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• Full Power Axial Offset (AO) band is ± 5%• Control rods vary from 0 to 175 steps withdrawn• Rod Insertion Limits (RILs) are a function of core ( )power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