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 ofMechanical 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 WallsSummary of Results

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

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 :

L G/ ( )l g oU g l o o/t l U

*d o/t t

*min min / l

*o o /z z l

*in in o/w w U

• Nondimensional drop detachment time :

• Nondimensional minimum film thickness :

• Nondimensional initial film thickness :

• Nondimensional injection velocity :

7

Numerical Simulation of Porous Wetted WallsNon-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

8

Numerical Simulation of Porous Wetted WallsEffect of Initial Perturbation

• Initial Perturbation Geometries

Sinusoidal

Random

Saddle

zo

s

zo

zos

9

Numerical Simulation of Porous Wetted WallsEffect of Evaporation/Condensation at Interface

• zo*=0.1, win

*=0.01, Re=2000

*=31.35

mf+=-0.005

(Evaporation)

*=25.90

mf+=0.01

(Condensation)

*=27.69

mf+=0.0

10

Numerical Simulation of Porous Wetted WallsDrop Detachment Time

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Numerical Simulation of Porous Wetted WallsMinimum Film Thickness

12

Numerical Simulation of Porous Wetted WallsEvolution of Minimum Film Thickness (High Injection/Thick Films)

Nondimensional Initial Thickness, zo*=0.5

Nondimensional Injection velocity, win*=0.05

Nondimensional Time

Non

dim

ensi

onal

Min

imum

Thi

ckne

ss

Minimum Thickness

Drop Detachment

13

Numerical Simulation of Porous Wetted WallsEvolution of Minimum Film Thickness (Low Injection/Thin Films)

Nondimensional Initial Thickness, zo*=0.1

Nondimensional Injection velocity, win*=0.01

Nondimensional Time

Non

dim

ensi

onal

Min

imum

Thi

ckne

ss

Minimum ThicknessDrop Detachment

14

Numerical Simulation of Porous Wetted WallsEquivalent Detachment Diameter

15

Experimental Validations

GF

ED

C

B

A

HI

J

A Porous plate holder w/adjustable orientation

B Constant-head plenum w/adjustable height

C Sub-micron filterD Sump pumpE ReservoirF CCD cameraG Data acquisition computerH Plenum overflow lineI Flow metering valveJ Flexible tubingK Laser Confocal Displacement

Meter

K

16

Experimental Measurement -- “Unperturbed” Film Thickness

Water 20 ◦Cwin = 0.9 mm/s = 0◦

Mean Liquid Film Thickness = 614.3 mStandard Deviation = 3.9 m

Laser Sensor Head

Target Plate

10 mm

Laser Confocal Displacement MeterKEYENCE CORPORATION OF AMERICA, Model # : LT-8110

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Experimental Variables

Experimental Variables• Plate porosity

• Plate inclination angle • Differential pressure

• Fluid properties

Independent Parameters• Injection velocity, win

• “Unperturbed” film thickness, zo

Dependent Variables• Detachment time

• Detachment diameter

• Maximum penetration depth

18

Experiment #W090 --“Unperturbed” Film Thickness

Time [sec]

Liq

uid

Fil

m T

hick

ness

[m

]

• Water 20oC, win = 0.9 mm/s, = 0o

• Mean Liquid Film Thickness = 614.3 m

• Standard Deviation = 3.9 m

+2

-2

19

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.33 0.36 0.40 0.43 0.46 0.50 0.53

Experiment #W090 -- Droplet Detachment Time

Droplet Detachment Time [sec]

Num

ber

Frac

tion

• Water 20oC, win = 0.9 mm/s, = 0o

• Mean Droplet Detachment Time = 0.43 s

• Standard Deviation = 0.04 s

• Sample Size = 100 Droplets

20

Experiment #W090 -- Calculated Detachment Time

Normalized Initial Perturbation Amplitude, s/zo

Det

achm

ent T

ime

[sec

]

Mean Experimental value = 0.43 s

+2

-2

Numerical Model

Experiment

21

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2

Experiment #W090 --Equivalent Droplet Detachment Diameter

Equivalent Droplet Diameter [mm]

Num

ber

Frac

tion

• Water 20oC, win = 0.9 mm/s, = 0o

• 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/zo

Equ

ival

ent

Dro

plet

Dia

met

er [

mm

]

