M. Yoda, S. I. Abdel-Khalik, D. L. Sadowski, M. D. Hageman, B. H. Mills, and J. D. Rader G. W. Woodruff School of Mechanical Engineering Extrapolating

M. Yoda, S. I. Abdel-Khalik, D. L. Sadowski, M. D. Hageman, B. H. Mills, and J. D. Rader

G. W. Woodruff School of Mechanical Engineering

Extrapolating Model Divertor Studies to

Prototypical Conditions

ARIES Meeting (7/10) 2

Objectives / MotivationObjectives• Experimentally evaluate thermal performance of gas-cooled

divertor designs in support of the ARIES team• Evaluate use of fins to enhance performance of current designs– Plate-type divertor– HEMP / HEMJ

Motivation• Experimental validation of numerical studies• Divertors may have to accommodate steady-state and transient

heat flux loads exceeding 10 MW/m2 • Performance should be “robust” with respect to manufacturing

tolerances and variations in flow distribution


Approach• Design and instrument test modules that closely match

divertor geometries• Conduct experiments that span expected non-dimensional

parameters at prototypical operating conditions– Reynolds number Re– Use air instead of He: difference in Prandtl numbers has

negligible effect on Nusselt number Nu• Measure cooled surface temperatures and pressure drop– Effective and actual heat transfer coefficients (HTC)– Normalized pressure drops P

• Compare experimental data with predictions from commercial CFD software


Thermal Enhancement• Most current divertor designs rely on jet impingement

to cool plasma-facing heated surface– 2D (rectangular) or 3D (round) jet(s)

• Can thermal performance of leading divertor designs be further improved by an array of cylindrical pin fins on heated surface?– Pin-fin array increases cooled surface area– Pins span gap between jet exit and cooled surface: bare

region in center of cooled surface to allow jet to impinge– Impact on actual heat transfer coefficient and pressure

drop?


Plate-Type Divertor • Covers large area (2000 cm2 = 0.2 m2): divertor area

O(100 m2)

100 cmCastellated

W armor0.5 cm thick

20– HEMJ cools 2.5 cm2; T-tube cools 13 cm2

– Accommodates up to 10 MW/m2 without exceeding Tmax 1300 °C, max 400 MPa

– 9 individual manifold units with ~3 mm

thick W-alloy side walls brazed together


Measurements• Temperature

distribution over cooled surface– Surface

temperatures Ts from 5 TCs

– Ts HTCs• Coolant P, T at

test section inlet, exit P

• Mass flow rate Re

GT Plate Test Moduleq

Brass shell

Al cartridge

In

Out

1 mm

Pin-fin array• 808 1 mm 2 mm fins • Increase

cooled area by 276% vs.bare surfacearea A = 1.6103 m2

• 2 mm “bare” strip for jetimpingement

Test module• Jet from H =

0.5 or 2 mm L = 7.62 cm slot

• Coolant: air• Cu heater block• Bare and pin-

covered cooled surfaces

• 2 mm gap• Brass, W have

similar k


Abare

1 mm

Cooled Surface

Thermocouples

Al cartridge

Brass shell

Adiabatic fin tip

Af

Ap

q


Effective vs. Actual HTC • hact = spatially averaged heat transfer coefficient (HTC)

associated with the geometry at the given operating conditions

• heff = HTC necessary for a bare surface to have the same surface temperature as a pin-covered surface subject to the same incident heat flux

• For pin-covered surface:

– Fin efficiency f depends on hact (f as hact)

– Ap = base area between fins; Af = area of fin sides; A = bare/projected area

eff p f f act( )h A A A h


Calculating Actual HTCFor pin-covered surfaces, iterate since f = f (hact)

1) Initial “guess” for hact same as for corresponding bare surface

2) Assuming an adiabatic fin tip, fin efficiency

3) Use f to determine new value of hact

4) Repeat Steps 2 and 3 until (hact, f) converge

c actf

act c

( )1tanh

( )

k A h PerL

L h Per k A

eff p f f act( )h A A A h

– Per = pin perimeter; L = fin length ; Ac = fin cross-sectional area

– f decreases as HTC increases


Effective HTC: Air h

eff [

kW

/(m2

K)]

