extrapolating experimental results for model divertor studies to prototypical conditions

M. Yoda, S. I. Abdel-Khalik, D. L. Sadowski and M. D. Hageman

Woodruff School of Mechanical Engineering

Extrapolating Experimental Results for Model Divertor Studies to Prototypical Conditions

ARIES Meeting (5/10) 2

Objective / MotivationObjective• Experimentally evaluate thermal performance of gas-cooled

divertor designs in support of the ARIES team• Evaluate variants of current designs to enhance their thermal

performanceMotivation• Experimental validation of numerical studies• Divertors may have to accommodate both steady-state and

transient heat flux loads exceeding 10 MW/m2 • Performance needs to 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 at conditions matching and

spanning expected non-dimensional parameters for prototypical operating conditions– Reynolds number Re– Use air instead of He

• Measure cooled surface temperatures and pressure drop– Effective and actual heat transfer coefficients– Normalized pressure drops

• Compare experimental data with predictions from CFD software for test geometry and conditions


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, T-tube cool 2.5, 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


Pin-Fin Array• Can thermal performance of leading divertor designs be further

improved?– Mo foam in 2 mm gap increased HTC by up to 50%, but also

increased pressure drop by up to 100% [Gayton et al. 2009]

– HEMP: coolant flows through pin-fin array [Diegele et al. 2003]

• Combine jet impingement cooling of plate-type divertor with pin-fin array– Pin-fin array increases cooled surface area like foam, but should have

less pressure drop– Pins span entire 2 mm gap, with 2 mm clear strip in center to allow jet

to impinge


666

GT Test Module

In

Out

Brass shell

Al cartridge

Plate design• Jet from H =

0.5 mm L = 20 cm slot

• Coolant: He• Bare cooled

surface• 2 mm gap

Test module• Jet from H = 0.5

or 2 mm L = 7.62 cm slot

• Coolant: Air• Bare and pin-

covered cooled surfaces

• 2 mm gap• Brass, W have

similar k

W Armor

W-alloy

Out

In

q q


777

Components2 mm slot (L) and 0.5 mm slot (R) Al inner cartridges

“Pins” surface brass shell

“Bare” surface brass shellA = 1.59103 m2


GT Air Flow LoopCu heater block• Three heaters• q = VI / A

Measure• Coolant P, T at inlet, exit P across module•

in 2 / ( )m Re m L


999

Experimental Conditions

Geometry Re q (MW/m2)

Prototype 3.3×104 10

H = 0.5, 2 mmBare, Pins 1.2×104 0.22

H = 0.5, 2 mmBare, Pins 3.0×104 0.49

H = 0.5, 2 mmPins 3.0×104 0.62

H = 0.5, 2 mmBare, Pins 4.5×104 0.62, 0.75


101010

Cooled Surface Temps.

4

5321

x

y

1 mmIn

Out

• Five thermocouples embedded 1 mm inside brass shell near center of slot to avoid edge effects

• Temperatures extrapolated to surface, then used to determine local heat transfer coefficients

• Spatially averaged HTC average of five local HTC results


Abare

1 mm

Cooled Surface

Thermocouples

Al cartridge

Brass shell

Adiabatic fin tip

Af

Ap

q


12

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 = 9.54104 m2; Af = 5.08103 m2

– A = 1.59103 m2

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


Effective HTC: Air h

eff [

kW/(m

2

K)]

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

Re (/104)

• Effective HTC of pin-covered surfaces 90-180% greater than actual HTC of bare surfaces

• Increase is less than increase in area (f < 1; hact may be less)


• Pressure drops rescaled to Po = 414 kPa:

• Pins increase P by 40% at most

P greater for H = 0.5 mm slot

Pressure DropsP

[kP

a]

o

sysPP P

P


Re (/104)


151515

Calculating Actual HTCFor pin-covered surfaces, iterate since f = f (hact)1) Initial “guess” for hact that for corresponding bare surface2) 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

( )1 tanh( )

k A h PerL

L h Per k A

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

– Pin perimeter Per = 3.14103 m; length L = 2 103 m; tip area Ac = 7.85102 m2

– f decreases as HTC increases


Actual HTC Bare Pins

hac

t [kW

/(m2

K)]

Re (/104)

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

• But pins increase cooled surface area by 276%


• To predict performance of plate-type divertor at prototypical operating conditions, convert hact measured for air to hact for He– Ts = 1300 °C; Tin = 600 °C; kHe = 323×103 W/(m K); W fins

• For bare surface correct for changes in thermal conductivity

• For pin-covered surface, correct for changes in f and thermal conductivity

171717

HTC for Helium

He airHeact act

air

kh h

k

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


18

Fin Efficiency: He vs. Air f lower for He

because HTCs higher

f as Re• Tungsten (k = 101

W/(m K)) fins for He, vs. brass (k = 115 W/(m K)) fins for air

f decreases if k decreases

Air He

f [

%]

Re (/104)


• Maximum heat flux

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

– Conductivity of PFC taken to be that of pure tungsten– Thickness of PFC LPFC = 2 mm

Calculating Max. Heat Flux

PFCT He He

p f f act W

1( )

LRA A h k A

Tmax

s in( )Rq

T T A


2020

Max. Heat Fluxq

max

[MW

/m2

]

Re (/104)


Fins• Increase qmax to

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

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


212121

Conclusions• H = 2 mm rectangular jet of He impinging on pin-covered

surface under prototypical conditions (Re = 3.3104) can accommodate heat fluxes up to 18 MW/m2 – Based only 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 k decreases

• Pin-fin array– Increases effective HTC by 90-180%, but decreases actual HTC– Increases P by at most 40% – H = 0.5 mm slot consistently gives lower heff and higher P than

H = 2 mm slot

extrapolating experimental results for model divertor studies to prototypical conditions

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