1. 1 NUMERICAL AND EXPERIMENTAL STUDIES OF THIN-LIQUID-FILM WALL PROTECTION SCHEMES S.I. ABDEL-KHALIK AND M. YODA G. W. Woodruff School of Mechanical Engineering Atlanta, GA 30332-0405 USA

2. 2 Numerical Simulation of Porous Downward Facing Wetted Walls  Seungwon Shin & Damir Juric Experimental Investigation of Liquid Film Stability on Porous Wetted Walls  Fahd Abdelall & Dennis Sadowski Experimental Study of Forced Thin Liquid Film Flow on Downward Facing Surfaces  J. Anderson, S. Durbin & D. Sadowski Primary Contributors

3. 3 Minimum Film Thickness Prior to Droplet Detachment Effect of Evaporation/Condensation on  Detachment Time  Detached Droplet Diameter  Minimum Film Thickness Numerical Simulation of Porous Wetted Walls (Follow up on Madison ARIES Meeting)

4. 4 Numerical Simulation of Porous Wetted Walls Problem Definition IFE Reactor Chamber (Prometheus-L) X-rays and Ions Liquid Injection

5. 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

6. 6 Numerical Simulation of Porous Wetted Walls Evolution of Minimum Film Thickness (High Injection/Thin Films) Nondimensional Initial Thickness, z o * =0.1 Nondimensional Injection velocity, w in * =0.05 Nondimensional Time Nondimensional Minimum Thickness Minimum Thickness Drop Detachment

7. 7 Numerical Simulation of Porous Wetted Walls Effect of Initial Perturbation Initial Perturbation Geometries Sinusoidal Random Saddle zozo ss zozo zozo ss

8. 8 Numerical Simulation of Porous Wetted Walls Effect of Initial Perturbation Sinusoidal z o,  s = 0.5 mm w in = 1 mm/s 0.31 0.38 0.30 Pb at 700K Random w in = 1 mm/s Saddle w in = 1 mm/s Detachment time  (s)

9. 9 Numerical Simulation of Porous Wetted Walls Effect of Liquid Injection Velocity w in 0.43 0.47 0.48 0.42 w in = 0 mm/s z o,  s = 0.2 mm  (s) w in = 0.1 mm/s z o,  s = 0.2 mm w in = 1 mm/s z o,  s = 0.2 mm w in = 10 mm/s z o,  s = 0.2 mm

10. 10 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

11. 11 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

12. 12 Numerical Simulation of Porous Wetted Walls Evolution of Minimum Film Thickness (Low Injection/Thick Films) Nondimensional Initial Thickness, z o * =0.5 Nondimensional Injection velocity, w in * =0.01 Nondimensional Time Nondimensional Minimum Thickness Minimum Thickness Drop Detachment

13. 13 Numerical Simulation of Porous Wetted Walls Non-Dimensional Representation where,,,,, Nondimensional Momentum Equation

14. 14 Numerical Simulation of Porous Wetted Walls Minimum Film Thickness

15. 15 Numerical Simulation of Porous Wetted Walls Minimum Film Thickness

16. 16 Numerical Simulation of Porous Wetted Walls Minimum Film Thickness

17. 17 Numerical Simulation of Porous Wetted Walls Evaporation/Condensation at the Interface where Nondimensional Mass Conservation

18. 18 Numerical Simulation of Porous Wetted Walls Evaporation/Condensation at the Interface Interface Advancement

19. 19 Numerical Simulation of Porous Wetted Walls Non-Dimensional Parameters For Various Coolants WaterLeadLithiumFlibe T (K)293323700800523723773873973 l (mm)2.732.652.142.128.257.993.353.223.17 U 0 (mm/s)163.5161.2144.7144.2284.4280.0181.4177.8176.4 t 0 (ms)16.716.414.814.729.028.618.518.118.0 Re445771.2161818311546177581.80130.8195.3

