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Computational thermal-Fluid-Dynamics (CtFD) Issues in Nuclear Fusion Reactors. R. Zanino, S. Giors, L. Savoldi Richard, F. Subba Dipartimento di Energetica, Politecnico, Torino, Italy. Outline. Introduction Selected topics: - PowerPoint PPT Presentation
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R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 1
Computational thermal-Fluid-Dynamics (CtFD) Issues
in Nuclear Fusion Reactors
R. Zanino, S. Giors, L. Savoldi Richard, F. Subba
Dipartimento di Energetica, Politecnico, Torino, Italy
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 2
Outline
• Introduction• Selected topics:
– Physics: Modeling plasma-surface interactions (PSI) in tokamaks CODE DEVELOPMENT only
– Magnet Technology: Modeling cable-in-conduit conductors (CICC) for the superconducting ITER coils CODE DEVELOPMENT + FLUENT
– Vacuum Technology: Modeling Turbo-Molecular Pumps (TMP) FLUENT only
• Conclusions and perspective
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 3
Introduction (I): Nuclear fusion
Potential: (almost) clean and unlimited energy!!
• Aim: realize a sufficient amount of nuclear fusion reactions
2D + 3T n (14.1 MeV) + 4He (3.5 MeV)
• Conditions: magnetically confine in a volume (~ 102-103 m3), for a sufficiently long time, a mixture (plasma = fully ionized gas) of deuterium (D) and tritium (T) with density ~ 1020-1021 m-3 and temperature ~ 10-20 keV
Heats the blanket Thermal energy Electric power
Heats the plasma Ignition
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 4
Components of a tokamak fusion reactor
• V = vacuum chamber, • PI = pellet injector, NBI = neutral beam injector, • FW = first wall, DP = divertor plate, • A = antenna for auxiliary plasma heating, • B = blanket, • Magnet system: CS = central solenoid, TF = toroidal field coil, PF = poloidal field coil, • C = cryostat, • SG = steam generator, T = turbine.
Vertical cross section through symmetry axis (sketch)
PF
CS TF
A B
V
DP DP
FW
SG
PLASMA
n Li T
D
PI, NBI
PF
C
T
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 5
Introduction (II): ITER
• ITER tokamak construction approved June 2005
• 10 GEuro project: 50 % EU, 50 % (JA, RF, US, CN, KO, IN)
• Reactor site Cadarache (F)
• 10 year construction (start 2007) + 20 year operation
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 6
Tokamaks: generalities
Toroidal geometry
Poloidal magnetic field generated by
plasma current
Complex magnetic field assembly for
confining and controlling the
plasma
Transformer principle
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 7
Introduction (IV): ITER goals
• Achieve inductive plasma burn with amplification factorQ = generated/injected powerof at least 5-10;
• Possibility of controlled ignition (Q ) not precluded
• Integrate the technologies essential for a fusion reactor (e.g. superconducting magnets, remote maintenance);
• Test components for a future reactor (e.g. divertor and torus vacuum pumps);
• Test tritium breeding module concepts for DEMO.
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 8
PSI in tokamaks: Geometry
Scrape-off layer (SOL)(“open” magnetic surfaces)
Main plasma (closed magnetic surfaces)
Limiter/First Wall
Divertor plates
Toroidal symmetry edge plasma problem is 2D :• radial r (across magnetic surfaces)• poloidal (around “small” torus circumference)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 9
Radiation from the plasma edge in a divertor tokamak
PSI in tokamaks: Physics
Plasma confinement is never perfect because of dissipation
The plasma interacts with the solid
walls
Immission of impurities from the walls into the plasma (e.g.. C in the case of graphite
walls) Erosion of the walls but also radiation from ionized impurities possible
switch-off of fusion reactions.
