ARIES: Fusion Power Core and Power Cycle Engineering
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Transcript ARIES: Fusion Power Core and Power Cycle Engineering
Scoping Study of FLiBe Evaporation and
Condensation
A. R. Raffray and M. Zaghloul
University of California, San Diego
ARIES-IFE Meeting
General Atomics
San Diego
July 1-2, 2002
July 1, 2002/ARR
1
Outline
• FLiBe properties used in analysis
- Vapor pressure as a function of temperature
- Other properties
• Condensation rates and characteristic time for FLiBe
• Aerosol source term
- Photon energy deposition and explosive boiling
- Estimate of amount of FLiBe expulsed from surface
• End-goal: example parameter window plot
July 1, 2002/ARR
2
FLiBe Vapor Pressure
•
•
•
•
e-mail communications among UCSD, ORNL and Berkeley
From Olander’s calculated values: log10 (P(Torr)) = 9.55-11109.56/T(K);
T= 773 K - 973 K
From ORNL’s measured values: log10 (P(Torr))=9.009-10444.11/T(k); T= 1223 K - 1554 K
Expression used for the analysis (fit from above two):
-
log10 (P(Torr))=9.3806-10965.26/T(K);
July 1, 2002/ARR
T = 773 K - 1554 K
3
Physical Properties for Film Materials
Property
Pb
FLiBe
Li
Tmelting (K)
600.5
732.2
452
Tboiling, 1 atm (K)
1893
1687
1590
Tcritical (K)
4836
4498.8 (* )
3223
Density (kg/m3)
11291 – 1.1647 T
2413 - 0.488 T
519.73 – 0.01 T
Log10 (Ptorr) =
9.38 - 10965.3/T
Log10 (Ptorr) =
7.764 - 7877.9/T
Vapor Pressure
Log10 (Ptorr) = 7.91 - 9923/T
CP (J/kg-K)
=183.6 -0.07 T -1.6x106 T-2
+ 3.5x10-5 T2+ 5x10-9 T3
2347
4227.57 - 0.0733 T
hfg (J/kg)
= 46.61 - 0.003 T +4.7710-7 T2
(=8.6x106 at 1893 K)
= 8.965106 - 2347 T (* *)
(= 5.3x106 at 1687 K)
= 4.9810-8 T2 - 2.05 T +
38.01
All temperatures, T, in K
(*) Xiang M. Chen, Virgil E. Schrock and Per F. Peterson, “The Soft-Sphere Equation of State for Liquid FLiBe,”
Fusion Technology, Vol. 21, 1992.
(**) Derived from Cp and the Cohesive energy @ 1atm.
July 1, 2002/ARR
4
Condensation Flux and Characteristic Time to Clear
Chamber as a Function of FLiBe Vapor and Film Conditions
0.5
M
j net
R2
P
P
c g e f
Tg0.5
T f0.5
jevap
Pg
Tg
• Characteristic time to clear chamber, tchar,
based on condensation rates and FLiBe
inventory for given conditions
•
• For higher Pvap (>0.1 Pa for assumed
conditions), tchar is independent of
•
• For lower Pvap as condensation slows
•
down, tchar increases substantially
July 1, 2002/ARR
Tf
jcond
For ~0.1 s between shots Pvap prior to next
shot could be up to ~10 x Psat
Not likely to be a major problem
Of more concern is aerosol generation and
5
behavior
X-ray Spectra and Cold Opacities Used in
Aerosol Source Term Estimate
• X-ray spectra much softer for indirect drive target (90% of total
energy associated with < 5 keV photons
• Cold opacity calculated from cross section data available from LLNL
(EPDL97)
July 1, 2002/ARR
6
Photon Energy Deposition in Vapor and Film
• Example Vapor Pressure = 1 mTorr
- Corresponding to TPb= 910 K; TFLiBe= 886 K; TLi= 732 K
• Photon energy deposited in vapor for R=6.5 m:
- ~1% in Pb vapor
- < 0.1% in FLiBe vapor
July 1, 2002/ARR
•
For film, most of photon energy deposited:
- within order of 1 mm for Pb film
- within order of 10 mm for FLiBe film
- important for aerosol source term
7
Processes Leading to Aerosol Formation following High
Energy Deposition Over Short Time Scale
Surface
Vaporization
Energy
Deposition &
Transient Heat
Transport
•Stresses and Strains
and Hydrodynamic
Motion
•Fractures and Spall
Film
X-Rays
Impulse
y
Induced
Thermal- Spikes
Mechanical
Response
Liquid
Fast Ions
Phase
Transitions
x
Slow Ions
• Surface Vaporization
•Heterogeneous Nucleation
•Homogeneous Nucleation
(Phase Explosion)
z
Spall Fractures
Impulse
Material Removal Processes
Expansion,
Cooling and
Condensation
July 1, 2002/ARR
Phase Explosion
Liquid/Vapor
Mixture
8
Vaporization from Free Surface
• Occurs continuously at liquid surface
Example results for Pb
• Governed by the Hertz-Knudsen equation for
flux of atoms
j
1
2 m k
e
Ps
Pv
c
Tf
Tv
e = vaporization coefficient,
c = condensation coefficient,
m = mass of evaporating atom,
k = Boltzmann’s constant,
Ps = saturation pressure
Pv = pressure of vapor
Tf = film temperature
Tv = vapor temperature
• Liquid-vapor phase boundary recedes with velocity:
Ion-like
heating
rate
Photon-like
heating rate
dr
jm
dt
• For constant heating rate, , and expression for
Ps =f(T), the following equation can be integrated
to estimate fractional mass evaporated over the
temperature rise.
