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NUMERICAL AND EXPERIMENTAL STUDIES OF THIN-LIQUID-FILMWALL PROTECTION SCHEMES

S.I. ABDEL-KHALIK AND M. YODA

G. W. Woodruff School of Mechanical EngineeringAtlanta, GA 30332-0405 USA

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• 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

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•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)

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Numerical Simulation of Porous Wetted WallsProblem Definition

IFE Reactor Chamber(Prometheus-L)

X-rays and Ions

Liquid Injection

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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 diameterMinimum film thickness prior to detachment

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

Nondimensional Initial Thickness, zo*=0.1

Nondimensional Injection velocity, win*=0.05

Nondimensional Time

Non

dim

ensi

onal

Min

imum

Thi

ckne

ss

Minimum Thickness

Drop Detachment

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Numerical Simulation of Porous Wetted WallsEffect of Initial Perturbation

• Initial Perturbation Geometries

Sinusoidal

Random

Saddle

zo

s

zo

zos

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Numerical Simulation of Porous Wetted WallsEffect of Initial Perturbation

Sinusoidal

zo, s = 0.5 mm

win = 1 mm/s 0.31

0.38

0.30

Pb at 700K

Random

win = 1 mm/s

Saddle

win = 1 mm/s

Detachment time (s)

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Numerical Simulation of Porous Wetted WallsEffect of Liquid Injection Velocity win

0.43

0.47

0.48

0.42

win = 0 mm/s

zo, s = 0.2 mm

(s)

win = 0.1 mm/s

zo, s = 0.2 mm

win = 1 mm/s

zo, s = 0.2 mm

win = 10 mm/s

zo, s = 0.2 mm

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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

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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

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

Nondimensional Initial Thickness, zo*=0.5

Nondimensional Injection velocity, win*=0.01

Nondimensional Time

Non

dim

ensi

onal

Min

imum

Thi

ckne

ss

Minimum Thickness

Drop Detachment

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Representation

A

T )(We

1)(

Re

1)( dAp

t fxxnuuguuu

L

G

Rel

oL lU

We2

lU oL

),()1(1/),( tIt L xx

),()1(1/),( tIt L xx

where

,

,)( GLg

l

glU o o

o U

lt , , ,

L

G

•Nondimensional Momentum Equation

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Numerical Simulation of Porous Wetted WallsMinimum Film Thickness

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Numerical Simulation of Porous Wetted WallsMinimum Film Thickness

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Numerical Simulation of Porous Wetted WallsMinimum Film Thickness

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Numerical Simulation of Porous Wetted WallsEvaporation/Condensation at the Interface

where

A)(

)1(

)1(2dAm

ρ

ρρuρ f

*f xxu

oL

f*f Uρ

mm

•Nondimensional Mass Conservation

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Numerical Simulation of Porous Wetted WallsEvaporation/Condensation at the Interface

x*ff

f mρ

udt

dxn

)1(

2

y*ff

f mρ

vdt

dyn

)1(

2

z*ff

f mρ

wdt

dzn

)1(

2

• Interface Advancement

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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

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

*=31.35 *=27.69 *=25.90

mf*=-0.005 mf

*=0.0 mf*=0.01

(Evaporation) (Condensation)

• zo*=0.1, win

*=0.01, Re=2000

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(Condensation)

(Evaporation)

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

*=25.69 *=25.13 *=25.74

mf*=-0.005 mf

*=0.0 mf*=0.01

• zo*=0.1, win

*=0.05, Re=2000

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(Condensation)

(Evaporation)

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

*=15.94 *=16.14 *=16.84

mf*=-0.005 mf

*=0.0 mf*=0.01

• zo*=0.5, win

*=0.01, Re=2000

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(Condensation)

(Evaporation)

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

*=17.11 *=16.94 *=17.83

mf*=-0.005 mf

*=0.0 mf*=0.01

• zo*=0.5, win

*=0.05, Re=2000

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment Time

Different Evaporation/Condensation mf* Values

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment Time

Different Evaporation/Condensation mf* Values

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment Time

Different Evaporation/Condensation mf* Values

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment “Diameter”

