1. Modelling for ITER of W, Be and Li Melting, W Cracking and Massive Gas Injection
FZ-Karlsruhe
I. Landman
Major contributions from B. Bazylev and S. Pestchanyi
KIT-FZ-Karlsruhe, Germany
All our modelling concerns transients (ELMs, disruptions)
Outline Relevant EFDA WP09-PWI Tasks
W melting /FZK/BS
Melt damages to Li /FZK/BS
Runaway damage to Be /FZK/BS
W cracking
MGI: Radiation impact on Be wall /FZK/BS
1 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

2. Disruptions (duration t ~ 3 ms)
Modelling of melting of W-macrobrushe with the code MEMOS
Main processes:
Melting (Navier-Stocks shallow fluid model)
Bulk thermoconductivity
Evaporation, vapour shield (melt motion due to gradient of vapour pressure)
Melt splashing
Resolidification
Melt pool depth ~ 200 µm.
Peak power load ~ 2.5 GW/m2
Vapour shield pressure ~ 5 bar
There are many parameters over which we calculate melt damage with MEMOS: W/Be, Q, t, J, , p||, Qlateral, …
Classification of ITER transient loads (divertor armour)
Disruptions (duration t ~ 3 ms)
Type
Max impact energy, Qmax
Max current, Jmax
MJ/m2
MA/m2
Maximal 30
Typical 10 5
Mitigated
1.5 (First wall)
ELMs (t ~ 0.5 ms)
Uncontrolled 15
‘Halve-controlled’ 2
Controlled 1
Example of disruption damage to W macrobrush armour
In 2009 MEMOS aimed at
Bulk target
SSP motion ( = 5 cm)
Cross-current
Tangential pressure
Lateral loads
2 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

3. Main results after 100 disruptions:
by W. Fundamenski
The heat loads at the outer divertor calculated with the MHD code FOREV
Reference pulse shape
Erosion profile after 20 disruptions
As an example:
Main results after 100 disruptions:
With moving (=5 cm) separatrix, the melt erosion (crater depth) is about 1.5 mm
If assuming fixed separatrix, the crater depth exceeds 5 mm
Q (MJ/m2) J
kA/cm2
P||
(mbar)
Vmelt (m/s)
Melt (µm)
Mount
(µm)
Crater
Comments 28
1.5
0.5 60 16 5
FOREV’s load, shield
0.37 8
2.6
--’’--
10.5
0.2 33
0.016
0.04
--’’--, vaporiz. only 3
0.45 35
0.7
1.57 7
0.17 12
3.5
Trian, no shield, 30
0.3 44 23
5.5
Rectangle, --’’-, 30
0.36 32
2.3
0.87
Ref. pulse shape 50
6.2
0.52
0.15 4
0.07
26(Lat)
0.12(Lat)
Triangle
0.55(Lat)
Rectangle
0.08
28(Lat)
1.5(Lat)
Those results need some appropriate systematization
3 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

4. W splashing: QDPA-T experiments and extrapolation upon ITERDm Vm
Plasma gun QSPA-T, p=2.4 bar
Q = MJ/m2, t = 0.5 ms, B=0
Distribution of droplets (Q = 1.6 MJ/m2, p = 2.3 bar). Dmax= 100 µm, Vmax = 25 m/s
Traces of droplets, Qthr=1.2 MJ/m2
Experimental investigations on the splashing of W melt layer were carried out at the plasma gun QSPA-T (Troitsk, Russia)
Upper Limit Log Normal distribution function f(x)  exp(-(ln(C(xmax/x-1)))2) matches the droplet emission measurements (x = D or V, =0.9, CD=0.4, CV=0.25)
Assuming the Kelvin-Helmholtz (KH) instability as the mechanism of droplet emission, the model parameters fKH and gKH were fitted to the experiments
Projecting the KH-model upon ITER a conclusion is drawn that the melt splashing would not occur (B. Bazylev et. al, PFMC-12, Juelich)
Inclined plasma impact
(a standalone 2D gas-dymamics code, B=0)
In the KH-model the droplet velocity U and the droplet size D are given by
In QSPA-T:
plasma velocity
V||p ~ 102 km/s
plasma density
p ~ 20 mg/m3
ITER parameters: V||p~300 km/s, p~0.1 mg/m3
I.e. Vm1 m/s, Dm  0.5 mm Dm>0.1 m means:
below splash-threshold.
Thus the splashing in ITER is not probable
Fitting the KH-model to the experiment: fKH = 0.4 and gKH = (W = 2 J/m2)
4 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

