Development of an evaporation boundary condition for DSMC method with application to meteoroid entry

Transcription

1 Development of an evaporation boundary condition for DSMC method with application to meteoroid entry F. Bariselli, S. Boccelli, A. Frezzotti, A. Hubin, T. Magin Annual METRO meeting 29th November 2016

2 Physics of a meteoroid entering the atmosphere Coupled physico-chemical phenomena occurring during meteoroid ablation Velocity: from 12 km/s to 72 km/s Size: from micro size grains to meters 2 / 26

3 Focus on the gas-surface phenomena VKI Plasmatron experiment: basaltic sample, 3 MW/m2 heat flux at the stagnation point Schematic of gas-surface interactions 2 Ordinary chondritic sample, 1 MW/m heat flux at the stagnation point 3 / 26

4 Objectives Goals Asses the importance in the competition among the different phenomena Develop an evaporation boundary condition capable of dealing with magma compositions (mixture of oxides) Couple the flow with the material response Introduce a method to compute chemistry of ablated species 4 / 26

5 1 Governing equations and numerical method Boltzmann equation Direct Simulation Monte Carlo method SPARTA numerical tool 2 Ablative wall Kinetic boundary conditions Melt-vapor equilibrium Extension to mixtures of oxides 3 Material response Material code Apparent heat capacity method Interface flow-material 4 Trajectory code 5 Gas phase chemistry Lagrangian solver 6 Conclusions and future work 4 / 26

6 1 Governing equations and numerical method Boltzmann equation Direct Simulation Monte Carlo method SPARTA numerical tool 2 Ablative wall Kinetic boundary conditions Melt-vapor equilibrium Extension to mixtures of oxides 3 Material response Material code Apparent heat capacity method Interface flow-material 4 Trajectory code 5 Gas phase chemistry Lagrangian solver 6 Conclusions and future work Governing equations and numerical method 4 / 26

7 Breakdown of the continuum regime Knudsen number = λ D = mesoscopic scale macroscopic scale Governing equations and numerical method Boltzmann equation 5 / 26

8 Boltzmann equation f(x, ξ, t) = one-particle velocity distribution function f t + ξ f X + F f ξ = { }}{ 4π ( f f 1 ff ) 1 gσdωdξ1 0 From microscopic to macroscopic world: ρ = ρv = ρe = f(x, ξ, t) dξ ξ f(x, ξ, t) dξ 1 ξ ξ f(x, ξ, t) dξ 2 q = ϕ = f(x, ξ, t) [ξ v w] n dξ 1 ξ ξ f(x, ξ, t) [ξ vw] n dξ 2 Governing equations and numerical method Boltzmann equation 6 / 26

9 Direct Simulation Monte Carlo method DSMC algorithm Each simulated particle represents a large number of real particles Free motion decoupled from collisions (for t < ν 1 coll ) Grid cells used to choose collisions partners and sample averages DSMC is not Molecular Dynamics Governing equations and numerical method Direct Simulation Monte Carlo method 7 / 26

10 SPARTA numerical tool Developed by Plimpton and Gallis at Sandia National Labs Open source software ( Object-oriented philosophy enables extensions Parallel implementation through domain decomposition Flow around MIR space station Apollo re-entering the atmosphere Governing equations and numerical method SPARTA numerical tool 8 / 26

11 1 Governing equations and numerical method Boltzmann equation Direct Simulation Monte Carlo method SPARTA numerical tool 2 Ablative wall Kinetic boundary conditions Melt-vapor equilibrium Extension to mixtures of oxides 3 Material response Material code Apparent heat capacity method Interface flow-material 4 Trajectory code 5 Gas phase chemistry Lagrangian solver 6 Conclusions and future work Ablative wall 8 / 26

12 Kinetic boundary conditions for Boltzmann equation [ξ v w] n<0 flux emerging from the wall {}}{ flux due to evaporation by the wall {}}{ f(ξ)[ξ v w ] n = g(ξ)[ξ v w ] n + K B (ξ ξ)f(ξ )[ξ v w ] n dξ } {{ } flux due to reflection by the wall K B (ξ ξ) = (1 α c ) [ξ v w] n 2π(RT w ) 2 g(ξ) = α e /α c evaporation/condensation coefficients (usually α e = α c = 1) ρ eq w equilibrium vapor density No need to assume equilibrium of the gas with the wall [ξ v w ] n > 0 ( exp ξ v w 2 ) 2RT w α e ρ eq ( w (2πRT w ) exp ξ v w 2 ) 3/2 2RT w Ablative wall Kinetic boundary conditions 9 / 26

