Computational thermal-Fluid-Dynamics (CtFD) Issues in Nuclear Fusion Reactors

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


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


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


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


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


Tokamaks: generalities

Toroidal geometry

Poloidal magnetic field generated by

plasma current

Complex magnetic field assembly for

confining and controlling the

plasma

Transformer principle


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.


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)


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


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)


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


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


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)


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


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!


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


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


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)


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


PSI in tokamaks: Results (IIa)FE model of scalar problems in divertor geometry

Adaptive grids

Anisotropic diffusion

Anisotropic advection


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


PSI in tokamaks: Numerical methods (IIIa) -- CVFE

Control volume boundaries Element sides

Nodes

B B


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


ITER superconducting magnet system (I)


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


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


Fluids•He

Thermophysical Properties of Materials in Cryogenic Conditions

Solids•Super-conductors (e.g., Nb3Sn, NbTi)•Conductors (Cu)•Structural (SS, Incoloy, Ti)


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)


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


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


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


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• …


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!


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


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


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


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)


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


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


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


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


CICC for ITER: (local) results (IIe)

Streamlines

Temperature contours (K)

Pr=5.1 (water)

Re=105Reattachment


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


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


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)


ITER : Model coils – CSMC & TFMC


ITER : Insert coils – CSIC & TFCI


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)


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)


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)


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


CICC for ITER: Performance assessment (II)

(Nb3Sn) Toroidal Field Model Coil test&analysis

(2001-2002)

Heater ON

Heater OFF


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


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


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


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)


_ _ _,

, , , , ,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)


(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)


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


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


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.]


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


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 (turbomolecular)

• High pressure stages (molecular-drag)

Knd


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


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)


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


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)


Frictio

n p

ow

er

(W)

Kn100 10-1 10-2 10-3


10-1

100

101

0

1

2

3

4

5

6

7

8(a)


Co

mp

ressio

n r

atio

Kn100 10-1 10-2 10-3


10-1

100

101

0

20

40

60

80

100

120

(b)


Fri

ctio

n p

ow

er

(W)

Kn100 10-1 10-2 10-3


• Very good accuracy up to Kn<10-1

• Remarkable slip-flow effect on friction power

• Need for slip flow boundary conditions demonstrated

Pressure (Pa)


Holweck Drag Pump

Drum geometry with parallel channels

carved on the stator

Periodicity model one channel only


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


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


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• …


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

Documents

Computational thermal-Fluid-Dynamics (CtFD) Issues in Nuclear Fusion Reactors