Multidimensional, multi-material and multiphysics modelling of Hydrogen transport in ITER

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Multidimensional, multi-material and multiphysics

modelling of Hydrogen transport in ITER

Rémi Delaporte-Mathurin, Jonathan Mougenot, Etienne Hodille, Y. Charles,

Christian Grisolia

To cite this version:

Rémi Delaporte-Mathurin, Jonathan Mougenot, Etienne Hodille, Y. Charles, Christian Grisolia. Mul-tidimensional, multi-material and multiphysics modelling of Hydrogen transport in ITER. 24th In-ternational Conference on Plasma Surface Interactions in Controlled Fusion Devices, Jan 2021, Jeju Island, South Korea. �hal-03120261�

𝐸

_𝑝,1

(eV)

𝑛

1

(at

.fr

.)

Example cost function



Error function

based on W TDS spectrum

 𝑓 𝒙 =

σ

𝑖

𝛼

𝑖

|𝑑

𝑖

−𝑑

sim

|

σ

_𝑖

𝛼

_𝑖

 𝛼

_𝑖

: weights

 𝑑

_i

: experimental data

 𝑑

_𝑠𝑖𝑚

: simulated data



Objective

: find the minimum

Tungsten

 W under 200 eV D

+

_{at 300K [2]}



5D

optimisation

(3 energies, 4 densities)

 𝐸

_𝑝,1

= 0.83 eV ; 𝐸

_𝑝,2

= 0.97 eV

𝐸

_𝑝,3

= 1.51 eV

 𝑛

₁

= 10

−3

at. fr. ;

𝑛

₂

= 7 × 10

−4

at. fr.

 Convergence reached in

a few hours

𝑇(K)

Desorption

flux (

m

−

2

s

−

1

)

R. Delaporte-Mathurin

1,2

, J. Mougenot

2

, E. A. Hodille

1

,

Y. Charles

2

, C. Grisolia

1

1

_{CEA, IRFM, F-13108 Saint Paul-les-Durance, France}

2

_{Université Paris 13, LSPM, CNRS, Paris Sorbonne Cité, F-93430 Villetaneuse, France}

Multidimensional, material and

multi-physics modelling of Hydrogen transport in

ITER



FESTIM

: a modelling tool for hydrogen transport modelling

 Well suited for

high-dimensional optimisation

 High inventory in ITER PFCs during resting phases



1D

modelling is

not sufficient

for

quantitative

estimation

of PFC inventory

 Reproducing experimental results can be

long

and

tedious

 Is it possible to

automatically fit

a thermal desorption spectrum and

identify

materials properties

?

 Can these properties be used to

perform complex multidimensional

simulations

?

 Is there a

discrepancy

between 2D and 1D simulations ?

1

st

_cycle

50

th

cycle

₁₀₀

th

_cycle

HIs retention

field during resting phases

1 × 10

21

9 × 10

20

8 × 10

20

7 × 10

20

6 × 10

20

5 × 10

20

4 × 10

20

3 × 10

20

2 × 10

20

1 × 10

20

0

m

−3

INTRODUCTION

METHODOLOGY

PROPERTIES IDENTIFICATION

APPLICATION: ITER MONOBLOCKS

CONCLUSIONS

𝑑𝑐

_m

𝑑𝑡

= 𝛻(𝐷𝛻𝑐

m

) + 𝑆 − ෍

𝑖

𝑑𝑐

_t,𝑖

𝑑𝑡

𝑑𝑐

_t,𝑖

𝑑𝑡

= 𝑘 𝑐

m

(𝑛

𝑖

− 𝑐

t,𝑖

) − 𝑝 𝑐

t,i

Hydrogen transport

𝜌𝐶

_𝑝

𝑑𝑇

𝑑𝑡

= 𝛻 𝜆𝛻𝑇 + 𝑄

Heat transfer

HIs Inventory over time

 Inventory limited by near surface

retention zone

 Inventory during implantations

keeps increasing

 Up to

95% error

between

1D

and

2D

HIs in

ven

tory

(g)

𝑡 (s)

Simulation parameters

 2 traps in

W

 1 trap in

CuCrZr

1 cm

References:

[1] Delaporte-Mathurin et al. (NME, 2019)

[2] Ogorodnikova et al. (JNM, 2003)

[3] Baldwin, Schwarz-Selinger, and Doerner (Nucl. Fusion, 2014)

[4] Hollingsworth et al. (Nucl. Fusion, 2019)

2D

1D



Finite Element

Methods

 FEniCS backend



FESTIM

code [1]

Inci

den

t

HIs flux

Heat

flux

10

22

m

−2

s

−1

0 m

−2

s

−1

10 MW m

−2

0 MW m

−2

100 s

0 s

500 s 600 s

4200 s

×100

W

Cu

CuCrZr

 Convective exchange

 Recombination

Co-deposited Be-D

 Co-deposited 1μm-thick Be-D under at

330K [3]



6D

optimisation

(2 energies, 2 densities, 2

initial occupancies)

 𝐸

_𝑝,1

= 0.75 eV ; 𝐸

_𝑝,2

= 0.93 eV

 𝑛

₁

= 10

−1

at. fr. ;

𝑛

₂

= 4 × 10

−2

at. fr.

 𝑓

₁

= 0.73 ; 𝑓

₂

= 0.28

 Convergence reached in

a few minutes

Desorption

flux (

m

−

2

s

−

1

)

𝑡(s)

Temperature

field

during

implantation



Maximum

surface

temperature

1471 K

 Homogeneous

temperature during

rests

The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille University - A*Midex, a French "Investissements d'Avenir" programme as well as from the French National Research Agency (Grant No. ANR-18-CE05-0012).Work performed under EUROfusion WP PFC.This work

has been carried out within the framework of the EUROfusion consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053.The views and opinions expressed herein do not necessarily reflect those of the European