Different Evaporation/Condensation mf* Values

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment “Diameter”

Different Evaporation/Condensation mf* Values

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment “Diameter”

Different Evaporation/Condensation mf* Values

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Results – Minimum Film Thickness

Different Evaporation/Condensation mf* Values

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Results – Minimum Film Thickness

Different Evaporation/Condensation mf* Values

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Numerical Simulation of Porous Wetted WallsNon-Dimensional Results – Minimum Film Thickness

Different Evaporation/Condensation mf* Values

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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)

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IFE chamber(Prometheus)

First Wall

Injection Point

DetachmentDistance xd

Liquid Film/Sheet

X-rays and Ions

Problem Definition

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2 mm nozzle17 GPM10.7 m/s10o inclinationRe = 20000

2 mm nozzle17 GPM10.7 m/s10o inclinationRe = 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)?

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Experimental ApparatusA Glass 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

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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° and 30° Surface inclination angle ( = )

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

Location for drop formation on free surface

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1.5 mm nozzle13 GPM10.9 m/s10° inclinationRe = 15000

13 GPM10.9 m/s

Re = 1500010° inclination

1.5 mm nozzle

Dimensionless Groups

• Reynolds number Re = U0 / = 3700–21,000

• Froude number Fr = U0 / (g cos ) = 15–115 Only group involving

• Weber number We = U02 / = 100–3200

• Film nozzle aspect ratio AR = (5 cm)/ = 25–50

• Fluid properties (water at 17–19°C into air at patm) Kinematic viscosity = 1.06 10–6 m2/s Density = 999 kg/m3

Surface tension = 0.073 N/m

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2 mm nozzle17 GPM10.7 m/s10o inclinationRe = 20000

Detachment Distance xd

xd

• xd = distance along plate from nozzle exit where film detaches at plate surface

• Instantaneous detachment distance xd varies by up to 2 cm reported xd 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]

• xd = 127.5 cm

125.4 cm 127.6 cm 128.9 cm

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0

500

1000

1500

2000

0 20 40 60 80 100 120

xd: Fr Effects

Fr

x d /

= 0.15 cm

= 0.2 cm = 0 = 10

= 30

• xd / as Fr

• xd / as

• Growth rate similar for all cases (except at low Fr)

• Account for different initial conditions with “virtual origin”?

= 0.1 cm

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Average Film Width W(x)

• W(x) measured from above (viewed through plate)

= 0.1 cm; = 30; Re = 7200; Fr = 81

2 mm nozzle13 GPM8.2 m/s10° inclinationRe = 15000

13 GPM8.2 m/s

Re = 1500010° inclination

2 mm nozzle

5 cm

x

y

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?

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0

1

2

3

4

5

0 200 400 600 800 1000

W(x): Effects

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)

• xc/ < xd/ for all cases

xd/

W/W

0

xc/ 400

Wc/W0 3.6

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0

1

2

3

4

5

0 200 400 600 800 1000

W(x): Re Effects

x /

W/W

0

= 0.2 cm (C) = 30• W independent

of Re for x/ < 400 (near-field)

• W independent of Re at high Re?

• xc/ < xd/ in all cases

xc/ 400

Wc/W0 3.6

xd/

Re = 7,500Re = 12,400Re = 18,600

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Initial Observations• Detachment distance xd

Fr most important parameter for detachment distance xd

For high-speed films, consistent growth rate in xd / Virtual origin to compensate for initial conditions

• Film width (y-dimension) W Maximum W 4–5 times initial value Near-field (x < xc< xd): W dominated by initial conditions

Far-field (x > xc): most important parameter for W

• Characteristic film width Wc = W(xc) most important parameter for Wc

For high-speed films, Wc independent of Fr, Re and

Summary

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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)?

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1.5 mm nozzle10 GPM8.4 m/s10° inclinationRe = 11500

10 GPM8.4 m/s

Re = 1150010° 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