5. Modelling with MEMOS of Li melting damage
Wall processes are assumed like that of W.
Li 40 m coating on W traget so far.
Target initial temperature 500 K (molten) and 300 K
Impact energy Q = 0.1 MJ/m2 and pulse duration 0.5 ms
Influence of JB force and tangential pressure are assessed
Main conclusions:
Even small ELMs completely remove Li away from W subtrat.
At both 300 K and 500 K the vapour shield does not develop.
Crater depth vs. cross-current on Li layer (B = T, 1 ms)
Influence of tangential pressure on Li surface solid and molten Li behave similarly
(1 mbar, Tmelt = 450 K)
Crater depth vs. tangential pressure (At crater depth above 40 µm, W outcrops)
5 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

6. Modelling with ENDEP and MEMOS of melting damage caused by runaways
(B. Bazylev et al., ICFRM-14, Sapporo, Japan)
Main features of the code ENDEP :
Diverse mechanisms of slowing down of relativistic electrons in target bulk
Applied magnetic field
Secondary avalanche processes
ITER specification (M. Sugihara):
E = 15 MeV, Q up to 25 MJ/m2, t = up to 0.1 s
Transversal energy of electrons E/E up to 0.2
incidence angle  = 1.5 deg
sandwich target (1 cm Be top, 1 cm Cu bulk)
MEMOS Ref. scenario: Q = 20 MJ/m2, Tw0 = 500 K, t = 0.1 s
Main results:
Evaporation 70 m (hvap)
melt pool mm (hmelt) (w/o vaporization 2 mm)
Weak dependence of hvap and hmelt on E/E
Distribution of energy deposition
Absorbed energy fraction vs. E/E
Melt layer gets thicker with Q and thinner with t
6 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

7. W cracking: QSPA-Kh50 experiments and PEGASUS simulation
S. Pestchanyi et al. To be presented at ICFNT-9, Dalian, China
In QSPA experiments W surface melts (Q = 0.75 MJ/m2) or not (0.45 MJ/m2)
Experimental results:
Crack width grows up with shot number
At large shot numbers the width saturates.
Maximum crack width:
0.75 MJ/m2: m
“ m
With surface melting
Q = 0.75 MJ/m2
Without melting
Q = 0.45 MJ/m2
Mesh of cracks after W irradiation after many shots. Crack pattern does not change.
Crack average width vs. shot number
Earlier PEGASUS simulated armour cracking above melting threshold
Now the code simulates below melting threshold
To achieve it, plasticity thermosetress was implemented in the thermomechanic model of the code
Theoretical background: the Kelvin-Voigt model:
 ~ 10 Mpa,  ~ E ~ 1 GPa,  ~ 50 s MPa
7 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

8. Mechanism of cracks appearence:
During the heating compressive thermostress appears in ~ 50 m sub-surface layer.
At the high temperature the deformations become plastic which relaxes stress
The following decrease of temperature fixes local material deformations beause it increases the viscosity .
This results in the cracks (because large tensile stress appears)
PEGASUS simulation: the net of cracks developed at the W sample below melting point At   50 s MPa, the average crack mesh size is of 0.5 mm and crack width 7 m (in agreement with the measured value).
8 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

9. Simulation of Massive Gas Injection with the code TOKES
I. Landman et al. To be presented at ICFNT-9, Dalian, China
TOKES is MHD tokamak plasma and wall code
2D code (toroidal symmetry)
Multi-fluid plasma (from D to W)
Radiation losses
Plasma is dumped into SOL and comes to wall
Wall sputtering and vaporization
Neutral fluxes in whole vessel
Preamble: After discussions in ITER our work in 2009 is focused on MGI.
To better simulate MGI, the code is significantly generalized: previous 1D plasma model  2D
2D plasma model is necessary because the radiation flush comes from rather cooled and located region of plasma edge
Aim of current simulations:
Estimation of maximum radiation impact on ITER wall during MGI, i.e. maximum Be wall temperature
Initial Be wall temperature 500 K
Main features of current MGI simulation:
Gas injector (G = Ar, Ne) is horizontal in mid-plane
Quasistationary radiation model (which is simplified compared to previous 1D plasma non-stationry model)
Standard ITER initial plasma profile (Ne(x) and Te(x))
T>0: Nm and Tm are functions of x and y (m = e, D, Ar)
The Euler’s equations for the longitudinal expansion of the fluids as well as 2D diffusion- and thermal conduction equations are numerically solved.
Inflow G(t) is assumed given:
inj
9 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman
Cadarache

