Correlations for Divertor Thermal-Hydraulic Performance at Prototypical Conditions

1. Correlations for Divertor Thermal-Hydraulic Performance at Prototypical Conditions M. Yoda, S. I. Abdel-Khalik, D. L. Sadowski, B. H. Mills and M. D. Hageman G. W. Woodruff School of Mechanical Engineering

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/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 = 0.220.75 MW/m2 • Coolant flow rate in terms of Reynolds number Re = 1.2104, 3.0104, and 4.5104, spanning prototypical Rep = 3.3104 • 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 qmax to Re, maximum surface temperature Ts, and pumping power as a fraction of incident thermal power  ARIES Meeting (7/11)

4. GT Plate Test Module q q Armor Brass shell 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 In In 2.4 cm 6 5.4 Out Out 2.2 cm Al cartridge ARIES Meeting (7/11)

5. Effective and Actual HTCs Ac = cooled surface area Ap = base area btw. fins Af = side area of fins ARIES Meeting (7/11) • 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 ↓

6. HTC for Helium • 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,  ARIES Meeting (7/11)

7. Calculating Max. q • 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/(mK) [pure W at 1300 °C] = thermal conductivity of pressure boundary ARIES Meeting (7/11)

8. Calculating Loss Coeffs. • 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 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 Tsand 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 ARIES Meeting (7/11)

10. Max. q vs. Re : Bare At Rep = 3.3104 •  > 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 Tin = 700 °C q[MW/m2] Ts = 1300 °C 1200 °C  = 10% 5% Re (/104) ARIES Meeting (7/11)

11. Max. q vs. Re : Fins At Rep = 3.3104 •  > 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 Tin = 700 °C q[MW/m2] Ts = 1300 °C 1200 °C 5%  = 10% Re (/104) ARIES Meeting (7/11)

12. βvs. Max. q: W = 2 mm 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 Tin = 600 °C Tin = 700 °C   Bare  Fins q[MW/m2] ARIES Meeting (7/11)

13. Eff. HTC vs.β: W = 2 mm heff [kW/(m2K)] Correlations (lines) • For W = 0.5 mm and 2 mm • C, D, E constants  Bare  Fins Tin = 600 °C Tin = 700 °C  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. β Correlations I ARIES Meeting (7/11)

16. β Correlations II ARIES Meeting (7/11)

17. heff Correlations ARIES Meeting (7/11)