thermohydraulicsin iter · 2009-04-30 · thermal diffusion coupled to cooling circuits +...

Roser Vallcorba MATEFU Spring Training School April 05-09, 2009

Thermohydraulics in ITER

Point of view of cryogenic simulation

Roser Vallcorba Matefu Spring Training School 2

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


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


�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?


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


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


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


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)


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


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)


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


supercritical helium

Low temperature ~5 K

Pressure drop ~1 bar

� High heat capacity

� Low viscosity


� 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..


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


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


� 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 ..


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


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


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


cicc conductor - diffusion

# 1 # 20

W1V1V2

C1C2

C3C4


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


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


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


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


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


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,


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


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


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


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


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


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 (*)


cryopumps


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


Model 1 Model 2

Model 3a (40°) Model 3b (50°)


Reynolds stress model

k-ω model


summary

thermohydraulicsin iter · 2009-04-30 · thermal diffusion coupled to cooling circuits +...

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