Post on 21-Dec-2015
April 22, 2002/ARR1
1. Concluding Sacrificial Liquid Film Activities 2. Starting Thick Liquid Wall Activities
A. R. Raffray, J. Pulsifer, M. Zaghloul
University of California, San Diego
ARIES-IFE Meeting
University of Wisconsin
April 22-23, 2002
April 22, 2002/ARR2
Outline
• Thin liquid film - Condensation
- Aerosol source term
- Documentation
• Thick liquid wall
- Key Issues
- How to address them within ARIES
April 22, 2002/ARR3
Condensation Flux and Characteristic Time to Clear Chamber as a Function of Pb Vapor and Film Conditions
- Characteristic time to clear chamber, tchar, based on condensation rates and Pb inventory for given conditions
- For higher Pvap (>10 Pa for assumed conditions), tchar is independent of Pvap
- For lower Pvap as condensation slows down, tchar increases substantially
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
1x100 1x101 1x102 1x103 1x1043x104
Vapor Pressure (Pa)
Pb:Film temperature = 1000KFilm Psat = 1.1 Pa
Vapor velocity = 0
Vapor Temp. (K)
1200
10,000
5000
2000
ƒƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ ƒ
æ
ææ æ æ æ æ æ æ æ æ
ø
ø ø ø ø ø ø ø ø ø ø
”
” ” ” ” ” ” ” ” ” ”
0
0.02
0.04
0.06
0.08
0.1
0.12
1x100 1x101 1x102 1x103 1x104 1x105 1x106
Vapor pressure (Pa)
ƒ
æ
ø
”
Pb film temperature = 1000KFilm Psat = 1.1 Pa
Vapor velocity = 0Chamber radius = 5 m
Vapor Temp.
10,000 K
5000 K
2000 K
1200 K
jcond
jevap
TfPg
Tg
jnet=MR2π
⎛ ⎝ ⎜ ⎞
⎠ ⎟
0.5Γσc
Pg
Tg0.5
−σePf
T f0.5
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
April 22, 2002/ARR4
Vapor Condensation Rate can be Affected by Presence of Non-Condensable Gas
• When pressure of vapor is of the same order as that of non-condensable gas, overall pressure equilibrium results in local vapor and gas gradients and condensation becomes diffusion-limited
P
Pv,o
Pg,o
Pg,i
Tv,o
Tv,i
Pv,i
jcond=Kv,gρvPg,lm
(Pv,o −Pv,i)
jcond = condensation flux (kg/m2-s)
Kv,g = binary mass transfer coefficient for diffusion of vapor and gas over
diffusion length (m/s)
v = vapor density (kg/m3)
Pg,lm = log mean pressure of non-condensable gas (Pa)
Pv,o, Pv,i = vapor pressure in chamber and at interface (Pa)
April 22, 2002/ARR5
Pb Vapor Diffusion Rate and Characteristic Time as a Function of Xe Gas Pressure for Different Pb Vapor Pressure Values
• At higher Xe pressure, Pb diffusion rate in Xe limits the effective condensation rate and decreases rapidly with increasing concentration of Xe (non-condensable gas)
• For the example considered the Xe pressure threshold for diffusion control is ~ 1.5 Pa for a Pb vapor pressure of 100 Pa and ~ 0.1 Pa for a Pb vapor pressure of 2 Pa
Chamber size = 5 m
Pb film temperature = 1000 K
Pb vapor temperature = 2000 K
Xe Pressure (Pa)
1x10-9
1x10-8
1x10-7
1x10-6
1x10-5
1x10-4
1x10-3
1x10-2
1x10-1
1x100
1x101
1x102
1x103
0 10 20 30 40 50 60 70 80 90 100
Pb Pressure(Pa)
100
2
Film Temp. = 1000 KPb Vapor Temp. = 2000 KChamber Radius = 5 m
10
0.01
0.1
1
10
100
1000
10000
0.01 0.1 1 10 100
2 Pa
10 Pa
100 Pa
Pb Pres.