Mean Experimental value = 7.69 mm

+2

-2

Numerical Model

Experiment

23

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

45 47 50 53 57 62 65 68

Experiment #W090 --Maximum Penetration Distance

Maximum Penetration Depth [mm]

Num

ber

Frac

tion

• Water 20oC, win = 0.9 mm/s, = 0o

• Maximum Mean Penetration Depth = 55.5 mm

• Standard Deviation = 5.1 mm

• Sample Size = 100 Droplets

24

Experiment #W090 --Calculated Penetration Distance

Normalized Initial Perturbation Amplitude, s/zo

Max

imum

Pen

etra

tion

Dep

th [

mm

]

Mean Experimental value = 55.5 mm

+2

-2

Numerical Model

Experiment

25

Experiment #W090 --Evolution of Maximum Penetration Distance

Time [sec]

Pene

trat

ion

Dep

th [

mm

]

Simulation

Experiment

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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

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Forced Film Concept -- Problem Definition

First Wall

Injection Point

DetachmentDistance xd

Forced Film

X-rays and Ions

Prometheus: Few mm thick Pb “forced film” injected tangentially at >7 m/s over upper endcap

~ 5 m

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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)

(cos )

U

Frg

2

U

We

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A Flat or Curved plate (1.52 0.40 m)

B Liquid filmC Splash guardD Trough (1250 L)E Pump inlet w/ filterF PumpG FlowmeterH Flow metering valveI Long-radius elbowJ Flexible connectorK Flow straightenerL Film nozzleM Support

frame

AB

C

DEF

G

H

I

J K

L MAdjustable angle

xz

gcos g

Experimental Apparatus

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• 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

AB

C

x yz

5 cm

Liquid Film Nozzles

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• 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)

• Dependent Variables Film width and thickness W(x), t(x) Detachment distance xd

Location for drop formation on free surface

Experimental Parameters

32

1 mm nozzle8 GPM10.1 m/s10° inclinationRe = 9200

Detachment Distance

33

0

400

800

1200

1600

2000

0 20 40 60 80 100 120

xd / vs. Fr: Wetting Surface

• Water on glass: LS = 25o

• xd increases linearly w/Fr

• xd as

• xd as

Fr

x d /

= 0 = 10 = 30 = 45

= 1 mm 1.5 mm 2 mm

wet

d

min

11.56 16.1δ

xFr

Design Window:Wetting Surface

34

0

400

800

1200

1600

0 20 40 60 80 100 120

xd / : Wetting vs. Nonwetting

• Wetting: glass; LS = 25o

• Nonwetting: coated glass; LS = 85o

• Nonwetting surface

smaller xd, or

conservative estimate

• xd indep. of

Fr

x d /

Open symbols Nonwetting Closed symbols Wetting = 1 mm = 1.5 mm= 2 mm = 0

nw

d

min

9.62 45.9δ

xFr

Design Window

35

xd: 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

0

20

40

60

80

100

120

140

160

180

0 1000 2000 3000 4000

We

x d [

cm]

= 1 mm 1.5 mm 2 mm

= 0 = 10 = 30

Effect of Inclination Angle(Flat Glass Plate)

37

0

20

40

60

80

100

120

140

160

0 500 1000 1500 2000

Detachment Distance Vs. Weber Number

We

x d [

cm]

= 0

Glass (LS=25o)

Stainless Steel (LS=50o)

Plexiglas (LS=75o) Rain-X® coated glass (LS=85o)

= 1 mm

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Effect of Weber Number on Detachment Distance(Flat and Curved Surfaces, Zero Inclination)

Plexiglas (LS = 70°)

We

x d [

cm]

Flat Curved

= 1 mm 1.5 mm 2 mm

= 0

39

Effect of Inclination Angle(Curved Plexiglas)

0

50

100

150

200

0 500 1000 1500

xd (

cm

)

• Curved nonwetting surface: Plexiglas ( = 70°); R = 5 m

• xd as

• xd as We

• xd values at = 0° “design window”

x d [

cm]

= 1 mm 1.5 mm 2 mm

= 0 = 10 = 30

We

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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

x /

W / W

o

0

1

2

3

4

0 200 400 600 800

= 2 mm = 0

Re = 3800 15000

Open Nonwetting Closed Wetting

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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

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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