Presented by Sergey Smolentsev (UCLA) with contribution from:
B. Pint (ORNL)
R. Munipalli, M. Pattison, P. Huang (HyPerComp)
M. Abdou, S. Saedi, H. Zhang A. Ying, N. Morley, K. Messadek (UCLA)
S. Malang (Consultant, Germany)
R. Moreau (SIMAP, France)
A. Shishko (Institute of Physics, Latvia)
Fusion Nuclear Science and Technology Annual Meeting
August 2-4, 2010
UCLA

• Status of R&D on development of MHD/Heat & Mass
Transfer models and computational tools for liquid metal blanket applications
• Examples : corrosion & T transport
OTHER RELATED PRESENTATIONS at THIS MEETING
TITLE Presenter Oral/Poster
Tritium Transport Simulations in LM
Blankets
Modeling Liquid Metal Corrosion
Integrated Modeling of Mass Transport
Phenomena in Fusion Relevant Flows
H. Zhang
UCLA
S. Saedi
UCLA
R. Munipalli
HyPerComp oral poster poster

Mass transfer in the LM flows is one of the key phenomena affecting blanket performance and safety
Traditionally, major considerations associated with the LM flows are the
MHD effects . But there are more….
Tritium permeation is an issue – no solution has ever been proven
Corrosion/deposition severely limits the interfacial temperature and thus represents an obstacle to developing attractive blankets at high temperature operation
Blanket: “Hot” leg. Mass transfer coupled with MHD. Corrosion. T production. T leakage into cooling He. Formation of He bubbles in PbLi and trapping T.
Ancillary system: “Cold” leg. Turbulent flows. Wall deposition and bulk precipitation.
T leakage into environment. T extraction. Cleaning up.

Blanket:
• Revisit maximum PbLi/Fe t (470 
?) and wall thinning (20
 m/year ?)
• Estimate T leakage into cooling He streams in the blanket
Ancillary system:
• Estimate T leakage into environment
• Model T extraction processes
• Model clogging/deposition
• Model clean up processes
Phenomena, design:
• Address “new” phenomena (i.e. He bubble formation in PbLi and trapping T by the bubbles)
• Find new design solutions/modifications
Challenge!
The whole PbLi loop, including the blanket itself and the ancillary equipment, must be modeled as one integrated system

• New phenomenological models for :
interfacial phenomena
- nucleation/crystallization
- particle-particle/wall interaction
- MHD effects on mass transfer
- T transport physics He bubble transport and trapping T by the bubbles is not well understood
• New material databases (He-T-PbLi)
• New mass transfer solvers and their coupling with existing MHD/Heat Transfer codes

• HIMAG as a basic
MHD/Heat Transfer solver
• Many UCLA research
MHD, Heat & Mass transfer codes
• CATRIS (in progress) as a basic mass transfer solver
• Many thermohydraulic / mass transport codes
The R&D on the development of new phenomenological models and their integration into numerical codes is underway

1. Dilution approximation, C i
< C i0

C i
 t

( V

) C i
 
( D C i i
)
 q i
2. Lagrangian particle tracking, C i
> C i0
 p
V d V p dt
 k
K 

1
F k
3. Multi-fluid model, C i
>> C i0
  i
 t
   i
V i
 j
N 

1
J ij
 
V i i
 t
  k
 i
V i
V i k   k σ i k   i g  j
N 

1
P ij

Example
#1
Riga experiment
#2
Tritium transport
#3
Magnetic trap
#4
Sannier equation
Description
Modeling of “corrosion” experiment in
Riga, Latvia on corrosion of
EUROFER samples in the flowing
PbLi at 550
 in a strong magnetic field
Numerical analysis of tritium transport in the poloidal flows of the DCLL blanket with SiC FCI under DEMO blanket conditions
Modeling of extraction of ferrous material suspended in the flowing liquid in a magnetic trap
Modeling of corrosion of ferritic/martensitic steels in turbulent
PbLi flows to reproduce existing experimental data and to address the effect of a magnetic field
Modeling status
Good match with experimental data on mass loss. Addressing groove patterns needs more sophisticated modeling.
Analysis for the front duct of the
DCLL DEMO OB blanket has been done using a fully developed flow model.
First “demo” results have been obtained using Lagrangian particle tracking model under some assumptions for B~ 0.1 T.
In progress. Computations are performed using the UCLA corrosion code (Smolentsev).
Turbulence in a magnetic field is modeled via “k-eps” model.

setup
Simulation of “CORROSION” EXPERIMENT in Riga
PbLi loop
EUROFER samples
B=0, B=1.7 T
T=550

C
U=2.5 cm/s, U=5 cm/s
Time=2000 hours
Rectangular duct, 2.7x1 cm 2
Courtesy of Dr. Andrej Shishko, Institute of Physics, Latvia
Two 12-cm sections of 10 samples in a row, one section at B=0 and one at
B=1.7 T

results
Mass loss, mg
U o
=2.5 cm/s U o
=5 cm/s
Macrostructure of the washed samples on the Hartmann wall in 3000 hrs at 550

