1. 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

2. ARIES Meeting (7/11) 2 Objectives / Motivation Objectives 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 q  max to 18 MW/m 2 (air results extrapolated to He) Motivation Provide design guidance Develop correlations that can be used in system design codes (Lane, Mark)

3. 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  = 0.22  0.75 MW/m 2 – Coolant flow rate in terms of Reynolds number Re = 1.2  10 4, 3.0  10 4, and 4.5  10 4, spanning prototypical Re p = 3.3  10 4 – Measure cooled surface temperatures and pressure drop  p  Heat transfer coefficients h and loss coefficients K L Extrapolate results to He at prototypical conditions Generate parametric design curves relating q  max to Re, maximum surface temperature T s, and pumping power as a fraction of incident thermal power 

4. ARIES Meeting (7/11) 4 GT Plate Test Module qq 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q In Out 2.4 cm 5.4

5. ARIES Meeting (7/11) 5 h act = spatially averaged heat transfer coefficient (HTC) at given operating conditions h eff = HTC for bare surface to have same T s as surface with fins subject to the same q  For bare surfaces, h act = h eff – q  = Electrical power to heater / A c – T s avg. extrapolated surface temp. For surfaces with fins – Fin efficiency η depends on h act  iterative solution – Assume adiabatic fin tip condition – As h act ↑, η ↓ and h eff ↓ Effective and Actual HTCs A c = cooled surface area A p = base area btw. fins A f = side area of fins

6. 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 T in = 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

7. ARIES Meeting (7/11) 7 Maximum heat flux – Surface temperature T s = 1200 °C and 1300 °C: maximum allowable temperature for pressure boundary Total thermal resistance R T due to conduction through pressure boundary, convection by coolant –  P = 2 mm = thickness of pressure boundary – k P = 101 W/(m  K) [pure W at 1300 °C] = thermal conductivity of pressure boundary Calculating Max. q 

8. 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.

9. 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 T in at constant pressure boundary surface temperature T s 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 K L – Heat flux defined using area of pressure boundary: heat flux on tile Plot  as a function of q  and h eff as a function of  for all four configurations

10. ARIES Meeting (7/11) 10 Max. q  vs. Re : Bare At Re p = 3.3  10 4  > 10% q   10 MW/m 2 for T s = 1200 °C q   12 MW/m 2 for T s = 1300 °C Compare with q   15 MW/m 2 for T in = 600 °C, T s = 1300 °C Re (/10 4 ) q  [MW/m 2 ] T in = 700 °C T s = 1300 °C 1200 °C  = 10% 5%

11. ARIES Meeting (7/11) 11 Max. q  vs. Re : Fins At Re p = 3.3  10 4  > 10% (less than bare case) q   13 MW/m 2 for T s = 1200 °C q   16 MW/m 2 for T s = 1300 °C Compare with q   18 MW/m 2 for T in = 600 °C, T s = 1300 °C Re (/10 4 ) q  [MW/m 2 ] T in = 700 °C 1200 °C  = 10% 5% T s = 1300 °C

12. ARIES Meeting (7/11) 12 β vs. Max. q  : W = 2 mm  T in = 600 °C T in = 700 °C q  [MW/m 2 ] Correlations (lines) Also for W = 0.5 mm For all T in = 600 °C, and T in = 700 °C, surfaces with fins: For T in = 700 °C, bare surfaces: A, B, C, D constants  Bare Fins

13. ARIES Meeting (7/11) 13 Eff. HTC vs. β: W = 2 mm h eff [kW/(m 2  K)]  T in = 600 °C T in = 700 °C  Bare Fins Correlations (lines) For W = 0.5 mm and 2 mm C, D, E constants

14. 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 T in from 600 °C to 700 °C decreases thermal performance – In all cases, pumping power exceeds 10% of incident thermal power for T in = 700 °C – Obtained exponential and power-law correlations (R 2  0.996 in all cases) for pumping power fraction at a given incident heat flux, and effective HTC at a given pumping power fraction

15. ARIES Meeting (7/11) 15 CD [m 2 /MW] T in = 600 °C Bare, W = 2 mm 8.91  10 –5 0.502 Fins, W = 2 mm 1.12  10 –10 1.102 Bare, W = 0.5 mm 5.02  10 –5 0.575 Fins, W = 0.5 mm 2.56  10 –6 0.627 T in = 700 °C Fins, W = 2 mm 3.03  10 –10 1.055 Fins, W = 0.5 mm 1.12  10 –6 0.831 β Correlations I

16. ARIES Meeting (7/11) 16 A B q  in [MW/m 2 ] C T in = 700 °C Bare, W = 2 mm 4.415  10 –9 7.075 –4.942  10 –3 Bare, W = 0.5 mm 1.419  10 –10 8.622 2.776  10 –3 β Correlations II

17. ARIES Meeting (7/11) 17 C [kW/(m 2  K)] D E [kW/(m 2  K)] T in = 600 °C Bare, W = 2 mm48.710.433514.54 Fins, W = 2 mm175.60.04069–103.9 Bare, W = 0.5 mm38.320.3111.02 Fins, W = 0.5 mm57.960.275414.53 T in = 700 °C Bare, W = 2 mm37.530.429714.5 Fins, W = 2 mm177.70.03857–110.5 Bare, W = 0.5 mm31.870.306110.92 Fins, W = 0.5 mm48.950.27114.36 h eff Correlations