Transcript How could be foreseen the tritium mass transfer - pressure dependence and other parameter to take into account in modeling

IEA Implementing Agreement on Nuclear Technology for Fusion Reactors
Liquid Breeder Blankets Subtask
Coordinating Meeting on R&D for Tritium and Safety Issues in Lead-Lithium Breeders
11-12 June 2007, Idaho Falls, ID, USA
How could be foreseen the tritium mass transfer
F. Gabriel 1, O. Gastaldi 1(presenter), L. Sedano2
(1 CEA, 2 CIEMAT)
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The TBM objectives
Demonstrate the capacity of tritium extraction while mastering
its inventory
– efficient technological components
– efficient remote control
– understanding the physical and chemical phenomena and their
interactions
– capitalize these knowledge in software tools
Knowledge modelling is required in order to represent in a
reliable way the different phenomena (in particular T mass
transfer phenomena)
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Recall of the needs in term of tritium management
Prediction capabilities of tritium transport modeling tools for
tritium transport simulation analyses is a major scientific
technical goal of fusion nuclear technology for ITER-TBM:
– To help the designer and optimize the technical choices
– To better understand future experimental tests
– To answer to safety concerns :
• Inventories prediction (help for accountancy methods)
• Tritium release estimation
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Understanding of T transport phenomena
Many phenomena could have an impact on tritium mass
transfer from LLE to helium coolant:
–
–
–
–
–
–
–
–
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Level of solubility
MHD impact of velocity profile,
Impact of He bubbles contained in PbLi (transfer to gas phase)
Boundary layer resistance
Diffusion under irradiation
Interface phenomena (sorption – desorption)
Isotopic swanping effect
…
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Understanding of T transport phenomena
Many phenomena could have an impact on tritium mass
transfer from LLE to helium coolant
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Different levels of modeling
Two complementary type of tools
– System analyses (ODE system – component = 2 inlets, 2
outlets and a transfer function)
•
•
loop control (main tritium rates, inventory)
global sensitivity analysis
– Component analysis (PDE system – multiphysics analyses)
•
•
•
qualification of the transfer function
local analysis and component optimization
model validation
Development of reliable system tools, a good knowledge of
phenomena is needed
In case of lack of knowledge, refined models associated with
analytical experiments are needed
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System approach tools developed in EU
Helium circuit
PbLi circuit
CTOUT _ TES
Development of
engineering tool (system
approach) based on
CTIN _ TES
– Steady state
– Fick’s law
– Simplified components
description
– Using mean values
DPbLi
T
E
S
2
1
FW
F
3FW
3CP
3SP
CP
SP
80 %
20 %
DHé
CTHé_ Moy
It allows to:
– Lead sensivity studies
– Determine what are the
major parameters (on
which priority must be
put in term of R&D)
f = Fuite
4
DHé
DCPS
CPS
GV
5
DSlip
Water
CTEau
2
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System approach tools developed in EU
Example of result:
25
100
10
15
10
1
5
0
0
0.1
100
50
PRF Blanket
Outgoing T flux (g/year)
g/an
T inventory in PbLi (g)
T inventory in He (g)
Except at the beginning of the range, quite progressive gain
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T inventories in loops (g)
Outgoing T Flux (g/year)
20
System approach tools developed in EU: TRICICLO
TRICICLO: system tool
Non –linear, (self)-coupled, multiparametric problem. (at a larger
scale)
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System approach tools developed in EU: TRICICLO
“Moving-slab” technique for tritium transport transient computation in
HCLL channel (unit symmetry from BB segmentation)
g ( y) 
g  L  4.5
 exp( 4.5  ( L  y ))
1  exp( 4.5  L)
SOURCE
V  A  Bc( x, y  dy, z )  c( x, y, x)  DIFF. BALANCE
 A  B  g ( y )dy  B  CP ( x, y, z  0)  dy  2SP ( x  0, y, z ) A  dy
LOCAL FLUX EXPRESSION
CP ( x, y , z  0) 
 cST ,CP ( x, y , z  0)




z
 DST ,CP 


T
(
x
,
y
,
z

0
)
Q
(
T
)