20. 20 Numerical Simulation of Porous Wetted Walls Effect of Evaporation/Condensation at Interface  * =31.35  * =27.69  * =25.90 m f * =-0.005m f * =0.0m f * =0.01 (Evaporation)(Condensation) z o * =0.1, w in * =0.01, Re=2000

21. 21 (Condensation)(Evaporation) Numerical Simulation of Porous Wetted Walls Effect of Evaporation/Condensation at Interface  * =25.69  * =25.13  * =25.74 m f * =-0.005m f * =0.0m f * =0.01 z o * =0.1, w in * =0.05, Re=2000

22. 22 (Condensation)(Evaporation) Numerical Simulation of Porous Wetted Walls Effect of Evaporation/Condensation at Interface  * =15.94  * =16.14  * =16.84 m f * =-0.005m f * =0.0m f * =0.01 z o * =0.5, w in * =0.01, Re=2000

23. 23 (Condensation)(Evaporation) Numerical Simulation of Porous Wetted Walls Effect of Evaporation/Condensation at Interface  * =17.11  * =16.94  * =17.83 m f * =-0.005m f * =0.0m f * =0.01 z o * =0.5, w in * =0.05, Re=2000

24. 24 Numerical Simulation of Porous Wetted Walls Non-Dimensional Results -- Detachment Time Different Evaporation/Condensation m f * Values

25. 25 Numerical Simulation of Porous Wetted Walls Non-Dimensional Results -- Detachment Time Different Evaporation/Condensation m f * Values

26. 26 Numerical Simulation of Porous Wetted Walls Non-Dimensional Results -- Detachment Time Different Evaporation/Condensation m f * Values

27. 27 Numerical Simulation of Porous Wetted Walls Non-Dimensional Results -- Detachment “Diameter” Different Evaporation/Condensation m f * Values

28. 28 Numerical Simulation of Porous Wetted Walls Non-Dimensional Results -- Detachment “Diameter” Different Evaporation/Condensation m f * Values

29. 29 Numerical Simulation of Porous Wetted Walls Non-Dimensional Results -- Detachment “Diameter” Different Evaporation/Condensation m f * Values

30. 30 Numerical Simulation of Porous Wetted Walls Non-Dimensional Results – Minimum Film Thickness Different Evaporation/Condensation m f * Values

31. 31 Numerical Simulation of Porous Wetted Walls Non-Dimensional Results – Minimum Film Thickness Different Evaporation/Condensation m f * Values

32. 32 Numerical Simulation of Porous Wetted Walls Non-Dimensional Results – Minimum Film Thickness Different Evaporation/Condensation m f * Values

33. 33 CONCLUSIONS Generalized charts have been developed to allow quantitative evaluation of effects of various operating and design variables on system performance  Identify “design windows” for successful operation of the wetted wall concept Experimental investigation to validate numerical results over desired parameter range underway (isothermal conditions)

34. 34 IFE chamber (Prometheus) First Wall Injection Point Detachment Distance x d Liquid Film/Sheet X-rays and Ions Problem Definition

35. 35 2 mm nozzle 17 GPM 10.7 m/s 10 o inclination Re = 20000 2 mm nozzle 17 GPM 10.7 m/s 10 o inclination Re = 20000 Objectives Determine “design windows” for high-speed liquid films proposed for thin liquid protection of IFE reactor chamber first wall Wall protection issues (in the absence of film dryout)  Detachment of film from first wall  Ejection of drops from film free surface  Downward-facing surfaces at top of chamber: greatest gravitational impact on detachment Implementation issues  How does film spread from injection point?  How does film flow around obstructions (e.g. beam ports)?

