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-hydraulicsReactivity
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
tCtndttdC
tCtndttdn
iiii
ii
)()()(
)()(1)()( 6
1
ttdttd
tttdttd
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())()(()(
))()(())()(()(
))()(()()(
tTtTCtTtThdttdTCM
tTtThtTtTkdttdTCM
tTtTktqdttdT
CM
inlllccll
ll
lcclcffcc
cc
cffcf
ff
)(2)(21)(1)(
)(2)(21)(1)(
)()(1)(1)(
00
221
0
tTtTtTdttTd
tTtTtTdttTd
tCMqtTtT
dttTd
inll
cl
l
lc
ccc
fcl
c
ffl
ff
f
f
t
tt
t
t
tt
t
t
t
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)
TdTd
dT
d
dTd cool
cool
cool
coolcoolant
coolant
coolantcoolant
steel
steel
absorber
absorber
fuel
fuelinT
diagrid fRR
TldTd
112)(91
dTdL
LZZ
dTTlTTdT
d insertion
insertion
steell
steel
fuel
fuel
T
Tmat
inmatoutmataxial
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
000000000000000000000000000000000000000000000000
0000000211
0
00000001111
000000011
ttt
tttt
tt
LZD
ll
cccc
ffff CMq
A
000000000000
020000
0
HR
B
t
000000000000000000000010000000000200000000010000000000100000000001
0
LZD
q
C
HR
D
000001000000
6
5
4
3
2
1
l
c
f
TTT
X
q
TTTT
Y out
l
c
f
HT
U 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
00 50 100 150 200 250 300
Reac
tivity
[pcm
]
Time [s]
BoCEoC
Reactivity
0
2
4
6
8
10
0 50 100 150 200 250 300
Tl[
K]
Time [s]
BoCEoC
Lead average temperature
-25
-20
-15
-10
-5
00 50 100 150 200 250 300
q [M
W]
Time [s]
BoCEoC
Power
-60
-50
-40
-30
-20
-10
00 50 100 150 200 250 300
Tf[
K]
Time [s]
BoCEoC
Fuel average temperature
0
2
4
6
8
10
0 50 100 150 200 250 300
Tc[K
]
Time [s]
BoCEoC
Clad average temperature
0
2
4
6
8
10
0 50 100 150 200 250 300
Tou
t[K]
Time [s]
BoCEoC
Core outlet temperature
RESULTS (2)
CONTROL ROD EXTRACTION (+50 pcm)
0
10
20
30
40
50
60
0 50 100 150 200 250 300
Reac
tivity
[pcm
]
Time [s]
BoCEoC
Reactivity
0
20
40
60
80
100
0 50 100 150 200 250 300
q [M
W]
Time [s]
BoCEoC
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]
BoCEoC
Lead average temperature
0
5
10
15
20
25
30
0 50 100 150 200 250 300
Tc[
K]
Time [s]
BoCEoC
Clad average temperature
0
5
10
15
20
25
0 50 100 150 200 250 300
Tou
t[K]
Time [s]
BoCEoC
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
)()()(sUsYsG
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
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