TRANSIENT EVALUATION OF A GEN-IV LFR DEMONSTRATION PLANT THROUGH A LUMPED-PARAMETER

ANALYSIS OF COUPLED KINETICS AND THERMALHYDRAULICS

Sara Bortot, Antonio Cammi

LEADER PROGRESS MEETING, W.P. 4

TASK 4.4

Preliminary definition of the Control Architecture

CIRTEN - POLITECNICO DI MILANO

November 18th, 2010, Bologna

OUTLINE

Context and goals

Reactor configuration

Analysis approach

Mathematical model

Simulation results

Conclusions

WORK PROPOSAL – TASK 4.4

CONTEXT and GOALS

► Lead-cooled Fast Reactor (LFR) selected by the Generation IV international

Forum (GIF) as one of the candidates for the next generation of nuclear

power plants

► significant technological innovations

need of a demonstrator reactor (DEMO)

study of plant global performances

refining/finalizing the system configuration REACTOR DYNAMICS

design of an appropriate control system

REACTOR CONFIGURATION

Parameter Value UnitThermal Power 300 MWthAverage Coolant Outlet T 480 °CCoolant Inlet T 400 °CAverage Coolant Velocity 3.0 m s-1

Clad Max T 600 °CClad Out Diameter 6.00 mmClad Thickness 0.34 mmPellet Outer Diameter 5.14 mm

Parameter Value UnitPellet Hole Diameter 1.71 mmFuel Column Height 650 mmFuel Rod Pitch 8.53 mmNumber of Pins/FA 744 -SS box beam inner width 45.65 mmSS box beam outer width 48.65 mmNumber of Inner/Outer FAs 10/14 -Pu Enrichment Inner/ Outer 29.3/32.2 vol.%

CORE LAYOUT

ANALYSIS APPROACH (1)

HΨ Ci

CORE

Tf Tc Tl

Tin

δρ(t) δψ(t)

δTin(t) δTf(t)

δTc(t)

δTl(t)

δq(t) δTout(t)

δTin(t)

δH(t)

δTf(t)

δTc(t)

δTl(t) δρ(t)

δH(t)

Kinetics

Thermal-hydraulics

Reactivity

Input

Tout

ANALYSIS APPROACH (2)

MAIN ASSUMPTIONS - NEUTRONICS

- neutron time fluctuations independent of spatial variations

- spectrum independent of neutron level

- core lumped source of neutrons with prompt heat power

- neutron population and neutron flux related by constants of

proportionality

POINT-KINETICS APPROXIMATION

ANALYSIS APPROACH (3)

MAIN ASSUMPTIONS – THERMAL-HYDRAULICS

- average channel representation

- single-node heat-exchange model

- 3 distinct temperature regions fuel

cladding

coolant

- energy balance over the fuel pin surrounded by coolant

- reactor power input retrieved from reactor kinetics

LUMPED-PARAMETER APPROACH

MATHEMATICAL MODEL (1)

NEUTRON KINETICS EQUATIONS

- ASSUMPTION t ≤ 0 steady state

- perturbation around steady state

solution

- linearization

SMALL-PERTURBATION APPROACH

with:

- ψ = n(t)/n0 = q(t)/q0

- ηi = Ci(t)/Ci0

)()()(

)()()( 6

1

tCtndt

tdC

tCtndt

tdn

iiii

ii

)()()(

)()(

1)(

)( 6

1

ttdt

td

ttt

dt

td

iiii

ii

MATHEMATICAL MODEL (2)

THERMAL-HYDRAULICS EQUATIONS

ASSUMPTIONS:

- constant properties

- axial conduction neglected

- Tl = (Tin + Tout)/2

SMALL-PERTURBATION APPROACH

Time constants:

- tf = MfCf/kfc

- tc1 = McCc/kfc

- tc2 = McCc/hcl

- tl = Ml/Γ

))(2)(2())()(()(

))()(())()(()(

))()(()()(

tTtTCtTtThdt

tdTCM

tTtThtTtTkdt

tdTCM

tTtTktqdt

tdTCM

inlllccll

ll

lcclcffcc

cc

cffcf

ff

)(2

)(21

)(1)(

)(2

)(21

)(1)(

)()(1

)(1)(

00

221

0

tTtTtTdt

tTd

tTtTtTdt

tTd

tCM

qtTtT

dt

tTd

inll

cl

l

lc

ccc

fcl

c

ffl

ff

f

f

MATHEMATICAL MODEL (3)

