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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 Overview Thin liquid protection (Prometheus) • Major design questions wall”: low-speed normal injection • “Wetted through porous surface Numerical simulations Experimental validations film”: high-speed tangential injection • “Forced along solid surface Experimental studies 2 Thin Liquid Protection Major Design Questions a stable liquid film be maintained over the entire surface of • Can the reactor cavity? the film be re-established over the entire cavity surface • Can prior to the next target explosion? a minimum film thickness be maintained to provide • Can adequate protection over subsequent target explosions? Study wetted wall/forced film concepts over “worst case” of downward-facing surfaces 3 Wetted Wall Concept--Problem Definition Prometheus: 0.5 mm thick layer of liquid lead injected normally through porous SiC structure Liquid Injection ~5m First Wall X-rays and Ions 4 Numerical Simulation of Porous Wetted Walls Summary of Results Quantify effects of velocity w • injection film thickness z • initial perturbation geometry & mode number • Initial angle • inclination • Evaporation & Condensation at the interface in o on detachment time • Droplet droplet diameter • Equivalent • Minimum film thickness prior to detachment Obtain Generalized Charts for dependent variables as functions of the Governing non-dimensional parameters 5 Numerical Simulation of Porous Wetted Walls Wetted Wall Parameters • Length, velocity, and time scales : l / g (L G ) Uo g l • • Nondimensional minimum film thickness : • Nondimensional initial film thickness : • Nondimensional injection velocity : Nondimensional drop detachment time : to l / U o * td / to *min min / l z zo / l * o win* win / U o 6 Numerical Simulation of Porous Wetted Walls Non-Dimensional Parameters For Various Coolants 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 7 Numerical Simulation of Porous Wetted Walls Effect of Initial Perturbation • Initial Perturbation Geometries Sinusoidal zo s Random zo Saddle s zo 8 Numerical Simulation of Porous Wetted Walls Effect of Evaporation/Condensation at Interface • zo*=0.1, win*=0.01, Re=2000 mf+=-0.005 (Evaporation) *=31.35 mf+=0.0 *=27.69 mf+=0.01 (Condensation) *=25.90 9 Numerical Simulation of Porous Wetted Walls Drop Detachment Time 10 Numerical Simulation of Porous Wetted Walls Minimum Film Thickness 11 Numerical Simulation of Porous Wetted Walls Nondimensional Minimum Thickness Evolution of Minimum Film Thickness (High Injection/Thick Films) Nondimensional Initial Thickness, zo*=0.5 Nondimensional Injection velocity, win*=0.05 Drop Detachment Minimum Thickness Nondimensional Time 12 Numerical Simulation of Porous Wetted Walls Nondimensional Minimum Thickness Evolution of Minimum Film Thickness (Low Injection/Thin Films) Nondimensional Initial Thickness, zo*=0.1 Nondimensional Injection velocity, win*=0.01 Drop Detachment Minimum Thickness Nondimensional Time 13 Numerical Simulation of Porous Wetted Walls Equivalent Detachment Diameter 14 Experimental Validations J B I H F G C A K E D 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 15 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 16 Experimental Variables Experimental Variables porosity • Plate inclination angle • Plate pressure • Differential • Fluid properties Independent Parameters velocity, w • Injection • “Unperturbed” film thickness, z Dependent Variables