1. IGNITION OF ALUMINUM PARTICLE CLOUDS BEHIND REFLECTED SHOCK WAVES Kaushik Balakrishnan 1, Allen L. Kuhl 2, John B. Bell 1, Vincent E. Beckner 1 1 Lawrence Berkeley National Laboratory 2 Lawrence Livermore National laboratory Supported by U.S. Department of Energy and Defense Threat Reduction Agency ICDERS 2011, #329

2. INTRODUCTION Al combustion is of interest – High energy content (7.4 Kcal/g) Al added to explosives and propellants Simulation of Al dispersion/combustion is challenging in explosion/shock flow fields – Ignition/burn models – Turbulent flow field – Two-phase modeling Use of experimental data in models – Empirical ignition model

3. IGNITION BY REFLECTED SHOCK WAVE Boiko et al.’s experiments (Russia) Krier/Glumac experiments (Univ. Illinois)

4. IGNITION BY REFLECTED SHOCK WAVE Wake convected into the particle cloud Reflected shock interaction with particle cloud: Richtmyer- Meshkov instability Clockwise/counter-clockwise vorticity Particle cloud convolutes wakeRM

5. FORMULATION

6. FORMULATION: THERMODYNAMICS Equation of state Le Chatelier diagram (Kuhl, 2006) Thermodynamic states computed using CHEETAH code Thermodynamic equilibrium assumed for reactants and products Quadratic curve-fits – u k (T) = a k T 2 + b k T + c k – K = fuel, oxidizer or products

7. NUMERICAL METHODS - AMR GAS PHASE: Higher-order Godunov method of Colella & Glaz, 1985; Bell et al., 1989 PARTICLE PHASE: Godunov method of Collins et al., 1994 ADAPTIVE MESH REFINEMENT (AMR) of Bell et al., 1989 IMPLICIT LARGE-EDDY SIMULATION (ILES) MASSIVELY PARALLEL SIMULATIONS (~1024 processors)

8. EMPIRICAL IGNITION MODEL

11. SUMMARY: IGNITION MODEL Initial: f = 0 Pre-ignition: 0<f<1 Ignition: f>1

12. SIMULATION CONFIGURATION Spherical Al particle cloud in shock tube; air everywhere 3.2m x 0.4m x 0.4m; left: inflow; walls everywhere else Shock wave initialized at x = 0.5m; 0.1 bar and 293 K for x>0.5m 5 cm particle cloud (4-6 µm Al flakes) injected at x=2.75 m at 2.25 msec 512x64x64 with 3 levels of refinement (ratio=2); ∆x 3 ≈0.78 mm

13. DIFFERENT SIMULATION CASES Caseρ s, g/m 3 MT g behind incident shock, K T g behind reflected shock, K 1200411101920 2100411101920 350411101920 41003.59251590 51003.810301780 EFFECT OF INITIAL CLOUD DENSITY AND SHOCK MACH NUMBER

14. RESULTS: log(ρ s ) M = 4; ρ s = 200 g/m 3 M = 4; ρ s = 50 g/m 3

15. MOVIE: M = 4; ρ s = 200 g/m 3

16. VORTICITY: M = 4; ρ s = 200 g/m 3 Vorticity due to wake: 1.2x10 5 sec -1 Due to reflected shock: 4x10 4 sec -1 Vorticity dependent on ρ s and M 2.83 ms 3.52 ms4.28 ms5.37 ms

17. MASS OF Al BURNED Burning trend depends on ρ s 90% Al by mass burns Present ignition model accounts for ρ s Wake-induced convolution/elongation of cloud for higher ρ s Increases surface area of cloud; hence more burning

18. BURNING REGIONS 200 g/m 3 50 g/m 3 TgTg Y air

19. EFFECT OF M (ρ s = 100 g/m 3 ) Higher M results in higher T g behind reflected shock Ignition occurs earlier More Al by mass burns MT g behind incident shock, K T g behind reflected shock, K 3.59251590 3.810301780 411101920

20. MASS AVERAGED T solid, K Caseρ s, g/m 3 M 12004 21004 3504 41003.5 51003.8

21. MASS WEIGHTED f

22. CONCLUSIONS A new empirical Al ignition model is proposed – Ignition time based on Boiko et al.’s experiments – Ignition temperature based on Gurevich et al.’s experiments – Cloud concentration effect RESULTS – ~90% Al (by mass) burns – Cloud density and M have profound effect – Mass-weighted f introduced

23. RESULTS FROM A COMPANION PAPER Shock Dispersed Fuel (SDF) charges Investigate Al burning, mixing, vorticity, dissociation and ionization effects

24. THANK YOU