M. Yoda, S. I. Abdel-Khalik, D. L. Sadowski, B. H. Mills and M. D. Hageman
G. W. Woodruff School of Mechanical Engineering
Correlations for Divertor Thermal-
Hydraulic Performance at Prototypical
Conditions
ARIES Meeting (7/11) 2
Objectives / MotivationObjectives• Develop generalized parametric design curves for estimating
maximum heat flux and pumping power requirements for the helium-cooled flat-plate (HCFP) divertor with and without fins– Similar curves already developed for modular finger-type design– Adding fins to HCFP increased maximum heat flux qmax to
18 MW/m2 (air results extrapolated to He)
Motivation• Provide design guidance• Develop correlations that can be used in system design codes
(Lane, Mark)
ARIES Meeting (7/11) 3
Approach• Conduct experiments with air on test modules that match initial
HCFP design– Four configurations: two slot widths (W = 0.5 and 2 mm); “bare”
cooled surface and cooled surface with 806 1 mm 2 mm fins – Incident heat fluxes q = 0.220.75 MW/m2
– Coolant flow rate in terms of Reynolds number Re = 1.2104, 3.0104, and 4.5104, spanning prototypical Rep = 3.3104
– Measure cooled surface temperatures and pressure drop p Heat transfer coefficients h and loss coefficients KL
• Extrapolate results to He at prototypical conditions• Generate parametric design curves relating qmax to Re,
maximum surface temperature Ts, and pumping power as a fraction of incident thermal power
ARIES Meeting (7/11) 4
GT Plate Test Moduleq
Brass shell
Al cartridge
In
Out
0.1• Air issues from 0.5 or 2 mm
7.62 cm slot, impinges on bare or finned surface 2 mm away
• Heated by Cu heater block• Measure cooled surface
temperatures with 5 TCs• Measure P, T at module inlet,
exit P• Measure mass flow rate Re
Armor
2.2 cm
6
q
In
Out
2.4 cm 5.4
ARIES Meeting (7/11) 5
• hact = spatially averaged heat transfer coefficient (HTC) at given operating conditions
• heff = HTC for bare surface to have same Ts as surface with fins subject to the same q
• For bare surfaces, hact = heff
– q = Electrical power to heater / Ac
– Ts avg. extrapolated surface temp.
• For surfaces with fins– Fin efficiency η depends on hact
iterative solution– Assume adiabatic fin tip condition– As hact ↑, η ↓ and heff ↓
effs in
cact eff
p f
qh
T T
Ah h
A A
Effective and Actual HTCs
Ac = cooled surface areaAp = base area btw. finsAf = side area of fins
ARIES Meeting (7/11) 6
• Extrapolate experimental data for air to estimate performance of He-cooled divertor at prototypical operating conditions– He at inlet temperature Tin = 600 °C and 700 °C
• Correct actual HTC for changes in coolant properties
• Cases with fins: correct for changes in effective HTC,
HTC for Helium
He airHeact act
air
kh h
k
He He Heeff p f act( )h A A A h
ARIES Meeting (7/11) 7
• Maximum heat flux
– Surface temperature Ts = 1200 °C and 1300 °C: maximum allowable temperature for pressure boundary
• Total thermal resistance RT due to conduction through pressure boundary, convection by coolant
– P = 2 mm = thickness of pressure boundary
– kP = 101 W/(mK) [pure W at 1300 °C]
= thermal conductivity of pressure boundary
s inmax
T
T Tq
R
Calculating Max. q
PT He
eff P
1R
h k
ARIES Meeting (7/11) 8
• To extrapolate pressure drop data to prototypical conditions, determine loss coefficient based on conditions for air at slot
• Determine pumping power based on pressure drop for He under prototypical conditions at same Re
– average of He densities at inlet, outlet • Pumping power as fraction of
total thermal power incident on divertor
Calculating Loss Coeffs.