13 MAGMA chemical multi-phase equilibrium solver How do we obtain the equilibrium properties? = ρ eq w i (material composition, T w ) ρ eq w i Developed by Fegley and Cameron, 1987 Mass balance, mass action algorithm Only stoichiometric reactions for change of phase Extensively validated vs. experimental data Already used to model vaporization in silicate lavas (under thermodynamic equilibrium assumption) Ablative wall Melt-vapor equilibrium 10 / 26

14 Extension to mixtures of oxides How do we choose the coefficients? α ei, α ci i {O, Si, SiO 2, Mg, MgO,...} Hp. 0: M x O y (l) x M (g) + y O (g) α ci = 0 i M, O Hp. 1: α cm = α em = α M = α Hp. 2: α co = α eo = α O Thermodynamic equilibrium has to be retrieved by kinetic approach ϕ eq i ϕ eq e M ϕ eq e O y k ϕ eq e Mk = ϕ eq i (α i, ρ eq w i, T w ) = ϕ eq c M M = ϕ eq c O k R ϕeq e Ok = x k ϕ eq e Ok k R = ϕ eq c O Ablative wall Extension to mixtures of oxides 11 / 26

15 Electron concentration around a non-ablating meteoroid Kn = 0.1 D = 1 cm H = 80 km V = 72 km/s non-ablating meteoroid m 3 typical e density for meteors Ambipolar diffusion assumption Gas phase chemistry frozen above 90 km electrons from metal species Ablative wall Extension to mixtures of oxides 12 / 26

16 Ablating meteoroid at 95 km altitude Pure magnesium: T wall = 925 K (melting temperature) v wall = 0 m/s α c = α e = 1 D = 1 cm H = 95 km V = 72 km/s Cooling effect of evaporation at the wall Adiabatic T 2.5M K >> T wall Geometric temperature: particles not characterized by this temperature in the thermal sense Translational temperature Ablative wall Extension to mixtures of oxides 13 / 26

17 Ablating meteoroid at 95 km altitude Delay in the excitation of the internal dofs Strong shielding effects of Mg vapor Rotational temperature Ablation products molar fraction Ablative wall Extension to mixtures of oxides 14 / 26

18 1 Governing equations and numerical method Boltzmann equation Direct Simulation Monte Carlo method SPARTA numerical tool 2 Ablative wall Kinetic boundary conditions Melt-vapor equilibrium Extension to mixtures of oxides 3 Material response Material code Apparent heat capacity method Interface flow-material 4 Trajectory code 5 Gas phase chemistry Lagrangian solver 6 Conclusions and future work Material response 14 / 26

19 Material response T Randomly and rapidly rotating sphere: t = k 2 T ρc p r + 2k 2 Ablating wall: moving mesh (fixed reference frame) Re-mapping procedure at each time step Finite differences, explicit time integration 1 ρc p r T r Derived variable [K m] Time [s]: Numerical solution Temperature [K] Time [s]: Numerical solution Distance from the surface of the sphere [m] Verification of the spherical coordinates: unsteady solution Distance from the initial surface position [m] Verification of the moving wall (re-mapping): steady solution Material response Material code 15 / 26

20 Tracking of the melting front CP Liquid (C S P + C L P )/2 + L/(2 T) Solid L C P S C P Position of the liquid-solid interface [m] Latent heat of melting [J/Kg]: 4e+05 4e+06 2e+07 Numerical solution 2 T Heat capacity T Time [s] Verification of the apparent heat capacity method: position of the melting front Apparent heat capacity method No need to deform the mesh to track the solid-liquid interface Position of the melting front obtained a posteriori Material response Apparent heat capacity method 16 / 26

21 Interface flow-material ϕ e ϕ c = ρ w v w ϕ e computed theoretically ϕ c directly from DSMC simulation No contribution of reflection (no net flux) Surface mass balance q c + q r q e + ɛσt 4 = ρ w h w v w + k T r + ɛσtw 4 w ϕ e computed theoretically q c, q r directly from DSMC simulation Surface energy balance Material response Interface flow-material 17 / 26

