fluid dynamic aspects of thin liquid film protection …3 thin liquid protection major design...
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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 simulationsExperimental validations
•“Forced film”: high-speed tangential injection along solid surface
Experimental studies
3
Thin Liquid ProtectionMajor 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
Prometheus: 0.5 mm thick layer of liquid lead injected normallythrough porous SiC structure
Liquid Injection
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 θ• 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= σ ρ −ρ oU g l= o o/t l U=
• Nondimensional drop detachment time : *d o/t tτ ≡
• Nondimensional minimum film thickness : *min min / lδ ≡ δ
• Nondimensional initial film thickness : *o o /z z l≡
• Nondimensional injection velocity : *in in o/w w U≡
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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 Initial Perturbation
• Initial Perturbation Geometries
Sinusoidal zo
εs
Random zo
Saddle zoεs
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Numerical Simulation of Porous Wetted WallsEffect of Evaporation/Condensation at Interface
• zo*=0.1, win
*=0.01, Re=2000
τ*=31.35
mf+=-0.005
(Evaporation)
τ*=25.90
mf+=0.01
(Condensation)
τ*=27.69
mf+=0.0
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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
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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 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/sθ = 0◦
Mean Liquid Film Thickness = 614.3 µmStandard Deviation = 3.9 µm
Laser Sensor Head
Target Plateθ
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 θ• Differential pressure• Fluid properties
Independent Parameters• Injection velocity, win
• “Unperturbed” film thickness, zo
Dependent Variables• Detachment time• Detachment diameter• Maximum penetration depth
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Experiment #W090 --“Unperturbed” Film Thickness
Time [sec]
Liqu
id F
ilm T
hick
ness
[µm
]
• Water 20oC, win = 0.9 mm/s, θ = 0o
• Mean Liquid Film Thickness = 614.3 µm
• Standard Deviation = 3.9 µm
+2σ
-2σ
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Experiment #W090 -- Droplet Detachment Time
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
Droplet Detachment Time [sec]
Num
ber F
ract
ion
• Water 20oC, win = 0.9 mm/s, θ = 0o
• Mean Droplet Detachment Time = 0.43 s
• Standard Deviation = 0.04 s
• Sample Size = 100 Droplets
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Experiment #W090 -- Calculated Detachment Time
Normalized Initial Perturbation Amplitude, εs/zo
Det
achm
ent T
ime
[sec
]
Mean Experimental value = 0.43 s
+2σ
-2σ
Numerical Model
Experiment
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Experiment #W090 --Equivalent Droplet Detachment Diameter
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
Equivalent Droplet Diameter [mm]
Num
ber F
ract
ion
• Water 20oC, win = 0.9 mm/s, θ = 0o
• Mean Droplet Diameter = 7.69 mm
• Standard Deviation = 0.17mm
• Sample Size = 100 Droplets
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Experiment #W090 –Equivalent Detachment Diameter
Normalized Initial Perturbation Amplitude, εs/zo
Equi
vale
nt D
ropl
et D
iam
eter
[mm
]
Mean Experimental value = 7.69 mm+2σ
-2σ
Numerical Model
Experiment
23
Experiment #W090 --Maximum Penetration Distance
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
45 47 50 53 57 62 65 68Maximum Penetration Depth [mm]
Num
ber F
ract
ion
• Water 20oC, win = 0.9 mm/s, θ = 0o
• Maximum Mean Penetration Depth = 55.5 mm
• Standard Deviation = 5.1 mm
• Sample Size = 100 Droplets
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Experiment #W090 --Calculated Penetration Distance
Normalized Initial Perturbation Amplitude, εs/zo
Max
imum
Pen
etra
tion
Dep
th [m
m]
Mean Experimental value = 55.5 mm
+2σ
-2σ
Numerical Model
Experiment
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Experiment #W090 --Evolution of Maximum Penetration Distance
Time [sec]
Pene
tratio
n D
epth
