Parametric Design Curves for Divertor Thermal Performance at Prototypical Conditions

1. Parametric Design Curves for Divertor Thermal Performance at Prototypical Conditions M. Yoda, S. I. Abdel-Khalik, D. L. Sadowski, B. H. Mills, and J. D. Rader G. W. Woodruff School of Mechanical Engineering

2. Objectives / Motivation Objectives • 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 qmax as a function of Re for different values of maximum surface temperature Tsand pumping power fraction  ARIES Meeting (10/10)

4. HEMP Divertor • HElium-cooled Modular divertor with Pin array: developed by FZK [Diegele et al. 2003; Norajitra et al. 2005] • 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 5105 modules needed for O(100 m2) divertor Finger + W tile 15.8 Pin-fin array W W-alloy 14 mm ARIES Meeting (10/10)

5. GT Test Module Forward flow Reverse flow • Operating coolant flow ratedetermined from energy balance (T = 100 °C) and incident heat flux of 10 MW/m2 • Re based on 7104 for reverse flow, 7.6104 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 q 2 2 5.8 1 10 mm 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 Effective vs. Actual HTC 6 ARIES Meeting (10/10)

7. 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 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 :   5055% for He at prototypical Re (vs. >90% for air near room temperatures) ARIES Meeting (10/10)

8. Calculating Max. q • 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 ARIES Meeting (10/10)

9. At prototypical Re: HEMJ, HEMP and fwd flow w/fins accommodate up 2123 MW/m2 at pressure boundary; 9.510.4 MW/m2 at tile surface Fins give little benefit for forward flow (beyond jet impingement) Max. q: HEMP/He HEMJ-like Rev w/o fins Fwd w/fins HEMP-like qmax[MW/m2] Ts = 1200 °C Re (/104) ARIES Meeting (10/10)

10. Calculating Loss Coeffs. • 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 ARIES Meeting (10/10)

11. At prototypical Re Forward flow has higher loss Fins increase loss for a given flow direction Fwd flow w/fins has highest KL Loss Coefficients KL HEMJ-like Rev w/o fins Fwd w/fins HEMP-like KL Re (/104) 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 Tsand 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 ARIES Meeting (10/10)

13. Design Curves: HEMJ • Ts = 1100 °C, 1200 °C, 1300 °C •  = 5, 10, 15, 20% • At Re = 7.6104 •   12% • q  23 MW/m2 • qt 10.4 MW/m2 • For  < 10%, Ts = 1200 °C • Re < 7104 • q< 22 MW/m2 • qt< 10 MW/m2 q[MW/m2] Ts increasing  increasing Re (/104) ARIES Meeting (10/10)

14. Design Curves: HEMP • Ts = 1100 °C, 1200 °C, 1300 °C •  = 5, 10, 15, 20% • At Re = 7.0104 •   13% • q 21 MW/m2 • qt 9.5 MW/m2 • For  < 10%, Ts = 1200 °C • Re < 6104 • q< 20 MW/m2 • qt < 9 MW/m2 q[MW/m2] Ts increasing  increasing Re (/104) 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 = 77.6104, 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 ARIES Meeting (10/10)