Multi-physics coupling
Application on TRIGA reactor
Student
Supervisors:
Romain Henry
Prof. Dr. IZTOK TISELJ
Dr. LUKA SNOJ
PhD Topic presentation
27/03/2012
FMF LJUBLJANA
1

A nuclear reactor is a “boiler” in which heat is
produced the fission of some nuclei of atoms
having high atomic mass
2

fission products
radioactive

2 to 3 prompt neutrons

High energy photons

The reaction is exo-energetic (~ 200 MeV)

1 fission produce 10^8 times more energy that
burning one atom of carbon
 delayed neutrons are emitted
 a chain reaction is possible
3

Thermal reactor: PWR,BWR
Fast reactor: SFR,LFR,GFR
4


Pool reactor
thermal spectrum

Water cooled

Pmax=250 kW
5

The multiplication factor k describes the
evolution of the neutron density between 2
generations

k<1:
The neutron density decreases
The power decreases
The reactor is sub-critical

k=1:
The neutron density is constant
The reactor is critical

k>1:
The neutron density increases
The power increases
The reactor is super-critical
ni 1
k
ni
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
Interaction neutron matter :
Notion of cross section (expressed in barns)
 Absorption (fission, capture), scattering
 Total cross section:
   
 interaction probability :
t
a
Pi 
s


i
t
 macroscopic cross section
for a given material (atoms density N):
  N
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
Natural U: 99.3% of U238 +0.7% of U235

Fuel Enriched in U235
8

Moderator:
◦ Very low atomic mass, optimal for the slowing
down process
◦ Very low cross section for capture in the thermal
range of energy
◦ high concentration of nuclei to favor the probability
of neutron scattering
 Water
9

Transport equation :
 

 
    
 
  
 
n(r , v , t )
 v .n(r , v , t )  v (r , v )n(r , v , t )   d 3v 'v ' s (r , v '  v )n(r , v ' , t )  s (r , v , t )
t
 Core modeling geometry (2D, 3D), isotopic
composition (fuel, moderator, …)
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


Flow phenomena for the coolant
(turbulence ,heat transfer )
Phenomena of importance in the evaluation
of fuel integrity.
CFD is a branch of fluid mechanics that uses
numerical methods and algorithms to solve
Navier-Stokes system
11

Navier-Stokes system for incompressible flow
with constant Newtonian properties:
◦ Continuity equation
◦ Momentum equation

.u  0



u
1
 .(u u )   2 u 
P
t


T
 .(Tu )   2T
t
◦ Energy equation

u
 Fluid velocity
 Thermal diffusivity  

c p
mc p
dT fuel
dt
 Pfission  h(T fuel  Tcoolant )
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
Example of
CFD result
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


The main goal : describe some behaviors that
pure neutron transport equation or pure
thermal-hydraulic models are unable to do
Research in neutron physics and nuclear
thermal-hydraulics require long computational
time on large parallel computer
Coupled models cannot rely on the most accurate
and advanced models from both
disciplines(simpler models that allow performing
simulations in a reasonable time)
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Tfuel,
Tmod
…
ThermalHydraulics
Neutronics
Power
distribution
…
15

Build a neutronic
core model accurate
 Full 3D description


3D single phase flow
description phenomena
2 codes working as 1
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
Validation of the model through
measurement with TRIGA reactor:
 Detectors devices allowing to measure neutron flux for
different configurations of the TRIGA core to deduce
the power distribution
 The temperature of the moderator is also easily
accessible, with thermocouple, from the reactor pool
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Temperature
reactivity
Number of
neutron
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
Reactivity ρ= (k-1)/k

Temperature increases
0

Absorption increases
-1 0
-2
20
40
60
80
100 T(°C) 120
Δρ/ΔT(pcm/°C)
-3
-4

Reactivity decreases
-5
-6
measurement
-7
-8
-9
-10
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
Point kinetic (Boltzmann with no space
dependence)
dn   

n   i Ci
dt
l
i
 C precursor
λ decay constant
 l Neutron lifetime
in critical reactor
 β proportion of
delayed neutron

Thermodynamic law mc p
dCi  i
 n  i Ci
dt
l
dT fuel
dt
 Pfission(n)  (T fuel  Tcoolant )
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Temperature
Δρ/ΔT
reactivity
Pfission
Point
kinetic
Number of
neutron
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
Build a full 3D model of the TRIGA reactor
 Simpler geometry
 Data easily available

See which application we can have for a
power reactor
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Thank you for
your attention
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