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