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ARIES Meeting, UCSD (March 2004)

Preliminary Assessment of Porous Gas-Cooled and Thin-Liquid-Protected Divertors S. I. Abdel-Khalik, S. Shin, and M. Yoda. ARIES Meeting, UCSD (March 2004). G. W. Woodruff School of Mechanical Engineering Atlanta, GA 30332 – 0405 USA. Outline. Porous Gas Cooled Divertors.

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ARIES Meeting, UCSD (March 2004)

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  1. Preliminary Assessment of Porous Gas-Cooled and Thin-Liquid-Protected DivertorsS. I. Abdel-Khalik, S. Shin, and M. Yoda ARIES Meeting, UCSD (March 2004) G. W. Woodruff School of Mechanical Engineering Atlanta, GA 30332–0405 USA

  2. Outline • Porous Gas Cooled Divertors • Thin-Liquid-Protected Divertors

  3. Porous Gas Cooled DivertorsObjective • Compare predictions of the MERLOT code against FLUENT (6.1.22) predictions • Assess impact of using the incompressible fluid continuity equation on MERLOT’s Predictions

  4. surface heat flux ro ri flow inlet to porous channel flow outlet from porous channel Porous Gas Cooled DivertorsTest Problem Definition • FLUENT has been used to solve the conservation equations (mass, momentum, and energy) • Assumptions • Laminar flow • Isotropic porosity • Either incompressible or compressible flow • Local thermodynamic equilibrium between the gas and solid matrix • Two-dimensional (r, ) • 60754 grid for r and  directional resolution r  ro=12 mm, ri=9 mm

  5. Porous Gas Cooled DivertorsEffective Heat Transfer Coeffcient Tin=823K, Tout=1423K Heat input : Q=30 MW/m2, Porous medium characteristic dimension : dp=0.1 mm, Porosity : =0.8 Effective heat transfer coefficient [W/m2K] Coolant: Helium at 823K & 4.0 MPa cpg=5191 J/kg K, kg=0.3 W/m K, g=3.9610-5 kg/m s, g=2.327 kg/m3 (for incompressible) Solid Structure : ks=100W/m K, s=19300 kg/m3,cps=132 J/kg K  [radian]

  6. Incompressible Compressible Porous Gas Cooled DivertorsTemperature Distribution Temperature [K] wall temperature helium gas bulk temperature  [radian]

  7. Porous Gas Cooled DivertorsPressure Drop Ergun equation Pressure drop P = Pressure drop [MPa] Pressure drop [MPa] Tin=823K, Q=5 MW/m2, dp=0.1 mm Porosity : =0.8 Porosity : =0.5 Velocity [m/s] Velocity [m/s]

  8. Porous Gas-Cooled DivertorsPreliminary Conclusions • Heat transfer coefficients predicted by MERLOT and FLUENT appear to be consistent • Pressure drop predicted by MERLOT is significantly lower than that predicted by FLUENT for either compressible or incompressible assumption • Acceleration pressure drop due to gas compressibility effects can not be ignored

  9. Thin-Liquid-Protected DivertorsObjective • This work is aimed at establishing limits for the maximum allowable temperature gradients (i.e. heat flux gradients) to prevent film rupture due to thermocapillary effects A maximum allowable surface temperature has been established to limit liquid evaporation and plasma contamination (~380 oC for Li)

  10. Thin-Liquid-Protected DivertorsProblem Definition • Initially, quiescent liquid and gas (u=0, v=0, T=Tm at t=0) open B.C. at top, periodic B.C. in x direction xl Gas (Air) Thin Film yl ho initial film thickness Liquid (Lithium) y Wall x Non-uniform wall temperature

  11. Phase 1 F Phase 2 Thin-Liquid-Protected DivertorsNumerical Method • Evolution of the free surface is modeled using the Level Contour Reconstruction Method • Two Grid Structures • Volume - entire computational domain (both phases) discretized by a standard, uniform, stationary, finite difference grid. • Phase Interface - discretized by Lagrangian points or elements whose motions are explicitly tracked.

  12. Thin-Liquid-Protected DivertorsGoverning Equations • A single field formulation • Constant but unequal material properties • Surface tension included as local surface delta function sources • Conservation of Mass • Momentum • Energy

  13. BtB AtA n Thin-Liquid-Protected DivertorsVariable Surface Tension Source Term NUMERICAL METHOD • Variable surface tension : o=6.6210-2 N/m o=1.7410-4 N/moC Tm=573 K • Force on a line element n : unit vector in normal direction t : unit vecotr in tangential direction  : curvature thermocapillary force normal surface tension force

  14. Thin-Liquid-Protected DivertorsMaterial Properties • Material property field (Liquid=>Lithium, Gas=>Air*) (L=504.8 kg/m3, G=1.046 kg/m3) (L=4.5110-4 kg/ms, G=2.010-5 kg/ms) (cL=4287 J/kgoC, cG=1008 J/kgoC) (kL=46.6 W/moC, kG=0.029 W/moC) * Effect of Liquid/Gas density ratio becomes insignificant for values  100

  15. Thin-Liquid-Protected DivertorsSteady State Results, very thin films y [m] y [m] x [m] time [sec] • Two-dimensional simulation with 0.01[m]0.001[m] box size and 25050 resolution • ho=0.2 mm, Ts=10 K

  16. Thin-Liquid-Protected DivertorsSteady State Results, very thin films velocity vector plot temperature plot • Two-dimensional simulation with 0.01[m]0.001[m] box size and 25050 resolution • ho=0.2 mm, Ts=10 K

  17. Thin-Liquid-Protected DivertorsSteady State Results, very thin films black : Ts=10 K blue : Ts=20 K red : Ts=30 K maximum y location y [m] y [m] minimum y location x [m] time [sec] • Two-dimensional simulation with 0.01[m]0.001[m] box size, 25050 resolution, and ho=0.2 mm

  18. Thin-Liquid-Protected DivertorsSteady State Results, moderate film thickness y [m] x [m] • Two-dimensional simulation with 0.1[m]0.01[m] box size and 25050 resolution • ho=2 mm, Ts=100 K

  19. Thin-Liquid-Protected DivertorsSteady State Results, moderate film thickness velocity vector plot temperature plot • Two-dimensional simulation with 0.1[m]0.01[m] box size and 25050 resolution • ho=2 mm, Ts=100 K

  20. Thin-Liquid-Protected DivertorsSteady State Results, moderate film thickness black : Ts=100 K blue : Ts=250 K maximum y location y [m] minimum y location time [sec] • Two-dimensional simulation with 0.1[m]0.01[m] box size, 25050 resolution, and ho=2 mm

  21. Thin Liquid-Protected DivertorsPreliminary Conclusions • Methodology can be used to determine the Limiting values for temperature gradients (i.e. heat flux gradients) necessary to prevent film rupture • In some cases (very thin films), limits may be more restrictive than surface temperature limits • Path Forward: • Generalized charts will be developed to determine the temperature gradient limits for different fluids and film thickness values

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