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 / Motivation Objectives 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/m 2 Performance should be “robust” with respect to manufacturing tolerances and variations in flow distribution

ARIES Meeting (7/10) 3 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

ARIES Meeting (7/10) 4 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?

ARIES Meeting (7/10) 5 Plate-Type Divertor Covers large area (2000 cm 2 = 0.2 m 2 ): divertor area O(100 m 2 ) 100 cm Castellated W armor 0.5 cm thick 20 – HEMJ cools 2.5 cm 2 ; T-tube cools 13 cm 2 – Accommodates up to 10 MW/m 2 without exceeding T max  1300 °C,  max  400 MPa – 9 individual manifold units with ~3 mm thick W-alloy side walls brazed together

ARIES Meeting (7/10) 6 Measurements Temperature distribution over cooled surface – Surface temperatures T s from 5 TCs – T s  HTCs Coolant P, T at test section inlet, exit   P Mass flow rate  Re GT Plate Test Module qq Brass shell Al cartridge In Out 1 mm Pin-fin array 808  1 mm  2 mm fins Increase cooled area by 276% vs. bare surface area A = 1.6  10  3 m 2 2 mm “bare” strip for jet impingement 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

ARIES Meeting (7/10) 7 A bare 1 mm Cooled Surface Thermocouples Al cartridge Brass shell Adiabatic fin tip AfAf ApAp qq

ARIES Meeting (7/10) 8 Effective vs. Actual HTC h act = spatially averaged heat transfer coefficient (HTC) associated with the geometry at the given operating conditions h eff = 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 h act (  f  as h act  ) – A p = base area between fins; A f = area of fin sides; A = bare/projected area

ARIES Meeting (7/10) 9 Calculating Actual HTC For pin-covered surfaces, iterate since  f = f (h act ) 1)Initial “guess” for h act same as for corresponding bare surface 2)Assuming an adiabatic fin tip, fin efficiency 3)Use  f to determine new value of h act 4)Repeat Steps 2 and 3 until (h act,  f ) converge – Per = pin perimeter; L = fin length ; A c = fin cross- sectional area –  f decreases as HTC increases

ARIES Meeting (7/10) 10 Effective HTC: Air h eff [kW/(m 2  K)]  2 mm Bare  2 mm Pins  0.5 mm Bare  0.5 mm Pins Re (/10 4 ) Effective HTC of pin-covered surfaces 90  180% greater than HTC of bare surfaces Increase is less than increase in area (lower h act and  f < 1)

ARIES Meeting (7/10) 11 Actual HTC: Air  Bare Pins h act [kW/(m 2  K)] Re (/10 4 ) Actual HTC for pin-covered surfaces lower than that for bare surfaces But pins increase cooled surface area by 276%, so h eff greater than h act of bare surfaces

ARIES Meeting (7/10) 12 Dynamic similarity dictates that Nusselt number Nu based on h act should be the same for air and He (small Pr effect) To predict performance of divertor at prototypical operating conditions, convert h act for air to h act for He Actual HTC: correct for changes in thermal conductivity k Pin-covered surface: correct for changes in h act and  f –  f  as Re  and as h act  –  f > 90% for air;  f  50  60% for He HTC for Helium

ARIES Meeting (7/10) 13 Maximum heat flux – T s = max. allowable temperature for pressure boundary; T in = 600 °C; k He = 323×10  3 W/(m  K); W fins – Total thermal resistance R T due to conduction through pressure boundary, convection by coolant – k PB and L PB pressure boundary conductivity and thickness – Plate: T s = 1300 °C; k PB that of pure W; L PB = 2 mm Calculating Max. q 

ARIES Meeting (7/10) 14 Max. Heat Flux: Plate/He q  max [MW/m 2 ] Re (/10 4 )  2 mm Bare  2 mm Pins  0.5 mm Bare  0.5 mm Pins Increases q  max to 18 MW/m 2 at expected Re, and to 19 MW/m 2 at higher Re Allows operation at lower Re for a given q  max  lower pressure drop For plate divertor, pin-fin array

ARIES Meeting (7/10) 15 Plate Conclusions H = 2 mm 2D jet of He impinging on pin-covered surface under prototypical conditions (Re = 3.3  10 4 ) can accommodate heat fluxes up to 18 MW/m 2 – 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 k PB decreases (lower η) Pin-fin array – Increases effective HTC by 90  180%, but reduces actual HTC – Increases  P by at most 40%

