1. 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

2. ARIES Meeting (5/10) 2 Objective / Motivation Objective Experimentally evaluate thermal performance of gas-cooled divertor designs in support of the ARIES team Evaluate variants of current designs to enhance their thermal performance Motivation Experimental validation of numerical studies Divertors may have to accommodate both steady-state and transient heat flux loads exceeding 10 MW/m 2 Performance needs to be “robust” with respect to manufacturing tolerances and variations in flow distribution

3. ARIES Meeting (5/10) 3 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

4. ARIES Meeting (5/10) 4 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, T-tube cool 2.5, 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

5. ARIES Meeting (5/10) 5 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

6. ARIES Meeting (5/10) 6 666 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 qq

7. ARIES Meeting (5/10) 7 777 Components 2 mm slot (L) and 0.5 mm slot (R) Al inner cartridges “Pins” surface brass shell “Bare” surface brass shell A = 1.59  10  3 m 2

8. ARIES Meeting (5/10) 8 GT Air Flow Loop Cu heater block Three heaters q  = VI / A Measure Coolant P, T at inlet, exit  P across module

9. ARIES Meeting (5/10) 9 999 Experimental Conditions GeometryRe q  (MW/m 2 ) Prototype 3.3×10 4  10 H = 0.5, 2 mm Bare, Pins 1.2×10 4 0.22 H = 0.5, 2 mm Bare, Pins 3.0×10 4 0.49 H = 0.5, 2 mm Pins 3.0×10 4 0.62 H = 0.5, 2 mm Bare, Pins 4.5×10 4 0.62, 0.75

10. ARIES Meeting (5/10) 10 Cooled Surface Temps. 4 5 3 2 1 x y 1 mm In 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

11. ARIES Meeting (5/10) 11 A bare 1 mm Cooled Surface Thermocouples Al cartridge Brass shell Adiabatic fin tip AfAf ApAp qq

12. ARIES Meeting (5/10) 12 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 = 9.54  10  4 m 2 ; A f = 5.08  10  3 m 2 – A = 1.59  10  3 m 2

13. ARIES Meeting (5/10) 13 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 actual HTC of bare surfaces Increase is less than increase in area (  f < 1; h act may be less)

14. ARIES Meeting (5/10) 14 Pressure drops rescaled to P o = 414 kPa: Pins increase  P by 40% at most  P greater for H = 0.5 mm slot Pressure Drops  P [kPa]  2 mm Bare  2 mm Pins  0.5 mm Bare  0.5 mm Pins Re (/10 4 )

15. ARIES Meeting (5/10) 15 Calculating Actual HTC For pin-covered surfaces, iterate since  f = f (h act ) 1)Initial “guess” for h act that 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 – Pin perimeter Per = 3.14  10  3 m; length L = 2  10  3 m; tip area A c = 7.85  10  2 m 2 –  f decreases as HTC increases

16. ARIES Meeting (5/10) 16 Actual HTC  Bare Pins h act [kW/(m 2  K)] Re (/10 4 ) Actual HTC for pin-covered surfaces lower than those for bare surfaces But pins increase cooled surface area by 276%

17. ARIES Meeting (5/10) 17 To predict performance of plate-type divertor at prototypical operating conditions, convert h act measured for air to h act for He – T s = 1300 °C; T in = 600 °C; k He = 323×10  3 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 17 HTC for Helium

18. ARIES Meeting (5/10) 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 (/10 4 )

19. ARIES Meeting (5/10) 19 Maximum heat flux – Total thermal resistance R T due to conduction through PFC, convection by coolant – Conductivity of PFC taken to be that of pure tungsten – Thickness of PFC L PFC = 2 mm Calculating Max. Heat Flux

20. ARIES Meeting (5/10) 20 Max. Heat Flux q  max [MW/m 2 ] Re (/10 4 )  2 mm Bare  2 mm Pins  0.5 mm Bare  0.5 mm Pins Fins Increase q  max to 18 MW/m 2 at expected Re, and to 19 MW/m 2 at higher Re Allow operation at lower Re for a given q  max  lower pressure drop

21. ARIES Meeting (5/10) 21 Conclusions H = 2 mm rectangular 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 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 h eff and higher  P than H = 2 mm slot