ST ,CP
 cST ,CP ( x, y , z  0) kT 2

z
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System approach tools developed in EU: TRICICLO
Simplified (reliability of the MODEL?) but TRANSIENT.
Main hypothesis:
– Diffusion (Fick’s law).
– No bubbles in Pb-Li (possible to be taken into account by an
apparent Pb-Li higher T solubility in Pb-Li).
– MHD drag transport take in a very simplified way (apparent
i.e.: reduced radial diffusivity).
– Interfacial resistance (He-film) can be endorsed in the model
(as a PRF of a barrier).
– Radiation effects in the steel (as factors in Diff. & Solub.).
– Accounting of isotopic swamping possible (Walbroek
theory).
– Dynamic accounting of gas chemistry criteria (oxidation
threshold) on EUROFER and INCOLOY for surface
characteristics.
– Precise sizing of INCOLOY 800 Steam Generator and
dynamic transfers (in surface limiting regimes through).
– CPS, TES, TRS transfers in/out with system efficiencies (DF
factors)
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System approach tools developed in EU: TRICICLO
Example of results:
– assessment of macroscopic behaviour
– But also sensitivity analysis
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System approach tools developed in EU: TRICICLO
Illustration of potential discussions on hypothesis: basic
controversial (unknowns ?) to write to express some fluxes.
ISOTOPIC SWAMPING:
H´-p.p.
H-p.p.
T-p.p.
BB
HCS
T-FLUX
Does T-flux vary with H-pp. or H´-pp. ?
Quantit. dependences on T., H, H’ pp ?
Isotopic effects would play on BBPC and PCSG fluxes
Experimental data on isotopic swamping is poor.
Dependencies from the Theory on Isotopic effect on transport in
[F. Waelbroek, Jül 1966, Dez. 1984 ] for gas-gas problems assumed.
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System approach tools developed in EU: TRICICLO
 ISOTOPIC SWAMPING EFFECTS: DIFFERENT SITUATIONS
HCLL
[F. Waelbroek, Jül 1966, Dez. 1984 ] pp. 109
CO-STREAM ISOT. SWAMP.
• Large permeation numbers
(diffusion-limited regimes)
for H and T
T-FLUX swamped a factor
T-FLUX
GAS
GAS
• Low permeation numbers
(surface-limited regimes)
for T & large for H
T-FLUX swamped a factor
 ( pH 2 ) ( f )
 ( pH 2 ) ( f )
• Large permeation numbers
(diffusion-limited regimes)
for H and T
HCPB
COUNTER-STREAM ISOT. SWAMP.
T-FLUX swamped factor
T-FLUX swamped a factor
 4 ( pH 2 ) (b )
 4 ( pH 2 ) (b )
T-FLUX
GAS
GAS
• Low permeation numbers (surface-limited regimes) for H and T co-/counter-stream
1
No effect
 STEADY STATE ISOT. SWAMP. MODEL IMPLEMENTED IN TRICICLO
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System approach tools developed in EU: TRICICLO
Uncertainties on Isot. Swamp. for TRICICLO
– Basic theory and experimental database for gas-gas mixtures.
– It is uncertain how a low solubility media (LM) in (f) position can
reduce H flux- back minimizing isotopic swamping effects.
– Isotopic swamping effects if taken into account should be
coupled with presence of permeation barriers and/or EUROFER
oxidation conditions (as it is tentatively done in TRICICLO tools) .
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Refined models – an illustration
General issue: The tritium concentration in the He and in the Pb-15.7Li are
evaluated by solving partial differential equations governing the tritium balance,
the thermal field and the velocity field in a simplified 2D geometrical
representation of the breeder unit at the mid equatorial plan.
Objective: evaluate the sensitivity effect of the Pb-15.7Li velocity profile on
engineering outputs 3, and Cf for the inboard and outboard equatorial
modules
HCLL Blanket modules
mLiPb
3
FW
LiPb
purification
1
Pump
2
LiPb Tritium extraction
from LiPb
GPbLi
Steam
generator
4
air
purification
5
He
He purification
GHe
Secondary circuit
QHe
mHe
Blower
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Refined models – an illustration
 Heat source and tritium source from Monte
free
Carlo analysis,
or
 Boussinesq approximation,
u (rmin , p)  u
 Inductionless MHD approximation,
 Inboard magnetic field = 10 T,
 Outboard magnetic field = 5 T,
 (rmin , p)   a
 Toroidal magnetic field,
 (rmin , p)  a
u (rmin , p)  u
 Perfect conductor side walls,
c(r
, p)  Ca
 Limited diffusion regime for the tritium, min
 Permeation Reduction Factor = 1,
 Steady state.
 (r, p)  ar  b
c(r, p)  0
Cl
Kl

Cw
Kw
 0
Inlet a)
Outlet a)
 (rmax , p)  in
 (rmax , p)  0
u ( rmax , p)  u
c( rmax , p)  (1   ) C f
 (r, p)  ar  b
c(r, p)  0
Cl
Kl

