Upload
phamduong
View
227
Download
4
Embed Size (px)
Citation preview
1
Chalmers University of Technology
n, March 28-29, 2012
LINGSTEMS
Chalmers Energy ConferenceChalmers University of Technology, Gothenburg, Swede
MULTI-PHYSICS MODELOF NUCLEAR REACTOR SY
Prof. Christophe DemazièreChalmers University of Technology
Department of Applied PhysicsDivision of Nuclear Engineering
SE-412 96 GothenburgSweden
E-mail: [email protected]
2
Chalmers University of Technology
cale systems.
fety analyses of nuclear reactor
1. Introduction
1. Introduction• Nuclear reactor systems = complex multi-physics and multi-s
Special modelling techniques required.
• Increase interest in advanced computational methods for sasystems.
• Plan of the presentation:
• nuclear reactors as multi-physics and multi-scale systems;
• modelling strategies of nuclear systems;
• deterministic modelling of nuclear systems.
3
Chalmers University of Technology
multi-scale systems
1942.
2. Nuclear reactors as multi-physics and multi-scale systems 2.1 Introduction
2. Nuclear reactors as multi-physics and
2.1 Introduction
• Tremendous evolution of nuclear reactor systems from:
Fig. 1 The Fermi reactor at the University of Chicago in
4
Chalmers University of Technology
uropean Pressurized Reactor
2. Nuclear reactors as multi-physics and multi-scale systems 2.1 Introduction
... to today’s reactors:
Fig. 2 An example of a Gen-III+ reactor being built: the E[from AREVA NP].
5
Chalmers University of Technology
V systems [from the US Depart-
2. Nuclear reactors as multi-physics and multi-scale systems 2.1 Introduction
... and to future reactor systems:
Fig. 3 The Sodium-Cooled Fast Reactor, one of the Gen-Iment of Energy (2002)].
6
Chalmers University of Technology
fissions induced by fast neutrons
fast neutrons
fast neutrons
neutrons leak-ing out during slowing-
down
1 s–
neutronsslowing-downs
eutron emission by fission
d the corresponding six-factor
2. Nuclear reactors as multi-physics and multi-scale systems 2.1 Introduction
• Constant need to predict the behaviour of such systems:
• in the early days, using “first-principles”:
fissions induced by thermal neu-
trons
fast neutrons absorbed in
the resonances
1 p– s
neutrons escaping the reso-nances
ps
neutrons leaking out during thermali-
zation
ps 1 t–
thermal neutrons absorbed in
materials other than fuel
p 1 f– st
neutronsthermalizing
pst
thermal neu-trons
absorbed in fuel
pfst
neutron thermalization nneutron slowing-down
Fig. 4 Illustration of neutron cycle in a nuclear reactor anformula.
keff pfst=
7
Chalmers University of Technology
aguar supercomputing centre at the Oaktional Laboratory, TN, USA, with a peak 2.33 petaflops [Image courtesy of theCenter for Computational Sciences, Oaktional Laboratory].
today
tremely sophisticated tools and models
2. Nuclear reactors as multi-physics and multi-scale systems 2.1 Introduction
• and with the development of computer technology:
a) The Zuse Z3 computer [from www.computerhis-tory.org].
b) The JRidge Naspeed ofNational Ridge Na
1941
From simple toolsand models...
... to ex
8
Chalmers University of Technology
, gas, liquid metal, salt, etc.).
to-coolant heat transfer;
mperature.
field, the flow fields and the fuel
2. Nuclear reactors as multi-physics and multi-scale systems 2.2 Multi-physics aspects
2.2 Multi-physics aspects
• Nuclear reactor systems = large and complex systems.
• Heat extracted from the nuclear core by a moving fluid (water
• Heat produced by self-sustained fission nuclear reactions.
• Multi-physics aspects of nuclear reactor systems:
• coolant properties depending on nuclear heating+fuel temperature depending on nuclear heating and fuel-
• nuclear heating depending on coolant density and fuel te
need to simultaneously determine the neutron density temperature field.
