Roser Vallcorba MATEFU Spring Training School April 05-09, 2009
Thermohydraulics in ITER
Point of view of cryogenic simulation
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Contents
� Interest of thermohydraulic analysis for ITER
� Superconducting conductors
� Supercritical Helium
� Cryoplant and cryolines distribution
� Heat load inventory
� Numerical tools for cryogenic simulations
� Simulating magnets: some results
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Why thermohydraulic analysis?
� Main subsystem components: superconducting magnet cryopumps
�18 toroidal field coils (~320 t each)
�1 central solenoid (6 powered modules) ~100 t*6
�6 poloidal field coils
�9 pairs of correction coils (~80 t)
�8 torus cryopumps
� plasma scenario
� hydraulic scenario
CSMC –JAERI courtesy TFMC - FZK courtesy
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�Helium cryoplant
likes operate in steady state
cryoplant
time (s) #cycle
Pow
er (
W)
heat power must be smooth
time (s) #cycle
Pow
er (
W)
�Plasma scenario
variable heat loads, mainly induced by the magnet system itself, by the plasma operations and by the nuclear heating…
cryodistribution
Why thermohydraulic analysis?
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Hydraulic scenario
Complex network:fully-scaled quasi-3D numerical model: thermal diffusion coupled to cooling circuits + superconductors
TF 7 double pancakes
100 helium channels – 32 cross sections
CS 240 pancakes
743 helium channels – 5 cross sections
PF 180 pancakes
597 channels, more than 200 manifolds
72 cross sections
�Large superconducting magnets cooled by forced flow of supercritical helium
3.5 million nodes
TF cross section
6 CS modules
Its main function is to supply users
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main cryo-distribution functions
�cool-down / warm-up all of sub-systems
�normal operation (depending of scenario)
� Control of heat load removal
� Control of smoothing load
� Control of cryopumps regeneration
� Recovery of fast discharge / quench
Supply of cryogenic users
magnets (4.5 K)
cryopumps (4.3 K)
thermal shields (80 K)
ACB
CVB
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system to be cooled under
the plasma scenario
heat exchanger model
2D
1D
The reference plasma scenario: 15 MA, 500 MW, plasma pulse of 1800 s, plasma duration 400s
The cooling mode is a major area, it has a direct impact on the conductor type,
the winding structure and the cryogenic layout
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heat control description
two main loops: casing and winding pack:
The coolant flows from bottom to top
max E field
performances of the heat load control process
Ref. Scenario: Heat Power into the bath - Voff / Von
0
5000
10000
15000
20000
25000
30000
35000
0 1800 3600 5400 7200 9000 10800time (s)
5 plasma pulses
Hea
t Pow
er (
W)
Total power exchange into helium bath (W) - Voff average power 26.1 KW
Control Power : 26.4KW
Total power exchange into helium bath (W) - Von: 26.4KW (mDH method)
Total power exchange into helium bath (W) - Von: 26.4KW (Qconv method)
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superconductors
Critical surface of niobium-titanium
General properties:
•Critical Temperature :The electricalresistance falls abruptly to zero under Tc
•Critical magnetic field and critical currentdensity Bc, Jc
•Meissner effect
•Transport of large currents in high magneticfields
In the 3D space (T, B, J) each superconductingmaterial can be characterized by its critical suface
The material is superconductor everywhere belowthis surface, and resistive above
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Cable-In-Conduit-Conductor CICC
�Transient heat transfer into the helium, limited by He enthalpy
�Take into account the electrical and thermal properties of superconductor material
�To ensure the nominal point (temperature, electrical field)
TFMC ENEA courtesy
�The strands
�The conduit (jacket + insulation)
�The bundle region: helium surrounding the strands in the cable(porous media)
�The hole region: helium flows in an independent cooling spiral tube
68 KA
supercritical helium
The cooling technique depends on the coil geometry
QTw
Tb
h
Q=hA(Tw-Tb)
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superconductor
• Electrical field
E=0
jc
�model
(V/m)E
B,T
�reality
jc
(V/m)E B,T
Ec
n
cc j
jEE
=
�engineering acceptance
Ec = 10 µV/m
�ITER acceptance
Ec = 2 µµµµV/m
� verification on conductor
(V/m)E
2 µV/m
x
• Temperature: verify that is in the acceptable range
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supercritical helium
Low temperature ~5 K
Pressure drop ~1 bar
� High heat capacity
� Low viscosity
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� Conductor AC losses
� Eddy current losses
� Nuclear heating
� Thermal radiation and conduction
heat load inventory for plasma scenario
heat load: time- and space-dependent
conductor
hydraulic circuit
� Circulating pumps
� Radiation and conduction in cryolines, feeders..
