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Fluid Dynamic Aspects of Thin Liquid Film Protection Concepts S. I. Abdel-Khalik and M. Yoda

Fluid Dynamic Aspects of Thin Liquid Film Protection Concepts S. I. Abdel-Khalik and M. Yoda. ARIES Town Meeting (Ma y 5-6, 2003). G. W. Woodruff School of Mechanical Engineering Atlanta, GA 30332 – 0405 USA. Overview. Thin liquid protection (Prometheus) Major design questions

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Fluid Dynamic Aspects of Thin Liquid Film Protection Concepts S. I. Abdel-Khalik and M. Yoda

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  1. Fluid Dynamic Aspects of Thin Liquid Film Protection ConceptsS. I. Abdel-Khalik and M. Yoda ARIES Town Meeting (May 5-6, 2003) G. W. Woodruff School of Mechanical Engineering Atlanta, GA 30332–0405 USA

  2. Overview Thin liquid protection (Prometheus) • Major design questions • “Wetted wall”: low-speed normal injection through porous surface • Numerical simulations • Experimental validations • “Forced film”: high-speed tangential injection along solid surface • Experimental studies

  3. Thin Liquid Protection Major Design Questions • Can a stable liquid film be maintained over the entire surface of the reactor cavity? • Can the film be re-established over the entire cavity surface prior to the next target explosion? • Can a minimum film thickness be maintained to provide adequate protection over subsequent target explosions? Study wetted wall/forced film concepts over “worst case” of downward-facing surfaces

  4. Wetted Wall Concept--Problem Definition Prometheus: 0.5 mm thick layer of liquid lead injected normally through porous SiC structure Liquid Injection First Wall ~ 5 m X-rays and Ions

  5. Quantify effects of • injection velocity win • initial film thickness zo • Initial perturbation geometry & mode number • inclination angle  • Evaporation & Condensation at the interface on • Droplet detachment time • Equivalent droplet diameter • Minimum film thickness prior to detachment Numerical Simulation of Porous Wetted Walls Summary of Results Obtain Generalized Charts for dependent variables as functions of the Governing non-dimensional parameters

  6. Numerical Simulation of Porous Wetted WallsWetted Wall Parameters • Length, velocity, and time scales : • Nondimensional drop detachment time : • Nondimensional minimum film thickness : • Nondimensional initial film thickness : • Nondimensional injection velocity :

  7. Water Lead Lithium Flibe T (K) 293 323 700 800 523 723 773 873 973 l (mm) 2.73 2.65 2.14 2.12 8.25 7.99 3.35 3.22 3.17 U0(mm/s) 163.5 161.2 144.7 144.2 284.4 280.0 181.4 177.8 176.4 t0 (ms) 16.7 16.4 14.8 14.7 29.0 28.6 18.5 18.1 18.0 Re 445 771.2 1618 1831 1546 1775 81.80 130.8 195.3 Numerical Simulation of Porous Wetted Walls Non-Dimensional Parameters For Various Coolants

  8. Numerical Simulation of Porous Wetted Walls Effect of Initial Perturbation • Initial Perturbation Geometries Sinusoidal zo s Random zo Saddle zo s

  9. mf+=-0.005 mf+=0.0 mf+=0.01 (Evaporation) (Condensation) *=31.35 *=27.69 *=25.90 Numerical Simulation of Porous Wetted Walls Effect of Evaporation/Condensation at Interface • zo*=0.1, win*=0.01, Re=2000

  10. Numerical Simulation of Porous Wetted WallsDrop Detachment Time

  11. Numerical Simulation of Porous Wetted WallsMinimum Film Thickness

  12. Numerical Simulation of Porous Wetted Walls Evolution of Minimum Film Thickness (High Injection/Thick Films) Nondimensional Initial Thickness, zo*=0.5 Nondimensional Injection velocity, win*=0.05 Nondimensional Minimum Thickness Drop Detachment Minimum Thickness Nondimensional Time

  13. Numerical Simulation of Porous Wetted Walls Evolution of Minimum Film Thickness (Low Injection/Thin Films) Nondimensional Initial Thickness, zo*=0.1 Nondimensional Injection velocity, win*=0.01 Nondimensional Minimum Thickness Drop Detachment Minimum Thickness Nondimensional Time