9
Chalmers University of Technology
essel of a Gen-II Pressurized e reactor pressure vessel, core [from Analysgruppen vid
2. Nuclear reactors as multi-physics and multi-scale systems 2.3 Multi-scale aspects
2.3 Multi-scale aspects
• Nuclear reactors = strongly heterogeneous systems. ~ 4 m
~ 13 m
~ 4 m
~ 3.5 m
Fig. 5 Schematic representation of the reactor pressure vWater Reactor. The data in black correspond to thwhereas the data in red correspond to the nuclear KSU].
10
Chalmers University of Technology
) fuel rods
9 - 12 mm
d) fuel pellets
~ 10 mm
fuel assemblies, fuel rods, and
2. Nuclear reactors as multi-physics and multi-scale systems 2.3 Multi-scale aspects
PWR
a) nuclear core b) nuclear fuel assemblies
~ 4 m
~ 3.5 - 4.5 m~ 21 cm
c
~
Fig. 6 Characteristic dimensions of nuclear cores, nuclearfuel pellets.
11
Chalmers University of Technology
10000 and 1 km/s;tens to a couple of cm;
l pins in a nuclear fuel assem-its emission and its absorp-
2. Nuclear reactors as multi-physics and multi-scale systems 2.3 Multi-scale aspects
• Physical phenomena at different scales:
• on the neutronic side: several characteristic lengths:neutrons: diameter of 10-15 m, speed varying between ca. average distance before interaction: between ca. several
Fig. 7 Schematic representation of a regular lattice of fuebly and of the path followed by a neutron between tion.
12
Chalmers University of Technology
r heating: ca. 1000 K on 0.5 cm;
r system.
on of the turbulent kinetic energy [m2/s2]n a Pressurized Water Reactor [from C.H. Mattsson, Determination of the fuel
namics via CFD for the purpose of noise.
2. Nuclear reactors as multi-physics and multi-scale systems 2.3 Multi-scale aspects
• on the thermal-hydraulic side:very large radial fuel temperature gradient due to nucleaeffect of the possible coolant evaporation;effect of turbulence in the coolant.
Fig. 8 Possible heterogeneities in the coolant in a nuclea
a) Radial distribution of the void fraction [1] in a BoilingWater Reactor (1/4 of a fuel assembly) [from H.Anglart, Thermal-hydraulic design of nuclear fuelassemblies - current needs and challenges (2006)].
b) Radial distributiin the coolant iDemazière and heat transfer dyanalysis (2006)]
13
Chalmers University of Technology
s
terministic methods neutron transport equation:
i-stage and complicated com-uting techniques
r E r E
E E r E ddE
id E i
i 1=
6
+ E f r E r E Ed
0
3. Modelling strategies of nuclear systems
3. Modelling strategies of nuclear system• For neutron transport:
Monte Carlo methods DeTracking the “life” of neutrons:
Very accurate but very CPU intensive tech-niques
Solving the
Fast but multp
r E T+
s r
0
4
1
4k--------- p E 1 – +
=
14
Chalmers University of Technology
stem code approachavier-Stokes equations and an conservation equationn a coarse mesh:
es but rely on many empirical correlations
3. Modelling strategies of nuclear systems
• For fluid dynamics and heat transfer:
CFD methods SySolving the Navier-Stokes equations and an
energy conservation equationon a fine mesh:
Very accurate but very CPU intensive tech-nique
Solving the Nenergy
o
Fast techniqu
15
Chalmers University of Technology
temsand at all scales (still) not feasi-
rt and system code approach)g) in safety analyses.
p computers.
rmal-hydraulic solver
4. Deterministic modelling of nuclear systems
4. Deterministic modelling of nuclear sys• Detailed modelling of nuclear reactors for the whole system
ble.
