSITION IN CM

/

/------------------------------------------------------------------

/ REFLECTOR INPUT

/------------------------------------------------------------------

/ D1 SIGMA-A-1 SIGMA-R D2 SIGMA-A-2

RSIGXY =

0.842226, 0.002334, 0.01665, 1.216053, 0.168569,

1.112634, 0.001691, 0.016199, 1.132475, 0.130118,

1.112634, 0.001691, 0.016199, 1.132475, 0.130118,

1.571311, 0.001269, 0.017787, 0.841855, 0.083441,

1.05437, 0.00164, 0.018808, 1.152173, 0.139569,

1.024226, 0.00163, 0.019419, 1.150326, 0.14364,

1.031988, 0.001624, 0.019575, 1.145179, 0.14502,

1.057603, 0.001662, 0.018818, 1.139235, 0.140638,

1.057603, 0.001662, 0.018818, 1.139235, 0.140638,

1.567911, 0.001212, 0.021867, 0.809809, 0.085243,

1.070826, 0.001703, 0.018772, 1.126109, 0.140738,

1.048859, 0.001644, 0.019485, 1.174971, 0.143493,

1.06863, 0.001651, 0.019061, 1.16457, 0.14092,

1.575697, 0.001145, 0.022225, 0.837973, 0.085789,

1.06863, 0.001651, 0.019061, 1.16457, 0.14092,

1.035553, 0.001663, 0.019466, 1.042465, 0.129628/

62

/

RSIGZ(1,1) =

1.6057, 0.0011318, 0.028939, 0.34948,

0.027232/bottom

RSIGZ(1,2) =

1.9696, 0.00091234, 0.023418, 0.4208, 0.022435/top

/------------------------------------------------------------------

/ MISCELLANEOUS USER INPUT

/------------------------------------------------------------------

/ REITERATION OF AP1000 GENERIC INPUT.

/

THETAF = 0.50 /

THETAXE = 0.50 /

RELPOW = 1.00 /

B10PERCE = 19.90 /

DEPLETE = ALL /

/

/------------------------------------------------------------------

/ DEPLETION STEPS INPUT

/------------------------------------------------------------------

/ DATABANK INFORMATION

/

RITEID = ADV1_HFP01 /

RITEUNIT = 1.00 /

/

/ ANC BURNUP STEP 1 - 0.0

/

BORONCON = 900.0000 /

DELTABU = 0.00 /

TAPEDIT = 0.00 /

#INCLUDE "boc_black_rcca"

#INCLUDE "boc_gray_rcca"

/

END

/


/


RITEUNIT = 1.00 /

/

63


/

BORONCON = 900.0000 /

DELTABU = 150.00 /

DEPLETE = ALL,EQXE /

/

END

/


/


RITEUNIT = 1.00 /

/


/

BORONCON = 800.0000 /

DELTABU = 350.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


/

BORONCON = 700.0000 /

DELTABU = 500.00 /


/

END

/


/


RITEUNIT = 1.00 /

/

64


/

BORONCON = 600.0000 /

DELTABU = 1000.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


/

BORONCON = 500.0000 /

DELTABU = 1000.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


/

BORONCON = 400.0000 /

DELTABU = 1000.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


65

/

BORONCON = 300.0000 /

DELTABU = 1000.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


/

BORONCON = 181.2500 /

DELTABU = 1000.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


/

BORONCON = 100.0000 /

DELTABU = 1000.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


66

/

BORONCON = 72.8571 /

DELTABU = 1000.00 /


#INCLUDE "moc_black_rcca"

#INCLUDE "moc_gray_rcca"

/

END

/


/


RITEUNIT = 1.00 /

/


/


DELTABU = 1000.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


/


DELTABU = 1000.00 /


/

END

/


/


RITEUNIT = 1.00 /

67

/


/


DELTABU = 2000.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


/


DELTABU = 2000.00 /


/

END

/


/


RITEUNIT = 1.00 /

/


/

BORONCON = 6.0000 /

DELTABU = 2000.00 /


/

END

/


/


RITEUNIT = 1.00 /

68

/


/

BORONCON = 0.0000 /

DELTABU = 2000.00 /


/

#INCLUDE "eoc_black_rcca"

#INCLUDE "eoc_gray_rcca"

END

/


/


RITEUNIT = 1.00 /

/


/

BORONCON = 0.0000 /

DELTABU = 776.00 /


/

STOP

Date: April, 2011

Academic Vita

Ian Davis

[School Address] [Home Address]

Department of Mechanical and Nuclear Engineering

The Pennsylvania State University 140 East College Ave, Apt 1

University Park, PA, 16802 State College, PA, 16801

Office Phone: N/A Home Phone: 215-964-1219

[email protected]

Education

B.S. in Nuclear Engineering, 2011, Penn State University, University Park, PA

Honors and Awards

President’s Freshman Award, Winter 2008

Dean’s List since first Semester, Fall 2007 - present

Oelschlager Trustee Scholarship in Engineering, Fall 2007

Academic Competitiveness Grant, Fall 2008

Exelon Nuclear Engineering Scholarship, Fall 2009

Monty Schultz Memorial Scholarship in Nuclear Engineering, Fall 2010

College of Engineering Fellowship, PSU, Fall 2011

Association Memberships

Penn State Engineering Ambassadors, Fall 2010 – Spring 2011

American Nuclear Society, Fall 2009 – Spring 2012

THON 2011 Rules & Regulations Committee Member, Fall 2010 – Spring 2011

Blue & White Society, Fall 2008 – Spring 2011

Professional Experience

Undergraduate Researcher in MNE Department, Fall 2010 – Spring 2011

- Continued research dealing with core design and fuel management for AP1000

Toshiba-Westinghouse Fellowship Program, Summer 2010

- Conducted research dealing with core design and fuel management

for Westinghouse’s AP1000 reactor

- Presented research to CEO of Westinghouse, Dr. Aris Candris

Teacher’s Assistant for CAS 100A: Effective Speech for Engineers , Spring 2009

- Gave technical presentations as examples for the students

- Graded homeworks and speeches

- Held out-of-class practice sessions

References

Dr. Kostadin Ivanov

Distinguished Professor of Nuclear Engineering

206 Reber Building

University Park, PA, 16802

Dr. Maria Avramova

Assistant Professor of Nuclear Engineering

231 Reber Building


Melissa Marshall

Toshiba-Westinghouse Undergraduate Fellows Program Coordinator

Lecturer in Communication Arts and Sciences

201E Reber Building


OPTIMIZATION OF WESTINGHOUSE’S AP1000 CORE DESIGN

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