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KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
1 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
Modelling for ITER of W, Be and Li Melting, W Cracking and Massive Gas Injection
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 05-02/FZK/BS
– Melt damages to Li 06-01/FZK/BS
– Runaway damage to Be 08-01/FZK/BS
– W cracking
– MGI: Radiation impact on Be wall 09-02/FZK/BS
FZ-Karlsruhe
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
2 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
35 40 45 50 55 60-200
-150
-100
-50
0
50
100 Q=15 MJ/m2, =5 ms
Su
rfac
e p
rofi
le (m
)
Distance along target (cm)
Example of disruption damage to W macrobrush armour
Melt pool depth ~ 200 µm.Peak power load ~ 2.5 GW/m2 Vapour shield pressure ~ 5 bar
Main processes:• Melting (Navier-Stocks shallow fluid model)• Bulk thermoconductivity• Evaporation, vapour shield (melt motion due
to gradient of vapour pressure)• Melt splashing• Resolidification
Modelling of melting of W-macrobrushe with the code MEMOS
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 30
Typical 10 5
Mitigated 1.5 (First wall) 0
ELMs (t ~ 0.5 ms)
Uncontrolled 15 30
‘Halve-controlled’ 2 5
Controlled 1 5
In 2009 MEMOS aimed at• Bulk target• SSP motion ( = 5 cm)• Cross-current• Tangential pressure• Lateral loads
There are many parameters over which we calculate melt damage with MEMOS: W/Be, Q, t, J, , p||, Qlateral, …
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
3 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
Q (MJ/m2)
JkA/cm2
P||
(mbar)Vmelt (m/s)
Melt (µm)
Mount(µm)
Crater(µm)
Comments
28 1.5 0 0.5 60 16 5 FOREV’s load, shield
28 0 0 0.37 60 8 2.6 --’’--
10.5 0 0 0.2 33 0.016 0.04 --’’--, vaporiz. only
10.5 3 0 0.45 35 1.3-1.6 0.7 --’’--
1.57 0.45 7 0.17 35 12 3.5 Trian, no shield, 30
1.57 0.45 7 0.3 44 23 5.5 Rectangle, --’’-, 30
1.57 0.45 7 0.36 32 2.3 0.87 Ref. pulse shape
1.57 0.45 7 0.36 32 50 6.2 --’’--
0.52 0.15 4 0.07 26(Lat) 0.12(Lat) 0 Triangle
0.52 0.15 4 0.07 26(Lat) 0.55(Lat) 0 Rectangle
0.52 0.15 4 0.08 28(Lat) 1.5(Lat) 0 Ref. pulse shape
by W. Fundamenski
Reference pulse shape
20 30 40 50 600,0
0,5
1,0
1,5
2,0
2,5
3,0Q=15 MJ/m2, =5 ms
t= 0.63 ms t= 1.33 ms t= 1.77 ms t= 2.1 ms t= 3.4 ms
Hea
t lo
ad (
GW
/m2 )
Distance along target (cm)
The heat loads at the outer divertor
calculated with the MHD code FOREV
30 35 40 45 50 55 60-1,0
-0,5
0,0
0,5
N=5 N=10 N=15 N=20 N=20 evaporation
Q=15 MJ/m2, =5 ms, = 5 cm
Su
rfa
ce
po
sit
ion
(m
m)
Distance along target (cm)
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
Those results need some appropriate systematization
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
4 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
• 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)
Plasma gun QSPA-T, p=2.4 barQ = 0.5-2 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
KH KH ||3 pp
w
U f V
KH KH 2||
5p p
D gV
In the KH-model the droplet velocity U and the droplet size D are given by
In QSPA-T:
plasma velocityV||p ~ 102 km/s
plasma density p ~ 20 mg/m3
ITER parameters: V||p~300 km/s, p~0.1 mg/m3
I.e. Vm1 m/s, Dm 0.5 mm. Dm>0.1 m means:below splash-threshold.Thus the splashing in ITER is not probable
Dm Vm
W splashing: QDPA-T experiments and extrapolation upon ITER
Inclined plasma impact(a standalone 2D gas-dymamics code, B=0)
Traces of droplets, Qthr=1.2 MJ/m2
Fitting the KH-model to the experiment: fKH = 0.4 and gKH = 0.6 (W = 2 J/m2)
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
5 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
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 JB 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.