He He 2HeHe He o o
He LHe
( )where
2
m p VW p K
L 2o o
( ,geometry)/ 2
pK f Re
V
He
HeW
q A
ARIES Meeting (7/11) 9
Parametric Design Curves• Provide guidance among different plate configurations and
operating conditions• Plot q as a function of Re for a given Tin at constant pressure
boundary surface temperature Ts and corresponding pumping power fraction for W = 2 mm– W appears to have little effect on HTC, and W = 0.5 mm has
slightly higher KL
– Heat flux defined using area of pressure boundary: heat flux on tile
• Plot as a function of q and heff as a function of for all four configurations
t
16 mm0.73
22 mmq q q
ARIES Meeting (7/11) 10
Max. q vs. Re : Bare
At Rep = 3.3104
> 10%• q 10 MW/m2
for Ts = 1200 °C
• q 12 MW/m2
for Ts = 1300 °C
• Compare with q 15 MW/m2 for Tin = 600 °C,
Ts = 1300 °C
Re (/104)
q [
MW
/m2
]
Tin = 700 °C
Ts = 1300 °C
1200 °C
=
10%
5%
ARIES Meeting (7/11) 11
Max. q vs. Re : FinsAt Rep = 3.3104
> 10% (less than bare case)
• q 13 MW/m2
for Ts = 1200 °C
• q 16 MW/m2
for Ts = 1300 °C
• Compare with q 18 MW/m2 for Tin = 600 °C, Ts
= 1300 °C
Re (/104)
q [
MW
/m2
]
Tin = 700 °C
1200 °C
= 10
%
5%Ts = 1300 °C
ARIES Meeting (7/11) 12
β vs. Max. q: W = 2 mm
Tin = 600 °C
Tin = 700 °C
q [MW/m2]
Correlations (lines)• Also for W = 0.5 mm• For all Tin = 600 °C,
and Tin = 700 °C,
surfaces with fins:
• For Tin = 700 °C, bare
surfaces:
• A, B, C, D constants
Bare Fins
exp{ }C D q
BAq C
ARIES Meeting (7/11) 13
Eff. HTC vs. β: W = 2 mm
hef
f [k
W/(
m2
K)]
Tin = 600 °C
Tin = 700 °C
Bare Fins
Correlations (lines)• For W = 0.5 mm
and 2 mm
• C, D, E constants
effDh C E
ARIES Meeting (7/11) 14
Summary• Developed generalized parametric design curves for plate-
type divertor based on experimental data of Hageman – Maximum heat flux related to Re for a given surface
temperature and corresponding pumping power fraction– Raising coolant inlet temperature Tin from 600 °C to 700 °C
decreases thermal performance– In all cases, pumping power exceeds 10% of incident
thermal power for Tin = 700 °C
– Obtained exponential and power-law correlations (R2 0.996 in all cases) for pumping power fraction at a given incident heat flux, and effective HTC at a given pumping power fraction
ARIES Meeting (7/11) 15
C D [m2/MW]
Tin = 600 °C
Bare, W = 2 mm 8.9110–5 0.502
Fins, W = 2 mm 1.1210–10 1.102
Bare, W = 0.5 mm 5.0210–5 0.575
Fins, W = 0.5 mm 2.5610–6 0.627
Tin = 700 °C
Fins, W = 2 mm 3.0310–10 1.055
Fins, W = 0.5 mm 1.1210–6 0.831
β Correlations Iexp{ }C D q
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AB
q in [MW/m2]
C
Tin = 700 °C
Bare, W = 2 mm 4.41510–9 7.075 –4.94210–3
Bare, W = 0.5 mm 1.41910–10 8.622 2.77610–3
β Correlations II
BAq C
ARIES Meeting (7/11) 17
C [kW/(m2 K)]
D E [kW/(m2 K)]
Tin = 600 °C
Bare, W = 2 mm 48.71 0.4335 14.54
Fins, W = 2 mm 175.6 0.04069 –103.9
Bare, W = 0.5 mm 38.32 0.31 11.02
Fins, W = 0.5 mm 57.96 0.2754 14.53
Tin = 700 °C
Bare, W = 2 mm 37.53 0.4297 14.5
Fins, W = 2 mm 177.7 0.03857 –110.5
Bare, W = 0.5 mm 31.87 0.3061 10.92
Fins, W = 0.5 mm 48.95 0.271 14.36
heff Correlationseff
Dh C E