DiffusionControlled
Condensation Controlled
Xe Pressure (Pa)
Film Temp. = 1000 KPb Vapor Temp. = 2000 KChamber Radius = 5 m
April 22, 2002/ARR6
Processes Leading to Aerosol Formation following High Energy Deposition Over Short Time Scale
Energy Deposition &
Transient Heat Transport
Induced Thermal- Spikes
Mechanical Response
Phase Transitions
•Stresses and Strains and Hydrodynamic Motion•Fractures and Spall
• Surface Vaporization•Heterogeneous Nucleation•Homogeneous Nucleation (Phase Explosion)
Material Removal Processes
Expansion, Cooling and
Condensation
Surface Vaporization
Phase Explosion Liquid/Vapor
Mixture
Spall Fractures
Liquid
FilmX-Rays
Fast Ions
Slow Ions
Impulse
Impulse
y
x
z
April 22, 2002/ARR7
Vaporization from Free Surface
• Occurs continuously at liquid surface
• Governed by the Hertz-Knudsen equation for flux of atoms
j =1
2πmkαe
PsTf
−αcPvTv
⎛ ⎝ ⎜
⎞ ⎠ ⎟
e = vaporization coefficient,
c = condensation coefficient,
m = mass of evaporating atom,k = Boltzmann’s constant,
• Liquid-vapor phase boundary recedes with velocity:
drdt
=jmρ
γ =dTdt
dr =α(Ps−Pv)
γρm
2πkT
⎛ ⎝ ⎜ )
12
dT
• For constant heating rate, , and expression for saturation pressure as a function of temperature the following equation can be integrated to estimate fractional mass evaporated over the temperature rise. The results are shown for Pb.
Photon-like heating rate
Ion-like heating rate
Ps = saturation pressure
Pv = pressure of vaporTf = film temperature
Tv = vapor temperature
• Free surface vaporization is very high for heating rate corresponding to ion energy deposition
• For much higher heating rate (photon-like) free surface vaporization does not have the time to occur and its effect is much reduced
April 22, 2002/ARR8
Vaporization into Heterogeneous Nuclei• Occurs at or somewhat above boiling
temperature, T0
• For heterogeneous nucleation, the 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=
αem
M2/3 2πmkT36
ρv2
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
1/3ΔHvT0
(T −T0)
• The equation can be integrated over temperature for a given heating rate, , and following some simplifying assumptions (Fucke and Seydel). The results are shown for Pb.
v = density of vapor in the nucleus,
Hv = enthalpy of vaporization per unit mass,
0 = density of saturated vapor at normal boiling
temperature (T0)
P0 is the external static pressure • Vaporization into Heterogeneous nuclei 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
Photon-like heating rate
Ion-like heating rate
April 22, 2002/ARR9
Phase Explosion (Explosive Boiling) (I)
• • RapidRapid boiling involving homogeneous nucleation both at and beneath the surface.
• 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:
a) by raising the temperature from the boiling point while keeping the pressure lower than the
corresponding saturation values (e.g. high heating rate)
b) by reducing the pressure from the saturated value while keeping the corresponding
temperatures lower than the saturated values (e.g. rarefaction wave)
• A metastable liquid has an excess free energy, so it decomposes explosively into liquid and vapor phases.
- As T/Ttc increases past 0.9, Becker-Döhring theory of nucleation indicate an an avalanche-like and explosive growth of nucleation rate (by 20-30 orders of magnitude)
April 22, 2002/ARR10
EEsenssens = Energy density required for the material to reach the saturation temperature = Energy density required for the material to reach the saturation temperature
Et = Total evaporation energy (= Esens + E Evaporation)E E ( 0.9 Ttc )= Energy density required heat the material to 0.9 T= Energy density required heat the material to 0.9 T tctc
Phase Explosion (Explosive Boiling) (II)Volumetric Model with Phase Explosion from Photon Energy Deposition
• Liquid and vapor mixture evolved by phase explosion shown by shaded area (~0.5 m for Pb with quality >~0.8; ~2.9 m for Li)
• Could be higher depending on behavior of 2-phase region behind• Very challenging to predict aerosol size and number from this
April 22, 2002/ARR11
Upper Bound Estimate of Combination of Number of Droplets and Droplet Size as a Function of Evaporated Film Thickness
• Suggest to do aerosol calculations for two case assuming a drop radius based on pressure and surface tension equilibrium:1. Assume all liquid in 2-phase region in aerosol form
2. Assume all liquid in explosive ablation layer in aerosol form
• Sensitivity analysis on droplet size
1x10101x10111x10121x10131x10141x10151x10161x10171x10181x10191x10201x10211x10221x10231x1024
0x100 2x10-6 4x10-6 6x10-6 8x10-6 1x10-5
10-10
10-9
10-8
rdrop(m)
10-7
10-6
Evaporated thickness (m)
April 22, 2002/ARR12
Proposed Outline of Thin Liquid Film Paper (I)(First draft to be written over next 3-4 months
and to be published in FE&D)
DRAFT1. Introduction (R. Raffray) (~ 0.5 page)
2. Example configuration (~ 0.5-1 page) (L. Waganer)
3. Driver requirements (~ 2 pages)- Heavy Ion beam (C. Olson, S. Yu) (~ 1 page)- Laser (M. Tillack, J. Sethian) (~ 1 page)
4. Target requirements (D. Goodin, R. Petzold) (~ 2 pages)- Indirect drive- Direct drive
5. Film analysis (S. Abdel Khalik, M. Yoda) (~ 2-3 pages)- Flowing film- Continuous injection from the back (e.g. through porous media)
6. Energy deposition (D. Haynes) (1-2 pages)- Based on Pb vapor pressure and any additional chamber gas- Other liquids (FLiBe?)
