Modeling Effort on Chamber Clearing for IFE Liquid Chambers at UCLA

Transcription

1 Modeling Effort on Chamber Clearing for IFE Liqid Chambers at UCLA Presented by: P. Calderoni own Meeting on IFE Liqid Wall Chamber Dynamics Livermore CA May 5-6 3

2 Otline his presentation will address two components of or modeling efforts on chamber clearing: - Vapor Condensation - Droplet clearing in a pressre decay field

3 Vapor Condensation Modeling - Approach Cople UCB model for condensation at a liqid / vapor interface (based on Schrage kinetic theory with snami calclations in -D volme Apply enhanced snami to simlate flibe vapor condensation experiments maintaining all assmptions implicit in snami and condensation model Compare with experiments Evalate effect of measred interface conditions: traces of non condensable gases vapor density dropping into transitions regime accmlation of less volatile BeF Generalize liqid / vapor interface model: add diffsional layer at the interface for non condensable gases add velocity and temperatre slip at the interface add diffsional layer at the interface for BeF

4 Gas dynamics modeling in IFE liqid chambers Gas dynamics regime characterized by Kndsen nmber: Kn λ L mean free path: λ characteristic length Kn <.1 Continm Regime 1 π d n Mean free path small compared to system - moleclar collision dominate - gas approximated as continos medim Upper limit of mean free path in HYLIFE: 4.7 cm Considering: Hard-sphere model diameter d 4 A Lowest density in HYLIFE chamber 3X1 13 #/cm 3.1 < Kn <.1 Slip regime Gas approximated as continos several mean free paths away from adjoining medim - Kinetic theory near interfaces to accont for both moleclar collisions and collision with system bondaries.1 < Kn < 3 ransition regime Moleclar collisions and collision with system bondaries are eqally important Kn > 3 Free Molecles Regime Moleclar collisions infreqent - rarefied gas kinetic theory applies

5 Condensation model assmptions -D gas dynamics calclation assmptions: wo dimensional geometry Gas phase is a continm Gas state changes are isoentropic everywhere except at shock waves which are treated as discontinities Liqid strctres are rigid - liqid inertia in the time scales of interest prevents strctres from moving or deforming - no work is transferred from gas to liqid Gas viscosity is negligible - viscos time scale L /ν >> dynamic time scale L/c Inside the volme gas is adiabatic - condction time scale L /α >> dynamic time scale L/c - radiative losses assmed to be negligible Flibe is an ideal gas law with constant γ - fitted EOS corrected for dissociation and ionization not effective in the considered range

6 Condensation model assmptions 1-D liqid / vapor interface assmptions: Vapor condenses only on liqid srfaces present as initial condition - no droplet ncleation in the volme Liqid layers are semi-infinite slabs - thermal diffsion length (α t 1/ << srface crvatre - initial layer is niform - liqid away from the interface remains constant - droplet spray cooling not considered Heat and mass transfer at the interface only in the normal direction - interface velocity de to mass addition is neglected becase of mass continity Heat transfer in the liqid layer by condction in the normal direction - a convection term de to condensing flx introdced in the energy eq Liqid srface is always in thermodynamic eqilibrim with the vapor - high mass transfer rates dring initial transient neglected - continm assmption Recombination and chemical diffsion effects for flibe are fast - vapor chemical composition is fixed by initial conditions Vapor composition is niform in the volme and at the interface Interface kinetic theory accommodation coefficients (sticking and evaporation are assmed to be 1

7 Interface condensation: Schrage theory ( [ ] dw d dv w v k m k m N dn b b w v 3/ exp π he effect of condensation on the moleclar motion is to impose a net flx in the direction normal to the interface: Integrating over v w and positive (toward : 1/ 1/ 1/ 1 exp k m erf k m k m m k n b b b b N π π φ Re-writing: ( [ ] { } s erf s e R p G s 1 1/ π π µ where ( 1/ 1/ 1/ 1/ γ γ γ µ M R R s p ρr Finally the net flx across the interface: 1/ 1/ 1 1 Γ ls ls e vs vs c k R p f R p f G π π