Cw
Kw
 0
Inlet b)
Outlet b)
free
or
u (rmin , p)  u
c(r, p)  0
 (r, p)  ar  b
A’
Breeding zone cell
A
LiPb inlet
B’
Horizontal
stiffening plate
LiPb outlet
LiPb
Breeding
distribution
zone
box
column
Engineering Outputs:
Cw
3  Dw dy
y

wall

Cf 
B
u C f dy
outlet b

C f dy
3
r
1
outlet b
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Refined models – an illustration
Sensitivity analysis based on the identification of the parameters of the
a
a
a
response surface
y ( X BC , X NC )  a0 (1  1 X BC  2 X NC  3 X BC X NC )
a0
a0
a0
XBC = choice of the fluid boundary condition
XNC = choice of the natural convection
Temperature distribution (°C) – B = 10 T
FW
a0
a1/a0 %
a2/a0 %
a3/a0 %
3 (g.m-2d-1) – 5 T
2.93 10-3
-0.08
-0.66
-0.10
Cf (mol m-3) - 5 T
0.0454
-0.10
0.26
-0.08
r (%) – 5 T
21.16
-0.08
-0.66
-0.10
B’
3 (g.m-2d-1) – 10 T
2.94 10-3
0.015
-0.21
-0.005
B
Cf (mol m-3) - 10 T
0.0453
- 0.023
0.066
-0.013
r (%) – 10 T
21.25
0.014
-0.21
-0.005
A’
A
Tritium concentration (at m-3) – B = 10 T
22
22
upper channel concentration profile
x 10
lower channel concentration profile
x 10
2
3.5
-4
u lower channel velocity profile
x 10
0
3
10
NE 2 - 10 T
1.6
NE 2 - 10 T
1.4
NE 2 - 5 T
NE 2 - 10 T
2.5
NE 2 - 5 T
NE 4 - 10 T
-0.2
NE 2 - 5 T
NE 4 - 10 T
1.2
2
1
8
NE 4 - 5 T
NE 4 - 10 T
NE 4 - 5 T
NE 4 - 5 T
at m - 3
-0.4
6
NE 2 - 10 T
NE 2 - 5 T
0.8
0.6
m s-1
1.5
m s-1
at m - 3
-5
u upper channel velocity profile
x 10
1.8
-0.6
NE 4 - 10 T
4
NE 4 - 5 T
1
0.4
-0.8
2
-1
0
0.5
0.2
0
0
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0
0.005
0.01
0.015
0.02
0.025
meter
meter
a) along AA’
b) along BB’
Concentration profile
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0.03
0.035
0.04
-1.2
-2
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0
0.005
0.01
meter
0.015
0.02
0.025
0.03
0.035
meter
a) along AA’
b) along BB’
Radial velocity
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0.04
Refined models – an illustration
Results:
– In the inboard and outboard equatorial HCLL modules
within the above listed assumptions, the permeation rate
towards the He circuit, the mean outlet tritium concentration
and the ratio of the permeation rate to the production rate
are almost insensitive to the magnetic field
– A concentration boundary layer is developed and could be
regarded as an equivalent Permeation Reduction Factor of
30 (which was not considered in the previous tritium
permeation estimations).
– Such results can be integrated in the system approach tools
as PRF
But even with refined model it is needed to solve some
persistent lacks of knowledge and uncertainties by
experimental campaign
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Many uncertainties and persistent lacks
Data lacks (persistent)
– Materials databases:
• Pb-15.7Li properties (like T solubility),
• Radiation spectral effects on T-transport properties in
EUROFER (& coatings)
– Base phenomena with large potential effect on T-transfers
in IBTC
•
•
•
•
•
•
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He-cavitation issues (bubble nucleation impact on tritium)
Validation (or not) of isotopic swamping mechanisms
Soret effect quantification
Trapping models
Coatings impact and associated representation
(He chemistry effects)
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Many uncertainties and persistent lacks
Data lacks (persistent)
– Systems definition and system parameter unknows.
• Key technological choices: Power Conversion System (SG)
for the IBTC
• Unknown dependencies: Do TES/LM efficiencies depend on
T p.p. ? - H-dopping effect ??? - (CPS, TRS) scaling & DFs
dependencies on (Q2, Q2O) stream p.p. ?
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Many uncertainties and persistent lacks – illustration (Ks)
Pb-Li eutectic alloy proposed in the 70´s with intensive
characterization of base properties work during 80´s in EU labs
(JRC, CEA, KfK) on eutectic (assumed as 83at%Pb-17at %Li).
Practical experience determining H-isotope´s solubility in Pb-Li
alloys shows how the measurement is potentially full of
parasitic effects:
(1) wall impact on solubility ()
(2) uncertainty in the eutectic composition ()
(3) impact of eutectic disproportioning ()
(4) role of M-impurities (¿ ?)
(5) Other ?
LM hydrodynamics (¿-?)
Li vapors and pressure gauge performances (-)
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Many uncertainties and persistent lacks – illustration (Ks)
(1) wall impact on solubility()
- confirmed for some early data
(corrected > 90´s measure: by
coating capsules: Al2O3, W,..),
- [ 2 o.o.m. values ] & wall material
solution activation -Es
(2) uncertainty in the eutectic
composition ()
- See previous presentation
(3) eutectic disproportioning ()
- not systematically checked & driving
potentially to incorrect overestimated
solubility
(in
connection
with
Liaggregation by clustering)
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 (LnK s Pb 17 Li )  1  (at .Li .  (at .Li )eut )
KsLi
(Ks)eut
Deviation from theoretical eutectic composition
[15.7(2)at%Li] at liquid phase and solubility
impact with Li aggregation.