  14. Numerical Simulation of Porous Wetted Walls Equivalent Detachment Diameter

  15. J B I H C A F G E D Experimental Validations A Porous plate holder w/adjustable orientation B Constant-head plenum w/adjustable height C Sub-micron filter D Sump pump E Reservoir F CCD camera G Data acquisition computer H Plenum overflow line I Flow metering valve J Flexible tubing K Laser Confocal Displacement Meter K

  16. Experimental Measurement -- “Unperturbed” Film Thickness Target Plate  Water 20 ◦C win = 0.9 mm/s  = 0◦ Mean Liquid Film Thickness = 614.3 m Standard Deviation = 3.9 m 10 mm Laser Sensor Head Laser Confocal Displacement Meter KEYENCE CORPORATION OF AMERICA, Model # : LT-8110

  17. Experimental Variables • Experimental Variables • Plate porosity • Plate inclination angle  • Differential pressure • Fluid properties • Independent Parameters • Injection velocity, win • “Unperturbed” film thickness, zo • DependentVariables • Detachment time • Detachment diameter • Maximum penetration depth

  18. Experiment #W090 -- “Unperturbed” Film Thickness Liquid Film Thickness [m] +2 -2 • Water 20oC, win = 0.9 mm/s,  = 0o • Mean Liquid Film Thickness = 614.3 m • Standard Deviation = 3.9 m Time [sec]

  19. Experiment #W090 -- Droplet Detachment Time Number Fraction • Water 20oC, win = 0.9 mm/s,  = 0o • Mean Droplet Detachment Time = 0.43 s • Standard Deviation = 0.04 s • Sample Size = 100 Droplets Droplet Detachment Time [sec]

  20. Numerical Model Experiment Experiment #W090 -- Calculated Detachment Time Detachment Time [sec] +2 Mean Experimental value = 0.43 s -2 Normalized Initial Perturbation Amplitude, s/zo

  21. Experiment #W090 -- Equivalent Droplet Detachment Diameter Number Fraction • Water 20oC, win = 0.9 mm/s,  = 0o • Mean Droplet Diameter = 7.69 mm • Standard Deviation = 0.17mm • Sample Size = 100 Droplets Equivalent Droplet Diameter [mm]

  22. Numerical Model Experiment Experiment #W090 – Equivalent Detachment Diameter Equivalent Droplet Diameter [mm] +2 Mean Experimental value = 7.69 mm -2 Normalized Initial Perturbation Amplitude, s/zo

  23. Experiment #W090 -- Maximum Penetration Distance Number Fraction • Water 20oC, win = 0.9 mm/s,  = 0o • Maximum Mean Penetration Depth = 55.5 mm • Standard Deviation = 5.1 mm • Sample Size = 100 Droplets Maximum Penetration Depth [mm]

  24. Numerical Model Experiment Experiment #W090 -- Calculated Penetration Distance Maximum Penetration Depth [mm] +2 Mean Experimental value = 55.5 mm -2 Normalized Initial Perturbation Amplitude, s/zo

  25. Experiment Simulation Experiment #W090 -- Evolution of Maximum Penetration Distance Penetration Depth [mm] Time [sec]

  26. Wetted Wall Summary • Developed general nondimensional charts applicable to a wide variety of candidate coolants and operating conditions • Stability of liquid film imposes • Lower bound on repetition rate (or upper bound on time between shots) to avoid liquid dripping into reactor cavity between shots • Lower bound on liquid injection velocity to maintain minimum film thickness over entire reactor cavity required to provide adequate protection over subsequent fusion events • Model Predictions are closely matched by Experimental Data

  27. Forced Film Concept -- Problem Definition Prometheus: Few mm thick Pb “forced film” injected tangentially at >7 m/s over upper endcap Injection Point ~ 5 m First Wall X-rays and Ions Detachment Distance xd Forced Film

  28. Contact Angle, LS Glass : 25o Coated Glass : 85o Stainless Steel : 50o Plexiglas : 75o Forced Film Parameters • Weber number We • Liquid density  • Liquid-gas surface tension  • Initial film thickness  • Average injection speed U • Froude number Fr • Surface orientation  ( = 0°  horizontal surface) • Mean detachment length from injection point xd • Mean lateral extent W • Surface radius of curvature R = 5 m • Surface wettability: liquid-solid contact angle LS • In Prometheus: for = 0 – 45, Fr = 100 – 680 over nonwetting surface (LS = 90)