Heat load peaks up to tens of MW/m2 Possible serious damage of plasma facing
components (walls) Lifetime issue
Radiation from the plasma edge in a first-wall/limiter tokamak
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 10
Plasma-Boundary electrostatic sheath
Ions: large mass, low speedElectrons: small mass, high speed
Random motion electric wall current charge accumulation electrostatic
sheath
Wall
Wall
ni profile
ne profile
main plasma
sheath
D~ 10-5 m
Particle flux n = ncs (not zero!!!)
Energy flux E = n
~ 8 (Ion + Electron contribution)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 11
Cosine Model
y
nDy
Lncsx /
MAIN PLASMA
B
From continuity: 0
yxyx Sn
y CDLenn n /0
L = Connection length (distance between walls)
Heat flux on the wall making a finite angle with B:
nBeqq qy
xx ˆcos0
n
wall
SOL
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 12
Power balance considerations (Lawson Criterion with impurities)
Output (losses): Pout = PL + PR
Pin = n2/4<V>E From fusion reactions
PL = 3nT/E Conduction/convection
PR = n nz (T,Z) Impurity radiation losses
IGNITION (= self-sustained reaction): Pin Pout
Limitation on the tolerable radiation from impurities PR ~ nz (T,Z) CHOICE OF MATERIAL!
Input: Pin
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 13
PSI in tokamaks: Modeling issues
• Fluid vs. kinetic plasma
(10-7 < Kn mfp/L < 101 range achieved in SOL!)• Complicating physics/geometry issues
– Multi-fluid (1 fluid = 1 ionization stage) for impurities, e.g., 6 fluids for C but, in principle, 74 fluids for W!
– Presence of non-magnetized, kinetic neutral particles Sources Monte-Carlo approach typically adopted
– Treatment of third (diamagnetic) direction (drifts, etc.)• Lack of consolidated fundamental knowledge on some issues
– Radial “anomalous” transport most often adopt diffusive Ansatz
– Boundary conditions (Debye sheath, etc)– Atomic physics database available (for some materials)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 14
PSI in tokamaks: Fluid (Braginskii) plasma model
jj
jjjjj
j
jrrjj
jjjjjjj
jj
jjjj
Qx
VqVp
dt
dTn
r
nDVn
RBVEeZnx
pdt
VdmnB
SVndt
dn
2
3
][
,
Sources from plasma-neutral interactions• j = i, e (pure plasma)• Complete Navier-Stokes solved
only along magnetic field B
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 15
PSI in tokamaks: Computational issues
• Huge transport anisotropy: Vr << V, r << SOL thickness << SOL length Stretched grid with very good alignment in is needed!
• Strong gradients from localized sources (adaptivity needed, …)
• Strong nonlinearities (transport coefficients along B T5/2, radiation/atomic physics rates (exponential), …)
• Different physical processes involved Often need to couple intrinsically different numerical approaches (e.g. CFD + Monte Carlo)
PROBLEM BEYOND CAPABILITIES OF STANDARD COMMERCIAL CODES
DEVELOPMENT NEEDED!