B=0 B=1.7 T
9
10
6
7
8
#
1
2
3
4
5
B=0,T
376
245
303
193
223
257
163
198
B=1.7,T
593
564
481
486
456
440
483
484
B=0,T
437
338
330
283
251
248
-
310
B=1.7,T
743
757
623
605
506
482
-
512
214
205
566
502
321
314
463
474
Mass loss is almost doubled in the presence of B-field
PbLi flow
Courtesy of Dr. Andrej Shishko, Institute of Physics, Latvia

results
~40
 m
FLOW
~ 500
 m
•Wall thinning: 1.5->1.4 mm
•Grooves: 40  m deep
Courtesy of Prof. Rene Moreau (SIMAP, France)
• In addition to wall thinning, periodic grooves aligned with the flow direction have been observed on the Hartmann wall
• Mechanism of groove formation is still not well understood
• A. Shishko (Latvia): higher velocity in the surface cavities causes higher corrosion rate.
The effect may be related to specimen machining
• R. Moreau (France): the grooves are due to instability mechanism associated with induced electric currents crossing the interface

mathematical model
Basic assumptions
• Fully developed, laminar flow
• Only Fe is considered
• Purely dissolution mechanism
• No oxygen passivation layer
• Mass transfer controlled corrosion
• Zero Fe concentration at x=0
Two BC types have been tested
(C
0 is the saturation concentration at given t)


2 z
U U
2



2 y
2

B
0

0


2 z
2



2
B B y
2
 
B
0 0

B
 z

U
 z


1

0 dP dx

0 z
  b : U

0, y
  a : U

0,
1

1


B
 z

B
 y

1 B
 t w w


1 B w t w

0

0
U

C
 x

D (
 2
 x
C
2



2 y
C
2



2 z
C
2
) x

0 : C

0 z
  b : D y
  a : D

C
 z

C
 y


(
0

C )

0
(
0

C )

0 or C

C
0 or C

C
0

material properties *
• Diffusion coefficient Fe-PbLi:
6.4E-09 m 2 /s **
• Saturation conc. C
0
: 6.26 g/m 3 ***
• PbLi viscosity: 1.08E-07 m 2 /s
• PbLi density: 9300 kg/m 3
• PbLi electrical conductivity:
0.7E+06 S/m
• Ha= 0 and 227.3 (1.7 T) ; C w
= 0.78
;
Re= 1157 and 2314
* At 550

C
** Based on equation of Sutherland-Einstein
*** Recommended by Riga people (=0.676 wppm).
100
Solubility of Fe in PbLi
0.1
0.01
10
1
Solubility experiments
Barker et al., 1988
Borgstedt et al., 1991
Grjaznov et al., 1989
Riga group, 2006
0.001
0.0001
1E-005
600 650 700 750 800 850
T, K
C o
: more than THREE order of magnitude difference ???

modeling results
B=1.7 T, Cw=0.78, U=2.5 cm/s
0.05
B=0, U=2.5 cm/s
0.04
B=0, U=2.5 cm/s
0.03
0.02
0.01
B=1.7 T, U=2.5 cm/s
0
-0.005
-0.003
-0.001
0.001
0.003
0.005
Z, m

modeling results
MASS LOSS: comparison with the experiment
BC : D

C
 n

(
0

C )

0
Riga group: C
0
=6.26 g/m 3 , K=4.27E-05 m/s
430
215
BC : C

C
0
Konys: 700
 m/year
500

C, 0.22 m/s, 0T
Grjaznov et al: C
0
=3.25 g/m 3

modeling results
Effect of the velocity and B-field on the wall and bulk concentration
BC : D

C
 n

(
0

C )

0
Riga group: C
0
=6.26 g/m 3 , K=4.27E-05 m/s

modeling results
Effect of the velocity
- no magnetic field
- Hartmann wall
Effect of B-field
-Hartmann wall
Wall effect
- with magnetic field

modeling results
Development length > 10 m (B=1.7 T, U=5 cm/s)
Wall concentration
Bulk concentration
BC : D

C
 n

(
0

C )

0
Riga group: C
0
=6.26 g/m 3 , K=4.27E-05 m/s

conclusions
• Riga experiment on EUROFER-PbLi corrosion has been successfully modeled (not including grooves)
• Higher corrosion rate of EUROFER samples in a presence of a magnetic field can be explained by the steep velocity gradient in the Hartmann layer
• Boundary condition at the solid-liquid interface is still an open issue. Saturation concentration at the wall can be used as a first approximation
• Uncertainty in experimental data on transport properties
( e.g.
saturation concentration) severely limits modeling predictions
• If to extrapolate to LM blanket conditions - the mass transfer development length can be more than 10 m