[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 imposesLower bound on repetition rate (or upper bound on time between shots) to avoid liquid dripping into reactor cavity between shotsLower 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
Prometheus: Few mm thick Pb “forced film” injected tangentially at >7 m/s over upper endcap
First Wall
Injection Point
DetachmentDistance xd
Forced Film
X-rays and Ions
~ 5 m
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Forced Film Parameters
Contact Angle, αLS
Glass : 25o
Coated Glass : 85o
Stainless Steel : 50o
Plexiglas : 75o
• Weber number WeLiquid density ρLiquid-gas surface tension σInitial film thickness δAverage injection speed U
• Froude number FrSurface orientation θ (θ = 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 αLS
• In Prometheus: for θ = 0 – 45°, Fr = 100 – 680 over nonwetting surface (αLS = 90°)
2ρ δ≡
σUWe
(cos )≡
θ δUFr
g
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Experimental ApparatusA 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
IJ K
L MAdjustable angle θ
xz
gcos θg
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Liquid Film Nozzles
AB C
x yz5 cm
δ
• Fabricated with stereolithography rapid prototyping
• δA = 0.1 cm; δB = 0.15 cm; δC = 0.2 cm
• 2D 5th order polynomial contraction along z from 1.5 cm to δ
• Straight channel (1 cm along x) downstream of contraction
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• Independent VariablesFilm nozzle exit dimension δ = 0.1–0.2 cmFilm nozzle exit average speed U0 = 1.9 – 11.4 m/sJet injection angle θ = 0°, 10°, 30° and 45o
Surface inclination angle α (α = θ)Surface curvature (flat or 5m radius)Surface material (wettability)
• Dependent VariablesFilm width and thickness W(x), t(x)Detachment distance xd
Location for drop formation on free surface
Experimental Parameters
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Detachment Distance
1 mm nozzle8 GPM10.1 m/s10° inclinationRe = 9200
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xd / δ vs. Fr: Wetting Surface
0
400
800
1200
1600
2000
0 20 40 60 80 100 120
• Water on glass: αLS= 25o
• xd increases linearly w/Fr
• xd↑ as θ↑
• xd↑ as δ↓
Fr
x d/δ
θ = 0°θ = 10°θ = 30°θ = 45°
δ = 1 mm 1.5 mm 2 mm
= −
wetd
min
11.56 16.1δx Fr
Design Window:Wetting Surface
34
xd / δ: Wetting vs. Nonwetting
0
400
800
1200
1600
0 20 40 60 80 100 120
• Wetting: glass; αLS = 25o
• Nonwetting: coated glass; αLS = 85o
• Nonwetting surface ⇒smaller xd, orconservative estimate
• xd indep. of δ
Fr
x d/δ
Open symbols NonwettingClosed symbols Wettingδ = 1 mmδ = 1.5 mmδ= 2 mmθ = 0°
= −
nwd
min
9.62 45.9δx Fr
Design Window
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xd: Wetting vs. Nonwetting
0
20
40
60
80
100
120
140
160
180
0 500 1000 1500 2000 2500 3000
We
x d[c
m]
• Wetting: glass (α= 25°)
• Nonwetting: Rain-X® coated glass (α = 85°)
GlassRain-X® coated glass
δ = 1 mm 1.5 mm 2 mm
θ = 0°
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0
20
40
60
80
100
120
140
160
180
0 1000 2000 3000 4000We
x d[c
m]
δ = 1 mm 1.5 mm 2 mm
θ = 0°θ = 10°θ = 30°
Effect of Inclination Angle(Flat Glass Plate)
37
Detachment Distance Vs. Weber Number
0
20
40
60
80
100
120
140
160
0 500 1000 1500 2000
We
x d[c
m]
θ = 0°
Glass (αLS=25o)Stainless Steel (αLS=50o)Plexiglas (αLS=75o)Rain-X® coated glass (αLS=85o)
δ = 1 mm
38
Effect of Weber Number on Detachment Distance(Flat and Curved Surfaces, Zero Inclination)
0
20
40
60
80
100
120
140
160
180
0 500 1000 1500 2000 2500 3000
Plexiglas(αLS = 70°)
We
x d[c
m]
FlatCurved
δ = 1 mm 1.5 mm 2 mmθ = 0°
39
Effect of Inclination Angle(Curved Plexiglas)
0
50
100
150
200
0 500 1000 1500
• Curved nonwettingsurface: Plexiglas (α = 70°); R = 5 m
• xd↑ as θ ↑
• xd↑ as We ↑
• xd values at θ = 0°“design window”
x d[c
m]
δ = 1 mm 1.5 mm 2 mm
θ = 0°θ = 10°θ = 30°
We
40
W / Wo: Wetting vs. NonwettingWetting (αLS = 25o)
• Marked lateral growth (3.5×) at higher Re
Nonwetting (αLS = 85o )
• Negligible lateral spreadContact line “pinned”at edges?
• Contracts farther upstream
x / δ
W/W
o
0
1
2
3
4
0 200 400 600 800
δ = 2 mmθ = 0°
Re = 380015000
Open NonwettingClosed 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
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AcknowledgementsGeorgia 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