36. 36 Experimental Apparatus AGlass plate (1.52  0.40 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

37. 37 Experimental Parameters 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° and 30°  Surface inclination angle  (  =  ) Dependent Variables  Film width and thickness W(x), t(x)  Detachment distance x d  Location for drop formation on free surface

38. 38 1.5 mm nozzle 13 GPM 10.9 m/s 10° inclination Re = 15000 13 GPM 10.9 m/s Re = 15000 10° inclination 1.5 mm nozzle Dimensionless Groups Reynolds number Re = U 0  / = 3700–21,000 Froude number Fr = U 0 /  (g cos  )  = 15–115  Only group involving  Weber number We =  U 0 2  /  = 100–3200 Film nozzle aspect ratio AR = (5 cm)/  = 25–50 Fluid properties (water at 17–19°C into air at p atm )  Kinematic viscosity = 1.06  10 –6 m 2 /s  Density  = 999 kg/m 3  Surface tension  = 0.073 N/m

39. 39 2 mm nozzle 17 GPM 10.7 m/s 10 o inclination Re = 20000 Detachment Distance x d xdxd  x d = distance along plate from nozzle exit where film detaches at plate surface Instantaneous detachment distance x d varies by up to  2 cm  reported x d values average of 20 independent realizations Typical images (8 ms exp.) of liquid film over a few seconds:  = 10°, Re = 8600,  = 0.1 cm (A) [ruler in inches] x d = 127.5 cm 125.4 cm 127.6 cm 128.9 cm

40. 40 x d : Fr Effects Fr x d /   = 0.15 cm  = 0.2 cm  = 0   = 10   = 30  x d /   as Fr  x d /   as   Growth rate similar for all cases (except at low Fr) Account for different initial conditions with “virtual origin”?  = 0.1 cm

41. 41 Average Film Width W(x) W(x) measured from above (viewed through plate)  = 0.1 cm;  = 30  ; Re = 7200; Fr = 81 2 mm nozzle 13 GPM 8.2 m/s 10° inclination Re = 15000 13 GPM 8.2 m/s Re = 15000 10° inclination 2 mm nozzle 5 cm x y W(x)W(x) Initially, film spreads after leaving nozzle (transition from no-slip to free surface at lower surface): “near-field” region Farther downstream, film thickens (due to gravitational and surface tension effects) and detaches: “far-field” region  Since mass/vol. flux constant at every x location, W must decrease  Does W decrease before detachment?

42. 42 W(x):  Effects x / x /   = 0   = 10   = 30   = 0.2 cm (C) Re = 18,000 W independent of  for x/  < 400 (near-field) W  as   for x/  > 400 (far- field) x c /  < x d /  for all cases xd/xd/ W/W0W/W0 x c /   400 W c /W 0  3.6

43. 43 W(x): Re Effects x / x /  W/W0W/W0  = 0.2 cm (C)  = 30  W independent of Re for x/  < 400 (near-field) W independent of Re at high Re? x c /  < x d /  in all cases x c /   400 W c /W 0  3.6 xd/xd/ Re = 7,500 Re = 12,400 Re = 18,600

44. 44 Initial Observations Detachment distance x d  Fr most important parameter for detachment distance x d  For high-speed films, consistent growth rate in x d /   Virtual origin to compensate for initial conditions Film width (y-dimension) W  Maximum W  4–5 times initial value  Near-field (x < x c < x d ) : W dominated by initial conditions  Far-field (x > x c ):  most important parameter for W Characteristic film width W c = W(x c )   most important parameter for W c  For high-speed films, W c independent of Fr, Re and  Summary

45. 45 Future Work Determine “design windows” for high-speed liquid films proposed for thin liquid protection of IFE reactor chamber first wall Wall protection issues (in the absence of film dryout)  Detachment of film from first wall  Ejection of drops from film free surface Implementation issues  How does film spread from injection point?  How does film flow around obstructions (e.g. beam ports)?

46. 46 1.5 mm nozzle 10 GPM 8.4 m/s 10° inclination Re = 11500 10 GPM 8.4 m/s Re = 11500 10° inclination 1.5 mm nozzle Drop Ejection from Free Surface Drops ejected from film free surface upstream of detachment Major issue for first wall protection: minimize drops in chamber