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 16
PSI in tokamaks: Numerical methods (I) -- FV
• FV were historically the first method adopted for CFD edge plasma modeling
• A number of widely used tools exists today– 5-point molecule (B2)– 9-point molecule (UEDGE and EDGE2D)
based on quadrilateral meshes optimized for divertor • Increasingly complex physical/numerical ingredients
added by many contributors over more than 20 years • Areas of active research development:
• Other geometries besides divertor First Wall/Limiter• Adaptive grid methods
• Some physics models are still not validated
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 17
PSI in tokamaks: Results (I)
Computed (B2-Eirene) vs. measured radiation intensity
Tomographic reconstruction
Profiles at the target
FV multi-fluid model of ASDEX Upgrade divertor
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 18
PSI in tokamaks: Numerical methods (II) -- FE
• First attempt at dealing with realistic geometries (early-to-mid ’90s)
• Extended to use adaptive grids (late ’90s)•Adaptive triangular grid generator written by INRIA [H. Bourouchaki et al] coupled with model electron heat advection/diffusion/radiation Finite Element solver• Mesh size and alignment controlled by locally defining the 2D metric• Mesh alignment guaranteed within a few degrees
• Conservation issue (see below)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 19
PSI in tokamaks: Results (II)FE model of ASDEX Upgrade divertor
Relatively slow convergence likely due to non conservation on finite grid
AD BC
n
Te
Ti
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 20
PSI in tokamaks: Results (IIa)FE model of scalar problems in divertor geometry
Adaptive grids
Anisotropic diffusion
Anisotropic advection
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 21
PSI in tokamaks: Numerical methods (III) -- CVFE
• Most recent attempt at dealing with complex geometries while still guaranteeing conservation
• Adopt triangular meshes. Force one element side to be always aligned with the B field
• Employ the Control-Volume Finite-Element technique to guarantee conservation on every finite-size mesh
• Segregated approach to couple continuity-momentum-energy equations
• First single-fluid application proved effective on the difficult (= previously untackled) First-Wall/Limiter geometry
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 22
PSI in tokamaks: Numerical methods (IIIa) -- CVFE
Control volume boundaries Element sides
Nodes
B B
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 23
PSI in tokamaks: Results (III)
200
400
600
800
1000 1200 14007.60
7.65
7.70
7.75
7.80
7.85
Number of nodes
Par
ticl
es [
1020
s-1
]
Mesh-independent value, estimated by Richardson extrapolation
R [m]
Z [m] V// [m/s] @ Top region
-6.3e4
-3.1e4
3.2e2
3.2e4
6.4e4
0.95 1.00 1.05 1.100.72
0.74
0.76
0.78
0.80
0.82
0.84
0.86
0.88
0.90
CVFE show good performance in regions where quadrilateral meshes would be too distorted
Spatial convergence tests on simple model problems were satisfactory
0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.0
0.2
0.4
0.6
0.8
R [m]
Z [
m]
CVFE model of IGNITOR first wall/limiter
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 24
ITER superconducting magnet system (I)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 25
Magnet windings
Current lead 80kACurrent
lead 80kA
Bus bar type2
TF-model
coil (TFMC)
Inter-coil
structure (ICS)
Vacuum vessel
Bus bar type1
CryostatExtension
PANCAKE WOUND LAYER WOUND
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 26
SC coils for fusion applications (e.g., ITER) carry high currents (up to ~ 70-80 kA) to generate high magnetic fields (up to ~ 13 T)
Low critical temperature SC (e.g., Nb3Sn or NbTi) are used in
multi-stage cable-in-conduit conductors (CICC) cooled by supercritical He @ ~ 5 K and 0.5 MPa
CICC for ITER superconducting coils
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 27
Fluids•He
Thermophysical Properties of Materials in Cryogenic Conditions
Solids•Super-conductors (e.g., Nb3Sn, NbTi)•Conductors (Cu)•Structural (SS, Incoloy, Ti)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 28
CICC for ITER: Modeling issues
• Conductor must be kept below critical temperature capability to reproduce/predict thermal-hydraulic transient:
Heat slug propagation Stability Quench propagation …
• Absence of diagnostics inside the conductors/magnets the conductor performance must be reliably extract from “global” (=inlet, outlet) measurements (T, dm/dt, p, V, I,…)
• The level of detail needed in the TH analysis (global vs. local analysis,
…) is function of the nature of the problem (slow vs. fast transient, …) and of the SC type (Nb3Sn vs. NbTi)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 29
