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Analiza zjawisk termo-hydraulicznych
w kablu nadprzewodnikowym typu CICC
z centralnym kanałem chłodzącym
dr inż. Monika Lewandowska
Plan seminarium
• Wprowadzenie
– Cable in Conduit Conductors (CICC’s)
– CICC’s w tokamaku ITER
– Istota zjawiska termosyfonu
•
•
•
•
Charakterystyka badanej próbki
Opis eksperymentu
Wyniki
Perspektywy
Cable in Conduit Conductors (CICC’s)
Scheme of the early CICC proposal
Bundle
Modern realizations of
CICCs to be applied
in magnets for fusion
technology
Hole
Przekrój typowej żyły kabla
nadprzewodnikowego typu CICC
The ITER project
• International
Thermonuclear
Experimental
Reactor
• Aim: produce energy from
nuclear fusion
• High magnetic field (11 T) to
confine the hot plasma
• Heavy heat loads on the coils
due to neutron flux
CICC’s mandatory!
CICC’s in ITER
Central Solenoid: 1152 Nb3Sn
Strands, 13 T, 45 kA
Toroidal Field Coil: 900 Nb3Sn
+ 522 Cu Strands, 68 kA, 11.3 T
Poloidal Field Coil: 1440 NbTi
Strands, < 45 kA, < 6 T
Gravity-buoyancy effect in a dual
channel CICC
In a vertically oriented dual channel CICC
with the coolant flowing downward, power
deposition in the bundle region causes the
reduction of the flow velocity due to the reduced
density of helium. Eventually, the back-flow
can occur, leading to quench.
Charakterystyka badanego kabla
(ITER TF)
Supercond. strands
Sub cable
Sub-cable wrap
Central spiral
Final cabling stage
Bundle void fraction
Cable jacket
ø 0.82 mm, 2 μm Cr plating, Cu/nonCu = 1
(2 sc + 1 Cu)×3×5×5 strands + 3×4 Cu core
Single layer 70 μm steel foil, ~50% coverage
Inner/outer ø 7/9 mm, 30% open surface
6 wrapped sub cables, 443.3 mm twist pitch
0.332
Inner/outer ø 40.5/43.7 mm, 316 LN steel
Schemat
oprzyrządowania
próbki
Fotografie oprzyrządowania próbki
Experimental setup
SULTAN = SUpraLeitende TestANlage
= Test facility for superconductors
Supercritical He:
Tinlet = 4.5 K or 6.5 K
pinlet = 1 MPa
mmax = 10 g/s
Typical set of raw data
7,8
T in
T0
TL1
TR1
TL2
TL3
TL4
TR4
TL5
TL6
TR6
TL7
TR7
T8
T out
7,2
7,0
6
6,8
1,5
1,0
6,6
0,5
6,4
6,2
0
200
400
600
800
time [s]
1000
1200
1400
5
0,0
Heater current [A]
7,4
2,0
mass flow rate [g/s]
7,6
Temperature [K]
2,5
7
Results
• We measured and analysed the temperature
deviations from the 1D model, which assumes
homogenous temperature in every cross
section n
• After a heated region the deviations ΔT
disappear exponentially with distance.
• The magnitude of ΔT is proportional to the
heating power per unit length and inversely to
the mass flow rate.
• ΔTmax may be readily estimated from the
obtained results.
R.Herzog, M.Lewandowska, M.Calvi, M.Bagnasco. C.Marinucci, P.Bruzzone, Helium
flow and temperature distribution in a heated dual channel CICC sample for ITER,
accepted for publication in IEEE Transactions of Applied Superconductivity
Assessment of the helium velocity in the
cooling channel and in the bundle
4.46
vH was estimated from the
time delay between the
rising edges of spot heater
SHa current and TRa
readings.
