Fluid Dynamic Aspects of Thin Liquid Film Protection Concepts S. I. Abdel-Khalik and M. Yoda ARIES...
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Transcript of Fluid Dynamic Aspects of Thin Liquid Film Protection Concepts S. I. Abdel-Khalik and M. Yoda ARIES...
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
11
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
17
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
26
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
27
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
28
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
29
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
30
• 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
31
• 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
38
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
40
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
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
43
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