time • Detachment diameter • Detachment • Maximum penetration depth in o 17 Liquid Film Thickness [m] Experiment #W090 -“Unperturbed” Film Thickness +2 -2 • Water 20oC, win = 0.9 mm/s, = 0o • Mean Liquid Film Thickness = 614.3 m • Standard Deviation = 3.9 m Time [sec] 18 Experiment #W090 -- Droplet Detachment Time 0.4 • Water 20oC, win = 0.9 mm/s, = 0o • Mean Droplet Detachment Time = 0.43 s • Standard Deviation = 0.04 s • Sample Size = 100 Droplets Number Fraction 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0.33 0.36 0.40 0.43 0.46 0.50 0.53 Droplet Detachment Time [sec] 19 Experiment #W090 -- Calculated Detachment Time Numerical Model Detachment Time [sec] +2 Experiment Mean Experimental value = 0.43 s -2 Normalized Initial Perturbation Amplitude, s/zo 20 Experiment #W090 -Equivalent Droplet Detachment Diameter 0.35 • Water 20oC, win = 0.9 mm/s, = 0o • Mean Droplet Diameter = 7.69 mm • Standard Deviation = 0.17mm • Sample Size = 100 Droplets Number Fraction 0.3 0.25 0.2 0.15 0.1 0.05 0 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2 Equivalent Droplet Diameter [mm] 21 Equivalent Droplet Diameter [mm] Experiment #W090 – Equivalent Detachment Diameter +2 Mean Experimental value = 7.69 mm -2 Numerical Model Experiment Normalized Initial Perturbation Amplitude, s/zo 22 Experiment #W090 -Maximum Penetration Distance 0.35 • Water 20oC, win = 0.9 mm/s, = 0o • Maximum Mean Penetration Depth = 55.5 mm • Standard Deviation = 5.1 mm • Sample Size = 100 Droplets Number Fraction 0.3 0.25 0.2 0.15 0.1 0.05 0 45 47 50 53 57 62 65 68 Maximum Penetration Depth [mm] 23 Experiment #W090 -Calculated Penetration Distance Maximum Penetration Depth [mm] Numerical Model Experiment +2 Mean Experimental value = 55.5 mm -2 Normalized Initial Perturbation Amplitude, s/zo 24 Penetration Depth [mm] Experiment #W090 -Evolution of Maximum Penetration Distance Experiment Simulation Time [sec] 25 Wetted Wall Summary general nondimensional charts applicable to a • Developed wide variety of candidate coolants and operating conditions of liquid film imposes • Stability 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 Predictions are closely matched by Experimental • Model Data 26 Forced Film Concept -- Problem Definition Prometheus: Few mm thick Pb “forced film” injected tangentially at >7 m/s over upper endcap ~5m X-rays and Ions Injection Point First Wall Detachment Distance xd Forced Film 27 Forced Film Parameters • • • • • • • U 2 We Weber number We Liquid density Liquid-gas surface tension Initial film thickness Average injection speed U Fr Froude number Fr U g (cos ) Surface orientation ( = 0° horizontal surface) Mean detachment length from injection point xd Contact Angle, LS Glass : 25o Mean lateral extent W Coated Glass : 85o Surface radius of curvature R = 5 m Stainless Steel : 50o Surface wettability: liquid-solid contact angle LS Plexiglas : 75o In Prometheus: for = 0 – 45, Fr = 100 – 680 over nonwetting surface (LS = 90) 28 Experimental Apparatus A Flat or Curved plate (1.52 0.40 m) I B Liquid film C Splash guard J D Trough (1250 L) E Pump inlet w/ filter H F Pump G Flowmeter G H Flow metering valve I Long-radius elbow J Flexible connector K Flow straightener L Film nozzle F M Support frame L K z x Adjustable angle M A B gcos g C E D 29 Liquid Film Nozzles 5 cm x y z A B C • Fabricated with stereolithography rapid prototyping • = 0.1 cm; = 0.15 cm; = 0.2 cm • 2D 5 order polynomial contraction along z from 1.5 cm to • Straight