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Heat load on TF, CS and PF+CC system
AC losses
Nuclear Heating winding
Nuclear Heating case
Eddy currents
Radiation and conduction case
Radiation and conduction cryolines-feederspumping
Heat load distribution on TF system
Nuclear heating
AC losses
Eddy currents
CS tie plates
R & C - case
R & C - cryolines feeders
Pump power - Winding
Pump power casingHeat load distribution on CS system
AC losses
Eddy currents
joints
Thermal and conductioncryolinespumping
Heat load distribution on PF+CC system
PF AC losses
CC AC losses
Cryolines and CTB
Supply/Return PF moduletubesPumping
~7 KW ~4 KW
~ 16 KW
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numerical problems to solve…
The transient behavior of superconducting cables is dete rmined by coupledthermal, hydraulic and electric effectsThe model must allow time-dependent thermohydraulic an alysis
local assignment of the heat losses, magnetic field
B,∆B, strain ε and currents in conductors
to treat simultaneous thermal,electric and hydraulictransients in cables
non uniform load distributions (AC, B …)
~ 400 m
• Smoothing of power
• Conductor temperature
• Electrical fields
• Mass flow distribution
• Heat transfer for fast transient
• Enthalpy balance
• Pressure drop
• Heat exchanger model
Access to
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� Gandalf� Flower� TEA� VINCENTA
� Commercial ANSYS,CFD …… no exhaustif
hydraulic parameters:
mass flow rate
pressure
velocity
temperature ..
VINCENTA
numerical solvers
Process flow: 1D approach
(channels + walls + conductors in parallel)
3D details
Conductor: 1D approach
Process flow + diffusion: quasi-3D
conductor parameters:
electrical field
temperature
velocity
temperature ..
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schematic view of hydraulic network
model considers the network of 1-D, 0-D and 2D components (or “lego” assembly)coupled by thermohydraulic in 1-D, associated to 2-D cross-section(each cross-section corresponds to a node of the thermohydraulic problem)in which the diffusion can be considered, thus obtaining a quasi-3D code. vincenta code
Collector defined a fluid volume (connection, buffer …) having uniform pressure, temperature and zero flow with external heating source
cross-section
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schematic view of hydraulic network
wall–wall Link (WW)
channel–wall Link (CW) collector-joint link (VJ)
wall W1
joint J1 J2
wall W2J4joint J3
channel C2
channel–channel Link
Node N
channel C1
collector V1
Node 1
V2
V3 V4
Vincenta code
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cicc conductor
C1
C2
W2
W3
W4
W1
Pump
W1 Strands
C1 Hole
C2 Bundle
W2 Jacket
W3 Insulation
W4 Pancake
� channels:C1 hole region - C2 bundle region.� walls:�W1 conductor strands�W2 stainless steel jacket�W3 epoxy insulation �W4 stainless steel pancake
heated CICC conductor
t
Q
+ 2D connection
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cicc conductor - diffusion
# 1 # 20
W1V1V2
C1C2
C3C4
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mathematical models
� helium flow (1D)
� conductor (1D)
� collector – joint (0D)
� valves (0D)
� 2D solids (2D)
� pumps (0D)
� electrical circuit
� heat exchanger (1D)
� material properties
�helium properties
Cryodata Inc.Thermophysical properties of fluidson low temperatures
GASPAK
HEPAK
METALPAK
Physical definition of
in the first approximation, thermal exchange is just considered as a heat exchangebetween the channel and an infinite wall.