22 1 Governing equations and numerical method Boltzmann equation Direct Simulation Monte Carlo method SPARTA numerical tool 2 Ablative wall Kinetic boundary conditions Melt-vapor equilibrium Extension to mixtures of oxides 3 Material response Material code Apparent heat capacity method Interface flow-material 4 Trajectory code 5 Gas phase chemistry Lagrangian solver 6 Conclusions and future work Trajectory code 17 / 26

23 Trajectory code Python implementation (cython to improve performances) Interface with MAGMA for wall equilibrium properties Interface with NASA atmospheric model for free-stream properties Sub time stepping for material response Flow update resolution can be fixed through input file Trajectory code 18 / 26

24 Trajectory-material response coupling No DSMC coupling: evaporation into vacuum (Knudsen-Langmuir) q flow = Λρ (H)V 3 8 Temperature [K] V = 15 km/s, D = m Core temperature Surface temperature Position from the core [m] 10-3 V = 15 km/s, D = m 1 Evaporating front 0.9 Melting front Molten thickness Altitude [km] Altitude [km] D = 2 mm V = 15 km/s Trajectory code 19 / 26

25 1 Governing equations and numerical method Boltzmann equation Direct Simulation Monte Carlo method SPARTA numerical tool 2 Ablative wall Kinetic boundary conditions Melt-vapor equilibrium Extension to mixtures of oxides 3 Material response Material code Apparent heat capacity method Interface flow-material 4 Trajectory code 5 Gas phase chemistry Lagrangian solver 6 Conclusions and future work Gas phase chemistry 19 / 26

26 Lagrangian solver LARSEN LAgrangian Reactor for StrEams in Nonequilibrium Atmospheric entry ows many chemical products (air, ablated species) thermal non-equilibrium (T, Tr, Tv) 2D / 3D geometries TOO EXPENSIVE! Result: only simple models currently employed HOWEVER... METEOROID TRAIL: detailled ionization mechanisms required... IDEA: introduce chemistry a posteriori! Gas phase chemistry Lagrangian solver 20 / 26

27 Chemistry of ablated species computed a posteriori 1) Simple simulation 2) Extract streamlines Y i 4) Refined results u(s) ρ(s) + ICs 3) Lagrangian solver s Velocity and density fields from baseline simulation assumed good enough Gas phase chemistry Lagrangian solver 21 / 26

28 LARSEN formulation From baseline simulation: u, ρ are given We still need: Species mass eq. s y i = ω i J i ρu Total enthalpy eq. s H = Q ext Species internal energy s e in i = Din i + Ω in i h in i ω i ρy i u J i ω i Q u = System of ODEs Gas phase chemistry Lagrangian solver 22 / 26

29 Hypersonic inert flow around a cylinder (b) (b) (b) Axisymmetric DSMC simulation Pure argon M = 10 Kn = 0.05 T correctly reproduced Temperature [K] (a) (b) (a) (a) (a) DSMC SPA LARSENLAR curvilinear abscissa [m] Gas phase chemistry Lagrangian solver 23 / 26

30 Relaxation behind a shock wave - refining chemistry Inviscid flow Fire-II capsule free-stream conditions air5: N 2 O 2 N O NO air11: air5 + N + O + NO + N + 2 O+ 2 e Temperatu Temperature [K] Mass fractions N 2 T well predicted ions concentrations well predicted neutral species concentrations improved distance from shock [m] distance from shock [m] O 2 NO SHOCKING - air5 LARSEN - air5 to air11 SHOCKING - air11 N Gas phase chemistry Lagrangian solver 24 / 26 N O O +

31 1 Governing equations and numerical method Boltzmann equation Direct Simulation Monte Carlo method SPARTA numerical tool 2 Ablative wall Kinetic boundary conditions Melt-vapor equilibrium Extension to mixtures of oxides 3 Material response Material code Apparent heat capacity method Interface flow-material 4 Trajectory code 5 Gas phase chemistry Lagrangian solver 6 Conclusions and future work Conclusions and future work 24 / 26

32 Conclusions and future work Conclusions Develop a DSMC evaporation boundary condition for silicates Couple flow-material-trajectory Develop a method to implement detailed chemistry a posteriori Future work Include dynamic of molten layer to gas surface interactions Add ionization of metallic species Assess recombination time of free electrons in the trail Conclusions and future work 25 / 26

33 Thanks for your attention Thanks to: B. Dias for the useful discussion G. Bellas for the help with LARSEN L. Zavalan, B. Helber, P. Collins for the experiments Conclusions and future work 26 / 26