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1
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
2
• 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
3
•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)
4
Numerical Simulation of Porous Wetted WallsProblem Definition
IFE Reactor Chamber(Prometheus-L)
X-rays and Ions
Liquid Injection
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 diameterMinimum film thickness prior to detachment
6
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
7
Numerical Simulation of Porous Wetted WallsEffect of Initial Perturbation
• Initial Perturbation Geometries
Sinusoidal
Random
Saddle
zo
s
zo
zos
8
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)
9
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
10
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
11
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
12
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
13
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
14
Numerical Simulation of Porous Wetted WallsMinimum Film Thickness
15
Numerical Simulation of Porous Wetted WallsMinimum Film Thickness
16
Numerical Simulation of Porous Wetted WallsMinimum Film Thickness
17
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
18
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
19
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
20
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
21
(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
22
(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
23
(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
24
Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment Time
Different Evaporation/Condensation mf* Values
25
Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment Time
Different Evaporation/Condensation mf* Values
26
Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment Time
Different Evaporation/Condensation mf* Values
27
Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment “Diameter”
Different Evaporation/Condensation mf* Values
28
Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment “Diameter”
Different Evaporation/Condensation mf* Values
29
Numerical Simulation of Porous Wetted WallsNon-Dimensional Results -- Detachment “Diameter”
Different Evaporation/Condensation mf* Values
30
Numerical Simulation of Porous Wetted WallsNon-Dimensional Results – Minimum Film Thickness
Different Evaporation/Condensation mf* Values
31
Numerical Simulation of Porous Wetted WallsNon-Dimensional Results – Minimum Film Thickness
Different Evaporation/Condensation mf* Values
32
Numerical Simulation of Porous Wetted WallsNon-Dimensional Results – Minimum Film Thickness
Different Evaporation/Condensation mf* Values
33
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)
34
IFE chamber(Prometheus)
First Wall
Injection Point
DetachmentDistance xd
Liquid Film/Sheet
X-rays and Ions
Problem Definition
35
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)?
36
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
37
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
38
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
39
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
40
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
41
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?
42
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
43
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
44
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
45
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)?
46
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