2 mm Bare 2 mm Pins 0.5 mm Bare 0.5 mm Pins

Re (/104)

• Effective HTC of pin-covered surfaces 90180% greater than HTC of bare surfaces

• Increase is less than increase in area (lower hact and f < 1)


Actual HTC: Air

Bare Pins

hac

t [k

W/(

m2

K)]

Re (/104)

• Actual HTC for pin-covered surfaces lower than that for bare surfaces

• But pins increase cooled surface area by 276%, so heff greater than hact of bare surfaces


• Dynamic similarity dictates that Nusselt number Nu based on hact should be the same for air and He (small Pr effect)

• To predict performance of divertor at prototypical operating conditions, convert hact for air to hact for He

• Actual HTC: correct for changes in thermal conductivity k

• Pin-covered surface: correct for changes in hact and f

– f as Re and as hact

– f > 90% for air; f 5060% for He

HTC for Helium

He airHeact act

air

kh h

k

He He Heeff p f f act( )h A A A h


• Maximum heat flux

– Ts = max. allowable temperature for pressure boundary;

Tin = 600 °C; kHe = 323×103 W/(mK); W fins

– Total thermal resistance RT due to conduction through pressure boundary, convection by coolant

– kPB and LPB pressure boundary conductivity and thickness

– Plate: Ts = 1300 °C; kPB that of pure W; LPB = 2 mm

Calculating Max. q

PBT He He

p f f act PB

1

( )

LR

A A h k A

s inmax

T

( )T Tq

R A


1414

Max. Heat Flux: Plate/He

qm

ax [

MW

/m2

]

Re (/104)

2 mm Bare 2 mm Pins 0.5 mm Bare 0.5 mm Pins

• Increases qmax to 18 MW/m2 at expected Re, and to 19 MW/m2 at higher Re

• Allows operation at lower Re for a given qmax lower pressure drop

For plate divertor, pin-fin array


151515

Plate Conclusions• H = 2 mm 2D jet of He impinging on pin-covered surface

under prototypical conditions (Re = 3.3104) can accommodate heat fluxes up to 18 MW/m2 – Based on heat transfer (vs. thermal stress) considerations

• Pin fins can reduce operating Re, and hence coolant pumping requirements, for a given maximum heat flux– Benefits of pin fins decrease as Re increases and/or kPB

decreases (lower η)• Pin-fin array– Increases effective HTC by 90180%, but reduces actual

HTC– Increases P by at most 40%


• HElium-cooled Modular divertor with Pin array: developed by FZK to accommodate heat fluxes up to 10 MW/m2

HEMP Divertor

Finger + W tile

Pin-fin arrayW

W-alloy

– He enters at 10 MPa, 600 °C, then flows through ~3 mm annular gap, pin-fin array

– He exits at 700 °C via inner tube

– About 5105 modules needed for O(100 m2) divertor

[Diegele et al. 2003; Norajitra et al. 2005]

15.8

14 mm


GT HEMP Test Module

qReverse flow• Coolant: air

• Nominal operating Re = 3.05104 chosen to give 700 °C exit temperature in HEMP

• Fabricated in brass (k similar to W)• Heated by oxy-acetylene torch: q 2.5

MW/m2

• Reverse flow: similar to HEMP• Bare and pin-covered cooled surfaces• Forward flow: round jet with exit dia.

2 mm impinges on cooled surface– 2 mm gap between inner cartridge, cooled

surface 10 mm

5.8

Forward flow

Test Section

q


Test Module• Pressure, temperature measured

at the instrumentation port• Reverse flow: like HEMP• Forward flow• Test section insulated with

Marinite blocks• 48 1 mm 2 mm fins on

1.2 mm pitch: ~3.6 mm dia. clear area in center increase cooled surface area by 351%

Module ComponentsCoolant Port

Inst

rum

enta

tio

n

Por

t

Coolan

t P

ort

q

Pin-Fin Array


Higher Heat Fluxes

• Test section heated with oxy-acetylene torch to achieve higher heat fluxes q– Reaches steady-state q up to

