Download EXPERIMENTAL STUDIES OF HIGH

Fluid Dynamic Aspects of
Thin Liquid Film
Protection Concepts
S. I. Abdel-Khalik and M. Yoda
ARIES Town Meeting (May 5-6, 2003)
G. W. Woodruff School of
Mechanical Engineering
Atlanta, GA 30332–0405 USA
Overview
Thin liquid protection (Prometheus)
• Major design questions
wall”: low-speed normal injection
• “Wetted
through porous surface
 Numerical simulations
 Experimental validations
film”: high-speed tangential injection
• “Forced
along solid surface
 Experimental studies
2
Thin Liquid Protection
Major Design Questions
a stable liquid film be maintained over the entire surface of
• Can
the reactor cavity?
the film be re-established over the entire cavity surface
• Can
prior to the next target explosion?
a minimum film thickness be maintained to provide
• Can
adequate protection over subsequent target explosions?
Study wetted wall/forced film concepts over “worst
case” of downward-facing surfaces
3
Wetted Wall Concept--Problem Definition
Prometheus: 0.5 mm thick layer of liquid lead injected normally
through porous SiC structure
Liquid Injection
~5m
First
Wall
X-rays
and Ions
4
Numerical Simulation of Porous Wetted Walls
Summary of Results
Quantify effects of
velocity w
• injection
film thickness z
• initial
perturbation geometry & mode number
• Initial
angle 
• inclination
• Evaporation & Condensation at the interface
in
o
on
detachment time
• Droplet
droplet diameter
• Equivalent
• Minimum film thickness prior to detachment
Obtain Generalized Charts for dependent variables as
functions of the Governing non-dimensional parameters
5
Numerical Simulation of Porous Wetted Walls
Wetted Wall Parameters
• Length, velocity, and time scales :
l   /  g (L  G )
Uo  g l
•
• Nondimensional minimum film thickness :
• Nondimensional initial film thickness :
• Nondimensional injection velocity :
Nondimensional drop detachment time :
to  l / U o
*  td / to
*min  min / l
z  zo / l
*
o
win*  win / U o
6
Numerical Simulation of Porous Wetted Walls
Non-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
7
Numerical Simulation of Porous Wetted Walls
Effect of Initial Perturbation
• Initial Perturbation Geometries
Sinusoidal
zo
s
Random
zo
Saddle
s
zo
8
Numerical Simulation of Porous Wetted Walls
Effect of Evaporation/Condensation at Interface
•
zo*=0.1, win*=0.01, Re=2000
mf+=-0.005
(Evaporation)
*=31.35
mf+=0.0
*=27.69
mf+=0.01
(Condensation)
*=25.90
9
Numerical Simulation of Porous Wetted Walls
Drop Detachment Time
10
Numerical Simulation of Porous Wetted Walls
Minimum Film Thickness
11
Numerical Simulation of Porous Wetted Walls
Nondimensional Minimum Thickness
Evolution of Minimum Film Thickness (High Injection/Thick Films)
Nondimensional Initial Thickness, zo*=0.5
Nondimensional Injection velocity, win*=0.05
Drop Detachment
Minimum Thickness
Nondimensional Time
12
Numerical Simulation of Porous Wetted Walls
Nondimensional Minimum Thickness
Evolution of Minimum Film Thickness (Low Injection/Thin Films)
Nondimensional Initial Thickness, zo*=0.1
Nondimensional Injection velocity, win*=0.01
Drop Detachment
Minimum Thickness
Nondimensional Time
13
Numerical Simulation of Porous Wetted Walls
Equivalent Detachment Diameter
14
Experimental Validations
J
B
I
H
F
G
C
A
K
E
D
A Porous plate holder w/adjustable
orientation
B Constant-head plenum
w/adjustable height
C Sub-micron filter
D Sump pump
E Reservoir
F CCD camera
G Data acquisition computer
H Plenum overflow line
I Flow metering valve
J Flexible tubing
K Laser Confocal Displacement
Meter
15
Experimental Measurement
-- “Unperturbed” Film Thickness

