MULTI-PHYSICS MODELLING OF NUCLEAR REACTOR · PDF file1. Introduction 2 Chalmers University of Technology 1. Introduction • Nuclear reactor systems = complex multi-physics and multi-scale

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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]

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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.

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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

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uropean Pressurized Reactor


... to today’s reactors:

Fig. 2 An example of a Gen-III+ reactor being built: the E[from AREVA NP].

5


V systems [from the US Depart-


... and to future reactor systems:

Fig. 3 The Sodium-Cooled Fast Reactor, one of the Gen-Iment of Energy (2002)].

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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


• 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=

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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


• 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

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, 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.

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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].

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) fuel rods

9 - 12 mm

d) fuel pellets

~ 10 mm

fuel assemblies, fuel rods, and


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.

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10000 and 1 km/s;tens to a couple of cm;

l pins in a nuclear fuel assem-its emission and its absorp-


• 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.

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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.


• 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)]

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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 – +

=

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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

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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

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p T Tt------ r t Vd 1

V--- k T T r t n Sd

S

1V--- q r t Vd

V+=


• 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

+ + +=

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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)].


• 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

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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.

Documents

MULTI-PHYSICS MODELLING OF NUCLEAR REACTOR · PDF file1. Introduction 2 Chalmers University of Technology 1. Introduction • Nuclear reactor systems = complex multi-physics and multi-scale