0.6
0.2
4.44
0.0
34
36
38
40
time (s)
42
44
46
48
SHa3 current (mA)
Tra2 (K)
0.4
Friction factor correlations
Hole
Bundle
• ITER DDD
• ITER DDD
f Eu H 0.45Re H0.034
f Eu B
• Zanino
h
h
Re H
Dh H
fUS H / 2
R(h ) 11.88 h
R(h )
0.742
19.5
0.0231
0.7953
Re
B
• Katheder
1
2
f H US
0.039
g
h
0.299
2h
2.5 ln
Dh H
3.75
h – spiral height, w – width, g – gap
R. Zanino, et al., IEEE Trans. Appl. Supercon. 10 (2000)
1066-1069
f Eu B
1 19.5
0
.
051
0.72 Re B 0.88
• Porous medium D-F
fUS B a / Re B b
• Porous medium A
fUS B a / Re B b / Re0B.14
H. Katheder, Cryogenics 34 (1994) 595–598 [ICEC supplement]
M. Bagnasco, et al, CHATS AS 2008
Hole friction factor: Zanino
vH (ML)
vH (MC)
vH ITER
vH Katheder
vH porous D-F
vH porous A
vB (ML)
vB Katheder
vB ITER
vB porous D-F
vB porous A
velocity (cm/s)
80
60
40
20
Hole friction factor: Zanino
TFS-07W1 data
Katheder
Porous medium D-F
ITER DDD
Porous medium A
400
200
0
0
0
4
8
total mass flow rate (g/s)
vH porous A
vB Katheder
vB ITER
vB porous medium
60
4
8
total mass flow rate (g/s)
12
600
pressure gradient at 4.4 K (Pa/m)
80
0
12
Hole friction factor: ITER DDD
vH (ML)
vH (MC)
vB (ML)
vH Katheder
vH ITER
vH porous DF
100
velocity (cm/s)
Pressure drop
and helium
velocity in TFS
experimental
data and
simulation
600
pressure gradient at 4.4 K (Pa/m)
100
vB porous A
40
20
Hole friction factor: ITER DDD
TFS-07W1 data
Katheder
Porous medium D-F
ITER DDD
Porous medium A
400
200
0
0
0
4
8
total mass flow rate (g/s)
12
0
4
8
total mass flow rate (g/s)
12
Pressure drop and flow velocities
experimental data and final model
80
TFS-07W1 data
Hole: 0.75*ITER DDD
Bundle: 0.73*Katheder
400
Hole: 0.75*ITER DDD
Bundle: 0.73*Katheder
vH (ML)
vH (MC)
vB (ML)
vH model
vB model
60
velocity (cm/s)
pressure gradient at 4.4 K (Pa/m)
500
300
200
40
20
100
0
0
0
4
8
mass flow rate (g/s)
0
12
m B
f (m total )
m total
4
8
mass flow rate (g/s)
12
Heat transfer in the ITER TF conductor
Stationary two-channel model
TH
phBH TB TH
x
TB
m B C p
phBH TH TB Q
x
temperature in the cooling hole
m H C p
temperature in the cable bundle
P / L 0 x L
Q( x)
xL
0
C p C p Tref , pref
Tref Tin P /(m totalC p )
TB
TH
mH
mB
Constant thermophysical parameters
phBH
Analytical solution
TB TB ( x, hBH )
hBH
TH TH ( x, hBH )
B.Renard, et al , Evaluation of thermal gradients and
thermosiphon in dual channel cable-in-conduit conductors,
Cryogenics 46 (2006) 629-642
Average heat transfer coefficient
between bundle and hole
1000
hBH (W/(m2K))
800
TFS
600
400
200
0
0
4
8
Total mass flow rate (g/s)
12
C. Marinucci, et al, Analysis of the transverse
heat transfer coefficients in a dual channel ITERtype cable-in-conduit conductor, Cryogenics 47
(2007) 563-576
Temperature profiles along the sample
experimental data and simulation
2.5
1.5
1
1
0.5
0
0
1
2
x (m)
3
P=4W
P = 10 W
P = 20 W
P = 30 W
P = 41 W
P = 51 W
1.5
0.5
0
Heaters H1+H2
2
T (K)
P=2W
P=6W
P = 10 W
P = 20 W
P = 30 W
P = 40 W
P = 50 W
2
T (K)
2.5
Heater H2
4
0
m total 8 g/s
hBH 535 W/(m2 K)
1
2
x (m)
3
4
Thank you for your attention