Target Plate
Water 20 ◦C
win = 0.9 mm/s
 = 0◦
Mean Liquid Film Thickness = 614.3 m
Standard Deviation = 3.9 m
10 mm
Laser Sensor Head
Laser Confocal Displacement Meter
KEYENCE CORPORATION OF AMERICA, Model # : LT-8110
16
Experimental Variables
Experimental Variables
porosity
• Plate
inclination angle 
• Plate
pressure
• Differential
• Fluid properties
Independent Parameters
velocity, w
• Injection
• “Unperturbed” film thickness, z
Dependent Variables
time
• Detachment
diameter
• Detachment
• Maximum penetration depth
in
o
17
Liquid Film Thickness [m]
Experiment #W090 -“Unperturbed” Film Thickness
+2
-2
• Water 20oC, win = 0.9 mm/s,  = 0o
• Mean Liquid Film Thickness = 614.3 m
• Standard Deviation = 3.9 m
Time [sec]
18
Experiment #W090 -- Droplet Detachment Time
0.4
• Water 20oC, win = 0.9 mm/s,  = 0o
• Mean Droplet Detachment Time = 0.43 s
• Standard Deviation = 0.04 s
• Sample Size = 100 Droplets
Number Fraction
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.33
0.36
0.40
0.43
0.46
0.50
0.53
Droplet Detachment Time [sec]
19
Experiment #W090
-- Calculated Detachment Time
Numerical Model
Detachment Time [sec]
+2
Experiment
Mean Experimental value = 0.43 s
-2
Normalized Initial Perturbation Amplitude, s/zo
20
Experiment #W090 -Equivalent Droplet Detachment Diameter
0.35
• Water 20oC, win = 0.9 mm/s,  = 0o
• Mean Droplet Diameter = 7.69 mm
• Standard Deviation = 0.17mm
• Sample Size = 100 Droplets
Number Fraction
0.3
0.25
0.2
0.15
0.1
0.05
0
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]
21
Equivalent Droplet Diameter [mm]
Experiment #W090 –
Equivalent Detachment Diameter
+2
Mean Experimental value = 7.69 mm
-2
Numerical Model
Experiment
Normalized Initial Perturbation Amplitude, s/zo
22
Experiment #W090 -Maximum Penetration Distance
0.35
• Water 20oC, win = 0.9 mm/s,  = 0o
• Maximum Mean Penetration Depth = 55.5 mm
• Standard Deviation = 5.1 mm
• Sample Size = 100 Droplets
Number Fraction
0.3
0.25
0.2
0.15
0.1
0.05
0
45
47
50
53
57
62
65
68
Maximum Penetration Depth [mm]
23
Experiment #W090 -Calculated Penetration Distance
Maximum Penetration Depth [mm]
Numerical Model
Experiment
+2
Mean Experimental value = 55.5 mm
-2
Normalized Initial Perturbation Amplitude, s/zo
24
Penetration Depth [mm]
Experiment #W090 -Evolution of Maximum Penetration Distance
Experiment
Simulation
Time [sec]
25
Wetted Wall Summary
general nondimensional charts applicable to a
• Developed
wide variety of candidate coolants and operating
conditions
of liquid film imposes
• Stability
 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
Predictions are closely matched by Experimental
• Model
Data
26
Forced Film Concept
-- Problem Definition
Prometheus: Few mm thick Pb “forced film” injected tangentially
at >7 m/s over upper endcap
~5m
X-rays
and Ions
Injection
Point
First Wall
Detachment
Distance xd
Forced Film
27
Forced Film Parameters
•
•
•
•
•
•
•
U 2
We 

Weber number We




Liquid density 
Liquid-gas surface tension 
Initial film thickness 
Average injection speed U
Fr 
Froude number Fr
U
g (cos )
 Surface orientation  ( = 0°  horizontal surface)
Mean detachment length from injection point xd
Contact Angle, LS
Glass : 25o
Mean lateral extent W
Coated Glass : 85o
Surface radius of curvature R = 5 m
Stainless Steel : 50o
Surface wettability: liquid-solid contact angle LS
Plexiglas : 75o
In Prometheus: for  = 0 – 45, Fr = 100 – 680 over nonwetting surface
(LS = 90)
28
Experimental Apparatus
A Flat or Curved plate
(1.52  0.40 m)
I
B Liquid film
C Splash guard
J
D Trough (1250 L)
E Pump inlet w/ filter
H
F Pump
G Flowmeter
G
H Flow metering valve
I Long-radius elbow
J Flexible connector
K Flow straightener
L Film nozzle
F
M Support
frame
L
K
z
x
Adjustable
angle 
M
A
B
gcos 
g
C
E
D
29
Liquid Film Nozzles
5 cm
x
y
z

A
B
C
• Fabricated with stereolithography rapid prototyping
•  = 0.1 cm;  = 0.15 cm;  = 0.2 cm
• 2D 5 order polynomial contraction along z from 1.5 cm to 
• Straight channel (1 cm along x) downstream of contraction
A
B
C
th
30
Experimental Parameters
Variables
• Independent






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
31
Detachment Distance
1 mm nozzle
8 GPM
10.1 m/s
10° inclination
Re = 9200
32
xd /  vs. Fr: Wetting Surface
2000
 = 1 mm




