Scoping Study of FLiBe Evaporation and Condensation

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); 973 K T= 773 K T= 1223 K - From ORNL’s measured values: log10 (P(Torr))=9.009-10444.11/T(k); 1554 K Expression used for the analysis (fit from above two): 10 July 1, 2002/ARR log (P(Torr))=9.3806-10965.26/T(K); T = 773 K - 1554 K 3 Physical Properties for Film Materials Property Tmelting (K) Pb 600.5 FLiBe 732.2 Li 452 Tboiling, 1 atm (K) Tcritical (K) Density (kg/m3) 1893 4836 11291 – 1.1647 T 1687 4498.8 (* ) 2413 - 0.488 T Log10 (Ptorr) = 9.38 - 10965.3/T 2347 = 8.965106 - 2347 T (* *) (= 5.3x106 at 1687 K) 1590 3223 519.73 – 0.01 T Log10 (Ptorr) = 7.764 - 7877.9/T 4227.57 - 0.0733 T = 4.9810-8 T2 - 2.05 T + 38.01 Vapor Pressure Log10 (Ptorr) = 7.91 - 9923/T CP (J/kg-K) hfg (J/kg) =183.6 -0.07 T -1.6x106 T2 + 3.5x10-5 T2+ 5x10-9 T3 = 46.61 - 0.003 T +4.7710-7 T2 (=8.6x106 at 1893 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, 1992. (**) Derived from Cp and the Cohesive energy @ 1atm. July 1, 2002/ARR 4 0.5  Pg Pf   M    j net      e 0.5   R2   c T 0.5 T f  g   Condensation Flux and Characteristic Time to Clear Chamber as a Function of FLiBe Vapor and Film Conditions jevap Pg Tg jcond Tf • Characteristic time to clear chamber, tchar, based on condensation rates and FLiBe inventory for given • For ~0.1 s between shots Pvap prior to conditions Pvap (>0.1 Pa for assumed • For higher next shot could be up to ~10 x Psat conditions), tchar is independent of • Not likely to be a major problem • For lower Pvap as condensation slows • Of more concern is aerosol generation down, tchar increases 5 and behavior July 1, 2002/ARR 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 • For film, most of photon energy • Photon energy deposited in vapor for R=6.5 m: deposited: - ~1% in Pb vapor - within order of 1 mm for Pb film - < 0.1% in FLiBe vapor - within order of 10 mm for FLiBe film - important for aerosol source term July 1, 2002/ARR 7 Processes Leading to Aerosol Formation following High Energy Deposition Over Short Time Scale Energy Deposition & Transient Heat Transport Surface Vaporization Liquid XRays Film Impulse Induced ThermalSpikes Mechanical Response •Stresses and Strains and Hydrodynamic Motion •Fractures and Spall Phase Transitions y Fast Ions x Slow Ions z Spall Fractures • Surface Vaporization •Heterogeneous Nucleation •Homogeneous Nucleation (Phase Explosion) Material Removal Processes Expansion, Cooling and Condensation Impulse Phase Explosion Liquid/Vapor Mixture 8 July 1, 2002/ARR Vaporization from Free Surface • Occurs continuously at liquid surface • Governed by the Hertz-Knudsen equation for flux of atoms Example results for Pb j  1 2 m k  e  P P  s   c v  Tf Tv  e = vaporization coefficient, Ps = c = condensation coefficient, pressure saturation m = mass of evaporating atom,v = pressure of P k = Boltzmann’s constant, vapor Tf = film temperature • Liquid-vapor phase boundary recedes vapor with Tv = temperature velocity: jm dr Ion-like heating rate Photon-like heating rate 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 dT   heating rate corresponding to ion energy 1 dt deposition 2  (Ps  Pv )  m dr  2kT   July 1, 2002/ARR  dT • For much higher heating rate (photon-like) free surface vaporization does not have the 9 time to occur and its effect is much reduced Vaporization into Heterogeneous Nuclei • Occurs at or somewhat above boiling temperature, T0 • Vapor phase appears at perturbations in the liquid (impurities etc.) • From Matynyuk, the mass vaporized into heterogeneous nuclei per unit time is given by: 1 /3   hfg dM e m 36   (T  T0 ) 2 /3   2  M 2  m k T  v  T0 dt 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 Example results for Pb Ion-like heating rate Photon-like heating rate • The equation can be integrated over temperature for a given heating rate, , and following some simplifying assumptions (Fucke and Seydel). July 1, 2002/ARR • 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 (e.g. rarefaction wave) sat • 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 avalanchelike and explosive growth of 11 nucleation rate (by 20-30 16 3 dN Gc  Aexp( ) ; Gc  3( o h fg  )2 dt kT July 1, 2002/ARR Photon Energy Deposition Density Profile in FLiBe Film and Explosive Boiling Region Sensible energy based on uniform vapor pressure following photon passage in chamber and including evaporated FLiBe from film Explosive boiling region as lower bound estimate for aerosol source term , ~5.52 mm for FLiBe 12 Cohesion energy (total evaporation energy) 0.9 Tcritical Sensible energy (energy to reach saturation) Explosive boiling region Evaporate d thickness 3.7 2-phase region 5.52 12.24 July 1, 2002/ARR Summary of Results for Different Film Materials under the Indirect Drive Photon Threat Spectra Pb vapor FLiBe vapor (1 mtorr  910 K) (1 mtorr  886 K) Li vapor (1 mtorr  732 K) Pvapor,interface / P0 Cohesive energy, Et (GJ/m3) Vapor quality in the remaining 2-phase region dexplosive boil. (mm) mexplosive boil. (kg) mtot(kg) 2.44105 9.14 0.15 2.46 12.89 13.91 1.92105 10.07 0.18 5.59 4.27 5.08 6.07104 11.51 9.0010-2 3.39 0.85 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: Vaporization depth: ABLATOR: 1.863 mm Simple volumetric model: 10.1 mm • 2.25 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 • 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 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 constraints (e.g. from R. Petzoldt) anp_reg1_kal_data 10 15 From P. Sharpe’s preliminary calculations for Pb 10 13 Number Concentration (#/m 3 ) 10 11 10 9 100 µs 500 µs 1000 µs 5000 µs 10000 µs 50000 µs 100000 µs 0.1 1 Particle Diameter (µm) 10 Tracking (only as example) 10 7 10 5 10 3 DD: 0.05 mm 100 ID: 580 mm • 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 15 July 1, 2002/ARR