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Many uncertainties and persistent lacks – illustration (Ks)
(4) role of M-impurities (¿?)
Steel corrosion products show high
solubility limits in Pb15.7Li (Ni > Mn > Fe
> Cr).
However, tritium solubility in dominant
(Fe) is comparable (10-8 at.fr. Pa-1/2) to
lower reference solubility data in
Pb15.7Li [Reiter], i.e.: amount of
impurity comparable to that of
measured eutectic.
In this sense, even for unprotected
samples and conservatively high
corrosion rate values for (cm s-1)
thermo-convection velocities (10-100
mg m-2 h-1), impurity impact can be
assumed as negligible.
Solubility limits for FM corrosion
components (Fe, Ni, Mn, Cr) in Pb-Li
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Many uncertainties and persistent lacks – illustration (Ks)
Two kinds of techniques have been used:
Results:
Hot Absorption (HA) techniques: gravimetric (HA-g) or
pressure drop (HA-p) versions,
Isovolumetric Desorption (ID) (desorbed gas pressure
evolution after absorption)
HA-g (o.o.m higher than actual
solubility values and no Sievert´s
law) ABANDONED.
First HA-p measurements shown first
Sievert´s dependencies and lower
values (> 1 o.o.m)
ID techniques seem to be as most
performant methode for measuring
Sievert´s
constant
and
a
refinement of HA-p methodes.
 Allows checking reversibility between absortion & desorption (key issue)
 can neutralize possible role of LM hydrodynamics
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Development plan
First step:
– Exchange on the way to represent the main transport
phenomena of tritium in LLE
– Establish a common basis of knowledge
– Prioritize the main issues in order to cover the lacks of
knowledge
– Develop experimental program in order to solve them (using
shared procedure and/or using cross checking)
Second step :
– Develop one (or several (depending on the objectives)) open
tool(s) for T transfer modeling
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Development plan of the tool – What is the need?
Potential users :
Design Engineer
 component simulation (validated models)
 sensitivity analysis
 complex meshing
 important CPU time
 user-friendly interface
 Physicist
 model validation
 experiment design
 interpreted language (easily model
implementation)
 numerical tools access
 Numerician
 software improvement
 basic programming level
 object-oriented language
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Development plan of the tool- How could we built it?
 Basic facts
 not really a commercial tool
 not that much users
 quite complex physics
 Shared development
 open access CFD based tools
 development divided among partners
 A team will integrate all developments in a QA
version
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Development plan - Preliminary road map for the 1st tool
 needs specification
 analysis of needs
 specification of criteria
 selection of a software
 research of potential software
 assessment of bests
 development of our application
 model implementation
 benchmark evaluation
 Experimental program
 in order to reduce data lack
 qualification of codes
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Conclusion (1/2)
Main issues to solve are:
– Permeation modeling
•
•
•
•
•
•
isotopic swamping
surface model
trapping model
coating and interface models
He chemistry effects
experimental validation
– Multiphysic analysis and validation
– He bubbling effect
– Constitutive law [C = f(P)]
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Conclusion (1/2)
Main issues to solve are:
– Permeation modeling
•
•
•
•
•
•
isotopic swamping
surface model
trapping model
coating and interface models
He chemistry effects
experimental validation
With or without
irradiation
– Multiphysic analysis and validation
– He bubbling effect
– Constitutive law [C = f(P)]
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Conclusion (2/2)
Main points to treat within the collaboration program:
– Definition of common way to describe phenomena in modeling
tools (benchmarking of the different available codes)
– Definition of specific experimental tests in order to obtain main
parameters of models
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Support to the discussion
Fundamental points:
– Establishment of a common database
– Definition of common LLE specifications with QA procedure for
its manufacturing – EU can propose some specifications (to be
discussed)
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Support to the discussion
For each issues what could proposed:
– Permeation modelling
•
•
•
•
•
•
isotopic swamping
surface model
trapping model
coating and interface models
He chemistry effects
experimental validation
– Multiphysic analysis and validation
– He bubbling effect
– Constitutive law [C = f(P)] – Sievert constant determination
What are the reference laws for these phenomena?
– What is the level of reliability?
– Which kind of experiments do we need to complete it?
– Is there existing facility or analytical bench able to do so?
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