It is also possible to regulate using a satured bath pressure
heat coming from the fluid has to be transferred to the saturated bath through a heat exchanger
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helium flow
transient parameters of a compressible helium flow inside a channel.
channel is described by a set of 1D equations: continuity, momentum and energyConservation laws are completed with transfer mass, momentum and energy to takeinto account the thermo-hydraulic coupling with different flows and solid materials
i
k
ki
iii
Ax
V
t
∑ ρΓ
=∂
∂ρ+
∂∂ρ
( )i
k
Vki
h
iiiiiii
ii
AD
VVfVP
xt
V
i
∑ ρΓ
+ρ−
=ρ+∂∂+
∂∂ρ 22
i
k
Hki
m
convmi
iiii
i
iiii A
QV
HVx
PVH
t
∑∑ ρΓ+
=
+ρ
∂∂+
ρ−+ρ
∂∂
22
22
ρ, P, H, V – helium density, pressure, enthalpy and velocity
mass, momentum and energy conservation
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conductor
transient temperature distribution in conductor components described bya 1D equation of heat balance with the transverse conductive and convectiveheat exchange and Joule heating terms
( ) ( )
∑∑∑ ++++
+
∂∂
+∂∂θ−=
∂∂
+
k
wallkm
n
condnm
i
convim
Joulem
mmmmm
mmmmm
QQQQ
x
TkAkA
xt
TCACA 221122211 cos
conductor n, mchannel i to the conductor m
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2D solid
tkn
knk
k
kVk
k
SSforr
TrT
rrx
TT
x
trxqt
TTC
×
∂∂
⋅κ∂∂+
∂∂
κ∂∂+
+=∂
∂
,)(1
)(
),,()(
To simulate transient heat diffusion in the winding composite a 2D modelis used in the Cartesian or axial-symmetrical approach.A differential equation for temperature over the given cross-section S of the winding k is:
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.03.8
3.9
4.0
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
Section # 5
Lenght (m)
Le
ngh
t (m
)
4.5
4.8
5.2
5.5
5.9
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circulating pump model
( ) ( ) 19.1
max
4.1
max
=
∆∆
+
rpmP
P
rpmm
m opop
The pumping process is modelled as adiabatic compression of fluid from inlet pressure Pin to outlet pressure Pout. The enthalpy change from Hin to Hout assumed to be isentropical during compression. The coefficient ~ 65 -70% is used to take into account non-isentropy for the Hout
m& = f(∆P)
m&
PinPout
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valve model
m&PinPout
The model valve is intended for calculating He mass flow through cryogenicelements, such as valves, holes, gaps, etc. It is assumed that mass flow through the valve is forced by pressure differencebetween the collectors to which it is connected.
The flow through the valve is modelled as isoentropical expansionof the compressible fluid from the inlet pressure(before the valve) to the outlet pressure
Depending on the pressure drop between the inlet/outlet, the outlet valvepressure is equal to the outside pressure (sub-critical flow out)or to the critical pressure (critical flow out, the outlet velocity is equalto the local sonic speed). In both cases, the full enthalpy (h+u2/2)of the flow under the isentropical expansion is conservative,
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heat transfer coefficient – friction factor
The heat transfer coefficient h is defined as a function of the Reynolds and Prandtl numbers Re and Pr, through the Nusselt number Nu.