8 Modeling the interface and liqid layer wo eqations to cople liqid and vapor properties at the interface: mass balance G ρ G t vs vs ρ x ls ls x energy balance Vapor stagnation enthalpy: Where for flibe h fg ( sat ( p Energy eqation with bc v fg In the liqid layer: G h ref vs ( t t l k pg ( x t x pl x [ ( p ] h ( ( c c l sat v t h vs c pg [ vs sat ( pvs ] hfg [ sat ( pvs ] vs ( x t t ( x t q int kl t x ( x t x ref α condction in the vapor neglected for short diffsion length - neglect radiation p sat ( x t x ls x Convection term added to accont for condensing mass across the interface - ls evalated from G

9 Initial non-eqilibrim conditions In early stages of condensation the contact of highly sperheated vapor with the cold srface cases high mass transfer rates at the interface - the effect (sction is to increase the vapor velocity that is evalated by snami Schrage theory fails to accont for high mass transfer rates becase of the srface eqilibrim assmption - velocity associated with mass flx predicted by the Schrage eq can be higher than physical limitations associated with sper sonic choking effect Gas dynamics limiting flx: γ c γ 1 γ 1 ρ γ 1 Gv max ρ c M M M v < γ 1 γ 1 γ 1 γ 1 γ 1 γ 1 1 γ 1 c Gv max ρ v v > c Correction: G min ( G k G v max

10 Nmerical iteration scheme Vapor (p at the interface are given by snami (as well as the gas dynamic limiting flx Eqilibrim assmption redces nknown liqid properties to one srface temperatre: ls G k ( h c vs G c Iteration step: k pl pl kl l l x kl x Newton-Raphson averaging method: Condensation gives the second eq to solve for and G: G k f c p vs 1 Γ π R vs 1/ n n 1 n n 1 n n ls ls G G( ls ls ls ( G ε n 1 ls f e p ls 1 π R ls 1/ n ls low n ls high n 1 l ls ( G( n ls low n new ls high n new ls n ls ( n ls n ls low or n new ls low n new ls n ls ( n ls n ls high In the liqid layer sing an pwind scheme for the condensation case: n i n 1 i α t ( x n n 1 n 1 n 1 G t n 1 n 1 [ ] [ ] i 1 i i 1 ρ x l i i 1 t < α ( x n G ρl x 1

11 Introdcing condensation effect in snami he condensation modle evalates G at each step - the mass flx condition mst now be sed at snami bondary cells interface instead of the sal adiabatic condition adopted at cells interfaces in the volme snami nmerical scheme reqires comptation of mass (continity momentm (Riemann solver across the discontinity and energy (adiabatic assmption flxes at the edge of each cell Mass flx is G Energy flx from same interface balance - written in snami terms: Energy flx γ p vs G ( γ 1 ρvs vs Momentm flx determined by mirror node introdcing sction velocity: U U L R ( ρvs vs pvs ( ρ p vs vs s vs U * * * * ( ρ p * * * ρ G G ρ * Gnorm < ε G vmax Iteration scheme: s G ρ vs k s k s k 1 s k 1 s (1 G (1 G k 1 norm k 1 norm if if G G > <

12 Nmerical domain geometry Backgrond gas is flibe considered as an ideal gas with: m.331 C γ C p v 1.4 kg mol Initial backgrond conditions specified as: ρ p W R e R γ 1 Uniform grid: 1 x 1 cells -.5 x.5 cm each Injected gas considered by snami as DEBRIS initially available in a 3 x 3 cell volme V Initial sperheated vapor conditions specified as total injected mass [kg] and total initial energy [J]

13 Code rns - parameters case stdy snami BC recovered: s s vs Bondary conditions: Open interface Impermeable srface Condensation op and bottom bondary are impermeable Parametric stdy for: Reference case: Initial liqid temperatre (constant at solid wall interface Liqid layer thickness Sticking coefficient at the interface 6 C.5 mm fc 1