CICC for ITER: Computational issues
• Multi-physics (TH + EM + ME) nature of the problem
• Timescales: 10-3 s 102 s
• Length scales: 10-6 m 102 m
• Complex structure of the cable bundle
• Complex interaction between cable constituents
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 30
CICC for ITER : Models (I) – Global 1D thermal-hydraulics
• Length ~ 102 m >> Diameter ~ 10-1-10-2 m 1D model• Compressible Euler-like flow of at least two fluid components: supercritical He (~ 5 K, 0.5 MPa) in annulus voids and in central channel • Heat conduction along at least two solid components: strands (SC + Cu) and jacket /conduit (SS, Incoloy, Ti, ...) • External (cryogenic) circuit model to provide “boundary conditions” in predictive simulations• Transverse coupling inside or between CICC, possibly through structures, requires Multi-conductor and/or Multi-dimensional model
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 31
Tcv
wvcx
A
A
vT
x
Tv
x
vT
t
T
cvwv
x
A
A
vc
x
pv
x
vc
t
p
vx
p
x
vv
t
v
vvev
ve
v
2
1
2
11
2
2222
CICC for ITER : Single-conductor model
(Mithrandir code)
RHS sources/sinks ( interaction with solids and other channels) include constitutive relations which require transport coefficients (friction factors, heat transfer coefficients) Local 3D models
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 32
CICC for ITER : Models (II) – Local thermal-hydraulics
• Recent idea: derive from local 3D models the constitutive relations for the radial transport fluxes to be used in global 1D models
• The commercial FLUENT code is used for 3D analysis
• Different issues could be addressed: Friction in the central channel Friction in the annular region (?) Friction/heat transfer coupling in the central channel• Mass transfer between central channel and annular region• …
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 33
CICC for ITER: Local CtFD model equations (1)
• Water and Air simulated @ 104 < Re < 106, hydrodynamic similarity envisaged for supercritical Helium
• Incompressible Reynolds-Averaged Navier-Stokes (RANS) equations, with constant temperature and transport properties are used:
• Linear energy equation, based on Reynolds analogy between turb. conduction and turbulent momentum transfer, solved for heat transfer problem:
• 2-layer k- model [Chen&Patel, AIAA J. (1988)] established as best choice closure for flow with separation in 2D [Arman&Rabas, NHTA (1994)], and confirmed in 3D [RZ, SG & RM, ACE (2006)]
i
j
j
iij
jiijjj
jij
i
j
i
x
U
x
US
uuSxx
PUU
xt
U
x
U
2
1
2
0
''' ' 2
2 /3ij i j t ij iju u S k
1, lim ,
t T
i i T i
t
U u t u t dtT
x x x
j effj j j
TE U E p k
t x x x
Prp t
eff molt
Ck k
2
; 2
ref
T
p
T
p vE h h C dT
CLOSUR
E REQUIR
ED!
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 34
CICC for ITER: Local CtFD model equation (2):
FLUENT Enhanced Wall treatment: If y+ < 1 2-layer k-
model
If y+ > 1 enhanced wall functionsyC
WALL
yC wy
y
Re y
y k
2-layer k- model:For Rey
> 200 standard k- model (fully turb. region)
For Rey < 200 one-equation model of Wolfstein (Viscosity-affected region)
3/ 2
Re /
Re /
3/ 4
1
1
0.09 0.418 70 2
y
y
t
Al
Al
l l
C l k
k l
l yc e
l yc e
C c C A A c
In the viscosity affected region only Mass, Momentum, k and (if needed) Energy conservation eqs. are solved for.
Then t and follow (after Wolfstein):
t and are smoothly blended between turbulent and viscosity affected regions, to avoid discontinuity across Rey=200
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 35
CICC for ITER : Local CtFD model equation (3)
p, where =
L
( ), where wall A
bulkbulk wall
A
p p z
T dT T
TT T d
v Ar
v A
SOLUTION• Finite Volume discretization, with second order upwind convective fluxes
and SIMPLE linearization of pressure-momentum-turbulence equations (solution by FLUENT commercial code)
• Incompressible, constant properties fluid linear energy equation is solved after the flow field solution is converged
BOUNDARY CONDITIONS:
WALL:
IN-OUT:
Periodicity on:
Given Tbulk,in
Given dm/dt (or viceversa)
AXIS (2D only):
0
/ 0
/ 0
wallT T
k n
p n
v
GridFLUENT 6.2 (axi, segregated, ske)
Jun 09, 2006
L
WALL
IN OUT
AXIS
z
/ 0, scalarr
, , , ,p k v
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 36
CICC for ITER: Results (IIa)
Unstructured hybrid mesh• hexahedral in the gap and wall boundary layer
• tetrahedral in the core
Friction in the central channel results
Validation
0.1717 0.34282 / 2.5ln 2 / 3.75 6.4 /
/ Re / 2
H
H
f h D h g h
h h D f
Experimental validation
CFD-based predictive correlation derived
Re
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 37
g/h = 4 RECIRCULATION
g/h = 8 RE-ATTACHMENT
2D effect [Webb et al., IJHMT (1971)] recovered in 3D!