REACTIVITY EQUATIONS

- αD = Doppler coefficient

- αL = coolant density coefficient

- αZ = axial expansion coefficient

- αR = radial expansion

coefficient

(Linked option) - αH = CR-related coefficient

- Function of fuel average temperature

cladding average temperature

coolant average temperature

coolant inlet temperature

externally introduced reactivity (ideal control rod)

HTTTTt HinRlLcZfD )(

REACTIVITY COEFFICIENTS CALCULATION

DOPPLER LEAD DENSITY

RADIAL EXPANSION

AXIAL EXPANSION

MATHEMATICAL MODEL (4)

T

dTd

dT

d

dT

d cool

cool

cool

coolcoolant

coolant

coolantcoolant

steel

steel

absorber

absorber

fuel

fuel

inTdiagrid f

RR

TldT

d

1

12)(91

dT

dL

LZZ

dTTlTTdT

d insertion

insertion

steell

steel

fuel

fuel

T

T

matinmatoutmataxial

outmat

inmat

*,

*,

)(1

*,*,

SIMULATIONS (1)

SOLUTION TECHNIQUE – MIMO (Multiple Input Multiple Output) SYSTEM

modelling equations state-space representation:

state vector: output vector: input vector:

UDXCY

UBXAX

66

55

44

33

22

11

654321

0

2211

0

00000000

00000000

00000000

00000000

00000000

00000000

0000000211

0

00000001111

000000011

LZD

ll

cccc

ffff CM

q

A

00

00

00

00

00

00

02

00

00

0

HR

B

0000000

000000000

0000001000

0000000200

0000000100

0000000010

0000000001

0

LZD

q

C

HR

D

00

00

01

00

00

00

6

5

4

3

2

1

l

c

f

T

T

T

X

q

T

T

T

T

Y out

l

c

f

H

TU in

SIMULATIONS (2)

TABLE II

DEMO core BoC reference data.

Quantity Value Units Quantity Value Units β1 6.142 pcm α - 235 pcm

β2 71.40 pcm αD - 0.1774 pcm K-1

β3 34.86 pcm αH 187 pcm cm-1

β4 114.1 pcm αL - 0.1204 pcm K-1

β5 69.92 pcm αR - 0.8715 pcm K-1

β6 22.68 pcm αZ 0.0088 pcm K-1

λ1 0.0125 s-1 τf 1.94 s

λ 2 0.0292 s-1 τc1 0.87 s

λ 3 0.0895 s-1 τc2 0.06 s

λ 4 0.2575 s-1 τl 0.16 s

λ 5 0.6037 s-1 τ0 0.21 s

λ 6 2.6688 s-1 Mf 2391 kg

Λ 8.0659·10-7 s Cf 317.5 J kg-1 K-1

β 319 pcm q0 300·106 W

TABLE III

DEMO core EoC reference data.

Quantity Value Units Quantity Value Units β1 6.224 pcm α - 268 pcm β2 72.33 pcm αD - 0.2019 pcm K-1 β3 35.34 pcm αH 70 pcm cm-1 β4 115.5 pcm αL - 0.1408 pcm K-1 β5 70.75 pcm αR - 0.9234 pcm K-1 β6 22.89 pcm αZ - 0.1949 pcm K-1 λ1 0.0125 s-1 τf 1.99 s λ 2 0.0292 s-1 τc1 0.89 s λ 3 0.0895 s-1 τc2 0.06 s λ 4 0.2573 s-1 τl 0.16 s λ 5 0.6025 s-1 τ0 0.21 s λ 6 2.6661 s-1 Mf 2391 kg Λ 8.4980·10-7 s Cf 317.5 J kg-1 K-1

β 323 pcm q0 300·106 W

TABLE II

DEMO core BoC reference data.

Quantity Value Units Quantity Value Units β1 6.142 pcm α - 235 pcm

β2 71.40 pcm αD - 0.1774 pcm K-1

β3 34.86 pcm αH 187 pcm cm-1

β4 114.1 pcm αL - 0.1204 pcm K-1

β5 69.92 pcm αR - 0.8715 pcm K-1

β6 22.68 pcm αZ 0.0088 pcm K-1

λ1 0.0125 s-1 τf 1.94 s

λ 2 0.0292 s-1 τc1 0.87 s

λ 3 0.0895 s-1 τc2 0.06 s

λ 4 0.2575 s-1 τl 0.16 s

λ 5 0.6037 s-1 τ0 0.21 s

λ 6 2.6688 s-1 Mf 2391 kg

Λ 8.0659·10-7 s Cf 317.5 J kg-1 K-1

β 319 pcm q0 300·106 W

TABLE III

DEMO core EoC reference data.

