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					  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
      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)                                        2
                        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 Ts and pumping power fraction 
ARIES Meeting (10/10)                                             3
                   HEMP Divertor
 • HElium-cooled Modular divertor with Pin array: developed
     by FZK
      – He enters at 10 MPa,    Finger + W tile   [Diegele et al. 2003;
                                                  Norajitra et al. 2005]
        600 °C, then flows
                                         15.8
        through ~3 mm annular
                                          W          Pin-fin array
        gap, pin-fin array
      – He exits at 700 °C
        through central port in
        inner tube
      – About 5105 modules         W-alloy
        needed for O(100 m2)                             14 mm
        divertor

ARIES Meeting (10/10)                                                  4
                GT Test Module
  • Operating coolant flow rate determined from
    energy balance (T = 100 °C) and incident heat Forwardflow
                                                     Reverse flow
    flux of 10 MW/m2  mHe  4.8 g/s                            q
     – Re based on mHe 7104 for reverse flow,
       7.6104 for forward flow:  at central port
                                                   2
  • Experiments: two divertor geometries and two
    flow configurations = Four cases
                                                           2
     – Coolant: air
     – Heated by oxy-acetylene flame:
       q < 2 MW/m2
     – Reverse flow w/pins like HEMP
                                                          5.8 1
     – Forward flow w/o pins like HEMJ, but with
       only 2 mm one jet                                10 mm

ARIES Meeting (10/10)                                            5
      Effective vs. Actual HTC
  • 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 q
                                      q A
                            heff 
                                   Ts  Tin Ac
  • For surfaces with fins: heff Ac  ( Ap   Af ) hact
     – 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
ARIES Meeting (10/10)                                                    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 flowing past
       W-1% La2O3 fins
  • Correct actual HTC for changes in coolant properties
                                   kHe  air
                           hact  
                             He
                                          hact
                                   kair 
  • Cases with fins: correct for changes in effective HTC, 
                        heff Ac  ( Ap  He Af ) hact
                         He                        He


       –   as Re and hact :   5055% for He at prototypical Re
         (vs. >90% for air near room temperatures)


ARIES Meeting (10/10)                                                  7
           Calculating Max. q
  • Maximum heat flux                  Ts  Tin
                                 
                               qmax 
                                           RT
     – 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                       A   P
                                                 RT  He 
                                                      heff Ac kP
     – 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
                         qt  ( A / At ) q  0.45 q

ARIES Meeting (10/10)                                            8
                   Max. q: HEMP/He
                HEMJ-like Rev w/o fins     At prototypical Re:
                Fwd w/fins HEMP-like       • HEMJ, HEMP and
                                              fwd flow w/fins
qmax [MW/m2]




                                              accommodate up
                                              2123 MW/m2 at
                                              pressure boundary;
                                              9.510.4 MW/m2
                                              at tile surface
                                              – Fins give little
                                                benefit for
                Ts = 1200 °C                    forward flow
                                                (beyond jet
                                                impingement)
                               Re (/104)
ARIES Meeting (10/10)                                              9
      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
                              p
                      KL             f ( Re,geometry)
                            oVo / 2
                                2

  • Determine pumping power based on pressure drop for He under
    prototypical conditions at same Re
               mHe pHe                             o (VoHe )2
                                                     He
        WHe                         where p He               KL
                  He                                   2
     – He average of He densities at inlet, outlet; mHe  4.8 g/s
  • Pumping power as fraction of total power           WHe
                                                  
                                                       q A

ARIES Meeting (10/10)                                               10
         Loss Coefficients KL
          HEMJ-like Rev w/o fins    K L  f ( Re,geometry)
          Fwd w/fins HEMP-like
                                    At prototypical Re
                                    • Forward flow
                                       has higher loss
 KL




                                    • Fins increase
                                       loss for a given
                                       flow direction
                                    • Fwd flow w/fins
                                       has highest KL


                        Re (/104)
ARIES Meeting (10/10)                                     11
    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 Ts and 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 qt  0.45 q

ARIES Meeting (10/10)                                                  12
              Design Curves: HEMJ
                                                   • Ts = 1100 °C,
                                                     1200 °C, 1300 °C
                                                   •  = 5, 10, 15, 20%
              Ts increasing                        • At Re = 7.6104
 q [MW/m2]




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




                                               • At Re = 7.0104
                                                  –   13%
                                                  – q 21 MW/m2
                                                  – qt 9.5 MW/m2
                                               • For  < 10%,
                                                 Ts = 1200 °C
                                 increasing      – Re < 6104
                                                  – q< 20 MW/m2
                                                  – qt < 9 MW/m2
                          Re (/104)
ARIES Meeting (10/10)                                            14
                        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)                                             15

				
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