• Only fast running methods (deterministic neutron transpoused and coupled in an a posteriori manner (Operator Splittin
methods that can be used by nuclear engineers on deskto
Deterministic neutron transport solver
Coarse the
Tf
16
Chalmers University of Technology
p T Tt------ r t Vd 1
V--- k T T r t n Sd
S
1V--- q r t Vd
V+=
4. Deterministic modelling of nuclear systems
• Equations solved in nuclear reactor safety analyses:
1vg-----g nt
------------- t Jg n t Jg n 1–
t –
---------------------------------------------- x y z =– T g n t g n t –
s0 g g n t g n t g 1=
G
gp 1 – g f g n t g n t
g 1=
G
i gd iCi n t
i 1=
6
+ + +
=
Ci nt
------------- t i g f g n t g n t g 1=
G
iCi n t –= i 1 ... 6 =
1V--- T c
V
kfk t
------------------ r t kfkvk r t +
kk r t k r t 1V--- kfk r t vk vS– r t – k r t + ndS
Ski
1V--- k r t ndS
Skw
+ + +=
17
Chalmers University of Technology
6 7 8 9 10 11 12 13 14 15
9.5
35.4
37.1
31.4
39.2
21.7
11.6
12.5
16.6
11.4
12.0
11.1
3.6
9.3
28.0
20.6
34.2
52.3
31.5
16.9
10.3
9.9
12.1
17.2
10.9
7.5
8.4
2.7
13.4
34.3
27.1
49.6
47.3
36.2
16.9
9.0
9.0
13.5
15.3
15.4
8.5
9.8
3.8
9.1
27.5
19.9
32.7
49.2
28.6
14.5
9.4
9.4
11.6
16.7
10.6
7.4
8.4
2.7
9.0
32.6
33.7
27.5
30.2
16.3
9.8
10.9
15.1
10.7
11.5
10.8
3.6
7.9
27.3
23.9
13.9
17.6
22.2
16.1
16.8
10.8
7.7
9.3
9.3
2.7
8.3
11.4
15.3
17.3
13.8
17.5
11.3
11.9
9.4
6.6
3.6
5.9
14.5
15.4
9.0
9.8
8.0
11.4
9.7
3.6
4.0
4.5
10.2
11.4
9.4
3.8
2.9
3.2
4.4
3.0
power distribution (% nominal power)
5
10
15
20
25
30
35
40
45
50
g a Main Steam Line Break ribution when the power is ghals-3 PWR; the transient is
ak is initiated at 52 s [from M. k calculations using a coupled ter reactor (2008)].
4. Deterministic modelling of nuclear systems
• Example of results that can be obtained from such methods: 1
1
2
2
3
3
4
4
5
5
6
7
8
9
10
11
12
13
14
15
4.8
6.1
4.0
6.7
6.7
15.7
15.7
12.0
4.3
3.2
8.9
24.3
25.5
13.0
13.1
9.6
13.3
11.0
4.0
10.3
14.9
23.4
27.3
20.8
23.2
14.0
14.0
10.6
6.9
3.7
8.5
30.7
27.7
17.9
25.2
32.4
21.0
20.4
12.4
8.3
9.7
9.7
2.9
Radial
Fig. 9 Evolution of the thermal power and reactivity durinMSLB (on the left hand-side) and radial power distmaximal at 115 s (on the right hand-side) at the Rinsimulated at hot zero power conditions and the breStålek, J. Bánáti, and C. Demazière, Main steam line breaRELAP5/PARCS model for the Ringhals-3 pressurized wa
18
Chalmers University of Technology
e modelling required.
for each field of physics.
multi-physics approaches;
5. Conclusions
5. Conclusions• Reactor statics and dynamics = multi-physics and multi-scal
• Multi-physics modelling usually carried out by separate tools
• Compromise in modelling to be found between:
• the level of details of the models;
• the necessary computational time;
• the required accuracy of the results.
• Intensive research on-going:
• for replacing Operator Splitting strategies by integrated
• for using hybrid Monte Carlo/deterministic methods;
• for using methods giving a high spatial resolution.