14 Liqid initial temperatre

15 Liqid layer thickness

16 Liqid initial temperatre

17 emperatre distribtion in the -D axisymmetrical nmerical domain as a fnction of time for the reference case

18 emperatre distribtion - middle cells Gas temperatres evalated by snami fall below the imposed initial backgrond temperatre when remaining mass is low

19 emperatre distribtion - op In the bondary cells at the top and bottom of the chambers the vapor interface is higher then snami evalated temperatre in the inner cells

20 Heat condction in the liqid layer

21 Pressre distribtion in the -D axisymmetrical nmerical domain as a fnction of time for the reference case

22 Pressre distribtion - middle cells Liqid srface eqilibrim assmptions not valid for transient condensation Ohno fitted eqation for flibe: p sat Ideal gas assmption for flibe overestimates vapor pressre dring high temperatres initial transient

23 Density distribtion in the -D axisymmetrical nmerical domain as a fnction of time for the reference case

24 Free moleclar regime Gas dynamics modeling in IFE liqid chambers.1 Kn L λ Direct Simlation Monte Carlo method HIBALL - Wisconsin (1989 KOYO - Osaka Un. ( solving Boltzmann eqation dv d g g t x v f t x c f t x v f t x c f c f F x nf c t nf Ω ( ] ( ( ' ( ' ( [ ( ( χ σ by decopling moleclar motion from collisions: *( (1 ( ( (1 *( x c F tj t x c F x c F td x c F Continm flid regime Hydrodynamic code snami HYLIFE - UCB ( NIF - LLNL UCB ( solving Eler eqation 1 ( ( e E p E p F E U x F t U ρ ρ ρ ρ ρ ρ ρ with the eq of state p( E p ρ

25 Proposed extension to gas dynamics slip regime Kinetic theory of gas dynamics on a diffsed srface in dilte gas conditions: references inclde older theoretical stdies of Cette flow conditions and newer nmerical stdies with DSMC methods ( models are based on imposing a velocity and temperatre slip to the gas near the srface to compensate for the difference in the velocity distribtion of the particles approaching and leaving the srface DSMC simlation show model is valid for Kn <.1 Proposed extension for snami is based on Harvie and Fletcher stdy (1 that explicitly inclde the mass flx in the velocity and temperatre slip formlation: v i v v Uλ x v l 1 (1 v λu Φfc f f m m (1 fc v (1 fc x v v λ Φ x i G Φ G U λ x t 5 U 9γ 4 f f ( 1 f f c c m l λu l fc (1 Φ f t ft fc (1 Φ( γ 1 x Φ 11.35λ 1.4.4Φ x

26 Droplet Clearing in a Pressre Decay Field Problem Definition: Droplet clearing represents another aspect of the chamber clearing isse. Droplets prodced from the blast shold be cleared away before the next shot. Approach: Start with the development of an incompressible code for analyzing droplet heat and mass transfer with respect to a known pressre decay Goal: Ultimately to cople the snani code with the developed incompressible free srface heat and mass transfer code for chamber clearing evalation Movie: A hot droplet reacting to the cold srronding environment

27 Droplet Heat ransfer and Phase Change with rchas: Preliminary Evalation rchas is a software program developed at LANL to simlate solidification manfactring processes most notably metal casting and welding operations. Inclde models and algorithms for: Interfacial motion and heat transfer Properties varying with temperatre Phase change finite volme method Simlations are flly 3 dimensional on nstrctred grids. Movie: A hot droplet falling down throgh a cold environment

28 Internal circlation cased by the temperatre difference is now employed in rchas code throgh Bossinesq approximation Boyancy force ρ g αρo g y x Melting temp73k Bottom temp73 k op temp53 k Initial temp inside droplet735 k initial temp otside droplet73 k

29 Assmptions & Near erm Goal he mass evaporated from the droplet into the srronding pressre field will be discarded Incorporate a time dependent temperatre bondary condition (set at sat corresponding to satrated temperate as a fnction of known pressre decay Await approval from LLNL to modify rchas code

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