10. Previous models used in TOKES
Validation of TOKES radiation model
Spatial profiles of Ne-ion density at different time moments and initial ne
cooling time versus max
0D model allows detailed ionization and radiation losses
10 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

11. Example of ITER MGI simulation (G=Ar):
Ar-ion density at different time moments
Te at the moment of reaching the separatrix value of q = 2. The mapping onto the (x,y)-plane with the varying numbers of radial plasma cells is shown.
Density distribution of neutral Ne-atoms
2 ms
To achieve most fast and adeqate simulation, sophisticated rectangular mesh for 2D plasma and very fine triangle mesh to guide slowly moving G-atoms are developed
Min triangle size ~ 0.5 cm
11 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

12. Comparison of TOKES simulation with DIII-D argon experiment 2007
E.M. Hollmann et al.,
Nucl. Fus. 48 (2008)
No validation yet, scaling ITER  DIII-D only: R  R/4, Bt 0.4Bt and Ip  Ip/10. Thus q(x) is self-similar.
The injector location remains like ITER’s. However, the gas inflow G(t) fits that of DIII-D.
Centre Te and averaged ne retrieved from DIII-D and predicted for ITER
Prad and Ar masses MG0 and MG for DIII-D and ITER
Cooling in TOKES is 2 times faster than that in DIII-D
The discrepancy is attributed to
the quasistationary radiative model of temporarily used 2D plasma
different locations of injector
Current model does not contain the ionization time ~ 1 ms
However, for ITER with expected TQ time >> 1 ms it can be adequate
Therefore the preliminary simulation of MGI in ITER seems reasonable
DIII-D size:
a=0.5 m
Bt = 2.1 T
Ip=1.5 MA
q95=3.5
Te0=2.5 keV
ne0=5×1019
12 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

13. Summary for ITER modelling
The results for ITER : Maximum temperature of Be wall surface during MGI
Wall temperature near X = 10.8 m for ITER
Wall radiation flux Qrad for ITER
Summary for ITER modelling
2 ms
8 ms
Neutral neon in vessel:
max =
7x1025 at/s
inj = 5 ms
13 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

14. Objectives High-Z- and liquid metals
(PWI-05-02: 0.6 PPY PS and 0.6 PPY BS; PWI-05-03: 0.3 PPY BS)
Further model W erosion for transient heat loads at varying surface shaping
Benchmark MEMOS (and PEGASUS) against plasma gun and tokamak data
Continue simulations for liquid Li to assess stability against transients
Transient loads and mitigation
(PWI PPY BS)
Simulate with ENDEP runaway heat loads and with MEMOS the following melt erosion.
Jobs for TOKES:
Further model impact of eroded atoms on plasma operation after ELMs
Transient loads on divertor and first wall plates
Further develop 2D radiative MHD multi-fluid plasma model
MGI simulations varying gases, gas inflow and valve positions.
Validate the codes against JET, AUG, TEXTOR, JUDITH and plasma gun data.
14 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman

15. Conclusions W melting and splashing:
For ITER weak transients (no vapour shield) absence of W melt splashing.
Assesments for Li:
Even small ELMs (0.1 MJ/m2) can completely remove Li away from W subtrat.
Runaways:
the vaporization of Be significantly decreases melt depth (2 mm  0.7 mm) (which decreases removal of Be by JB force)
W cracking:
Plasma gun experiments allowed validation of PEGASUS plastisity model.
Massive Gas Injection:
The radiation flush can result in ITER wall temperature above Be melting point.
Melting can be avoided decreasing inflow of injected gas (keeping the cooling time within 7 ms)
15 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009
I.S. Landman