For fully developed turbulent flow in smooth tubes, the following relation isrecommended by Dittus and Boelter (1930) :Nud = 0.023Red
0.8 Prn
the exponent n has the following values :
n=0.4 for heating of the fluid
n=0.3 for cooling of the fluid
The friction factor for pressure drop in pipe
Kateder correlation for CICC’s conductors
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toroidal field conductor
�Normal operation mode
temperature and electrical field evolution along the
first turns of pancake at the end of the plasma burn
7 double Cable-In-Conduit pancakes – Nb3SnLength of one conductor ~380 m, 11 turns
THCoil task courtesy
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toroidal field conductor
�Disruption mode
� Large induced currents are generated by the fieds variation
� A large amount of energy is released in a very short time
� The structure temperature increases veryquickly after disruption then the heat diffuses in the structure
�One part is removed by structure channels
�P
�One part is transferred to the windingpack
�T,E
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CS cryogenic layout
CS system : detail of mass flow rate during plasma initiation and ramp up
-400
-300
-200
-100
0
100
200
300
400
500
5400 5410 5420 5430 5440 5450 5460 5470 5480 5490 5500
time (s) (cycle #4)
Mas
s flo
w r
ate
(g/s
)
CS3U feederCS2U feeder
CS1U feederCS1L feederCS2L feeder
CS3L feeder
lot of energy into a constant volume in a short time
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CS system
� hydraulic parameters T, P
Heat exchanger temperature on CS cryogenic loop
4,2
4,4
4,6
4,8
5
5,2
5,4
5,6
5,8
6
5400 5600 5800 6000 6200 6400 6600 6800 7000 7200
time (s) (pulse #4)
Tem
pera
ture
(K)
CS SHe inlet heat exchanger = CS outlet valve (2.09 Kg/s)
CS SHe inlet heat exchanger = Cs outlet valve (1.91 Kg/s)
CS outlet heat exchanger SHe (1.91 Kg/s)
CS outlet heat exchanger She (2.09 Kg/s)
Pressure evolution on CS cryogenic loop
300000
350000
400000
450000
500000
550000
600000
650000
700000
750000
800000
5400 5600 5800 6000 6200 6400 6600 6800 7000 7200time (s) pulse #4
Pre
ssur
e (P
a)
CS inlet pump
CS outlet pump = CS inlet valve
CS SHe inlet heat exchanger = CS outlet valve
CS outlet SHe (*)
2 Kg/s
~ 7 KW
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PF system
� hydraulic parameters T, P
1.8 Kg/s
~ 4 KW
Temperature evolution on PF cryogenic loop
4,2
4,3
4,4
4,5
4,6
4,7
4,8
4,9
5
5400 5600 5800 6000 6200 6400 6600 6800 7000 7200time (s) pulse #4
Tem
pera
ture
(K
)
Temperature V213 - PF inlet pump Temperature V214 - PF outlet pump = input valveTemperature V215 - PF SHe inlet = PF outlet valveTemperature V217 - PF SHe BathTemperature V216 - PF outlet SHe
Pressure evolution on PF cryogenic loop
3,30E+05
3,50E+05
3,70E+05
3,90E+05
4,10E+05
4,30E+05
4,50E+05
4,70E+05
4,90E+05
5,10E+05
5400 5600 5800 6000 6200 6400 6600 6800 7000 7200time (s) pulse #4
Pre
ssur
e (P
a)
Pressure V213 - PF inlet pump Pressure V214 - PF outlet pump = PF inlet valvePressure V215 - PF SHe inlet= PF outlet valvePressure V216 - PF outlet SHe (*)
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cryopumps
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1 2 3 4
~ 1 m
~ 0.2 m
~ 7 mm
cryopumps : 3D model - CFX
helium flow distribution and the pressure losses in the cryopanels of the Prototype Torus Cryopump in nominal pumping mode (steady state)
� Pumping efficiency: optimized flow distribution bet ween the 4 channels
SHe (4.5 K; 3.5 bar)
50 g/s
Courtesy of FZK
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Model 1 Model 2
Model 3a (40°) Model 3b (50°)
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Reynolds stress model
k-ω model
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summary
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