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

2. ARIES Meeting (10/10) 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

3. 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 K L – 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 T s and pumping power fraction 

4. ARIES Meeting (10/10) 4 HElium-cooled Modular divertor with Pin array: developed by FZK 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 through central port in inner tube – About 5  10 5 modules needed for O(100 m 2 ) divertor [Diegele et al. 2003; Norajitra et al. 2005] 15.8 14 mm

5. ARIES Meeting (10/10) 5 Forward flowReverse flow GT Test Module qq 10 mm 5.81 2 2 Operating coolant flow rate determined from energy balance (  T = 100 °C) and incident heat flux of 10 MW/m 2  – Re based on 7  10 4 for reverse flow, 7.6  10 4 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/m 2 – Reverse flow w/pins like HEMP – Forward flow w/o pins like HEMJ, but with only 2 mm one jet

6. ARIES Meeting (10/10) 6 h act = spatially averaged heat transfer coefficient (HTC) at given operating conditions h eff = HTC for surface w/o fins to have the same surface temperature T s as surface w/fins subject to the same heat flux For surfaces with fins: – Iterative solution, since pin efficiency  depends on h act – Assume adiabatic fin tip boundary condition  A = area of outer surface of shell endcap  A c = area of inner surface of shell endcap  A p = base area between fins  A f = total fin surface area exposed to coolant 6 Effective vs. Actual HTC

7. ARIES Meeting (10/10) 7 Extrapolate experimental data for air to estimate performance of He-cooled divertor at prototypical operating conditions – He at inlet temperature T in = 600 °C flowing past W-1% La 2 O 3 fins Correct actual HTC for changes in coolant properties Cases with fins: correct for changes in effective HTC,  –   as Re and h act  :   50  55% for He at prototypical Re (vs. >90% for air near room temperatures) HTC for Helium

8. ARIES Meeting (10/10) 8 Maximum heat flux – Surface temperature T s = 1200 °C max. allowable temperature for W-1% La 2 O 3 pressure boundary Total thermal resistance R T due to conduction through pressure boundary, convection by coolant –  P = 1 mm thickness of pressure boundary – k P thermal conductivity of pressure boundary Define q  in terms of area A = 113 mm 2 of pressure boundary – Heat flux on HEMP tile of area A t = 250 mm 2 Calculating Max. q 

9. ARIES Meeting (10/10) 9 q  max [MW/m 2 ] Max. q  : HEMP/He At prototypical Re: HEMJ, HEMP and fwd flow w/fins accommodate up 21  23 MW/m 2 at pressure boundary; 9.5  10.4 MW/m 2 at tile surface – Fins give little benefit for forward flow (beyond jet impingement) Re (/10 4 ) HEMJ-likeRev w/o fins Fwd w/finsHEMP-like T s = 1200 °C

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

11. ARIES Meeting (10/10) 11 Loss Coefficients K L At prototypical Re Forward flow has higher loss Fins increase loss for a given flow direction Fwd flow w/fins has highest K L Re (/10 4 ) KLKL HEMJ-likeRev w/o fins Fwd w/finsHEMP-like

12. 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 T s and corresponding pumping power fraction  – T s determined by thermal stress and material limits –   10% recommended – Since heat flux defined using area of pressure boundary, heat flux on tile

13. ARIES Meeting (10/10) 13 Design Curves: HEMJ q  [MW/m 2 ] Re (/10 4 ) T s = 1100 °C, 1200 °C, 1300 °C  = 5, 10, 15, 20% At Re = 7.6  10 4 –   12% – q   23 MW/m 2 – q t  10.4 MW/m 2 For  < 10%, T s = 1200 °C – Re < 7  10 4 – q  < 22 MW/m 2 – q t  < 10 MW/m 2  increasing T s increasing

14. ARIES Meeting (10/10) 14 Design Curves: HEMP q  [MW/m 2 ] Re (/10 4 ) T s = 1100 °C, 1200 °C, 1300 °C  = 5, 10, 15, 20% At Re = 7.0  10 4 –   13% – q  21 MW/m 2 – q t  9.5 MW/m 2 For  < 10%, T s = 1200 °C – Re < 6  10 4 – q  < 20 MW/m 2 – q t  < 9 MW/m 2  increasing T s increasing

15. 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  10 4, HEMJ- and HEMP-like configurations accommodate heat fluxes up to 23 MW/m 2 / 10.4 MW/m 2 at pressure boundary / plasma-facing surface, but pumping power >10% of total power