ARIES Meeting (7/10) 16 HElium-cooled Modular divertor with Pin array: developed by FZK to accommodate heat fluxes up to 10 MW/m 2 HEMP Divertor Finger + W tile Pin-fin array W 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 5  10 5 modules needed for O(100 m 2 ) divertor [Diegele et al. 2003; Norajitra et al. 2005] mm

ARIES Meeting (7/10) 17 GT HEMP Test Module qq Reverse flow Coolant: air Nominal operating Re = 3.05  10 4 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/m 2 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q ARIES Meeting (7/10) 18 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 Components Coolant Port Instrumentation Port Coolant Port qq Pin-Fin Array

ARIES Meeting (7/10) 19 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/m 2 within ~15 min – Enables transient heating Ceramic sleeve protects insulation and thermocouples (TC) from flame

ARIES Meeting (7/10) 20 Temp. Measurements Heated surface TC Cooled surface TCs q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 HTCs 12 mm r

ARIES Meeting (7/10) 21 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 h act and  f < 1) h eff [kW/(m 2  K)] Re (/10 4 ) Bare  Pins Re = 3.05  10 4

ARIES Meeting (7/10) 22 Actual HTC: Air h act [kW/(m 2  K)] Re (/10 4 ) Forward flow Like plate, h act for pin-covered surfaces lower than those for bare surfaces – Pins increase cooled surface area by 351% Bare  Pins

Maximum heat flux – T s = max. allowable temperature for pressure boundary; T in = 600 °C; k He = 323×10  3 W/(m  K) – Total thermal resistance R T due to conduction through pressure boundary, convection by coolant – k PB and L PB pressure boundary conductivity and thickness – HEMP: T s = 1200 °C; k PB that of W-1% La 2 O 3 ; L PB = 1 mm ARIES Meeting (7/10) 23 Calculating Max. q 

ARIES Meeting (7/10) 24 For He Bare, pin-covered surfaces both accommodate >10 MW/m 2 at nominal Re Pin-covered surfaces worse than bare surfaces at higher Re Error bar: 10% decrease in k PB 24 Max. q  : Forward Flow q  max [MW/m 2 ] ‒ Bare ‒ Pins Re = 3.05  10 4 Re (/10 4 )

ARIES Meeting (7/10) 25 For He HEMP design (pin-covered surface) accommodates >10 MW/m 2 at nominal Re Error bar: 10% decrease in k PB to account for effects of neutron irradiation q  max [MW/m 2 ] ‒ Bare ‒ Pins Max. q  : Reverse Flow Re = 3.05  10 4 Re (/10 4 )

ARIES Meeting (7/10) 26 q  max [MW/m 2 ] Bare/Forward Pins/Forward Bare/Reverse Pins/Reverse Max. q  : HEMP/He Re = 3.05  10 4 Re (/10 4 ) HEMP configuration (reverse flow, pin- covered surface) has best thermal performance – No jet impingement

ARIES Meeting (7/10) 27 Pressure drops rescaled to P o = 414 kPa and T o = 300K Pins increase  P by 25% in forward flow, 75% in reverse flow at nominal Re Pressure Drops Δ P ΄ [psia] Re (/10 4 ) Bare/Forward Pins/Forward Bare/Reverse Pins/Reverse

ARIES Meeting (7/10) 28 ANSYS FLUENT ® v12.1 – Mesh: Gambit – RNG k-ε turbulence model – Non-equilibrium wall functions Two numerical models – 2D axisymmetric (bare) – 3D 60° symmetric (bare + pins): ~3.8  10 5 cells No insulation included; adiabatic walls – BC confirmed by simulations Numerical Simulations 50 mm 6

ARIES Meeting (7/10) 29 Preliminary Results: Bare h act [kW/(m 2  K)] Re (/10 4 ) Re = 3.05  10 4 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/m 2  Expts.  2D CFD 3D CFD

ARIES Meeting (7/10) 30 HEMP Summary Experimental studies of forward and reverse flow for cooling bare and pin fin-covered surfaces – At nominal operating Re = 3.05  10 4, best thermal performance from HEMP configuration (reverse flow with pins): accommodates heat fluxes up to 13 MW/m 2 – 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

ARIES Meeting (7/10) 31 ARIES Meeting (7/10) 31 Forward Flow Max. Heat Flux: He q  max [MW/m 2 ] Re ‒ Bare ‒ Pins Re = 30500

ARIES Meeting (7/10) 32 ARIES Meeting (7/10) 32 Reverse Flow Max. Heat Flux: He q  max [MW/m 2 ] Re ‒ Bare ‒ Pins Re = 30500