Main/core flow
Shear stress w
Cf
CICC for ITER: Results (IIb)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 38
SIMPLE convergence example
CONVERGENCE CRITERIA:
Variation of relative to asymptotic value < 2%
In this case, ~ 2000 SIMPLE iterations would have been enough
Evolution of , for a given dm/dt
Din =6 mm, g=8 mm, Re=8104, fields pre-initialized with a coarser mesh solution
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 39
CICC for ITER: Results (IIc)
3 3x19
33x7 33x7
ITER TFMC
3x3x5x4x6
Friction in the cable bundle
Compute permeability of complex cable patterns?!
Axial flow contours
Validation
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 40
Friction in porous media
Jp
K K
��������������������������������������������������������
2 2p Ju u
x K K
2
2 2
1
( / )out fluid
K
K Apf
L dm dt
( / )
ReKfluid
dm dt K
A
1
ReKK
f J
Darcy Forchheimer
Permeability (m2)Inertial constant
1D flow velocity3D Seepage velocity
Friction factor Reynolds number
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 41
CICC for ITER: Results (IId)
Heat exchange in 2D rib roughened tube: Validation
p/h=10
h/D=0.04
p
D
h
• Presented numerical results are grid independent• Very good agreement of friction factor• Acceptable agreement of St, slightly better for air (Pr=0.71) than
for water (Pr=5.1)
St = Nu/Re Pr
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 42
CICC for ITER: (local) results (IIe)
Streamlines
Temperature contours (K)
Pr=5.1 (water)
Re=105Reattachment
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 43
CICC for ITER: (local) results (IIf)
Computed Reynolds/Colburn local analogy between momentum and heat transfer is not
verified
Colburn-like analogy between global f and St, is not verified owing to the strong
contribution to f of form drag vs. friction drag, which does not have any analogy in
heat transfer
Pr=5.1
Re=105
20.5
, ,Re Pr
wf
effw
w bulk
cU
dTk
Nu hD dnSt Nu h
k T T
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 44
2-fluid code needed to reproduce T evolution @ different sensors
bundle-hole heat diffusion
CICC for ITER: Heat slug propagation (I)
T
t v
T
x k
2T
x20
Cp
TH
tCpvH
TH
x
ph
AH
TB TH
Cp
TB
tCpvB
TB
x
ph
AB
TH TB
Nb3Sn conductor TH test&analysis (1997)
T
t v
T
x k
2T
x20
For the average temperature, under suitable assumptions:
Taylor-Aris dispersion
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 45
Quench propagation
Reservoir
RV RV
CV
Current lead terminals Sample terminals
Gas reservoir p=1.2bar, T=300K
Heater
Ohmic heater
JTV JTV
VALVE-BOX
COLD-BOX
CRYOSTAT p=1.3bar T=4.2K
SAMPLE
Cryogenic circuit
CICC for ITER: Quench propagation (I)
Nb3Sn conductor test&analysis (1997)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 46
ITER : Model coils – CSMC & TFMC
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 47
ITER : Insert coils – CSIC & TFCI
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 48
CICC for ITER: StabilityStability tests on the CS Insert Coil
(JAERI Naka, Japan, 2000)
ICS-TC-04H
Inductive heater
Outlet joint
Inlet joint
Tin pin
Tout pout
pcnt VT-11
VT-09
VT-10
VT-08
VT-07
(dm/dt)in
(dm/dt)out
He flow
Stability margin vs T margin
Stability margin vs dm/dt
Nb3Sn conductor test&analysis (2000)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 49
CICC for ITER: Quench propagation (II)
CS Insert Coil tests(JAERI Naka, Japan, 2000)
TF Conductor Insert tests(JAERI Naka, Japan, 2002)
Propagation of quench front
Nb3Sn conductor test&analysis (2000, 2001)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 50
Use Mithrandir model for each CICCUse Mithrandir model for each CICC
LongitudinalLongitudinal coupling with circuit code coupling with circuit code
Very general coil topology can be simulated with this strategy!