Quantity Value Units Quantity Value Units β1 6.224 pcm α - 268 pcm β2 72.33 pcm αD - 0.2019 pcm K-1 β3 35.34 pcm αH 70 pcm cm-1 β4 115.5 pcm αL - 0.1408 pcm K-1 β5 70.75 pcm αR - 0.9234 pcm K-1 β6 22.89 pcm αZ - 0.1949 pcm K-1 λ1 0.0125 s-1 τf 1.99 s λ 2 0.0292 s-1 τc1 0.89 s λ 3 0.0895 s-1 τc2 0.06 s λ 4 0.2573 s-1 τl 0.16 s λ 5 0.6025 s-1 τ0 0.21 s λ 6 2.6661 s-1 Mf 2391 kg Λ 8.4980·10-7 s Cf 317.5 J kg-1 K-1

β 323 pcm q0 300·106 W

ERANOS-2.1, JEFF-3.1 data library calculations

RESULTS (1)

LEAD INLET TEMPERATURE PERTURBATION (+10 K)

-12

-10

-8

-6

-4

-2

0

0 50 100 150 200 250 300

React

ivit

y [pcm

]

Time [s]

BoC

EoC

Reactivity

0

2

4

6

8

10

0 50 100 150 200 250 300

Tl[

K]

Time [s]

BoC

EoC

Lead average temperature

-25

-20

-15

-10

-5

0

0 50 100 150 200 250 300

q [M

W]

Time [s]

BoC

EoC

Power

-60

-50

-40

-30

-20

-10

0

0 50 100 150 200 250 300

Tf[K

]

Time [s]

BoC

EoC

Fuel average temperature

0

2

4

6

8

10

0 50 100 150 200 250 300

Tc[K

]

Time [s]

BoC

EoC

Clad average temperature

0

2

4

6

8

10

0 50 100 150 200 250 300

Tout[K

]

Time [s]

BoC

EoC

Core outlet temperature

RESULTS (2)

CONTROL ROD EXTRACTION (+50 pcm)

0

10

20

30

40

50

60

0 50 100 150 200 250 300

React

ivit

y [

pcm

]

Time [s]

BoC

EoC

Reactivity

0

20

40

60

80

100

0 50 100 150 200 250 300

q [M

W]

Time [s]

BoC

EoC

Power

0

50

100

150

200

250

0 50 100 150 200 250 300

Tf[°

C]

Time [s]

BoCEoC

Fuel average temperature

0

2

4

6

8

10

12

0 50 100 150 200 250 300

Tl[

K]

Time [s]

BoC

EoC

Lead average temperature

0

5

10

15

20

25

30

0 50 100 150 200 250 300

Tc[K

]

Time [s]

BoC

EoC

Clad average temperature

0

5

10

15

20

25

0 50 100 150 200 250 300

Tout[

K]

Time [s]

BoC

EoC

Core outlet temperature

RESULTS (3)

REACTOR CORE OPEN-LOOP STABILITY

Study of the system representative TRANSFER FUNCTION

qualitative insights into the response characteristics of the system

STABILITY all the system poles with negative real parts

)(

)()(

sU

sYsG

Pole location.

Pole Value at BoC [s-1] Value at EoC [s-1] P1 - 0.0188 - 0.0120 P2 - 0.0201 - 0.0214 P3 - 0.0785 - 0.0801 P4 - 0.199 - 0.208 P5 - 0.561 + 0.125i - 0.580 + 0.136i P6 - 0.561 - 0.125i - 0.580 - 0.136i P7 - 2.48 - 2.47 P8 - 6.58 - 6.54 P9 - 27.1 - 27.0 P10 -3.96·103 -3.80·103

CONCLUSIONS

► preliminary evaluation of DEMO core dynamics

► coupling of NEUTRONICS and THERMAL-HYDRAULICS

► prediction of DEMO reactions to 10°C increase of lead inlet T

50 pcm insertion by ideal CR

► stable system

► significant impact of reactivity insertion on reactor power (steady state: + 32/25 %

nominal value at BoC/EoC) and fuel temperature (+ 276/220 K at BoC/EoC)

► model with satisfactory capability of predicting the system response to both

perturbations (small errors figured)

► generally slight impact of assuming the fuel linked to the cladding or the radial

expansion driven by the coolant average temperature

► useful tool allowing a relatively quick, qualitative analysis of fundamental dynamics

and stability aspects

WORK PROPOSAL

► Primary loop modeling

► Secondary loop modeling

► Coupling between primary and secondary loops

► Sensitivity analysis

► Control and measured variables definition

► Control strategy assessment (SISO loops and Multi-variable control, e.g. MPC)

TASK 4.4

Preliminary definition of the Control Architecture