M. Yoda, S. I. Abdel-Khalik, D. L. Sadowski, B. H. Mills, and J. D. Rader
G. W. Woodruff School of Mechanical Engineering
Parametric Design Curves for Divertor
Thermal Performance at Prototypical
Conditions
ARIES Meeting (10/10) 2
Objectives / MotivationObjectives• Evaluate whether fins enhance performance of finger-
type modular divertor designs– HEMP: primary cooling from flow through fin
array– HEMJ: primary cooling from jet impingement
• Develop generalized charts for estimating maximum heat flux and pumping power requirements
Motivation• Provide design guidance for various divertor concepts• Generalized charts can be incorporated into system
design codes
ARIES Meeting (10/10) 3
Approach• Conduct experiments on test modules that closely match
divertor geometries with and without fins– Operate at wide range of Reynolds numbers Re spanning
prototypical operating conditions– Use air instead of He– Measure cooled surface temperatures and pressure drop– Evaluate heat transfer coefficients (HTC) and loss
coefficients KL
– Use data to determine corresponding HTC and pressure drop for He
• Generate parametric design curves giving maximum heat flux qmax as a function of Re for different values of maximum surface temperature Ts and pumping power fraction
ARIES Meeting (10/10) 4
• HElium-cooled Modular divertor with Pin array: developed by FZK
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 through central port in inner tube
– About 5105 modules needed for O(100 m2) divertor
[Diegele et al. 2003; Norajitra et al. 2005]
15.8
14 mm
ARIES Meeting (10/10) 5
Forward flowReverse flow
GT Test Module
q
10 mm
5.8 1
2
2
• Operating coolant flow rate determined from energy balance (T = 100 °C) and incident heat flux of 10 MW/m2 – Re based on 7104 for reverse flow,
7.6104 for forward flow: at central port• Experiments: two divertor geometries and two
flow configurations = Four cases– Coolant: air– Heated by oxy-acetylene flame:
q < 2 MW/m2
– Reverse flow w/pins like HEMP– Forward flow w/o pins like HEMJ, but with
only 2 mm one jet
He 4.8 g/sm
Hem
ARIES Meeting (10/10) 6
• hact = spatially averaged heat transfer coefficient (HTC) at given operating conditions
• heff = HTC for surface w/o fins to have the same surface temperature Ts as surface w/fins subject to the same heat flux
• For surfaces with fins: – Iterative solution, since pin efficiency depends on hact
– Assume adiabatic fin tip boundary condition A = area of outer surface of shell endcap Ac = area of inner surface of shell endcap Ap = base area between fins Af = total fin surface area exposed to coolant
6
Effective vs. Actual HTC
eff c p f act( )h A A A h
effs in c
q Ah
T T A
q
ARIES Meeting (10/10) 7
• Extrapolate experimental data for air to estimate performance of He-cooled divertor at prototypical operating conditions– He at inlet temperature Tin = 600 °C flowing past
W-1% La2O3 fins
• Correct actual HTC for changes in coolant properties
• Cases with fins: correct for changes in effective HTC,
– as Re and hact : 5055% for He at prototypical Re (vs. >90% for air near room temperatures)
HTC for Helium
He airHeact act
air
kh h
k
He He Heeff c p f act( )h A A A h
ARIES Meeting (10/10) 8
• Maximum heat flux
– Surface temperature Ts = 1200 °C max. allowable temperature for W-1% La2O3 pressure boundary
• Total thermal resistance RT due to conduction through pressure boundary, convection by coolant
– P = 1 mm thickness of pressure boundary
– kP thermal conductivity of pressure boundary
• Define q in terms of area A = 113 mm2 of pressure boundary – Heat flux on HEMP tile of area At = 250 mm2
Calculating Max. q
PT He
eff c P
AR
h A k
s inmax
T
T Tq
R
t t( / ) 0.45q A A q q
ARIES Meeting (10/10) 9
qm
ax [
MW
/m2
]
Max. q: HEMP/HeAt prototypical Re:• HEMJ, HEMP and
fwd flow w/fins accommodate up 2123 MW/m2 at pressure boundary; 9.510.4 MW/m2 at tile surface– Fins give little
benefit for forward flow (beyond jet impingement)
Re (/104)
HEMJ-like Rev w/o finsFwd w/fins HEMP-like
Ts = 1200 °C
ARIES Meeting (10/10) 10
• To extrapolate pressure drop data to prototypical conditions, determine loss coefficient based on conditions for air at central port (at end) of inner tube
• 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 power
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 He 4.8 g/sm
HeW
q A
ARIES Meeting (10/10) 11
Loss Coefficients KL
At prototypical Re • Forward flow
has higher loss• Fins increase
loss for a given flow direction
• Fwd flow w/fins has highest KL
Re (/104)
KL
HEMJ-like Rev w/o finsFwd w/fins HEMP-like L ( ,geometry)K f Re
ARIES Meeting (10/10) 12
Parametric Design Curves• Provide design guidance for different divertor configurations at
prototypical conditions• Consider only the cases with highest heat flux, lowest loss
– HEMJ-like: forward flow (single jet impingement), no fins– HEMP-like: reverse flow, fins
• Plot q as a function of Re at constant pressure boundary surface temperature Ts and corresponding pumping power fraction – Ts determined by thermal stress and material limits
– 10% recommended – Since heat flux defined using area of pressure boundary,
heat flux on tile t 0.45q q
ARIES Meeting (10/10) 13
Design Curves: HEMJq
[M
W/m
2]
Re (/104)
• Ts = 1100 °C,
1200 °C, 1300 °C = 5, 10, 15, 20%• At Re = 7.6104
– 12%– q 23 MW/m2
– qt 10.4 MW/m2
• For < 10%, Ts = 1200 °C– Re < 7104
– q< 22 MW/m2
– qt< 10 MW/m2 increasing
Ts increasing
ARIES Meeting (10/10) 14
Design Curves: HEMPq
[M
W/m
2]
Re (/104)
• Ts = 1100 °C,
1200 °C, 1300 °C = 5, 10, 15, 20%• At Re = 7.0104
– 13%– q 21 MW/m2
– qt 9.5 MW/m2
• For < 10%, Ts = 1200 °C– Re < 6104
– q< 20 MW/m2
– qt < 9 MW/m2
increasing
Ts increasing
ARIES Meeting (10/10) 15
Summary• Experimental studies to evaluate adding pin fins to modular
finger-type divertor designs – Reverse flow and forward flow (jet impingement)– Use measured pressure drops to estimate loss coefficients and
coolant pumping power as fraction of total power • Developed generalized parametric design curves for HEMJ- and
HEMP-like configurations (best thermal performance)– Maximum heat flux vs. Re for a given surface temperature
and corresponding pumping power fraction– At Re = 77.6104, HEMJ- and HEMP-like configurations
accommodate heat fluxes up to 23 MW/m2 / 10.4 MW/m2 at pressure boundary / plasma-facing surface, but pumping power >10% of total power
