July 1, 2002/ARR 1 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 2 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 3 FLiBe Vapor Pressure communications among UCSD, ORNL and Berkeley From Olander’s calculated values: log 10 (P(Torr)) = /T(K); T= 773 K K From ORNL’s measured values: log 10 (P(Torr))= /T(k); T= 1223 K K Expression used for the analysis (fit from above two): -log 10 (P(Torr))= /T(K); T = 773 K K

July 1, 2002/ARR 4 Physical Properties for Film Materials T 2 T + = 4.98  T  T T =  T (* *) (= 5.3x10 6 at 1687 K) T T 2 = T  T 2 ) (=8.6x10 6 at 1893 K) h fg (J/kg) – 0.01 T T11291 – TDensity (kg/m 3 ) T melting (K) LiFLiBe PbProperty Log 10 (P torr ) = /T Log 10 (P torr ) = /T Log 10 (P torr ) = /T Vapor Pressure (* ) 4836 T critical (K) T = T -1.6x10 6 T x10 -5 T 2 + 5x10 -9 T 3 C P (J/kg-K) T boiling, 1 atm (K) 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, (**) Derived from Cp and the Cohesive 1atm.

July 1, 2002/ARR 5 Condensation Flux and Characteristic Time to Clear Chamber as a Function of FLiBe Vapor and Film Conditions Characteristic time to clear chamber, t char, based on condensation rates and FLiBe inventory for given conditions j cond j evap TfTf PgTgPgTg For ~0.1 s between shots P vap prior to next shot could be up to ~10 x P sat Not likely to be a major problem Of more concern is aerosol generation and behavior For higher P vap (>0.1 Pa for assumed conditions), t char is independent of For lower P vap as condensation slows down, t char increases substantially

July 1, 2002/ARR 6 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 7 Photon Energy Deposition in Vapor and Film Example Vapor Pressure = 1 mTorr -Corresponding to T Pb = 910 K; T FLiBe = 886 K; T Li = 732 K Photon energy deposited in vapor for R=6.5 m: -~1% in Pb vapor -< 0.1% in FLiBe vapor For film, most of photon energy deposited: -within order of 1  m for Pb film -within order of 10  m for FLiBe film -important for aerosol source term

July 1, 2002/ARR 8 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 Film X-Rays Fast Ions Slow Ions Impulse yy xx zz

July 1, 2002/ARR 9 Vaporization from Free Surface Occurs continuously at liquid surface Governed by the Hertz-Knudsen equation for flux of atoms  e = vaporization coefficient,  c = condensation coefficient, m = mass of evaporating atom, k = Boltzmann’s constant, Liquid-vapor phase boundary recedes with velocity: For constant heating rate, , and expression for P s =f(T), the following equation can be integrated to estimate fractional mass evaporated over the temperature rise. P s = saturation pressure P v = pressure of vapor T f = film temperature T v = 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 Photon-like heating rate Ion-like heating rate Example results for Pb

July 1, 2002/ARR 10 Vaporization into Heterogeneous Nuclei Occurs at or somewhat above boiling temperature, T 0 Vapor phase appears at perturbations in the liquid (impurities etc.) From Matynyuk, the mass vaporized into heterogeneous nuclei per unit time is given by: The equation can be integrated over temperature for a given heating rate, , and following some simplifying assumptions (Fucke and Seydel).  v = density of vapor in the nucleus, h fg = enthalpy of vaporization per unit mass,  0 = density of saturated vapor at normal boiling temperature (T 0 ) P 0 is the external static pressure 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 Photon-like heating rate Ion-like heating rate Example results for Pb

July 1, 2002/ARR 11 Phase Explosion (Explosive Boiling) RapidRapid boiling involving homogeneous nucleation High heating rate -P vapor does not build up as fast and thus falls below P T surface - 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 < P sat (e.g. high heating rate) - reducing P from P sat while keeping T >T sat (e.g. rarefaction wave) A metastable liquid has an excess free energy, so it decomposes explosively into liquid and vapor phases. -As T/T tc > 0.9, Becker-Döhring theory of nucleation indicates avalanche-like and explosive growth of nucleation rate (by orders of magnitude) ;

July 1, 2002/ARR 12 Photon Energy Deposition Density Profile in FLiBe Film and Explosive Boiling Region Cohesion energy (total evaporation energy) Evaporated thickness Explosive boiling region 2-phase region Sensible energy (energy to reach saturation) 0.9 T critical Explosive boiling region as lower bound estimate for aerosol source term, ~5.52  m for FLiBe Sensible energy based on uniform vapor pressure following photon passage in chamber and including evaporated FLiBe from film

July 1, 2002/ARR 13 Summary of Results for Different Film Materials under the Indirect Drive Photon Threat Spectra T sat estimated from P vapor,interface initial vapor pressure (P 0 =1 mtorr) heated by photon passage plus additional pressure due to evaporation from film based on chamber volumeT sat estimated from P vapor,interface  initial vapor pressure (P 0 =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 (m tot vs. m explosive,boil. )Adding the vapor component from the 2-phase region remaining after explosive boiling only slightly increases total expulsed mass (m tot vs. m explosive,boil. ) m tot would be lower-bound source term for chamber aerosol analysis m tot would be lower-bound source term for chamber aerosol analysis Li vapor (1 mtorr  732 K) FLiBe vapor (1 mtorr  886 K) Pb vapor (1 mtorr  910 K) 9.00  Vapor quality in the remaining 2-phase region Cohesive energy, E t (GJ/m 3 )  m tot (kg)  explosive boil. (  m) 6.07   10 5 P vapor,interface / P m explosive boil. (kg)

July 1, 2002/ARR 14 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/cm 2 assuming a square pulse over 3 ns Melting depth -ABLATOR:10.6  m -Simple volumetric model:10.1  m Vaporization depth: -ABLATOR:1.863  m -Simple volumetric model:2.25  m Explosive boiling depth: -ABLATOR (assumed as depth where nucleation rate > s -1 ): 4.32  m -Simple volumetric model (T~ 0.9 T crit ): 4.14  m Results from simple model reasonably close to ABLATOR results suggesting that the simple model could be used for scoping analysis

July 1, 2002/ARR 15 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 constraints (e.g. from R. Petzoldt) 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 From P. Sharpe’s preliminary calculations for Pb Example Aerosol Operating Parameter Window 100 ID: 580  m DD: 0.05  m Tracking (only as example)