1600
xd / 
1200
1.5 mm
•
2 mm
•
 = 0
 = 10
 = 30
 = 45
•
•
800
Water on glass: LS
= 25o
xd increases linearly
w/Fr
xd as 
xd as 
wet
 xd 
   11.56 Fr  16.1
 δ min
Design Window:
400
0
0
20
40
60
80
100
120
Wetting Surface
Fr
33
xd / : Wetting vs. Nonwetting
1600
Open symbols Nonwetting
Closed symbols Wetting
 = 1 mm
 = 1.5 mm
= 2 mm
 = 0
xd / 
1200
800
•
coated
• Nonwetting:
glass;  = 85
Wetting: glass; LS = 25o
LS
o
surface 
• Nonwetting
smaller x , or
d
conservative estimate
• x indep. of 
d
400
nw
0
0
20
40
60
Fr
80
 xd 
 9.62 Fr  45.9


100 δ 120
 min Design Window
34
xd: Wetting vs. Nonwetting
 = 1 mm 1.5 mm 2 mm
180
 = 0
160
glass (
• Wetting:
= 25°)
xd [cm]
140
120
• Nonwetting:
Rain-X coated
100
®
80
glass ( = 85°)
60
40
Glass

Rain-X® coated glass   
20
0
0
500
1000
1500
2000
2500
3000
We
35
Effect of Inclination Angle
(Flat Glass Plate)
 = 1 mm 1.5 mm 2 mm
180
160
xd [cm]
140
120
100
80
60
  = 0
  = 10
  = 30
40
20
0
0
1000
2000
3000
4000
We
36
Detachment Distance Vs. Weber Number
160
 = 0
 = 1 mm
140
xd [cm]
120
100
80
60
40
 Glass (LS=25o)
Stainless Steel (LS=50o)
20
 Plexiglas (LS=75o)
 Rain-X® coated glass (LS=85o)
0
0
500
1000
1500
2000
We
37
Effect of Weber Number on Detachment Distance
(Flat and Curved Surfaces, Zero Inclination)
 = 1 mm
 = 0
180
160
1.5 mm
2 mm
xd [cm]
140
120
100
80
60
40
Plexiglas
20
(LS = 70°)
Flat

Curved   
0
0
500
1000
1500
2000
2500
3000
We
38
Effect of Inclination Angle
Detachment Distance vs. Weber Number for Plexi-glass Curved Plate at 0°, 10°
and 30° Inclination
(Curved Plexiglas)
200
 = 1 mm
1.5 mm
2 mm
nonwetting
• Curved
surface: Plexiglas
150
( = 70°); R = 5 m1.5 mm, 0°
xd (cm)
xd [cm]
1 mm, 0°
• x  as  
• x  as We 
values at  = 0°
• x“design
window”
d
100
d
  = 0
  = 10
  = 30
50
2 mm, 0°
1 mm, 10°
1.5 mm, 10°
2mm, 10°
1 mm, 30°
1.5 mm 30°
2 mm 30°
d
0
0
500
We
1000
1500
We
39
W / Wo: Wetting vs. Nonwetting
4
 = 2 mm
 = 0
Wetting (LS = 25o)
lateral growth
• Marked
(3.5) at higher Re
3
W / Wo
Nonwetting (LS = 85o )
lateral spread
• Negligible
 Contact line “pinned”
 Re = 3800
 15000
2
at edges?
• Contracts farther upstream
1
0
0
200
400
600
800
Open Nonwetting x / 
Closed Wetting
40
Cylindrical Dams
all cases, cylindrical obstructions modeling protective dams
• Inaround
beam ports incompatible with forced films
• Film either detaches from, or flows over, dam
y
y
x
y
x
x
41
Forced Film Summary
windows for streamwise (longitudinal) spacing
• Design
of injection/coolant removal slots to maintain attached
protective film
 Detachment length increases w/Weber and Froude numbers
chamber first wall surface requires fewer
• Wetting
injection slots than nonwetting surface  wetting
surface more desirable
protective dams around chamber
• Cylindrical
penetrations incompatible with effective forced film
protection
 “Hydrodynamically tailored” protective dam shapes
42
Acknowledgements
Georgia Tech
Faculty : Damir Juric
• Academic
Faculty : D. Sadowski and S. Shin
• Research
: F. Abdelall, J. Anderson, J. Collins, S. Durbin, L. Elwell, T.
• Students
Koehler, J. Reperant and B. Shellabarger
DOE
• W. Dove, G. Nardella, A. Opdenaker
ARIES-IFE Team
LLNL/ICREST
• R. Moir
43