2.5 MW/m2 within ~15 min

– Enables transient heating

• Ceramic sleeve protects insulation and thermocouples (TC) from flame


Temp. Measurements

Heated surface TC

Cooled surface TCs

q

1

1 mm • Five type-E TC (1 at center of heated surface or r = 0 mm; 4 over cooled surface) embedded 1 mm from surface– Cooled surface TCs:

r = 0, 1, 2 and 3 mm• Extrapolated cooled

surface temperature data used to determine average HTCs12 mm

r


Effective HTC: Air Forward flow• Effective HTC of

pin-covered surfaces 20-60% greater than HTC of bare surfaces

• Like plate, increase is less than increase in area (lower hact and f < 1)

hef

f [k

W/(

m2

K)]

Re (/104)

Bare Pins

Re = 3.05104


Actual HTC: Air h

act [

kW

/(m2

K)]

Re (/104)

Forward flow• Like plate, hact

for pin-covered surfaces lower than those for bare surfaces– Pins increase

cooled surface area by 351%

Bare Pins

• Maximum heat flux

– Ts = max. allowable temperature for pressure boundary;

Tin = 600 °C; kHe = 323×103 W/(mK)

– Total thermal resistance RT due to conduction through pressure boundary, convection by coolant

– kPB and LPB pressure boundary conductivity and thickness

– HEMP: Ts = 1200 °C; kPB that of W-1% La2O3; LPB = 1 mm


Calculating Max. q

s inmax

T

( )T Tq

R A

PBT He He

p f f act PB

1

( )

LR

A A h k A


For He• Bare, pin-covered

surfaces both accommodate >10 MW/m2 at nominal Re

• Pin-covered surfaces worse than bare surfaces at higher Re

• Error bar: 10% decrease in kPB

2424

Max. q: Forward Flowq

max [

MW

/m2

]

‒ Bare‒ Pins

Re = 3.05104

Re (/104)


For He• HEMP design

(pin-covered surface) accommodates >10 MW/m2 at nominal Re

• Error bar: 10% decrease in kPB to account for effects of neutron irradiation

qm

ax [

MW

/m2

]

‒ Bare‒ Pins

Max. q: Reverse Flow

Re = 3.05104

Re (/104)


qm

ax [

MW

/m2

]

Bare/ForwardPins/ForwardBare/ReversePins/Reverse

Max. q: HEMP/He

Re = 3.05104

Re (/104)

• HEMP configuration (reverse flow, pin-covered surface) has best thermal performance– No jet

impingement


• Pressure drops rescaled to Po = 414 kPa and To = 300K

• Pins increase P by 25% in forward flow, 75% in reverse flow at nominal Re

Pressure Drops

sys o

o sys

T

T

PP P

P

ΔP

΄ [p

sia]

Re (/104)

Bare/ForwardPins/ForwardBare/ReversePins/Reverse


• ANSYS FLUENT® v12.1– Mesh: Gambit 2.4.6– RNG k-ε turbulence model– Non-equilibrium wall

functions• Two numerical models

– 2D axisymmetric (bare)– 3D 60° symmetric (bare +

pins): ~3.8105 cells• No insulation included;

adiabatic walls– BC confirmed by

simulations

Numerical Simulations50 mm

6


Preliminary Results: Bareh

act [

kW

/(m2

K)]

Re (/104)

Re = 3.05104

Forward flow• 3D w/in 15% of

experimental results near nominal Re; w/in 5% at higher Re– Turbulence

models?• 2D predictions >

3D predictions, experimental results– q = 0.5–2.3

MW/m2

Expts. 2D CFD 3D CFD


HEMP Summary• Experimental studies of forward and reverse flow for

cooling bare and pin fin-covered surfaces– At nominal operating Re = 3.05104, best thermal

performance from HEMP configuration (reverse flow with pins): accommodates heat fluxes up to 13 MW/m2

– But fins increase P by 75% and 25% in reverse and forward flow, respectively, compared with bare surface cases

– Reverse flow with fins alternative to impingement jet cooling

– Fins have negligible benefit for forward flow (jet impingement)

• Numerical simulations– Initial results in qualitative agreement with experiments

Documents

M. Yoda, S. I. Abdel-Khalik, D. L. Sadowski, M. D. Hageman, B. H. Mills, and J. D. Rader G. W. Woodruff School of Mechanical Engineering Extrapolating