channel (1 cm along x) downstream of contraction A B C th 30 Experimental Parameters Variables • Independent 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) • Dependent Variables Film width and thickness W(x), t(x) Detachment distance xd Location for drop formation on free surface 31 Detachment Distance 1 mm nozzle 8 GPM 10.1 m/s 10° inclination Re = 9200 32 xd / vs. Fr: Wetting Surface 2000 = 1 mm 1600 xd / 1200 1.5 mm • 2 mm • = 0 = 10 = 30 = 45 • • 800 Water on glass: LS = 25o xd increases linearly w/Fr xd as xd as wet xd 11.56 Fr 16.1 δ min Design Window: 400 0 0 20 40 60 80 100 120 Wetting Surface Fr 33 xd / : Wetting vs. Nonwetting 1600 Open symbols Nonwetting Closed symbols Wetting = 1 mm = 1.5 mm = 2 mm = 0 xd / 1200 800 • coated • Nonwetting: glass; = 85 Wetting: glass; LS = 25o LS o surface • Nonwetting smaller x , or d conservative estimate • x indep. of d 400 nw 0 0 20 40 60 Fr 80 xd 9.62 Fr 45.9 100 δ 120 min Design Window 34 xd: Wetting vs. Nonwetting = 1 mm 1.5 mm 2 mm 180 = 0 160 glass ( • Wetting: = 25°) xd [cm] 140 120 • Nonwetting: Rain-X coated 100 ® 80 glass ( = 85°) 60 40 Glass Rain-X® coated glass 20 0 0 500 1000 1500 2000 2500 3000 We 35 Effect of Inclination Angle (Flat Glass Plate) = 1 mm 1.5 mm 2 mm 180 160 xd [cm] 140 120 100 80 60 = 0 = 10 = 30 40 20 0 0 1000 2000 3000 4000 We 36 Detachment Distance Vs. Weber Number 160 = 0 = 1 mm 140 xd [cm] 120 100 80 60 40 Glass (LS=25o) Stainless Steel (LS=50o) 20 Plexiglas (LS=75o) Rain-X® coated glass (LS=85o) 0 0 500 1000 1500 2000 We 37 Effect of Weber Number on Detachment Distance (Flat and Curved Surfaces, Zero Inclination) = 1 mm = 0 180 160 1.5 mm 2 mm xd [cm] 140 120 100 80 60 40 Plexiglas 20 (LS = 70°) Flat Curved 0 0 500 1000 1500 2000 2500 3000 We 38 Effect of Inclination Angle Detachment Distance vs. Weber Number for Plexi-glass Curved Plate at 0°, 10° and 30° Inclination (Curved Plexiglas) 200 = 1 mm 1.5 mm 2 mm nonwetting • Curved surface: Plexiglas 150 ( = 70°); R = 5 m1.5 mm, 0° xd (cm) xd [cm] 1 mm, 0° • x as • x as We values at = 0° • x“design window” d 100 d = 0 = 10 = 30 50 2 mm, 0° 1 mm, 10° 1.5 mm, 10° 2mm, 10° 1 mm, 30° 1.5 mm 30° 2 mm 30° d 0 0 500 We 1000 1500 We 39 W / Wo: Wetting vs. Nonwetting 4 = 2 mm = 0 Wetting (LS = 25o) lateral growth • Marked (3.5) at higher Re 3 W / Wo Nonwetting (LS = 85o ) lateral spread • Negligible Contact line “pinned” Re = 3800 15000 2 at edges? • Contracts farther upstream 1 0 0 200 400 600 800 Open Nonwetting x / Closed Wetting 40 Cylindrical Dams all cases, cylindrical obstructions modeling protective dams • Inaround beam ports incompatible with forced films • Film either detaches from, or flows over, dam y y x y x x 41 Forced Film Summary windows for streamwise (longitudinal) spacing • Design of injection/coolant removal slots to maintain attached protective film Detachment length increases w/Weber and Froude numbers chamber first wall surface requires fewer • Wetting injection slots than nonwetting surface wetting surface more desirable protective dams around chamber • Cylindrical penetrations incompatible with effective forced film protection “Hydrodynamically tailored” protective dam shapes 42 Acknowledgements Georgia Tech Faculty : Damir Juric • Academic Faculty : D. Sadowski and S. Shin • Research : F. Abdelall, J. Anderson, J. Collins, S. Durbin, L. Elwell, T. • Students Koehler, J. Reperant and B. Shellabarger DOE • W. Dove, G. Nardella, A. Opdenaker ARIES-IFE Team LLNL/ICREST • R. Moir 43