Fluid Dynamic Aspects of Thin Liquid Film Protection Concepts S. 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 Liquid Injection Prometheus: 0.5 mm thick layer of liquid lead injected normally through porous SiC structure X-rays and Ions ~ 5 m First Wall

5 Numerical Simulation of Porous Wetted Walls Summary of Results Quantify effects of injection velocity w in initial film thickness z o 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 Obtain Generalized Charts for dependent variables as functions of the Governing non-dimensional parameters

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

7 Numerical Simulation of Porous Wetted Walls Non-Dimensional Parameters For Various Coolants WaterLeadLithiumFlibe T (K) l (mm) U 0 (mm/s) t 0 (ms) Re

8 Numerical Simulation of Porous Wetted Walls Effect of Initial Perturbation Initial Perturbation Geometries Sinusoidal Random Saddle zozo s zozo zozo s

9 Numerical Simulation of Porous Wetted Walls Effect of Evaporation/Condensation at Interface z o * =0.1, w in * =0.01, Re=2000 * =31.35 m f + = (Evaporation) * =25.90 m f + =0.01 (Condensation) * =27.69 m f + =0.0

10 Numerical Simulation of Porous Wetted Walls Drop Detachment Time

11 Numerical Simulation of Porous Wetted Walls Minimum Film Thickness

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

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

14 Numerical Simulation of Porous Wetted Walls Equivalent Detachment Diameter

15 Experimental Validations G F E D C B A H I J APorous plate holder w/adjustable orientation BConstant-head plenum w/adjustable height CSub-micron filter DSump pump EReservoir FCCD camera GData acquisition computer HPlenum overflow line IFlow metering valve JFlexible tubing K Laser Confocal Displacement Meter K

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

17 Experimental Variables Plate porosity Plate inclination angle Differential pressure Fluid properties Independent Parameters Injection velocity, w in Unperturbed film thickness, z o Dependent Variables Detachment time Detachment diameter Maximum penetration depth

18 Experiment #W Unperturbed Film Thickness Time [sec] Liquid Film Thickness [ m] Water 20 o C, w in = 0.9 mm/s, = 0 o Mean Liquid Film Thickness = m Standard Deviation = 3.9 m +2 -2

19 Experiment #W Droplet Detachment Time Droplet Detachment Time [sec] Number Fraction Water 20 o C, w in = 0.9 mm/s, = 0 o Mean Droplet Detachment Time = 0.43 s Standard Deviation = 0.04 s Sample Size = 100 Droplets

20 Experiment #W Calculated Detachment Time Normalized Initial Perturbation Amplitude, s /z o Detachment Time [sec] Mean Experimental value = 0.43 s Numerical Model Experiment

21 Experiment #W Equivalent Droplet Detachment Diameter Equivalent Droplet Diameter [mm] Number Fraction Water 20 o C, w in = 0.9 mm/s, = 0 o Mean Droplet Diameter = 7.69 mm Standard Deviation = 0.17mm Sample Size = 100 Droplets

22 Experiment #W090 – Equivalent Detachment Diameter Normalized Initial Perturbation Amplitude, s /z o Equivalent Droplet Diameter [mm] Mean Experimental value = 7.69 mm Numerical Model Experiment

23 Experiment #W Maximum Penetration Distance Maximum Penetration Depth [mm] Number Fraction Water 20 o C, w in = 0.9 mm/s, = 0 o Maximum Mean Penetration Depth = 55.5 mm Standard Deviation = 5.1 mm Sample Size = 100 Droplets

24 Experiment #W Calculated Penetration Distance Normalized Initial Perturbation Amplitude, s /z o Maximum Penetration Depth [mm] Mean Experimental value = 55.5 mm Numerical Model Experiment

25 Experiment #W Evolution of Maximum Penetration Distance Time [sec] Penetration Depth [mm] Simulation Experiment

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 First Wall Injection Point Detachment Distance x d Forced Film X-rays and Ions Prometheus: Few mm thick Pb forced film injected tangentially at >7 m/s over upper endcap ~ 5 m

28 Contact Angle, LS Glass : 25 o Coated Glass : 85 o Stainless Steel : 50 o Plexiglas : 75 o 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 x d 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 AFlat or Curved plate ( m) BLiquid film CSplash guard DTrough (1250 L) EPump inlet w/ filter FPump GFlowmeter HFlow metering valve ILong-radius elbow JFlexible connector KFlow straightener LFilm nozzle MSupport frame A B C D E F G H I J K L M Adjustable angle x z gcos g Experimental Apparatus

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

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

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

33 x d / vs. Fr: Wetting Surface Water on glass: LS = 25 o x d increases linearly w/Fr x d as Fr x d / = 0 = 10 = 30 = 45 = 1 mm1.5 mm2 mm Design Window: Wetting Surface

34 x d / : Wetting vs. Nonwetting Wetting: glass; LS = 25 o Nonwetting: coated glass; LS = 85 o Nonwetting surface smaller x d, or conservative estimate x d indep. of Fr x d / Open symbols Nonwetting Closed symbols Wetting = 1 mm = 1.5 mm = 2 mm = 0 Design Window

35 x d : Wetting vs. Nonwetting We x d [cm] Wetting: glass ( = 25°) Nonwetting: Rain-X ® coated glass ( = 85°) Glass Rain-X ® coated glass = 1 mm 1.5 mm 2 mm = 0

36 We x d [cm] = 1 mm 1.5 mm 2 mm = 0 = 10 = 30 Effect of Inclination Angle (Flat Glass Plate)

37 Detachment Distance Vs. Weber Number We x d [cm] = 0 Glass ( LS =25 o ) Stainless Steel ( LS =50 o ) Plexiglas ( LS =75 o ) Rain-X ® coated glass ( LS =85 o ) = 1 mm

38 Effect of Weber Number on Detachment Distance (Flat and Curved Surfaces, Zero Inclination) Plexiglas ( LS = 70°) We x d [cm] Flat Curved = 1 mm1.5 mm2 mm = 0

39 Effect of Inclination Angle (Curved Plexiglas) Curved nonwetting surface: Plexiglas ( = 70°); R = 5 m x d as x d as We x d values at = 0° design window x d [cm] = 1 mm1.5 mm2 mm = 0 = 10 = 30 We

40 W / W o : Wetting vs. Nonwetting Wetting ( LS = 25 o ) Marked lateral growth (3.5 ) at higher Re Nonwetting ( LS = 85 o ) Negligible lateral spread Contact line pinned at edges? Contracts farther upstream x / W / WoW / Wo = 2 mm = 0 Re = OpenNonwetting Closed Wetting

41 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 x y x y x y

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