April 22, 2002/ARR13
Proposed Outline of Thin Liquid Film Paper (II)(First draft to be written over next 3-4 months
and to be published in FE&D)
7. Chamber clearing (thermal and mass transfer analysis)- Condensation scoping analysis (R. Raffray) (1 page)- Source term for aerosol formation (A. Hassanein, D. Haynes) (2 pages)- Aerosol analysis (P. Sharpe) (1 page)
8. Design window (Raffray, others)(1 page)- Aerosol size and concentrations- Incorporate estimate based on conditions and driver and target requirements
9. Radiological issues (L.El-Guebaly) (0.5 page)- Choice of liquids- Effect on overall waste disposal issues
10. Safety issues (D. Petti, L. El-Guebaly) (0.5 page)
11. Key remaining issues (R. Raffray, all) (0.5 page)
12. Conclusions (R. Raffray, all) (0.5 page)
Total = ~ 17 journal pages
April 22, 2002/ARR14
Beam ports and solid shielding structure (same both sides)
Stationary grid of cylindrical jets
Porosity in liquid blanket
Venting path for target and ablation debris
Oscillating liquid jets
Heavy ion target
Schematic of a potential thick-liquid pocket,showing major pocket features.
Some Thoughts on Assessing the Thick Liquid Wall Option (I)
Major issues tend to be design dependent; e.g. for HYLIFE
Hydraulics • Jet formation to assure coverage while
providing pocket for target explosion and channels for driver firing and target
injection, and chamber clearing• This is is being addressed by an ongoing
modeling and experimental fluid dynamics program
- ARIES would not be able to provide much more in this area within the time frame and scope of the study
Chamber clearing• Return chamber environment to a condition
which allows successful target and driver propagation
- Many issues similar to thin liquid wall option, including aerosol formation and condensation
- Fluid dependent (analysis should be done for FLiBe and other fluids?)
April 22, 2002/ARR15
Some Thoughts on Assessing the Thick Liquid Wall Option (II)
Interface and integration issues • Areas where ARIES could best provide some insight, trade-offs and design windows
• Demand on nozzle- Mechanical design of nozzle (moving parts)- Reliability for such demanding performance - Effect of malfunction
- irradiation effect- out of phase oscillation- nozzle choking because of impurity in fluid
- fluid chemistry control requirements- presence of debris and holhraum materials
• Choice of fluid and structural materials- Shielding performance (what is the goal, class C???)- Lifetime of structural materials- Power cycle. Can it be optimized?
- Poor thermal conductivity of FLiBE- ok for volumetric heat deposition- poor heat transfer leads to large HX or T between primary and secondary fluids
- Pressure drop and pumping power
April 22, 2002/ARR16
Some Thoughts on Assessing the Thick Liquid Wall Option (III)
Interface and integration issues
• Adequate shielding for last focus magnet- Further analysis?
• Specific target and driver requirements for thick liquid wall option- Vapor pressure of FLiBe (opening of pocket would create a pressure increase due to suction effect)- Aerosol formation (droplets)- Possible condensation of FLiBe in lines (effect on heavy ion beam)
• Gaps required for driver and target- Possibility of bare wall seeing photons and ions in direct line of sight
- effect of off-centered micro-explosion- consequences- would you a thin liquid film be needed?
• Safety issues- e.g. possible accident scenarios