• Free surface vaporization is very high for heating
dT
rate corresponding to ion energy deposition
dt
(Ps Pv ) m
dr
2kT
July 1, 2002/ARR
1
2
dT
• For much higher heating rate (photon-like) free
surface vaporization does not have the time to occur
and its effect is much reduced
9
Vaporization into Heterogeneous Nuclei
• Occurs at or somewhat above boiling
temperature, T0
Example results for Pb
• Vapor phase appears at perturbations in the
liquid (impurities etc.)
• From Matynyuk, the mass vaporized into
heterogeneous nuclei per unit time is given by:
dM
dt
M
2 /3
e m
2 m k T
36
2
v
1 /3
hfg
T0
(T T0 )
v = density of vapor in the nucleus,
hfg = enthalpy of vaporization per unit mass,
0 = density of saturated vapor at normal boiling
temperature (T0)
P0 is the external static pressure
• The equation can be integrated over
temperature for a given heating rate, , and
following some simplifying assumptions
(Fucke and Seydel).
July 1, 2002/ARR
Ion-like
heating
rate
Photon-like
heating rate
• Heterogeneous nucleation is dependent
on the number of nuclei per unit mass
but is very low for heating rate
corresponding to ion energy deposition
and even lower for photon-like energy
deposition
10
Phase Explosion (Explosive Boiling)
• Rapid boiling involving homogeneous
nucleation
• High heating rate
- Pvapor does not build up as fast and thus falls
below Psat @ Tsurface
- superheating to a metastable liquid state
- limit of superheating is the limit of
thermodynamic phase stability, the spinode
(defined by P/v)T = 0)
• A given metastable state can be achieved in
two ways:
- increasing T over BP while keeping P < Psat
(e.g. high heating rate)
- reducing P from Psat while keeping T >T sat
(e.g. rarefaction wave)
1 6
dN
Gc
G
Aexp(
);
c
3( o h fg )2
dt
kT
3
July 1, 2002/ARR
• A metastable liquid has an excess free
energy, so it decomposes explosively into
liquid and vapor phases.
-
As T/Ttc > 0.9, Becker-Döhring theory of
nucleation indicates avalanche-like and
explosive growth of nucleation rate (by
20-30 orders of magnitude)
11
Photon Energy Deposition Density Profile in FLiBe Film
and Explosive Boiling Region
Cohesion energy (total evaporation energy)
0.9 Tcritical
Sensible energy
based on uniform
vapor pressure
following photon
passage in
chamber and
including
evaporated FLiBe
from film
Sensible energy (energy to reach saturation)
Explosive
boiling
region
Evaporated
thickness
2-phase region
3.7
July 1, 2002/ARR
5.52
12.24
Explosive boiling
region as lower
bound estimate for
aerosol source
term , ~5.52 mm
for FLiBe
12
Summary of Results for Different Film Materials under the
Indirect Drive Photon Threat Spectra
Pb vapor
(1 mtorr 910 K)
FLiBe vapor
(1 mtorr 886 K)
Li vapor
(1 mtorr 732 K)
Pvapor,interface / P0
2.44105
1.92105
6.07104
Cohesive energy, Et (GJ/m3)
9.14
10.07
11.51
Vapor quality in the
remaining 2-phase region
0.15
0.18
9.0010-2
dexplosive boil. (mm)
2.46
5.59
3.39
mexplosive boil. (kg)
12.89
4.27
0.85
mtot(kg)
13.91
5.08
1.21
• Tsat estimated from Pvapor,interface initial vapor pressure (P0=1 mtorr) heated by photon
passage plus additional pressure due to evaporation from film based on chamber volume
• Adding the vapor component from the 2-phase region remaining after explosive boiling
only slightly increases total expulsed mass (mtot vs. mexplosive,boil.)
• mtot would be lower-bound source term for chamber aerosol analysis
July 1, 2002/ARR
13
Comparison of Simple Explosive Boiling Estimates with
ABLATOR Results
• ABLATOR graciously provided by LLNL
• ABLATOR is an integrated code modeling energy deposition and armor thermal
response including melting, evaporation, boiling and spalling
• In the interest of time comparison done for a case already available in ABLATOR input
file
• Results for Al armor under given X-ray spectra and fluence 32.5 J/cm2 assuming a
square pulse over 3 ns
•
•
Melting depth
ABLATOR: 10.6 mm
Simple volumetric model:
10.1 mm
Vaporization depth:
ABLATOR: 1.863 mm
Simple volumetric model:
2.25 mm
• Explosive boiling depth:
ABLATOR (assumed as depth where nucleation rate > 1024 s-1): 4.32 mm
Simple volumetric model (T~ 0.9 Tcrit): 4.14 mm
• Results from simple model reasonably close to ABLATOR results suggesting that the
simple model could be used for scoping analysis
July 1, 2002/ARR
14
Example Aerosol Operating Parameter Window
• Use explosive boiling results as input for aerosol calculations
• Perform aerosol analysis to obtain droplet concentration and sizes prior to next shot
(NOT DONE YET)
• Apply target and driver anp_reg1_kal_data
constraints (e.g. from R. Petzoldt)
10 15
From P. Sharpe’s preliminary calculations for Pb
Number Concentration (#/m 3 )
10 13
10 11
10 9
10
7
10 5
10 3
DD: 0.05 mm
Tracking (only as example)
100 µs
500 µs
1000 µs
5000 µs
10000 µs
50000 µs
100000 µs
0.1
1
Particle Diameter (µm)
10
• Need aerosol analysis for explosive boiling source case for Pb and FLiBe
• Need target tracking constraints for FLiBe
• Need to finalize driver constraints on aerosol size and distribution
July 1, 2002/ARR
100
ID: 580 mm
15