KIT - Die Kooperation von Forschungszentrum Karlsruhe GmbH und Universität Karlsruhe (TH) 1 EFDA...

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





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, …





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 )


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)


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





• 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)





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)





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





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





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)





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





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





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





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





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





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.





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)

KIT - Die Kooperation von Forschungszentrum Karlsruhe GmbH und Universität Karlsruhe (TH) 1 EFDA...

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