Combustion of 10–100 μm aluminum droplets in detonation products gases

• Published in: Propellants, explosives, pyrotechnics explosives, pyrotechnics, 2023-07, Vol.48 (7), p.n/a
• Main Authors: Kuhl, Allen L., Grote, David P., Springer, H. Keo
• Format: Article
• Language: English
• Subjects: Aluminum; aluminum combustion in detonation products; Burnout; burnout times; Continuum modeling; Detonation; droplet combustion model; Droplets; Dynamic models; Fireballs; Fluid flow; Initial conditions; INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Reynolds number; Similarity solutions; Thermodynamic equilibrium; Turbulent combustion; turbulent mixing; two-phase conservation laws
• ISSN: 0721-3115; 1521-4087
• DOI: 10.1002/prep.202200107

We describe a two‐phase model of combustion effects in aluminized high explosive (HE) charges. It is based on: (i) a Gas Dynamic Model of the expansion of the detonation product gases and their turbulent combustion with air; and (ii) a Heterogeneous Continuum Model of aluminum (Al) droplets and their combustion with the detonation product gases. Initial conditions are based on an analytical similarity solution for a cylindrical Chapman‐Jouguet (CJ) detonation propagating at the CJ detonation velocity. The CJ jump conditions are computed at the thermodynamic equilibrium state by the Cheetah code, assuming the Al droplets are inert. We assume that the Al is 10 % of the charge mass and occurs as droplets at the CJ state. Different initial droplet diameters, ranging from 10 to 100 microns, are studied. A hydrodynamic combustion model based on large Damköhler numbers is employed in this study, -3σ(1+0.276Re)/Kdw2 ${-3\sigma (1+0.276\sqrt{Re})/\left(K{d}_{w}^{2}\right)}$ . It has a square‐root dependence on the Reynolds number (Re) and inversed‐squared dependence on the droplet diameter ( dw ${{d}_{w}}$ ). The burnout time ( tB ${{t}_{B}}$ ) of the Al droplets has a three‐halves dependence on the droplet diameter, tB∼(dw0)3/2 ${{t}_{B}\sim {{(d}_{w}^{0})}^{3/2}}$ . After burnout, the detonation products act as detonation products of the HE charge with active Al. They turbulently mix with air and form a combustion layer on the outer edge of the fireball. Details of the two‐phase model, initial conditions and evolution of the flow field will be described.