Transient Methods in MPACT with Internal TH

FY16.CASL.008Tom DownarAng Zhu Yunlin XuBrendan KochunasDan Jabaay

2

FY16.CASL.008 MilestoneImplement VERA transient capability with internal heat conduction feedback for PWRs for analysis of Reactivity Insertion Accidents (RIA)

• The goal of this milestone is to implement and demonstrate in MPACT the solution of the transient capability for PWRs using internal heat conduction capability.

• The validation of MPACT will be performed using both Hot, Zero Power (HZP) and Cold, Zero Power (CZP) rod ejection experiments performed at the SPERT facility.

• The MPACT capability for a PWR with VERAIN will be demonstrated using the numerical simulation of a control rod ejection from the Watts Bar Unit I reactor.

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Transient Transport 2D/1D Formulation in MPACTRay Tracing (2-D MOC)

Global 3-D CMFD Problem

Axial Leakage as Sourcez

Local 2-D MOC Problems

Different Composition and Temperature Cell Average Flux

& Axial Leakage

Low Order Transport

47 energygroups

( )' '' 1

1 1 (1 ) 4

m m m Gg g g m m mm

m m tg g pg dg d gg g gT gBgg z

Sv t x y h

ϕ ϕ ϕ µη ε ϕ χ β ψ χ φ ϕ ϕπ =

∂ ∂ ∂ + + + Σ = − + + Σ − − ∂ ∂ ∂

∑

4

Background

• CASL Science Council Report (11/15/2015): – “One area of future concern is the computational

resource requirements needed for the transient full core simulation of such accidents as a control rod ejection.”

– “It is recommended that the viability of such simulations be investigated.”

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• Pure transport transient calculation is computationally very expensive.• Objective of the TML method is use multi-level transient solvers to capture

the physical phenomenal in different time domains to maximize the numerical accuracy and minimize the computational burden.

Transient Multi-level (TML) Method*

Space domain

*Ang Zhu, Yunlin Xu and Thomas Downar. “A Multi-level Quasi-Static Kinetics Method for Pin-Resolved Transport Transient Reactor Analysis”. Nuclear Science and Engineering, 2016, 182(4).

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Governing equations

• Transport

• CMFD

• EPKE

( )

4

0 0

1 ( , , , ) ( , , , ) ( , ) ( , , , ) ( , ', ', ) ( , ', ', ) ' '( )

1 ( , , )(1 ( , )) ( , ) ( , , ) ( , )4

t s

p F d d

E t E t r t E t E t E t d dEv E t

E t t S t E t S t

πϕ ϕ ϕ ϕ

χ β χπ

∞∂= − ∇ −Σ + Σ Ω

∂

+ − +

∫ ∫r Ω Ω r Ω r Ω r Ω Ω r Ω

r r r r r

( , ) ( , ) ( , ) ( , ) ( , ), 1, 2,...,6kk F k k

dC t t S t t C t kdt

β λ= − =r r r r r

( ) ( ) ( )( )

0

1 ( , , ) ( , , ) ( , , ) ( , ' , ) ( , ', ) '( )

( , , ) ( , , ) , , ( , ) , , ( , ) ( ) ( , )

s

t F dk k k k Fk

E t D E t E t E E t E t dEv E t

E t E t E t S t E t C t S t

φ φ φ

φ χ χ λ β

∞∂= ∇ ∇ + Σ →

∂

−Σ + + −

∫

∑

r r r r r

r r r r r r r r r

( , ) ( ) ( , ) ( ) ( , ), 1, 2...,6kk F k k

C t S t C t kt

β λ∂= − =

∂r r r r r

0

( ) ( )( ) 1( ) ( ) ( )( )

eff

k kk

t tdp t p t t tdt t

ρ β λ ζ−= +

Λ Λ ∑ 0( ) ( ) ( ) ( ) ( ), 1, 2...,6( )

effkk k k

d t t p t t t kdt tζ β λ ζΛ

= − =Λ

D hat term

Adjoint flux

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Transport solve CMFD solve EPKE solve

TML Flow Chart

8

For Equations see:

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• 60 assemblies radially and 20 layers axially

• Initial core inlet temperature is at 502 oF ±4 oF.

• Initial Power is 19 ± 1 MW.• Coupled with MPACT internal

TH module.SPERT III E-core cross-section MPACT radial model

MPACT axial modelSPERT Transient Experiments

Comparison of SPERT Critical Condition (k=1) w/ KENO-CE and MPACT

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SPERT Benchmark: Power Distribution Comparison of MPACT with KENO Monte Carlo• Comparison of Axial

Power

• Comparison Radial Power (Peak Plane)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 20 40 60 80 100

Asse

mbl

y-av

erag

ed P

in P

ower

Height (cm)

KENOMPACT

KENO 0.867±0.021 0.978±0.022 1.108±0.024

MPACT 0.862 0.975 1.103Rel. Diff.(%) 0.6% 0.3% 0.5%

.868±0.021 1.043±0.023 1.410±0.027 1.572±0.028

0.863 1.040 1.398 1.5560.5% 0.4% 0.8% 1.0%

1.000±0.022 1.537±0.028 2.354±0.045 2.198±0.034

.997 1.521 2.317 2.1650.3% 1.0% 1.6% 1.5%

1.197±0.025 2.050±0.042 2.315±0.035 3.185±0.052

1.190 2.020 2.278 3.1140.6% 1.5% 1.6% 2.2%

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• SPERT Test 60 is a hot zero power super prompt critical transient ρ = $1.17• Can be challenging to model since power rises from 50w to above 400 MW in 0.2s.