TransverseTransverse coupling is explicit in time coupling is explicit in time
Time scale separation along and across CICC solve 3D problem as several coupled 1D problems.
CICC for ITER : Multi-conductor model
(M&M code)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 51
CICC for ITER: Performance assessment (I)
Voltage Tap for Quench Detection
Voltage Tap for Voltage measurement
Carbon Thermometer
Platinum Thermometer
Pressure
Differential Pressure
Flow Meter
Resistive Heater
Control Valve
Joint
Insulation Break
Choke Tube
Interface
TC
TU
P
DP
Interface for TF Insert
Cernox ThermometerTS
Helium flow shematic for Model coil
SHe
1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B 7A 7B 8A 8B 9A 9B 10A 10B
DP
P
DP
P
DP
P
P P P
TOP OF COIL
BOTTOM OF COIL
DP P
TU
TC
TU
TC
P
TS TS TS TS TS TS TS TS TS TS TS TS TS TS TS TS TS TS TS TS
TS TS TS
11A 11B 12A 12B 13A 13B 14A 14B 15A 15B 16A 16B 17A 17B 18A 18B
DP
P
TU
TCDP
P
TU
TCDP
P
TU
TC
TUTU
TC TC TCTC
TU TU
TC TC TC TC
P
TU
TC
P
TU
TC TC TC
TU
TC
P
TU
TC TC TC
TU
TC
P
DP P
TU
TC
TS
From AA
To AA
TS
TS
M980206a/T.IJADW-97-056a
Cryogenic circuit
Coil topology
(Nb3Sn) Central Solenoid Model Coil test&analysis
(2000-2002)
TCS test
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 52
CICC for ITER: Performance assessment (II)
(Nb3Sn) Toroidal Field Model Coil test&analysis
(2001-2002)
Heater ON
Heater OFF
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 53
CICC for ITER : Multi-solid Multi-channel model (I)
(M3 code)
•Transient 1D heat conduction equation for M current carrying Cable Elements (refinement down to the strand level allowed)• 1D Euler-like set of equations for N hydraulic channels (down to petal level)• Transient 1D heat conduction equation for K “jacket”-like components (jacket, wrapping, spiral,…)
M
+
3N
+
K
______________
M+3N+K equations
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 54
CICC for ITER:heat slug propagation (II)
2194
mm
1055
mm
805
mm
655
mm
435
mm
Driver = (azimuthally) local heater
NbTi Poloidal Field Conductor Insert Full Size Joint Sample - TH tests
(2004)
Reproduce temperature evolution @ different T sensor
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 55
CICC for ITER : Models (III) –Electromagnetism
• Thermal-Hydraulics of CICC is only part (and not even the “most important” one) of the story• CICC performance depends on current distribution among the strands, which may be non-uniform because of non-uniform contacts at joints EM model of cable (and joints) [Bologna U., Udine U.] requires the temperature of the different cable elements THELMA code
Discretize cable cross section nested down to single strand
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 56
THELMA EM cable model (I)
L1
L2
LEXT
MEXT,2
–
IEXT
M12
I1
I2
+
M21
MEXT,1
VGEN
U1
+
+
+
1 21 1 12 1,
EXTEXT GEN
dI dI dIU L M M V
dt dt dt
_
,01
_,
, ,1
, ',, ' '
, , , , , ,
N CE L
N EXTEXT
EXT
V x t I x tm x x dx
x t
dI tM x
dt
E x I x t T x t B x t
