AN EMPIRICAL MODEL FOR THE IGNITION OF ALUMINUM PARTICLE CLOUDS BEHIND BLAST WAVES

IGNITION OF ALUMINUM PARTICLE CLOUDS BEHIND REFLECTED SHOCK WAVESKaushik Balakrishnan1, Allen L. Kuhl2, John B. Bell1, Vincent E. Beckner1

1 Lawrence Berkeley National Laboratory 2 Lawrence Livermore National laboratorySupported by U.S. Department of Energy and Defense Threat Reduction AgencyICDERS 2011, #329

INTRODUCTIONAl combustion is of interest High energy content (7.4 Kcal/g)Al added to explosives and propellantsSimulation of Al dispersion/combustion is challenging in explosion/shock flow fieldsIgnition/burn modelsTurbulent flow fieldTwo-phase modelingUse of experimental data in modelsEmpirical ignition modelIGNITION BY REFLECTED SHOCK WAVEBoiko et al.s experiments (Russia)Krier/Glumac experiments (Univ. Illinois)IGNITION BY REFLECTED SHOCK WAVEWake convected into the particle cloudReflected shock interaction with particle cloud: Richtmyer-Meshkov instabilityClockwise/counter-clockwise vorticityParticle cloud convoluteswakeRMFORMULATIONFORMULATION: THERMODYNAMICSEquation of stateLe Chatelier diagram (Kuhl, 2006)Thermodynamic states computed using CHEETAH code Thermodynamic equilibrium assumed for reactants and productsQuadratic curve-fitsuk(T) = akT2 + bkT + ckK = fuel, oxidizer or products

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

EMPIRICAL IGNITION MODEL

EMPIRICAL IGNITION MODEL EMPIRICAL IGNITION MODEL

SUMMARY: IGNITION MODELInitial: f = 0Pre-ignition: 00.5m5 cm particle cloud (4-6 m Al flakes) injected at x=2.75 m at 2.25 msec512x64x64 with 3 levels of refinement (ratio=2); x30.78 mmDIFFERENT SIMULATION CASESCases, g/m3MTg behind incident shock, KTg behind reflected shock, K1200411101920210041110192035041110192041003.5925159051003.810301780EFFECT OF INITIAL CLOUD DENSITY AND SHOCK MACH NUMBERRESULTS: log(s)M = 4; s = 200 g/m3

M = 4; s = 50 g/m3

MOVIE: M = 4; s = 200 g/m3

VORTICITY: M = 4; s = 200 g/m3

Vorticity due to wake: 1.2x105 sec-1Due to reflected shock: 4x104 sec-1Vorticity dependent on s and M2.83 ms3.52 ms4.28 ms5.37 msMASS OF Al BURNED

Burning trend depends on s90% Al by mass burnsPresent ignition model accounts for sWake-induced convolution/elongation of cloud for higher sIncreases surface area of cloud; hence more burningBURNING REGIONS

200 g/m350 g/m3TgYairEFFECT OF M (s = 100 g/m3)

Higher M results in higher Tg behind reflected shockIgnition occurs earlierMore Al by mass burnsMTg behind incident shock, KTg behind reflected shock, K3.592515903.810301780411101920MASS AVERAGED Tsolid, K

Cases, g/m3M1200421004350441003.551003.8MASS WEIGHTED f

CONCLUSIONSA new empirical Al ignition model is proposedIgnition time based on Boiko et al.s experimentsIgnition temperature based on Gurevich et al.s experimentsCloud concentration effectRESULTS~90% Al (by mass) burnsCloud density and M have profound effectMass-weighted f introducedRESULTS FROM A COMPANION PAPER

Shock Dispersed Fuel (SDF) chargesInvestigate Al burning, mixing, vorticity, dissociation and ionization effectsTHANK YOU