DCLL Geometry (not to scale)
• DCLL DEMO blanket conditions (outboard)
• Poloidal flow in a front duct with a 5-mm SiC/SiC FCI
• HIMAG is used to simulate
MHD flow, assuming fully developed flow conditions
• CATRIS is used to simulate tritium transport in the multi-material domain, including PbLi flow, SiC
FCI and Fe wall
• Goals : ( 1 ) T permeation into He; ( 2 ) sensitivity study
0.3 m
B z
FCI x y
Outflow
Inflow
RAFS wall 5 mm thick y
SiC wall 5 mm thick z
207 mm
231 mm
2 mm gap
211 mm
•Neutron wall loading (peak): 3.08 MW/m 2
•Surface heating: 0.55 MW/m 2
•PbLi Tin/Tout: 500/700

C
•Flow velocity: 6.5 cm/s
•Magnetic field: 4 T
•Inlet T concentration: 0
•T generation profile:
4.9E-09 Exp(-3y), kg/m 3 -s

Pb17Li
Physical properties
RAFS SiC FCI
Solubility mol/m 3 /Pa 0.5
[1,2,3]
0.0005
0.1
D m 2 /s
1.0 × 10 -9
7.0 × 10 -9
Solubility mol/m 3 /Pa 0.5
[4]
0.0025
D m 2 /s
Solubility mol/m 3 /Pa 0.5
1.5
× 10 -8 0.117
D m 2 /s
σ
S/m
[5,6]
5.0
× 10 -16 5
500
Low
High
1.
Mas de les Valls, E., Sedano, L.A., Batet, L., Ricapito, I., Aiello, A., Gastaldi, O., Gabriel, F. (2008) Lead-lithium eutectic material database for nuclear fusion technology . J. Nuc. Mat. 376 , 353-357.
2.
Reiter, F. (1991) Solubility and diffusivity of hydrogen isotopes in liquid Pb-Li.
Fusion Eng. and Design. 14, 207-211.
3.
Aiello, A., Ciampichetti, A., Benamati, G. (2006) Determination of hydrogen solubility in lead lithium using sole device.
Fusion Eng. and Design. 81, 639-644.
4.
Aiello, A., Ciampichetti, A., Benamati, G. (2003) Hydrogen permeability and embrittlement in Eurofer 97 martensitic steel . ENEA Report SM-A-R-001.
5.
Causey, R.A., Wampler, W.R. (1995) The use of silicon carbide as a tritium permeation barrier. J. Nuc. Mat. 220-222 ,
823-826.
6.
Causey, R.A., Karnesky, R.A., San Marchi, C. (2009) Tritium barriers and tritium diffusion in fusion reactors . http://arc.nucapt.northwestern.edu/refbase/files/Causey-2009_10704.pdf
There is a considerable degree of uncertainty in the physical properties, particularly for the solubility of T. That is why sensitivity study is needed.

The electrical conductivity of FCI may have a strong effect on the T transport via changes in the velocity, especially in the 2-mm gap
Side-wall jets in the bulk
Hartmann-wall gap flows

=100 S/m, Ha =15,900
Side-wall gap flow s

T concentration (10 -6 kg/m 3 ) for cases with low (0.001 mol/m 3 /Pa 0.5
) and high (0.05 mol/m 3 /Pa 0.5
) solubility of T in PbLi
X=0.5 m
Low solubility
X=0.5 m
High solubility
X=1.5 m X=1.5 m

Fluxes of tritium through the steel. S= 0.001 mol/m 3 /Pa 0.5
, units are 10 -9 kg/m 2 /s
More T permeation occurs from the
Hartmann gap, where velocity is low
Total tritium loss in the front duct
# D S σ T leak
10 -9 m 2 s -1 %
8
9
10
5
6
7
3
4
1
2
2.54
2.54
2.54
2.54
2.54
2.54
1
2.54
7
2.54
mol m -3 Pa -
1/2
Ω -1 m -1
0.01
0.01
0.01
0.0005
0.001
0.005
0.05
0.1
0.01
0.01
5
50
500
5
5
5
5
5
5
5
1.99
1.65
0.60
0.35
0.36
0.06
1.30
1.40
1.35
2.08
Total T leakage < 2%

• Due to very low diffusion coefficient of T in SiC, FCI can be considered as a T permeation barrier
• All tritium generated in the bulk flow remains there.
Tritium permeation occurs mostly from the gaps, especially from the Hartmann gap, where velocity is very low
• Electrical conductivity of the FCI has indirect effect on T transport via changes in the velocity profile: higher

smaller leakage
• Total T leakage into He can be estimated as 2% of all tritium generated in the blanket (not taking into account pressure equalization openings and 3D flow effects)
• More accurate databases for physical properties are needed