  29. Experimental Apparatus A Flat or Curved plate (1.52  0.40 m) B Liquid film C Splash guard D Trough (1250 L) E Pump inlet w/ filter F Pump G Flowmeter H Flow metering valve I Long-radius elbow J Flexible connector K Flow straightener M L I Adjustable angle  J K x A z B H gcos  g G C L Film nozzle M Support frame D E F

  30. 5 cm x y z A  B C Liquid Film Nozzles • Fabricated with stereolithography rapid prototyping • A = 0.1 cm; B = 0.15 cm; C = 0.2 cm • 2D 5th order polynomial contraction along z from 1.5 cm to  • Straight channel (1 cm along x) downstream of contraction

  31. Experimental Parameters • Independent Variables • Film nozzle exit dimension  = 0.1–0.2 cm • Film nozzle exit average speed U0 = 1.9 – 11.4 m/s • Jet injection angle  = 0°, 10°, 30° and 45o • Surface inclination angle  ( = ) • Surface curvature (flat or 5m radius) • Surface material (wettability) • DependentVariables • Film width and thickness W(x), t(x) • Detachment distance xd • Location for drop formation on free surface

  32. Detachment Distance 1 mm nozzle 8 GPM 10.1 m/s 10° inclination Re = 9200

  33. xd / vs.Fr: Wetting Surface • Water on glass: LS = 25o • xd increases linearly w/Fr • xd as  • xd as   =1 mm1.5 mm2 mm   = 0   = 10   = 30   = 45 xd / Design Window: Wetting Surface Fr

  34. xd /: Wetting vs. Nonwetting • Wetting: glass; LS =25o • Nonwetting: coated glass; LS = 85o • Nonwetting surface smaller xd, orconservative estimate • xd indep. of  Open symbols Nonwetting Closed symbols Wetting  =1 mm  =1.5 mm • = 2 mm  = 0 xd / Design Window Fr

  35. xd: Wetting vs. Nonwetting  =1 mm 1.5 mm 2 mm  = 0 • Wetting: glass ( = 25°) • Nonwetting: Rain-X® coated glass ( = 85°) xd [cm] Glass   Rain-X® coated glass    We

  36. Effect of Inclination Angle(Flat Glass Plate)  =1 mm 1.5 mm 2 mm xd [cm]   = 0   = 10   = 30 We

  37. Detachment Distance Vs. Weber Number  = 0  = 1 mm xd [cm]  Glass(LS=25o) Stainless Steel(LS=50o) Plexiglas (LS=75o)  Rain-X® coated glass (LS=85o) We

  38. Effect of Weber Number on Detachment Distance(Flat and Curved Surfaces, Zero Inclination)  =1 mm1.5 mm2 mm  = 0 xd [cm] Flat   Curved    Plexiglas (LS = 70°) We

  39. Effect of Inclination Angle(Curved Plexiglas)  =1 mm1.5 mm2 mm • Curved nonwetting surface: Plexiglas ( = 70°); R = 5 m • xd as   • xd as We  • xd values at  = 0° “design window” xd [cm]   = 0   = 10   = 30 We

  40. W/Wo: Wetting vs. Nonwetting Wetting (LS = 25o) • Marked lateral growth (3.5) at higher Re Nonwetting (LS = 85o ) • Negligible lateral spread • Contact line “pinned” at edges? • Contracts farther upstream  = 2 mm = 0 Re = 3800  15000 W/Wo x/ Open Nonwetting Closed Wetting

  41. y y x x Cylindrical Dams • In all cases, cylindrical obstructions modeling protective dams around beam ports incompatible with forced films • Film either detaches from, or flows over, dam y x

  42. Forced Film Summary • Design windows for streamwise (longitudinal) spacing of injection/coolant removal slots to maintain attached protective film • Detachment length increases w/Weber and Froude numbers • Wetting chamber first wall surface requires fewer injection slots than nonwetting surface  wetting surface more desirable • Cylindrical protective dams around chamber penetrations incompatible with effective forced film protection • “Hydrodynamically tailored” protective dam shapes

  43. Acknowledgements Georgia Tech • Academic Faculty : Damir Juric • Research Faculty : D. Sadowski and S. Shin • Students : F. Abdelall, J. Anderson, J. Collins, S. Durbin, L. Elwell, T. Koehler, J. Reperant and B. Shellabarger DOE • W. Dove, G. Nardella, A. Opdenaker ARIES-IFE Team LLNL/ICREST • R. Moir

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