3D SPERT test 60 (Super-Prompt HZP)

0

50

100

150

200

250

300

350

400

450

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Powe

r (MW

)

Time (Second)

Test 60 Power

Measured_Power

MPACT

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35Re

activ

ity ($

)

Time (Second)

Test 60 Reactivity

MPACT

Measured

Note: These are preliminary results since1. Cases run w/ 56-group library (need to rerun w/ current lib)2. run w/ internal TH conduction only (need to rerun w/ Transient CTF

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TML applied to 3D SPERT Test 60

CaseRunning time

(2880 cores on Titan)

MPACT 1.0 ms (Ref.) 3 hrs 26 mins

MPACT 5ms 1 hr 13 mins

MPACT TML(5ms for MOC time step,

2.5ms for CMFD time step,and 1 ms for PK time step)

1 hr 31 mins

• Difficult test since power rises from 50w to ~400 MW in 0.2s• Reference is presented by using fine time step (1 ms)• TML results in >50% run time reduction without loss of accuracy

0

50

100

150

200

250

300

350

400

450

500

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Powe

r (MW

)

Time (s)

1ms

5ms

5ms TML

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

0.00E+000 5.00E-002 1.00E-001 1.50E-001 2.00E-001 2.50E-001 3.00E-001

Powe

r (MW

)

Time (second)

Test 86 PowerMeasured_powerMPACT_Power

0.00E+000

2.00E-001

4.00E-001

6.00E-001

8.00E-001

1.00E+000

1.20E+000

0.00E+000 5.00E-002 1.00E-001 1.50E-001 2.00E-001 2.50E-001 3.00E-001

Rho

Time (second)

Test 86 Reactivity

Measured_RhoMPACT_Rho

SPERT Test 86 (Super-prompt HFP)

SPERT Test 84 (Sub-prompt HZP) ρ = $0.46

0

5

10

15

20

25

30

35

40

45

0 0.2 0.4 0.6 0.8 1 1.2

Powe

r (MW

)

Time (second)

Test 84 power

Measured_Power

MPACT_power

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

3.00E-01

3.50E-01

4.00E-01

4.50E-01

5.00E-01

0 0.2 0.4 0.6 0.8 1 1.2

Reac

tivity

(Rho

)

Time (Second

Test 84 Reactivity

Measured_Reactivity

MPACT_rho

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Code Verification: New Transient Regression Test Problems in MPACT

Test Name Input Type Transient Solver Option Size Dimension XS Lib Perturbation # of ProcsSinglepin_null Standard Standard 1x1 Pin 2-D 47 G Const 1Singlepin_HZP Standard Standard 1x1 Pin 2-D 47 G Ramp 1Singlepin_HFP Standard Standard 1x1 Pin 2-D 47 G Ramp 1SPERT_2D Standard Standard 3x3 Assem 2-D 47 G Ramp 9SPERT_2D_CMFD Standard CMFD Only 3x3 Assem 2-D 47 G Ramp 9SPERT_2D_TML Standard Transient Multi-Level 3x3 Assem 2-D 47 G Ramp 9SPERT_3D_HZP Standard Transient Multi-Level 1x1 Assem 3-D 8 G Ramp 10SPERT_3D_HFP Standard Transient Multi-Level 1x1 Assem 3-D 8 G Ramp 101a_null VERA Transient Multi-Level 1x1 Pin 2-D 47 G Const 14a-2D VERA Transient Multi-Level 3x3 Assem 2-D 8G MVCR 94-mini VERA Transient Multi-Level 3x3 Assem 3-D 8G MVCR 16

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MPACT Transient Demonstration:Application to Watts Bar PWR

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Watts Bar: Partial Ejection of Bank D

• Not a realistic accident, but provides a superprompt transient for testing MPACT

• Scenario:– In total, 9 Rods– Withdraw 80 steps in 0.1 seconds – Run on EOS w/ 4234 Processors– 16 Azimuthal, 2 Polar– 0.05 Ray Spacing– NEM Axial Nodal Solver– MG Transport Sweepers

230 steps is fully withdrawn

MPACT Transient Input:

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Watts Bar Partial Ejection of Bank D(TML w/ 5 ms Time Step)