Influence of tangential pressure on Li surface solid and molten Li behave similarly(1 mbar, Tmelt = 450 K)
Crater depth vs. cross-current on Li layer (B = T, 1 ms)
Crater depth vs. tangential pressure (At crater depth above 40 µm, W outcrops)
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
6 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
Modelling with ENDEP and MEMOS of melting damage caused by runaways
Main features of the code ENDEP :• Diverse mechanisms of slowing down
of relativistic electrons in target bulk
• Applied magnetic field
• Secondary avalanche processes
(B. Bazylev et al., ICFRM-14, Sapporo, Japan)
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)
Distribution of energy deposition
Absorbed energy fraction vs. E/E
MEMOS Ref. scenario: Q = 20 MJ/m2, Tw0 = 500 K, t = 0.1 s
Main results:
• Evaporation 70 m (hvap)
• melt pool 0.5-0.7 mm (hmelt) (w/o vaporization 2 mm)
• Weak dependence of hvap and hmelt on E/E
Melt layer gets thicker with Q and thinner with t
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
7 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
W cracking: QSPA-Kh50 experiments and PEGASUS simulation
Mesh of cracks after W irradiation after many shots. Crack pattern does not change.
In QSPA experiments W surface melts (Q = 0.75 MJ/m2) or not (0.45 MJ/m2)
Crack average width vs. shot number
Experimental results:
• Crack width grows up with shot number
• At large shot numbers the width saturates.
• Maximum crack width:
• 0.75 MJ/m2: 60 m
• 0.45 --“-- 7 m
With surface meltingQ = 0.75 MJ/m2
Without melting Q = 0.45 MJ/m2
S. Pestchanyi et al. To be presented at ICFNT-9, Dalian, China
Earlier PEGASUS simulated armour cracking above melting thresholdNow the code simulates below melting thresholdTo achieve it, plasticity thermosetress was implemented in the thermomechanic model of the code
Theoretical background: the Kelvin-Voigt model:
1u
Eut
max~ 1 expt
uE
E
~ 10 Mpa, ~ E ~ 1 GPa, ~ 50 s MPa
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
8 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
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).
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)
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
9 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
Simulation of Massive Gas Injection with the code TOKES
Cadarache 23.04.09
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
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
I. Landman et al. To be presented at ICFNT-9, Dalian, China
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:
Initial Be wall temperature 500 K
inj
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
10 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
Previous models used in TOKES
Validation of TOKES radiation model
0D model allows detailed ionization and radiation losses cooling time versus max
Spatial profiles of Ne-ion density at different time moments and initial ne
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
11 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
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.
Example of ITER MGI simulation (G=Ar):
Density distribution of neutral Ne-atoms
2 ms
Min triangle size ~ 0.5 cm
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
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
12 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
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
Comparison of TOKES simulation with DIII-D argon experiment 2007
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.
Cooling in TOKES is 2 times faster than that in DIII-DThe 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
E.M. Hollmann et al.,Nucl. Fus. 48 (2008) 115007
DIII-D size:a=0.5 mBt = 2.1 TIp=1.5 MAq95=3.5Te0=2.5 keVne0=5×1019
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
13 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
Wall temperature near X = 10.8 m for ITER Wall radiation flux Qrad for ITER
Summary for ITER modelling
The results for ITER : Maximum temperature of Be wall surface during MGI
2 ms 8 ms
Neutral neon in vessel:max =7x1025 at/sinj = 5 ms
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
14 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
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-07-02 1.5 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.
KIT - Die Kooperation von
Forschungszentrum Karlsruhe GmbH
und Universität Karlsruhe (TH)
15 EFDA SEWG meeting, Ljubjana 1-2 Oct 2009I.S. Landman
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 JB 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)
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