For each CE: simple lumped parameter model (i-th sub-cable)
Distributed parameter model (-th CE)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 57
_ _ _,
, , , , ,1 1 1
N CE N CE N EXTEXT
EXT
I dI tg V x V x g M x
x dt
g
I
II dx
x
Idx
x
Try to express voltage drop across CE as a function of the unknown currents I
Conductance per unit length
S,
THELMA EM cable model (II)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 58
(assume a reference value for V on the first CE NCE –1 equations (*))
1 * ,* , * , * ,
x tx t x t x t
x
IV G S
Contribution of induction terms
between CE
Matrix of transverse conductance-per-unit-length
Longitudinal voltage
* *1* * *
1 0
* *
, ',, , , ' '
, , , , , ,
L
EXTEXT
x t x tx t x t x x dx
x x t
d tx x x t T x t B x t
dt
i i
G S m
IM E i
Change variable: I i = I - IUN (NCE –1 unknowns). Substituting (matrix form)
THELMA EM cable model (III)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 59
voutk t v inlk tek t Rkik t Mk,sd
dtis t
s
js,k ts Gk,s vk t vs t
s ik,s t
s
Unknowns
Voltage driven components (saddle)
Current driven components (strands)
THELMA EM joint model
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 60
CICC for ITER: Performance assessment(III)
PFISWIn W
In NW
Out NW
Out W
Field center
PFISNW
TTTTT
T T T T TT
T
T P
T PT P
T P
H
H H
H H
H
I
He
• Sudden quench reproduced
• Voltage precursors (spikes) caused by sudden current redistribution
NbTi short sample test&analysis
(2004, 2006)
TCS test
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 61
CICC for ITER : Models (IV) –Mechanics
Critical current density jC depends also on strain of Nb3Sn filaments Mechanical model of cable is needed! [Padova U.]
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 62
Vacuum technology:Turbomolecular Pumps (TMP)
in Tokamak vacuum systemTokamak vacuum vessel (e.g., JET, 200 m3) needs to be evacuated to high vacuum pressure < 10-8 mbar, before the operation is started.
Relatively large throughput of neutrals, released during operation in the divertor region, needs to be removed as well.
THE JET VACUUM SYSTEM IS MAINLY MADE OF:• ROUGH PUMPING SYSTEM (ROOTS BLOWERS):
For roughing down the vacuum vessel to < 10-2 mbar• TMPs:
For reaching high vacuum pressure ( < 10-8 mbar) in the vessel and other diagnostics sub-systems
During glow discharge vessel cleaning process For Cryo-pumps regeneration once they are saturated
• CRYO PUMPS For pumping high throughput of gases in the divertor
and neutral beam injection systems during operation
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 63
Operating parameter range for a 103 l/s HTMP:• pinlet: 10-3 10-9 mbar; poutlet: 10-1 20 mbar
• Mass flow rate (@ pinlet = 10-3 mbar) 10-6 kg/s (about ZERO !!!)
• Rotor peripheral speed 300 350 m/s (close to N2 thermal&sound speed)
Hybrid turbomolecular pumps (HTMP) introduction
10-3 <Kn 100
Viscous or transition regime
Fluid model (Navier-Stokes eqs.)
Kn 100
Molecular (and transition) regime
Kinetic models (Boltzmann eqs.)