0

0.2

0.4

0.6

0.8

1

1.2

0

500

1000

1500

2000

2500

0 0.05 0.1 0.15 0.2 0.25 0.3

Reac

tivity

($)

Perce

nt Po

wer

Time (s)

Bank D with TML Power and Rho vs Time

Power

Total Reactivity

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Watts Bar Partial Ejection of Bank D

Case Time StepTML

EnabledRun Time

(hrs)

Full Bank D1 ms No 8:735 ms No 2:325 ms Yes 3.33

0

500

1000

1500

2000

2500

3000

0 0.05 0.1 0.15 0.2 0.25 0.3

Perce

nt Po

wer

Time (s)

Bank D Core Power vs Time

5 ms, No TML

5ms, TML

1 ms, No TML

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VERAView: R. Lee / A. Godfrey

20

Time 0.0 s

21

Time 0.045 s

22

Time 0.095 s

23

Time 0.3 s

24

Watts Bar Central Rod Eject• Full ejection of central Bank D rod

only ($0.22)• No need for TML

25

Time 0.0 s

26

Time 0.035 s

27

Time 0.045 s

28

Time 0.075 s

29

Time 0.3 s

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Summary• An efficient transient numerical algorithm was developed and

implemented in MPACT• SPERT Test 86, 60 and 84 results were performed and show

acceptable accuracy of the MPACT transient solver. • The computational feasibility of a Watts Bar core transient

capability with MPACT was demonstrated.

Future Work• In FY17, The transient performance of CTF and the

coupling of MPACT and CTF will be investigated in anticipation of FY18 VERA-CS milestone (w/ BISON)

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FY17 RIA/Transient Milestones• RTM (MPACT)

– Control Rod Cusping Treatment (RTM L3)– Adaptive Time Stepping Method (RTM L3)– Improve CMFD Efficiency (RTM L3)

• PHI (CTF/VERA-CS)– Continued Development of CTF for Transient* (PHI L3)– Investigation of Coupled MPACT/CTF Coupling Numerics (PHI L3)– Perform validation cases w/ VERA-CS Transient (RTM-PHI L3)

• AMA (CTF/VERA-CS)– Validation of CTF for RIA* (AMA L3)– Assess and Demonstrate MPACT Transient RIA Capability for a

Commercial Reactor (AMA L3)

*CASL-I-2014-0119-000 Yixing Sung (WEC) et al.

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Comparison of Rate of Change of IntrapinAngular and Scalar Flux• 2D 3x3 Pin Cell Problem• Boron poisoned “control rod”

in center• Remove boron within 0.1

second = $1.24

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0

5

10

15

20

25

30

35

0 0.05 0.1 0.15 0.2 0.25 0.3Re

activ

ity ($

)

Norm

alize

d Pow

er

Time (seconds)

total power

reactivity

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Comparison of Rate of Flux Change

• Both angular (MOC) flux and pin flux shape change rates increase as reactivity increases

• However, angular flux shape changes much slower than the pin flux shape change

0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

3.00E-04

3.50E-04

4.00E-04

0 0.05 0.1 0.15 0.2 0.25 0.3

Norm

alize

d Sha

pe C

hang

es

Time (seconds)

angular flux shape

pin flux shape

0.00E+00

5.00E-04

1.00E-03

1.50E-03

2.00E-03

2.50E-03

3.00E-03

3.50E-03

4.00E-03

4.50E-03

0 0.1 0.2 0.3

Nor

mal

ized

Sha

pe C

hang

es

Time (seconds)

angular flux shape

pin flux shape

Accumulated Shape Change

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Test Problem for TML Performance Analysis

• An 3D assembly stripe from SPERT Experiment. • $1.14 rod worth is withdrawn in 0.05 second.• 40 2.4 GHz AMD processors.

MPACT whole core radial model MPACT model transient rod assembly MPACT axial model

35

0

10

20

30

40

50

60

0 0.05 0.1 0.15 0.2

Nor

mal

ized

Pow

er

Time (Second)

CASE 1

CASE 2

CASE 3

CASE 4

-3

-2

-1

0

1

2

3

4

5

0 0.05 0.1 0.15 0.2Abs

olut

e Er

ror

Time (Second)

CASE 2

CASE 3

CASE 4

CASE 5

CASE 6

2

1

( )1 1( )

Ni

i ref i

p tN p t

ε=

= −

∑

Case Description Transport step size CMFD step size EPKE step size Error(to case1) Time (hr) Time (to case 3)1 Pure Transport 0.2 ms(Reference) - - - 39.1 985%2 Pure Transport 1 ms - - 2.26% 15.67 395%3 Pure Transport 5 ms - - 20.2% 3.97 -4 Three level 5 ms 1 ms 0.2 ms 0.642% 5.03 127%5 1 & 2 level 5 ms 0.2 ms - 0.713% 10.05 253%6 1 & 3 level 5 ms - 0.2 ms 3.05% 4.15 105%

Test Problem Results

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