• Low pressure stages (turbo- molecular)
• High pressure stages (molecular-drag)
Knd
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 64
HTMP: Gaede and Holweck drag stages
HTMP with Gaede stages HTMP with Holweck stages
Tangential drag, tangential flow
Tangential drag, helicoidal flow (with axial component)channel stripper
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 65
V
Inlet section
Outlet section
Moving wall
Clearance
Periodic cut
Gas flow
Drag Stages: Introduction
Principle Momentum is given to the working gas by friction with the moving channel wall
The abrupt section change causes most streamlines to bend towards the
outlet, and gas kinetic energy to revert into pressure, creating a local
compression effect (2D model)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 66
HTMP drag stages Navier-Stokes model
• Typical flow conditions in HTMP drag stages:– Compressible (Mach 0.75 - 1)– Laminar (Re < 2000)– Viscous to transition (10-3 < Kn < 1)
• Equations:– Conservation equations for mass, momentum and energy (with viscous heating
included)– Ideal gas equation of state, temperature dependent gas properties
• Boundary conditions:– Outlet pressure imposed– Inlet mass flow rate imposed– Wall temperature and speed (rotor) from experiment– Slip-flow boundary conditions (viscous slip + thermal jump) on solid walls.
• Solution:– SIMPLE algorithm, by means of FLUENT commercial code
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 67
The Gaede pump3D slip-flow model validation
10-1
100
101
0
1
2
3
4
5
6
7
8(a)
Outlet pressure (mbar)
Com
pre
ssio
n r
atio
Kn100 10-1 10-2 10-3
Experimental dataNo-slip modelSlip model
10-1
100
101
0
20
40
60
80
100
120
(b)
Outlet pressure (mbar)
Frictio
n p
ow
er
(W)
Kn100 10-1 10-2 10-3
Experimental dataNo-slip modelSlip model
10-1
100
101
0
1
2
3
4
5
6
7
8(a)
Outlet pressure (mbar)
Co
mp
ressio
n r
atio
Kn100 10-1 10-2 10-3
Experimental dataNo-slip modelSlip model
10-1
100
101
0
20
40
60
80
100
120
(b)
Outlet pressure (mbar)
Fri
ctio
n p
ow
er
(W)
Kn100 10-1 10-2 10-3
Experimental dataNo-slip modelSlip model
• Very good accuracy up to Kn<10-1
• Remarkable slip-flow effect on friction power
• Need for slip flow boundary conditions demonstrated
Pressure (Pa)
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 68
Holweck Drag Pump
Drum geometry with parallel channels
carved on the stator
Periodicity model one channel only
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 69
Pressure profile along a channel (pout=10 mbar, Kn10-2)
• Very good local agreement (nonlinear pressure profile along channel)
• Very good agreement for friction power with both N2 and Ar.
Friction power, 250 sccm test
The Holweck pump: 3D slip-flow model validation
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 70
3D CFD Model
RES
S
B
RS-B
Rhv
RES-BRAIR-GAP
WES
WR
QRQS
Measured
QR (W)
Need the whole stage to predict the rotor
temperature
Couple the CFD gas model with a thermal lumped parameter body model
Holweck Hybrid Model
Working point:intersection of CFD and body thermal characteristics
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 71
Conclusions and perspective
• Computational Thermal Fluid Dynamic analysis has led to significant improvement of understanding and design in several nuclear fusion applications over the last 10-20 years
• In ITER perspective, although the design is partly fixed, some key challenges are still issues, e.g.:
• Multi-fluid modeling of plasma-surface interactions, aimed at realistic assessment of heat loads on and erosion of plasma-facing components, radiation from the plasma• Multi-physics modeling (including CtFD) of superconducting CICC, aimed at realistic extrapolation from short sample to coil performance• …
R. Zanino, et al., Scuola Estiva UIT, Certosa di Pontignano, 8 Settembre 2006 72
Standard k- model(Launder Sharma 1979)
2 /t c k k
i
k
i
x
u
x
u
''
j
iij
jkTj
j x
U
x
kkU
xt
k
2
1 2i
j T ijj j j
UU C C
t x x k x k
C1=1.44C2=1.92C=0.09k=1.0=1.3 Prt=0.85
' '1 1
2 2i i iik u u